ML19270F609

Analysis of Hypothetical Core Distruptive Events in Clinch River Breeder Reactor Plant.

ML19270F609
Person / Time
Site:	Clinch River
Issue date:	04/30/1978
From:	Brown N, Mcelroy J, Switick D ENERGY, DEPT. OF, CLINCH RIVER BREEDER REACTOR PLANT
To:
Shared Package
ML19270F608	List: ML19270F607 ML19270F609
References
CRBRP-GEFR-00103, CRBRP-GEFR-103, CRBRP-GEFR00103, CRBRP-GEFR103, NUDOCS 7902270421
Download: ML19270F609 (175)

Text

CRBRP-GEFR-00103 UC-79P APRIL 1978 s

CLINCH RIVER BREEDER REACTOR PLANT AN ANALYSIS OF HYPOTHETICAL CORE DISRUPTIVE EVENTS IN THE CLINCH RIVER BREEDER REACTOR PLANT TOPICAL REPORT J. L. McElroy D. M. Switick N. W. Brown F.M. Chou W. P. Damerow F. C. Rodgers Prepared for Westingbouse Corporation and the U S. Department of Energy under Contracts 54-7AO-192908 Work Agreement G533 General Electric Company Fast Breeder Reactor Department 0293 6 %

Sunnyvale, Cahfornie 94086 L Any Further Distribution by any Holder o" this Document or of the Data Therein to Third Parties Representir:g Foreign Interest, Foreign Governments, Foreign Companies and Foreirn Subsidiaries or Foreign Divisions of U. S. Companies Should be Coordinated with the Director, Division of Reactor Research and Development U. S. Department of Energy. i

O NOTICE This report was prepared as an account of work sconsored by an agency of the United States Government. Neother the United States Government nor the agency. nor any of their employees. nor any of their contractors. subcontractors. or their employees.

makes any warranty, express or ompIred. or assumes any legalliabritty or tesponsibt! sty for the accuracy, completeness or usefulness of any information. apparatus. product or process disclosed. or represents that its use would not intnnge privately owned rights.

This report has boon reproduced cirectly from the best available copy.

Available from USDOE TechnocalInformation Center. P.O. Box 62. Oak Rodge. TN 37830 0

Price: Paper Copy $7 75 (domestic)

$10 25 (toreign)

Microficho $2 25 (domestic)

$3 75 (torergn)

O Pv nied in the Uneted States of Amenca USDOE Teemal Wmmeon Center Oaa n,oge Tenneme

ACKNOWLEDGEMENT This report is dependent upon information developed by many persons during the licensing discussions on the CRBRP HCDA event. The authors have developed new information and edited it into a consistent report with the information previously in the CRBRP PSAR.

We wish to acknowledge the major contributions made by the authors of ANL/ RAS 75-29. In addition, Dr. L. M. Zull (GE) and Dr. E. L. Fuller (now at EPRI), although not involved in authoring this report, contributed both analysis and major sections of the original text. And lastly our thanks to the typists L. Kindred, V. Bumsted, M. Shergalis and N. Corona.

i

ABSTRACT O

The results of hypothetical core disruptive event analyses for the Clinch River Breeder Reactor Plant performed during the period of January 1975 to January 1977 (with the SAS3A and VENUS 11 computer codes), are reported.

The analytical results cover a large number of parametric cases includ-ing variations in design parameters, initiating conditions and phenomenological assumptions. Reactor core configurations at the beginning and end of an equilibrium cycle are evaluated.

Accident progression branch points leading to either hydraulic pressure (within fuel assembly duct structural capacity) or hydrodynamic pressure (exceeding fuel assembly duct structural capacity) fuel disruption modes are evaluated. The phenomenological processes of molten fuel pools are described ano be consequences of energetic recriticality, including Behrens' effects, are examined.

The energetic consequences are evaluated based upon both fuel exapnsion @

thermodynamic work potential and a relative probability assignment. It is concluded that the structural loads which result from 101 megajoules of available expansion work at sodium slug impact on the reactor closure head, (equivalent to 661 megajoules of fuel expansion work to one atmosphere),

is an adequate energetic consequence envelope for use in specifying the Structural Margins Beyond the Design Basis.

11

TABLE OF CONTENTS Page Abstract ii List of Tables ix List of Figures xii

1. Introduction 1-1

2. Summary and Conclusions 2-1

3. SAS3A Code System 3-1 3.1 Physical Processes Related to Accident Progression 3-1 3.2 Phenomenological Modeling 3-4 3.2.1 Fuel Characterization in Steady State 3-4 1 3.2.2 Fission Gas Release from Fuel 3-4 3.2.3 DEFORM / TOP Failure Model 3-7 3.2.4 SAS/FCI Module Description 3-9 3.2.5 LOF Driven TOP Failures 3-13 3.2.6 PLUTO Code Auxiliary Calculations 3-15 3.2.6.1 PLUTO Code Description 3-15 3.2.6.2 PLUTO Code Applications 3-17 3.2.7 Post-FCI Blockage Modeling (SASBLOK) 3-18 3.2.8 Sodium Voiding Model Summary 3-21 3.2.9 PRIMAR Summary 3-23 3.2.9.1 Accommodation of Inlet Plenum Pressure 3-23 Fluctuations 3.2.9.2 Factors Affecting the Use of PRIMAR-2 in SAS3A 3-24 3.2.10 Cladding Relocation Model (CLAZAS) Summary 3-27 3.2.11 Fuel Motion Model (SLUMPY) Summary 3-28 3.2.12 Reactivity Feedback Algorithms 3-32 3.2.12.1 Doppler Reactivity feedback 3-32 3.2.12.2 Axial Expansion Feedback 3-33 3.2.12.3 Radial Expansion Feedback 3-34 3.2.12.4 Material Relocation feedback 3-34 3.2.13 Point Kinetics vs Space-tirc.e Kinetics 3-36

4. SAS Reactor Model and Input Assumptions 4-1 iii

Page Neutronics and Steady-State Result; S.

5.1 Model and Procedure Details 5-1 5-1 g

5.2 The BOEC Core Configuration 5-2 5.3 The E0EC Core Configuration 5-4

6. Initiating Phase Analysis of Unprot(:ted Transient Overpower (TOP) 6-1 6.1 TOP in E0EC Configuration at Fu 1 Power 6-1 6.1.1 Base Case Ramp Rate of 10./sec 6-1 6.1.1.1 SASBLOK Core Region Analysis 6-3 6.1.1.2 SASBLOK Above Cort ulockage Analysis 6-6 6.1.2 Effects of Ramp Rate Uncertainty 6-10 6.1.2.1 Design Ramp Rate of 2.4c/sec 6-11 6.1.2.2 Extreme Ramp Rate of 50c/sec 6-12 6.1.2.3 E0EC TOP: 3$/sec Raip Rate and Greater 6-12 6.1.3 Effects of Phenomenological Uncertainties 6-13 6.1.3.1 Fission Gas Release Melels 6-13 6.1.3.' HEDL Empirical fuel Pir Failure Criteria 6-14 6.1.3.3 Forced Midplane Failure at 2.4c/sec 6-15 6.1.3.4 6.1.3.5 Forcal Midplane failure v.10c/sec Forced Midplane Failure at loc /sec Without 6-16 g 6-17 Axial Expansion 6.1.3.6 Axial Failure Location Uncertainty 6-18 6.1.4 Effect of Design Uncertainties 6-20 6.1.4.1 Doppler Magnitude 6-20 6.1.4.2 Material Worths 6-21 6.1.5 Summary and Conclusions on E0EC TOP Event 6-21 6.2 TOP in 80EC Configuration at Full Power 6-23 6.2.1 Base Case Ramp Rate of 10c/sec 6-23 6.2.2 Effect of Ramp Rate Variation 6-27 6.2.2.1 Design Ramp Rate of 2.4c/sec 6-27 6.2.2.2 Limiting Ramp Rate of 20c/sec 6-28 6.2.2.3 Extreme Ramp Rate of 50c/sec 6-29 6.2.3 Effects of Phenomenological Uncertainties 6-30 6.2.3.1 Fission Gas Delease Model 6-30 iv 0

Page 6.2.3.2 HEDL Fuel Pin Empirical Failure Correlation 6-32 6.2.3.3 Additional Fuel Pin Failure Criteria 6-33 6.2.3.4 Forced Midplane Failure 0 2.4c/sec 6-36 6.2.3.5 Forced Midplane Failure 010c/sec 6-37 6.2.4 Effect of Design Uncertainties 6-39 6.2.4.1 Doppler Magnitude 6-39 6.2.4.2 Materiai Worths 6-40 6.2.5 Summary and Conclusion on BOEC TOP Event 6-40 6.3 Unprotected Startup Accident in E0EC Configuration 6-43 6.3.1 Effect of Ramp Rate 6-43 6.3.1.1 Ramp Rate of 10c/sec 6-43 6.3.1.2 Ramp Rate of 20c Aec 5-44 6.3.2 Sunmary and Conclusions on E0EC TOP at Startup 6-45

7. Initiating Phase Analysis for Unprotected Primary Flow Coastdown 7-1 7.1 Loss of Flow (LOF) Event in Ef.EC Configuration at Full Power 7-1 7.1.1 Best Estimate Analysis 7-1 7.1.2 Ef fect of Phenomenological Uncertainties 7-4 7.1.2.1 CLAZAS and Limited Initial Fuel Motion 7-4 7.1.2.2 Gravity Draining of Cladding 7-8 7.1.2.3 No Fission Gas Dispersal in SLUMPY 7-9 7.1.2.4 No Axial Expansion Reactivity Feedback 7-9 7.1.3 Effect of Design and Data Uncertainties 7-10 7.1.3.1 Doppler Magnitude Uncertainty 7-10 7.1.3.2 Sodium Void Worth Uncertainty 7-11 7.1.3.3 Fuel Reactivity Worth Uncertainty 7-12 7.1.3.4 Primary flow Decay Rate Uncertainty 7-13 7.1.3.5 Core Flow Orificing Variation (Design 7-13 Evaluation) 7.1.4 Summary and Conclusion on E0EC LOF Event 7-17 7.2 Loss of Flow (LOF) in BOEC Configuration at Full Power Range 7-19 7.2.1 Best Estimate Analysis 7-19 7.2.2 Ef fect of Phenomer.ological Uncertainties 7-23 7.2.2.1 CLA7AS and Limited Initial Fuel Motion 7-24 v

Page 7.2.2.2 lio Fission Gas in SLUMPY 7-25 7.2.2.3 fio Axial Expansion Reactivity 7-27 g 7.2.3 Effect of Design and Data Uncertainties 7-28 7.2.3.1 Doppler Coefficient Uncertainty 7-28 7.2.3.2 Sodium Void Worth Uncertainty 7-29 7.2.3.3 Fuel Reactivity Worth Uncertainty 7-30 7.2.3.4 Primary Flow Decay Rate Uncertainty 7-31 7:2.3.5 Core Flow Orificing Scheme Variation 7-32 7.2.4 Summary and Conclusion on 80EC L0:~ Event 7-32

8. Initiating Phase Analysis of Unprotected, Combined Step Reactivity 8-1 Insertions and Loss of Flow Events (STEP /LOF) at Full Power 8.1 Effect of Thirty Cent STEP /LOF in the B0EC Configuration 8-1 8.2 Effect of Thirty Cent STEP /LOF in the E0EC Configuration 8-6 8.3 Sunmary and Conclusion on Combined Reactivity Step Insertion 8-9 and Loss-of-Flow Event

9. Initiating Phase Analysis of Unprotected Combined Reactivity Ramp 9-1 Insertion - LOF (TOP /LOF) Event at Full Power 9.1 Effect of T0P/LOF in BOEC Configuration 9-1 9.1.1 Design Ramp Rate Insertion (2.4c/sec) 9-1 g 9.1.2 Limiting Ramp Rate Insertion (20c/sec) 9-3 9.1.3 Effect of Clad Relocation Phenomena on Design Rate 9-5 T0P/LOF 9.1.3.1 Gravity Draining of Cladding 9-5 9.1.3.2 Molten C1 adding - Sodium Vapor Coupling 9-7 (CLAZAS) 9.2 Effect of T0P/LOF in E0EC Configuration 9-9 9.2.1 Design Ramp Rate Insertion (2.4c/sec) 9-9 9.2.2 Molten Cladding - Sodium Vapor Coupling (CLAZAS) 9-10 9.3 Sunmary and Conclusion on T0P/LOF Events at Full Power 9-11

10. flon-Energetic Reactor Core Disruption Phase Evaluations 10-1 10.1 Potential for Partial Core Damage with In-Place Heat Removal 10-1 10.1.1 Reactivity Insertion Events 10-1 10.1.2 Loss-of-Flow Initiated Events 10-3 vi h

Page 10.2 Transition to Molten Pool 10-4 10.2.1 Potential for Existence of Steel Blockages 10-4 10.2.2 Extended Fuel Motion 10-6 10.2.2.1 Fission Gas Effects 10-6 10.2.2.2 Steel Vapor Pressure Effects 10-6 10.2.2.3 Fuel / Steel Penetration of Blanket 10-7 Str cture 10.2.2.4 Fuel / Steel Ejection from Core Region 10-10 10.2.3 Disruption of Fuel Assembly Structure 10-10 10.3 Behavior in a Bottled-Up Mclten Pool Region 10-12 10.3.1 Boiling Flow Regimes 10-12 10.3.2 Heat Transfer at Boundaries 10-13 10.3.3 Molten Fuel Pool Density 10-14 10.4 Reactivity Effects in a Disrupted Geometry 10-16 10.5 Sununary and Conclusions on Non-Energetic Disruption 10-18

11. Energetic Reactor Core Disruption Phase Evaluation 11-1 11.1 Introduction 11-1 11.2 Hydrodynamic Disassembly During Initiating Phase 11-5 11.2.1 Unprotected Reactivity Insertion Events 11-5 11.2.1.1 B0EC Derign Ramp Rate (2.4c/sec) With 11-5 Forced Midplane Failure 11.2.1.2 E0EC 10c/sec Ramp Rate With Forced Midplane 11-6 Failure 11.2.1.3 E0EC Hypothetical 35/sec Ramp Insertion 11-7 11.2.2 Unprotected Loss of Flow Evento 11-7 11.2.2.1 BOEC: Neglect Fuel Axial Expansion 11-7 11.2.2.2 BOEC: Neglect Fission Gas Fuel Dispersal 11-7 in SLUMPY ll.2.P.3 B0EC: CLAZAS With Limited I.nitial Fuel 11-8 Mo ti on 11.2.2.4 E0EC: Arbitrary 405/sec Ramp Insertion 11-8 11.2.?.5 E0EC: Aug. '75 Flow Ori fice Scheme 11-9 Neglecting Fission Gas Fuel Dispersal in SLUMPY vii

Page 11.2.3 B0EC: Unprotected Step Reactivity Insertion With LOF 11-9 11.2.4 BOEC: Unprotected Reactivity Ramp Insertion Wita LOF 11-10 11.3 Hydrodynamic Disassembly During Tronsition to a Molten Pool 11-10 11.4 Hydrodynamic Disassembly of a Homogenized Molten Pool 11-13 11.4.1 Pool Initial Conditions and Effect of Initial Power 11-13 11.4.2 Consideration of Bubble Collapse (Behren's Effect) 11-15 11.5 Summary and Conclusions on Energetic Core Disruption 11-15 Evaluations

12. Definition of Pressure-Volume Relationship Used to Specify the 12-1 Structural Margin Beyond the Design Base 12.1 Definition of Thermal Source 12-1 12.2 Uncertainties in Thermal-Mechanical Energy Conversion 12-4 12.3 Thermodynamic Work Potential for Structural Margin 12-6 Assessments

13. References 13-1 Appendix A - SASBLOK Summary A-1 Appendix B - Summary of Experimental Bases Employed in SAS LOF B-l Modeling Appendix C - An Analysis of the Reactivity Effects of Bubble C-1 Collapse in a Boiled-Up Molten Pool in CRBRP O

viii

LIST OF TABLES Table No. Ti tle Page 2-1 Definition of Accident Sequence Categories 2-3 2-2 Summary of Energetics Consequence Spectrum 2-4 3-1 Dif ferences Between SAS/FCI and PLUTO 3-39 4-1 SAS3A Input for BOEC LOF Base Case 4-20 4-2 Nominal Core Pressure Drops for Highest Flow 4-30 Orifice Zone in CRBRP (No Gravity Heads Included) 5-1 00EC Neutronics Comparison 5-7 5-2 Doppler Cocfficients by Channel for the BOEC Core 5-8 5-3 E0EC Neutronics Comparison 5-9 5-4 Doppler Coefficients by Channel for the E0EC Core 5-10 6-1 E0EC Base Case Fuel Conditions Prior to Failure in 6-46 Channel 8 6-2 E0EC 50c/sec Comparison of Pin Failure Estimates 6-47 6-3 E0EC TOP Midplane Failure Core Conditions at 6-48 Transition to Disassembly 6-4 BOEC Base Case Fuel Conditions Prior to Failure in 6-49 Channel 10 6-5 Sodium Boiling at Initial Pin failure Time 6-50 6-6 BOEC 50c/sec Comparison of Pin Failure Estimates 6-51 7-1 Event Sequence for E0EC LOF Base Case 7-35 7-2 Event Sequence for E0EC LOF CLAZAS and Limited 7-36 Initial Fuel Motion Case 7-3 Event Sequence for E0EC LOF Clad Draining Case 7-37 7-4 Event Sequence for E0EC LOF - No Fission Gas in 7-38 SLUMPY Case 7-5 Event Sequence for E0EC LOF - No Axial Expansion 7-39 7-6 Comparison of E0EC Flow Orificing Schemes 7-40 7-7 CRBRP EUEC LOF Flow Orificing Variations Timing and 7-41 Sequence of Events 7-8 CRBRP E0EC LOF No Fission Gas Parametric Timing and 7-42 Sequence of Events 7-9 Event Sequence for BOEC LOF Base Case 7-43 ix

LIST OF TABLES (Continued)

Table flo. Ti tl e Page 7-10 Event Sequence with CLAZAS and Limited Initial 7-44 Fuel Motion 7-11 Event Sequence for 80EC LOF Cases with fio Axial 7-45 Expansion Reactivity 8-1 Sequence of Significant Events 80EC STEP /LOF 8-10 Event 8-2 Cross Sectional Areas in Channel 6 for PLUTO 8-11 Calculations (from SAS3A) 8-3 Channel 6 PLUTO Results 8-12 8-4 Channel 10 Cavity Conditions in SAS/FCI and PLUTO 8-13 B0EC 30 Cent STEP /LOF 8-5 Time Sequence for E0EC Thirty Cent STEP /LOF 8-14 9-1 Sequence of Significant Events, BOEC T0P/LOF Event 9-14 Insertion of 2.4c/ss with 30% Overpower Pump Trip 9-2 Fuel Pin Cavity Conditions in SAS/FCI and PLUTO 9-15 BOEC T0P/LOF Base Case: Channels 6 and 10 9-3 9-4 Event Sequence for BOEC 20c/sec T0P/LOF Sequence of Events in B0EC T0P/LOF with Molten 9-16 9-17 g

C1 adding Gravity Drainage 9-5 SAS Sequence of Events in BOEC T0P/LOF with Molten 9-18 Cladding - Sodium Vapor Coupling 9-6 Sequence of Significant Events, E0EC T0P/LOF Event 9-19 10-1 Values of the Stability Parameter K 10-21 10-2 Power Density and Flow Regime Characteristics 10-22 11-1 Summary of BOEC TOP 2.4c/sec Forced Midplane 11-18 Failure Disassembly Calculations 11-2 Suninary of E0EC TOP Midplane Failure Disassembly 11-19 Calculations 11-3 Disassembly Calculation for a 3$/sec Insertion in 11-20 E0EC Configuration 11-4 Summary of BOEC LOF Disassembly calculations 11-21 11-5 Sunmary of E0EC LOF Disassembly Calculations 11-22 11-6 Suninary of BOEC Thirty Cent STEP /LOF Disassembly 11-23 Calculation 9

x

LIST OF TABLES (Continued)

Table No. Ti tle Page 11-7 Sunmary of 80EC T0P/LOF Disassembly. Calculations 11-24 11-8 Sucmary of Disassembly Calculations for Transition 11-25 Phase Rec;iticality 12-1 Pressure Volume Relationship for Structural Margin 12-7 Beyond the Design Base xi

LIST OF FIGURES Figure No. Title Page 3-1 Unprotected Reactivity Insertion Accident 3-40 Progression Diagram 3-2 CRBRP Unprotected LOF Accident Progression Diagram 3-41 3-3 Clad Strength for Various Assumptions 3-43 3-4 Basic Components of the SAS/FCI Model 3-44 3-5 Treatment of Fuel-Coolant Interaction Zone 3-45 Interfaces 36 Effect of Pump on Voiding of the Mark-IIA Loop 3-46 (From Ref. 23) 3-7 SASBLOX Evaluation Logic Flow 3-47 3-8 Accuracy of Point Kinetics Reactivity in a CRBRP 3-48 E0EC LOF Transient 4-1 Assembly Assignment Numbers 4-31 4-2 SAS AssemblyCRBRP Channel Selections for the BOEC 4-32 Case 4-3 SAS Assembly CRBRP Channel Selections for the E0EC 4-33 Case 4-4 SAS Coolant Mesh Used for Representation of the CRB 3 Core 4-34 O 4-5 Pi, p Flow Decay Curves for CRBRP 4-35 4-6 Core and Blanket Mesh Spacing for SAS3A 4-36 5-1 Scheme for Generation of SAS Neutronics Data 5-11 5-2 B0EC Fuel Worth by Channel 5-12 5-3 BOEC Coolant Void Worth by Channel 5-13 5-4 80EC Cladding Steel Worth by Channel 5-14 5-5 E0EC Fuel Worth by Channel 5-15 5-6 E0EC Coolant Worth by Channel 5-16 5-7 E0EC Cladding Steel Worth by Channel 5-17 5-8 Steady-State BOEC Model Used in FX-2 Showing 5-18 SAS Channels and Control Positions 5-9 BOEC Pin Linear Powers by Channel 5-19 5-10 BOEC Na-In Doppler by Channel 5-20 0

xii

I.!ST OF FIGURES (Continued)

Figure flo. Title Page 5-11 BOEC Fuel, Clad, Coolant, and Structure Steady- 5-21 State Temperature Profiles 5-12 Steady-State Radial Pin Temperature Distribution 5-22 in Channel 1 BOEC Case 5-13 BOEC Steady-State Fuel-Clad Radial Gap Profiles 5-23 5-14 BOEC Steady-State Fission Gas Retention Curves 5-24 5-15 Steady-State E0EC Model Used in FX-2 Showing SAS 5-25 Channels and Control Positions 5-16 E0EC Pin Linear Power by Channel 5-26 5-17 E0EC fla-In Doppler by Channel 5-27 5-18 E0EC Channel 8 Fuel, Clad, Coolant, and Structure 5-28 Steady-State Temperature Profiles 5-19 Steady-State Radial Pin Temperature Distributions 5-29 in Channel 8 E0EC Case 5-20 E0EC Steady-State Fuel-Clad Radial Gap Profiles 5-30 5-21 Restructuring Isotherms Channel 8 E0EC Case 5-31 5-22 E0EC Steady-State Fission Gas Retention Curves 5-32 6-1 Power and Reactivity Traces for the LuLC TOP 6-52 Base Case 6-2 Coolant Reactivity via Channel for the E0EC TOP 6-53 Base Case 6-3 Fuel Reactivity via Channel for the E0EC TOP Base 6-54 Case 6-4 Computed FCI Zone for the E0EC TOP Base Case 6-55 6-5 Fuel and Cladding Temperatures for the E0EC TOP 6-56 Base Case 6-6 PLUTO Reactivity Determination for the E0EC TOP 0-57 Base Case 6-7 Pressure-Time Histories for the [0EC TOP. Base 6-58 Case 6-8 SASBLOK Simulation Compared with Original FCI 6-59 Solution 6-9 Power and Reactivity Following Fuel Failure 6-60 (Blockage Coef ficient = 800) 6-10 E0EC Channel 5 Simulation of FCI Through Vapor 6-61 Collapse xiii

LIST OF FIGURES (Continued)

Figure No. Ti tle O

Page 6-11 E0EC Channel 5 Flow Response. (Blockage 6-62 Coefficient = 800) 6-12 E0EC Channel 5 Midplane Fuel Conditions 6-63 (Blockage Coefficient = 800) 6-13 E0EC Channel 5 Midplane Sodium and Steel 6-64 Conditions (Blockage Coefficient = 800) 6-14 E0EC Channel 5 FCI Simulation and Delayed 6-65 Boiling (Blockage Coefficient = 2000) 6-15 E0EC Channel 5 Flow Response (Blockage 6-66 Coefficient = 2000) 6-16 E0EC Channel 5 Fuel Midplane Conditions 6-67 (Blockage Coefficient = 2000) 6-17 E0EC Channel 8 FCI Simulation and Delayed Boiling 6-68 (Blockage Coefficient = 800) 6-18 E0EC Channel 8 Flow Response (Blockage Coefficient 6-69

= 800) 0-19 E0EC Channel 8 Midplane fuel Conditions 6-70 6-20 (Blockage Coefficient = 800)

E0EC Channel 8 Midplane Sodium and Steel Conditions 6-71 g

(Blockage Coefficient = 800) 6-21 E0EC Channel 8 FCI Simulation and Delayed Boiling 6-72 to Code Termination (Blockage Coefficient = 2000) 6-22 Ejected Fuel Located Within or Outside of Core and 6-73 Blanket Region vs Tima 6-23 Effect of Mass of Ejected Fuel Upon Coolant 6-74 Temperature Rise for Blockage (50% Porosity) 6-24 Coolant Temperature in the Blockage vs Time 6-75 6-25 Power and Reactivity Traces 6-76 6-26 Fuel Temperatures at the Core Midplane 6-77 6-27 FCI Zone Growth 6-78 6-28 Pin and FCI-Zone Pressure History 6-79 6-29 1 ower and Reactivity Traces 6-80 6-30 Coolant Reactivity by Channel 6-81 6-31 Fuel Reactivity by Channel 6-82 O

xiv

L]ST OF FIGURES (Continued)

Figure No. Ti tl e Page 6-32 Fuel and Clad Conditions at Core Midplane 6-83 6-33 FCI Zone Growth 6-84 6-34 E0EC TOP 3$ /sec Case: Power and Reactivity 6-85 Traces 6-35 E0EC TOP 3$/sec Case: Channel 5 Fuel and Clad 6-86 Thermal Conditions 6-36 E0EC TOP 3$/sec Case: Coolant Reactivity 6-87 Components by Channel 6-37 E0EC TOP 3$/sec Case: Fuel Reactivity 6-88 Components by Channel 6-38 E0EC TOP 3$/sec Case: Channel 5 FCI Zone Growth 6-89 6-39 E0EC TOP 2.4c/sec Midplane Failure: Power and 6-90 Reactivity Traces 6-40 EDEC TOP 2.4c/sec Midplane Failure: Fuel 6-91 Reactivity Components by Channel 6-41 E0EC TOP 2.4c/sec Midplane failure: Coolant 6-92 Reactivity Components by Channel 6-42 E0EC TOP 2.4c/sec Midplane Failure: Channel 8 6-93 and Channel 1 FCI Zone Growth 6-43 Power and Reactivity Traces 6-94 6-44 Fuel and Clad Conditions at Core Midplane 6-95 6-45 FCI Zone Growth 6-96 6-46 Fuel Reactivity by Channel 6-97 6-47 Coolant Reactivity by Channel 6-98 6-48 E0EC TOP No Axial Expansion Case: Net 6-99 Reactivity for Parametric Variation of Failure Location 6-49 E0EC TOP No Axial Expansion Case: Fuel 6-100 Reactivity in Channel 8 for Parametric Variation of Failure Location 6-50 E0EC TOP'No Axial Expansion Case: Net 6-101 Reactor Power for Parametric Variation of Failure Location 6-51 B0EC TOP Base Case: Power and Reactivity Plots 6-102 xv

LIST OF FIGURES (Continued)

O Figure No. Ti tle Page 6-52 BOEC TOP Base Case: Pressure Histories and FCI 6-103 Zone Development 6-53 BOEC TOP Case: Molten and Solid fuel Marses 6-104 in the FCI Zone 6-54 Comparison of SASBLOK Simulation of SAS/FCI 6-105 Base Case BOEC TOP 6-55 BOEC SASBLOK Simulation of Base Case FCI Fvent 6-10E 6-56 Reactor Power and Net Reactivity for B0EC TOP 6-107 Base Case - SASBLOK Analysis 6-57 BOEC TOP Base Case Channel 2 Midplane Conditions 6-108 vs Time 6-58 BOEC TOP 20c/sec: Power and Reactivity Traces 6-109 6-59 BOEC TOP 20c/sec Case: Channel 10 FCI Zone 6-110 Grow th 6-60 BOEC TOP 20c/sec Case: Coolara and Reactivity 6-111 Components by Channel 6-61 Power and Reactivity Traces for BOEC 50c/sec 6-112 Ramp h 6-62 B0EC 50c/sec Case Coolant Reactivity by Channel 6-113 6-63 B0EC 50c/sec fuel Motion Reactivity by Channel 6-114 6-64 BOEC 50c/sec Case: Channel 10 Fuel and Clad 6-115 Midplane Conditions 6-65 B0EC 50c/sec Case: Channel 10 FCI Zone Growth 6-116 6-66 BOEC 50c,'sec Case: Channel 3 Fuel and Clad 6-117 Midplane Conditions 6-67 BOEC 50c /sec Case: Channel 3 FCI Zone Growth 6-118 6-68 Channel 9 Localized Boiling and FCI Zone Growth 6-119 6-69 Comparison of Pin Failure Conditions 6-120 6-70 FCI Zone fuel, Sodium and Fission Gas Mass 6-121 (Smith Model) 6-71 FCI Zone Interface and Pressure Profiles 6-122 (Smith Model) 6-72 Power and Reactivity Traces (Smith Model) 6-123 O

xvi

LIST OF FIGURES (Continued)

Figure No. Title Page 6-73 Power and Reactivity Traces witn Burst Pressure 6-124 Suppressed 6-74 Channel 9 Localized Voiding Pattern with Burst 6-125 Pressure Suppressed 6-75 Maximum Cladding Plastic Strains with Burst 6-126 Pressure Suppressed 6-76 Power and Reactivity Traces: Fresh Pin Plastic 6-127 Failure Strain = .002 6-77 Channel 1 FCI Zone Pressure and Voiding Profiles: 6-128 Fresh Pin Plastic Failure Strain = .002 6-78 B0EC TOP 2.4c/sec Midplane Failure: Power and 6-129 Reactivity Traces 6-79 BOEC 2.4c/sec Midplane Failure: Coolant Reactivity 6-130 Con:ponents by Channel 6-80 BOEC 2.4c/sec Midplane Failure: Fuel Reactivity 6-131 Components by Channel 6-81 BCEC TOP loc /sec Midplane Failure: Power and 6-132 Reactivity Traces 6-82 BOEC loc /sec Midplane Failure: Coolant and Fuel 6-133 Reactivity Components by Channel 7-1 Power and Reactivity Traces for E0EC LOF Base 7-46 Case 7-2 Coolant Reactivity by Channei for E0EC LOF Base 7-47 Case 7-3 Reactivity Component Plots E0EC LOF Base Case 7-48 7-4 Voiding Profile for Channel 8: E0EC LOF 7-49 Base Case 7-5 Core Midplane Temperatures E0EC LOF Base Case 7-50 7-6 Early Expansion of Peak Channel fuel in E0EC LOF 7-51 Base Case 7-7 Later Settling of Peak Channel fuel in E0EC LOF 7-52 Base Lase 7-8 Fuel Configuration in Channel 3 at Initiation of 7-53 Collapse of Upper Segment: E0EC LOF Base Case 7-9 Fuel Configuration During slumping of Upper Segment 7-54 in E0EC LOF Base Case 7-10 Maximum Slumped Configuration in Channel 3: E0EC 7-55 LOF 6a3e Case xvii

LIST OF FIGURES (Continued)

O Figure No. Title Pafg_

7-11 Representative Break-Up of Fuel in the Second 7-56 Burst: E0EC LOF Base Case 7-12 Representative Expansion of Lower Power Fuel 7-bi in the Second Burst: E0EC LOF Base Case 7-13 Inlet Pressure Trace: E0EC LOF Base Case 7-58 7-14 Power and Reactivity Traces for the Burst Phase 7-59 of the CLAZAS and Limited Fuel Motion Casr.

7-15 Reactivity Components for the Burst Phase of 7-60 the CLAZAS and Limited Initial Fuel Motion Case 7-16 Voiding Profile for the Peak Channel of the 7-61 CLAZAS and Limited Initial Fuel Motion Case 7-17 Early Cladding Relocation Showing formation of 7-62 the Upper Plug via CLAZAS 7-18 Later Cladding Relocation Showing Effects of 7-63 Fuel Vapor Pressure Development 7-19 Final SLUMPY Configuration Channel 1 7-64 7-20 Final SLUMPY Configuration Channel 8 7-65 g 7-21 Inlet Plenum Pressure Following Voiding 7-66 7-22 E0EC LOF Clad Draining Case: Power and 7-67 Reactivity vs Time 7-23 E0EC LOF Clad Draining Case: Reactivity vs 7-68 Time 7-24 E0EC LOF Clad Draining Case: Clad Reactivity 7-69 vs Time 7-25 E0EC LOF No Fission Gas in SLUMPY: Power and 7-70 Reactivity vs Time 7-26 E0EC LOF No Fission Gas in SLUMPY: Components 7-71 of Reactivity 7-27 E0EC LOF No Axial Expansion Reactivity: Power 7-72 and Reactivity vs Time 7-28 E0EC LOF No Axial Expansien Reactivity: Fuel 7-73 Reactivity vs Time 7-29 E0EC Core Doppler Coeff ient Variations: Power 7-74 vs Time 7-30 E0EC Core Doppler Coefficient Variations: 7-75 Reactivity vs Time O

xviii

LIST OF FIGURES (Continued)

Page Figure No. Title _

7-31 E0EC Core Sodium Void Worth Variations: Power 7-76 vs Time 7-32 E0EC Core Sodium Void Worth Variations: 7-77 Reactivity vs Time 7-33 Venus Driving Pcuttivity: No Fission Gas' 7-78 Parametric Case 7-34 Power and Reactivity Traces: BOEC LOF Base Case 7-79 7-3b Voiding Profile in Channel 9: BOEC LOF Base 7-80 Case 7-36 Voiding Profile in Channel 2: BOEC LOF Base 7-81 Case 7-37 Fuel Motion Reactivity by Channel: BOEC LOF 7-82 Base Case 7-38 Voiding Profile for Channel 6 Following an FCI: 7-83 BOEC LOF Base Case 7-39 Sodium Mass Flow-Rate Comparison Following Pin 7-84 Fa i l u re . BOEC LOF Base Case 7-40 PLUTO Pressure and Reactivity Histories Following 7-85 Pin Failure: BOEC LOF Base Case 7-41 Initial Fuel Motion Following Pin Failure in 7-86 PLUTO for the BOEC LOF Base Case 7-42 Later Fuel Motion Following Pin Failure in PLUTO 7-87 for the 80EC LOF Base Case 7-43 Inlet Pressure ilistory: BOEC LOF Base Case 7-88 7-44 Chugging Dynamics Channel 1: BOEC LOF Base Case 7-89 7-45 initial Movement of Fresh Fuel: BOEC LOF Base 7-90 Case 7-46 Start of Significant Slumping of Fresh Fuel: 7-91 BOEC LOF Base Case 7-47 Final Observed Slumped Condition of Fresh Fuel; 7-92 BOEC LOF Base Case 7-48 Initial Expansion of Irradiated fuel: BOEC LOF 7-93 Base Case 7-49 Beginning of Irradiated Fuel Collapse: BOEC 7-94 LOF Base Case xix

LIST OF FIGURES (Continued)

Figure flo. Title Page 7-50 Irradiated Fuel Slumping: B0EC LOF Base Case 7-95 7-51 Power and Reactivity Traces: CLAZAS and 7-96 Limited Initial Fuel Motion 7-52 . Reactivity Components: CLAZAS and Limited 7-97 Initial Fuel Motion 7-53 Fuel Reactivity per Channel: CLAZAS and 7-98 Limited Initial Fuel Motion 7-54 BOEC LOF No Fission Gas in SLUMPY: Power and 7-99 Reactivity vs Time 7-55 BOEC LOF No Fission Gas in SLUMPY: Coolant 7-100 Voiding and Fuel Motion Reactivity vs Time 7-56 BOEC LOF No Axial Expansion Reactivity 7-101 (15 cm Rip): Power and Reactivity vs Time 7-57 BOEC LOF No Axial Expansion Reactivity 7-102 (30 cm Rip): Power and Reactivity vs Time 7-58 B0EC LOF No Axial Expansion Reactivity: 7-103 O

Channel 6 Reactivity vs Time 7-59 BOEC LOF No Axial Expansion Reactivity: 7-104 Channel 8 Reactivity vs Time 7-60 BOEC LOF No Axial Expansion Reactivity: 7-105 Channel 10 Reactivity vs Time 7-61 BOEC Core Doppler Coefficient Variations 7-106 7-62 BOEC Core Doppler Coefficient Variations 7-107 7-63 BOEC Core Sodium Void Worth Variations 7-108 7-64 BOEC Core Sodium Void Worth Variations 7-109 8-1 B0EC Thirty Cent STEP /LOF - Power and Net 8-15 Reactivi ty 8-2 BOEC Thirty Cent STEP /LOF - Power, Net 8-16 Reactivity and Voiding Sequence Detail xx O

LIST OF FIGURES (Continued)

Figure No. Title Page 8-3 PLUTO and SAS/FCI Channel 6 Reactivity Histories 8-17 8-4 BOEC STEP /LOF Channel 10 FCI Reactivity 8-18 Feedba cks 8-5 BOEC STEP /LOF Channel 10 Fuel Distribution 8-19 t-6 E0EC Thirty Cent STEP /LOF Event: Power + 8-20 Reactivi ty vs Time 8-7 Sodium Distribution at Initial Fuel 8-21 Disruption - E0EC Thirty Cent STEP /LOF 9-1 Cen.bined Reactivi ty Insertion and Loss of Flow 9-20 in BUEC Configuration: Power and Reactivity vs T i c'e 9-2 BOLC T6P/LOF Base Case: PLUTO and SAS/FCI 9-21 Results for Channels 6 and lf 9-3 BOEC 20c/sec T0P/LOF: Power and Reactivity 9-22 Traces 9-4 BOEC 20c/sec T0P/LOF: Coolant Reacti vity 9-23 Components by Channel 9-5 BOEC 20c/sec T0P/LOF: Fuel Reactivi ty 9-24 Components by Channel 9-6 BOEC T0P/LOF with Molten Cladding Gravity 9-25 D ra i n i n(1: Comparison of FCI Feedbacks in Channels 6 and 10 with SAS/FCI and PLUTO 9-7 VENUS Ramp Estimate for BOEC T0P/LOF with 9-26 CLAZAS 10-1 Flow Regimes in a Boiling Fuel Pool in CRBRP 10-23 11-1 VENUS-II E0EC Confit1uration for Disassembly 11-26 Calculation 11-2 Reactivity vs Distance from Core Center for 11-27 E0EC LOF Innediate Re-entry Case xxi

LIST OF FIGURES (Continued)

Figure No. Title Page 11-3 Reactivity vs Penetration for 18 fuel Assembly 11-28 Fal l-In 11-4 Reactivity Gradient as a Function of Penetration: 11-29 18 Fuel Aseembly Fall-In 12-1 Thermal Source Specification of Structural 12-8 Margin Beyond the Design Base O

O xxii

1. Introduction This report documents Hypothetical Core Disruptive Accident (HCDA) eval-uations for the Clinch River Breeder Reactor Plant (CRBRP) which demonstrate that HCDA's are expected to be non-energetic. Additionally, conservative evaluations were performed to determine a rational envelope for energetic consequences and specify the mechanical work source for the Structural Margin Beyond the Design Base (SMBDB). The analyses were p'wformed using the SAS3A and VEfiUS II computer codes (Refs. 1 and 2). Argonne National Laboratory (ANL) has completed more detailed ana!"ses, using the SA53C computer code (Psef. 3), which both support the validity of the SAS3A ten-channel model used in this study and confirm the basic conclusions on energetics in the CRBRP.

The results of a wide spectrum of hypothetical core disruptive accident evaluations ci the Clinch River Breeder Reactor Plant are presented beginning with accident initiation, then proceeding through several alternate accident paths and finally assessing, where appropriate, any energetic consequences.

As discussed in the following, this report is an extension of an assessment of HCDA events performed by Argonne National Laboratory of the CRBRP in 1975 (Ref. 4). To provide a comprehensive analysis of the SAS3A HCDA evaluations for the CRBRP within a single report, selected portions of the original ANL evalu6: ions from Reference 4 have been integrated into this report. Using the reactor physics and SAS modeling of the ANL assessment, the present work broadens the scope of the ANL analysis to include a greater range of core disruptive accident initiators (e.g., reactivity insertions with overpower pump trip and reactivity insertions during reactor startup) and parametric variations related to design and phenomenological uncer tainties.

Desigr. variations have encompassed the impact of core orificing schemes LOF events as well as the more classical physics parameters, e.g. , Doppler coefficient and sodium void worth. Phenomenological modeling has been extended to include an assessment of post-fuel-coolant-interaction blockages, loss-of-flow driven transient overpower reactivity ramp deteminations, and bubble collapse effects during homogenized looli energetic disassemblies. Phenomeno-logical uncertainty analyses have included ramp rates, failure locations, 1-1

and failure criteria for TOP events, as well as fission gas and axial expansion effects during L0f events.

The evaluations consider the reactor core configuration at both the beginning and the end of the first year in a three year equilibrium reload cycle (80EC and E0EC). The more recent Afil SAS3D study (Ref. 3) examines the reactor response at the end of the third year in the cycle. The extene;ve parametric analyses performed are considered to be sufficient to support a general conclusion on energetics consequences in the CRBRP. Evaluations of the reactor response in the beginning of life (BOL) singular configuration were performed for the initial CRBRP PSAR submittal. These evaluations indicated that no major increase in the consequence spectrum resulted from the BOL core configuration.

The analysis approach has been to use engineering judgements to define scenarios of decending probability for a given accident initiator. In order of decreasing probability, analyses are performed which predict the best estimate (category 1), then introduce current design and thermophysical data uncertainties (category 2), major phenomenological behavior uncertainties (category 3), and finally arbitrary assumptions intended to rationally envelope the results (category 4).

g It has been recognized that even less probable assumptions could be hypo-thesized. Such sequences, based on unsupported arbitrary assumptions which may even violate empirically supported understanding of materials behavior were not investigated herein as their contribution toward an engineering assessment of HCDA consequences in the CRBRP was considered to be of no value.

The value of the probabilistic approach is in its ability to surface, for further consideration, both the margins which exist and the nature of the assumptions involved in determining the SMBDB.

The SMBDB was specified based upon calculations of the structural damage potential which could result from postulated events leading to hydro-dynamic disruption of the reactor core.

O l-2

The conclusions reached herein are therefore bast j upon assessments of both the probabilistic and deterministic factors described above. It was g considered that only through this combination of factors could the results of HCDA analyses be placed into a rational perspective of reactor safety.

Section 2.0 provides a summary and conclusion frcm the extensive analyses that have been completed.

Section 3.0 identifies the important processes in the HCDA and relates these to SAS3A modeling.

Section 4.0 defines the reactor core parameters that were modeled in the SAS3A code. Also, the input assumptions on the best estimate cases are d bcussed.

Section 5.0 discusses the development of the neutronic parameters that are required as input to SAS3A.

Section 6.0 contains the SAS3A evaluations of the unprotected transient overpower i .itiated events for the BOEC and E0EC cores. Several cases that e va l ua te. accidents initiated from startup are included.

Section 7.0 contains the SAS3A evaluations of the unprotected loss-of-flow initiated events for both the 3dEC and E0EC cores.

Sections 8.0 and 9.0 eveluate combined reactivity and flow reduction events which are significantly less probable than the TOP or LOF events. This was done to assure that no dramatic changes in consequences are present in the HCDA consequence spectrum.

Section 10.0 evaluates the non-energetic path through the transition phase which is most likely to develop from the LOF initiating phase.

Section 11.0 presents evaluations of the hydrodynamic disassembly that may develop from in tiating phase or transition phase. These are the less likely paths and in some cases are c.-bitrary.

Section 12.0 defines the pressure-volume relationship at scciated with the Structural Margin Beyond the Design Base and its basis.

Three appendices provide supplemental information pertinent to the overall HCDA evaluations.

1-3

2. Suanary_a_nd Conclusions A variety of hypothetical core disruptive event initiators have been addressed for both the beginning and end of an equilibrium cycle configuration in the Clinch River Breeder Reactor Plant. Based upon either a BOEC or E0EC reactor configuration (first year of a three year cy le), a best estimate result was determined. Analyses of less probable data values and phenomeno-logical uncertainties were performed to determ:1e the associated uncertainty in thermal consequences. An assessment of the consequences was then performed based upon two treassres. A quantity was selected to relate the thennal energy release of each scenario with the poteni.ial to result in mechanical damage of the primary coolant boundary. This quantity is the thermodynamic work potential (pressure-volume relationship) resulting from an isentropic expansion of the fuel to a volume consistent with sodium slug impact on the reactor head. A subjective assignment of the sequence into one of four pr ' ability categories was made. This assignment is dependent upon the likeliho u of the initiator, whether expected or less probable values for parameters are employed, and whether specific, conservative assumptions are employed to de ennine a cational envelope of the consequences. The categories are defined to range from the best estimate (category 1) through arbitrary enveloping analyses (category 4). Table 2-1 sun.marizes the definition of the accident sequence categories utilized in this report.

The results of the analyses presented indicate that the energetic conse-quences of hypothetical core disruptive events in the CRBRP are benign. It was shown that the BOEC configuration is more likely to result in an energetic consequence than is the E0EC configuration. This sensitivity is due to the highest power-to-flow assemblies being newly loaded fuel in the 80EC. New fuel tends to compact and add reactivity upon pin disruption because fission gas is not sufficiently available to cause rapid dispersal. Thus new fuel canr.ot initially of fset the continued sodium void reactivity additions.

However, even for tM: COEC configuration seve^al uniikely design and pheno-menological assumptions must be r fe before consequences approach the SMBDB.

Table 2-2 summarizes the scenarios analyzed in tenns of a probab;lity category, fuel final average temperature, internal fuel energy stored above the melting point, and the isentropic work available at sodiun slug impact 2 -1

on the reactor head. The SMBDB thermal equivalents which are considered to form a rational envelope of CRBRP energetics consequences are also included for camparison. Further details on this equivalency are provided in Section 12. h All category 1 and 2 events (except for the BOEC LOF with 150% void worth) result in negligible energetics consequences. The reactor core is mostly coolable in place (TOP) or will gradually melt down and permanently disperse fuel by steel or fuel vaper pressure without energetic consequences.

Use of pessimistic category 3 assumptions leads to a range of consequences encompassing negligible to muderate energetics. The sensitivity of the B0EC configuration to LOF conditions becomes apparent at this level. Examples of phenomenological assumptions made include midplane cladding failures in TOP events, omission of nitigating effects such as axial expansion during LOF events, and postulated reentry of large fuel masses to generate recriticalities. For hydrodynamic disassembly paths, the driving ramp rates have been estimated to be on the order of fif ty dollars per second. For these conditions fuel vapor pressure is assumed to be the only dispersive mechanism.

If additional arbitrary conservatisms are introduced on top of category 3 assumptions, enveloping consequences are established and defined as category

4. These sequences typically result in hydrodynamic disassembly of the reactor core. The arbitrary conservatisms take the form of increased driving ramp rates (70-100 $/sec).

The major phenomenalogical uncertainties in an energetics assessment for the CRBR are considered to be the LOF driven TOP failure and potential for recriticalities af ter loss of core geometry.

Based upon the broad range of reactor conditions and phenomenological assumptions analyzed, it is concluded that the probability of a hydrodynamic disassembly re.;ulting in final average core temperatures greater than 4300 K is significantly less than the expected, negligible energetic consequences of HCDA's. To approach the SMSDB thermal source term (4800 K average tempera-ture) an additional, arbitrary level of conservatism must be added. Thus, the probability of exceeding the energetic consequences associated with the SMBDB, given that an HCDA were to occur, is very low.

9 2-2

TABLE 2-1 DEFINITION OF ACCICENT SEQUENCE CATEGORIES PROBABILITY CATEGORY DEFINITION 1 Sequences based on nominal design data and best understand-ing of phenomenology.

2 Sequences based on more conservative design data or minor variations in model uncertainties, such as nadeling of fission gas release rates.

3 Sequences based upon pessimistic assumptions of phenomeno-logical behavior intended to enhance the energy release.

Neglecting axial expansion of the fuel pin during an LOF is a n exa...pl e .

4 Sequences based on arbitrary pessimistic assumptions in the initiating phase or transition phase intended to produce bounding ef fects for Category 3.

2-3

TAaLE 2-2 SLTf%Rf GF ENERGETICS COMSEQUEhCE SPECTRt71

1. EACTOR CO2E FLEL lRO2ESILITY F FI AAL A'.E Da;E ENER0f ABOVE FUEL EIPANSION WORK CATE00RY TEWE 3AME FL'EL 50LI:X;5 AT ha SLUG IMPACT CASE CEstelrTICM

• t N N SM309 .. 43')0 W OO 101 E0EC-TCP N 2296 287

• 8 Base Case Inse-tton Rate of 10 t/sec 2 4 312 -

Cesign in,ertten Rate of 2.4 t/sec 1 2251 Entreet !nsertton Rate cf 50 t/ set 3 2422 280 Hypotactical :nsertion Rate of 3 f /sec 4 3720 4125 la Altercate fisston Gas Release N del 2 2444 434 Arbitrary Midple-e Fat t ure at 2.4 usec 3 23B4 62 Tea t/sec Insertion wi t* Failare Forced at 0.27 of Core weight and No Antal Espansica 3 2470 99 Ten t/sec Insertion with Failure Tarte' at 0.73 of Core Heigmt and ho Aatal Expansion 3 2450 96 Arettrary "telane F4tlare at 10 c/sec 3 3410 322') 12 (ett9 or withcut Amial Espansion)

~

• essentially zero.

9 O e

TABLE 2-2 50 MARY Of ENERGETICS CONSEQUEhCE 5FECTRJM (Continu- 3) l REACTOR CCDE FUEL JFRCBASILITY F i f.: A.E R AGE [NE R GY ASOVE FUEL IIPASSION WORK CASE LE5CR:PTICN CATEGORY TC P. E RATURE FUEL SOLIDUS AT ha SLUG IPPACT

'E N MJ FrtC-Tcp Ease Case lesertion Rate of 10 t/sec 2 214B 260 Dasign Insertton Rate of 2.4 t/sec 1 2370 sic 8 4

• Limitirg lesertien Rate of 20 t/sec 2 1891 E=trew Inserticn Rate cf 50 t/sec 3 2504 332 Alternate Fission Gas Release Medel 2 2480 495 Alternate Fuel Pin Failure Criteria 2 2459 356 379^ 4335 26 7

U1 Areitrary widplane Failure at 2.4 t/sec e abstrary 75 5/sec Driving kate 3

4 4M5 5400 53 A r bi t r a ry Midsiane Failure at 10 C/sec 3 2 Fd 64 ECEE _TCP at 5 E typ Ease Case Insertion Rate cf 10 t/sec 2 2802 525 Limiting Insertion Rate cf 20 t/ set 2 2640 138 Ertt.l0F Base Case 1 s3040 s2100 CL AZA5 and Limited Initial f uel Wotton 3

• 3330 s2650 Gravity Drainaga of Cladding 2 s3040 +2100 he91 ect Fission Gas Dispersal of Fuel 3 s3330 s2b50 in SLUMPY heglect Fuel Antal Thermal Espansion 3 s3040 s2100 Arbitrary 40 $/sec Disassently Cal- 4 4277 6060 74 culation

• Essentially zero.

TABLE 2-2 Sutt.,;f Of EM T'a T!C5 CWEcit.CE irECTPLM (Continued)

SEACTO4 C0cf FUEL pct?CILITY F i fif t AVt=:Of [*,f&c.f N:0.f CASE OE5CRIPTICN FUEL EJ.'A?.5fCN hCat CAIFCCEV Tiur[MT ikt TUEL 50t!GU2 AT Na SLUG 1* PACT

• K MJ MJ EGEC-10r (Conttro,ed)

TL9pler Uncertainty 0 ITJ Percent of Magnitude 2 s M49 -2100

• 0 e1 Fercen t o f N'v.i t ude 2 s3J47 2100

• 5 ;d i ten Vaid Wirth UncertainA 9 IW Tercent cf Ngnitu e 2 s314] -21C3

• ro 0 EO Percent of Ma rit tade 2 -3040 s2100 *

& fuel.karth C '. Crit'"U 0 120 Percent of M,gnitade 2 - 30 0 -2100

• 0 83 Fercent of 4,ritude 2 s 3C4 ) 2100

• T r_iy rr f 1... Cw atjincert4tne .-

0 123 Fercen t o f Decay ka te 2 1040 -2101

• 8 h> reru nt of Cece/ Rate 2 .3GO 2101

• T 1. .w Orificing Scn.-.m vari 4 ties 0 Au m t 1975 Sch*.e 2 30 0 2100

• e he slet tic.) f is s ion G4 s Twel D i s pe rs a l 3 4841 7974 132 8 Desecoer l]76 5thene 2 M4] 21 r,Q

• e Neglect'o] fission Gas f uel D i s r.ers a l 3 s3a41 2100 *

-b-

• to rntially zero.

e O O

-t TABtt 2-2 10:?1M y Of Lt.I kis ilC5 O". J.JJl fai[ 50CC1kUM (Contiraa d)

[A e frV tu[L lp i . . . . !Y ' '

'l !t ' ' .' l IU(t IIP.* M!GN WCH CASI l'ISCulPT!GN CAftlokY II 't'I v alUb t IAL 5(11005 A T h s si t.. MIACT MJ

______. . . _ _ _ _ _ _ _ . _ ___.._'A_..__ . __-

MJ PhiC-t14 Bn e (.n e 1 3D40 2}OO

• g CIA!A5 arid Limited initial fuel Motion 3 E . $UG 64 F u ri Listersal in lhealectfissionGas Si lHP f 3 ,J4 3 51a/ 65

, hr ylet t f ue l As i a l 'spons son 3 4h4 575's 64 (LAZAs with SA5 l[.1 f;nlit.eir Ur i v i r.9 Iunstion 4 41 dr. 5713 7x 7

Dol pler Uni erta i nty 8 I?o Percent o' Marinitude 2 3030 *2100

• 8 60 Fercent of Magnitwe 2 - 3M1 ~2100

• i Spdiirm Void Woyt5 lira e r t a i n ty 8 150 I'e rt en t o f Magn i tude 2 4153 55f.0 72 f

i8 50 Per(ent of Ma.niitude 2 - 3'14 3 2l00

• F u+ 1 hear t ivi ty Wer th tjrter tenty 8 1/0 Ferc.ent of Mo.;ni tude 2 - f.40 2100

• 4 h0 Fertet,t of Magnitude  ? 3040 2100

• Pr ma ry f lw [w ay, lfw . e t e i n ty 4 120 Fercent of Dec or were 2 1040 .2100

• 8 80 Percent of Decay Pate  ? 3043 7100

• Dec 1976 Flow Orifice 50,e= 2 2915 SPH *

• I nevit ia lly zetu.

TABLL 2-2 5tt94ARY Cr [NEPi.ITILS Cr*MQutt(.E SPitIkts* (Conclus !)

RCACIUk C';ki It'[L fP0M31Llif f l%~ L A lt hML LNEMY AW.C fUrt EDFAN510N WQpir, CASL CLSCR!fi!UN Call CT.V TLM^t! AitWL FULL 53LICU"5 AT Na Mtf IMPACT

't M M BOE C-S T [ Pfi n F_

b.irty Cent inser ucn 3 4225 5370 63 f of C-ST Li'jt o s It.it ty Cent inseitnun 3 35v6 31 h

• BuEC-ThPLLCf Des t yr. Insertion Rate of c.4 (/sec 3 4253 N5MO $70 9 brevity Dra t oa;e o f ClaJdin] 3 4153 6643 N93 8 CLAZA2 M.aticn of LlajJti.a 4 4415 3254 5170 h Litra t is.g I isertion Pste of 20 c/sec 3 sJ040 llM

• ECil-TGP/tur '

Design insertton Rate of 2.4 c/sec 3 304 J N21 DJ

• 9 Lt AT A's Matt on c f L i s1Jirej 4 - 3 '4 a '2100

• 3 Tra isi t ti,n Ftm >e-lis oli s t a ke antrj a*  !

1 41/3 tq70 -

Arbitrary 2d 1/sec drivin) r +-p 3 55 Arbitrary 3 7 1/ ser if r t v t w1 raw 4 Alt t 5'13 50 Arbitrary 45 1/sec c1risiwj r enip 4 4150 - 2] 53 Arcitrary 63 5/sec .feiving raa4, 4

, 4103 g 7110 l 94

. I t rar.s i t i on Pria se -Ik,i > + ii zet C ure *

• s A Litr ary 21 = orm.ina l powe r (t,ne 'nel 4 4'.41 tej--D e, J Arbitrary 2.1 x nor inal tower 4 4652  ! 7J40 9)

Arbi trary 210 m e.unir.e l power 4 413..  !, 5 5'J 3  ! 30 base rese with Butble Cull.p.e 4 4615 l *.7/40 i -87 i i _

• tssentially

• • All ( n e, zero. -prot. Lilit y u tegory / tunsc Neoces are sj04uh, sllu0 MJ witWt signi f icant fuel espansion work .

artitrary.

O O O

3. SAS3A Code System 3.1 Physical Processes Related to Accident Proj3ression The physical processes which are inherent within a mechanistic analysis of unprotected events in the CRBRP are both inter-disciplinary and complex.

However, for the purpose of establishing a rational bound on the thermal energy release associated with such events, it is possible to focus on those specific dominant processes which define branch points in the accident pro-gression path leading to increased energetics. Thus, only those physical processes considered most important in a determination of the potential ener-getics, or requiring clarification, are discussed in the following sections on phenomenological modeling within SAS3A.

Disruption of tt,e reactor core can only occur due to an unprotected imbalance between energy generation and heat removal by the heat transport systems. A different set of physical processes will be dominant depending upon whether the imbalance in energy generation and heat removal is due to enhanced energy generation (transient overpower, TOP), reduced heat removal (loss of flow, LOF), or both imbalances (STEP /LOF and T0P/LOF).

For the case of enhanced energy generation the dominant physical processes are chronologically considered to be the following:

a. steady state neutron irradiation effects on the fuel pins

b. transient loading and penetration of the cladding barrier by fuel

c. interaction of ejected fuel pin materials witq the subcooled flowing sodium

d. neutron kinetics effects of fuel and sodium displacements

e. heat removal from the disrupted fuel assembly geometry Figure 3-1 depicts the accideat progression paths which can occur and the branch points afforded by the above processes. One end state to a TOP progres-sion identified herein is reactor operation at normal power ic ils with partial core damaga. This end state will occur if fuel removal by pin rupture and fuel sweepout approximately balances the total reactivity insertion. Thermal feedback effects will then balance the reactivity difference to result in a critical state.

3-1

If instead, the imbalance is originated by a reduction in the energy removal, in particular a loss of all primary pumping power, then the set of dominant physical processes becomes: h

a. steady state neutron irradiation effects on the fuel pins

b. sodium boiling and voiding of the fuel assemblies with associated reactivity effect

c. interact. ion of hydraulic forces within an assembly with molten cladding - hydraulic and reactivity effects

d. disruption and relocation of fuel in the sodium voided assemblies

e. overpower failure of fuel pins into sodium voided assemblies

f. overpower failure of lowest power fuel pins in assemblies with liquid sodium present.

Figure 3-2 presents an accident progression diagram for the LOF event in CRBRP showing the phenomenological branch points of major interest. Since the LOF sequence is of principal importance in assessing CRBRP energetics, an explana-tion of the expected progression path is appropriate. g The initial branch point is represented by the Plant Protection System (PPS). A basic assumption for this assessment is that the PPS does not respond.

If it were to respond, as designed, an HCDA event would not occur.

Due to the reduced primary flow and inlet plenum pressure, sodium boil-ing, flow reversal and voiding of the high power-to-flow assemblies can occur.

For CRBRP, this voidir.g would result in a positive reactivity feedback. As the spatial region of sodium voiding (with positive feedback) grows, cladding starts to melt. A significant amount of cladding can melt prior to any fuel mel ting. The potential relocation of the molten cladding combined with the growing sodium void region constitutes the first major phenomenological branch in the progression path. Alternate paths have been based upon the associated reactivity effects. For CRBRP the center path, corresponding to mild reacti-vity effects of steel relocation (<30c), is believed to be most probable. An O

3-2

initial decrease in reactivity is associated with cladding drainage toward the ir.idplane. Strong prompt critical excursions could only occur for massive, coheren' and rapid steel upward motions; a very improbable event.

Tha disruption of the fuel in the sodium voided, molten cladding regions becomes the next phenomenological branch point. When fuel disruption criteria are based upon melting of unrestructured fuel (fission gas bearing) or large melt f ractions (150 percent), disruption occurs at core powers ten to thirty times rated; approximately 1-3.5 KW/gm. At these heating rates the retained fission gases are expected to provide an inherent motive force to disperse fuel and result in negative reactivity feedback. If the associated negative reactivity effect is strong enough, the power will be reduced such that sodium voiding can proceed in a benign manner If initial fuel motions are not dispersive then the power and reactivity will continue to rise and approach prompt critical conditions. At this point the central branch recognizes that TOP type pin ruptures can occur into sodium voided ar emblies prior to ruptures into sodium filled assemblies. The SAS3A computer code employed herein cannot model such events which could be signifi-cant in reducing the net reactivity from near prompt critical. This SAS code limitation is considered to result in a conservative estimate of energetic consequences.

Finally, a major phenomenological branch exists in the behavior of pin ruptures into sodium filled assemblies (LOF/ TOP). Compactive fuel motion at this branch is considered to be the only probable initiating phase path for energetic consequences on the order of the SMBDB. Development programs are being identified to produce information to support the judgement that it is highly unlikely that these types of failures produce reactivity ramp rates sufficient to exceed the SMBDB.

Alternate initiating scenarios which combine both aspects of the energy imbalance (TOP /LOF, STEP /LOF) usually are closely relat'ed to the LOF accident.

This is a result of the relative magnitude and timing of the reactivity insertion portion of the event.

3-3

3.2 Phenomenological Modeling 3.2.1 Fuel Characterization in Steady State The SAS3A code contains a steady-state fuel characterization model to O

internally calculate fuel restructuring and fuel / clad swelling, detennine the effect of the restructuring and swelling on material properties, and make the fuel characterization corrpatible with the predicted steady-state fuel temperatures. The routine also predicts fission gas release from the steady-state fuel pin.

The fuel characterization procedure is initiated by calculating a steady-state fuel temperature distribution based on an input design description.

The code then assigns fuel nodes to each of the three types of fuel struc-tures; columnar, equiaxial, and unrestructured based on input correlations of restructuring isotherms. The total (reference temperature) mass of each fuel type is obtained with proper observation of conservation of mass require-ments. Working with reference mass and volume of each type, the swelling of fuel is calculated based on input swelling rates for each fuel type. The restructuring radii are readjusted, fuel properties are brought up to date, a new temperature profile is calculated, and the procedure reper'.ed until converged.

Clad swelling, which can affect fuel restructuring strongly through its effect on fuel / clad gap, is evaluated using a correlation based on tempera-tures and fast fluence. Fuel density and thermal conductivity are calculated by a temperature dependent correlation or may be input as tabular data.

Fission gas release is calculated by a modified Dutt Correlation depen-dent on burnup and linear heat rate (Ref. 5). The released gas pressurizes the gas plenum and central c tity (if any) with pressure equilibrium between the two volumes assumed.

3.2.2 Fission Gas Release from Fuel Fission gases, notably Xenon and Krypton are produced by uranium fi.-

sioning. During prolonged operation at power, any given fuel pin will a tain an equilibrium concentration of fission gases retained within the fuel.

The amount and distribution of the retained gases is a function of the local O

3-4

fuel temperature and burnup. For CRBRP fuel design and reactor conditions, the retention of fission gases has been empirically correlated to linear power and burnup (Ref. 5). This correlation, which also assumes all retained gas to be in unrestructured fuel, was adopted within SAS.

It has been recognized for some time that upon fuel melti.ng the retained fission gases could provide a motive force for fuel pin failure an \ DISA55EM3LY DISASSE E

• TP: Transition Pt.ase Figure 3-2 CRBRP Unprotected LOF Accident Progression Diagram (Continued)

• • gc- Transition Phase or Low Energy Disassembly g h

8 k

\

7 -

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\ BURST IRRADIATED CLAD (5) 5 -

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6 N

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2 UutI4I j l l 500 700 900 1100 CLAD TEMPERATURE, C Note: Numbers in () indicate SAS strength tables:

(1) through (4) from Ref. 46 (5) from Ref. 15 Figure 3-3 Clad Strength for Various Assumptions A

3-43

O o

TIME DEPENDEN1 ~~~~

FUEL EJECTION F ilE L

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CAVITY LAGRANGIAN CELLS F OR FUEL RE ACTIVITY C ALCUL ATION Sta/ F CI Figure 3-4 Basic Components of the SAS/FCI Model O

3-44

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N-FUEL COOLANT SIRUCTURE N FUEL COOLANT STRUCTURE PIN CH ANNEL PIN CHANNEL (A) (B)

INTERACTION ZONE lNTERACTION ZONE EXPANSION IN ONE EXPANSION IN TWO DIRECTION DIRECTIONS Figure 3-5. Treatment of Fuel-Coolant Interaction Zone Interfaces 3-A5

ao , ,

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0 0.010 0.020 0.030 TIME (SECOND9 HEDL 7403-70.9 Figure 3-6 Effect of Pump on Voiding of the MARK-IIA Loop &

(From Ref. 23) W 3-46

SAS TPANSIENT Ev,SAS BLCK 5;g g ga 7.................. LUA1,01 l N3 DO

---d 18H. NEUIRONIC

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SOLUT!CN'S ( SIPULATION OF SAS3A FCI COMPARE 7 '

ANALYSIS FCI SOLUTION

+

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SAS3A CODE INTRODUCE BLOCKAGE, TERN! NATION WITH CORE IN EXCITED ADJUST CORE F0WER NOTE 1: CONTINUED FCI THEFEAL STATE t. GAS EUBBLE TYPE TREATMENT IN AN ALREADY FAltED ASSEP3ly IS CURRENTLY UNAVAILABLE.

YES(NOTE 1)

ARE DDITIONAL FCI'S FREDICTED?

/h0 CORE NO C00tASLE WITH YES BLOC VAGF u LEVEL o EST. PEACTIVITY EffECIS DETERM!NE CONFIGURATIONS ON FUEL RELOCATION  : OF A00VE CORE IN FULLY BLOCLED ASSEMBLY C00LABLE BLOCKAGES o o i "

LARGE SMALL REACTIVITY REACTIVII( UNC00LAPLE C00LABLE SLCC) AGE ELOC6 AGE EFFECT EffECT l VENUS ESTIMATE ESilMATE (END )

ANAliS[S DIAL VS AXIAL PADI A!. VS AXI AL PROFAGATION OF BLOCFACE DAMAGE RELOCATION (END) "

GO NO TO XI1101 D% FHASE7 COES BLOCFACE RfLOCATE 1.0 NO C00LABLE SUBCRITICAL YES f YES CChflGURAi!CN?

\ END) fERfUFM XIIIGN fHASE Figure 3-7 SASBLOK Evaluation Logic Flow 3-47

O L-m SOLID CURVE - QUASISTATIC 5- DOTTED CURVE - PT. KI!4ETICS WITH TiOliLIriEAR D TRIAtiGLES - PT. KIriETICS WITH LIriEARIZED D ,

w n o~ [\

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I Figure 3-8 Accuracy of Point Kinetics Reactivity in a CRBRP E0EC LOF Transient O O O

4. SAS Reactor Model and input Assumptions This section deals with input setup for the SAS code, excluding the neutronics data which are discussed in Section 5. Two basic models were assembled to represent a beginning-of-equilibrium-cycle (B0EC) and end-of-equilibrium-cycle (E0EC) core configuration at year one in the three year equilibrium cycle. These decks were then modified to represent the specific event sequt.nce being considered, e.g. , loss-of-flow (LOF) or reactivity insertion-transient overpower (TOP).

The first decision that must be made in formulating SAS input is the division of the core into SAS channels. Nominally, it is desirable to group assemblies on the basis of power, ori fice zone and burnup. Assembly location is also important since transition to two-dimensional geometry is required for calculation of neutronics data. It is not possible to meet all these requirements in the context of only ten channels. Full satisfac-t Jn of power, orifice zone, and burnup can only be obtained by representing the core with 33 channels as given in the assembly identification shown in Figure 4-1. At the time the decks were originally set up for this study, coding limitations in the processing routines for neutronics calculations made it impossible to assign a mixture of channels to a number of radial positions.

Hence, an assembly location restriction was observed. For the 30EC case, the next most important quantity is fuel burnup. Fresh and irradiated fuel is expected to behave in a fundamentally different fashion. The channel selections for the BOEC case, determined by subassembly location and burnup, are shown in Figure 4-2. The odd-numbered channels consist of fresh assemblies; the even-numbered channels are irradiated assemblies. Calculated steady-state results for this choice of assembly assignments are compared with design values in Section 5. The EOFC selection is easier since burnup effects are not as critical. Here, core power was used as the priority parameter in addition to assembly location, since event sequences in the burst phase of the accident most crucially depend on core power. The E0EC case channel selections are shown in Figure 4-3. Steady-state results will be discussed in the next section.

With the channel arrangement established, the characteristics of the individucl channels must be defined. It is not practical to exhaustively treat 4-1

O all the input values in all cases. This section will present all the input numbers in the 80EC LOF cases, show how the other cases differ, and discuss those input assumptions that are considered to be the most critical in determining the calculated results.

The SAS3A input for the BOEC LOF case is presented in Table 4-1. The latest version of SAS3A input description was included in Ref. I for use in translation of the numbers. The fomat of Table 4-1 is as follows:

a. Integer variables are first in a 1216 FORMAT. The first field, LOC, on each card gives initial input location treated by that card. The second field gives the number of input locations to be read in on the card (in the present card arrangement this variable is ten). The remaining ten varibbles are actual input filling locations LOC to LOC + 9.

b. Floating point variables are treated next in a (216, SE12.5)

FORMAT. The first field, LOC, again gives the initial input location. The second field gives the number of variables treated which in this case is five. The remaining five variables fill input locations LOC to LOC + 4.

c. In both the integer and floating point input, numbers are given in the conment card columns 73-80. These are points representing the key input decisions to be discussed. This discussion follows.

Pointer 1 refers to the basic assembly arrangement is SAS. The bases for these choices were discussed in connection with Figure 4-2 and 4-3 above.

Pointer 2 refers to LOC = 22 for the selection of equally spaced radial nodes in the fuel. The use of this option results in a more reasonable estimation of the fuel pin centerline temperatures due to the linear extrapolation algorithm employed by the heat transfer calculation.

Pointer 3 refers to LOC = 42 for a specification of one zone. This analysis makes no attempt to treat the radial blankets, it is anticipated that the reactivity effects from the radial blankets will generally be small h 4-2

and negative. Further, due to the significant axial plutonium concentration gradient and highly variable power density as a function of core lifetime, reasonable calculations of radial blanket phenomena are beyond the scope of the SAS3A code and the present study.

Pointer 4 refers to additional integer input that specifies options as to the interpretation of later floating point variables. This is mainly a matter of style, but these choices are important for understanding the meaning of other input.

Point + 5 refers to LOC = 176 for specification that the sodium film motion option is to be used. Sodium film motion is essential to avoid the buildup of unrealistic films on structure, the fission gas plenum, and other cold condensing surfaces. The presence of these thick films would unrealistically increase the sodium vapor pressure drop in the voiding model.

Pointer 6 refers to LOC = 191, which turns on the modified Gruber fission gas release option described in Ref. 9.

Pointer 7 refers to the three pin failure groups assumed in the SAS/FCI calculation. This option was inserted to model fuel pin failure incoherence, and it is useful in high power situations where a significant power gradient exists across an assembly. However, the fuel ejected from the later failure groups interacts with all the sodium in the FCI zone, while the fragmentation and mixing time constant is evaluated starting with the first pin group to fail. Hence, late rapid heat transfer from fuel to sodium may occur, resulting in a sustained overpressure in the FCI zone. A late flow reversal is then possible. Fuel motion in the channel may then be interpolated from the sodium interfaces as downward and positive. This is unrealistic as has been pointed out by Wider (Ref. 21).

Pointer 8 refers to the pin failure criterion to be selected. The burst criterion is the only mechanistic criterion presently integrated into the SAS3A code. The -4 option gives maximum flexibility in varying the cladding strength as a function of temperature.

Pointer 9 refers to LOC = 640, which specifies the steady-state fuels categorization option. The program thus will automatically restructure 4-3

the fuel in line with the internal correlations and the floating point input parameters. g Pointer 10 refers to the SAS/FCI molten fuel ejection option. After fuel pin failure, a mixture of molten fuel, solid fuel, and fission gas is ejected with component proportionality based on volume fractions inside the pin cavity.

Pointer 11 refers to the fuel type table to be used for evaluating cladding strengths in the pin failure criterion. Since fresh and irradiated fuel differ in cladding properties, different tables are used.

Pointer 12 refers to the cladding relocation model. The base case assumes that clad does not move independently of fuel. Two arguments can be made to justify this assumption. First, at the time of sodium boiling initiation, radial temperature gradients of s225 C are present across an assembly. Hence, cladding in a fuel assembly does not melt coherently.

Draining of cladding is prevented by incipient flooding due to sodium vapor streaming, concentrating the sodium vapor pressure drop over a region of molten cladding. However, because of the interconnected channel effect (a flooded channel must see the same pressure gradient as a unflooded h channel), molten cladding films initially flooded must very quickly unflood because of vapor flow diversion to subchannels where cladding is yet to become molten. The result may be little net movement of cladding. Second, the pins are predicted to fail and release fission gas very close to the melting point. Fission gas is likely to significantly affect sodium con-densation and the axial pressure gradient in these assemblies. In particular, fission gas could significantly delay upward driven sodium-vapor-induced cladding motion or even cause clad draining. Since CLAZAS appears to overestimate the degree of upward cladding motion even in the absence of the above two phenomena, the best estimate option, given available models, is to assume no sodium vapor effects on cladding.

Pointer 13 refers to LOC = 833. In the pessimistic cases when CLAZAS was used, the thennal response of the blanket pellets does not promote rapid freezing of cladding. Unless the first cladding to penetrate the blanket is stopped early while in a partially molten condition, the model tends to fill the entire blanket with a solid slug of cladding. This seems entirely g 4-4

unreasonable. Hence, until fuel motion, cladding is only permitted to penetrate two nodes or 14 cm into the blanket. After fuel motion this restriction is removed, since the boundary motion of the fuel compressible region is determined from the clad segment positions.

Pointer 14 refers to the assumption of fission gas slip relative to fuel in irradiated channels. No slip is assumed in fresh channels since no fission gas is assumed available for the SLUMPY calculation.

Pointer 15 refers to LOC = 871. This forces the temperature check for initiation of slumping in a given axial node to be made on unrestructured fuel. Hence, in irradiated fuel, slumping can start with the first unrestructured fuel to melt.

Pointer 16 refers to the SLUMPY molten fuel density of 7.82 gm/cm ,3 This is an initial value for internal SLUMPY use for rezoning purposes, incompressible flow, and fission gas pressure calculations. This density corresponds to the saturated liquid density at the assumed ambient pressure o f 3 a tm. The input value is intended to slow down fuel compaction beyond this density, if the fuel is lder than the corresponding saturated tem-perature. This parameter is hence a compensation for the fact that DEFORM does not calculate fuel pin radial expansion af ter clad melting, so that at slumping initiation the fuel in a pin segment may be too dense for its thermodynamic state. Computationally, a little extra space in the coolant channel is convenient when colder fuel is flowing over intact pins.

Pointer 17 refers to time constants for fission gas release after fuel pin breakup. The values are 3 sec for solid fuel and 0.1 sec for molten fuel. For solid fuel, the 3 secs corresponds to a general time for release of gas by surface diffusion, assuming random migration of gas bubbles. In molten fuel, bubble migration is not constrained to mechanisms that require independent migration of individual atoms, as in volume diffusion, surface diffusion, or evaporation condensation. Instead, the bubbles can move by the cooperative motion of a large number of atoms; this mechanism is termed viscous flow. Quantitative analysis of the role of viscous flow in the kinetics of gas release and swelling is still preliminary. However, indications are that bubble kinetics are much more rapid in systems where 4-5

viscous flow is the dominant transport mechanism. Hence, 0.1 secs was taken g as a reasonable time constant for release of gas from molten fuel.

Pointer 18 refers to the heat transfer coefficient assumed in SLUMPi for heat transport between unrestructed fuel and steel. SLUMPY fuel motion in CRBRP SAS analyses takes place for only a few hundred milliseconds af ter fuel pin breakup. Time for extensive fuel- teel mixing is not available.

The rate of heat flow should be determined b.. the thermal conductivity of the fuel. The area of contact seems to be dictated by the initial thickness of the cladding. The resulting considerations lead to a selection of 3.2 x 10 ergs (gm of unrestructured fuel)-I sec ("C)-I as the heat flow rate into steel in a given compressible mesh. This number tends to raise steel temperatures from a few hundred degrees to almost a thousand degrees centi-grade in the few hundred milliseconds during the SLUMPY calculations done for the cases in this report. However, initial clad temperatures are suf-ficiently low such that steel vapor pressures are not calculated to contribute significantly to fuel dispersal in this time frame. Obviously, other selec-tions for this parameter can either force actual equilibration of fuel-steel temperatures, or consider steel to be significantly more adiabatic.

Pointer 19 refers to fission gas availability in SLUMPY. No fission gas effects were assumed for fresh fuel. Fission gas availability in irradiated fuel cases was based approximately on the length of time between clad melting and fuel motion, with rough guidance from what fission gas the Gruber calculation algorithm (Ref. 9) predicts will move to grain boundaries by the time of fuel motion. The numbers for the BOEC case are all fairly high, since most of the heatup of irradiated fuel occurs during the burst phase of the accident. Lower numbers were selected for the slower heating peak E0EC case, channels, e.g., 0.4 for Channels 1 and fi of the E0EC core.

Pointer 20 refers to the fraction of fission gas, associated with fuel pin breakup, that provides an instantaneous overpressure to the compressible region. Due to the positive reactivity from sodium voiding, breakup of fuel generally occurs during a burst mode. The Gruber model suggests that rapid fission gas migration to grain boundaries can occur in a very short time O

4-6

under burst conditions. Hence, it is nominally assumed that 20% of the available gas is available instantly, providing overpressures that are generally on the order of several atmospheres af ter fuel has expanded into the channel.

Pointer 21 refers to the lower boundary assumed for fuel motion, the core-blanket interface. Little restructuring takes place near the boundary of the core. Hence, breakup of irradiated fuel occurs at a very low average fuel temperature. In addition, the cladding temperature is also generally low (near the melting point) due to the sodium chugging phenomena. In the SLUMPY time scale, fuel penetration into the blanket may be neutronically overly optimistic. In the parametric cases which used the CLAZAS model, the lower boundary for fuel rrotion is based on cladding segment positions.

These tend to restrict fuel motion to ever, aigher positions in the core.

Pointer 22 refers to the hydraulic diameters used in SLUMPY for movement of the compressible fuel region over (a) fuel with intact cladding, (b) bare fuel segments, and (c) within areas where boundaries are defined solely by the assembly can walls. Changing these numbers can significantly affect the frictional restraints for quasi-solid fuel.

Pointer 23 refers to the compressible equation-of-state coefficient for 0 2 single-phase fuel-steel mixtures,1. x 10 cm /sec , which is actually the square of the assumed velocity of sound. Obviously, a sonic velocity

~

of 10,000 cm/sec is unrealistically low. It was assumed to be low to increase the time step sizes, since the time step is inversely proportional to the velocity of sound. Fortunately, the Doppler effect tends to control heatup phenomena to the millisecond time scale and single-phase regions are generally small such that acoustic relief is not a problem. Other wave effects seem to have little effect on the reactivity history. In the overall context of a one-dimensional fuel motion model, this assumption is not considered to be an important limitation.

Pointer 24 refers to the initial fission gas assumed to be below the compressible region. The cases in this study assumed that sufficient fission gas must slip downward out of the compressible region to build up a gas pressure above the ambient pressure before any effect on moving fuel is 4-7

calculated. (The nominal zero default value assumes an initial gas density equal to the ambient pressure below the compressible region so that any additional gas produces an overpressure). Since fuel pin breakup is likely to be an incoherent process, the initial gas to escape downward probably is not trapped as would be assumed by a rigorous one-dimensional model.

Pointer 25 refers to the fuel particle slip diameter of 0.02 cm. This assumes at least several grains of fuel conglomerated together. Due to the quasi-steady state algorithn ad 3 actually compute fission gas slip, the effect on the calculation may correspond to that of a somewhat larger real particle size. This particle size causes pressure gradients to rapidly equilibrate, but does not allow broken up fuel to rapidly settle (unless the overall fuel length is very small). This degree of slip seems to be consistent with the HEDL out-of-pile fuel motion exneriments (Ref. 8).

Pointer 26 refers to the upper boundary for fuel motion in SLUMPY. For irradiated fuel the same arguments apply as in the selection of the lower boundary at the core-blanket interface (Pointer 21). For fresh fuel the slumping initiation criterion is a 50% melt fraction. Hence, fresh fuel should not be as cold (nonmolten) as irradiated fuel. Further, cladding should be closer to the fuel melting point near the top of the core. Hence, the boundary limiting the upward motion of fresh fuel was selected as the end of the upper blanket.

Pointer 27 refers to the connection of SLUMPY fuel motion to the sodium vapor pressure drops in the channel and to quasi-solid fuel viscosity.

Sodium vapor effects are C assumed to influence cladding relocation (Pointer 12). 'herefore, to be consistent no sodium vapor effects were assumed to influence fuel relocation. TREAT LOF experiments have generally found fresh fuel to slump slowly (Ref. 36). Hence, a viscosity similar to that from high temperature thennal creep data,105 poise, is assumed for fresh fuel of zero melt fraction. This is decreased linearly to the molten fuel value of 5 centipoise (Ref. 40). This results in accelerated slumping as more and more fuel becomes mol ten. Since irradiated fuel is broken up by fission gas, quasi-solid irradiated fuel should not have the cohesive character of fresh fuel. The compromise adopted was to assume a 0.5 poise value for irradiated fuel with zero melt fraction. This also is decreased g linearly to 5 centipoi se for fully molten fuel.

4-8

Pointer 28 refers to the rate assumed for heat transfer between un-restructured and restructured fuel. The same arguments applied in Pointer 18 are used, except that a nominal thickness of unrestructured fuel of 0.06 cm was used to define the contact area. Since the fuel vapor pressure is bas,ed on the average fuel temperature, the results should not be quite as sensitive to this parameter as to the heat going from unrestructured fuel to steel.

Pointer 29 refers in general to the remaining SLUMPY properties for fuel and steel. These are taken from Ref. 40.

Pointer 30 refers to the spring constant. Values that are approximately more than ten times the value in Table 4-1 can lead to oscillations in DEFORM and should be avoided in the current SAS3A code.

Pointer 31 refers to the gap conductance, which is given by 1.0 h = 0.18 +

9 Ar + 0.000132 0.61 +

k 9

where 2

h = fuel-cladding gas conductance (watt /cm - C),

g or = gap (cm),

kg= 0.0002 00

~

m s of He DI = Dilution = moles of He + moles of fission gas In addition, radiation and solid-solid contact conduction (when Ar = 0) 2 are included. A gap conductance minimum value (0.37 watt /cm - C) has been assumed, since, if the gap is large, it is likely to be asymmetric.

Pointer 32 refers to cladding thermophysical properties. The emissivity is 0.3. The heat of fusion, the heat capacity, and the melting temperature are all values associated with the melting transition and are taken from Ref. 41. Remaining properties in this group are evaluated at 815 C from Ref. 42.

4-9

Pointer 33 refers to sodium superheat. Current knowledge suggests that the value for bulk sodium superheat is zero (Ref. 23). However, SAS3A calcu-lations must be done with a finite number of bubbles, i.e., nine. Formation of nine bubbles will suppress additional bubble formation until one of the bubbles condenses. Hence, the sodium will superheat. This problem may be avoided if all bubbles require a minimal amount of superheat, for example, ten degrees in CRBRP type geometry. Now each bubble grows bigger, lasts longer, and fewer bubbies are required per unit length. Of course, this approach is not rigorously correct. When th( code indicates that it woul'd like to form more than nine bubbles, it suggests that the SAS-assumed flow regime of slug flow should possibly be modeled instead by an annular flow regime. However, such problems only exist in CRBRP around voiding initiation in the hottest channels while the power is low. It is not believed that the exact timing of the first channels to void should significantly affect the accident consequences. Hence, the above pres-cription appears to be adequate for the present analysis.

pointer 34 refers to the structure-to-cladding surface area ratio y2 ~

It is considered, as in the FTR LOF analysis (Ref. 43) that the temperature of the can wall is more important than the wire wrap temperatures. Hence, g

the same algorithm as used in Appendix A of Ref.43 was used to evaluate y 2'

The only difference is that the subassembly lattice triangular pitch is 4.76 in. in CRBRP versus 4.715 in. in the FTR. Hence, the heat capacity of sodium between assembly duct walls is higher than in the FTR case.

Pointer 35 refers to the orifice parameters for the highest-power channel. Selecting proper orifice parameters is only one part of the larger task of modeling pressure drops properly in SAS3A. Pressure drops, neglecting the gravity heads, for the highest flow orifice zone are shown in Table 4-2 broken down into four regions. These pressure drops were transcribed to the SAS coolant mesh shown in Figure 4-4 according to the following prescription. The 28.9 psi in Region 1 was absorbed by the con-traction coefficient of 1.0 and an orifice coefficient of ten. Rigorously, the inlet pipe to plenum losses and the core support losses belong in the primary loop. However, the SAS voiding model is known to reverse flow too quickly after voiding initiation, and predict too great a chugging 4-10

amplitude in the later stages of voiding. The increase ii the orifice coefficient provides a partial compensation for these difficulties. The 23.5 psi pressure drop of Region 2 was assigned to the SAS lower reflector Since the friction coefficient, f, is (between coolant nodes 1 and 2).

detennined by the pin bundle, the free parameter here is the hydraulic diameter, assuming a formula of the type Ap = fD h , Cu resulting calculation gives D = 0.265 cm for the lower reflector. The 44.2 psi pressure drop in Region 3 corresponds to the pin bundle (the space bei. een coolant nodes 2 and 27). The hydraulic diameter is O termined from y2 and the volume fraction of the coolant. Its value is 0.389 cm. Subtracting '

out the acceleration pressure drop due to the velocity increase resulting from the density decrease due to heating, the friction coefficient is determined as 0.382. Region 4 was assigned to the upper SAS reflector (coolant nodes 28 to 30). The 3 psi bundle exit loss was used to obtain a hydraulic diameter of 0.5929 cm, assuming a friction factor, f, of 0.382.

The remaining 4.8 psi was used to determine an expansicn coefficient of 1.749, which the SAS code treats as a loss tenn. The final information needed to complete the pressure drop modeling is the nominal pump head of 162.6 psi . Again excluding the gravity head, this gives a primary loop pressure drop of 58.2 psi.

Pointer 36 refers to the pump head decay constants. The calculational benefits of a smooth representation of the inlet plenum pressure versus time made it desirable to find an analytical form for the pressure decay rather than use the other SAS3A option of a linear interpolation between input data points. The available SAS equation is 2

Aphead = ^P o **P (~U -a l t-at2 3 where a), a2 and are input constants. It was not found possible to 3

exactly fit the desired flow curve over the entire range of interest, approximately 0-20 seconds. If the decay is initially simulated correctly, the flow curve tends to drop too low. If the value of 20 secs is reasonable, the curve initially drops too slowly. Finally, it was decided to just take the flow curve, which actually can be fit by an equation of the above 4-11

form and take Aphead = hYo (f ow) where x is determined by the best fit to the intended flow. The resulting best value of x seems to be 2.0. This g fit is shown in Figure 4-5. All points fit within 5% and the fit is particu-larly good around 10-12 seconds where voiding is starting in the LOF accidents.

Pointer 37 refers to some crucial coolant parameters in the voiding model. These are the minimum initial liquid slug length and the fraction of the two-phase. friction factor used to simulate the frictional interaction between sodium vapor and sodium film on cladding and structure. The value of 2 cm for the minimum initial liquid slug length is standard for starting LOF problems. This parameter is then further adjusted downward as voiding progresses. In this study a value of 10 cm was used for the minimum initial slug length in TOP cases. This was done to delay the necessity of combining pure sodium vapor bubbles with the FCI zone (which SAS3A cannot do at present). A two-phase friction factor multiplier is reasonable if sodium film motion is to be calculated, since this prescription simulates flooding. If the sodium film motion calculation is not wanted, a better value for this input factor is zero. This will avoid concentration of the vapor pressure drop in regions of unrealistically thick sodium films pro-duced by condensation.

Pointer 38 refers to slumping initiation criterion. The slumping cri-terion for irradiated fuel is set at 0.1 C below the melting point of un-restructured fuel. A melt fraction of 0.5 has beer, chosen as the criterion for fresh fuel .

Pointer 39 refers to fission gas release assumptions relative to gas release following application of the modified Gruber model described in Ref. 9. The same numbers were used for all the base cases. The assumptions made in choosing these were that (a) five percent of all released gas is assumed to go to the fission gas plenum if the gas is released before pin failure, and (b) that five percent of the steady-state fission gas is never released.

Pointer 40 refers to the 'uel pellet radius. This study uses pellet diameters and fuel densities that are slightly different from the current design but with the same fuel mass. Because SSFUEL does not model pellet cracking, the hot steady-state fuel-clad gap is too large and the temperature drop across it too severe. Increasing the cold gap to the new design radius g

would only increase the error believed to exist in the current computations.

4-12

Pointer 41 gives the mesh spacing in the core and blanket. Fig. 4-6 summarizes these numbers. The equal nodal lengths lead to greater ease in cladding relocation and more accurate coolant heat transfer calculations.

Pointer 42 refers to the inlet temperature of 388 C (730 F). The voiding coherence is probably sensitive to this number; thErefore, in marginal cases such as the LOF E0EC with cladding and limited fuel motion, it may determine whether or not a FCI occurs as a result of a LOF sequence.

Pointer 43 refers to the mass flowrate by channel which also signifi-cantly influences assembly voiding incoherence.

Pointer 44 gives the traction of total powr

• and flow represented explicitly by the SAS3A channels. The corresponding number for the E0EC case 0.889. The flow fraction is a very important primary loop parameter since it sets up the magnitude of the core bypass.

Pointer 45 refers to the primary loop. The most important quantities seem to be those setting the steady-state pressure drop in the primary loop (Pointer 35), the cover gas pressure indicating the overall system pressuri-zation, the primary loop pipe length and cross sectional area indicating the primary loop inertia, the total pump head (Pointer 35), the fraction of flow represented by the channels (Pointer 44), and the inlet plenum volume, which gives some idea of inlet plenum pressurization.

Pointer 46 refers to the nodal power shape. These values come from the FX-2 neutronics calculations to be discussed in Section 5. The powers as input here are actually nodal powers in watts at steady-state, provided they are multiplied by the fraction of core power represented explicitly by the channels.

Pointer 47 refers to delayed neutron data and the prompt neutron life-time.

Pointer 48 refers to the basic neutronics data for fuel worths, Doppler coefficients, and voiding reactivity. These come from FX-2 calculations to be discussed in the next section.

Pointer 49 refers to the effective axial expansion coefficient. The SAS axial expansion algorithm (density feedback) is based on the assumption of a negligible reactivity contribution from any fuel which has expanded 4-13

into the axial blanket. The resulting reactivity feedback is significantly too negative. The current study corrected for this error by running a h combination LOF-TOP case well into voiding, weighting the axial expansion in each channel by the fuel worth of the channel, and using this weighted core expansion to normalize the density feedback to the design value cf

-0.12c/ mil. The resulting input value to model full expansion reacitivity feedback was 0.30 as shown in Table 4-1. In pure transient overpower cases, axial expansion may not be as effective because of fuel contact with cladding.

Hence, the effective expansion feedback was reduced by half to 0.15. Further, it should be noted that no axial expansion feedback is calculated after either clad melting or SLUMPY initiation in a given channel. This significantly reduces the role of axial expansion in the burst phase of a transient as can be seen by examination of the reactivity component plots in Section 7.

Pointer 50 refers to the cladding strength tables. There are five different " fuel types". The table values for fuel types 1 and 2 are the clad yield strengths from the Nuclear Systems Materials Handbook (Ref. 42) where the values have been extrapolated beyond the temperatures in the Hand-book (927 C) by a fit of the form g 12 10 a =

Y A[T + B]

where A and B are fitting constants, and T ( C) is the cladding temperature.

These tables are used for the yield point in the pressure-dependent gap conductance (Pointer 31). Fuel type 3 is based on burst strength valtes taken from the Handbook, where a relationship of the above form is again used for extrapolation beyond Handbook values. This table is used as the basis for failure of fresh fuel in TOP situations. Fuel type 4 is based on the ultimate tensile strength taken and extrapolated from the Handbook.

These values were not used in the pin failure criterien for the current study since they may be overly optimistic. Fuel type 5 is based on the transgranulhr to intergranular fracture mode transition for irradiated clad-ding from where curves for the shift in net hoop stress at failure for tempera-ture rises of 10 F/sec and 200 F/sec are presented (Ref.14). For a 10c/sec ramp in CRBRP the temperature near failure is rising at about 100 F/sec. The 9

4-14

difference in the given curves was logarithmically fit to arrive at the numbers given for fuel type 5. Fuel type 5 was then used in the burst failure criterion to predict pin failure for irradiated cladding (as input by Pointers 8 and 11). Figure 3-3 shows curves for all these tables including the Smith-Stevenson fit (Ref. 7). The fuel type number is indicated in parenthesis. Pin failure in slow transient overpower situations is quite sensitive to the slope of the clad strength as a fenction of temperature.

It is presently felt that the extrapolation to high temperatures made by the Smith-Stevenson curve is unrealistic.

Pointer 51 refers to the initial film thickness of 0.0146 cm. This corresponds to a void fraction of 0.85 (with the wetted perimeter of the wrapper wire treated as referenced in Pointer 34). An 0.85 void fraction is in the range suggested by Ref. 28.

Pointer 52 refers to the cracking parameter of 15 atm. Hence, the fuel is presumed to crack when the internal pin pressure is 15 atm above the gas plenum pressum. Cracking then affects the subsequent fuel pin dynamics as explained in Section 3 2.4.

Pointer 53 refers to the clad wastage allowance. These fractions indicate the degree to which the pin failure criterion must be satisfied before pin failure is actually predicted. They are based on assuming a 2 mil wastage at a burnup of 45,000 MWD /T and assuming that the watage is directly proportional to the square root of the burnup. Since the clad burst failure strengths in fuel type 5 (Pointer 50) are actually taken from what is presumed to be cladding irradiated with oxide fuel inside the clad (Ref.14), application of these wastage factors may not be rigorously correct. However, these pins were irradiated in EBR-II and would have mostly U-235 fissions for heating. The fuel in CRBRP is heated mostly by Pu-239 fissions. When the fissile isotope is switched from uranium to plutonium, there occurs a significant drop in the zirconium fission products, with a corresponding increase in the noble metal fission products, i.e., rhodium and paliadium. As a result, when Pu-239 is the fissioning fuel, significant increases in the quantity of available oxygen are to be expected with increasing burnup (Ref. 44). Since cladding 4-15

functions as an oxygen sink by uniform oxidation or by intergranular pene-tration clad wastage corrections may be expected to be higher in CRBRP than in EBR-II. Also, preliminary PLUTO analyses of TREAT experiments indicate that pin failure caused by a burst criterion based on uniform high internal pin pressure tends to produce results that involve too much molten fuel and fission gas at pin failure. This is probably a fault of the simplicity of the burst criterion, which has also been pointed out by Majumdar (Ref. 49) and it suggests that use of wastage correction is a step in the right direction.

Pointer 54 refers to the rip length. The TOP cases used a short rip length of 5 cm. This seems consistent with the small failures prodeced by such transient overpower failure threshold tests as H5 (Ref. 46). In LOF cases that fail with sodium in the channel, cladding temperatures are far more uniform. Hence, longer rips ar7 to be expected. Nominally, 15 cm was input. However, this was adjusted to pin failure if another value seemed appropriate. For a discussion of such an adjustment, see the analysis of B0EC-LOF with cladding and limited fuel motion in Section 7.2.

Pointer 55 refers to SAS/FCI default parameters. The algorithms for h computing the appropriate values for these parameters are discussed in SAS/FCI summary in Section 3.2.4.

Pointer 56 refers to the SAS/FCI heat transfer assumptions between fuel and sodium. The Cho-Wright model was selected with the standard 10 msec fragmentation and mixing time used by the authors (Ref.18). The fuel particle size was selected as 250 microns in radius based on the Cronenberg analysis of the H2 experiment (Ref.16). The resulting heat transfer coefficient was multiplied by 1 a where a is the sodium void fraction.

This is to account for the reduction in heat transfer as sodium vapor is produced. When these assumptions are coupled with the presence of fission gas from the SAS/FCI reservoir and the internal pin cavity, the FCI should tend in the direction of the mild interactions predicted by Fauske (Ref.17).

Pointer 57 refers to the theoretical density fractions for unre-structured, equiaxed, and columnar grain growth fuel. The unrestructured density was chosen to be consistent with fuel pellet radius (Pointer 40).

The equiaxed and columnar densities were based both on the uniestructured h 4-16

fuel density and on a LIFE-II study on fuel of FTR fabricated density, i.e. , 90.4% of theoretical .

Pointer 58 refers to the 10 sec ejection cutoff time. This number prohibits the lower interface of the FCI zone from crossing that section of the pin associated with the rip length before 10 sec. If this time was short, the lower interface would eventually sweep all the fuel up and out of the interaction zone for all truly mild FCIs, i.e., ones with little or no flow reversal. Due to the uncertainty in plugging phenomena, the total sweepout result was deemed to be overly optimistic.

Pointer 59 refers to the pin fractions and the time delays used for the various pin failure groups. The groups are subdivided fairly equally, but the time delays are purposely short due to the problems mentioned in the Pointer 7 discussion. However, it can be noted that 2 and 4 msec delay times may be quite appropriate to a prompt critical situation.

Pointer 60 gives the burnup in full power reactor days. These were obtained by averaging over the appropriate assemblies in Figs. 4-2 and 4-3.

Pointer 61 refers to the fast flux (greater than 0.1 MeV) to power ratio.

Pointer 62 refers to the fact that this study assumed a pure Dutt correlation for retained fission gas (Ref. 5).

Pointer 63 refers to fuel swelling as a function of bur nup. As in the fuel density relationships (Pointer 57) these results were based on a LIFE-II study of FTR fuel.

Pointer 64 refers to the restructuring isothenns. Since there is no input (except at LOC = 880 in the fixed point locations), the restructuring isotherms relationships are:

T(columnar)= 41532/(16.08 & In(B))( C),

T(equiaxed) = 44320/(22.04 + in(B))("C),

B is the local burnup in (!GId/T).

4-17

Pointer 65 describes further gas release input. For fresh fuel, (the odd numbered channels) these are the standard Smith-Stevenson numbers g (Ref. 7). For irradiated fuel, the modified Gruber model is appropriate (Ref. 9). These values force retention of 0.25 of the released fission gas until melting which seems to allow reasonable fuel pin failure condi-tions for TOP accidents, but due to the instantaneous nature of fission gas release, they may be overly pessimistic in pin pressurization following a LOF-initiated FCI.

Pointer 66 refers to the constants in the function fonns assumed for fuel density and fuel thermal conductivity. The fuel density relation-ship comes from a 1972 linear fit to nonlinear data by G. Horne (HEDL).

Compared to recent HEDL recommendations, the predicted expansion for solid fuel seems to be high, although the magnitude of density temperature derivative is under-estimated above a temperature of s2000 K. The relation-ship used is ps = 11.03 f/[1 + 2.772 x 10 (T - T ) + 6.864 x 10-9 (T - T ) ], and r r om = 8.774/[1 + 9.3 x 10-5 (T - Tm )]

where pg = solid fuel density, (gm/cm3 ),

p = m lten fuel density, (gm/cm 3) m r

= reference temperature (27 C),

T = fuel temperature ( C),

T = fuel melting temperature m

(1 - f) = fuel porosity (depends on restructuring).

The fuel thermal conductivity is based on HEDL recommendations for the LIFE code. The relationships used are I

k= (2.1 - f)f - 1.0 -3 + 5.83 x 10 -13T k3 f < 0.95 0.288 + 2.52 x 10 T k 4-18

I -13 k= 3. 0 f - 1. 0 + 2.91 x 10 T f > 0.95

-2 k 5.75 + 5.03 x 10 T k where k = thermal conductivity, i'y = T + 273.16 for T < Tm ,

T k

=T m + 273.16 for T 3 i m Since the porosity is a function of burnup via the swelling parameters (Pointer 63), these thennal conductivities are quite close to the corre-lation used in the design analyses. Due to limited sensitivity of the accident to the fuel thermal conductivity (gap conductance is far more uncertain), the above relationships are believed adequate.

Pointer 67 refers to the stainless steel worths. The details in obtaining these numbers are describet in the next section.

4-19

TABLE 4-1 h

SAS3A INPUT FOR BOEC LOF BASE CASE POINTER CRP9 P BEC flCD A ANL PHVS!ct DATA RA52 CASE 4 ARCH 1975 T d!$ 15 A 1054 0F F t.0 W 09 TPAR$!1NT UNDrRC00 LING ACCIOtWT -

1 In 11 Jo in u 1 10 217 0 6 14 1 11 la 6 19 15 16 1R Su 19 1A A inn 60

't 1.

• 1 1 e o n 1 6 10 a1 29 2 11 14 n 20 20 in 10 15 2 0 0 0 1 1 1 u1 ft 0 1 5 1 1 1 1 1 1 1

%1 en 1 1 1 1 1 1 1 1 61 19 1 1 1 0 0 0 0 0 0 0 1 1 71 10 1 1 1 1 1 1 1 1 At le 7 7 7  ? 2 2 2 2 2 2 1

91 10 1 1 1 1 1 1 1 1 1 e g g g g g g g 101 10  %  %

10 0 0 75 0 0 0 n u 111 i 1 1 n 0 0 0 0 0 9 tal 13 0 0  %

151 11 ' n n 0 L 0 0 0 1 0 161 in

• O r 0 0 0 6 0 o 1 n 1 7 n 1 n  %

171 In 0 0 0 1 6 0 0 0 0 0 11 7 A 1A1 10 0 141 10 1 0 f 0 0 n 0 0 o 4 A 7

AD1 In 1 1 1 } 1 1 1 1 1 1

'11 10 -4 -4 -u -u -u -u -u -u -u -u 9 0 0 0 15 1 9 611 10 1 0 0 1 1 661 10 1 1 1 1 1 1 1 1 1 1 10 1

871 11 1 1 1 1 1 1 ) 1 1

',  ; 5 5 5  %

721 11 5 's  % 5

) 1  % 11 701 11 1  % 1  % 1 5  %

7 f.1 19 6 14 0 9 'l 0 6 0 0 0 171 1 '1 17 19 1/ 0 0 0 S 0 0 A Til l in 12 6 0 0 0 0 n 12 16 12 e 19 u7 1 0 a 0 711 in 1 1 e 411 In 7 's l' 73 0 0 10 24 0 ?u 17 ue 0 0 1 n i P11 19 in 14 le is 11 0 2 2 2 2 2 12 A21 1 7 2 2 All 11 7 7 7 0 m n 0 0 0 0 11 au) 7 12 0 1 1 0 1 n 1 0 to in A51 11 1 0 1 0 1 500 0 1 1 1 pe 1 11 1 1 1 1 1 1 1 n 7 1 0 0 0 0 0 u 1 15 871 in 1 0 0

-1 r4D 1 *s - 1. 00 '; n16 - 01 1.00r0np no 1.msonet 00 %.nn000r-02 A.tuonnr 65 if

.  % i.1 1.nonanr-01 0.0 1. 00 0 0 0 r- 01 0.e 11  % 1.1S n n't r . 91 0.0 1.01000P-01 0.0 1.00000r-01 16 5 n.0 1. 0 0 6 0 n l 00 0.0 1.0n001r On n n o

• 1.nnonqr en n.q 1.nqnnor 00 0.e 1.n00nnt On 17 71 3s  % 1.10609r Of 1.aun10' 00 p.o 5.00000E 00 1.nnn00r-07 18 7,110 0 e r - n 1 n.r 9.0 0 0 F0 r-01 a.n 19 u1  % 0.0 u f. G 9.006019-11 6." 4.00000r-01 n.1 P.0annne-qi 51 1 0.0 2. n e P 9 01 - 01 0.0 2.109aor-61 0.n 7"

%* ". 7.00100'-n1 0."  ?.01000E-01 1.0 7.00n00r-01 61 5 1.%0'in' 01 1.50enor 01 1.56qnce 01 1.560900 01 3.%0000r 01 21 60  % 1.50010r of 1.%nenor 01 1.50000r 01 1.50000F 01 3.%000ng 01

'I '. 1.1 g n n o t - 11 6.1 u 0 0 0 r- 01 1.1 n n 00 r. 01 0.n 5,n000nr 0A 22 7A  % 1. ne 't 01 E on 1.e1010E 0H 1.01000m 08 1.60600t 09 1.n.9nor 08 21 HI '. 1.Onnnnt da 1.09C00E 0A 1.0060nr OR 1.00000r 0A 0.n Int  ; 6.0 0.0 0.0 0.0 1. 0 n000r- 99 16% 5 1.n14n0r 69 1.an000E-rm 1.00000r-09 1.n 0 0 n o r-0 9 1.on00ne-n: 7e 111  % 1.0000nt nq 1.1in00E-01 1.nnnnnt-09 1.09100'.-09 0.0 11*  % 4.0 7. conner-n2 1.507000-01 0.0 n.o 25 121 5 7. 96 7 01r 01 1.nonqnt-07 1.6 5000r 0 2 1.30000F 07 1.6%000E 07 26 126 5 1.10 0 n 0 E 02 1. f

• Cenr 0 2 1.110 002 02 1.65000r 02 1.100n0r 07 til 5 1.650165 n? 1.10000F 02 0.0 0.0 0.0 4-20

TABLE 4-1 (Continued)

POINTER 27 141 5 0.0 0.n 1.00000t 05 5.00000t-01 1.Ononnr os 146  % %.00000t-01 1.00000r 05 5.0000nt-n1 1.00000t 05 5.n00002-01 1%1 5 1.00011E 05 5.00000r-01 2. 7 249 2t-01 2.72s92t-01 2.724977-01 l  % '. 7 r49 m o s 1. 7 J 0 91'- 01 2. 7 2 4 9 2 t-01 2.72u477-01 2.724977-61 thi 5 2.724?lt-01 2.72412r-01 1.00000t n0 1.00000E 00 1.00nnot no 100  % 1.00000t on 1.0000nr On 1.0000nt 01 1.00100r 00 1.00000F 00 171 S 1.90000E 01 1.00n00r 60 2.91000r-02 1.00000t 06 1.00noor 06 17A 5 1. 00110 e O A 1.00000t CA 1.06000r 06 1.00000t 06 1.0an00F 06 28 tot 5 1.000002 0% 1.00000F 06 3.000002 06 5.02000t-01 1.10000r 07 21 18A 5 n.1Aq00t-01 2. 9 ) C o n r- 01 7.000nor 00-1.00000E 02-l.0000Dr 02 191 5-1.01000r. n ?- 1,6000n r 0 2- l.110nn t 0 2- 1.0 00 0 0 t 0 2-0.0 1. 00000r 02 in6  %-1.00090t 0 7- 1. On 000r 0 2- 1.00C 00 t 02 n.n 0.0 208 5 1.7A700r il 2.Annoor 02 2.70000r 02 0.0 1.90000t-01 6.R200n r 11 216 5 0.0 0.0 0.0 221 5 A.12990r 11 f . 9 7 010 r 11 6.a2000r 11 6.820nnt 11 6.m200et 11 225 5 A.82010E 11 A.P201Cr 11 6.R2000t 11 6.92100r 11 5.uAnnne 0% 16 211 5 5.4einot 0; ( 49010r 05 5.49000r 05 5.ua000r 05 5.44000t 05 216 5 %.uPo01' 05 5.cor00r 05 %.umonor 05 5.4R000r 05 7.9A7002 on 241 5 7.1n70St 01 8.72tuot-n1 4.u4600t-02 2.01000t-02 0.0 7.09100r-01 0.6 Ju6 '- 7. 04110 E- 01 0.n 0.0 11 256 5 0.1 n.e 1.900002-01 6.10000r-01 1.12n00r-nt 2A1  % 1. 7 0 5 01 t - 11 1. 7 0 % C O E - 01 1.71%00E-01 ).70500r-01 1.7n%607-01 264 l.70501E-11 1.7050nt-01 1. 715 0 0 E -01 J . 7 0 5 n o r- 91 3.70%nor-01 271  % 7.201012-05 2.AA000r-Ou 2.5700ft-n1 2.71600r-04 2.58000E-91 276  % 1.1610 0 E - S u 7.56000r-03 J.86000E-04 2.17000r-01 1.sonner nu 2A1 5 1.67131r 10 1.1190nt 01 1.69000t no 1.1010nr 00 1.Aonnor on 206 5 1.15'nSt n^ 1.f9n16t on 1.11000t 00 1. 6 40 0 0 t 00 1.19600r no

1. I n nn e r- 19 241 5 1.16190'-In 1.10 0 n0 f - 10 1.110 n e r. - 10 1.10 0 0 0 r- 10 206 5 1.10n11r-11 1.10 0 0 0 r- 10 1.110002-10 1.1010 0 r- 10 1.6 1.Innn02-10

% 1.1m ir n r .1; n.

• n 0n07- n 1 r,n 0.n 101 111 4 1.171117 Ol 1.42700t-05 u.70500r 03 2. 5 2 9 h o r.- 01 1.JA%"PP-01 12 1H 5 1. 0010 ) r - 0 2 1.uur00r-0) r..Aqq00E-01 u.44000t 01 1.212nor 02 11 141 i 6. f.f ) n n r - 91 1.00nnor-n1 2.00n102-01 1.non017 01 9.066ner 61 14 lu6 5 1.40anir-rq 4.?n6mCT 01 4.70%0nr 00 1.19000r-01 0.q 151 5 f 00ront 91 1.0nrmnr na 1.01orgt q0 1,00nonr 00 1.nnennr on 156 5 1.nn1F1r r0 1.rnnarr ^0 1.n10r,0r 60 1.00000t 00 1.n0nnot 00 161

' 1.orq10t ai 1.09001r an 1.onnenr 00 1.000007 30 1.000rer on 16, 5 1.001onr er 1.00000r On 1.n9000t 09 1.0n000r 0.1 no 1.190nnt 1.Snonor 01 01 171 i J.6nq11F qi n.e r.0 15 176  % 1.00111' 01 1.010010 01 1.aq00nt 01 1.106012 01 1.60F09r 11 lal 1,rolong of 1, nnnno r 01 1,qqqn0E 01 1.nqncor 01 1.onnnor 01 146 5 1,rniont of 1.1010er 01 1.10100F 01 1.01010f 01 1.orna0t 01 191 5 1.09101r 11 1.6n'00t S1 1.00n00r n1 1.11n00r 01 n.n 16 196 5 1. 010 n 0 - r 2 5. 01 r o a r. 0 y 5,nqq00t 01 1,5qqnog.01 7.anenor-01 401 5 s.03n1)! 01 5.00nanF 0} % 010007 n2 1.00900t 01 2.n"Sn02 62 496  % 5.00010! 1) 5.00r007 na 0.0 1.011312-01 1.n*01er-35 a11 5 1.0011nr-05 1.rno0r,r of 1. 0 6 q r 0 r 06 1.9110nt 06 1.6000er e6 414 5 1.00000' fA 1. r n o on' n6 1. 91 F 0 0 r. 06 1.On00nr 06 1.n0010e nA h21 5 1.000011 06 1.00nint GA l.9 )or nf -0 2 5.Onnnor n 1 1.nnn0nr c.o 01 424 5 - 1. 2 010 0 E - C l 1. u n a d e ? - O u 2. 7' 700r n1 0.1 1. t u n n ny- n2 0.r 0.0 0.1 (26  % 0.0 17 n11 '

u.da*01t-01 8.r secr1 01 s.010ncr n1 1.110iat On u.irnnnr n1 o1.  ; ),bsprr1 u.61119F 31 2.76690r 01 u.1000qr 01 2.16A90r 61 19 Au1 '. i.r101rr 01 7. ' 6 ' i n' ol u.e1000t 01 2.16610E 0) %.00n*0r-"1 ob% i 1.*S*1)! 04 ' . On000 t-r 1 1.nq000t 00 %.00100'-01 1.conent 00

1. 51 5 % .1* S 'i r- 11 1.nnronF 00 %.060C0'-01 1.09000r 60 0."

696  ; 1.0^11]r ^1 n.* e.1 0.0 f.0 721 6 0.0 0.r r.0 0.0 1.on00nr 01

2. % ' 191 r )1 s.16nner.12 1.nu. ort 61 2.01006t-01 5.010007-12 1)%

111 4 s.nconar e1 ? . ' o r a r r - 12 1.qn000r-12 0.0 0.1 2u01 5 !.100000 01 1.qqnr97 00 1.10100t 90 1.00000r On 1 On0qn' 00 240A i 1.no^ ele n1 1.6000nr 00 1.0'0007 10 1.10100T 00 1.nnon0r 00 4-21

TABLE 4-1 (Continued) h P0! TITER 2511 i %.27000E-01 1.66010E 00 1.80000R-04 0.0 0.9 2631 5 5.00090 2-02 5.00000t-0 2 5. 0 00005-0 2 5. 00000t-0 2 5.00000r-n? 19 2 A 16  % %.n0000t-02 L.0 0000*-02 5.000002 -02 5.0n000 t-o? 5.nnnnnr-n; 2 nut  % %;'1111t-n1 5.90010r n2 5.000003-02 5.n0000t-02 '.n00eer-n2 26uA  % % 00900t-02 5.000002-02 5.0 00008-02 S.00 000 2-0 2 %.00 0n0R-0 7 2946 5 0.0 n.0 0.0 0.0 2. e 7 0 0 n t- 01 to 2951 5 7.u70018-01 2.47600t-01 2.4700nt-01 2.47000t-01 2.41000t-01 2956 5 2.47000R-01 2.470002-01 2.47000E-01 2.e7000t-01 0.0 1106 5 0.0 0.n 0.0 0.0 2.5uonor-01 1151 5 2.sul06P-01 2. 5 4 000 r-01 7.5u0not-01 2.50000E-01 2.%ucone-01 1156  % 2. %# 101R- 01 2. S u c00E- 01 2.506n02-01 2.54000t-Di 0.0 1346  % 0.0 0.0 0.0 0.0 7. 4 210 0 F - 01 1151  % 2.42101r-01 2. 0 210 0 r- 01 7.92100r-01 2.92100r-01 2.921nnt-01 1156 5 2.92100t-01 2.92100E-n1 2.92in02-01 2.97100E-01 0.0 3546  % 0.0 0.0 0.0 0.0 2.121onF-01

}551 5 0.n 1.21920t n2 1.952602 01 9.00000P 00 7.01400R 01 #1 1%56  % 7.n140nt C0 7.01u00F 00 1.01400t 00 7. 014 0n t 90 7.01tnor 00 1561 5 1.034102 60 7.03400r 00 7.n14D02 00 7.01400E 00 7.n1400' 00 1%66  % 1.63401r 00 7.01400t 00 7.n140nt 00 7.0140nr 00 7.0140nt 00 1571 5 1.01410E on 1.045002 et 1.95260F 11 9.00000r nn 7.nlu00r on 15'A 5 7.014662 00 7.01400r 00 7.n1400t 00 7.91400r 01 1.0140'r 60 1981  % 7.01unor 01 7. 0140 0 r 0 0 7. n 1u 00 t no 7.014 0n t no 7.n14nr' 00 1%A6 5 7.01000t on 7.01010F no 7.n1400t 00 7.0140nr 00 7.n140nr nn 1591  % 7.0luont on 1.44%Por el 1.95260F 01 9.00C 70 r 60 7.014n0R on 1516  % 7.01100R C6 7.01400t 00 7.nlunor no 7.01100r OS 7.01u002 nn 16ni  % 7.0110Sr 00 1.01410r 01 7. i lu n 0 F nn 7.01000E 00 7.034nnt on 1606  % 7.niuC9r Ca 7.n1400' no 7.014002 n n 7. 014 0 0 E 00 7.01u0nr ni 1611 5 7.01400r 01 1.uu500r n1 1.9%2Apr of 1.00000R 00 1.0340nr no 1616  % 7.63400r 61 7.01u90r no 7.nlu0er 00 7.niment 00 7.n1460E 00 1621  % 7.01401E 00 7.0140n t n0 7. 014 0 e r 01 7.014nor 00 7.01onar no J625 5 7.01400r no 7.01400r 06 7.n19 net 01 7.01100r 01 7.01 ann' nn 1511 5 7.014 nit in 1.44% Ant 01 1.952'Or 01 1.n9000r 00 7.014not 00 3616  % 7.0140!r 09 7.010007 On 7.01400* On 7.01499E 00 7.014n0r nn 1641  % 7.m3409E n1 7.01unot 90 7. 01 u 0 0 5 00 7. 010 0 0 t 60 7.ntu0er 00 1646  % 7. 914 0 c e ril 7.0141nr 00 7.01un0F 01 7.01400* 10 7.n100nr on 1651  % 7.0 ? 400 R qi 1.ku% Air 01 1.1%26nr 11 1.00000t n0 7.01406E na IF 56  % 7.011not on 7.01000r 00 7.nluc0E 00 7.01400r 00 7.ntenor nn 1661  % 7.13un1g on 7.n3000r 00 7.01000t 00 7.01403t On 7.n14nce no 1666 5 1.019nor 00 7.0140nr nq 7.01u nnt on 7.0140CF 00 7.0140nr no 1671  % 7.93411E 0' l.11590r of 1.95260E 01 9.00000t n0 7."140nr nn ih76  % 7.11401E 01 7.014nor on 7.ntuent 00 7.014 no r On 7.n turn t no 1t81  % 7.114 01 P, n1 7.01u00E 00 7. 01400t 00 7.0140nr 09 7.nleonr 00 16A%  % 7.11000r 01 7.01u00t 00 7.11400t 00 7.01401t 00 7.niunnr nn 1691  % ?.Jiandt nn 1.445ROF 61 1.957A0r 01 1.00nont 00 7.nis00* nn 1696  % 7.0}400R 01 7. 01 u 0 0' 00 7.01u005 f. ) 7.01000F 00 7.e lu0n r no 1701  % 7.11ue0g on 7.03400r 00 7.01400t 00 7.0)unct 00 7.61onnr no 1706 5 7.114nnt en 7.01u00r On 7.q1un0* On 7.0thn0F 10 7.0140nr no 1711  % 7.13441t 06 1.445Anr 01 1.95260' 01 9.000n9E 00 7.014nhr nn 1714  % 7.11000g 01 1.01400g 60 7.010n02 01 7.01u00g nn 7.01onnr no 1171 5 7.nluqq' 00 7.0)u00r 00 7.01400t 00 7.n330nr 00 1.01a00r no 1726  % 7.014n1' On 7.n140nr no 7.014002 00 7.91acqr 00 7.ola no r On 1711  % 7.91416E 0' 1.ug53nt nt 1. 9 % 2 ( n r 01 9.n00002 00 7.014ene nn 1716  % 7.1)uSOE ni 7.01400r 09 7.01unce 00 7.n140nr 00 7.niuno r 60 1741  % ?.11461E no 7.014nor 00 7. n 11 C n R 00 7.01400t 00 7.niennr an 1746  % 1.4)uqqr en 7.n14n0F 01 7.01un0E 00 7.n1401E Sn 7.ntuant 60 17%9  % 7.11mont no 1.4uG9er 01 1.77500'-0t n.n 0.0 17%6  % 61 . 0 a. J '200r- n1 0.0 7.7nqnot o f 1.9777mr 17 a2 1751  % 1,1rimo' 09 5.%7r;rt 02 5.5FAsat 02 5.576;nr 02 6.laqant 07 176%  % %.1812 9 r u . 6 4 f 6 0r 0 2 5.178not 02 %.1A996E 02 u .10 %10 ' 0 7 41 3771  % u,1851or 1? n.n 0.0 0.0 0.0 177A *. 4.1h000E 61 a . 0 0 0 00 r - 01 0.1 0.0 9.876nnr-n1 en 1781  % /.646519-01 7. 6 4 8.% e r - 01 2.AuA50t-01 2.64650E-91 2. 6 4 6% 0F- 01 4-22

TABLE 4-1 (Continued)

POINTER 1786 5 2. 6 4 6 50 E- 01 2.6465CE-01 2.64650E-01 2.64650E-01 2.64650t-01 1791 5 5.929002-01 5.92900r-01 5.929002-01 5.929002-01 5.929002-01 3796 5 5.929002-01 5.92100r 01 5.929002-01 5.92900E-01 5.1290nt-01 1806 5 1. 81910 2 2. 5 0 0 0 0 t- 01 0.0 0.0 0.0 3811 5-2.19591E 02 4.74980t 0 2 5.5 2171t 02 9.706612 02 4.540ner of 45 1A16 i 2.73000E C5 1.000002-01 0.0 2.47000t-01 1.000002 04 3821 5 5.09600t 01 1.519242 04 1.319508 04 4.2u600t 01 1.00000r 00 3826 5 1.000102 04 1.12300t 08 0.0 0.0 0.0 1851 5 8.516272 01 8.e8744r 01 1.22005E 02 1.e4312E 03 2.1.1416r 01 46 3856 5 2.174272 01 2.529572 01 2.61449F 03 2.619 24 E 0 3 2.60 313 R 01 3A61 5 2.50562t 01 2. 3505 2r 01 2.119 20! 03 1.88131E 03 1.55316E 01 1R66 5 1.21259E 01 1.5172EE 02 4. 72 4 94 r 01 2.411142 01 2.192012 61 3871 5 1.186624 02 2. 61917 E 0 2 2. A 2 7 81 t 0 2 1. 5 4110 E 01 1.40922r 01 1976 5 2. 0 4 512 t 01 2. 22 04 2r 01 2.12 9 762 01 2.16R77E 0) 2.141692 01 38A1 5 2.25071t 01 2.10151r 01 1.8954ft 03 1.6 5n 14 e 01 1.17480r n1 3RP6 5 1.00Rl8r 01 2.17101E 02 1.2273RR 02 7.55142r 01 7.814192 01

i41 5 9.05519P 01 1.100132 01 1.18791t 02 1.75119E 03 2.01199E 03 in96 5 2.28219e 01 2.4766er 01 2.602092 01 2.652712 01 2.62A04E 01 1901 5 2.53111e 01 2. 3 7129 r, 01 2.1584ut 03 1.89775E 03 1.56 346r of 1*06 5 1.20223E C1 1.5pr97r 02 4.65428r 01 2.16093F 01 2.19651r 01 3911 5 1.674uir 07 2.74911r 02 7.912295 02 1.41717F 03 1.65547F 01 in16 5 1.467542 01 2.02115r 01 2.114695 01 2.14155t 01 2.11450r 01 1121 5 2.021772 01 1. b 8 0 2 ] E 01 1.69419e 01 1. 4 6 3 4 7 E 01 1.21410E 01 1926 5 9.43057E C2 2.01972r 02 1.0miu9! 02 6.57278E 01 6.67010P 01 1911 5 1.52210E 01 7.R194ur 01 1.07121P 12 1.50578E 01 1.e47077 01 1936 5 2.064119 01 2.7214PF 01 2.1.1A50r 01 2.11112r 01 2.21112r 01 1941 5 2.19040E 01 2. 019 2 H F 01 1.419a7E q) 1.60549E 01 1.10 716 F of 1146 5 1.9A115P C2 1. 5 f P 1E P 02 1.4497CE 01 2.358112 01 1.41452r 01 1951 5 2.56577F 02 2.02045r 02 2.20073r 02 1.2A617e 01 1.49751r 01 1956 A 1. 5 6 19 5 P 01 1.74941r 01 1.74161t 01 1.79n17E 01 1.714552 01 3961 5 1. 611 hi t 01 1. 4 A v 2 4 r 61

• 11757P 01 1.11159E 01 9.112 e 1 r 02 1966 5 7. 2 011 e r 02 1.11157F 02 7.2 02 9 4M 01 4. 4 0 414 E 01 5.04171r 01 1371 5 5.1A156r 01 6.d RF 7J r 01 9.741942 01 1. 6 6171 R 0) 1.94111F 01 1976 6 2.1746At 01 7.1171?r 0) 2.471292 01 2.41179 r 01 2.16 7 7 2 P 01 19A1 5 2.221142 01 1.97k94F Ol 1.716772 0) 1. 4 6 8 9 5 E 11 1.17791r 01 ISA6 5 a.414125 02 1.25744r 02 1.099712 of 1.52A11t il 1.156922 01 1991 5 1.50146' 02 1. 2 4 517 r 0 2 1.51116e 02 1.42489r 01 1.61567F 01 1994 5 1.12 917 F n1 2.01C4(7 01 2.19116P 01 2,14 77 u r 01 2.14560P 01 4001 5 7.011695 9s 1. 91^ lo r 0 3 1.59733E 01 1.35134r 0) t.11457F 01 4106 5 d 071912 02 1. ? 15 9 0 F 07 5.78617E 01 1.71112t 01 1.1aA44r 01 4011 5 4.49 25 it 01 5.21291r 01 7.874262 01 1.475642 0) l.7612AP 11 4015 5 2. ".10 7 4 t 01 2.19208F 01 2.10cesg 01 2,11127t 01 2,ygetje 01 4021 5 2.17112L P1 1.09164F 01 1.7711AE 01 1.52790E 01 1.2111AF 01 40)6 5 5 1551,2 07 1.2611ht of 2.4409At 01 1.41042E 01 1.1291AP of 4011 5 1.91Ae79 07 9.n1955r 01 1,n4140E 02 1. n 5 5 7 6 r 01 1.77191E 01 4016 5 t.uS752E c' 1. '9 ? a 5r 01 1. 6 7 N e t 01 1. 7 05 7 I r 01 1.61139r 01

'4041 5 1.59?lhe 01 1 u675Ir 01 1.10 e l f E 01 1.12711r 01 9.7654P' 07 4046 5 1.2%665R 12 9.10r41r 01 4.61n05F 01 2,9 010 6 r 01 1.14074r 01 4051 5 1. 2 7111 E Go 1.15740t 11 1.25130P 09 1.rae7aE 00 1.10402r no 4056 5 4. 6 5 0 21 P- 01 1.1011p r 0 0 1.01169E 00 1.07027r on 7.94574r-01 4061 5 0.0 4.75000r r4 5.611 rot-07 8.14500E-05 7. % 5 a 0 0 r- 04 40h6 5 4. '41130 P - O u 1. 7 9 7 00 r - 01 5.54100r-04 1.71200'-Ou 1.290?or-02 47 4071 5 1.121097-0) 1.13 H 10 E- 01 1.45000r-01 1.119 0 0 r 0 0 3.74100E 00 407f  ; 1. 4 4 514 r O' 1.Sa179r 00 5 . 5 n s f. 7 R 10 7.114 0 9 r S O 9.17mS5r on 46 4001 5 1.1065tr 01 1. 2 7 019 f 01 1.14472P 01 1. 414 6 5 r o f 1.41n14e 01 40R6 5 1,12n25r c1 1.In17sr 11 1.00t97R 01 P.1129?r on 6.171072 00 4091 5 4.u7991! 01 7.46915r 00 1.716R*P 00 P .11011r - 11 2.924752-01 u096 5 9.15 411 t- 01 2.41129F 00 1.10056E 00 5.11111E 00 6.Ka7atr 00 4101 5 4.037Ast 09 4.17750r on 1.95507R 00 1.029017 01 1.0104%E 01 4106 i 4.d5715E CA A.ula0!r 00 7.15819e 00 5.71372r 01 4.m 7 9au r OS 4111 5 1.12414r no 2.15/42r 00 1.14011P 00 5.56246E-01 1.69205r-91 4114 5 1.1%9612 00 2.390*C' 00 4.s74112 00 6.011677 00 7.7;a10r 00 4-23

TABLE 4-1 (Continued) h POINTER 4171  % 0.97wA4r n1 1. e a ". 41 r 01 1,1951ut 01 1.7Itoer 11 1. 7117 a r n 1 4126  % 1.117777 01 1. 619 29 r 01 M.671112 On 7.017172 01 %.17110' 00 4111 5 1,91496r 00 2.f6314r 00 1.192042 00 5.951452-01 1.9642RP-01 4136  % 7.72261E-n1 1. 91 A6 7 E 0 0 1.1102ft 00 4.102162 00 5.16166r 00 4tal 5 6.42412P C0 7.3267)r 00 7.14091r 09 8.197u2r 00 4.02nq1r 00 4146 5 7.49247R 00 6.65169r 00 %.61110 r 00 4.5491;r 00 1.519%)r 00 4151 i 2.8619%e 00 1. 6 9 F 0 4 t Oc a .1 8 5 9 9 7. - n 1 1.R9756E-01 1. ten 6tr-01 4156 5 1.529uhE-11 2. 4 719 4 r 00 1.19 0.11 E n0 5.2869)' 00 6.691922 61 4161 5 p.09%nnt On 9.71449r 00 1.01132E 01 1.0447]E 01 1.071702 01 4166 5 1.509$4R 00 H 44042r 00 7.1210$E 09 5.61711E on 4.10 97%E 00 0171 5 1. 0 u Si e r. 01 1.97e71r en 1.01977E 00 4.94171E-01 1.6111Ar-01 4176  % 6.25459r-01 1.64n1)r 06 2.62544E 00 3.6 7R44r on u.%e426r 00 41A1 5 %.4220Ar 00 6.2001;r 00 6.70112E 00 6.8560ag 00 6,64 0iir 00 4106  % 6.In?9%P 01 5.3405)r PO 4.41996E no 1.uA%12E OS 2.615a6r 01 4191 5 1.46941r n1 1.11914E 00 A.naly;g-ql 2,7 3 n2 5 r-n 1 9. n 715 4 r- 0 2 4196 5 8.1712 0 E - 01 2.214917 00 3.61190E in 5.151RRE 09 6.7%9A%r 00 4201 5 A.112 R 7 E On 0.5%%15r 00 1.0111u r 31 1.05905r 01 1.0 717 A r 01 0206 5 9.16n%7' na 8.0111;r on n. 31oy 7e On 4.9es11r nn 1.51un;E no u211  % 2.16141r 03 1.41f76r 00 7.61746E-01 1.11176 r- O ' 1.'?' sir-01 4216 9 5.9114IE-01 1. 6 A 14 % E 01 2.4 28 2 4 r 00 a.21506F 00 5.616;1r On 4721  % 6.9654%F Aq R . 0 51 p;r On p.72717r n3 a q1637e 00 n. Sos 71r on 4226 5 7.80)11E On 6.62116F 00 %. 7195 8r On 4.0 2% )2r n1 2.naA12P no 4211  % 1.1g17ar n1 1.11'59r n0 %.610277-01 2. 7191e r-01 n.16547t-n?

0136  % %.09715E-91 1.62641r 01 7. H 16 0 8 r 01 4.1%n61r 00 5.9"624r no 4731  % 7.42126E 01 a.(7CRQr MO 9.41201r no 9.771750 cc 1. 4 5 A n u r ni 4246 5 1.6]A09e no 7.44009F 00 6. 0 '4 3 8 0 r o n 4. 611% 1r 00 1.17654' 00 4251  % 2,18 9 5 )r 00 1.3?alte 00 7.15297g-n1 1.17qqrr 01 1.17177P-01 4256 5 2.91733r-n1 9. 2 5 R 9 7 r-01 1.70107r 90 2. 76 716 r 60 3.anin77 00 4261  % 4.A10922 no %.64121F 01 6.19172r 00 6.37512r 01 6.1 A 171 r 00 4266 5 5.616152 00 4.P5517r no 1. 9 u F I S P 00 1.07n218 09 7.15991E nn 4271 i 1.u11552 00 A.04201F-01 q.1504nr-01 1.11121g-11 A 5714nP-12 4??6 5 - 1. 0 3 511 E- Sa - 1. 7120 F F - 0 4 - 1. 4117 8 r - 0 4 - 7. 9 % ) 1 L F - 0 4 - f . 7111 C P- 0 8 41A1  %- 7. 59111 E- 0 4- 1. u s 7 41r n o - 4. n ? A 01 e 7. 7 a 1 ] u r-q u - 1. 9 7 9 4 % r n u 4786 5 - 1.12 A 1 )r -Q u - S. L 61% 1 F 0 0 - ).14 0 6 0,- O ri- 1. 0 6 5 7 u r- 0 4- 3. q A as 7 r- no 4201 A- 4.1% 12 7 E- S u- 7. p n 1 A 4 r- r u- 2. u o 2 6 p r n u - 1. 7 % 4 % 1 E 7. A N '11 r- 0 4 4796  % 1.00777E-91 1. 9 9121 r-0 2 L .19 312 E - 0 2 0.11111t - 0 7 7. 5 u 611r- 0 2 4101 S a,216u3r-cy a . 2 0 5 741 - 0 7 H.152107-02 n.n'511r-02 7. 7 3

• t'n t -n ?

4106  % 7. ta sa u r-0 2 6. c n 41R 7-0 2 ' .112 2 R P-0 2 u . 26 04 A r-12 1.11151 r - 02 a111 5 7.17 u 16 7- q / 1.(45627 07 p.%0170'-61 1.111112-01 2.19616r-61 4116 5 7. ' .1d o r - n 2 1. 9 2 01( F- 0 2 %.14 0 50 '- 12 5.110 0 7 7- 0 2 6.19 6 61F- 0 7 u 121 % 7.ir H5E-12 A.? ? 5 6%F-02 p .a101og-12 0.06129P-02 P.a1;ott-n?

4126  % 9.179170-02 7.22uS7E-07 5 A772nE-02 u.446alr-07 1.119%1r-n2 4111  % 2.19 4 % 9 r- 0 2 1.7Ac5fr-n? 6.na203r-nj 1.17 2 9 q '- 01 1.AnuA)g-01 a114  % 7.47241*-07 1.49Fuur-07 5. 6 u o 7%r-n 2 5.17 7 3 2 r- 0 2 6. 7 7 4 9 6 F- 02 4141  % 7.15%62E-n? A. 7 7 0 8 4 r- 0 2 1.n 4 0 51r - 0 2 9.21%%ar-n7 9.nA7477-07 4346  % 0.15241E-62 7.47919g-n? r,142nir-02 4. A A 1 A u r- 0 2 1. % n 7 e A'- 0) 4151 '

1.9PA27' n2 N. 0 211PF- 01 1. o ms 6 a E -01 9.A1111r-14 %. A9 75 A P-Ou 41%% 5 3.1 A 4617-0 2 4.117 78 r-0 7 %.170A6E-02 5. 71 F A % 2- 0 2 6. 5151 a r- 0 2 4161 5 7. 6 2 R 10 E - 0 2 a . % 019 4 r - 0 7 0.07779r-n2 a.174mir-q2 p,qa nn u r-0 2 4166 5 4.12 4 5 4 r - 12 1.11t % 1r-0 2 %. 7 615 7 E-n 2 4. u 0 616 '- 0 2 3.116170-02 4171  % 1. 4115 7 E- 0 7 1.1 % A lt r- 0 ? 1.11799t-01 1.555157-01 8.6%1262-04 4176  % 2. 94 ')91 E - q ? i.90159t-07 A.417704-02 5. 9 7151 E- 0 7 7.17 616'- n ?

0131 5 9.16 7 H O E- 0 2 A.M5179r-02 H.78120r-n2 n. 6 2 n6 7 E -0 2 A. 7 7111 r- 0 )

43A6 5 7.41540E-0? 6. ;6 917 E-6 2 5.14161 E -0 2 4. 219 0 6 7- 0 2 3. r. A 119 2- 0 2 y111  % 1.18 0 71 r - 0 ? 1. 4 7 ? O Pr- 0 2 6.0 0 4 31r -61 2.115;ay-o1 1,5637;r-q) 4196 5 '8. 75 64 S E-il 6. 4 5 74 6 t-0 2 8. 55 4 6 7 2-0 2 A.5F911r-02 1.917727-01 44n1 i 1. 0514 IE- n 1 0.17 P 1 r'- 0 2 a.00409F-02 7.1A796r-02 6.6073ay-n2 u40% 5  %.536$Fr-02 v.21)$5'-02 1.11772'-02 2. 4 2 2 6 % r- 0 2 1. 71 A A e r- 07 4411 '

1. 01 n ?.1 r - q 2 1.On11Ar-02 i , 71112 r, - 01 1. s n 17 2 E - 01 1.);qa6r-qi 4416  % 1. *17 417 t- 12 5.10 01n t-0 2 1. q u u s n r -0 2 1. 412 A i r- 0 2 0.777067-02 4421  % 1. 69111 r - 0 ? q. 9 A n 14 t- 0 2 9.12979E-02 0.51141r-02 a,6eSi77-02 4426 5 6.95771E-01 1.91777E-02 2 ?5687E-02 1. 6 5 551 r- 0 7 1.181R Ar- 02 4-24

TABLE 4-1 (Continued)

POINTER 4411  % 7. 4 9 012 E- 01 7.1 16 6 5 r- 01 3.27601t-01 1.162262-01 7.55229t-04 4416 ', 1.1147/P-0/ 4. 41/ 4 7P- 0 2 7. 9 7 012 2 -0 2 5. 912 70 r-0 2 1.15AA7P-07 4441 3 J.11111E-01 9.10 0 3 7 7-0 2 9. 61105 2-0 2 9. 4 4 6 5 0 P-0 2 R. 9 7 611 r- 0) 4u4%  % 7.16 0 7 4 E - 0 2 5. 5 0 9 9 72- 0 2 1. 9 6 7 718 -02 2.9 2 5 05 r-0 2 2.1140 9 t-0 7 44%1  % 1.48712t-02 1. 50 4Ro t-0 2 5. 7 ra 3 4 t-0 3 2. 516 9 6 2- 0 3 1. 4 R is

• P - 01 4456 6 2.46195P-02 1. 6 4154r- 0 2 6. %b 2 57t -0 2 5. 2 5011 r-0 2 6. 4111n P-0 2 4461 5 7.61712P-02 8.6 0 50 2 P-0 2 4.151oH E-0 2 9. 3917 3 2- 0 2 8. 9 971nt- 02 4466 5 7.9040st-02 6.;A017P-02 5.09511R-02 1. 9164 6 P-0 2 2.469*St-62 0471 5 1.18507'-02 1. 01110 r- 0 2 9. 3 6 0 61 E - 0 3 1. 6 8 817 t- 01 2.17 2 7 %F- 01 447% 5 2.26140P-02 1.1111HP- 0 2 5. 7 4 2 76 E -n2 4. 6 010 7 F-0 2 6.0 2;61 F -0 2 44A1 5 7.19112 t-0 2 H . u ) 4 4 21-0 7 9.15 4 8 4 r-0 2 9. 50 6 6 5T- 0 2 9.219262-07 44R6  % 4,20114 t- 0 ? 7. 0 % 7 4 37- 0 2 5. 5 711 A'-02 4.291532-02 1.0A0077-n2 4491 5 7.nd297t-02 2. 0 017 5 t - 0 7 1. 0 2 % 4 8 2 -0 2 4. 4 0 510 E- 01 2.19 9 7 7t- 01 4446 5- 7. 7 0 6 u S F- 0 2- 1. 74 5 2 0 r 1.16 5 51E 00-9.655422-01 1. u 16 3 P 00 4501 5 1.61721E 01 5. 5114 2 t n o 6. a 512 0 t 0 0 7.21411E 00 7.01514E 00 4506 5 6.10A17F 00 S .1015 6 F 00 3.5A1377 00 1.9015Ar u0 2.54424r-01 4511 5 - 1.13115 R 00- 1.1116 7 F 0 0 - 5.11161 E 1. 7 810 9 E 4. 4 4 4 0 % F- 0 7 hi16  % - 6. A 6 0 51 P- C '- 3. 9 % 11 H F 1. 015 4 7 P. 00-7.27180P-01 1. 34 e t e r on 4521 5 1.14 5 A ) E 01 4.91901r 01 6.043102 00 6.51229E 00 6.17504P 00 457A  % 5. 54 % )4 r 01 4. 14 1str 00 2.u t s ine OS 1.2622Ar qo-1.c6414r-01 uS11 5-1.2%551' 11-1.1120IF 0 7 - u . 4 6 R 2 9 P 1. A 6 u ) 1 r a . A 4 7117- 0 7 4%16  %- %. 6 4 7 ? 4 t - 0 2 - 1.1214 nF 7.11 t S 8 r. 5. 2 4 9 5 A t - 31 1. in 6 u A P no 4541  % 7. 5 H 117 0 91 1.51449E 00 u.16755E 00 5.78977t n0 5.14460' no uS4A  ; u. 5111or ^^ l 5A154T 00 2.14504' 01 1.14114r 00 1.%%001P-92 4551  % - 9 . /, 9 191F-01-1.1)O95F 0 0- 5.14 5 0 0 r 1. u 1110 E 3. % u 216 t- 3 2 uA56  %- 7.1r e a 5 g- r i- 1. 7 4 u ;1r A . 5111 u t 5. u l a 16 r -01 1.106A7P 01 4561 5 7.711A1P 0' 4.2q2 tor OS 5.111r t.P 00 5.uA477E 00 5.77115' 00 4566  % 4 . 5 5 ; 6 4 r. nn 1. 6 A t 0 7r o n 7.7311't 01 9.46411t-01-1.764A7E-01 4571 5-1.194lir on-1. P a n 7 7 t 1.1110 C P 1. 0 4 719 P 7. 7156 3 '- 0 7 4%76  %- 4.13 7 0 ) r 3,112 q s y H .17 M.1 r 7. A 15 2 6 7 - 01 7. A 9 79' t-01 4501  % 2. I$ 411 e n ' 1.64511P til 4.54501E 00 a.94762r On 4.7%C40P 01 45P6  % u.12121P q1 1,1A526r 31 7, n a 112 e qq 9.66167t-01-A."1111P-n>

4511  % - H . 4 2 6 9; r P .17 5 u 1 r 1. u q10 7 E 1. 0 4 0 % 4 t 2. A u S 7 7 P- 0 2 459h  %- A. 5 717 3 5- 0 h 1. ' ) ? s 7[ n t - n . o r.0 u p r. .n i - 6. 4 6 919 7 -01 7.?997AE-01 4601  % 2.11394F n) 1.90911r 01 u.au1%'E 00 5.32191t no c.17?tAe no 4606 5 k.56074E ni 1.72151r e1 ) . ' % % 01 t 00 1.51n16r OS 4.4;?lAr n1 4611  %- l.1h u 4 % r - n t 1. s l A s11 1. 4 7 71 v r 4. 6 u 15 % E- 0 2- 8,5411 A P- 01 461% 5- P. u 2 l u l E- 0 2- u .19 r in r 0 q u 12 0 E - n 1 - 1. 8110 0 - 01 1.1554QP-01 u621 5 1.11401E 01 2.;272ut 01 1.31612E 01 1.69577F 00 1.6A173r 60 4026  ; 1.11471t (1 2.971 Alt on 7.u11572 00 1.506A4r OO 5.A2rnor-01 L h il 5 - 2.1 )i 4 t r 01 - 1.1 A 114 T -n 1- 1.15 2 F 9 t 1, 7 r 911 r - n 2- 7. 6177 4 P - 01 46]'  % - 9.1 P 4 3 0 r . 0 2- 4. % % 9 0 p t 1.16 4 5 4 P OS-1.41617E 00-4.A2n26P-61 4641 5 u.96129*.q1 1.)'111r 01 1.wcA79r 00 2.12758F 00 7.S962AP 00 ue4/ 5 1. 4 e M u r 01 1. * /15 % no 1.01ArAr 01 4.S1166F-01-2.nu1%RE-01 4651 5-n . 5 6171

• n 1 - u . P 7 4 A u r- n 1 1, 7 A p e.g g 5. u 7 7 51 E- 0 2- 1. n; 9 7 0 E- 0 2 46Sn ' - 6. t a a 71 g- C 1- u .17 F 5 0 f 1.1212 f r 01- 1,61214 r 0 0 - 1. 01 d% F nn 4f61 5 - 5. 76 4 71 r 1. 7 % '.1 H E n 1 1.0w663r-01 1. 317 5 7 t - 01 0.24312P 61 46A' N 1.6041Ar-11 2.1a641r n1 1. 2 ' ? ? 4 E - 0 2 - 2. 5 5 9 4 2 r 5. % %910 P -01 4671  % - 4.111 u s t - 11 R .11( 14 r - 01 3, 1719 I r - 01.F . 41171 r- 0 2- 1, A 5 A A J R- 02 4676  %- 5. ;'5;1 E - 0 7- 1.10 n 2 F F 9.1117 8 r - 11 1. 6 7 711 ' n o - 1. 6 4 7 7 6 E 00 4601 5-1.61121! 11- 1. 5 5 '9 a r ( 0- 1. 4 4 7 51 r 0 0 - 1. u ? 917 2 0 0- 1.15 4 7 6 E 09 4A45  %-1.266%1P Ob 1.16 /15 r 0 0- 1.17 2 4 2 t 00-1.10471E Co-9.a16A2r-01 4691 5 - 4. 6 2 7 2 4 r u. P ) 17 5 t ^ 1- 1. P l u S 2 P 6. 3 0 2 9 9 9- 0 2- 1. u o 15 2 t- 0 7 A04A  % 1. 00 3 91 r- 01 0.0 n.0 0.0 0.0 49 51u6  % q.c A,11;qcr.o2 (, a qqqo E-0 2 4.10 5 A 0 r- 0 7 1. 4 h 2 9 0 P - 0 2

%151  % 1.'0610'-03 2. 7 7 esr t- r 2 2.atorCr-02 y,211pnt-92 2,04140r-n?

' 1 % ~i  % 1.9954 E-1* 1.912367-92 1, A 9110 r. - 0 2 1.91410E-12 1.91510P-07 5161  % 1."h111r. 07 7. r 111r r . r2 7.12s1qt-02 7.;n02nF-07 2.1%n2nP-o; 5166  % 1.1%)))r al .) .11'30 01 0 ? 5. u " 101 F - 6 2 4.115 6 0 r - 0 2 1.u679nt-02 5171 5 1.'0611P-12 2.f7C;fr-02 2.u19ACP-02 2.21190E-12 2.14140r-07 5176  % 1.19541E-12 1.11'130 02 1.91510r-02 1. n g g 10 g - n ; 1,91 % 1 n e - 0 7 51A1  % 1.16190 r- 0 2 2. 011107-02 2.12510'-02 2.20010t-02 2.1502nP-02 4-25

TABLE 4-1 (Continued) h POINTER 51A6  % 1.15 0 712-0 2 9. 0 7 4 90 t-0 2 6. 7 5 4 09 8-02 4.67740s-02 1.94560R-02

%111  % 1. 4 2 510 P- 02 1. 0 4 2 7 00- 0 2 2. 7 5 6 9 0 P-0 2 2. 50 2 7 0 t- 0 2 2. 3 m S2 0r- 02 9196 5 2. 2 7 3 60 2- 02 2. 20110 t-02 2.16190 P- 02 2.15 810 t-0 2 2.14 210 t-0 2 5201  % 2.21ee03-c2 2.31410r-02 2.u1110R-02 2.50770t-02 2.67780R 02 9206 5 2.677908-02 1. 0110 0 r - 01 6.666792-02 5.031502-02 4.21460R-02 5211 5 1.662102-02 1. 2 % 120 t-0 2 2. 9 416 02-0 2 2. 7188 0 t-0 2 2. 5 5 02 0R- 02 5216 5 2. e 3 0 9n 2- 0 2 2.15160 r- 0 2 2.1116 0g -n 2 2.1014 n r-0 2 2.1310 01-0 2 5221 5 2.18100 t-0 2 2. u 7 a a 0 E-0 2 2. s a 9 A C E-0 2 2. 6 812n t- 0 2 2. 4 6 3102- 02 5226 5 2. 86110 t-02 9. 4 5 P 5 8 t- 0 2 6. 2 4112 t-n2 4.6 6 97 7 7-0 2 1. 9 3 69 0 2-02 5231 5 1. 4112 2 E- 0 2 1. 017 4 2 r- 0 2 2. 7 5 2118-0 2 2. 5 3 8 5 2 r-0 2 2.1m in nr- 02 5736  % 2.269A6t-02 2.19 752r-n2 2.16 012t-02 2.154 tir-9 2 0.1.010 r-0 2 5241 5 7.211512-02 2.31n26t-0) 2. 2171 ~ P-0 2 2. %0119 2- 0 2 2. 6 7 317P- 02 5246 5 2.6742ar-02 0.0 7.000r e 02 4.61001r 02 %.%00002 07 5251  % 7.001101 07 m 50000 r 0 2 1.60000t 0) 1.1%0not 01 1.10000P 01

%256  % 1.45600E 01 1.6000nr al 1.750002 01 1.960 00 t 01 2.n5 0no r 01 5261 5 2.2090nr 01 2.15n00 r a 1 7.50000r 01 2.6n00n r 01 7. 76 6 00r 61 52(6 5 5. 06 0no r o ' 2. 61r ecr- 01 2.01200E-01 1.017802-01 1.146207-01 5271 5 1.22591P-n1 1.7856nr-n1 1.31760r-11 1.14100r-01 3. e 5 010 P - 01 5276 5 1. 510 6 0 t - 01 1. f 4 010 t- 01 1.79*60E-01 1.1RS20t-n1 u.711702-01

%781 5 4.iS191P-n1 4. 9 6110 E-n 1 5.41720t-01 6.55250'-01 5.07000'-01

$206  % 5.02000E-01 2. 6 4 0 r- 01 7.a1200*-n1 1.11790E-01 3.146262-01 5491 5 1.12590E-01 1. ? q 5% n t -01 1.1176nt-01 1.1 P 10 0 r - 01 1.e5010E-n1 526A S 1.%1060r-01 1.70010r-01 1.79nA0r-01 1.19520E-01 4.7117nP-01

% 10 1 5 a.5618nt-01 4. 9 A 110 F -01 %.447202-01 6.%52%0r-01 5.02 nner- n1 S in 4  % %.026nnt-01 2. 6 9 s u o r- n 1 2.H1200r-01 1.11'A0t-11 1.1957nr-01 4111  % 1.2251nt-01 1.2A%6ny-Of 1.11760t-11 3.19100r-01 1. u S )1 nt- n 1 5116  % 1. 514 61 r - n 1 1.640160-01 1.74HA09-91 1. ant 20r-01 a.21076P-01

% 121 5 4.%A119t-n1 4. 4 6110 f -01 5.a17?nr-11 6.552%nt-01 %.02nnor-01

'. l ? ^ 5 %.07101E-01 2. t e s u n t - 01 2.41200'-01 1.017 A 0 E- 01 1.1862nr-n1 5111  % 1.77591R-01 1. 2 8 %6 fi r - e 1 1.117 eor-n1 5.141nqr.01 1.asq1nr n1 9114  % 1. 516 6 0 E - 01 1. f 4 010 7 - 01 1.744607-01 1.ga%;0r-11 c,71176r-n1 5141  % 4.561tle-01 u . 96110 E-01 '.4472nE-01 6. 5 5 2 A9 t- 01 %.070607-n1

%346 5 %.n2110t-01 2. 6 9 C4 0 r - 01 7.41200C-n1 1.n1790r-01 1.1tA70r-n1 5351  % 1.72%11'-11 1.28%607-01 1.11760t-01 1.19116F-01 1. 4 % A 10r- 01 5 1 % *. 5 1. % 19 6 6 r - n 1 1. 6 4 010 r- 61 1.74460E-01 1.18%70E-01 u . 7117 n t n 1

%161 5 4.;s 1999-;11 4. 9 611n r-01 (44770*-q1 6.s52%nP-01 % . 0 7 n n e r - 01 5164 5 % 02001r et 1,0 0 0 n 01' 2 8.09100E 02 4.0n000r 17 5.5000nP 02

%171  % 7.90001r J? H.50010F 02 1.10000t 0) 1.150nce ni 1.)nnnor 0) 5176  % 1.4%09nr 91 1. o n f 0 n r 01 1.75000' 01 1.9nq0nr 11 2.n5600P 01

%1A1  % 2./0100' n1 2.35000P 0) 2.5600er 01 2.76600E 0) 2.76910r n1

%186  % 5.80009r n) 0.n7incr 01 ".46660F On 1.74150T 00 9.%6690t On

$191 4 9.100n3C 0^ H.771nor n1 8 15honP 00 8.162n0F 00 7.pagnor en 5119  % 6.4110nr to n,6 n.0 C.0 D.0

%40A 5 n.' n. 3 A nno r o n n.117 00 r n9 9. 7110 0 r 0 0 9.conorr 00 5411 5 n.u150nr n1 p.?410nr n9 7.u1rC0r 60 7.140nn' no 6.6%nn0P 00 541' 5 %.9710*' n' n.0 n.n 0 0 0.0

%Q26  % n.o 1.09110e 01 1.ol10nr 11 1.02401t n1 1.n971nr 61 5411  % 9. 7916 6 E 11 9.20nmar no p.10none 00 8.1%000t On 7. torn 0' on 5036  % 6.f10935 01 0.0 c.n n,0 0.0

'446  % 0.n i.nH700' O1 1.oH10nr 01 1.n6900t of 1.nunnar 61 54%1  % 1.92100r 01 9.% 9 000r nn 5.6 50rnr 00 R.4eonnt 00 7.7n00nr 00 Su;6 5 A.11on3r 01 0.0 a.n 0.1 0.0 5 4 f. A  % 0.0 1. P u S2nr 01 1.112212 01 1.01143r 01 9.4?n67r n1 5471  % 9.60%n1' 01 9.7H07%r 00 H.7uo0nt 00 8.5545mr 00 7.mmo%02 00

%u?6  % 7.!un99' rn n.0 n.n n.0 n.o 54d5 i n.1 1. 0 0 006 7 0 2 5. 0 0 000 P 02 1.00100t 01 1.50nn0P 03 5441 9 7.100019 01 7. 76 710r 01 2.7670nt 01 1.000n6F 01 e.00&o12 01 5496 5 5.10999t 61 0.0 q.0 0.9 n.n 5506 5 0.6 1. 9110 0 r 12 1.%110nt 12 1.nA000r 12 9.%nn0nt 11

%511  % a,5nn01g 11 7,5qnn0R 11 A.500nn* 11 0,6 0,n 5 5 2 t>  % 0.0 1.90100L 12 1.540C0t 12 1.06100r 12 9.%$00nP 11 5%31  % H.50160r. 11 7.5n enor 11 6.50000t 11 0.0 0.0 0

4-26

TABLE 4-1 (Continued)

P0lflTER 5%46  % 0.0 1.90100r 12 1.590005 12 1.06000r 12 9.ionnn* 11 55%1  % w.500nor 11 7.50000r 11 6.50n005 11 0.0 0.0 5566  % 0.0 1.40100r 12 1.510not 12 1.06000r 12 9.50near 11 5571 5 P.'>0000t 11 7.50r00r 11 f.50000t 11 0.0 0.0 5586  % 0.0 1. 0 0100 t 12 1.590002 12 1.06000r 12 9.50nn0R 11 5591  % A.40nonP 11 . 50000r 11 5.50000R 11 0.0 0.0 5606  % 0.0 1. 0 0 0.10 r 0 2 5. 0 0 0 00 R 02 1.00000t 61 1.10000s n1 5611  % 1.20000t n1 1.300Cor 03 1.40000t 03 1.50000t 01 2.n0000r 0) 5626 5 0.0 h. 2 8100 r 09 5. 815 00t 01 5. 26900 t 09 a e61ner n9 50

%631  % 1.a15007 69 1. 0 '.10 0 r 0 9 2.12500E 09 1.90100r 09 1.19200E 09 5636  % 1.16101r. 04 9.24800r 08 7.17500r 08 6.76000t 09 5.7100er 08

%641 5 2.fA000' 09 0.n 0.0 0.0 0.0 56u6 5 0.0 6. 2 R 300 r. 0 9 5.A16Cor 09 5.26100r 09 4.46100r 09 56%1  % 1.a15Cor 00 1.fu100r 09 2.12600t 09 1.60100t 09 1.19200F 09 5e56 5 1.16inct 09 9.?eMoor 08 7.17 5 00 t 06 6.76000t 08 5.71onor na 56f 1  % 2.6b000r 04 n.0 0.0 0.0 0.0 5 66 5 0.0 9.15000F 09 8.550nor 09 7.45000r 0 9 6.00000t n9 5671  % 5.u0nC0r r1 u P1000r 09 u.26000r 09 1.70000t 09 1.110002 09 5675 5 2.91000E 02 2.62000E ng 2.14rnor 09 1.1)o00r 09 1.12000F 09 5691  % 1.17000F nA 0.0 0.0 0.0 0.0 5606  % 0.0 0.07890r 01 7.%9700r 09 6.80600t 09 %.4nu00E S4 5691

• 4.5%100r Oi 1.C4*CCF 01 /.6%0rnr 09 1.91400r 01 1. a p n 0 0 r n g 5696 5 1.16 4 n 1 r n s 1,17%rrt 09 1,12J00r 19 1,15600r 09 9.150nor 14 5701  % %. 9 0 Gar f 4 0.0 r.1 0.0 0.0 5106  % 4.1 's . I s n o o r 09 8.55000r 09 7.45000t 09 6. 00ncOr Oa 5711 5 W.;4000r 01 1.00Co0E 09 1.0100rr 09 2.77001r 09 1.11onor 09

%716 '. 1. 7H n1)r n l 1.t%n00r 01 1.5%*002 09 1.45000r 69 1.17nnor 69

% $ 21 5 7.17 noir 06 f.0 0.3 0.0 n.0

% 72%  % 0.n 5.00^00F 01 2.00000R 02 3.0010Sr 02 6.000007 62

%711 ~. 6.501307 n) 7.n0000f 02 7.50000% 07 A.01000F 02 9.%Annor 02 5716 5 9.7A011e 9/ 4.490000 02 9.27000E 02 9. % 0 00 0 t 02 1.on00nr n1 5741 5 1.1710 0 F 01 0.0 0.^ 0.0 0.1 574r, '. 0.1 0.0 0.9 - 1. 9 0 0 0 0 t - 0 4 - 4 . 9 0 0 0 0 F - 9 )

57c1  % 1 40 610 r 1. 7 a r m n r- 0)- ; . 4 75 n c t 2. 4 % n n 1 T-0 2 - 1. O n o n 0 r-0 2 575%  %-1.00111r-n1 9.n 7.00000F 01 1.nonnor-01 3,50nnor-01 5761 6 4.00100r-11 4.%e000f-01 5.n100CP-01 5.51903r-01 6.nn060r-n1 576n  % 2.or0011 '31 n.r 0.0 0.6 0.n Sna6 5 9,a 1, c a r y r no (,iq000E 00 2.52800E-01 2.%240nE-01 5891 ', 1 uf1110-n2 1.nC01ne-0; 4. 217 do r q o 5 ;& O 91r-0 4 u .1h on or- 01 $1

%Als  % %.32000E-04 4. L 5 n or F -01 5.11100E-04 2.14010F-01 5.lue06t-ou

'911  % l.de 100F-11 . 11nerg-nu 2.4;100r-0) 1. 0 4 0 0 0 r 01 1.651onr 01 5116 "e 9.14 711r e l 1.14 2 01F 01 9.147209 11 2.%eq00 r 11 1.nnnner n;

$411  % 2.S*11)r 01 1. 01101 r 0 ? /.%:lo00r of 1.non00E 02 ?.5hnqo' n1

%11n 5 1. On i n 9; C2 /. 61r nar n1 1.0600nr 02 1. 0 0 0 n 0 E 01 1.onn007 01 5071 '. 1.001Cor 01 1.cor76r 01 1. ran00 g 01 1. 0 0 9 0 0 E 11 1.00n00E n1 S q ."  ; 1.nnqnq- 11 1,naroq[ c1 1,nqqrer 01 1,no100r-02 1.c0000r-n?

' 9 11 5 1.00^1nt-02 1.00000r-07 .ronn0t-02 1.n01nor-07 1. 0 0 q 0 0 r - 0 7 5 41 r. % 1. 00 a no r- 0 2 1.cff^nt-02 1.n'rr07-02 %.11100r of 1. n a n o 0 F n1

%u1 5 1.500010 01 1.00011r On 1.71900E 09 5.On11nr-01 1.;0000r 01 $2 6941 '. 4. 5011]r- r ? 1.rorror n1 1.n'Occr 04 n.o 0.9 G011  % 1.700130 61 A. 4nroo r-r 1 9.1110rr-01 p.in0007-61 9. 7 0 0n e r- 01 51 61n a  % 4.'0'00)-01 4.70000r-01 n.51onor-01 0.A010nt-01 A.AGOoi--61 6011 5 1.5009)r 01 1.50010r 01 1. %n0 c 0 E 01 1. 0 010 0 r 01 1.50nenr 01 54 6116 5 1.5nonrE c1 1. t c r o r t 01 1 %n00cr 01 1.%0100r 01 1 %n00qr 01 6051  %-1.00003r. 00-1.0106CE Or-1.n'000F 00-1.000001 00-1.corant no $%

8O' 5-1.60^11r C1 '.nor1CF rn-1.n9000r 00- 1.000 no r 0 0-1.n n nm o r 00 60r 1 5-1.oronot O'-1.000001 6 0 - 1. 0 0 0 C o r 0 0 - 1. n n o n o r 00-1.01000F 00 006' C - 1. 9 C n o n t 14- 1. r n 0 0 r r r o.1.10 n 0 0 r 0 0 - 1. 0100 n r O n - 1. n 01n n e 0 0 bo71  %-1.001006 0^ - 1. r in 01 r 0 0- 1. o n n e n! 0 0- 1. n 0 0 '0 F 0 0- 1. 0 0 00 0 r 0 0 6n18 '. - 1. 0 0 010 F #0-1.01 Fore 00-1.000000 00-1.orn00! 00-1.aiornr 00 An01  ; 1.On30ir 01 1.0n000t 00 1.ninCCF 00 i.00000F 00 1.rocent 00 60R5  % 1.Onn9er n) 1.001nor r0 1.10000r 30 1.10000* 00 1.nn000r on 4-27

O TABLE 4-1 (Continued)

POINTER 6101  % 6.10101E 01 6.3n030t 00 6.19000t 00 6.10000t 00 A.lonnor 00 4106 5 6.10 0 0 0 E 01 A.100nor 00 6. 3non02 00 6.100002 00 6.10000P 00 6111  % % 00000p. 01 %.00000t 01 5.00000t at 5.00000t 01 5.000no r 61 6116 5 5,00000, 01 %.000001 n1 5.n0000E 01 %.00000r 01 5.on000R 01 5-1.00000g 00-1.00000E 00-1.non00R 00-1.000 00 2 00-1.0000n r 00 $6 6121 6176  % = 1. 60 0 00 t 00- :. 00 000 t 00- 1. 000 n o t 0 0- 1.0 0 0 0 0 3 00-1.000nnP on 6111 5-1.00000E 00-1.00000t On-1.00n00t 00-1.00009t 00-1.n000nt 00 6136 5- 1.00 000 0 00- 1.60 000 P 0 0- 1.00000 r 0 0- 1.0 0 0 00 t 0 0- 1.n0 0 00r 00 6141 5 2. 50 000t- 07 2. %0 0007-0 2 2. %0000E-02 2.50000 2-0 2 2.%nnne r-0 2 h146  % 2.50000E-02 2.5000nt-n2 2.50000r-02 2.5non0E-02 2.500607-02 6151 5 2.50000E-02 2. 50000r- 0 2 7.5n0002 -02 2.50000 t-0 2 2.%0 n00 E-6 2 6156  % 2.%n10nt-02 2.50000E-02 2.%0000r-n2 7.500002-02 2.500ner-n?

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TABLE 4-1 (Continued)

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-1 END 4-29

O TABLE 4-2 NOMINAL CORE PRESSURE DROPS FOR lilGilEST FLOW ORIFICE ZONE IN CRBRP (N0 GRAVITY HEADS INCLUDED)

. Region gjpsi)

1. Inlet Pipe to Plenum 4.6 Core Support 9.0 Assembly Inlet and Orifice 15.3

2. Neutron shield 22.5 Pin Bundle Entrance 1.0

3. Rod Bundle (Blankets, Core, and Gas Plenum) 44.2

4. Rod Bundle Exit 3.0 Upper Internals 4.4 0.4 O

Plenum to Outlet Pipe TOTAL 104.4 4-30 &

29 28 30 27 SI 31 26 22 28 32 25 23 CR 19 25 24 17 g in 25 32 5 12 24 27 31 18 21 CR 16 13 CR 23 28 30 Ig 4 21 22 29 29 30 12 14 11

! 11 15 8 14 17 68 68 g SR 10 16 CR 30 23 CR 13 10 8 3 7 15 5 20 22 5 2 3 4 9 31 17 7 27 4 CR 6 6 SR 13 19 23 16 1 2 8 12 32 26 21 15 2 1 1 7 11 18 24 14 - 3 CR 10 6 CR 6 10 CR 25 25 11 7 1 3 14 24 18 1 15 21 26 12 8 2 1 2 32 SR 6 6 CR 16 23 19 13 3 7 4 17 27 31 9 4 2 3 8 5 22 20 5 15 7 16 10 SR 10 13 CR 28 30 CR 17 8 15 11 9 68 68 14 22 4 14 12 20 29 29 21 11 CR 19 30 28 23 CR 13 It 27 24 12 5 21 18 31 25 18 9 17 24 32 25 CR 23 25  !

19 31 68 27 29

\ /

Figure 4-1 Assernbly Assignment Numbers 4-31

O

! 9 10

\

10 9 9 10 8 8 to 8 CR 8 10 10 7 5 7 7 10 9 7 5 6 6 7 10 10 I CR 6 6 CR 8 9 10 8 6 5 5 5 6 8 10 9 7 5 4 4 '5 6 9 9 CR 6 4 SR 4 6 CR 10 8 6 4 2 3 4 6 8 10 6 5 3 2 2 5 7 9 8 6 CR 2 2 SR 6 8 10 6 4 2 1 2 4 6 10 7 5 2 1 1

\ 3 5 \ 7 10 CR 4 2 CR 2 4 CR 10 7 5 3 1 1 2 5 7 10 6 4 2 1 2 4 6 10 8 6 SR 2 2 CR 6 8 9 7 5 2 2 3 5 6 10 8 6 4 3 2 4 6 8 10 CR 6 4 SR 4 6 CR 9 9 6 5 4 4 5 7 9 10 8 6 5 5 5 6 8 10 9 8 CR 6 6 CR 8 10 10 7 6 6 6 7 9  !

10 7 7 6 7 10 8 CR 8 10 10 8 8 10 9 9 10 10 9 10 Figure 4-2 SAS Assembly CRBRP Channel Selections for the BOEC Case O

4-32

! 10 10 10 10 10 10 9 9 10 9 g CR g 9 7 7 8 ID 10 8 6 7 8 10 10 8 7 CR 6 CR 9 10 10 9 6 5 5 7 9 10 10 9 7 5 7 4 4 5 7 10 10 5 4 6 CR 10 10 CR 6 4 SR 3 4 6 9 9 6 4 3 2 3 5 7 10 10 7 5 3 CR 2 SR 6 9 9 6 2 7 10 10 7 4 2 1 5 3 1 1 5 8

CR 9 9 CR 4 2 1 5 8 5 3 1 2 4 10 10 7 4 2 3 2 CR 9 9 6 SR 2 2 3 5 7 10 10 7 5 3 4 3 4 9 9 6 3 6 SR 4 6 CR 10 10 CR 4 4 4 5 1 10 10 7 5 5 5 7 9 10 10 9 7 5 6 6 CR 9 10 10 9 CR 7 6

! 7 8 10 10 8 7 7 8

\ 10 10 g8 9 9 9 9 CR 10 9 9 10 10 10 10 L \/

Figure 4-3 SAS Assembly CRBRP Channel Selections for the E0EC Case 4-33

COOL ANT MESH O

30 317.50 H ANDLING SOCKET. TOP 29 300.99 - -

L O A D PAD, E ND C AP, AND 28 EXTRA SPACE p 284.48 ,

26 E 254.00 - -

b u

z 25 $ 223.52 - -

FISSION G AS PLENUM m

a 24 3 193.04 - -

e C

23 0 162.56 (

s P UPPER BL ANKET E 3 g = i27 0  :

a s s

e 5

e e

d

• ACTIVE CORE 35.56 LOWER BL ANKET 2 0 00 ,

LOWER SHIELO ORIFICE

• BLOCK. AND FUEL ROD ATTACHMENT 1 -93.472 Figure 4-4 SAS Coolant Mesh Used for Representation of the CRBRP Core 4-34

1.0 N

\

\

\

\ EXPECTED FLOW CURVE a8 -

\

\

O -EXP - 0.17 9 t + 5 X 10-3t 2 - 7 X 10'5t 3' = f C SAS FLDW DECAY: CALCUL ATED FROM Ap HE AD

• a POI '

N 0.6 - N s

N \

? 4w

. a h [. M g 0.4 -

a N a2 --C._ 4 _ n ,

0.0 O 5 10 15 20 TIME, SECONDS Figure 4-5 Pump Flow Decay Curves fcr CRBRP

HE AT inANSFER MESH HEAT TR ANSF ER COOLANT N00E NODE OIMEN510NS IN CENilME TE R$

23 162.56 20 22 14 458 148 10 - -

UFFE R 19 21 7 034 BLANKET 141.07 --

18 20 7.034 134.03 - -

17 19 7 034 o 121 00 16 18 7 034 E

a 119 97 15 17 p 7.034 e 112.93 --

14 16

" 7 034 w 105 90 - -

13 15 y 7 034

$ 98 87 ACTIVE 12 14 m 7 034 CORE

$ 91.83 11 13 3 7 034 0 84 80 - -

CORE 10 12 a w 7.034 p

77.76 " --

4 9 11 > @ 7 034 P 7013  ;- -

8 10 $

W

$ 7 034 9

63 10 g- 7.034 7 g o 56 66 - -

6 8 g 7 034

> 49 63 5 7 7 034

• 42.59 - -

4 6 7034 35 56 3 5 7 034 28526 - -

2 4 9 000 19 526 - -

LOWER BLANKET 1 3 19 526 P

2 0 00 Figure 4-6 Core and Blanket Mesh Spacing for SAS3A h 4-36

5. Neutronics and Steady-State Results 5.1 Model and Procedure Details This section deals with the generation of power profiles, fuel, sodium, and steel worth distributions, and the Doppler coefficients for use in SAS3A. The scheme used was first formulated and applied by Smith (Ref. 47) in the analysis of the FTR LOF HCDA. The general procedure is illustrated in Figure 5-1. Two subroutines (HOCUS and POCUS) are used: the first to map the SAS3A geometry, including material volume fractions and fuel temperatures onto the FX-2 (Ref. 39) r-z geometry and the second to map the FX-2 power and reactivity worths back onto the SAS3A geometry. In this mapping procedure, each SAS3A channel was represented by an annular ring in the FX-2 two-dimensional cylindrical model, A consistent initial power and temperature distribution was obtained by iterating between the SAS3A steady-state calcu-lation and the FX-2 fission source. Wit 1 the converged steady-state model, material reactivity worth tables and Doppler coefficients were obtained by means of first-order perturbation theory.

Cross sections for the above calculations were generated (Ref. 48) 2 starting from the current ultrafine group library for the MC -2 code (Ref. 49),

2 which is based on ENDF/B-III data. The MC -2 code was used to produce a 212-group fine group library (with resonance cross sections omitted) for use by the SDX code (Ref. 50). A single MC2 -2 case was run to produce this library. The composition of a core pin was modeled and the extended P-1 transport option of MC 2-2 was chosen to generate a 2040-group spectrum for use in collapsing to 212 groups. A one-dimensional (radial) model of the CRBRP, with inner core, outer core, radial blanket, and reflector explicitly represented was then constructed for SDX. At each of four temperatures (300U K, 1100 K, and 2200U K, and 4400 K), SDX runs were made in which (a) the resonance cross sections appropriate to each of the four regions were 2

computed using the MC -2 algorithm and added to the cross section in the 212 group library, (b) a one-dimensional 212 group diffusion theory calculation was performed for the model described above, and (c) 27 group broad group cross sections were produced for each isotope of interest in each of the four regions, using the space-dependent 212 group fluxes generated above.

By merging the output of these four runs, a single 27 group library was constructed and used as the basis for further calculations.

5-1

The actual isotopic compositions used in power and worth calculations for the BOEC and E0EC cores were generated by using the eq ilibrium cycle g option of the REBUS-2 code (Ref. 51) as reported in Reference 48. The REBUS-2 results were in the fom of isotopic compositions by radial region on its r-z model of the CRBRP. For a given SAS3A ch innel on the FX-2 r-z mesh, the RESUS-2 compositions were recombined in a proportion to the number of assemblies of.each burnup within that channel.

A B0EC and E0EC HEX-Z analysis has been performed using VENTURE (a 3-dimensional diffusion theory code) (Ref. 52) for a one third reactor sector.

The material worths for the removal of sodium, stainless steel, and fuel were calculated using first order perturbation theory with three dimensional fluxes. Comparisons of the axial worth histogram with Figures 5-2 through 5-4 and 5-5 through 5-7 showed reasonable agreement.

5.2 The 80EC Core Configuration The assembly channel selections were presented in Figure 4-4 The FX-2 annular region area for each channel was determined by the number of assemblies in that channel and the area per assembly at steady-state conditions. Hot axial zone heights are determined by H0CUS, given the cold $

reactor axial dimensions. Figure 5-8 shows the reactor model used in FX-2.

The control material in Ring 4, Ring 7 flats, and Ring 7 corners was repre-sented by three annuli. To obtain a critical system, the density of boron-carbide in these annuli was reduced by 50%. This was necessary because an annular representation over-estimates control material worth.

The axial power traces for the various channels in the BOEC core are shown in Figure 5-9. These are drawn by connecting powers at nodal midpoints using hot core dimensions. (In these figures and those which follow the label A through J correspond to Channels 1 through 10, respectively.) The SAS heat transfer mesh was defined in Figure 4-6. These powers are compared in Table 5-1 to power obtained from the design calculation by averaging the same assemblies. It can be seen that agreement is reasonable except for Channels 6, 9 and 10. The power and power-to-flow ratio in Channel 6 are low due to the unique position of Channel 6 on either side of the most inserted control rod. Channels 9 and 10 differ because they were grouped on the basis of burnup, not position. Channel 9 was then placed inside of 5-2

Channel 10 to preserve the high design power / flow ratio typical of all the fresh channels. (The computational system did not allow Channels 9 and 10 to be intermixed.) Consequently, Channel 9 has too high a power; Channel 10 has too low a power. To obtain a better representation of the power in Channel 6, either a synthesis of two-dimension r-z and planar hexagonal results would have to be performed or a three-dimensional neutronics calculation would have to be done. The representation for Channels 9 and 10 can be improved by using more channels, such that the outer assembly ring could contain both high and low power irradiated assemblies. The consequences of the use of the present FX2 calculation is to increase the incoherence between fresh and irra-diated assemblies. This is not serious for Channel 9, since little positive or negative reactivity is produced from the events in this channel. liowever, the low power to flow ratio in Channels 6 and 10 almost assures a sodium fuel interaction during the burst phase of a LOF accident unless fuel motion is monotonically dispersive in the first assemblies to melt (the fresh assemblies).

Figures 5-2, 5-3, 5-4 give the fuel worth, sodium void worth, and steel worth for each channel, The fuel worth in the blanket region is that of actually moving core fuel into the blanket since this is the most important effect that the fuel worth gradient should account for in the calculation (the blanket fuel is assumed to stay in place). The reactivity effect of moving all the sodium out of positive regions of the represented SAS channels is 3.3$. The Doppler coef ficients for the channels are given in Table 5-2.

Doppler profiles are given in Figure 5-10. The control rod effect in Channel 6 is quite noticeable. The lower blankets are seen to have a particularly high Doppler coefficient due to spectral sof tening and the high U-238 content.

However, this may be misleading since the lower blankets do not heat up significantly in an accident (the power is low and adjacent sodium is cold).

The steady-state temperature distributions for Channel l are shown in Figure 5-11. This indicated a peak fuel temperature of around 2000 C and also a significant temperature drop across the fuel-cladding gap. The gas temperature drop (s375 C) is shown more clearly in Figure 5-12, which gives the temperature profile for the peak axial node (the node below the core 5-3

midplane). The fresh fuel is assumed to have ten days burnup so that a slight central void exists. The reason for the large temperature drop is the large g fuel-cladding gap that the model presumes to exist in fresh fuel. This gap is shown in Figure 5-13. All of the five fresh channels have a radial gap of 0.005 cm or larger. The effect of these high temperatures in fresh fuel is to increase the steady-state stored energy in the fuel and decrease the potential transient Doppler contribution. Both effects would tend to augment meltdown processes. (Irradiated fuel will be discussed in connection with the E0EC case in Section 5.3.) Finally, the steady-state fission gas-retention curves are shown in Figure 5-14. This figure indicates both the differences in gas concentration between fresh and irradiated fuel and the peaking in stored fission gas that occurs near the ends of the irradiated pins.

5.3 The E0EC Core Configuration The assembly channel selections for this case were presented in Figure 4-3. Figure 5-15 gives the FX-2 geometry. The control material is completely withdrawn from the core for this case.

The axial power traces for this case are shown in Figure 5-16. The h comparison to the corresponding design calculation is shown in Table 5-3.

In this case, all power-to-flow ratios are fairly close to unity, and no significant deviations exist with respect to design values. This might be expected since the assembly ring geometry was chosen on the basis of design powers. However, this procedure does have the restriction on locating channels so they can be placed in two-dimensional rings. Removal of this restriction would permit the representation of core incoherence. Hence, this E0EC representation may have the opposite problem of the BOEC case, i.e. , here the overall core representation is too coherent rather than too incoherent,* 4 and a LOF-induced FCI is far less likely.

Figures 5-5 to 5-7 give the fuel worth, the sodium void worth, and the steel worth for E0EC core. In this case, removal of sodium from all of the SAS channel volune where the voiding reactivity is positive gives a 3.5$ reactivi ty ef fect. The Dopplar coefficient breakdown is given in Figure 5-17 and Table 5-4.

O

• 0f course, both cases suffer from unrealistic coherence effects resulting from representing assembly groupings by single pins.

5-4

The temperature profiles for the peak Channel 8 are shown in Figure 5-18. Like the 80EC case, the peak fuel temperatures are calculated as around 2000 C and a large fuel-clad gap temperature drop exists, which from Figure 5-19 can be estimated as around 400 C. Examination of the gap width curves (Figure 5-20) indicates a calculated gap of slightly less than 0.001 cm. A gap conductance of slightly greater than 0.4 watts /cm *C or 700 Btu /(hr - ft - F) was estimated for this condition. This explains the large temperature drop, but it does not indicate how realistic is the result.

Actually, the result probably in producing fuel temperatures that are too high, since the restructuring isotherms are too far out radially in what is conventionally thought of as medium and low power fuel, e.g., the restructuring pattern for Channel 8 with a peak power of around 320 watts /cm (s10.5 kw/ft, hot dimensions) is shown in Figure 5-21. This condition would be conservative, since more restructuring implies increased steady-state fission gas release, more molten fuel available at pin failure in TOP situations, lower transient Doppler and axial expansion feedbacks, and shorter transient times before fuel melting. The final curve for this section is the fission gas retention curve, Figure 5-22. This indicates that more gas is retained in regions of highly unrestructured fuel concentrations, and that at high burnups gas densities tend to saturate so that all unrestructured fuel has roughly the same amount of retained fission gas.

The temperature drop across the gap in Fiaure 5-12 is greater than the temperature drop across the gap in Figure 5-19 because the gap conductance 2

(W/cm C) is larger in the 80EC Channel 1 fresh pin than in the E0EC Channel 8 irradiated pin.

As a result of the low burnup (10 full power days) in 80EC Channel 1 the dilution, DI, defined as DI _

M les of He Moles of He + nolm of fission oas is approxim ttly 31;, chien wear that only 91 of the gas in the fuel-cladding gap is fission product gas. H uv.e v e r , as a result af the hich burnup (274 full power days) :n LOLC Channel 3 the dilution is approximately 150, which means that 35 of tht n:, " th' t uel-claddinq qap is fission product uas. Fission 54

product gas is predominantly xenon (Xe), which has a much lower themal conductivity than helium. The relationship between the dilution, DI, and the thermal conductivity (Kg ) of the gas in the gap 1s

=

k g 0.0002 (15)DI The thermal conductivity (k g

) is a factor in the equation which is used to compute the gap conductance. This equation is given in Section 4.

It is observed that the gap conductance equation is a function of the radial gap and the thermal conductivity of the gas in the gap. Hence the gap conductance depends on the relative values of these two variables; neither variable clearly predominates the o.ther over the entire relevant range of the equation.

O O

5-6

TABLE 5-1 BOEC NEUTRONICS COMPARISON Design Calculations FX2 Caiculations SAS Channel Normalized No nnali zed Normalized Nornalized

(= s.a.) Burnup Power Power / Flow Power Power / Flow c,

1 (6) F 1.335 1.165 1.271 1.109 2 (18) I 1.173 1.024 1.157 1.010 3 (6) F 1.304 1.138 1.261 1.100 4 (18) I 1.050 0.984 1.049 0.984 5 (18) F 1.110 1.040 1.104 1.034 6 (36) I 0.896 0.938 0.865 0.906 7 (18) F 1.106 1.040 1.107 1.041 8 (24) I 0.997 0.934 1.012 0.~948 9 (36) F 0.958 1.132 1.070 1.265 10 (36) 1 0.81 8 0.956 0.795 0.929 F - Fresh fuel I -

Irradiated fuel

TABLE 5-2 DOPPLER COEFFICIENTS BY CHANNEL FOR THE B0EC CORE DopplerConstant(Th)

Channel Sodium in Sodium Out 1 -0.000304 -0.000183 2 -0.000920 -0.000546 3 -0.000343 -0.000215 4 -0.000795 -0.000487 5 -0.000679 -0.000398 6 -0.000759 -0.000495 7 -0.000347 -0.000221 8 -0.000403 -0.000248 9 -0.000278 -0.000175 h 10 -0.000398 -0.000289 Total -0.005226 -0.003257 5-8

TABLE 5-3 E0EC t4EUTRONICS COMPARISON Design Calculations FX2 Calculations SAS Normalized flo nnal i zed Normalized Normalized Channel No. SA Power Powe r/ Flow Power Power / Flow 1 6 1.211 1.056 1.237 1.079 2 12 1.036 0.904 1.086 0.947 V' 3 12 1.125 0.981 e 1.137 0.992 4 18 0.984 0.922 1.017 0.953 5 18 1.115 1.045 1.099 1.030 6 18 0.956 0.945 0.976 0.965 7 24 0.920 1.023 0.922 1.025 8 12 1.260 1.099 1.24 0 1.081 9 30 '.006 0.943 1.031 0.949 10 48 0.884 1.070 0.851 1.030

TABLE 5-4 h

D0PPLER COEFFICIENTS BY CHANNEL FOR THE E0EC CURE Doppler Coefficient (T h)

Channel Sodium In Sodium Out 1 -0.000348 -0.000218 2 -0.000558 -0.000344 3 -0.000595 -0.000382 4 -0.000764 -0.000485 5 -0.000762 -0.000459 6 -0.000661 -0.000414 7 -0.000753 -0.000481 8 -0.000303 -0.000191

-0.000579 -0.000364 O

9 10 -0.000617 -0.000435 Total -0.005940 -0.003773 O

5-10

CROSS SECTIONS TRANSFER OF MODEL VOLUME FRAcil0NS TO h

CALCUL ATl0NS FX2 (R Z) GRID USING HOCUS (SUBSitTUTION FOR TSORIV IN SAS) i r CALCULATE NEW POWER SHAPES CONSISTENT Wilil '/98 UME FR ACTIONS WITH FX2 U

CONVERT NEW POWER SHAPES BACK TO THE SAS GRl0 WITH POCUS U

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NO U

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Al FUEL, SODIUM, AND STEEL MASS PERTURBAil0NS

8) FUEL TEMPER ATURE PERTURB ATION (FOR 5001UM IN DOPPLER CDEFFICIENTS)

C) FUEL TEMPERATURE PERTURBATION FOR SODIUM OUT FLUXES (FOR S001UM OUT DOPPLER COEFFICIENTS)

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5-32

6. Initiating Phase Analysis of Unprotected Transient Overpower (TOP) 6.1 TOP in E0EC Configuration at Full Power 6.1.1 Base Case Ramp Rate of 10Jlsec This case is a best-estimate analysis of a reactivity insertion accident without scram at the end of an equilibrium cycle in CRBRP, The reactivity insertion selected for evaluation here is that corresponding to a 3.205 rod continuous withdrawal at a reactivity insertion rate of 10 cents per second, which is four tines higher than the design maximum of 2.4 cents per second.

The IOC/sec ramp rate was used in these analyses as a representative low ramp rate approriate for parametric analysis. Analyses are included to show that this assumption is valid.

The initial reactor power increase is moderated by the inherent feedbacks such that at initial fuel failure (12 seconds) the power is 3.6 times nominal and the net reactivity is 36 cents supercritical. Table 6-1 shows the fuel pin midplane conditions 250 msec prior ta failure. The damage severity caused by the fuel and clad heatup and fission gas loading is also indicated in the table at failure of Channel 8, at 0.M of the core height. Channel S failure follows just 24 msec later at 0.76 of the core height. Fuel motions to the failure sites followed by expulsion and fuel-coolant interactions rapidly tenninate the nuclear excursion with approximately -65 of fuel motion re-activity.

Experimental data (EBR-II and TREAT irradiations) are available on the behavior of irradiated fuel specimens which match the microstructural char-acter of Channels 5 and 8 (Ref. 46). An empirical correlation of fuel rod damage based in part upon fission gas loading of cladding during thermal up-set has reasonably normal;2ed TREAT data for such fuel (Ref. 53) and supports the mechanistic approach used to predict fuel pin failure (see Section 6.l.3.2).

The power and reactivity traces for this event, to the time of SAS/FCI termination, are shown in Figure 6-1. The driving reactivity sources of channel dependent sodium voiding and fuel notions are shcwn in Figures 6-2 and 6-3.

The FCI zone development for Channel 8 is shown in Figure 6-4. Flow reversal develops due to fission gas and sodium vapor pressures in the FCI zone.

6-1

Consensation of sodium vapor and expansion of the FCI zone reduces these g pressures, allowing the lower interface to return. A vapor bubble then forms below the FCI zone and expands. The calculation is terminated when the vapor bubble tries to combine with the FCI zone due to SAS coolant dynamics modeling 1imi tations.

The fuel and cladding temperatures at the fuel centerline are shown in Figure 6-5. Fuel centerline melting occurs at about 8 sec and the core midplane melt fraction at failure is 40%. Pin centerline melting actually extends from the top of the lower blanket to the bottom of the upper blanket at pin failure. The radial melt fraction (fuel solidus isotherm) at the failure location was 28%. The flow reversal induced by the fuel-coolant interaction extends the FCI zone interface below the core midplane, temprarily causing a temperature transient in the cladding. The cladding near the top of the U

core is calculated to reach 1300 C even though the FCI model ignores direct contact and heat transfer from fuel in the coolant channel with cladding.

Hence, development of fuel-cladding blockages cannot be excluded although the neglect of assembly radial incoherence and possible internal pin cavity over-pressurization before failure are definite pessimistic aspects of the h calculation.

To provide further insight into the TOP phenomena, PLUTO calculations were done on both Channels 8 and S. The reactivity traces from PLUTO for Channel 8 are shown in Figure 6-6. PLUTO predicts slightly more than -25 in shutdown reactivity which is not as optimistic as the SAS/FCI result of

-3$ (shown in Figure 6-3) but combined with a similar negative reactivity from Channel 5, PLUTO calculates neutronic shutdown. PLUTO tends to predict that a considerable amount of fuel first moves inside the pin toward the failure location, which is followed by upward motion of fuel in the coolant channel. However, since the peak of the total fuel density curve monoton-ically increases, and since PLUTO does not possess an algorithm for fuel plugging, this calculation cannot support fuel sweepout as represented in S AS/ FCI .

Comparison of SAS/FCI results with PLUTO yields other observations with respect to the assumptions employed to calculate FCI's. Figure 6-7 shows pressure histories as computed by both codes. In SAS/FCI the three pin failure h group cavities depressurize as governed by the pin ejection orifice model.

6-2

Af ter suf ficient fuel has been ejected into the channel and the ~.0 msec fragmentation and mixing time is over, sodium vapor pressures are produced which peak at 40 atm and thus cause flow reversal. The sodium sapor is slowly condensed and the FCI zone pr essure drops significantly or.ce the upper interface blows out of the channel at about /5 msec. PLUTO bases fuel ejection on equilibrating the pin pressure with the coolant channel pressure at the point of pin rupture. Due to the relatively high ratio of fission gas mass to molten fuel mass within the pin cavity, t ission gas is responsible for most of the pressurization of the coolant channel. However, the amount of free fission gas available to the overall plUf0 calculation is a constant.

The ejection of fission gas from the pin is assumed to instantaneously lower the gas temperature f rom the cavity fuel temperature to the far lower mass-averaged temperature of the sodium and fuel components in the interaction zone thus decreasing the gas pressure. The toolant channel void volume rapidly increases due to the compressible treatment of the coolant. Hence, the pressures in Pl.Ul0 rapdily dec rease to stabilize around the inlet pressure of 9 atm. The coolant accelerations in pl uTO occur more rapidly than SAS/FCI due to the compressible treatment of liquid sodium in PLUTO. However, the driving pressures and ultimate velocities are higher in SAS/fCI due to more efficient contact and hence transfer of energy between fuel and coolant. In general the comparison between PLUTU and SAS/fCI suggests that as the analytic treatment of fuel-coolant interactions li. ore closely models experimental results, the ef fects of sodium vapor pressures produced by a fuel-coolant interaction will probably become more benign.

6.1.1.1 SASBLOK Core Re.gion Analysis The SASBLOK evaluation was initiated at 11.77 sec just prior to failure in the high power assemblies (G). The simulation covered the FCI tine interval until the SAS3A system was unable to continue or, 258 milliseconds. After 258 msec, the fission gas bubbles were suitched back to represent the sodium vapor which actually was present in the FCI mnes. The future description of these vapor regions was determined by the narmal SAS coolant dynamics routines. Power decreases to 0.79 ano 0.725 were introduced to represent the core fuel material loss in 5 and 8, r espectively. Figure ti-8 provides a comparison between the FCI solution and the SASBLOK simulation of the net reactivity, inlet plenum pressure and Channel 8 midplane fuel melt fraction during the FCI time scale, as inditated in the fi qu ' t , agreement between the two solutions is reasunable, ti-3

Since the amount of fuel expelled is quite large in this case, the approach employed was to study the response of the reactor and damaged assemblies to a range of potential blockage effects so that a best estimate judgment could be made on the viability of continued core region cooling for the expected accident progression path to be followed (see Figure 3-7).

The original SASBLOK calculations used a relationship between physical flow blockages and an equivalent loss coefficient determined from a simple parallel flow network. With this basis equivalent loss coef ficients of 200 to 2000 were used to represent local areal blockages of 60 to 90 percent of the flow chanrel. More detailed analyses and experimental comparisions have been performed subsequently which indicated that the simple parallel flow network grossly overestimated the flow resistance of such blockages. These subsequent analyses (described in Appendix A and su:nnarized in Figure A-1) indicate that loss coefficients of 200 to 2000 are more representative of areal blockages of 87 to 97 percent. For consistancy the text reflects these more appropriate values of blockage equivalency. Thus, the SASBLOX calcula-tions presented are believed to provide very conservative estimates of the potential for core region neltdown.

The eighteen fuel assemblies represented as SAS Channel 5* were deter- $

mined to be coolable for the range of blockages introduced. Figures 6-9 through 6-13 show the reactor power and net reactivity, simulatcd FCI bubble, nonnalized flow response and midplane thermal responses for a blockage coef-ficient of 800 (note: Figure 6-9 extends the original SAS/FCI solution of Figure 6-2). At an equivalent areal blockage of 97 percent of the flow area, liquid sodium flow is reestablished in about 400 msec at 15 percent of rated.

However, the stored energy in the fuel pin and coolant at this power to flow level is sufficient to reinitiate boiling in the core at about 1.40 seconds af ter failure. Since a large flow obstruction exists above the core, the boiling which takes place is at high pressure (s 9 atm). Although some temp-orary cladding dryout occurs, the decreasing power / flow ratio and high inlet pressure result in 15 percent of rated flow being reestablished at approxi-mately 2.45 seconds past failure. For longer times, the flow in the core region is well subcooled and stable. Figure 6-14 through 6-16 show the two-phase history, nonnalized flow behavior and midplane fuel thermal conditions for Channel 5 with a blockage loss coefficient of 2000.

O

• 7 kw/ft average and 38 GWD/T burnup.

6-4

The twelve peak power assemblies represented as SAS Channel 8 exhibits a greater range of behavior for the blockages studied. At a loss coefficient of 200 (87? planar blockage), boiling continues for about 360 msec after the failure with single phase sodium flow reestablished at about 39 percent of rated flow with the reactor well subcritical. When the loss coefficient is raised to 800, boiling continues for less than 400 msec af ter the failure and flow is reestablished at 21 percent of rated flow. Sodium boiling is re-initiated at about 1.25 seconds af ter failure. This occurs at a lower per-cent of blockage with respect to Channel 5 due to the higher linear power and power / flow ratio in Channel 8. Again, the liquid flow reestablishes at 21 percent of rated flow some 3 seconds af ter failure. For greater times, the thermal-hydraulic situation is stable as indicated by figures 6-17 through 6-20.

Increasing the blockage futher to an equivalent 97 percent of the cross-sectional area (loss coefficient - 2000) results in the possible crossover to clad melting. The calculation was only carried out to 3.52 seconds past failure since the high pressure two-phase solution encountered numeric prob-lems and the results seemed marginal. Although the flow might recover even in this severe blockage (the two-phase dynamics are given in Figura 6-21) a general result is established. That is, large downstream flow disturbances (equivalent to approximately >97 percent of the cross-sectional area of the flow) must occur before the damaged core region carinot be cooled. This con-clusion, although based on no in-core blockage, would not rule out some degree of in-core blockages as long as they are reasonably small. A quantitative estimate of " reasonably small" is provided in the discussion to follow.

Confirmation of the estimates will be possible once the experiments described in Section 3.2.7 are completed and more calculations are pertonred on in-core, as well as, downstream blockages.

When the inherent, two-dimensional power-to-flow incoherencies withit Channel 8 fuel assemblies (i.e. , pin failure tines , locations and fuel ejec-tions) were considered along with the abnve indicated high degree of planar blockages required to prevent stable flow heat reuoval from the damagcd core region, the conclusion was that the probability of adequate core heat removal is high.

6-5

Since Channel b was seen to be coolable and the reactor is still well subcritical, long-term heat removal is available for the E0EC-TOP event in CRBRP. The last point to consider is the final configuration and deposition of the fuel which was expelled into the coolant channels.

6.1.1.2 SASBLOK Above Core Blockage Analysis This section f.ocuses upon the downstream fuel blockage, assuming that stable, quasi-steady reduced sodium flow exists through the damaged fuel assemblies. Information is sought on (1) the representation of blockage hydraulic effects within SAS, (2) configurations of blockages which are coolable (defined as no fuel mel ting) for a range of flow and power.

Once a fuel-coolant interaction has occurred and the fuel has been swept out of the core region, the possibility for the ejected fuel to become lodged in the fission gas plenum region outlet exists due to particulate agglomeration or plateout. If blocking does not occur within these regions, the ejected fuel is transported into the upper internals structure and then into the vessel outlet plenum.

To perform calculations of the effect of blockages upon the reactor and $

the blocked region, the amount and the composition of the actual blockage were ascertained. For these calculations, the amount of fuel available for blockage was obtained from the SAS/FCI results for the E0EC-TOP base case.

Figure 6-22 shows the amount of fuel which has been injected into the coolant flow stream as a function of time. The curves depict the total amount of fuel ejected from the pin, the proportion of the ejected fuel that is in the active core region, and the amount of fuel that has been transported beyond the active core region in the SAS/FCI solution. As previously described, SAS Channels 5 and 8 experienced FCI's. Channel 8 failed at 12.000 seconds and Channel 5 at 12.024 seconds; both in a non-autocatalytic reactivity loca-tion. By 12.250 seconds all of the ejected fuel has been swept out of the active core region. Channel 8 ejected a total of 48 grams per fuel pin while 5 ejected 37 grams per fuel pin. Channel 5 represents eighteen assemblies and Channel 8 represents twelve assemblies, thus producing a total ejected fuel mass of 145 kg and 125 kg, respectively. These amounts of fuel were subse-quently used to determine the core hydraulic disturbance due to blockage and heat addition within the blocked region. The composition of the blockage was assumed to be either a porous particle bed with liquid sodium flowing through it, a solid fuel blockage, or a composite blockage composed of solid fuel, 6-6

stagnant sodium vapor, fission gas, and stainless steel cladding. These configurations were selected as the most likely to occur during a reactivity insertion event.

Using the SAS model with blockage loss coef ficients as described in Appendix A, flow and temperature and pressure through the porous blockages were calculated. By selecting a range of loss coefficients, the maximum blockage size for non-boiling sodlum was calculated. Three loss coefficients were selected for use in analyses to give a range of core flow conditions when used in the SAS calculation. As for the previous calculations, selected loss coefficient values were chosen to correspond to singular areal cross section blockages of 88, 95 and 97%.

The results of the SAS calculations, which are important to an analysis of the blockage are the pressure profile, coolant temperature and mass flow up and downstream of the blockage. Since the SAS code does not currently calculate the temperature rise through the blockage, parametric calculations were made for various masses of fuel. Figure 6-23 shows the temperature rise across a blockage with 504 void fraction as a function of mass ejected per pin and power at the blockage location. The relationship among these three para-meters is valid for single phase liquid flew through and around the blockage.

Significant temperature rises can occur at high power levels; howcVer, at decay heat levels typical of blockages external to the core neutron flux, temperature rises of less than 150 C occur. Results of these parameter cal-culations and SAS runs are presented in Figure 6-24 for 951 blockage in SAS Channels 5 and 8. The decay power levels and coolant inlet and exit tempera-tures for the blockage have been calculated and compared to saturation temp-eratures. The coolant inlet temperature to the blockage does not exceed the saturation temperature; however, the resulting temperature rise and pressure loss through the t; lockage produces coolant temperatures that exceed saturation tempe ratures . Thus, two-phase flow could be expected for an areal blockage of 95%. It is of interest to note that although tne analysis is not valid for the perind of time when two-phase flow exists, single-phase liquid flow is reestablished after 22 seconds based on the SAS temperature solution. The addi-tional flow resistance generated by a two-phase condition in the blockage is small compared to the blockage ef fect and would have a small effect upon the solution.

A comparison of the temperature rise across the blockage as a function of the hydraulic resistance allcwed an extrapolation to lower values which showed that Channel 5 would pemit a maximum blockage of 37; and still have single-phase flow throuyn the blockage while Channel 8 would permit an 80% blockage.

6-7

Calculations were perforrmd to determine whether melting of the particle h bed would occur at coolant temperatures below the saturatien temperature.

Figure A-2 depicts the spherical particle diameter that produces a center melting terrperature of 2767 C for various coolant temperatures and power levels. Since these maximum spherical diameters greatli; exceed particle bed values, melting should not occur due to heat conduction within the solid fuel.

In summary, for porous blockages that have flow through the blockage and configurations which maintain core geometry, the maximum blockage that can be liquid cooled is an 80's areal blockage.

Solid blockages have been postulated to occur where core geometry has not been maintained due to structural failure, above the core where liquid fuel has solidified, or when initially porous blockages have melted and then resolidified to form a solid mass of material. It is of interest to deter-mine the maximum sizes of the blockages that can be maintained in a coolable state. In the previcus section, the maximum solid fuel spherical size that can be maintained without melting was calculated. g Figure A-2 can also be used to evaluate individual solid spherical blockages exceeding core flow geometry. The curve shows that at 8% decay power levels, a spherical blockage on the order of 3 cm in diameter can be cooled. This diameter represents a fuel assembly frontal area blockage of 7~.

Similar calculations have been done for a cylindrical configuration where the centerline of the fuel was maintained at 2767 C, the melting tempera-ture of the f uel . Curve #1 of Figure A-3 shows the diameter that produces centerline melting with the outer surface cooled by liquid sodium. At a decay heat generation level of M of steady-state power, a cylindrical blockage dia-meter of 2.5 cm can be cooled. This represents an approximate frontal area blockage of 11 pins or 5% of a fuel assembly. Curve #2 represents the same Calculation, however, the thermal conductivity of the fuel was replaced by an effective conductivity based upon the volume percentage of material in the fission gas region of the assembly. This represents the case where the previous porous blockage had vaporized the liquid sodium and clad has melted and formed a g 6-8

composite blockage. This case shows that at 8% power a blockage diameter of 10 cm would be cooled without melting of the blockage. This diameter repre-sents a frontal area blockage of approximately 797. The resulting increase in diameter over the solid fuel diameter primarily resulted from the increase in effective thermal conductivity due to the addition of the cladding. Thus, for solid or non-porous blockages, the maximum frontal area of a fuel assembly that can be blocked and maintained at Bi power without melting is between 5 and 794 depending upon the blockage composition. This would indi-cate that temporary, two-phase condi tions can be tolerated within the blockage.

If the blockage area exceeds the values calculated in the previous sections, the blockage configuration cannot be maintained in a coolable solid form, and the possibility of melting and relocation exists. This relocation can be postulated to take place in several modes depending upon the forces dCling upon the blockdge. The forces that Would act on the blockage are gravity forces and shear forces due to the coolant flow. These forces, if large enough, will tend to relocate the blockage to more stable configurations.

To analyze these relocations, some melting progression must be calculated or postulated. Since the heat source is primarily due to internal generation, the melting front will propagate from the center outward to the surface. If there is any cooling flow, the highest cooling will be at the front or leading edge while the rear or trailing edge will be the hottest, thus the melt front will reach the rear or downstream area first. It is likely that the shear forces will tend to arag the melted fuel further downstream to a -smaller and coolable configuration and to reduce the frontal area of the blockage. If the melting front tends to be uniform, it is then likely that the blockage will tend to " flatten" due to pressure forces similar to a falling liquid droplet.

This configuration does not appear to be a stable configuration because event-ually the high pressure forces will break the body up into smaller coolable blockages or move the blockage further downstream until it is e3cted from the fuel assembly region or restricted due to structural res.istance. The former relocation seems to be the more probable although both should eventually reach a stable coolable configuration.

If coolant flow does not exist, and hence fluid forces on the melting blockage are absent, the molten fuel will descend toward a lower location 6-9

due to gravity. The rate at which the molten fuel moves downward has been estimated from a simplified falling film analysis, along with a molten fuel $

penetration analysis to determine freezing distances. The magnitude of molten fuel droplets that could form and fall due to gravity has been estimated.

The falling film analysis assumed the film thickness was half the minimum distance between fuel pins and the film surface was the outer surface 2

of the fuel pin. A mass velocity of 244 gm/cm sec with a corresponding linear velocity of 28 cm/sec was calculated. These velocities indicate that for the 48 gm/ pin calculated in the SAS E0EC base case analysis, the total mass of ejected material would take less than 2 seconds to be relocated from some blocked position. Although this analysis has shown relatively high flow rates, these rates cannot transport fuel over large distanced due to the solidification of the fuel. Freezing would limit the downward travel of the fuel and slow the rate of relocation. Estimates of freezing distances were calculated using the methods in Appendix A. Using an initial and melting temperature of 2767U C and a clad temperature of 1000 C, a freezing length of 8 cm was calculated. This indicates that the downward movement of fuel will be of the flow-freeze type which will reduce the downward rate of motion. A calculation of the magnitude of molten fuel droplets that can be formed and fall due to gravity was performed. By equating the weight of the droplet of fuel to the surface tension that keeps the droplet from falling, a diameter of 0.63 cm with a corresponding mass of 1.l gm was calculated.

This indicates that relatively small droplets will be formed.

It can be generally concluded from these analysis that if the solid blockage does not remdn in place, relocation of the melting fuel due to gravity should be relatively slow and in small masses.

6.1.2 Effects of Ramp Rate Uncertainty The followir.g additional ramp rate studies were performed to determine the effect of ramp rate on the accident event scenario.

O 6-10

6.1.2.1 Design Rang Rate of 2.4Hsec The base TOP case considered used a reactivity ramp of four times the design maximum control rod withdrawal rate of 2.4(/sec. Hence, an investigation of the consequences of a 2.4c/sec. design basis ramp was conducted. The power and reactivity traces are shown in Figure 6-25.

Since a long time was available (40 seconds) over which fission gas would be released from the fuel, 70% of the released gas was assumed to escape to the fission gas plenum. Only 30% of the released gas w s assumed to pressurize the internal pin cavity. This leads to a higher melt fraction than the base case at pin failure (150% at the core midplane).

Figure 6-26 illustrates the fuel pin temperatures and melt fractions during the prolonged pin heatup stage. The length of time that fuel is molten inside the pin can lead to uncertainty on fuel relocation within the pin before failure, although the small amount of free space in the central cavity at failure, 0.16 cm , indicates that the consequences of such fuel relocation would not significantly change the results. (The roughness in the melt fraction curve in Figure 6-26 is due to the finite node treatment of the small radial displacement between the fuel liquidus and solidus in this quasi-steady state case).

The lower ramp rate and increased tin;e to failure appears to increase core incoherence, as no other channels were predicted to fail in this case.

Since Channel 8, by itself, may be insuf ficient to guarantee neutronic shutdown (since SAS/FCI may be overly optimistic with respect to negative fuel reactivity), additional pins may fail in other assemblies. The SASBLOX calculation to simulate these failures was not done since the base case description is considered adequate to describe the core response.

The increase in the ratio of molten fuel mass to fission gas mass at pin failure mildly increases the energetics of the calculated fuel-coolant interaction. Figure 6-27 on the voiding dynamics and Figure 6-28 on pin and FCI zone pressures tend to demonstrate this. In comparison to the base case, the Icwer interf ace proceeds downward another 7 cm before flow recovery, and the peak FCI zone pressures are computed to be about 7 atm higher. The current analysis thus suggests a slightly greater tendency of fuel to plug following neutronic shutdown.

6-11

6.1.2.2 htreme Ramp Rate of 50c/sec A 50c/sec ramp rate without scram is included since it allows for a @

wide range of uncertainties and other initiating nechanisms which could affect the maximum insertion rate. The power and reactivity traces for this case are shown in Figure 6-29. The channel dependent voiding and fuel motion reactivity plots are given in Figures 6-30 and 6-31. Assuming scram does not occur, Channe.15 fails at 3.12 sec into the transient near the top of the core. Channels 1 and 8 fail almost simultaneously at about 9 msec after the initial failure. The final failure occurs in Channel 10 at 109 msec af ter the initial failure.

The fuel and clad temperatures at the core centerline of Channel 5 are shown in Figure 6-32. Fuel centerline melting begins at 2,3 sec, The core midplane melt fraction at failure is approximately 35 percent, The FCI zone development and sodium flow for channel 5 is shown in Figure 6-33. Some flow reversal occurs due to the fission gas and sodium vapor pressures. The clad temperature near the top of the core is calculated to reach 1100 C. Since fuel-clad heat transfer and plateout are not currently modeled, the development of fuel-cladding blockages cannot be excluded. This $

was also true in the E0EC-TOP base case of 10c/sec.

The calculation is teminated when a vapor bubble formed below the FCI zone tries to combine with the FCI zone due to previously mentioned SAS modeling 1 imitations.

The normalized power has decreased to 0.30 and fuel motion reactivity of approximately -105 is sufficient to insure shutdown if major fuel-cladding blockages do not develop.

6.1.2.3 E0EC TOP: 3$/sec Ramp Rate and Greater A study of these higher ramp rates was conducted to determine if a different accident sequence would occur at higher ramp rates.

The normalized power and net reactivity traces for the 3$/sec ramp rate case are given in Figure 6-34. Initial pin failure occurs at 0.637 sec in Channel 8 at an axial location 22 cm above the core midplane. Channel 1 fails 4 msec later at 22 cm above the midplane, and Channel 5 fails 5 msec after the initial failure at 14 cm above the midplane. The fuel and cladding g 6-12

thermal conditions at the core midplane in Channel 5 are shown in figure 6-35.

Negative fuel motion reactivity in Channels B, I and 5 causes the power and net reactivity to decrease from 33.5 and 0.905 at the time that Channel 8 fails to 15.7 and 0./75 at 0.6534 seconds (see Figure 6-34). The power and net reactivity then begin an exponential increase, which brings the reactor superprompt critical, and results in the terminat!)n of the transient by means of a hydrodynamic disassembly.

The reactivity increase results f rom the continued addition of positi

voiding reactivity due to expanding fuel-coolant interaction zones (especially Channel 5) overcoming the negative fuel iration reactivity addition. This may be observed frau the channel dependent coolant and fuel motion reactivity traces given in figures 6-36 and 6-37. lhe development of the FCi zone in Channel 5 is shown in Figure 6-38. The failures became autocatalytic at this time and the reactor is driven superprompt critical by the sodium voiding in the failed thannels. Additional negative fuel motion reactivity introduced by the failure of Channel 3 at 22 cm above the core midplane at 0.65 sec is not sufficient to reverse the trend of the accident. Shortly thereaf ter, at 0.66 sec, the initial cunditions necessary to begin hydro-dynamic disassembly calculations with the VENUS II code arr ;atisfied.

For ramp rates of 3$ per sec and greater prompt criticality was achieved and sustained u? to the termination of the calculations, therefore the minimum ramp rate required to achieve and sustain prompt criticality in an E0EC core is between 50c/sec and 3$/sec.

6.1.3 Effects of Phenomenological Uncertainties 6.1.3.1 Fission Gas Release flodels The E0EC base case used the Gruber transient fission gas release corre-lation for all pins. A study was conducted using the Smith fission gas release model (based upon gas release during n.el ting, Ref. 7) to examine accident scenario dif ferences which may result from di f ferences in the two models. The power and reactivity are reasonably similar. Initial pin failures occurs in Channel 8 with both models. The Smith model fails approxi-mately 0.8 sec later than the Gruber model with a slightly lower pin pressure (320 vs 380 atm), but a slightly higher clad temperature (900 vs 860 C) and power (4.0 vs 3.6). Initial pin failure occurreu at the same axial location 6-13

in both cases. The Gruber model had three times as much fission gas mass but less molten fuel mass, resulting in a milder FCI. In the base case h Channel 5 fails 20 msec af ter Channel 8. With the Smith fission gas release model, Channel 1 fails approximately 60 msec after Channel 8. It was concluded from the reactivity predictions that sufficient negative reactivity is available from both fuel motion within the pins and in the coolant channels to assure neutronic shutdown and similar consequences.

6.1.3.2 HEDL Empirical Fuel Pin Failure Criteria The Hanford Engineering Development Laboratory (HEDL) is developing an empirical correlation (based upon TREAT experiments) of fuel pin failures during TOP events (Ref. 53). This method was adopted by the FFTF Project as the fundamental approach to failure prediction and employed in the safety review of TOP HCDAs (Ref. 54).

The correct application of the HEDL empirical relation defined in the correlation requires the usage of the self-consistent methodology developed at HEDL. The damage parameter calculations presented herein were performed by HEDL at the request of the CRBRP Project and based upon the status of the correlation as represented by Ref. 54 h Only the 504/sec case was analyzed since the correlated experimental data base was limited to ramps between 50t/sec and 3$/sec. Use of the correlation for ramps of less than 50t/sec cannot presently be justified.

By employing SAS3A power histories (with failure suppressed), the HEDL methodology was applied to predict fuel rod thermal history, the damage para-meter value and to estimate failure conditions.

Table 6-2 summarizes the SAS calculated 50d/sec pin failure sequence, and also presents failure predictions for Channel E and 8. The damage parameter was not calculated for Channel 1 but <:ould be expected to behave in the same manner as 8. The 1EDL correlation predicted that Channel 5 would fail first at 2.65 sec, % reas the SAS3A burst pressure criterion predicts initial failure in the same channel at 3.12 seconds. The channel is predicted to fail at slightly higher axial locations in the core using the damage parameter. The earlier failure time predicted by the HEDL correlation O

6-14

results in less molten fuel available for a fuel-coolant interaction. Hence, a less energetic FCI is expected in Channel 5, with less fuel motion negative reactivity due primarily to the smaller amount of rolten fuel. This same conclusion is also applicable to Channel 8.

In general the HEDL correlation was found to predict earlier failure times, smaller melt fractions, and similar axial failure elevations in the core. Although a complete analysis of the 50c/sec transient using the HEDL correlation was not performed, the energetics are judged to be on the same order of magnitude as predicted by the SAS3A analysis.

6.1.3.3 Forced Midolane Failure at 2.4c/sec This case differs from the 2.4 cents per second previous case in that the axial failure location is specified to be at the core midplane. The power and reactivity traces are given in Figure 6-39. Initial pin failure occurs in Channel 8 at 42.5 seconds into the transient with a net reactivity of 17.3 cents and normalized power of 2.98. The fuel motion and coolant ,

reactivity components are shown in Figures 6-40 and 6-41; and the growth of the FCI zone in Channel 8 is shown in Figure 6-42. Due to internal fuel motion toward the midplane failure location, the normalized power and fuel motion positive reactivity reach their maximum values of 6.87 and 37 cents, respectively, at 24 msec af ter failure. The fuel motion reactivity then decreases as fuel in the FCI zone moves upward in the coolant channel as calculated by SAS/FCI.

At 55 msec af ter the initial failure Channel 1 is predicted to fail.

The normalized power has decreased to 3.78 and the fuel motion positive reactivity has decreased to 7.3 cents. The FCI zone growth is shown in Figure 6-42. As the FCI zones in Channels 1 and 8 expand upward the coolant voiding reactivity increases, resulting in an increase in the normalized power to a value of 4.16 at 72 msec af ter the initial . failure. At approx-imately 74 msec, the lower FCI zone interface in Channel 8 began moving 6-15

upward, as shown in Figure 6-42. This results in a large negative fuel g motion reactivity adcition as the fuel is carried upward in the channel.

At 96 msec, the coolant voiding reactivity reaches a nayimum value of 37 cents. The fuel motion reactivity is -90 cents, the net reactivity is -45 cents, and the normalized power has decreased to 1.80.

At approximately 250 msec, the pressure dif ferential driving the fuel and fission gas from the Channel 8 pin cavity into the FCI zone had dropped to less than 0.5 atm, and fuel ejection was tenninated. The FCI zone in Channel 8 proceeded to move upward as shown in Figure 6-42.

Local coolant boiling is seen to occur below the upward moving FCI zone as the liquid sodium contacts the hot cladding.

At 370 msec, the reactor was 4.62$ subcritical, due primarily to the fuel motion reactivity of -4.93$. The normalized power was 0.49 and the net reactivity ramp rate was -1.9$/sec. The reactivity remaining to be inserted (assuming that control rod withdrawal continues) was 2.17$.

With allowance for Doppler, sodium void and expansion effects the reactor will be 1.84$ subcritical at the termination of the rod withdrawal.

Therefore, the calculation of this case was terminated at 370 msec.

g The effects of fuel blockages in the failed channels can be assesscd by comparison with the SASBLOK E0EC TOP 10?/sec base case calculations.

These calculations indicated that for a 887 areal blockage, sodium flow would stabilize in Channel 8 at 39% of the steady state value following some local coolant boiling af ter the FCI zone was swept out of the channel.

Channel I was not analyzed in th; SASBLOK study since it did not fail. How-ever, since the steady state power in Channel I was slightly less than in Channel 8 dnd a comparable amount of molten plus solid fuel was available in the pin cavity for ejection into the FCI zone (62.1 versus 64.6 grams) the subsequent sweepout behavior of Channel 1 should be similar to Channel 8.

6.1.3.4 Forced Midplane Failure at 10t/sec This case represents a best-estimate scenario of events when the axial failure location is forced to occur at the core midplane. It must be emphasized O

6-16

that fuel failure models predict that failure occurs well above the midplane.

The power and net reactivity traces of the initiating phase of the accident are given in Figure 6-43. Pin failure is calculated to occur first in Channel 8 at approximately 12.3 seconds into the transient.

Figure 6-44 shows the fuel and clad thermal conditions at the midplane failure location. Molten fuel in the pin moves toward the midplane failure location, where the fuel-coolant interaction in the channel causes sodium voiding.

The c',nnel voiding and coolant flow profiles are shown in Figure 6-45.

These two events result in positive reactivity feedback from the displacement of both fuel and liquid sodium. The fuel and coolant reactivities by channel are shown in Figure 6 46 and Figure 6-47. Channels 1, 5 and 10 fail at approximately 23, 23 and 33 msec af ter the initial failure, respect-ively. When Channel 10 fails, the criteria for disassembly are satisfied and the calculations are switched to a disassembly phase analysis using the VEf4US code. At this time the reactor is superprompt critical with a net reactivity of 1.059$ and a normalized power of 155. The net, coolant, and fuel motion reactivity ramp rates are 23,18, and 28 $/sec, respectively.

Approximately 42% of the pins have failed. The disassembly phase analysis of this case is discussed in Section 11.

6.1.3.S Forced Midplane Failure at 10 g/sec Without Axial Expansion A SAS3A initiating phase calculation has been made which repeats the previous E0EC TOP midplane failure case except that fuel expansion reactivity feedback was additionally ignored. The course of the accident progresses in a similar fashion except that the time scale was compressed; failure in the first pin occurring in Channel 8 at 10.34 seconds instead of 12.23 seconds. If similar criteria for transition to the VEf4US disassembly calculation are employed the transition occurs at 10.369 seconds instead of 12.262 seconds.

Table 6-3 shows core conditions at the transition from SAS to VENUS

-l at an inverse period of <500 sec for the cases with and without f9el expansion. The ne' w tivity for the two cases is ainost identical but the power level, :mur, fuel temperature, and void fraction are all somewhat lower for +'- c' thout fuel expansion. The slightly higher driving ramp 6-C

rate and the general compression in the time stale is a direct result of the neglect of fuel expansion negative reactivity f emack h The difference between the two cases was not judged sufficient to justify a VENUS run. No significant difference in total energy release would be expected. The net result of increasing conservatism by neglecting fuel expansion feedback was to accelerate the events, shortening the time span but had no significant ef fect on total energetics of the accident.

6.1. 3. 6 Axial Failure location Uncertaintv Two variations on the previous case were run by forcing failures to occur at locations 3 nodes (22.? cm) above and below the core midplane at the tin,e failure was predicted to occur at the core midplane. As each channel was predicted to fail at the midplane, a restart was made forcing that channel to fail at the selected location at the time predicted.

This procedure was necessary to avoid inconsistencies of failure time, melt fraction, and cavity volumes introduced by the dependence of the failure criteria on assumed failure location. The 27.2 cm distance was chosen because it approximated failure in the upper and lower quarter of the axial core length. O Figure 6-48 shows the net reactivity trace f rom the three cases produced by this study. Figure 6-49 shows the fuel motion feedback from Channel 8; the lead and dominant cf.annel in all cases. Fiqure 6-50 shows net reactor power for the three cases. Care A is the reference case, in which all channels are predicted to f all at the core midplane. Case B is the case where failure is forced below midplane while Case C is the case where failure is forced symmetrically above the midplane.

'n Case A, Channel 8 f ails a t 10. 341 seconds , followed quickly by Channel 1 at 361 seconds and by Channel 5 at 10.3% seconds. By the time Channel 10 f , at 10.370 seconds, the core is well above pror.pt critical and is on a divergent power excursion. Channel 8 fuel mo_.on feedback rises rapidly to a maximum of 30.45 and starts to decrease, but the exponentially rising power produces additional molten fuel for further compaction. With all channels forced to fail at the midplane an energetic disassembly is evident.

O 6-18

In Case B, a slight increase in net reactivity is noted following failure of Channel 8 at 10.341 seconds. This soon becomes a significant decrease in reactivity as the interaction zone initiates flow reversal and expands downward away from the core midplane. Af ter about 40 milliseconds, the core pressure drop overpowers the interaction zone pressure and the fuel is swept back through the core midplane producing a reactivity pulse almost returning the reactivity to its original value. Channel 1 fails at 10.374 seconds and goes through a similar sequence of events following Channel 8 by an almost constant time lag.

The combined effects of sweeping fuel upward through the core midplane (i.e., sweepback) in Channels 8 and 1 cause Channel 5 to fail at 10.440 seconds. Channel 5 fails at the midplane in Case B and introduces significant

($0.41) positive reactivity. By this time however, Channel 8 is in its "sweepout" phase and is capable of overcoming the positive feedback introduced by unannel 5. The only effect of the midplane failure in Channel

5. is to delay nuclear shutdown by about 100 milliseconds. By 10.470 seconds, Channel 5 has joined the general sweepout of fuel which makes the core subcritical by 10.850 seconds.

Case C results in a slight decrease of reactivity upon initial failure because of the asymmetry of fuel worth about the core midplane. This is followed quickly by a rise in reactivity feedback as the interaction zone causes flow refersal and expands downward toward the midplane. A sharp drop in reactivity results when positive flow is reestablished and fuel sweepout begins. Channel 1 also fails in this case at 10.379 seconds producing a similar feedback history. Because there is no "sweepback" effect as in Case B Channel 5 does not fail before Channel 8 sweepout begins the shutdown phase. Channels 8 and 1 fuel motion cause permanent shutdown at 10.564 seconds.

The three cases discussed here provide a basis for evaluating the effect of failure location on TOP energetics. Failures both above and below the core midplane (Cases B and C) do not result in hydrodynamic disassembly because of fuel motion from the high worth center toward lower worth regions in both cases. The above and below core midplane failures are not synnetric in energetics, however, because of the "sweepback" phenomena which 6-19

exists only in the lower section of the cnre. Determination of the exact boundary of the central " disassembly region" has not been attempted since it is sensitive to variations in parameters such as pin failure criteria, failure size, and post failure fuel motion.

6.1.4 Effect of Design Uncertainties _

The effect of estimated uncertainties in several E0EC core design parameters are discussed in the following sections.

6.1.4.1 Doppler Magnitude Expected values of the Doppler constants used in the end of equilibrium cycle cores are presented in Table 5-4. However, since it is estimated that a 20% uncertainty may be associated with the expected values, additional SAS model runs were made to investigate the effect of Doppler uncertainties on the course of the transient overpower accident. The Doppler reactivity calculations in SAS are based on the volume averaged temperature of each axial fuel pin segment. The total Doppler reactivity feedback component for the reactor at any time is given by the sunmation over :ll axial segments in all channels.

A study of reactivity insertion of 3.20$ at a ramp rate of 10c/sec without scram for cores with Doppler coefficients of 0.8,1.0 and 1.2 times the expected values, was performed with an earlier core model and SAS code version. The differences in reactor core modeling and SAS code improvements are not considered to significantly change the calculated Doppler coefficient effects on the accident scenarios. It was found that as the Doppler coefficient is increased, initial pin failure occurs later in the transient with a lower power and smaller melt fraction. Since less molten fuel is available, negative reactivity feedback due to fuel motion is decreased, and the neutronic shutdown margin is decreased. A reduction in the Doppler coefficient causes initial pin failure to occur earlier in the transient at a higher power and larger melt fraction. A larger amount of molten fuel is available for expulsion into the coolant channel, which should slightly increase the neutronic shutdown margin. In both cases, the axial failure locations were in the upper third of the active core and not significantly affected by the Doppler variations.

O 6-20

Following pin failure, reactivity is introduced by fuel expulsion from the pins into the coolant. The ultimate course of the accident is largely dependent on fuel motion reactivity feedback. A m11d fuel-coolant interaction occurs as fuel is expelled fram the pin into the coolant for several hundred milliseconds following failure initiation. The ultimate course of the acci-dent, that is, neutronic shutdown due to fuel sweepout, did not appear to be affected by the 20% variation in Doppler coefficients.

6.1.4.2 Material Worths Uncertainties of approximately 20% may exist in the calculated worths of fuel and sodium. Material worth sensitivity studies performed in the FTR transient overpower analysis (Ref. 54) are considered to be applicable to the CRBRP. A uniform reduction in fuel worth values by a factor of 0.82 would result in less fuel motion negative reactivity than the base case. The failure of a second channel may occur sooner than in the base case due to the higher power and net reactivity. More molten fuel may also be available to insure neutronic shutdown.

An increase in the sodium void positive reactivity worth could result in increased energetics consequences in the CRBRP For expected failure locations in the upper third of the reactor core such increases would be minimal since the fuel relocation is an order of magnitude more important. If near midplane failures are arbitrarily assumed, as in Section 6.1.3.4, then the driving ramp rate in VEtiUS could be augmented by the increased void worth. However, the VENUS bounding cases performed in Section 11 demonstrate that such effects would not be of concern in CRBRP.

6.1.5 Sunmary and Conclusions on E0EC TOP Event The present best estimate based on the initiating phase accident calculations is that low ramp rate (2.4?/sec - 20c/sec) initiation leads to early accident termination with low energetics. Pins fail high in the core into flowing, significantly subcooled liquid sodium. Fuel ejected into this coolant stream tends to be quenched, and hydraulically swept up the coolant channel due to the pressure drop and flow rates that exist. The negative reactivity effect of these phenomena is substantial, and the vast 6-21

majority of core assemblies are cooled intact and in place. The 2.4 c/sec case is calculated to have a slightly more energetic FCI than the base case due to larger molten fuel-to-fission gas mass ratio at failure. The SAS3a calculations indicate that initial pin failure may not result in sufficient negative reactivity to guarantee neutronic shutdown. Additional pins may fail in other assemblies before neutronic shutdown occurs. At the termination of SAS3A calculations, sufficient negative reactivity is available for neutronic shutdown if significant fuel-clad blockages do not occur. Even with the assumption of a higher ramp rate of 50c/sec, low energetics result.

For ramp rates of 3$/sec and greater, prompt criticality was achieved and sustained up to the temination of the calculations; therefore the minimum ramp rate required to achieve and sustain prompt criticality in an E0EC core is between 50c/sec and 35/sec. The most energetic TOP event results in hydro-dynamic disassembly based upon arbitrarily assuming pin midplane failures (Category 3). Relative to the E0EC base case accident, the SASBLOK calcula-tions examined the coolability of failed channels with areal blockages of 88 to 97 percent. The degree of areal blockages studied was high since large amounts of fuel were expelled during initial pin failure. The core region of the failed fuel assemblies (represented in SAS Channels 5 and 8) was found to be coolable for less than the maximum blockage examined. A porous blockage mass in a region above the core was found to be coolable in place for an areal blockage of up to 80 percent. It is probable that larger areal blockages would break up and relocate axially into coolable configurations in the upper plenum regions.

There are no significant differences in total energy release between forced midplane failure at 10c/sec and forced midplane failure at 10c/sec without axial expansion. The net result of increasing conservatism by neglect-ing fuel expansion feedback was to accelerate the events, shortening the time span, but it had no significant effect on total energetics of the accident.

The parametric variation of failure location without axial expansion showed that failures both above and below the core midplane do not result in hydrodynamic disassembly. The above and below core midplane failures are not symmetric in energetics. Failure at the midplane is predicted only at very high ramp rates; in general the slower the reactivity ramp the higher O

6-22

the predicted failure location will be.

A comparison of the effects of two-current transient fission gas release models (the modified Gruber and the Smith) in predicting pin failure showed slightly different pin failure sequences, but no significant change in accident energetics or termination path.

The HEDL damage parameter empirical fuel pin failure correlation was used to predict failure in two SAS channel types during a SOC /sec trans-ient. A comparison of the damage parameter failure predictions with those cdlculated using the burst pressure failure criterion in the SAS3A code indicated that the damage parameter correlation predicted failures at earlier times in the transient with smaller melt fractions and comparable axial failure elevations in the core. Although a complete analysis of all ten core channels was not performed, the energetics consequences were judged to be on the same order of magnitude as predicted by the SAS3A analysis.

A + 20 percent variation in the Doppler coef ficients did not signi-ficantly af fect the energetics or the termination path. The effects of fuel and sodium void worth variations of up to twenty percent are not expected to significantly change the ultimate course of the TOP accident for pin failures calculated to occur in the upper one-third of the core.

In conclusion, the TOP accident in an E0EC core is a low energetic event in which failed fuel assemblies can be cooled in place following neutronic shutdown. For the initiating phase of such an acchent to lead directly to a mild disassembly, core midplane failures not Jredicted by current models or reactivity insertion rates far in excess of oesign would have to be postulated. For probabilistic category three a1d four acsumptions the energetic consequences of hydrodynamic disassembly are less than the conditions selected to specify the SMBDB.

6.2 TOP in BOEC Configuration at full Power 6.2.1 Base Case Ramp _ Rate of 10ysec This case presents a best estimate analysis of a reactivity insertion without scram accident at the beginning of an equilibrium cycle in CRBRP.

The reactivity insertion of 3.2$ at 10c/sec has the same basis for parameter evaluations discussed in Section 6.1, 6-23

Starting from full power steady state conditions, the inherent Doppler and axial expansion feedback mechanisms moderate the effect of a 10c/sec g

ramp insertion such that af ter 11.3 seconds, the reactor power and the net reactivity are approximately 3.7 x nominal and 38 cents supercritical.

Due to the thermal upset, gross melting has progressed throughout the core fuel. Table 6-4 depicts fuel midplane conditions and damage severity for the ten channels with the fresh fuel grouped together. The low gas content and unaffected cladding strength of the fresh fuel pins combine to keep the damage severity low even for substantial mel t fractions. The high damage severity in Channels 6, and especially 10, is due primarily to the absence of significant restructuring which, based acon the Gruber calculation of solid fuel gas release, allows large amounts of fission gas to be released early in the transient. A degree of uncertainty still exists in calculating the fission gas release from low power microstructure fuel and its relationship to cavity pressurization. Based upon the preliminary experimental data which was available (TREAT HUT 5-5A and 5-5B), fuel of low power microstructure appears to have a higher failure threshold than previously believed. Thus, the present SAS3A treatment probably underpredicts h the failure threshold. This uncertainty in fission gas release is addressed parametrically by assuming different release models and arbitrary failure locations.

For the base case Channel 10* is predicted to fail with a high gas content at a midplane melt fraction of 16%. The associated cladding midwall temperature was 707 C and the damage severity at the failure node (70%

of core height) was 1.05. Values presented in Table 6-4 were obtained from the last SAS3A detailed print 233 milliseconds prior to Channel 10 failure.

The resulting power and reactivity traces are given in Figure 6-51.

As suggested by the fuel reactivity plot, the pin has depressurized af ter 50 msec, and fuel ejection stops at about this point. The pressure history details and resulting FCI zone interface movement are shown in Figure 6-52.

• 5.3 KW/Ft average and 43 GWD/T burnup.

O 6-24

The small amounts of molten fuel in the FCI zones, the cushion provided by fission gas, and effect of the nominal core pressure drop suffice to eliminate flow reversal for all practical purposes. The total molten and solid fuel ejected from the pin is slightly under 19 grams. Figure 6-53 shows the time dependent sweepout of fuel. All but slightly more than 3 grams are calculated to be swept out of the top of the coolant channel. The total fuel reactivity associated with the fuel movement to the failure site and additional sweepout was -2.2$.

Conditions (i.e. , fuel reactivity, pressure, flow) in the SAS/FCI zone stabilize in about 376 msec. The bulk of any void spaces is fission gas with only a slight, transient amount of sodium vapor being generated prior to 376 msec. Only this phase of the FCI solution affected the reactor transient.

The SASIROK evaluation initiates at approximately 233 msec prior to the failure in Channel 10 to complete an evaluation of the accident. The FCI generated reactivity and hydraulic feedbacks are simulated with the progranrned reactivity function and the tabular fission gas release option.

Af ter 376 msec, the volu.ne of fission gas in tne FCI solution is matched and the SAS coolant dynamics routines allowed to predict the futuregbehavior of the bubble. 7.

Starting with the release of fission gas, a linear increase in the Channel 10 exit loss coefficient from 1.75 (design value) to 200 (equivalent to 87 areal percent blockage), is introduced over 752 msec to represent blockage formations above the core.* At 752 msec, the power generation in Channel 10 is reduced by ten percent to account for the core fuel loss in the FCI.

Figure 6-54 presents a comparison of the ef fective SASBLOK simulation with the original reactivity and power conditions during the FCI event.

The fission gas bubble introduced (FCI free volume) and its hydraulic sweepout during the SASBLOK analysis are shown in Figure 6-55. The sodium flow is quickly re-established at 59 percent of rated within Channel 10, but gradually stabilizes at the lower blocked value of 50f of rated flow.

• The exit coef ficient only aff ects the flow af ter the Tabular Fission Gas Model is terminated.

6-25

Due to the fuel expulsion, the reactor is rendered subcritical g

(-1.7$) and rapidly gives up its stored energy to the primary sodium flow (full pump head exists' As the stored energy is decreased, the neg-ative reactivity contributions from Doppler and axial expansion are eliminated and, in fact, become positive. This effect coupled with the continuing ramp insertion acts to keep the power from falling below 0.68 of nominal and returns the reactor power to nominal by 18.6 seconds, or about seven seconds af ter the initial failure.

At termination of the total reactivity insertion of 3.2$, the reactor is once again in an upset thermal condition with a power and net reactivity of 3.3 x nominal and 31 cents, respectively.

The eventual result of the continued transient is a failure of the eighteen fuel assemblies represented as Channel 2*, at 32.98 seconds and approximately 77 percent of the core height. Of all the fuel, only Channels 4 and 8 have accumulated a damage severity exceeding that reached at the time of the initial failure on Channel 10. (Channel 10, due to its lower power density has not yet remelted any fuel and additional fuel expulsion would not be expected).

g The reactor power and reactivity are summarized in Figure 6-56 (an extension of Figure 6-51). Also, the midplane conditions for Channel 2 are presented from a time just prior to Channel 10 failure to SAS3A termination in Figure 6-57.

A substantial negative reactivity addition results from the movement of fuel in Channel 2 which terminates the accident. Based upon the calculation presented in Section 6.1.1 on the degree of blockage required to cause fuel melting in Channel 8 (highest power) of the E0EC core, it was inferred that a coolable configuration for Channel 2 would result. The core is -4.35$

subcritical and the stored thermal energy is being reduced via the normal heat removal path.

An alternate path may exist due to severe cracking of fuel during the initial subcritical transient. Substantial cracking of fuel would likely result in equalization of pin cavity and plenum pressures, thus reducing O

• 7.5 KW/ft average and 54 GWD/T burnup.

6-26

the potential for additional damage in irradiated pins. Following a return to nominal power, it is expected that through plastic flow and healing, the pin cavities would once again act to seal in released gases. 'he impact of the above scenario would be delayed failures in irradiated fuel or local boiling and clad failure in high power-to-flow fresh pins leading to subcriticality. An example of the latter case follows in Section 6.2.3.3.

6.2.2 Effect of Ramp Rate Variation The following additional ramp rate studies were conducted to deter-mine the effect of ramp rate on the accident event progression.

6.2.2.1 Design Ramp Rate of 2.4 c/sec Phenomenologically, only two potential differences have been identified between the maximum design ramp rate of 2.4(/sec and the 10(/sec ramp rate scenarios. The first, and considered most important, is a reduction in the potential for the central fuel cavity to trap released fission gases and pressurize. Since the time span for fission gas release and thermal expansion effects is much longer (40 vs 10 seconds) much of this gas may escape to the plenum before expansion and self-healing thermal effects (such as molten fuel extrusion into cracks) can take place. To conservatively account for these potential phenomena, seventy percent of the released fission gases (as opposed to five percent in the base case) wa assumed to go directly to the plenum, thus substantially reducing the r. ary loading force for cladding failure.

Secondly, the potential for internal pin relocation of fuel has been identified as a phenomenological uncertainty. Calculations on the maximum available free volume within the pin and consideration of the observed effects of fission gases released during both out and in-pile heating of irradiated fuel (Refs. 8 and 34) support the conclusion that this phenomenon would be a second order effect on the fuel pin failure.

The slower design rate insertion is expected to enhance the p tential for sodium boiling to occur in the higher specific power fresh fuel assemblies.

However, sodium boiling did not occur prior to pin failure in Channel 2 at 39.8 seconds into the transient. The failure is predicted to occur at 0.76 6-27

of the core height (22 cm above the midplane) with a 45 percent midplane fuel melt fraction. At this time, a ninimum subcooling of approximately g

62 C occurs in Channel 9 (fresh fuel) in the upper axial blanket region.

The fact that Channel 10 did not fail in this case as it did in the base case is associated with the modeled reduction in fission gas entrapment within the pin cavity.

The expulsion of fuel in Channel 2 rapidly renders the core subcritical at -2.57$ net reactivity. However, as in the base case, this state is unstable in that the continued insertion will bring the reactor recritical and additional fuel failures must occur to assure permanent shutdown.

Based upon previous calcclations it was judged unnecessary to perform SASBLOX analysis in this case. One additional channel failure is expected with benign consequences.

6.2.2.2 Limiting Ramp Rate of 20 c/sec This insertion rate is based upon the physical limit at which the rods can be driven prior to disengagement of the drive mechanisms. The power and net reactivity traces for this case are shown in Figure 6-58.

Initial pin failure occurs in the same channel as the 10t/sec case (Channel 10) but earlier in the transient (6.45 vs 11.54 sec) with a lower internal pin pressure (694 vs 809 atm) but a higher clad temperature (805 vs 782 C) and normalized power (4.7 vs 3.6). The axial failure location was the same as in the base case (approximately 14 cm above the core midplane) due to the combination of lower internal pin pressure but higher -ladding temperature.

The amount of molten fuel available for a fuel-ceolant interaction was approximately the same for both cases, but the 20(/sec case had approximately thirty percent less fission gas mass, resulting in a slightly more energetic FCI than the base case. The development of the FCI zone and the sodium flow in Channel 10 is shown in Figure 6-59.

The fuel motion and coolant reactivity components in Channel 10 are shown in Figure 6-60. The negative fuel motion reactivity component introduced by SAS/FCI calculated fuel motion in Channel 10 results in a net reactivity g 6-28

of -1.13$ and a normalized power of 0.74 at the tennination of the SAS

• code calculations at 1.7 seconds af ter pin failure. The continued progranmed reactivity insertion will bring the reactor recritical and additional fuel pin failures would be expected to assure neutronic shutt.cwn.

6.2.2.3 Extreme Ramp Rate of 503/ g To determine whether a step increase in energetics consequences exists for postulated extreme ramp insertions, a 50c/sec case was investigated. The power and reactivity traces for this case are shown in Figure 6-61. The channel dependent voiding ar.d fuel motion reactivity plots are given in Figures 6-62 and 6-63.

Initial pin failure occurred in the same channel as in the base case (Channel 10) but arlier in the transient (3.047 vs l'.54 sec) with a lower pin pressure (527 vs 809 atm.) but a higher clad temperature (808 vs 782 C) and normalized power (8.0 vs 3.76). Figure 6-64 shows the fuel and clad midplane thermal conditions. The axial failure location was lower in the 50c/sec case than in the base case (approximately 7 vs 14 cm above the core midplane) primarily due to the dowr, ward shif t and increase in peak clad ling tempera ture.

Table 6-5 shows that for the 50c/sec TOP case, sodium boiling occurred at 3.039 sec in Channel 9 prior to the initiation of pin f ailure in Channel

10. This makes the 50c/sec case unique from the lower ramp rate TOP cases in that it alone experiences coolant boiling prior to pin failure. The results of the two 104/sec cases shown in Table 6-5 inJicate that if initial failure is suppressed at and beyond the calculated initial failure time of 11.54 seconds, sodium boiling will begin in Channel 9 at 12.05 seconds. Therefore, as the irradiated pin failure time is delayed, conditions which would result in sodium boiling in Channe' 9 are more closely approached.

The amount of molten fuel availsole for a fuel-coolant interaction was approximately the same for both cases, but the 50c/sec case had approximately fifty percent less fission gas mass, resulting in a slightly mort energetic FCI than the base case. Figure 6-65 shows the FCI zone development ano sodium flow in Channel 10.

6-29

Channel 3 is calculated to fail approximately 3.4 msec af ter Channel

10. At failure, the thermal conditions in the fresh Channel 3 pin were g

different than those of the irradiated Channel 10 pin. The Channel 3 pin failed with a lower pin pressure (285 vs 527), but a higher clad tempera-ture (1001 vs 808 C) and midplane fuel melt fraction (48 vs 11%) than Channel

10. Approximately four times as much molten plus solid fuel but only one-tenth as much fission gas is available for the fuel-coolant interaction, re-sulting in a more energetic FCI in Channel 3 than in Channel 10. The Channel 3 fuel and clad themal conditions at midplane and the FCI zone development and sodium flow are shown in Figures 6-66 and 6-67 respectively.

The final pin failures in this transient occur simultaneously in Channels 1 and 6 at approximately 10 msec af ter the initial pin failure.

The failure conditions in the fresh Channel 1 resemble those in Channel 3 in many respects, such as pin pressure (280 vs 285), clad temperature (1012 vs 1001 C), and molten and solid fuel and fission gas available for FCI.

Similarly, failure conditions in the irradiated Channel 6 resemble those in Channel 10 in many respects such as pin pressure (496 vs 527),

clad temperature (810 vs 808 C). However, Channel 6 has a larger midplane melt fraction than Channel 10 resulting in fif ty percent more molten fuel but only slightly more fission gas. A more energetic FCI therefore occurs in Channel 6 compared to Channel 10. The negative fuel motion reactivity component introduced by SAS/FCI calculated fuel motion in the channels results in a net reactivity of -3.83$ and normalized power of 0.62 at the termination of the SAS3A calculations. Sufficient negative reactivity is therefore available for neutronic shutdown. The clad temperature near the 0

top of the core is calculated to reach approximately 1150 C. Since fuel-clad heat transfer and fuel plateout are not currently modeled in SAS/FCI, the development of fuel-clad blockages must be considered. The E0EC base case SASBLOK blockage conclusions are applicable here, even though a larger number of assemblies have failed than in the base case.

6.2.3 Effects of Phenomenological Uncertainties 6.2.3.1 Fission Gas Release Model A study was conducted to compare the difference in accident progression g 6-30

paths as predicted by two transient fission gas release correlations.

At present the Gruber correlation is not applicable to fuel having less than 100 days of burnup. The B0EC core fresh fuel (odd numbered) SAS channels therefore use a fuel melt criterinn for fission gas release proposed by Smith (Ref. 7) . In the BOEC base case (Section 6.2.1), however, only irradiated pins are predicted to fail. A study was therefore conducted using the Smith model for both fresh and irradiated pins. The results indicated that the Smith correlation predicts initial failure of the Channel 9 (fresh) pin at 12.25 sec as opposed to the base case initial failure of Channel 10 at 11.54 sec. The initial failure prediction difference is due to several factors. In the BOEC core SAS modeling Channel 9 was placed inside of Channel 10 to preserve the high design power to flow ratio typical of the fresh fuel channels. Since the computational system did not allow Channels 9 and 10 to be intemixed, the power in Channel 9 was too high and in Channel 10 too low. In addition, with the Gruber model fission gas release from the unrestructured fuel begins well before the solidus temperature of 2767 C is reached (and may be quite significant by 2200 C),

whereas the Smith model allows no fission gas release until the solidus temperature is reached. Therefore, fission gas is released earlier in the transient and the cavity pressure is larger with the Gruber than with the Smith model. The cavity pressure in Channel 10 was therefore lower with the Smith model, which is why it did not fail as in the base case at 11.54 sec.

Shortly af terwards, however, at 12.07 sec coolant boiling began in Channel

9. Fioure 6-68 shows the localized boiling pattern. Pin failure finally occurs in Channel 9 with a cavity pressure of 325 atm and a clad temperature of 1000 C at the failure location. The high local clad temperature caused the pin to fail with a low cavity pressure. In contrast, the base case Channel 10 pin failed with a cavity pressure of 810 atm and a clad failure location temperature of 780 C. Figure 6-69 presents a comparison of the cavity pressure, melt fraction, and damage fraction obtained by using the Gruber and the Smith fission gas release models.

At failure the Smith model pin has a large molten fuel to fission gas mass ratio, as seen from the e.iected fuel and fission gas plots in Figure 6-70.

The large molten fuel to fission gas mass ratio results in a more energetic 6-31

fuel-coolant interaction than was calculated when the base case irradiated pin in Channel 10 failed. The Channel 9 voiding profile and FCI zone g pressures are shown in Figure 6-71 to demonstrate this. The larger molten fuel to gas ratio is due to significant melting of columnar and equiaxed fuel, which was modeled to retain two orders of magnitude less fission gas than the unrestructured fuel at normal operating conditions prior to the transient.

Since a majority of the retained fission gas is in the unrestructed fuel, the Smith model results in large molten fuel to fission gas ratios until progressive unrestructured fuel melting allows release of the 'ission gas held in the unrestructured fuel. The Smith model power and reactivity traces in Figure 6-72 suggest that the negative fuel reactivity of approximately -2.5$

is not sufficient to guarantee neutronic shutdown As in the base case, a return to overpower conditions coupled with the failure of additional pins is probable and ultimate shutdown is predicted from transport of more fuel from the core region.

6.2.3.2 HEDL Fuel Pin Empirical Failure Correlation The Hanford Engineering Development Laboratory (HEDL) is developing an empirical correlation (based upon TREAT experiments) of fuel pin failures g during TOP events (Ref. 53). This method was adopted by the FFTF Project as the fundamental approach to failure prediction and employed in its safety review of HCDA's (Ref. 54).

The correct application of the unique empirical relation defined in the correlation requires the usage of the self consistent methodology developed at HEDL. The damage parameter calculations presented here-in were perfonned by HEDL at the request of the CRBRP Project and are based upon the status of the correlation as represented by Ref. 54.

Only the 50c/sec case was analyzed since the damage parameter experimental data base was limited to ramps between 50c/sec and 3$/sec. It is felt that use of the correlation for ramps of less than 50c/sec cannot presently be justified.

By employing SAS3A power histories (with failure supprcssed) the HEDL methodology was applied to predict fuel pin thermal history, the damage parameter value and to estimate failure conditions.

O 6-32

Table 6-6 presents the SAS3A predicted failure sequence along with the HEDL estimates of failure in Channels 10 and 4. Channels 10 and 6 fail prior to 4 in the SAS analysis based upon the lower amounts of restructuring and therefore, enhanced fission gas available for cavity pressurizatioris; Channel 4 never does fail in the SAS analysis, although it has up to 33 percent midplane melting. The reason for the di f ference in channels analyzed is tiat the channel selection for HEDL analysis was done prior to the SAS analysis. Channels 1 and 3 in SAS are relatively fresh fuel and fall outside the HEDL correlation range. It is not clear if the HEDL methodology would estimat.e failure in other SAS channels prior to 4 or 10. The only comparison which is valid is on Channel 10 which is quite good, based upon degree of melting and axial location of failure.

In general, the HEDL correlation is judged to predict failure earlier in time, with somewhat less fuel energy an I at comparable elevat. ions in the co re . Although a complete comparison was not performed, the similarity in failure axial location and fuel pin thermal conditions allow the conclusion that the predicted energetics consequences using the Hl.DL correlation would be of the same order as the SAS analysis.

6.2.3.3 Additional fuel Pin Failure Criteria The burst pressure failure criterion described in Sectio. 3.2.3 is the only mechanistic failure criterion programmed into the SAS3A code.

Tables of claa strength versus temperature for both fresh and irradiated cladding were described in Section 4 and shown in Figure 3-3. To examirle the sensitivity of the accident scenario to the tailure criterion, two additional studies were conducted.

The first study was conducted to detennine pin conditions if pin failure was not allowed to nccur prior to the inception of coolant boiling in the channels. The BOEC core model was use 1 with the internal pin pressure 6

failure option (Mi All = -2) set to an unrealistic value of lx 10 atm to preclude pin failure Lefore boiling. The power and reactivity plots are given in Figure 6-73. Boiling first occurs in Channel 9 at time 12.05 sec.

The transient is thus far almost identical to the BOEC case which used the Smith fission gn release model Ior all pins (see Section 6.2.3.1). The voiding profile for thannel 9 is sheur: in f i gure h- 74.

b-33

The clad temperatures and internal pin pressure increase such that the pin is expected to fail during the voiding time span shown. Therefore, if an irradiated pin does not fail first, fresh pin failure due to coolant boiling may occur.

The potential for fresh pin failure to occur on the basis of clad straining in the B0EC core was also examined. At present, a strain based pin failure criterion is not available in the SAS3A code. However, the DEFORM module of the SAS2A code, with elastic fuel and elastic-plastic cladding deformation relations, does calculate the permanent (or plastic) deformation at the clad inner and outer surface. The deformation calculations are based upon two expansion mechanisms; differential thermal expansion betweer the fuel and clad, and fuel melting, which allows melting fuel to expand freely into the central pin cavity. DEFORM does not model transient fuel expansion (or swelling) due to fission gas coalescence and expansion at grain boundaries, which may be a significant clad straining mechanism. Additional limitations of the present DEFORM module are that fuel cracking is not modeled fission gas and fuel vapor pressure loading of fuel and clad 1.s not modeled, and melting fuel cannot relocate axially in the pin. Recognizing the limita-g tions of DEFORM, a series of additional calculations were included in versions of the TSDRIV and TSPRNT of the SAS3A code. In TSDRIV the following additions were made:

1. Statements were added to calculate the elastic and plastic strain components at the clad inner and outer surface. Cladding dimensions calculated by DEFORM were used. Hence, the calculated strains are based on the limitations of DEFORM as previously discussed.

2. A clad plastic strain failure criterion was included. The criterion compared the ratio of the calculated plastic strain at each axial node to a specified plastic failure strain input value. This arrangement allowed utilization of the existing f ailure logic in TSDRIV.

3. A failure logic based on the natisfaction of either burst stress or plastic clad strain was included.

g 6-34

In addition, in the TSPRNT module, the fuel-clad gap, gap conductance, clad thickness and the elastic and plastic components of strain at the clad inner and outer surfaces are calculated and printed at every detailed print step.

Maximum values of the clad plastic strain calculated for the DOEC case in which pin failure was not allowed to occur are shown in Figure 6-75.

Plastic straining occurs first in irradiated Channel 2. Figure 5-13 showed that the initial (steady state) fuel-clad gap in Channel 2 is smaller than the fresh fuel gap in Channel 1. The mechanism of differential thermal expansion therefore caused the gap in the irradiated Channel 2 to close and plastically strain the clad before these events occurred in the fresh pins. Clad plastic straining is seen to occur in irradiated Channels 2, 4, and 8 before plastic straining is calculated to occur in the fresh Channels 1 and 3. The fresh pin plastic strains, however, soon become larger than those of the irradiated pins. It is not presently clear that this calculational result is realistic since the model does not adequately treat three important phenomena. The first of these is the availability of free volumes within the fuel pin cavity for expansion of mol ten f uel . Thc current model is believed to underestimate this potential and result in excess clad plastic strains, particularly for fresh fuel. Secondly, no account is taken for the solid state fuel swelling expected due to fission gas bubble growth and expansion at the grain boundaries in irradiated fuel. The current model is believed to underestimate the cladding strain in irradiated fuel pins due to neglect of this phenomenon.

Thirdly, the contribution of the cavity pressure to straining of the cladding is not accountet for. Inclusion of this phenomenon would increase the potential plastic strain of irradiated as compared to fresh fuel pins due to the higher inherent pressure loading in irradiated fuel pins. Despite the modeling limitations in DEFORM, the maximum strains at the termination of the SAS code calculations were on the order of one percent plas tic strain ir, the fresh pins and one-half of one percent in the irradiated pins. By that time, however, an initial pin failure would have been predicted with' the burst pressure failure criterion.

A final study was performed to examine the effects of early fresh pin failure in a BOEC core. A soncubat unrealistically low plastic strain failure 6-35

value of 0.2 percent was specified for the fresh pins. The power and reactivity traces are shown in Figure 6-76. Pin failure occurs sim-g ultaneously in Channels 1 and 3 at 11.5 seconds into the transient.

The pressure history and FCI zone development for Channel 1 are shown in Figure 6-77. Both channels fail near the core midplane. The melt fractions, are approximately 0.48 and much more molten fuel than fission gas is present at failure. The net reactivity reaches approxi-mately -0.60$ due to fuel motion where the SAS calculations are termi-nated as a vapor bubble formed below the FCI zone tries to combine with the FCI zone. At the termination of the calculations, the FCI zones are still expanding and additional negative fuel motion reactivity is expected. Additional pin failures, however, are probable before neu-tronic shutdown would be assured.

6.2.3.4 Forced Midplane Failure 9 2.4Usec This case is based upon the best estimate of a TOP transient having a 2.4t/sec ramp with the modification that the failure location in all channels is specified to be at the axial midplane. The primary effect of constraining the pin failure site to the axial midplane is g

to cause a positive reactivity contribution due to internal fuel motion toward the failure location from lower fuel worth regions. It should be noted that the burst failure criterion used in the best estimate case predicted fuel pin failure at an axial location approximately 22 cm above the core midplane.

Channel 2. as in the best-estimate case, is the first channel to experience pin failure, but as a result of the midplane failure criterion, Channel 2 fails at 40.45 seconds into the tr ansient as compared to 39.8 seconds in the best estimate case. At the time of failure, the reactor power is 3.05 x nominal and the net reactivity is 18 cents.

Power and net reactivity histories for the transient are shown in Figure 6-78. As a consequences hf pin failure in Channel 2, positive reactivity contributions are made to the excursion from two sources.

Fuel motion in Channel 2 from regions of lower fuel worth to higher fuel worth as molten fuel migrates toward the midplane failure site is the O

6-36

first source of positive reactivity. Rapid voiding of sodium in a positive coolant region due to the fuel-coolant interaction in Channel 2 is the second source. Coolant and fuel motion reactivity histories by channel are shown in Fiqures 6-79 and 80. The combination of both reactivity contributions causes the power level to increase to 14.8 x nominal and the net reactivity to 81c by 40.49 seconds into the trans-ient when Channel 8 also experiences pin failure. Large amounts of reactivity are added from Channel 8 by the sources as in Channel 2.

This produces an autocatalytic effect causing midplane pin failures in Channels 4 and 6 within the next 10 msec. Contributions of positive reactivity from coolant voiding and fuel motion in Channels 2, 4, 6, and 8 cause the excursion to attain prompt criticality at 40.50 seconds. The power level has reached 70 x nominal and the reactivity ramp rate is 505/sec. Necessary conditions are met to perform a hydro-dynamic disassembly calculation using the VENUS code and the initiating phase calculations are tenninated at this point. The disassembly phase analysis for this case is discussed in Section 11.2.1.1, 6.2.3.5 Forced Midolane Failure 0 10c/sec This case is based upon best estimate modeling of phenomenology modified by the constraint that fuel pin failures must occur at the axial midplane for all channels. As in the previous case of a 2.4c/sec ramp rate with forced midplane failures, this constraint results in a con-servative phenomenological modeling of the transient in that it causes a positive reactivity contribution to be added due to molten fuel moving into higher fuel worth regions as it migrates to the failure site.

At 11.635 seconds into the transient Channel 10 experiences pin failure. The power level at this time is 3.81 x nominal and the net reactivity is 37 cents. Reactor power and net reactivity histories are depicted in Figure 6-81. Since there is a rela.tively small melt fraction a t the core midplane in Channel 10, molten fuel motion is limited and consequently its positive reactivity contribution is small.

Coolant voiding as a result of the molten fuel-coolant interaction in Channel 10 causes substantial negative reactivity to be added since 6-37

Channel 10 is in a nega ive void worth region. Thus, fuel pin failure in Channel 10 is self-mitigating to the extent that positive reactivity contributions from fuel motion are counterbalanced by negative reac-tivity from rapid coolant voiding. Coolant and fuel reactivity his-tories are shovn in F inure 6-82.

The power.and net reactivity levels peak 9 msec later at 4.06 x nominal power and 41d, respec tively. Power and net reactivity slowly decline f or another 9 msec at which time pin failure occurs in Channel ,

6. Like Channel 10, Channel 6 has a relatively small fuel melt frac-tion and thus fuel motion and its accompanying positive reactivity contribution is small. Meanwhile the FCI region in Channel 10 is expanding rapidly and its negative reactivity contribution then com-pensates for positive contributions from fuel motion in Channels 6 and 10. At 11.664 seconds into the transient the reactivity contribu-tion from fuel motion in Channel 10 becomes negative as does the fuel motion reactivity component from Channel 6 about 20 msec later due tc fuel sweepout from the core region, peactor power and net reactivity continue to decrease until at the final calculation time (12.525 h seconds) they are 0.36 x nominal and -5.0S$, respectively.

Comparison of this case with the previous case (2.4d/sec ramp rate) reveals widely varying results. The 10d/sec case tenninated benignly with limited fuel pin failure while the 2.4d/sec case resulted in hydro-dynamic disassembly. Superficially this might tend to indicate a sen-sitivity to ramp rate with an increasingly energetic transient re-sultine as the ramp rate is decreased. However, closer inspection of the accident sequences reveals that the factor that detennines the widely differing outcomes of the two transients is that initial pin failure occurred in a positive void worth region in the 2.4c/sec case and in a negative void worth region in the 101/sec case. In addition, initial pin failure occurred in a channel (Channel 2) having a signifi-cantly higher fuel melt fraction in the 2.4t/sec case than in the 10c/sec case (Channel 10). This resulted in a larger positive reactivity con-tribution from greater fuel motion in the 2.4c/sec case than in the O

6-38

10c/sec case. Ultimately the differences in the outcome of the two cases comes down to the fact that Channel 2 was first to fail in the 2.4c/sec case while Channel 10 was first to fail in the 10c/sec case.

The cause of Channel 2 failing first in the 2.4c/sec case and Chan-nel 10 failing first in the 10c/sec case was not due to the difference in ramp rate, but rather to the difference in the amount of fission gas assumed to pressurize the fuel pin cavity. In the 10c/sec case, only 5% of the fission gas is released to the plenum prior to pin failure while in the 2.4c/sec case, 70% is released to the plenum.

These values are based on engineering judgments of the phenomenolog-ical behavior of fission gas for the two different ramp rates and are uncertain. The key point here is that the differences in the out-comes of the two cases are not primarily ramp rate dependent, but rather they are dependent upon modeling of fission gas release phe-nomena that are not well understood. Application of base case assump-tions on fission gas release mechanisms to the 2.4c/sec case would result in Channel 10 fe ilures and benign shutdown.

It is also important to note that the results of these two cases demonstrate that it cannot be stated a priori that fuel midplane failures always result in hydrodynamic disassembly, but that considera-tion must be made of fuel melt fractions as they relate to fuel motion rates and of the nature and magnitude of void worths for the regions involved.

6.2.4 Effect of Design Uncertainties The effect of estirrated uncertainties in several BOEC core design parameters is discussed in the following sections.

6.2.4.1 Doppler Magnitude Expected values of the Doppler coefficients used in the beginning of equilibrium cycle core are presented in Table 5-2. Based upon cri-tical experiments, it was estimated that a 20f uncertainty may be asso-ciated with the expected values, a study was conducted to examine the effects of Doppler coef ficients of 0.8,1.0 and 1.2 times the expected 6-39

values in an end of equilibrium cycle core 10c/sec reactivity insertion transient. The results of that study are reported in Section 6.1.4.1.

It was concluded that the ultimate course of the accident was not affected by the slight variations in initial pin failure time, power, melt frac-tion, and axial location due to the 20% Doppler coefficient ' variation.

The same conclusion is expected to apply to the beginning of equilibrium cycle core.

6.2.4.2 Material Worths An uncertainty of approximately 20% in the calculated worths of fuel, sodium, and stainless steel may be attributed to the cross-sec-tion data or to the calculated delayed neutron fraction. Calcula tions were performed on the FTR (Ref. 54) and are considered to be valid for the CRBRP.

Far greater uncertainty compared to that present in material worths exists in the phenomenological nature of the TOP accident. The physical location of the failure site, conditions causing pin failure, presence of fission gas at the f ailure site, etc. , are all of greater importance in the outcome of the TOP accident and are known with much less cer-tainty than the material worths. In light of these facts, it is be-lieved that while variations in material worths will certainly in-

. fluence to some extent the accident path in the TOP excursion, this effect will be minor and of secondary importance when compared to un-certainties in phenomenological modeling in the TOP accident.

6.2.5 Suninary and Conclusions on BOEC TOP Event The present best estimate initiating phase accident calculations based on the insertion of 3.2$ of reactivity is that a 2.4c or loc /sec ramp leads to multiple irradiated pin failures with fuel sweepout, neutronic shutdown, and low energetics. The lowest power fuel from the outer ring of assemblies is predicted to have a very small central void and be largely unrestructured. As the power increases during the transient, a high internal gas pressure develops in these pins be-cause a large amount of fission gas must be acconinodated by the small O

6-40

available volume. Thus the pins in these assemblies fail early, but relatively little molten fuel is ejected and swept out of the core.

The continued SASBLOK evaluation, for an 87 areal percent blockage in Channel 10, showed that the FCI zone fission gas bubble is swept out of the channel by sodium flow which stabilizes at 50% of the steady-state rated flow. The reactor is temporarily rendered subcritical due to the fuel sweepout until the continued ramp insertion returns the reactor to nominal rated power at about seven seconds after the initial failure. The power and net reactivity at the termination of the total reactivity insertion of 3.2$ are such (3.3 x nominal and 31t) that the additional failure of Channel 2, followed by fuel sweepout and neutronic shutdown, is the most probable path to accident ter-mination.

At a lower insertion rate of 2.4c/sec, the allowance for lono term (140 sec) escape of fission gases from the fuel results in non-failure of the low power microstructure fuel represented as Channel

10. Instead, the higher power (7.5 KW/f t) irradiated fuel of Channel 2 fails and renders the reactor temporarily subcritical, As in the base case, additional failures would be necessary to assure permanent shutdown.

A 20c/sec case was performed and followed much the same accident path that the 10c/sec case followed. Channel 10 failed first just as it did in the base case but significantly earlier (6.46 sec compared to 11.54 sec). This case is slightly more energetic than the base case, but termination of the transient is also predicted to occur in a benign fashion.

An arbitrary insertion at 50c/sec also resulted in benign energe-tics. The higher energy deposition does result in additional fresh fuel failures in Channels 1 and 3 besides the irrad'iated fuel failures in 10 and 6. However, all the failures were nco-autocatalytic and generate sufficient negative reactivity to tenninate the sequence on the firs t bur's t.

A comparison of the effects of two current transient fission gas re-6-41

lease models (Gruber and Smith) in predicting pin failure resulted in different pin failure sequences but no significant change in acci-g dent energetics or termination path. Use of the Smith model led to ini-tial failure in Channel 9 due to high local clad temperature resulting from local coolant boiling in that channel. The larger molten fuel to fission gas mass ratio at failure resulted in a more energetic fuel-coolant interaction and more negative fuel motion reactivity than the base case. At the termination of the calculations, the 2.5$

of negative reactivity is not sufficient to guarantee neutronic l shutdown. As in the base case, a return to overpower conditions ,

coupled with the failure of additional pins is probable.

Calculations of fresh and irradiated pin clad plastic straining during the 10c/sec transient indicated that initial failure of irradi-ated pins based on the burst pressure criterion will occur before nominal (approx.1%) plastic clad straining develops in fresh or irradiated pins.

The HEDL damage parameter empirical fuel pin failure correlation was used to predict failure in two SAS channel types during a 50c/sec transient. A comparison of the damage parameter failure predictions with those calculated using the burst pressure failure criterion in the SAS3A code indicated that the HEDL correlation predicted failures at earlier times in the uransient with smaller melt fractions and com-parable axial failure elevations in the core. Although a complete analysis of all ten 80EC core channels was not performed, the energetics were judged to be on the same order of magnitude as predicted by the SAS3A analysis.

Two TOP cases were analyzed with forced midplane pin failures and ramp rates of 2.4c/sec and 10c/sec. The outcome of these two cases varied greatly with the 2.4c/sec case terminating in a hydrodynamic, disassembly and the 10c/sec case terminating with limited fuel pin failures and core cooling in place. The differences between these two cases is not so much the result of different ramp rates but rather of differences in phenomenological modeling specifically in the amount of 9

6-42

fission gas released to the plenum prior to fuel pin failure. This modeling is based primarily on engineering judgment and possesses a substantial degree of uncertainty. It becomes apparent from results of these two cases that it cannot be assumed a priori that midplane fuel pin failures in TOP accidents will be autocatalytic in nature and progress to hydrodynamic disassembly. Uncertainty in.the values of the Doppler coefficient or of the various material worths is con-sidered to be of secondary importance when compared to the uncertainty in phenomenological modeling.

In conclusion, a category one or two TOP event in a BOEC core is a low energetic event in which the failed assemblies are cooled in place by flowing sodiua following neutronic shutdown. Only when cate-gory three pessimistic assumptions are made, such as large reactivity insertion ramp rates (greater than 50c/sec) or pin failures at the core midplane, can arguments be made for core disassembly with energetic consequences.

6.3 Unprotected Startup Accident in E0EC Configuration _

This section discusses the results of startup control rod with-drawal accidents. The analysis was initiated at full power, full flow conditions with nominal inlet temperature conditions. This step was necessary to assure consistent steady state fuel structure in the pins.

Within a time span of 3 seconds, a programmed reactivity step of -$7.00, a flow r~ ate of 40% nominal, and inlet tauperature of 316 C (Hot Standby Conditions) were attained and then held constant over an extended period of time. The startup accident was initiated with programmed reactivity insertions of 10 c/sec and 20 c/sec when the core temperatures became stabilized at the new conditions. At the initiation of the rod withdrawal transient from this offset zero time, the power was 0.06 x nominal.

6.3.1 Effect of Ramp Rate 6.3.1.1 Ramp Rate of 10c/sec Channel 8 initiates voiding at 69.246 seconds followed by Channels 6-43

1, 5, 4, and 3. Each channel is an individual event with a delay of $

(typically) several hundred milliseconds between events.

Slumping begins in Channel 8 at 70.522 seconds followed in the next 10 msec by Channels 1, 5, and 3. All of these channels fail high on the pin. A brief period of positive fuel reactivity is encountered as the void to' ward the core center is occupied by fuel and fission gas followed by strong negative reactivity as fuel is moved out of the core by the expanding fission gas. Channels 10 and 6 undergo FCI's at 70.531 and 70.544 seconds, respectively; in both instances failure is above the core midplane and fuel motion is dispersive after a brief period of fuel compaction.

The conbination of void and initially positive fuel motion reacti-vity causes a peak power of 81.7 x nominal (full power) and 97.4c net reactivity at 70.532 seconds. By 70.627 seconds the core is several dollars subcritical and at ('.4 x nominal power. With 40% flow being maintained, no further damage should occur.

6.3.1.2 Ramp Rate of 20c/sec h Channel 8 voids at 35.604 seconds followed by Channels 1, 3, and 5 all introducing positive void worth. Channels 4 and 7 start to void later but fail to complete voiding before core shutdown. Channels 2, 6, 9, and 10 never initiate voiding. With 40% flow being maintained by the pumps, a significant pressure drop still exists across the core and flow reversal ir more difficult to achieve. The void reactivity drives the core to a peak power of 16.3 x nominal (full power) and 83.5c net excess reactivity at 36.125 seconds.

Channels 8 and 1 slump at 36.24 and 36.129 seconds, respectively, and both introduce negative reactivity due to fission gas dispersion of fuel in the upper channel. Channels 10 and 6 undergo FCI's at 36.124 and 36.192 seconds, respectively. Both FCI's occur in the upper channel and are dispersive af ter a brief period of fuel compaction.

Once fuel begins to move, the power and reactivity drop rapidly and with 40% flow being maintained no further damage is likely. Re-entry 0

6-44

of slumped fuel from above in the face of the imposed pressure drop is not likely.

6.3.2 Summary and Conclusions on E0EC TOP at Startup Two startup accidents with ramp rates of 10 and 20c/sec were in-vestigated. In both cases, the combination of negative reactivity contributions from molten fuel disper sal by fission gas and from FCI's occurring significantly 'bove the core midplane limit the progression of the transients and subsequently result in benign termination of the accidents. The 10c/sec case does come sufficiently close to prompt critical (97.4c) that modeling uncertainties could conceivably place it in the energetic category. I!owever, the structural margins would not be approached. The startup cases are both judged to most likely result in a damaged but still coolable core geometry.

If tha positive startup power coefficient (operative at low core power to flow values) were to have been included in these E0EC start-up accident events, an approximate thirty cents of additional reactivity would be inserted during the period just following reattainment of criticality and prior to nominal pcwer levels. A review of the reactor response during this interval for the analyses nerformed herein re-vealed that the positive power coefficient ef fect would likely occur prior to sodium voiding, at Sc/sec or less for desiqn reactivity in-sertion rates, and be mostly offset by Doppler and axial expansion feedbacks. Its general influence would be to accelerate the fuel themal upset and lead to a higher probability of fuel pin failures into sodium filled assemblies. The 20c/sec case effec.ively demonstrates this be-havior when compared with the 100/sec insert ion for the faster transient, fuel sit.mping in the highest power channel occurred simul-taneously with an FCI in Chaanel 10. As sta ted in the text this pin failure occurs in a manner which rapidly terminates the excursion without significant energetics and limits further reactor damage.

Since the maximu11 positive power coefficient reactivity effect in the 30EC cor. figuration is approximately sixteen cents, instead of thirty, its effect on an accident progression would be much less.

Additionaliy, since the positive power coefficient would not exist at full power, none of t he liCDA evaluations initiated from full power are impacted.

6-45

TABLE 6-i E0EC BASE CASE FUEL CONDITIONS PRIOR TO FAILURE IN CHANNEL 8 Midplane Ilidplane Damace Severity SAS Average Average Fuel fielt Clad Wall Primary /f ailure Channel Linear Power Burnuo Fraction Temperature Loadino/ t.oad (kw/ft) IGWD/fJ (%) ("C) (%}

l 7.8 42 35 717 91 2 6.6 89 26 669 28 o, 3 7.1 58 28 682 52 1.

4 6.2 90 24 676 31 5 7.0 38 25 699 94 6 6.1 76 18 673 41 7 5.8 70 17 691 51 8 8.0 43 38 712 103 9 6.4 84 24 668 31 10 5.5 59 15 700 66 e G #

TABLE 6-2 E0EC 50c/SEC COMPARISON OF PIN FAILURE ESTIMATES Failure Predicted Usino SAS3A Burst Pressure Failure Criterion -

Fraction of Time Normalized Melt Fraction At Active Core Channel 1_Sec) Power Midolane Failure Site Heicht 5 3.121 7.39 0.329 0.264 0.76 1 3.129 7.18 0.403 0.281 0.85 8 3.130 6.38 0.433 0.308 0.85 T

Failure Estimates (1) Usir.g HEDL Self-Consistent Empirical Correlations Fraction of Time Normal i zed Melt Fraction At Active Cort Channel (Sec) Power Midplane Failure Site Heicht 5 2.65 5.082 0.255 Note (2) 0.81 8 2.70 5.259 0.395 Note (2) 0.88 NOTES:

(1) Only Channels 5 and 8 were analyzed.

(2) Incipient Melting.

TABLE 6-3 E0EC TOP MIDPLANE FAILURE CORE CONDITIONS AT TRANSITION TO DISASSEMBLY With Fuel Expansion Without Fuel Expansion Time, sec 12.262 10.369 Normalized Power 155 ' 134 Net Reactivity, $ 1.059 1.054 VENUS Driving Ramp, $/sec 46 53 g Peak Fuel Temperature, C 4049 3984 Fraction of Core Voided, % 8.6 6.2 e G G

TABLE 6-4 BOEC BASE CASE FUEL CONDITIONS PRIOR TO FAILURE IN CHANNEL 10 Midplane Midplane SAS Average Average Fuel Melt Clad Wall Channel Linear Power Bu_rn lu Fraction Temperature Damace Severity (kw/ft) [GWD/T) (%) ( C) (%)

1 8.6 1.7 48 764 11 3 8.6 1.7 47 757 14 es 5 7.5 1.5 34 740 10

$ 7.5 1.5 756 10 7 38 9 7.3 1.4 36 806 12 2 7.5 53 35 714 45 4 6.7 60 25 718 52 8 6.7 54 26 714 46 6 5.6 45 16 705 56 10 5.3 43 14 703 74

TABLE 6-5 SODIUM BOILING AT INITIAL PIN FAILURE TIME Time Boiling Begins Initial Pin Fail-BOEC Case in Channel 9, (sec)* ure Time, (sec)*

10c/sec, "best estimate" No Boiling 11.54 10t/sec, pin failure suppressed 12.05 No Failure 50c/sec, "best-estimate" 3.039 3.047 T'

8

• Time after start of ramp insertion O O O

TABLE 6-6 BOEC 50c/SEC COMPARISON OF PIN FAILURE ESTIMATES Failure Prediction Using SAS3A Burst Pressure Failure Criterion Fraction Time Normalized Melt Fraction At Of Ai 'ive Channel (Sec) Power Midplane Failure Site Core I.aioht 10 3.047 7.99 0.111 0.063 0.60 3 3.051 7.82 0.478 0.236 0.85 1 3.057 5.96 0.487 0.242 0.85 c, 6 3.057 5.96 0.170 0.096 0.60 Failure Estimates Using HEDL Self-Consistent Empirical Correlation II)

Fraction Time Normalized Melt Fraction At Of Active Channel (Sec) Power Midplane Failure Site Core Height 4 2.84 5.74 0.284 Note (2) 0.81 10 2.92 6.01 0.139 0.118 0.65 NOTES:

(1) Only channels 4 and 10 were analyzed.

(2) Incipient Melting

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6-52

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t, p,i ',ny' p , ,! ,q, o, o" ,i ,, i , ,o e

, o ', 'p,

,e d

i i

i o ,

i l l,

,9. ,, ,,ot i i,! i, ! q' inl ,1  !!I

-, 4 'q ,

q ,i i I 120 / 'n 1, , '

' j , , qn o' l ' ,ph1 '

V U (i ;L ,,h -

0.010

' ' i l /l J , , j,,n,i/,hJ,Jlj 1' o , t M lg i 11, '" I r ' . ,/ N J, lio ',b , n ii ' b libllIlli ,,unt J&

Ij/ I ,( ',,L,,i j','J li, k

\

\V" h' I i,'i, t '

t i

i' TOP OF CORE t i . ,,."

' l , , , ' l i, 'i h, /> , i - - - _ _ _ _.

70 li ni ih,F' i

l l l

-0.010 0 0.04 0.08 0.12 0.16 0.20 0.24 TIME SINCE ST ART OF VAPOR F ORMATION (SECONDS)

Figure 6-4 Computed FCI Zone for the E0EC TOP Base Case 6-55

i d,

4 0

3900 , , 1.2 i i i TOP E"~*

• ASE CASE 10 CENTS PE R SECOND R AMP FUEL CON 0fil0NS VS TIME CHANNEL NUMBER I POSITION = 33.2 '

U CENTER LINE g 2700 -

0.8 cc ,^

H /

< MASS AVERAGE f 5 2100 -

, '/ O.B s

g w , ,, s

-4 1500 -w--"'

SURFACE "-

A 900 -

-- " "" M ' . 0.2 f F R ACTION 200 0.0 1100 1.2 TOP EDEC B ASE CASE 10 CENTS PER SECOND RAMP CL A0 CONDITIONS VS TIME

_ CHANNEL NilMBER 8 P051Tl0N = 83.2 _

_ CLAD 700 -

[' " "1 0.8 z

~~~, COOLANT g 500

______. - 0.6 2 9 $

i "

Q 300 -

0.4 100 -

0.2 FRACil0N I I I I i

-100 I I 0.0 0 2 4 6 8 10 12 14 16 TIME (SECONOS)

Figure 6-5 Fuel and Cladding Temperatures for the E0EC TOP Base Case 6-56

TOP E0EC CH ANNEL 8 PLUTO 0.0 -

-0.2 -

s00iuu

$ -0.4 -

d -0.6 -

z 5

5 -0.8 -

TOTAL m

fn -1.0 - r C FUEL '

g

-1.2

~

3 W

f ti

-1.4 '

<z m

-1.6

~1.8 -

-2.1 -

-2.2 -

0 20 40 60 80 100 120 TIME (MIL LISECONDS)

Figure 6-6 PLUTO Reactivity Determination for the E0EC TOP Base Case 6-57

O 103 8 -CHANNEL 8 CRBRP TOP E0EC 6 B ASE CASE l~ PIN CALCULATED BY h 2 )

SAS/FCI

$ jg2 I FCIZONE 05 8 -

. _ _ _ F AltllRE GROUP 1 o 6

_ , _ _ FAILURE GROUP 2

... F AILURE GROUP 3 2

a

$ r e

"6a -

4 ~ -

2 -

FCIZONE I I I I 100 O 50 100 150 200 250 TIME (MIL LISECONDS) 103 8

6

- TOP EDEC CHANNEL 8 g

~

4 g CALCULATED BY PLUTO

=

2 -

b 102 _

o 8 -

3 6 -

N 4

w g 2 -

N 101 -

M

o. g 8 -

4 -

2 -

I I I I 100 O 20 40 60 80 100 120 TIME (MILLISECONDS)

O Figure 6-7 Pressure-time Histories for the E0EC TOP Base Case 6-58

3 2 - --- SAS8t0CK SIMUL AT10N (>--() FCISOLUT10N (ENDS AT 254 MSEC)

MEL T F R ACTION 0.42 $ $ _

1 - *% -

0.41

( 's s - 0.40 g " 5 m s c a r

< 0 0.39 s g 8 8

8 b ~I ~

RE ACTIVITY 5

- - 16 g a m

< w y -2 - -

14 x N M e \

w -

12 z N 3 lE \

-3 ,-~~- g---- , -

10 <

> V O -

8 M P R E S$U R E

}5 c

-4 - -

6

{

\ -

4 s

N m

-5 - N -

2 g s

r

~~,,~~ -

0 w

-6 I I -2 ~z 0 100 200 300 TIME Fil0M INITI AL F AILURE (MIL LISECOND)

Figure 6-8 SASBLOK Simulation Compared with Original FCI Solution 6-59

O 10I 5 8 -

6 -

~

4 -

E 2 -

1 <

x a W I o U

n.

1 z

j o 100 _ _ _; -

H 8 -

j t-

1. ~~~

k 6 -

\ , ,

f--

o

1 e - 5 - -3 4

~

I

$ #,# RE ACilVITY b

e y POWER ~5

{

L/,p I I I I I I 10-1 -7 10.0 12,5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 TIME (SECONDS)

Figure 6-9 Power and Reactivity Following Fuel Failure (Blockage Coefficient = 800)

O 6-60

370 0.310 0.0 = 12.01 SEC 320 0.260

- f l\\

5 l \

l

\ Na RE ACTIVITY y 270 g U -

0.210 E l

\ E d j \ $

$ \ d

< ll it,*p.

/" l

\ o S a m 220 -l[llnMf h,h -

0.160 >.

o I!lOfjiMi$y,. t-c 2 S jkn$"W %

- i :i[f"!i%.. ..

ig ;M y,g%ijflp,1

-n t.x; J b' U i y 170 -

hhjhh lh[lbk -

0.110 E i0 qwi....

H ,N. 7 UPPE R lp,n p[w%;,,; d; W% A. . ..,;j:% W!.;.Ka(M,,$l f """

5 a

/N r c , u..c a , a , :J! &

120

{j w j p+1gyfy:,; { CORE 0.060

%p%.j'-[;li-((dhogui#g{

h' l0 -

kW

,N"'

[ll!ih

\

\

\

y /

i  ;

70 0.010 0 0.15 0.30 0.45 0.60 0.75 TIME SINCE START OF VAPOR FORMATION (SECONDS)

Figure 6-10 E0EC 2hannel 5 Simulation of FCI Through Vapor Collapse 6-61

O 1.0 5.5 -

4.0 - lO 5 lgl e ,i S II g 2.5 yj lil I

s g i mui i.e _.

I i

I h L~~

-0.5  %,,1 ST ABILIZED FLOW = 0 21 OUTLET I f I l i

-2.0 12.00 12.15 12.30 12.45 12.60 12.75 12.90 TIME (SECONDS)

Figure 6-11 E0EC Channel 5 Flow Response (Blockage Coefficient = 800) 6-62

3900 1.2 3300 - -

1.0 13 e 2700 - -

0.8 CENTERLINE TEMP.

5 cc 2100 -

\s -

0.6 g E

N g g ASS M AVERAGE TEMP.

d 1500 \g -

0.4 cc o - SURF ACE TEMP. \

900 - Ns -

0.2 FRACTION ~~~% __-----.a I ' ' ' I -~ '

300 -

0.0 10.0 12.5 15 0 17.5 20.0 22.5 25.0 27.5 30.0 TIME (SECONDS)

Figure 6-12 E0EC Channel 5 Midplane fuel Conditions (Blockage Coefficient = 800) 6-63

O 1100 1.2 CLAD TEMP.

/ STRUCTURE TEMP.

900 - -

1.0

/ 's N

N

$ 700 -

's N -

0.85 5 o y s E g 500 -

COOLANT TEMP.

0.6 y E ti

• e 300 - -

0.4

• g 100 -

F R ACil0N

-100 -

0.0 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 TIME (SECO NOS)

Figure 6-13 E0EC Channel 5 Midplane Sodium and Steel Conditions g (Blockage Coefficient = 800) 6-64

310 0.310 5 270 -

0.0 = 11.09 SEC -

0.260

• /g U lI w

E I /vI l

t 1

m 230 f, f- Na RE ANITY _ 0.210 g E l1  ! Na FILM DRYOUT $

x s: I g a S I 8 m

I;s I:

r. / In ,

o 190 h7 / , ,. l f .g. , '

0.160 -

E ad  ;

I I

.'w.' . ,!,, . 'c.

l w-e a

H g

pi

, :. ;:1l gy ,

,.t..,',

m I :, ; M ' <t j I, ;g - .g.gy fjp[;-]

g 150 g.,I:ji UPPER ,

q., -

0.110 g, o BLANKET , lfil t'.

93 i

@ I.lFlf- (j/ g,'Jj ,qn f Isf,. ,, - p % l.fj p' y

3 5

J,M ' *tJ~;J,A UR* ii' '

pl 0.060 w

110

.w1 ,/ i m i r .a Q' ,

- 'n p ,e ' .7,7 -

i

.; \

fi. gg CORE i ' \^

? s'/ 'p):p, I

70

't  ! I 1 0.010 0 0.5 1.0 1.5 2.0 2.5 3.0 TIME SINCE START OF VAPOR FORMATION (SECONDS)

Figure 6-14 E0EC Channel 5 FCI Simulation and Delayed Boiling (Blockage Coefficient = 2000) 6-65

7.0 5.5 -

4.0 t

{ 2.5 jl STA8ILIZED FLOW = 0.15 7 INLET 1.0 U,\ --

f- - . w~

-0.5 -

T GUTLET I ' ' ' ' ' I

-2.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 12.0 TIME (SECONDS )

Figure 6-15 E0EC Channel 5 Flow Response (Blockage Coefficient = 2000)

1. 9 0

3500 1.2 CENTERLINE TEf.1P.

3100 - -

1.0 2600 0.8

,U -

[ f.1 ASS AVER AGE TEf.1P. ,

5 ~~ Y G 's 8 0.5 2 cn C

E 2100 -

N~~%~~ ___

ae o

2 c'n d b d \s% 2 0.4 "-

2 1600 -

SURF ACE TEf.1P.

r- r 1100 - [ s --- - 0.2

' F R ACTION

' I I I ~

600 O.O 11.6 12.1 12.6 13.1 13.6 14.1 14.6 15.1 1!LS TIME (SECONDS)

Figure 6-16 E0EC Channel 5 Fuel Midplane Conditions (Blockage Coefficient = 2000)

370 0.110 0.0 = 11.99 SEC 5 320 , f i -

0.090

$ k t I\

E d Na REACTIVITY I)\

SI I I

\ \

I A lp ,

h 270 /g  ; -

0.070 g

$ bl!I, g h th !!I Und t ;d '

!  ! Na FILM DRYOUT l '

g 20 jgg , pp\f7%.,q -

Om0 g 5

s 170 kitsr lht

$!j;Rn l

/A>>!g!MdMf{@S;i i MM MYhi.h nh ! @di ih, ; ' 0.030 5 ip!

b h

]

5 120 hk)"

- ia * !"%

/

ft.hkkhhkkhhh itii 0.010 C

?"%g # ,, / Md

" Kkg,i dD S @U Ig!j . . ,;;UH"!g h q; $6 1 ECii!W [ \ -

.n %1lh:%

I h g CORE .

yy kh"""g. ""

g "kh;gf 70 -0.010 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 TIME SINCE START OF VAPOR FORMATION (SECONOS)

Figure 6 17 E0EC Channel 8 FCI Simulation and Delayed Boiling (Blockage Coefficient = 800) 9 -O e

7.0 5.5 -

3: 4.0 t-3 l

l 2.5 h N I s i g g INLET z 1.0 t-r ly ST ABILIZED FLOW @ 0.21

- 0. 5 g 1,4

• LOUTLET I I I I I I '

-2.0 12.0 12.8 13.6 14.4 15.2 16.0 16.8 17.6 18.4 TIME (SECONDSi Figure 6-18 E0EC Chancel 9 Flow Response (Blockage Coefficient = 800) 6-69

O 3800 1.2 3200 -

1.0

_ CENTERLINE TEMP.

5 2600 -

0.8 m w S  %

5 \ g Q

g 2000 -

\s,'s MASS AVERAGE TEMP.

2 0.6 $

$ 's E

1. SURF ACE TEMP. N g d 1400 - \ -

0.4 E

's W 's,'s 800 -

,'N  %

0.2 FRACTION N ','==. --

s m 200 I -- ' ' ' -

' I 0.0 10.0 12.5 15.0 17.5 20.0 22 5 25.0 27.5 30.0 TIME (SECC;JDS)

Figure 6-19 E0EC Channel 8 Midplane Fuel Conditions (Blockage Coefficient = 800) 6-70

1400 1.2 CL AD TEMP.

1150 -

1.0 G

\g STRUCTURE TEMP.

f 900 -

0.8 g

/ 's a x

i

!$ 650 -

4

/ N -

0.6 o

• COOL ANT TEMP. $

400 -

0.4 150 -

0.2 F R ACTION I- - ' ' ' l- ' --

-100 O.0 10.0 12.5 15.0 17.5 20.0 22.5 25 0 27.5 30.0 TIM E (SECONDS)

Figure 6-20 E0EC Channel 8 Midplane Sodium and Steel Conditions (Blockage Coefficient = 800) 6-71

O_

mm3aOC

• bk u$C 0

0 a 0 0 0 0 0 0 s 0 5 0 5 1 4 '. g 6 4 1 0 c.

1 1 0 0 0 -

l 0

- - - - T - 4 E n RK E E N R o i

P A 0 t P C U L B a I

5 n i

T 3

3" 5 m I

• h T" .'.g=

"n V .

I r y

1IEg=E._5Mm .- .- e f8M-.M-

lI l L

'5, G e. ' , ' % :T <

=_

a_ 5= W "5M>p -

)

T

• "s m

1 S e

...$. D

[ ,

d ai!- $ Eg=[p"U I L  ! ,'

9'i'.

P - 0 o m' ,.[ ,

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E Y E E E , C T

I hw=M t.i. _EEn 2 s E. == L'y1=Ii "

E t

o V rI

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l. S Wmc'!r(pi;j

(

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AWE-I T

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N g n

fp'lp,fVIf,,1, O hb .*M=,_ya ..

A l

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E j

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fA. T l imf.f.

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R j

=

qM[m _

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_= p

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p O d 0 Ig 5=

E =

. f . , Fh=7. = m_

~ l 1

1 i

,r

- =

_ ,Ug'7g lp F e 0 y 0 A/ 6, ' , '  ;

j

. i. ,

m=_ _  ;

0 R

O a 2

.WI l ls ,g'qe [.

2 P e =

g !i, - A O

D

,E)/ ph.

a3E. V

= . t ilg g

/ [#" 5k- M.. .. :q$. . .ga.

=.5

.L>. ,'

F O

d n e a i n

4

= K'

\ .

'o T c f

"h f -. 5 R n i

.[

_3 "

'\l 7m [$IM._

z4gs . 3 - ,. A o f j,,I q ,

,g-3a.]g% I 1

T S

i f t e Il .

E a o l =.. 3. Q' C klf .E i2= a=_ G C

N l.

n. e j.<3='.7 9" i

T sj -

I g

S i U  :',. / i" 0 S a O f I E k C

Y R

D 4\ g 1

IM T

I C

c o

E F l S M

/ B 7 L / 8 (

9 FI / l 1

1 N a / ' 5 e f 0 n

=

f n 0 h a 0 i

', ,r g h h C

il,?

. dI , ;. i .

% g 5. g i g' i .

lkn0" f I[;i k. ,

l

' i i k l' j - ;

0 C

E 0

E 0

• 0 0 0 0 0 5

• 5 0 5 0 5 3 3 2 2 1 1 1

2 5 g ~om< ~ .e $ -

6 e

r u

g i

F e

[N

70 OF MWD M CHANNEL SYMBOL PE R PIN PER CHANNEL NO. 5 37 g 145 kg NO. 8 48 g 125 kg S AS E 0EC TOP @ 10 CENTS /SEC y 50 -

<t j TOT AL FUEL EJECTED I

E ft 40 -

g 7--

3 ,'

d 30 -

40 s 7 u.

j FUEL OUTSIDE OF CORE

$ f \ AND BL ANKET REGION E /

/ \

s 20 -

j

/

/ /g

! [ \ FUEL IN CORE AND 10 -

f BL ANKET REGION

/ / N l /  %

0 I I -

12.0 12.1 12.2 12.3 TIME (SECONDS)

Figure 6-22 Ejected fuel Located Within or Outside of Core and Blanket Region vs Time 6-73

1600 g 1400 _

't (1

y 1200 -

I 100% POWER = 120 W ATTS/GR AM g

3 8

d 1000 _

E 5

$ s

< /

$ 800 - %POWEA /

8 /

m 100

/

o /

w

/

E 600 -

i

/

6 60 5 /

$ /

Y 400 -

/

/

/

,/ */

/ /

200 -

s' /

/

, / ,- / ,/#p ~~~~

5-0

- -____~~ -__7_

30 40 50 MASS OF EJECTED FUEL / PIN ~GR AMS Figure 6-23 Effect of Mass of Ejected Fuel Upon Coolant Temperature Rise for Blockage (50% Porosity) g 6-74

1400 S AS E DE C T DP @ lOCE Nik3EC 1300 -

/~N 1 \

\

/ '

l N 1200 -

l \ ISAT BEFORE BLOCKAGE

. s If  %

F I l/ g Ns N

\

EXIT U l \ g

< 1100 -

l s

d j N

N\

s IhtET 1000 -

\ \

E N \

=

a TSAT AFTER BLOCKAGE

\

\ \

900 - \ N

• \ \

s \

w \

r \

z MASS OF EJECTED FUEL

< 800 - CHANNEL SYMBOL PER FIN PER CHANNEL E N O. 5 --- Ug 145kg \

\ _

N O. 8 45g 125 kg y 700 - - 10 5

_ 9 DECAY POWER b n

600 -

- 8 2 m

% BLOCKING TIME y U g

500 I I I 6 h w

12 14 16 18 20 22 24 M TIME (SECON DS)

Figure 6-24 Coolant Temperature in the Blockage vs Time 6-75

10 3.0 8 -

- TOP E0EC 2.4 CENT *. PER SECOND R AMP POWER + RE ACTIVITY VS TIME

~

2.0 4 -

POWER 2 __

4' -

1.0 E 5

cn 5 a y g a.

300 I

_ ga -

o 8 -

[

$ 6 RE ACTIVITY l 5

~

s -

- 1.0 m 4 -

l m o cc

= - I e i -

-2.0 2 -

I i

' ' ' I I I N 10-1 -- _3,g 0 6 12 18 24 30 38 42 48 TIME (SECONDS Figure 6-25 Power and Reactivity Traces O O O

5100 TOP E0EC 2.4 CENTS PER SECOND R AMP FUEL CONDITIONS VS TIME CHANNEL NUMBER 8 POSITION = 33.1 4300 -

1.0 G

3500 -

0.85 a 2 m o r :E

< z CENTERLINE TEMP. g 0.6 o

{2700 -

3 N

",//-[  ?

w 1900 - -

0.4

{ MASS AVERAGE TEMP..,f e .-

/

1100 --.

[ SURF ACE TEMP. p -4 - 0.2

-x F

p 300

/ 'R ACTION

' -- I l -- 'I I I 0.0 0 6 12 18 24 30 3S 42 48 TIME (SECONOS)

Figure 6-26 Fuel Temperatures at the Core Midplane 6-77

410 0.130 ifTERFACEL C Of VS T P E CHANNEL NUMBER 8

. 0.0 = 41.40 SE C -

i r- 1 ii k :"!"!l,:K! D 'i.%';; ]1 b 310 -

h h  ! -

l 0.090 I iA Qll hp iAm$)fm!h

=

3 B* -

I\flh,[qf%N f?

Mhbbh -

!b 210 0.050

- b/ .$l $ e $'!pf)i W 160 l

h,j -

0.030 ,E l h ji , - i h

$ ' bb BEN 5

110

' kbf d h

0.010

=

V f,

1(Lasfehi" 1, 77 7 7- ,

_0.0,,

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 TIME SINCE START OF VAPOR FORM ATION (SECONDS)

L' 1M'h"a;"2 """""

HA NEL NWBER 8 4.5 -

0 h 3.0 -

/\

b

( DUTLET g- ]

1.5

) \

,bh

-f /

INLET l 0.0

- 1.5 -

I

-3.0 41.39 41.44 41.49 41.54 41.59 41.64 41.69 41.74 41.79 TIME (SECONOS)

O Figure 6-27 FCI Zone Growth 6-78

103 CH ANNEL 8 CRBRP TOP 2.4 CENTS /SEC g

4 - r "

I/

e 2 i E 102 z 8 1 g 6 -

3 4 s '

E

!E 101 -

h 8 -

6 s 4 - ' N, ,

FCIZONE 1 I I f I 0

10 O 50 100 150 200 250 300 350 TIME (MILLISECONDS)

Figure 6-28 Pin and FCI-Zone Pressure History 6-79

101 1

g _

6 -

RE ACTIVITY l

4 -

- -1 1

1 1

2 _

l

-3 m cc cc POWER l N E

e \ 8 o

? $ 100 l E

-5 a

8 -

l $

y 6 -

CRBRP EDEC TOP $0.50/SEC RAMP RATE POWER + RE ACTIVITY V5 TIME c: h

~

4 -

E t:

=

1 2 - -

-9 1

1 I I I 10-1 I I I I

-11 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TIME (SECONOS)

Figure 6-29 Power and Reactivity Traces e G #

0.39  ;  ;  ;  ;  ;  ; [

CRBRP EDEC TOP $0.50/3EC R AMP R ATE 0.20 - COOL ANT RE ACTIVITY VS TIME m LINES NUM8EREO 0 10 a ~

(nj g I

T 2

T 1

0.00 q

2 ti -0.10 -

5 cc

-0.20 -

- 0.30 0.30 CRSRP E0EC TOP $0.50!$EC R AMP R ATE 0.20 - COOLANT RE ACTIVITY VS TIME E LINES NUMBERED 5

a 0.10 BY CHANNEL 8

' " ~ , . .

~ 0.00 -.- - , x, 5

g -0.10 -

E

-0.20 -

in 1 I I I I I

-0.30 I O 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TIME (SECONDS)

Figure 6-30 Coolant Reactivity by Channel 6-81

I I l I I I I CRBRP E0EC TOP $8.50/SEC A AMP RATE FUEL RE ACTIVITY VS TIME 0.0 LINES NUMBERED 2.3,4 E BY CHANNEL

$ -0.8 -

g Ig O

g 1 E -1.6 -

t i E I b -2.4 -

5 I l

-3.2 -

-4.0 0.8 CRBRP EDEC TOP $0.50/SEC RAMP RATE F UEL RE ACTIVITY VS TIME 0.0 O

LINES NL'MBERED 5,7,9 m BY CHANNEL l

- ,1 1

3 -0.8

I g -1.6 -

I

$ I\ 20 U -2.4 -

l

- 3. 2 I I I I I '

-4.0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TIME (SE CONDS)

Figure 6-31 Fuel Reactivity by Channel g 6-82

3 '" '

i I I I I I I CRIRP E DEC TOP $0.54/3E C R AMP RATE 2800 FUEL CON 0lil0NS VS TIME _. 1.0 CH ANNEL NUMBER 5 CENTERLINE u POSITION = B3 4 w 2300 -

,/ - 8.8 m a / a

1. MASS AVERAGE

1. 0.6 e

$ 1800 -

p -

o

a. s

E w _

'- p u

3 1300

- SURFACE A - 0.4 e E

800 -

- -- -- __ /[ / - 0.2 F R A C TION /

300 Y 0.0 CRBRP EDEC TOP $9 56/3EC R AMP R ATE CL AD CONDITIONS VS TIME CH ANNEL MUMBER 5 POSITION = 83.4 [

900 - -

1.0 I

U CLAD \

\ E 700 p- [,)

e COOLANT 0.8 [

- g C 500 .- #' -

0.6 z 9

lE F w ST R U CT U R E y a 300 - -

0.4 5 a

~ ~

FRACTION I I I I I I I

-100 0.0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TIME (SECONDS)

Figure 6-32 Fuel and Clad Conditions at Core Midplane 6-83

f TERF ACE 10C AT OPJ VS I f.

5 370 -

"^"" " 8 " '

0.26

~

g 0.0 = 3.12 eg w l \  ;

& l kld\! I f QI&ibi h Wl'$;Q dl l

~

! is i

$ /  ; 'idOllll ih 6

i

;  ; ']~

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Figure 6-47 Coolant Reactivity by Channel O 6-98

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O 12 CHANNEL 18 CRERP TOP IDEC BASE CASE A A -MOLTEN FUEL a -sotto FUEL 10 s { S M $a-e E e "6 A S w B 0 $4 G 2 8 ^ 2 B

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4 g X - SAS!FCI REsULTS ua

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                             - - - DAMAGE SEURITY

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m! ' mmGj0 2* >

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c. , COULANT REACTIUITY US I I r1E t on s r.o r; re; r, li v C 'iG'i'e f L

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       .24 6
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       .16 E                                                   LINES NUMBERED BY CH ANNEL            10
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t 1 I I I 1 1 I 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 TIME IN SECONDS Figure 6-62 BOEC 50c/sec Case Coolant Reactivity by Channel 6-113

          .00 h
         .05
 .       .10        -

m 5, g '.15 - E

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2 U

       .25        -

Q LINES NUMBERED 3

       .30        -

BY CHANNEL i

                         !    I      l         l    l         l      [

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      .00 g

7. 8, 9

      .05 m     .10         -

x 5 a 8 .15 - E C 3 .20 - 6 A U =c E .25 - LINES NUMBERED

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BY CHANNEL g I l l 1 I l 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 TdE IN SECONDS Figure 6-63 B0EC 50c/sec fuel Motion Reactivity by Channel h 6-114

2800 ,

                                                                            ~

2400 - 2 G_ E 2000 - E h1600 3 H z 3 d 1200 - 0.4  % 2 8 1 = CENT ER LINE TEMP. 5 2 = MASS AVER AGE TEMP; z 800 - 0.2 a 3 = SURF ACE TEMP. 4 = FR ACT10N 4 y a 400 1 1 I I I I I 0.0 $ 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 0.0 TIME IN SECONDS 1.0 900 1 = CL AD 2 750 - 2 Coat ANT - g 0.8 3 = STRUCTURE u 4 = FR ACTION

                                                                                -    0.6 600      -

s o 2 0.4 g 2 450 - s-2 U U E .300 - 0.2 E ' d

               -                                                                  - 0.0 150 4

0 0.8 1.2 1.6 2.0 2.4 2.8 3.2 0.0 0.4 TIME IN SECONDS Figure 6-64 BOEC 50c/sec Case: Channel 10 Fuel and Clad Midplane Conditions 6-115

6 a 8 ^ t- N BOEC TOP 50 CENTS /SEC W/CR ACKING yo INTERF ACE LOCATION VS TIME g

      - 0.0 = 3.04 SE C o

$5 co CHANNEL NUMBER 10 m

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  =   -

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[ . g  !! l llll [ - - - RE ACTIVITY E g= 1 1 1 1 I I I c 0.000 0.015 0.030 0.04 5 0.060 0.075 0.090 0.105 0.120 TIME SINCE START OF VAPOR FORMATION ( SEC ) O

  =r 80EC TOP 50 CENTS /5EC W/CR ACKING NORM AllZE0 FLOW VS TIME H

CH ANNEL NUMBER 10

                                                                       ,*'p....-2
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em -

                                    /

u- # N / = INLET @] -

                    /                                       --- O U T LE T 5

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O FUEL CON 0lil0NS VS TIME O o - o - _ ]M _o 1 = CENTER LINE TEMP. 2 = MASS AVERAGE TEMP. W - 3 = SURF ACE TEMP. 2_ M y $ "E 4 = FRACTION $ o $E m ~ m 2 z A O 2 4 g Yc x eN o W = w u. E _ _ N 2

    $             I       I        I          I     :     I                   g 0.0        .4       .8     1.2        1.6  2.0    2.4  18        3.2 8
    "                                                              2 CL A0 CONDITIONS VS 11ME o

g _ i_ - u 1 = CL A0 - o ~ 2 COOL ANT ,^ 3~ $E 3 = STRUCTURE $ f 4 = FR ACTION $ c C 8 _ m 2

• m z 2 9 W o $

Q a m u O - - N o l l I I l l I 4 y 00 .4 .R 1.2 1.6 2.0 2.4 2.8 3.2 TIME IN SECONDS Figure 6-66 B0EC 50c/sec Case: Channel 3 Fuel and Clad Midplane Conditions 6-117

5 O fy,5 )' INTERF ACE LOCAil04 V5 TIME se

       ~                                                                    -

O CH ANNEL NUMBER 3 0.0 = 3.04 S E C

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   "?
       -        ----- OU TL E T CHANNEL NUMBER 3 e                                                           ,
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6-118

2 3 ',J 0 8 I 2 0 f h I t w o I r G 4 ) e I 2 S n o 0 D N Z O I C E C S F l ( N d 0 O n I 2 I a 0 T g 1 a A n M i d l R l

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               ---              SMITH-STEVENSON 900   -

6 FCI CH AN NE L 10 0.9 O FCI CH ANNEL 9 800 - - 0.8 O MELT FRACTION DATA POINTS f 0.2 _ 700 / z 0.7

                                                             /                                 b 3                                                                                  C        P 5  600 g-   0.6 g m

' = m 5 0.5 m $ 500 - b

                                                                                      =

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                                                                       /

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                                       --     9m- . ~~ ~. P          u 0.0    -

0.0 V 0 1 9 10 11 12 13 TIME (SECONDS) Figure 6-69 Comparison of Pin Failure Conditions O O O

101 , __1 g_ y 500tuM E h 10 0 _ 2 E o CHAf1NEL 9 BOEC TOP SMITH to-1 _ FISSION GAS RELEASE N c E <t s 10-2 _ b O Fl5510N GAS 10-3 - [ '~~~~~~  %~% G LA 10-4 25 3 o MOLTEN FUEL 20 - / } $ / $ / a_ 15 -

                                                     /

o CHANNEL 9 BOEC TOP SMITH a FISS10ft GAS RELEASE z " 10 - C o b s - SOLID FUEL =  % , 2 / __ _ _ _ _ _ _ _  % =%. . a f . I I ' ' ' O 0 20 40 60 80 100 120 140 TIME (MIL LISECONDS) Figure 6-70 FCI Zone Fuel, Sodium and Fission Gas Mass (Smith Model) 6 -1 21

O

                           ,           ,           ,          ,        ;       ,       g CilArtNE 9 80EC TOP SMITH                        4
      '5'        - FISS Ofl GAS RELEASE                            /1 /l
                                                                 / y us?tt
 $ 300           -

j 7

 =                                             /

p. /

g 250 - j / urPER FClINTERFACE C / u /

 $ 209          -                  l 5                             /

y / g 150

                          ,/
                       /

100 - LOWER FCllNTER 50 102 8 - CIIANNEL 9 BOEC TOP SMITH 6 - FISS10fl GAS RELEASE 4 ~

                                                      ---- PIN C AVITY OF G ROUP 1
                                                      --- PtN CAVITY OF GROUP 2 y      y      _         g                             ---- PIN CAVITY OF GROUP 3 05                       \g 5                            4 vs     6 U

f 4 - 2 1 1 I I I I 100 O 20 40 80 80 100 120 140 TIME (Milliseconds) Figure 6-71 FCI Zone Interface and Pressure Profiles (Smith Model) O 6-122

101 3.0 0 - BOEC TOP SMITH FlSSION G AS RELEASE MODEL POWE R + RE ACTIVITY VS TIME 6 - 2.0 4 - POWER m x 1.0 y 2 - 5 2 se o

                                                    - - - - - -                                o e              ,,,_______------                                                                 -

o 10 - 0 u 8 - e f6 l

                                                                                         - 1.0 <

z 4 - m RE ACTIVITY g $ 2 - 1

                                                                                         -2.0 I

i

                                                                                         -3.0 10-I 0         2          4         6         8      10        12         14        IE TIME (SECONDS)

Figure 6-72 Power and Reactivity Traces (Smith Model) 6-123

O 101 1.0 8 - 6 0.8 4 - POWid m 0.6 $ , 2 - g w o 5 o o z o 100 u 8 - 0.4 { N 6

                                          ~~'
                              ,,                                           {

E ' - 0.2 <

        ~

4 E / REACTIVITY

          /
            /                                                              $
        /                                                        -

0.0 2 _ I I I I I I I 10-1 -0.2 0 2 4 6 8 to 12 14 16 TIME (SECONDS) Figure 6-73 Power and Reactivity Traces With Burst Pressure Suppressed O 6-124

340

                                                                                                                                                            -0.300 INTERFACE LOCATION VS TIME CHANNEL NUMBER S                                                o. i !

s, e'!d, ( O_0 = 12.05 SEC j 8EhpM gj G 300 - s s's ,E[g@ l fig,N[!M [!p i k j j f;jj - -0.350 t N s/

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                                                                                                                                                           -0.550 x                                                                                                                                      ,.

I ' I ' 100 I I '

                                                                                                                                                           -0.600 0.000             0.10         0.20                   0.30                  0.40         0.50                 0.60                  0.70       0.80 TIME SINCE START OF VAPPR FORM ATION (SECONDS)

Figure 6-74 Channel 9 Localized Voiding Pattern With Burst Pressure Suppressed

O 1.E-1 NOTE: NO PL ASTIC STRAINING OCCURRED IN CHANNELS 6 AND 10 1 NUMBERS INDICATE SAS CHANNELS 1.E-2 - [\ 3 r[ 's

                                                           ,/l
                                                              /:'

1.E-3 - #

                      ~ ~~~~~                               4 i_                    M,, *   '

S 1.E-4 b a. a W 1.E-5 - I i 10 11 12 13 TIME INTO TRANSIENT (SECONDS) Figure 6-75 Maximum Cladding Plastic Strains With Burst Pressure Suppressed O 6-126

2.0 101 g _ BOEC TOP, F RESH PIN PL AS F AIL STRAIN = 0.002 POWER.+ RE ACTIVITY VS TIME I 6 - __ 1.5 4 - POWER E 1.0 ea 2 J e o ua 5: RE ACTIVITY jj h a 100 l- 0.5 ;

                                                          ,__           - I                e e

a s - i a

                          "_                                                               g y     6 g

l- 0.0 $ $ 4 l m = - I b i t- - 0. 5 2 I I I I I I I -1.0 10-1 4.5 6.0 7.5 9.0 10.5 12.0 0 1.5 3.0 TIME (SECONDS) Figure 6-76 Power and Reactivity Traces: Fresh Pin Plastic Failure Strain = .002 6-127

.            BOEC TOP FRESH PIN PL AS F All STR AIN-0.002 330        CHANN L U               1                                  .

0.210 0.0 11.51 ,gffj g 5 270 ' 0.170 3 5 f C~?q %h s I ~

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Fuel Reactivity Components by Channel 6-1 31

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7. Initiating Phase Analysis for Unprotected Primary Flow Coastdown_

7.1 Loss of Flow (LOF) Event in E0EC Ccnfiguration at Full Power 7.1.1 Best Estimate Analysis This case provides a best-estimate scenario (within the scope of current-ly available models) to deccribe the events following an unprotected, flow coastdown in CRBRP for a core at the end of the first year of a three-year equilibrium cycle. The timing of the various events (boiling, initiation of cladding melting, and fuel motion) is given in Table 7-1. The power and net reactivity histories, describing both the overall accident and the burst details, are given in Figure 7-l. Boiling occurs first in Channel 8, which represents the highest power assemblies in the outer enrichment zone. The void reactivity slowly builds up until the reactor is near prompt critical. The channel representation of the voiding reactivity is shown in Figure 7-2. As flow reversal occurs in each channel there is a somewhat abrupt increase in voiding reactivity. A core representation using a more detailed channel description can be expected to further smooth out the reactivity effects of sodium voiding. The reactivity component plots are shown in Figure ? 3. Cladding steel is presumed to mix with the fuel and its reactivity contribution is combined with the fuel reactivity in Figure 7-3. The sodium voiding reactivity ramp in the burst phase is about 55/sec. Doppler and axial expansion feedback suffice to hold the reactivity below prompt critical up the the point of fuel pin break-up. Following fuel breakup, first in Channel 8, then in Channels 1, 3, and 5 (the freshest highest power fuel) there is an abrupt decrease in power due to a fission-gas-induced fuel dispersal . Channels 1 and 8 break up exten-sively, and form a fission-gas, fuel, and steel dispersion, which begins to settle but contributes very little reactivity in the time scale of the remaining SAS calculation. However, the SLUMPY model in Channel 3 and, to a lesser extent in Channel 5, still possesses an appreciable upper fuel segment. The limited resistance of the fission-gas, fuel and steel dispersion existing only in the center of these assemblies is insufficient to prevent the fall of these upper segments. The resultant second burst (from positive fuel motion reactivity) is terminated by a fission-gas-induced dispersal of fuel in all the other channels. The model used here predicts that these 7-1

fission gas pressures act rapidly enough to prevent the second burst from going prompt critical. At the conclusion of the initiating phase of the acci- g dent, the pin geometry in the entire ire has been disrupted, the average core temperature is approximately near the fuel melting point, and fuel and steel boiling should be starting in the peak assemblies, since the peak fuel temperatures are predicted to be 3390 C and peak steel temperatures are estimated at 2900 C. Detailed plots of the important phenomena of interest are presented in Figures 7-4 through 7-13. The voiding profile in the peak channel is given in Figure 7-4. Due to a lack of cladding relocation and plugging, the channel does not pressurize and the lower part of the core remains relatively cool from sodium chugging. It also should be noted that each inward oscillation of the lower sodium interface tends to send a packet of vapor up the channel. Some of this vapor condenses on the fission gas plenum; this film is later stripped off by additional vapor streaming, and it tends to evaporate as the channel pressure decreases due to the uncovering of colder condensing steel surfaces. Temperatures of fuel, cladding, coolant, and structure in Channel 8 are shown in Figure 7-5. The sodium temperature stays at the local saturation temperature once vapor has formed due to the assumptions in the voiding model. The cladding terrarature increases rapidly once dryout occurs. Cladding then melts and is about 2300 C at the start of fuel motion. (Beyond the start of fuel notion, clad temperatures are calculated in SLUMPY and are not shown on the present plot.) The fuel temperatures slowly increase in the preboiling phase of the transient. There is a significant decrease in the fuel surface temperature once the first radial cladding node is completely molten and good thermal contact between the fuel surface and the cladding is established. When fuel motion starts, there is a significant radial temperature gradient in the fuel pin due to the high reactor power level and the effect of the cladding heat sink. (The fuel surface temperature calculation is also discontinued follow-ing the start of fuel motion.) In the burst phase, the average fuel tempera-ture rises sharply. At the conclusion of the SAS run, the average fuel temperature is cooling off due to rapid heat transfer to mixed-in steel and high heat transfer to the structure, which is now above 1300 C. O 7-2

A limited SLUMPY representation of fuel motion in Channel 8 is shown in Figures 7-6 and 7-7. The line shading in these drawings is intended to be representative of the local fuel density. The stubs represent the upper and lower pin segments. The " SAG" number of each figure represents the distance the upper segment has slumped. Figure 7-6 shows the early fuel expansion phase. The higher pressures toward the bottom tf the drawing are due to breahp of the last SAS axial node and the subsequent associated release of fission gas. The later settling-out of fuel is represented in Figure 7-7. Here the gas pressure has adjusted to approximately counter-balance the forces of gravity. The channel is pressurizing due to the high density fuel near the top, which restricts fission gas slip and escape (although this may simply be due to the one-dimensional character of the model). Fuel motion in Channel 3, one of the channels responsible for the second burst, is shown in Figures 7-8 through 7-10. The configuration at the start of the collapse of the upper segment is shown in Figure 7-8. Here most of the fission gas has slipped out of the compressible region and the pressures are beginning to stabilize around the the input ambient value of 3 atm. The configuration af ter the upper segment has fallen 4.35 cm is shown in Figure 7-9. The void in the center is due to the expansion of the region of higher pressure shown in Figure 7-8, coupled with the limited ability of fission gas to slip through regions of relatively dense fuel. Also, there is less energy in the dispersed fuel in Figure 7-9 than in Figure 7-8 due to losses to entrained steel and to the adjacent structure. The maximum slumped configuration before the breakup of additional nodes is shown in Figure 7-10. The upper segment has now fallen 9.53 cm. This corresponds to an acceleration of 0.75 g between Figure 7-9 and Figure 7-10. The further movement of fuel in this channel is basically dispersive. Figures 7-11 and 7-12 show fuel motion in Channel 7, one of the channels to disperse in the second burst. Figure 7-11 shows a configuration at the beginning of the expansion, while Figure 7-12 shows a configuration near the end. In general, the second burst causes far too much of the pin structure to break up in all channels to permit the model to calculate sufficient gas escape from the compressible regions to cause a further collapse of upper pin segants and u coird power burst in SAS. 7-3

As a final note on the base case, the voiding reactivity from Channel 8 stabilizes out at a maximum of about 14 cents. One of the characteristics h of CRBRP is that the peak channels do not, by themselves, insert large amounts of voiding reactivity. It is the voiding in a large number of average assemblies that leads to a power burst. This later voiding tends to be limited by back pressure that builds up in the inlet plenum. The inlet plenum pressure as.a function of time is shown in Figure 7-13. The outlet pressure is approximately 1.4 atm, and it is not affected much by the transient. Hence, at the time of the first burst there is a pressure drop of more than 2 atm across the core, which is probably significant in limit-ing the rate of voiding reactivity additions. Continued subcritical decay heat generation leads to a slow meltdown of the fuel and steel components in the reactor core. With the loss of core geometry, the SAS3A analysis must be terminated. The progression of the LOF event is continued into a transition phase and addressed in Section 10.

'.l.2   Effect of Phenomenological Uncertainties

'.'..c.1 / CLAZAS and Limited Initial Fuel Motion This case examines the E0Er ' # - rase with more pessimistic assumptions. First, CLAZAS is used for claddim, r aiocation. The CLAZAS module over-estimates the degree of upward cladding motion, and hence adds unrealistic amounts of additional positive reactivity on top of the posiuve reactivity from sodium voiding. Second, no fission gas is assumed to be immediately available for overpressurization of the SLUMPY compressible region upon fuel pin breakup. Fission gas release is assuned to occur only as given by the time constants of 0.1 sec for molten fuel and 3.0 sec for solid fuel. This is slow with respect to a prompt critical burst if one should develop. Thim, since clad is moved by the sodium vapor pressures, fuel should be moved in a similar fashion. Hence, the fuel compressible region pressures are taken from the sodium vapor pressures given by the voiding model whenever these sodium pressures are below the fission gas pressures or below the fuel plus steel vapor pressures. In return, a high friction factor is assigned to the voiding model in the compressible fuel regicn. By itsel f, this assump-tion would tend to sweep the fuel up the channel and result in reactor shut- g down due to the increasing plenum pressure as the accident progresses. How-ever, a fourth assumption is added. All fuel is assumed to obey the viscosity 7-4

relationship for fresh fuel, i.e., the fuel viscosity is assumed to be approximately 100,000 poise, and decrease linearly as a function of melt fraction to the 5 centipoise value for fully molten fuel. Hence, appre-ciable fuel movement is not seen until fuel is fully molten. Due to the high power that develops from sodium voiding and cladding relocation, a fairly long section of fuel becomes molten nearly simultaneously. The-transient high pressures due to the chugging of the lower sodium interface will then tend to compact the lower part of this molten column toward the midplane, resulting in additional positive reactivity. The timing of the events in the sequence is given in Table 7-2. It should be emphasized that the clad solidus point is taken from the inner clad node next to the fuei. Clad motion does not occur until all but 5% of an axial cladding node is at the liquidus. The power and reactivity traces during the burst phase of the transient are shown in Figure 7-14, and the components of the reactivity are shown in Figure 7-15. This case first suggests that the addition of cladding relocation reactivity to sodium voiding reactivity is not sufficient by itself to result in an energeti. excursion. However, a situation does develop where the reactor power is between ten and twenty times nominal power while the fuel is becoming fully molten in the peak channel. Then, the anticipated sodium-vapor-induced fuel compaction occurs simultaneously in the 12 assemblies of Channel 8. This results in a prompt critical burst, terminated mainly by a fuel vapor expansion in Channels 1 and 8. Since the compaction is induced so close to prompt critical only a short time exists for fuel acceleration; hence, the extra rama rate due to fuel motion is modest, approximately 20 to 30 dollars per second. The peak fuel temperatures are about 4920 K. The average temperature of core fuel is 3330 rs. It is not possible to carry this case further out in time with the SAS3A model, although a slow, monotonic, somewhat benign fuel dispersal from this point is likely. These average core temperatures are certainly still quite low. The reference to the clad solidus point being taken at the inner clad node is to emphasize that the clad solidus time in Table 7-2 is not the time clad motion begins. In the SAS3A code, the clad solidus time is that time at which a node begins to melt (reaches clad solidus) while the clad does not begin to relocate until all but the outer node, 5% of the clad, 7-5

has completely melted (reached clad liquidus). Since the inner clad node is hottest, that node usually reaches the solidus temper ature first. The voiding profile for Channel 8 is shown in Figure 7-16. Plugging of the coolant channel following the reentry at approximately 2.5 sec af ter voiding initiation results in a slight lowering of the upper sodium inter-face and an acceleration of cladding melting in the downvard direction. Due to the pressurization effect of the cladding blockage, the lower part of the core is considerably hotter than in the base case when fuel motion starts. The most representative CLAZAS cladding segment relocation plots for high power fuel are those in Channel 1, as shown in Figures 7-17 and 7-18. Figur_ 7-17 displays the typical CLAZAS result, where molten cladding is forced upward until a complete blockage is established, covering an entire node at about 14.6 sec. Cladding then begins to slowly move downward in an oscillatory fashion. Unrestructured fuel begins to melt which initiates fuel relocation at about 15.3 sec. As suggested by the middle drawing of Figure 7-18, fuel and cladding are calculated to occupy the same core loca-tion. Since the current models are not easily amenable to mixing of clad with fuel; clad and fuel motion must continue with separate calculations. g To perform a conservative estimate, an attempt is made to accelerate cladding motion outward from the core midplane and restrict fuel motion. This is done by computing clad segment force balances from the fuel pres-sure in the SLUMPY compressible region. The upper bnwidary interface on the fuel compressible mesh is not allowed to move upwar antil all cladding above the core midplane is out of the compressible mesh. The lower boundary interface is not allowed to move downward until all cladding below the core midplane is out of the compressible mesh. Once boundary fuel interfaces are free to move, they a m assumed to attach themselves to the closest clad-ding segment. This results in a large amount of upward cladding movement in Channel 1 as shown by the lait drawing in Figure 7-18. However, the SLUMPY computed expansion may be reasonable as shown in Figure 7-18, except for the upper node that has overexpanded in following n.oving clad. (The high pressures toward the lower part of Figure 7-19 are transient pressures due to compression of the fission gas in these cells. Slip of this gas will soon equalize pressures throughout the compressible region.) In contrast .to Channel 1, the highest temperature fuel in Channel 8 gets pushed above g the midplane in the sodium vapor compaction stage. The resolting fuel 7-6

pressure distribution does not allow cladding to clear the upper fuel region in the burst phase of the accident. Hence, motion of the upper fuel inter-face is restricted in the case of Channei 8. The final SLUMPY configuration is shown in Figure 7-20. Althougn sodium voiding, cladding relocation, and fuel motion were not coupled for this type of situation, Figure 7-20 demon-strates that the assumptions in this case were not optimistically dispersive. The inlet plenum also responds more vigorously than in the base case. A plot of inlet plenum pressure from initiation of voidng is chown in Figure 7-21. Comparing this pressure trace with that shown in Figure 7-13, it can '+ seen that voiding in the lower power assemblies is initially more coherent. Then, the prompt critical burst raises the inlet pressure tem-porarily to almost its steady-state value by initiating a coherent flow reversal in all channels. This pressure will rapidly decline as the sodium film is fully evaporated from hot clad in newly-voided subassemblies. Finally, an observation should be made regarding pin failure and the possibility of a fuel-coolant interaction in partially voided subassemblies. In tne base case, pin failure was usually predicted from loss of clad strength as the clad melting point was approached due to loss of sodium in the associ-ated coolant channel. Since the internal cavity pressures were generally low, these failures were assumed to be benign. In this case, the low power chan-nels tend to fail such that the initial FCI zone is bisected by the liquid sodium interface. The SAS3A code cannot handle such situations of failure into a quasi-voided FCI zone. However, the reactivity effect of such a f ailure is probably negative or at least small . For example, Channel 4 is predicted to fail at a node whose midpoint is 14 cm above the core midplane. This is the location of the liquid sodium interface. Fuel motion in the channel will probably be biased in the upward direction since there is almost a 6 atm pressure drop axially due to inlet plenum pressurization. Fuel motion inside the pin may be initially negative as molten fuel moves from the center-line up to the failure. However, such fuel notion will soon be indeterminate as the average cladding temperature is nearly 1200 C over a 42 cm length at failure, and development of a 42 cm rip from the midplane upward seems likely. Such a failure will probably accelerate sodium voiding and introduce some positive voiding reactivity. Fuel motion inside the remaining lower part of the pin toward the midplarte could also occur, Nevertheless, the fuel motion in the channel should dominate, and this should introduce negative reactivity, 7-7

i.e., fuel should move primarily from the midplane region where the liquid-sodium-fuel-coolant-interaction is occurring, upward toward the region where h only sodium vapor plus fuel exists. 7.1.2.2 Gravity Draining of Cladding One of the characteristics of the CLAZAS model is that it tends to dis-perse the molten cladding in a primarily upward direction. However, the R-Series experiments in TREAT (Ref. 59) suggest that it could move primarily downward. To determine the consequences of such motion, CLAZAS was slightly modified to allow removal of the effects of sodium vapor on cladding, thus allowing it to drain under the force of gravity. The event sequence for this case is given in Table 7-3, the power and reactivity behavior in Figure 7-22, and the components of reactivity in Figure 7-23. As for the base case, 1ere are two bursts, both of them sub-prompt critical. The clad draining case is milder during the first burst because the clad motion from Channels 1 and 8 is negative (see Figure 7-24). This condition results because the cladding first melts above the core mid-plane and, upon falling through the core center, is causing more parasitic absorption in the high-worth regions of Channels 1 and 8. This action, com-bined with fission-gas-induced fuel expansion in Channel 8, causes a rapid termination of the initial burst. The shutdown effect is so strong that the reactor actually goes subcritical for a time. Then, however, the combined effects of additional sodium voiding and positive reactivity from cladding that has finally moved below the core midplane, cause a second burst to occur. This burst is terminated by fission-gas-induced fuel dispersal in all of the other channels before prompt criticality is reached. As in the-base case, entrance into the transition phase seems likely, following ter-mination of the second burst. The most important point to be made from this case is that the direction of clad motion (if there is any at all) is important in the determination of energy release. When the cladding moved upward, a superprompt critical burst resulted which, although mild and quickly terminated, nevertheless brought the core into a molten state (3300 K average fuel temperature, 4920 K peak fuel temperature). For the clad draining case, the peak fuel temperature was about 4100 K at the end of the second burst. This is higher g than in the base case, undoubtedly because no rapid mode of heat transfer from the fuel is available once the clad moves. flevertheless, the fuel temperatures are not high enough to contribute much work .nergy. 7-8

7.1.2.3 flo Fission Gas Dispers." in SLUMPY Since the normal use of CLAZAS, combined with limited initial fuel motion, leads to c 'uperprompt critical burst, the consequences of making other pessimistic assumptions must be considered. Since fission gas provides such a strongly dispersive mode of fuel motion in SLUMPY, more energetic consequences are to be expected if its effects are ignored than are predicted in the base case analysis. The event sequence of this case is given in Table /-4; the power and reactivity behavior is shown in Figure 7-25. The reactor experiences a superprompt critical burst caused by the positive reactivity added from fuel slumping in all channels except Channel 4, along with continued positive reactivity from sodium voiding. The cor :nents of the reautivity are plotted in Figure 7-26. The reactivity goes through prompt critical at 15.665 sec, with a driving ramp rate from sodium voiding and fuel motion of about 155/sec.

• Such a ramp rate is too low to initiate a hydrodynamic disassembly so that a termination with SLUMP'i is more appropriate. DJTing the burst, the peak .

s power is about 600 times nominal (slightly less than for the CLAZAS case)- , termination occurs by fuel vapor expansion in Channels 1 and 8, just as in U the CLAZAS case. The peak fuel temperatures are about 5000 K with an . equivalent vapor pressure of 47 bar. 7.1.2.4 No Axial Expansion Reactivity Feedback This case differs from the base case only in that it does not take any credit for the negative reactivity effects of axial expansion. Again, no cladding motion is allowed until fuel starts to slump; then molten cladding moves with the fuel . The event sequence for .his case is shown in Table 7-5, and the power and reactivity behavior appec.r in Figure 7-27. As in the base case, there is a mild initial burst, which is turned over by Doppler reac-tivity and terminated by a fission-gas-induced fuel expansion in Channels 1, 3, 5 and 8. However, since the burst is a bit stronger than that of the base case, the pins in Channels 4 and 6 fail during th_e termination phase. The failure locations are above the core midiplar.e, so that the fuel motion reactivity following the fuel-coolant interactions is strongly negative as the fuel is swept out of tne channels. The SAS3A calculation is thus termin-ated af ter only one mild burst. 7-9

Examination of the fuel reactivity behavior (Figure 7-28) reveals that the fuel in Channels 1, 3, 5 and 8 is beginning to slump back into the core g at the end of the transient. If the fuel-coolant interactions had not occurred, then it is evident that the double-burst behavior seen in the base case would have again taken place. Since the initial burst for this case was a little stronger than the base case, the second burst probably would have been stronger as well. It is sufficient to state at present that this case falls midway between the base case and the no fission gas dispersal case, and hence would be bounded by the ' .tter if fuel-coolant interactions had not occurred. Since they did occ' he consequences are less than those of the base case. 7.1.3 Effect of Design and data Unc .rtainties 7.1.3.1 Doppler Magnitude Uncertainty Figures 7-29 and 7-30 show the effect of varying the Doppler coefficient value by 20%. 7.1.3.1.1 Increased Doppler Coefficient Increasing the Dopoler coefficient by 20% produces results similar to the decreased void worth case. Coolant voiding progresses gradually build-ing up the power level to about 5 x nominal. At approximately 15.85 seconds, the lower power channels begin to void causing a power pulse to 24 x nominal and initiating slumping in t:.e higher power channels. The channels intro-duce enough negative reactivity due to fission gas driven fuel dispersion to tenninate the power pulse. During the low power period following slumping, the core enters a very incoherent molten fuel state with channels alternating dispersal and compac-tion as new nodes are added to the slumped fuel and as the pressurizing gas slips out. Because of the temporal and spatial incoherence, no additional power pulses of any significance vere noted before termination of the initiating phase due to disruption of channel geometry. 7.1.3.1.2 Decreased Doppler Coef ficient A reduction of 20% in the Doppler coefficient speeds up the timescale of events but does not change the sequence or final result significantly. Voiding in the high and average power charnels results in a more or less g 7-10

gradual rise to a level of 10 x nominal power. At 14.03 seconds, slumping is initiated i the high power channels and fuel begins to disperse driven by fission-gas release. Additional voiding in the lowest power channels drives the power up to 47 x nominal at 14.12 seconds before fuel dispersal becomes sufficiently strong to reverse the power rise. The higher power levels in this case results in a more coherent dis-persal of fuel from all channels. By the time the initiation phase termi-nates, at 14.28 seconds due to disruption of channel geomatry, all channels have slumped nd dispersed significant quantities of fuel. The core is 3.68 ; subcritical and power below normal . A transition phase termination resembling the base case is expected. 7.1.3.2 Sodium Void Worth Uncertainty Figures 7-31 and 7-32 show the effect on power and net reactivity of varying sodium void worth by 50%. 7.1.3.2.1 Increased Sodium Void Worth If void worth is increased by 50%, the sequence of events is both accelerated and modified by the additional reactivity. The first significant power pulse, driven by voiding of the high power channel, occurs at 14.50 seconds reaching 24 x nominal power This pulse corresponds to a similar pulse in the base case at 15.65 seconds. This first power pulse is termi-nated by slumping accompanied by fission-gas driven fuel dispersion in the high power channels. As the fission gas in these channels is dissipated during the lower power level period, the dispersed fuel begins to collapse inward and is joined by voiding in the low power channels to fonn a secondary power pulse, reaching a peak value of 67 x nominal at 14.62 seconds. The energy deposited during this period causes additional nodes to slump in Channel 8 plus initial failures in all other channels except Channel 4, resulting in strong negative feedback due to fission gas dispersion of fuel . The core goes subcritical at 14.65 seconds and the power continues to decline. As a result of declining power following slumping, the dispersed fuel along with still intact upper core segments, begins to collapse in the low power channels, particularly Channels 6, 7, ard 10. This coherent collapse of 45% of the core drives the core into a prompt-critical excursion at 14.778 seconds with a driving ramp of 40$/sec. The burst is quickly ter-minated however within 4.5 msec by Doppler feedback plus renewed expulsion of fuel in the high power channels driven by fuel vapor pressure. The 7-11

peak power during this burst reaches 352 x nominal. By this time channel geometry has been largely disrupted and the initiating phase terminates. g 7.1.3.2.2. Decreased Sodium Void Worth if the sodium void coefficient is reduced by 50%, a pronounced st. etch-out of the accident progression timescale occurs. The power level remains at or below nominal until about 18.6 seconds when Channels 2, 4, and 6 void at approximately '.he same time increasing the power level to 1.8 x nominal. At 'this point fuel slumping occurs in Channel 8 which has been voided for some 5.9 seconds. At this low power level, the fission gas available in Channel 8 tends to slip past the fuel rather than disperse the fuel particles. Also, the upper pin segment collapses causing fuel compaction rather than dispersion. This gets the power level up to 9 x nominal, sufficient to initiate some dispersion in Channel 8 and also to fail Channel l which follows much the same scenario as Channel 8. Power reverts to a level of about 2.6 x nominal. By this time, all channels have voided so no FCI-type f ailuresare pos-sible. Continued collapse of the core section by section until a transition phase state is reached with t energetic disassembly appears inevitable. 7.1.3.3 Fuel Reactivity Worth Uncertainty Increasing the fuel worth by 20% has only a slight effect until fuel motion begins at 15.68 seconds. Some minor variation of timing does occur because of the effect on fuel expansion feedback. The initial void driven power pulse reaches a value of 30 x nominal and is terminated by fission gas driven dispersion of fuel in the high power channels. Because of the greater fuel worth, the drop in power and reactivity is more pronounced with the core going subcritical for 0.103 seconds. The lower power levels lead to a more abrupt collapse of the partially dispersed fuel and upper fuel segments. This event incombination with the greater fuel worth results in a prompt-critical excursion on the second power burst. Prompt critical is reached at 15.855 seconds with a power level of 54 x nominal at a rate of 255/sec , conditions which are marginal for a disassembly calculation. The burst is shutdown in SLUMPY within 8.6 msec from a peak power of 826 x nominal by fuel vapor pressure drivmdispersion of the high h power channels plus additional fission gas driven dispersion of the lowest power channel. 7-12

Decreasing the fuel worth by 20% causes only minor effects on timing prior to fuel motion, as in the case of increased fuel worth. Because of the reduced fuel worth, the first void driven power pulse reaches a value of 52 x nominal before fuel motion can reverse the power burst. The collapse of partially dispersed fuel and upper pin segment proceed as in the base case but the secondary power pulse goes briefly prompt critical because additional energy is required to move more fuel to compensate for the lower worth. A very mild burst results with the prompt critical phase lasting only 2.5 msec and the power reaching only 141 x nominal. Final dispersion results from fission gas driven dispersion of the lowest power channels leaving open the possibility of a third burst; however, this third burst, if any, lies properly in the transition phase since channel geometry has been largely disrupted by this point. 7.1.3.4 Primary Flow Decay Rate Uncertainty Increasing the flow coastdown coefficient t y 205 compresses the time-scale of events by a similar amount. Fuel motion is initiated at 12.60 seconds instead of 15.60 as in the base case. The more rapid sequence of voiding gives greater coherency and the first power burst goes to 60 x nominal before fission gas driven dispersal takes over. There are no other observable differences between the coastdown rates and the final results are similar. Decreasing the flow coastdown coefficient by 20% causes a pronounced stretchout and slow collapse similar to the low void worth case. Fuel motion finally occurs at 20.90 seconds and at a power level of only 4.3 x nominal. The initial motion is a collapse of fuel and upper core segment caused by escape of released fission gas at the low power levels. This leads to an increase in power driven by the collapsing fuel in the high power channels until the power reaches about 10 x nominal, at which point the fuel begins to disperse. The dispersion is driven by new nodes failing and releasing gas at the higher power levels. A scenario similar to the low void worth case is indicated with eventual collapse into a transition phase. 7.1.3.5 Core Flow Orificing Variation (Design Evaluation) The effects of flow redistribution on HCDA energetics have been inves-tigated by following design changes in orificing patterns which have occurred over the past two years. The cases referenced in this report use the flow orifici. , pattern in effect during May of 1975 when the base cases were being set up and run. Two changes in orificing patterns have been made 7-13

since then, in August 1975 and December 1976. The changes relative to the base case are shown in Table 7-6. For each change two case < were investi- g gated; the best estimate case (Section 7.1.1) and the no fis; ion gas in SLUMPY parametric (Section 7.1.2.3). The particular parametric case was chosen because it was the most energetic and judged most likely to result , in a hydrodynamic disassembly. At each change of flow orificing pattern, the re-runs were limited to these two cases.* 7.1.3.5.1 Flow Orificing Scheme - August 1975 7.1. 3. 5.1.1 Best Estimate Case The base case loss of flow with revised flow distribution resulted in even milder energetics than the reference case, despite, or because of, significant changes in sequence and type of events during the course of the transient. Decreased flow in the lead channels caused an acceleration of events; for example, boiling begins in Channel 8 at 11.07 seconds instead of at 11.71 seconds. Events in Channels 4 and 5 are accelerated even more by the correspondingly greater reduction of flow in those channels. The timing of events in the reference base case and the revicc:' flow E0EC base case are shown in Table 7-7. h On the other hand, Channel 10 with its 11% increase in flow allocation is not accelerated nearly as much as i.he early channels. Caannel 10 begins boiling 3.04 seconds after Channel 8 instead of 2.54 seconds. Because of the delayed boiling in 10 and the higher power levels caused by the rela-tive acceleration of voiding in Channel 5, Channel 10 does not void the core region prior to reaching clad failure criterion (burst pressure) at 14.226 seconds. The upper blanket and gas plenum regions have voided, however, and these upper voids collapse rapidly under influence of the expanding FCI zone. The failure occurs slightly above the core midplane with a 15 cm length and fuel motion in the channel is preferentially upward because of the low impedance of the voided region above the core. As a result, the fuel motion feedback from Channel 10 is monotonically negative af ter a brief and very small positive pulse due to initial fuel motion within the pin. O

• Detailed analyses of the December 1976 orificing pattern have been made with SAS3D and these are reported in Ref. 3.

7-14

The Channel 10 failure occurs af ter Channels 8,1, 3, and 5 have slumped and begin to disperse fuel by expansion of their contained fission gas. The combined effect of fission gas dispersal and the FCI in Channel 10 serves to reduce reactivity below one dollar subcritical and the power level to less than nominal, much lower than the corresponding valuec in the reference case. As in the reference case, the fission gas eventually slips past the dispersed fuel in the slumped channels and begins to fall back into the core by gravity. In the reference case, the fuel collapse produces a second, more vigorous, reactivity pulse which eventually shuts down the reaction by fuel vapor pres-sure dispersal of Channels 8 and 1 without exceeding prompt critical values. The revised flow base case was not carried that far because the extremely low power levels and cold fuel caused numerical difficulty and excessive running time in the SLUMPY rcutine. Because the reactivity and power level are much lower just prior to the second pulse, and because the upper section of Chan-nel 3 has completely collapsed on the lower section,thus ceasing any positive feedback, it does not appear possible to even match the second power pulse observed in the reference case. At most, a gradual approach to a transition phase state can be anticipated. 7.1.3.5.1.2 No Fission Gas Parametric This case is identical to the base case (revised flow) except that fission gas is arbitrarily ignored as a dispersion mechanism in SLUMPY, This a .sumption is internally inconsistent in that fission gas is assumed present and active as a dispersal /compactive mechanism in those channels which experience a fuel-coolant interaction, however, it shows the consequence of failure to disperse fuel in the early channels for whatever reason. The timing and sequence of events is identical to the base case until the first fuel pin failures occur in Channel 8 at 15.605 seconds in the reference case, or 14.084 seconds in the revised flow case. The timing of events for this parametric case is shown in Table 7-8. A more coherent initial collapse, caused by Channel 5 joining the early channels sooner, combined with a lack of negative feedback from Channel 10, cause a much higher and more rapid driving ramp. Relative to the reference case, a super-prompt critical state is reached on the fuel collapse of the early channels alone at 14.1569 seconds with Channel 8 providing most of the 7-15

driving reactivity. At prompt critical, Channel 10 still has about 50% of its original flow because of voiding in other channels and is still rela-tively cold even during the early part of the prompt critical burst. At a power level of 253 times nominal with an internal pin pressure of 253 atmospheres, Channel 10 ruptures at a location slightly above the midplane and a FCI is initiated. Because the channel is essentially full-of sodium at thi point, the FCI zone expands slowly relative to the prompt critical time scale. With the very high cavity pressure, the SAS/FCI model predicts large positive fuel motion feedback as the central cavity dis-charges fuel into the stationary FCI zone in the channel. This reactivity addition offsets the Doppler feedback which had begun to reverse the reac-tivity pulse and the prompt critical burst is sustained for several mili-seconds longer. Eventually SAS predicts shutdown due to fuel vapor pressure but at pressures for which SAS channel geometry cannot be maintained. The transition point between SAS and VENUS was selected at a point just prior to prompt critical at a net reactivity of $0.98 and power level of 106 times nominal. Because of the delayed FCI in Channel 10, a very non-linear driving ramp was necessary. To better define the driving reactivity for VENUS input, a PLUTO case for Channel 10 was run to obtain reactivity feedback from a more realistic fuel motion model than that provided by SAS/ FCI. The reactivity ramp from SAS and from SAS modified by the PLUTO results for Channel 10 are shown in Figure 7-33. Results of the VENUS analysis are 'Jiven in Section 12.2.2.5. 7.1.3.5.2 Flow Orificing Scheme - December 1976 7.1.3.5.2.1 Best Estimate Case This case does not differ significantly in final resul' trom esmer of the other two orificing schemes. All best estimate cases t, rminate by fuel vapor pressure driven fuel dispersion on the second power burst. The December 1976 and August 1975 cases diffe only in details of timing of events (see Table 7-7). In both cases, Channel 10 fails in an FCI mode with a voided plenum and upper blanket resulting in ejection of the fuel in the channel from the core region. 7.1.3.5.2.2 No Fission Gas Parametric Little difference exists between this case and the August 1975 case h 7-16

until fuel motion begins in Channel 8 (see Figure 7-8). This fuel motion begins earlier because of the more coherent voiding of the lead channels. Fuel motion begins when voiding is essentially complete in all channels except 6, 7, and 10. Reactivity is decreasing from the first void driven peak (sub-prompt critical) because of Doppler and fuel expansion feed-backs. Following slumping, a slow gravity collapse causes a relatively slow rise in reactivity until a super-prompt critical condition is reached at 14.10 seconds. The driving ramp is less than 20$/sec at prompt-critical . The burst is terminated 4 milliseconds later by increasing Doppler feed-back. Peak power is 312 x nominal at 14.106 seconds. As might be expected from the flow distribution (Table 7-6), Channel 10 is intermediate in state from the reference case (fully voided) and the August 1975 case (sodium filled). In this case, the lower slug fills the core, but the upper blanket and plenum regions are voided. Channel 10 reaches FCI failure criteria at 14.105 seconds just following the prompt-critical burst. As in the best estimate case, the FCI zone expands rapidly into the voided region resulting in substantial negative reactivity. The FCI fuel expulsion in Channel 10 is joined by fuel vapor pressure driven dispersion in Channel 8 to drive the core subcriticai . 7.1.4 Summary and Conclusion on E0EC LOF Event The most likely course of events for the E0EC unprotected loss-of-flow accident is given in the base case analysis. The work potential for this case is negligible - virtually no fuel vapor pressures were generated. Each of the two bursts was terminated by fuel dispersal from the action of fission gas. The second burst was due to slumping of fuel that had not been sufficiently dispersed in the initial burst. Although the SAS3A model could not continue the analysis, it would seem possible that another (third) burst could occur. From physical principles presented in the transition phase analysis (see Section 11), it appears that such a burst would be very mild. It is therefore judged that the accident energetics for the E0EC LOF base case are minimal, increasing the void worth by SOM or the fuel worth by 20% increases the consequence of the best estimate cases. A brief super-prompt critical 7-17

burst develops from collapsing fuel but is quickly terminated within SLUMPY by fuel vapor pressure driven dispersion of fuel in the high power channels. The super-prompt critical bursts are of the order of 4-8 milliseconds dura-tion and are entered with driving ramps of less than 25$/sec and power levels of less than 60 x nominal. These conditions do not justify disassembly cal-culations using the VENUS code. When upward clad motion is allowed, a mild super-prompt critical burst results which is terminated by fuel vapor expansion in Channels 1 and 8. The driving ramp rate is not large enough to trigger a reactor disassembly, but is sufficient to generate a moderate amount of energy. When only downward clad motion is allowed (the Clad Draining case), the work potentia'. is nearly zero. There are two bursts, just as in the base case, but they are even milder than those of the base case. This situation results because of the negative reactivity effects of clad falling through the core center after initially melting above the core midplane. The power rise is thus slower, and the remaining consequences are less severe than in the base case. The importance of fission gas as a mitigator of accident consequences is apparent in all of the cases considered in the E0EC LOF analysis. Its importance is made particularly evident in the case where it was neglected. By making this pessimistic assumption, the reactor is forced into a super-prompt critical state on the first (and hence only) burst. S.oce the driving ramp rate at prompt critical is only about 15$/sec, a hydrodynamic disassembly does not result. Instead, termination occurs due to fuel vapor expansion in SLUMPY in the same manner as for the CLAZAS and limited initial fuel motion case. Neglecting the negative reactivity effects of axial expansion leads to an uncertain result from the current SAS3A model. The first burst apparently behaves as expected (shutdown following a subprompt critical burst) when fuel-coolant interactions occur in Channels 4 and 6. Since the pin failure loca-tions are above the core midplane, rapid shutdown results. If, on the other hand, the FCIs do not occur, a second burst probably would result although it would not be expected to be superprompt critical either. 7-18

Variation of flow distribution between cnannels had little effect in the best estimate case. For the parametric case neglecting fission gas driven dispersion, however, flow redistribution resulted in an energetic disassembly. Without the adverse flow distribution, a mild disassembly occurred but by reducing flow to the high power channels and forcing flow into low power channels (August 1976 orificing), the sequence of fuel pin failures resulted in a prompt-critical burst with an accelerating driving reactivity. In conclusion, only a combination of adverse flow distribution and total neglect of fission gas as a dispersive force (while retaining fission gas as a compacting medium), resulted in an energetic disassembly. All other cases involving super-prompt critical bursts were terminated by vapor pressure driven dispersion of fuel in high power channels. Hence, the energetic con-sequences of an LOF event in the reference E0EC configuration are seen to be small and rather insensitive to Category three assumptions. To bound this reference design analysis, Section 11 will present an arbitrary 40$/sec disassembly calculation from the peak of the second power burst. 7.2 Loss of Flow (LOF) in BOFC Configuration at Full Power Range 7.2.1 Best Estimate Analysis This case provides a best-estimate scenario to describe the events fol-lowing a flow coastdown without scram in CRBRP for a core at the beginning of the first year of a three-year equilibrium cycle. The timing of key phenomcaa is given in Table 7-9. Power and reactivity traces are shown in Figure 7-34. Boiling occurs first at about 10 sec into the transient in Channel 9, the channel with the highest power-to-flow ratio. The voiding profile for Channel 9 is shown in Figure 7-35. The lined areas represent the limit of vapor progression, the cross-hatched areas represent regions of dryout (less than 10% initial film thickness), the clear area in the middle of the core represents clad whose inner node next to the fuel has reached the solidus temperature, and the dotted line plots the voiding reac-ti vi ty . Channel 9 is sufficiently far out in the second enrichment zone that its voiding reactivity contribution is negative. The power begins to slowly incroase when the highest pcNer fresh assemblies (Channels 1 and

3) begin to boil at about 11.5 sec. Finally, following flow reversal in the highest power irradiated channel (Channel 2), occurring at about 13.8 sec, the power rises to about six times nominal, leading to a rapid acceleration of the developing accident seq w nce- For example, Figure 7-36 shows the 7-19

voiding profile in Channel 2. Here cladding starts to melt 1.2 sec after voiding initiating, as compared with the 2.4 sec interval in Channel 9. $ The actual burst phase is finally initiated by flow reversal in Channels 4 and 8. This sub-prompt critical burst first causes slumping in the peak fresh assemblies, fuel dispersal in the peak irradiated channel (Channel 2), fuel motion in the other lower power voided assemulies, and finally an FCI in the unvoided channels (Channels 6 and 10). The fuel motion reactivity traces for this case are given in Figure 7-37. The fuel-coolant interaction is initiated at a moderate power (%.5 times nominal), but during a time when the reactivity is dropping off sharply due to fuel dispersal in higher power voided assemblies. The failures are predicted at the ~ core midplane and there is some positive voiding reactivity, as might be expected, from the Channel 6 voiding profile shown in Figure 7-38. However, the power does not significantly increase due to the overall fuel dispersal occurring at this time. The primary fuel motions in Channel 6 and 10 become the fuel that has been ejected into the coolant channel. These are negative as the SAS/FCI Lagrangian mesh expands following the voiding interfaces. Neutronic shut-down in a relatively cold core results (the average fuel temperature is near the fuel melting point). At SAS3A termination, all channels are voided, the fuel in the higher power irradiated assemblies is starting to settle and/or slump, and the fresh assemblies are still slowly slumping, although the entrained steel will cause boilup in the highest power fresh channels within a short time. A monotonic fuel dispersal driven by increasing steel vapor pressures under quasisteady-state conditions is expected. Since the treatment of fuel dispersal by SAS/FCI may be overly optimistic, PLUTO calculations were run for the post failure dynamics in Channel 6. The comparison of the sodium mass flow rate in PLUTO and SAS/FCI is given in Figure 7-39. The sodium in the PLUTO calculations responds faster than the SAS/FCI calculation due to the compressible nature of the sodium slugs in PLUTO. However, due to the continuing interaction of all the fuel in the interaction zone with all the sodium and due to the continuing release of fission gas within the fuel pin, the driving pressures in SAS/FCI tend to be maintained longer and flow recovery of the lower interface occurs later O 7-20

while the upper interface acquires a higher velocity. (The extremely high velocities approximately 100 msec after failure of SAS/FCI correspond to the upper liquid slug ueing blown out the top of the assembly.) Figure 7-40 shows the rapid decrease in pressure in the interaction zone as calculated by PLUTO, as well as the PLUT0-calculated fuel and sodium void reactivity. While a moderate degree of sodium voiding reactivity is apparent due to the initial rapid axial movement of the compressible sodium, PLUTO also predicts fuel reactivity to be negative. The reason for negative fuel reactivity is shown on Figures 7-41 and 7-42. Basically, fuel is being swept up the channel due to the inlet plenum pressurization, 4.67 atm, which exists at pin failure and used as PLUTO input. Figure 7-40 shows that PLUTO does not predict such a strong negative insertion of fuel motion reactivity as does SAS/FCI. Also, fuel plugging in the coolant channel could reduce the amount of negative reactivity further. Hence, a second mild burst induced by fuel slumping is possible. A mechanis-tic integrated calculation of such a second burst is not possible with current models. However, even if most of the negativc reactivity in Channels 6 and 10 is ignored, Figure 7-37 indicates that the slunping ramp should not be exces-sive. The initiating phase of the accident will then most likely terminate with some fuel vapor formation in the peak fresh channels (Channels 1 and 3), along with some fission-gas-induced fuel dispersal in the irradiated channels (particularly the now voided low power Channels 6 and 10). The same driving pressures leading to coolant expulsion in Channels 6 and 10 also af fect the inlet plenum. A plot of the inlet plenum pressure for this case along with the details following the fuel-coolant interaction is shown in Figure 7-43. The FCi pulse inlet plenum effect is characterized by the first pressure fluctuation in Figure 7-43. The second pressure pulse is due to the near simultaneous flow reversal in most of the reactor following the attempted reentry of liquid sodium into the hot voided regions. The first large rise, which is due to the FCI occurring in Channels 6 and 10 to about 10.8 atm, occars at about 14.59 sec; the second rise slightly after 14.63 sec is due to an almost simultaneous flow-reversal of coolant from many hot assemblies following the attempted reentry. This reentry is shown 7-21

as it affects Channel 1 in Figure 7-44. Since the SAS3A calculation indicated a tendency for fuel and liquid sodium to occupy the same position at the same time, there is a calculational inconsistency that introduces some uncertainty. Use of PLUTO-computed FCI pressures would definitely reduce the calculated effect, as would the realistic evaluation of incoherence, which is expected to be present since the FCI assemblies possess a large radial power gradient. At he time of the inlet pressure pulse and sodium re-entry attempt, all of the fuel assemblies not involved in the FCI (s2/3 of cora) have sodium voided regions and have undergone some degree of fuel pin disruption. Con-sistent with the best-estimate assumption of minor cladding relocation, the SLUMPY treatment of the disrupted regions has the fuel and steel intermixed into a compressible zone; thus regions of independent molten steel do not exist. At the lower extremities of these disrupted regions (below the mid-plane) the majority of fuel and steel particle temperatures are below melting and are settling lower due to gravitational effects. The magnitude of the inlet plenum pressure fluctuation is considered to be evaluated conservatively. The bases for this conclusion are:

l. The fact that inlet plenum expansion, which is effective in reducing O

pressure fluctuations on FCI time scales, has been neglected (see Section 3.2.9).

2. Coherent, analytic representation of FCI events within 72 fuel assemblies (SAS Channels 6 and 10) by two, single fuel pins (Table 7-9) results in greater inlet plenum pressuriz: tion.

3. Calculations with PLUTO indicate that SAS/FCI model estimated FCI pressures larger in magnitude and duration than PLUTO.

Thus, the degree and extent of liquid sodium re-entry has been conserva-tively estimated via the FCI event and inlet plenum pressure calculations. The SLUMPY plots provide an indice' ion of the fuel collapse modes calculated in the LOF BOEC Base Case. Figures 7-45 through 7-55 show the SLUMPY representation of fuel motion in Channel 1. The line shading in these drawings in intended to be representative of tne local fuel density. The stubs represent the upper and lower pin segments. The " SAG" number of each figure G 7-22

represents the distance the upper segment has slumped. Figure 7-45 shows the almost uniform density of fresh fuel while the viscosity is high, i.e., before any of the fuel is fully molten. After the middle region does indeed br ome fully molten, the high viscosity for quasi-solid fuel tends to promote the development of a highly dense zone below the molten region and a voided zone above the molten region (see Figure 7-46). The center region is slump-ing out of the middle of the core. The final slumped configuration at the conclusion of the calculation is shown in Figure 7-47. Here the middle region has slumped into a significantly densified zone. Figure 7-48 shows the initial fuel expansion taking place in Channel 8, and helping to termniate the first burst. The fuel in the slumped region is beginning to stratify as fission gas slip is enhanced in regions of high void fraction and restricted in regions of low void density. The stratification is even more observable in Figure 7-49 as the upper segment begins to collapse. The final SLUMPY plot, Figure 7-50, shows an upper segment collapse of 3.33 cm in 100 msec. This is an acceleration of about 2/3 g, which is on the same order as that observed in Channel 3 in the E0EC case. It can also be observed that the lower inter-face of the compressible region changes from 64 cm in Figure 7-48 to 53 cm in Figure 7-49 to 45 cm in Figure 7-50. A simple fit to an expression of the form d = 1/2 a ( t) +V g t yields an initial velocity for V of g -433 cm/sec but an average upward acceleration of about 4.5 g. The motion of the compres-sible region (except that part associated with the upper segment movement) can be expected to quickly but tenporarily terminate due to lack of driving pres-sures and high friction in the hydraulically narrow channels furnished by the pin stubs in both directions. Continued subcritical decay heat generation leads to a slow meltdown of the fuel and steel components in the reactor core, With the loss of core geometry, the SAS3A analysis must be terminated. The progression of the LOF event is continued into a transition phase and addressed in Section 10.

7. 2. 2 Effects of Phenomenologiul Uncertainties The uncertainties in the relationships among the phenomenological models suggests that more pessimistic cases be examined to gain a better appreciation of the total spectrum of consequences. Further, the experimental data base is somewhat incomplete relative to the possible phenomena occurring in this accident. Hence, it is worthwhile to examine the sensitivity of the ener-getics to introduced category three conservatisms.

7-23

7.2.2.1 CLAZAS and Limited Inil.ial Fuel Motion The assumptions for this case are based upon the same reasoning given g for the similar E0EC analysis presented in Section 7.1.2.1, The timing of the phenomena is given in Table 7-10. The power and reac-tivity traces are shown in Figure 7-51. The reactivity corrponents are given in Figure 7-52. One important contribution to fuel motion is from a sodium-vapor-driven fuel compaction from the lower part of the core toward the mid-plane in all six subassemblies of Channel 1. The increase in core incoherence over the E0EC case with CLAZAS and limited fuel motion now initiates an FCI in Channels 6 and 10 as the reactivity crosses prompt critical. The 10 msec fragmentation and mixing time constant and the large 500-micron sized particles for heat trar.sfer tend to limit the degree of pressurization of the FCI zone in this short, prompt critical time scale. The main phenomenon calculated by SAS/FCI is a movement of molten fue! inside the pir toward the rupture. Hence, the rip length used becomes crucial. SAS/FCI does not have the capability of enlarging the rip length as a function of time. The procedure adopted here, which is believed conservative, was to first observe that the pin faibre M el predicted failure at the mid-plane due to the melt radius bias in the loading function. The mid-wall clad-ding temperature at the midplane was 970'C. The cladding temperature along the antire pin M, /e the core midplane up to the blanket was 996 +8 C. Below the midplane the cladding was signi' icantly colder. Hence, if the fuel melt radius and internal pin pressure in:rease af ter a failure, as they do in this case due to the prompt critical conjition of the reactor, the failure should rapidly propagate upward rather than downward. It was decided to anticipate this movement by centering the rupt ure at the n-de above the midplane (equiva-lent to raising the failure midpoint 7 cm) and at suming a rip length of 28 cm (which gives an initial upper FCI :ane boundary a c the top of where the internal pin cavity is located at failure). The failure should at least partially extend below the midplane due to 1ne control rod bias in the power density. The resulting reactivity increase from the FCI channels becomes very rapid toward the end of the transient. At this time, the fuel is melting at the end of the pins and increasing fission gas pressure is hence instantaneously available. The accelerating fuel ejection is being forced from the originally 7-24

defined pin failure location, and an assumed uniform depletion of fuel density is occurring within a pin cavity covering the entire longth of the pin. The fuel motion reactivity plots for this case are given in Figure 7-53. The sndium vapor driven fuel compaction in Channel I and the continuing positive fuel reactivity from Channels 6 and 10 can both be seen. The average final core temperature for this case is 4550 K. However, because of the power difference between fresh and irradiated fuel, this may not be indicative of the true final state of the core. For example, the peak fuel vapor pressure is 680 atm, 28.5% of the fuel in the core has a temperature above 5200 K, and the average temperature of this 28.5% hot fuel is 5730 K. Due to these high fuel temperatures, the potential work-energy of this case may be quite large. Furthermore, it should be noted that a SLUMPY calculation of this case is pessimistic due to the assumption of orely allow-ing axial expansion of fuel, Since a hydrodynamic disassembly develops the VEtiUS codc is applicable. A transition was made to VENUS at a power of 440 times nominal- a period of 2 msec, and a driving reactivity of 50$/sec. These results and parametric variations are discussed in Section ll. 7.2.2.2 No Fission Gas in SLUMPY The CLAZAS and SLUMPY assumptions made above were purposely highly con-servative to create a situation designed to driv ( the core into SAS/FCI at prompt critical with rising power to demonstrate the autocatalytic character of the SAS/FCI model. Removing fission gas effects from irradiated fuel in the base case SLLMPY calculation achieves a similar result. The event sequence is virtually identical to that of the base case (Table 7-9). How-ever, since fission gas is not allowed to disperse the fuel, there is posi-tive reactivity added from fuel slumping sufficient to achieve super-prompt critical conditions. In addition, the fuel-coolant interactions in Channels 6 and 10 occur just at prompt critical. The pins in these channels fail at the cere midplane, thus leading to increasing amounts of ' positive reactivity due to fuel motion within the pins toward the failure points. It should be noted that such motion is promoted by the action of fission gas (which has been neglected in SLUMPY for this case). This is an inconsistency in assumptions that may be introducing large conservatisms in the evaluations. The power 7-25

and reactivity behavior is shown in Figure 7-54, the fuel motion reac-tivity it shown in Figure 7-55. Note that the contribution to the fuel motion reactivity from SLUMPY is beginning to level off, whereas that from SAS/FCI is accelerating rapidly, and is determining the future course of the accident. The SAS3A calculation was terminated when a 2 millisec reactor period was reached. At this time, the power is over 500 times nominal, the reactivity is 1.07$ and increasing at the rate of 50$/sec. VEtiUS is used to complete the analysis. It is instructive to consider what the course of events would have been if fission gas effects had been neglected in Channels 6 and 10 as well. Fuel would have eventually slumped in these channels and the fuel motion reactivity would most likely have been described by a smooth extrapolation of the segment of Figure 7-55 labeled "SLUMPY", Since the driving reactiv-ity ramp rate from fuel slumping is about 10$/sec through prompt critical (as can be inferred from Figure 7-55), a very mild reactor disassembly could be inferred, the consequences of which would be bounded by the mildest cases presented in Section 11. The importance of the role of fission gas in mitigating accident conce- g quences is now clear. By providing a prompt method of fuel dispersal after melting, it prevents an autocatalytic addition of , eactivity due to fuel slumping. Fortunately, however, the reactivity ramp rates associated with the absence of fission gas fuel dispersal are small. It is only wher the two autocatalytic effects of fuel motion, namely fuel slumping and fuel motion within pins due to SAS/FCI predictions, are unrealistically combined that fairly energetic bursts result. Just as in the case where CLAZAS was used and initial fuel motion was restricted, the cladding temperatures above the core midplane were close to or above 1000 C at the time of pin failure in Channels 6 and 10. However, a 15 cm rip length, centered at the core midplane, was used for Wiis use. It is clear that this assumption is conservative, so it was decided to in-vestigate the consequences of varying the rip length at failure in the con-text of investigating the consequences of making another pessimistic assump-tion, namely, that of neglecting the negative reactivity effects of axial expansion. This case is discussed next. O 7-26

7.2.2.3 No Axial Expansion Reactivity This case differs from the base case only in that it does not take any credit for the negative reactivity effects of axial expansion. In the same manner as for the base case, no cladding relocation is allowed until fuel starts to slump; then molten cladding moves with the fuel. The event sequence, as computed with SAS3A, is shown in Table 7-11. The most important feature of this case is that, because of the more rapid increase in power following sodium voiding relative to the base case, fuel-coolant interactions occur in Channels 6, 8, and 10. In each cf these channels, tie pin failure is predicted at the core midplane. Subsequent reactor behavior depends upon the size of the rip length chosen. The base case was run with an assumed rip length of 15 cm. When this value is chosen for the present case, the reactor goes superprompt critical due to sodium voiding and positive fuel motion reactivity in the pins repre-sented by Channels 6, 8, and 10. the power and reactivity behavior is shown in Figure 7-56. The fuel motion reactivity is an important burst initiator here because fuel moves significantly toward the pin centers. To assess the reasonableness of such predicted behavior, it is necessary to consider the cladding temperature distribution in the failed pins. For this case, the cladding temperature is close to 1000 C over a pin length of 30 cm, and is not much cooler further away f rom the core center. At these temperatures, the cladding is extremely weak, and would probably f ail over a much greater length than 15 cm, or, if the original failure length were 15 cm, the rip would very rapidly expand. SAS/FCI does not have a time-dependent rip length model in it; therefore, a variation of this case was performed with the rip length set at 30 cm. The event sequence is virtually identical to the 15 cm rip case, but the reactor behavior is markediy different. Fuel does not move toward the core center to any great extent; indeed, the fuel motion reactivity in Channels 6, 8, and 10 quickly becomes negative, and the burst is terminated before prompt criticality is reached, as can be seen in Figure 7-57. Figures 7-58 throuch 7-60 point out the coolant and fuel motion reactiv-ity behavior for the two cases. It should be noted that Channel 8 had a 15 cm rip length in both cases, since a 30 cm rip would have caused an over-lap between a failed portion of the pin and a voided region of the channel.

                                   /- 27

The coolant reactivity behavior is therefore identical for the two cases in this channel. The overall reactivity behavior of Channel 6 (the most active of the three) is the same for the two cases until Channel 10 fails, although the sodium is voiding more quickly ar.d the fuel motion is somewhat less for the 30 cm case during this period. Therefore, the behavior in Channel 8 is the same until Channel 10 fails. From then on, the fuel motion reactivity tends to decreas.e in all channels for the 30 cm rip case (because the fuel is now in the coolant channels) and the transient is terminated. This is to be contrasted with the rapidly increasing fuel motion reactivity in the lo cm rip case (which is due to motion of fuel that is still primarily' within the pins) which sends the reactor into a sustained super-prompt critical burst. Thus, it is clear that allowing gross fuel motion within pins toward the core center dramatically increases the magnitude of tSe burst, to the extent that reactor disassembly is predicted. The two cases lead to vastly different termination sequences. The assumption of a 15 cm rip length is prcbably pessimistic for this case; the cladding is simply too hot over too long a segment of the pin to remain intact over such a large resultant length upon pin failure. The analysis of the 15 cm case is completed with VENUS-II and presented in Section 11. h One final coment should be made about the use of SAS/FCI in this analy-sis. A model that is easily driven into an autocatalytic mode when the reac-tor is near prompt critical, and that continues to calculate accelerating amounts of positive reactivity no matter how the fuel temperature changes, can be used to'obtain an arbitrarily high energy deposition. It is firmly believed that such behavior is unrealistic. Indeed, it is not even clear that energetic fuel-coolant interactions can occur in loss-of-flow accidents. Until more suitable models treating the consequences of pin failures in sodium-filled channels are developed, it is believed that the approach of assuming large failure lengths is reasonable. 7.2.3 Effect of Design and Data Uncertainties 7.2.3.1 Doppler Coefficient Uncertainty Figures 7-61 and 7-62 present the power and net reactivity traces resulting from varying the Doppler coefficient by +201. 7 28

Increasing the Doppler coefficient by 20% has a similar effect to lower-ing the void coefficient (as discussed in the following section) except that the early oower plateau is somewhat higher and therefore the time scale is not stretched quite as far. Events proceed as in the reduced void coefficient case with the initial slumping by fresh fuel pins occurring at 15.44 seconds. Because of the increased Doppler feedback magnitude the power peak is turned at only 46 times nominal when the irradiated feel begins to disperse, flothing in the sequence of events occurs which would suggest that the eventual outcome would be different from the base case. Decreasing the Doppler coefficient by 20% has the effect of compressing the time scale but only by about half as such as the increased void worth case. In this case, Channel 8 retains its base case characteristics by slumping in a dispersive mode instead of an FCI failure. As a result, the sequence of events closely parallels the base case but on a somewhat accel-erated time scale. The peak power reached during the fresh fuel collapse driven power burst was 76 times nominal, flothing was observed which would change the conclusion of the base case. 7.2.3.2 Sodium Void Worth Uncertainty Figures 7-63 and 7-64 show the power and net reactivity traces result-ing from varying the sodium void worth by i 50% from the nominal value. The principal effect of increasing void worth by 50% was to accelerate the time scale of events by 6% to 11%. This acceleration in turn increased the coherence of voiding and fuel pin failures. Events occurred in the same sequence and type except that Channel 8 was forced into an FCI type failure before voiding completion. As in the base case, the high power fresh fuel pins slumped first, introducing small positive fuel motion reactivity. They were followed by the high power irradiated pins in Channel 2 which introduces strong negative feedback due to fission gas driven dispersion, turnin.g the burst around just snort of prompt critical, At this point, however, the two cases diverge when Channels 8, 6, and 10 fail in sodium-filled channels, introducing strong positive void reactivity and fuel compaction which takes the core prompt critical at a rate of about 255/sec. 1-29

The reason for the prompt-critical disassembly in this case is the transfer of Channel 8 from a dispersive mode to a reactivity driving mode and the inability of the high power irradiated fuel to disperse rapidly enough on the compressed timescale to offset the fuel compaction of the FCI channels. 7.2.3.2.2 Decreased Sodium Void Worth Reducing the sodium void worth by 50% has the effect of stretching out the timescale of events and making voiding ario fuel motion more incoherent. The reduced void worth is insufficient to drive the core to twice nominal power on voiding because of offsetting Doppler and axial fuel expansion feedback. Not until slumping occurs in the high power fresh fuel beginning at 17.39 sec does the power begin to rise. The slumped fresh fuel introduces significant positive reactivity, reaching 98d and a power of 100 times nominal before the irradiated fuel begins to slump at 17.51 sec. The irradiated fuel is rapidly dispersed by fission gas introducing large negative feedback, driving the core subcritical by 17.55 sec. Despite the greatly stretched timescale, the events do not significantl.' differ from the base case and the eventual consequences must be regarded as similar. Fallback of the dispersed fuel and eventual transition into a molten pool is the most probable outcome. 7.2.3.3 Fuel Reactivity Worth Uncertainty Decreasing the fuel reactivity worth by 20% has the effect, at least initially, of compressing the timescale through its effect on fuel expansion feedback. The effect is similar to, though lesser in magnitude, than the decreased Doppler coefficient case. Fuel motion in the fresh fuel begins at 14.05 sec instead of 14.50 sec as in the base case. After fuel motion begins events progress as in the base case, but.the amplitude of fuel motion feedback is decreased. Some marginal but insignificant stretchout of events can be seen. Power peaks at 90 times nominal just before irradiated fuel dispersion begins. The amount of fuel being dispered by fission gas in the irradiated ch"nels is so large in relation to the positive feedback that the 20% decreas is of little consequence. As in the decreased Doppler coefficient case no significant changes in final results would be expected. 7- 30

Increasing the fuel worth by 20% delays the progress of the transient slightly because of its effect on fuel expansion feedback. The initial void driven power burst is initiated at about 14.45 sec when Channels 4 and 8 begin to void. By that time all other channels except 6 and 10 have fully voided. Fuel motion begins at 14.57 sec in the high power fresh fuel chan-nels. These channels, without fission gas to disperse fuel, initiate a slow gravity driven collapse which drives the power and net reactivity to peaks of 59.7 times nominal and 95.6c at 14.61 sec. At this time the high power irradiated channels slump and undergo a fission gas driven fuel dispersion. This, in combination with the Doppler reactiv ity turns the power burst around. Shortly thereafter, Channels 6 and 10 undergo pin failure and enter a fuel coolant interaction. In both cases the initial fuel compaction phase is ov. powered by the dispersion of fuel in the other irradiated channi ls and the power decline continues. By 14.65 sec the reactivity has become lore than 4$ subcritical and the power is below nominal. The case was terminated at this point, however, some evidence exists that fuel dispersed by fission gas may be beginning to fall back and the fresh fuel channels continue a slow collapse. Channels 6 and 10 are pro-viding entirely negative reactivity at that point. An eventual fall back and recriticality of at least part of the fuel is possible, however, that analysis more properly lies in the transition phase area. 7.2.3.4 Primary Flow Decay Rate Uncertainty If the flow coastdown coefficients are increased by 20%, a faster coast-down results leading to the anticipated timescale compression and accelera-tion of events. Fuel motion begins in the fresh fuel at 11.77 sec instead of at 14.50 sec as in the base case. Unlike the increased void worth case, however, there is no added reactivity associated with each event and the power remains relatively low, peaking at 56 times nominal just before irradiated fuel dispersion begins. The lower power level allows Channel 8 to proceed as in the base case with s' umping and fission gas driven dis-persion. Other than the more rapid sequence of events, no change was noted relative to the base case. 7-31

If the flow coastdown coefficients are decreased by 20%, a slower coast-down results leading to a stretchout of events relative to the base case. This stretchout without added reactivity results in greater time incoherence and a gradual subsidence into a transition phase state. Eventual dispersion of fuel will occur after channel geometry is destroyed by the slow meltdown of voided channels. 7.2.3.5 Core Flow Orificing Scheme Variation The flow orificing scheme of December 1976 was used to run a B0EC loss-of-flow base casa to determine the effect of the new flow rates on that core. The first power and reactivity pulse, to 30 times nominal and 0.933$ net, was reached at 13.684 seconds driven by voids in Channels 1, 2, 3, 4, 5, and 7. Doppler and fuel expansion succeed in turning the reactivity downward before slumping in the early fresh fuel channels begins at 13.725 sec. Channels 1 and 3 slump initially, followed 18 msec later by 9 and joined by 5 and 7 at 57 msec. All of these are fresh fuel channels and go through a slow gravity collapse. This increasing fuel motion feedback results in a second power and reactivity peak at 13.789 seconL of 35 times nominal and 0.914$ net, which is turned around by increasing Doppler plus the slumping of irradi-ated Channels 2 and 4, which introduce negative fuel motion because of fission gas driven fuel dispersion. A third and higher peak is reached at 13.825 seconds of 60 times nominal and 0.958$ net driven by FCI's occurring in Channels 6, 8, and 10 beginning a t 13.800 seconds. Large positive void reactivity and some positive fuel motion reactivity drive this third peak. The fuel motion in these channels becomes negative af ter a brief period, however, and in combination with the fission gas driven dispersion of the other irradiated channels results in a shutdown state. 7.2.4 Summary and Conclusion on B0EC LOF D ent The most likely course of events for the 80EC unprotected Loss-of-Flow accident is given in the base case analysis. The work potential for this 7-32 O

case is nearly zero, since virtually no fuel vapor pressure was generated. The mild power burst resulting from sodium voiding was terminated by the combined action of fuel dispersal f )m the release of fission gas into Channels 2, 4, and 8 and from fuel expulsion following fuel-coolant inter-actions in Channels 6 and 10. All of the:e channels are made up of irradi-ated fuel. Figure 7-37 shows that some of the dispersed irradiated fuel is beginning to reen'r ne core although Channels 6 aid 10 have provided suf-ficient regative reactivity to override the slumpiag. With the availability of improved modeling it may develop that fuel-coolant interactions may not be predicted in Channels 6 and 10, or if they were predicted, it may develop toat the course of the accident could be followed further. In the former instance, a second burst would be likely (especially since Channels 6 and 10 would then be acting in a manner similar to the other irradiated fuel channels). In the latter instance, a second burst may be possible, although unlikely. If a second burst did result, its consequences would not be severe, since it would be very similar to that resulting in tha case where the effects of fission gas were neglected. In this case, the fuel all melted at approximately the same time, thus providing for very coherent fuel slumping. Figure 7-55 shows that the ramp rates fr m , lumping of both fresh and irradiated fuel channels acting together are small at high power. When the slumping starts at low power (as would be the case for a second burst), only the irradiated fuel would be reentering. There would be an insufficient amount of reentering fuel to orovide a super-prompt critical burst at a high ramp rate. Indeed, it would be very unlikely for the reactor to go super-prompt critical. In any event the consequences would be bounded by the mildest cases presented in Section 11. Therefore, it is concluded that, given the present state of analytical capability, the base case consequences are not energetic. Even if modeling improvements change the scenario to include a second burst, the consequences would still be benign. Increasing the sodium void worth by 50% increases the energetics. A disassembly is indicated by the reactor history but at a very low driving ramp rate. Variation of other Category two parameters result only in mild energetics. 7-33

If upward clad motion is allowed and initial fuel motion is limited, or if axial exparsion reactivity is neglected, then a super-prompt critical h burst is predicted, caused by positive fuel motion within fuel pins in Channels 6 and l'. The most likely path to termination of this case is via a disassembly calculation in VENUS, starting with a power level of 440 times nominal, and a ramp rate of 50$/sec. The energetic consequences of such Category three assumptions are moderate. However, there is some uncertainty involved in the choice of ramp rate, since SAS/FC: predicts accelerating amounts of feel motion towards the pin centers if too small a rip length is chose. If unreasonably small values of rip length are arbitrarily assumed for the analysis, then the resulting ramp rates may be high enough to place the accident consequences near the Structural Margin Beyond the Design Base. If, on the other hand, the size of the rip is chosen to be along the entire length of the weak portion of the pin, then the reactor may not go super-prompt critical and the energetic consequences would be mild. When fission gas effects are neglected in SLUMPY (but not in SAS/FCI) the reactor is predicted to go super-prompt critical in a manner similar tn that predicted when upward clad motion is allowed. Thus the consequences would be similar. If, however, SAS/FCI is not invoked for Channels 6 and 10

   ~

(which would in effect be treating fission gas in a more consistent manner in all channels), then a very mild disassembly is predicted, which may not be sufficient to disrupt the entire core. The consequences would therefore be significantly less. In conclusion, it can be seen that even if pessimistic Category three assumptions are made to account for phenomenological uncertainties, the B0EC LOF accident would not lead to an energetic situation that would challenge the Structural Margin Beyond the Design Base. Only with unrealis-tic Category fe"r assumptions, which would cause large-scale positive fuel motion within pins , c LOF driven TOP failure mode, can energy releases be predicted that in some cases exceed the energetics used to specify the Structural Margin Beyond the Des,jn Base. O 7-34

TABLE 7-1 EVENT SEQUENCE FOR E0EC LOF BASE CASE Channel Relative Average Voiding Cladding Fuel Number Power Burnup Initiation Solidus Temp. Motion (Subassemblies) (Power / Flow) (M',4D/MT ) (Sec) (Sec) (Sec) 1 (6) 1.237 (1.079) 92,200 11.89 13.56 15.63 2 (12) 1.086 (0.947) 89,200 14.48 15.66 15.88

      ? (12)     1.137 (0.992)           57,800            13.63           15.00    15.68

, 4 (18) 1.017 (0.953) 89,500 14.55 15.84 15.88 5 (18) 1.099 (1.030) 37,700 13.30 14.68 15.68 6 (18) 0.976 (0.965) 76,500 14.51 15.74 15.88 7 (24) 0.922 (1.025) 70,000 14.14 15.69 15.88 8 (12) 1.240 (1.081) 43,300 11.71 13.35 15.60 9 (30) 1.031 (0.949) 83,600 14.48 15.69 15.88 10 (42) 0.851 (1.030) 58,700 14.26 15.68 15.88

TABLE 7-2 h EVEfiT SEQUEt4CE FOR E0EC LOF CLAZAS AND LIMITE0 INITIAL FUEL MOTION CASE Channel Number Voiding Clad Clad Fuel (Suba ssed.blies) Initiation Solidus Motion Motion 1 (6) 11.89 13.55 14.31 15.13 2 (12) 14.43 15.19 - 15.20 3 (12) 13.63 14.79 15.15 15.18 4 (18) 14.47 - - 15.21 5 (18) 13.30 14.60 15.06 15.18 6 (18) 14.46 - - 15.21 7 (24) 14.14 - - 15.20 8 (12) 11.71 13.35 14.08 15.10 9 (30) 14.45 - - 15.20 h 10 (48) 14.32 - - 15.20 0 7-36

TABLE 7-3 EVENT SEQUEf1CE FOR E0EC LOF CLAD DRAINING CASE Channel Voiding Clad Fuel Number Ini tia tir,n Motion Motion (Suba ssemblies) (Sec) (Sec) (Sec) 1 (6) 11.89 14.32 15.68 2 (12) 14.47 16.02 16.16 3 (12) 13.63 15.63 16.15 4 (18) 14.62 None None 13.30 15.32 16',11 5 (18) 6 (18) 14.61 16.17* 16.17 7 (24) 14.16 16.11 16.17 8 (12) 11.71 14.08 15.62 9 (30) 14.48 16.07 16.17 10 (48) 14.24 16.17* 16.17

• Clad moves when fuel melts 7-37

O TABLE 7-4 EVENT SEQUENCE FOR E0EC LOF-No FISSION GAS IN SLUMPY CASE VOIDING INITIATION FUEL MOTION CHAtlNEL fiUMBER (SEC) (SEC) (SUBASSEMBLIES) 11.89 15.628 1 (6) 14.48 15.660 2 (12) 13.63 15.651 3 (12) 14.55 15.667 4 (18) 13.30 15.653 5 (18) 14.51 15.662 6 (18) 14.14 15.661 7 (24) 11.71 15.605 8 (12) 9 (30) 14.48 15.660 g 14.26 15.663 10 (48) O 7-38

TABLE 7-5 EVEtiT SEQUEt4CE FOR E0EC LOF - f40 AXIAL EXPAtiSION CHAT 4NEL NUMBER VOIDItiG INITIATION FUEL MOTION (SUBASSEMBLIES) (SEC) (SEC) 1 (G) 11.24 14.116 2 (12) 13.50 3 (12) 12.79 14.139 4 (18) 13.54 14.177* 5 (18) 12.50 14.139 6 (18) 13.53 14.176* 7 (24) 13.18 8 (12) 11.08 14.108 9 (30) 13.50 10 (48) 13.31

• Fuel-Coolant Interaction 7-39

O TABLE 7-6 COMPARIS0N OF E0EC FLOW ORIFICING SCHEMES

                                     % CHANGE RELATIVE REFER                   TO REFERENCE CilANNEL NO. gm/cm[NCE sec      MC.Is75~        DEC. 19RI 1            557.7            - 4.0%         -0.9%

2 557.7 - 4.0 -0.9 3 557.7 - 4.0 -0.9 4 519.0 - 7.6 -8.2 5 519.0 - 7.6 -8.2 6 491.8 - 2.5 -3.2

     '/            437.5           + 3.4          -5.9 8             557.7           - 4.0          -0.9 9             518.9           + 1.0           +3.6 10             401.7           +11.2           +4.8   h 9

7-40

TABLE 7-7 CRBRP E0EC LOF FLOW ORIFICING VARIATIONS TIMING AND SEQUENCE OF EVENTS W C x BC e

                      ,          -                 $5 3    6                 a          d        $$       $5 W    z e

se 5s xs ;t $ Mb r$ et i u d5 SG eG 5 $ 88 BM de d$ S$ A 11.203 11.726 12.713 14.116 14.080 = 1 B 11.888 12.467 13.551 15.634 15.355 = C 11.581 12.086 13.091 14.102 14.024 = 2 A 13.502 13.758 14.170 - 14.131 = B 14.479 15.067 15.635 15.880 15.671 = C 13.646 14.015 14.251 - 14.115 = 3 A 12.984 13.291 14.047 14.209 14.097 = B 13.626 14.099 14.974 15.676 15.624 = C 13.146 13.408 14.021 14.113 14.020 = 4 A 13.316 13.641 14.170 - 14.141 = B 14.547 15.297 15.829 15.884 15.718 = C 13.239 13.686 14.097 - 14.074 = 5 12.170 12.646 13.532 14.198 14.097 = b 13.300 13.680 14.669 15.683 - C 11.627 12.242 13.316 14.108 14.020 = 6 A 13.580 14.056 14.303 - 14.188 = B 14.508 15.306 15.738 15.884 15.696 = C 13.522 14.021 - - 14.121 = 7 A 13.614 14.186 - - 14.207 = B 14.141 14.741 15.690 15.882 15.679 = C 13.101 13.479 14.105 - 14.081 = 8 A 11.073 11.541 12.575 14.084 - B 11.711 12.249 13.571 15.605 15.549 = C 11.435 11.862 13.004 1?.028 13.967 = 9 A 13.651 13.973 14.292 - 14.188 = B 14.484 14.928 15.667 15.880 15.683 = C 13.973 14.051 14.256 - - 10 A 14.113 14.226 - - 14.226 B 14.246 14.880 15.680 15.880 15.697 = C 13.968 14.138 - - 14.138

• Stable bubble penetrates core region A Revised flow case, August 1975 B E0EC Base case C Revised Flow December 1976

=  Burst pressure criteria met in voided channel 7-41

O TABLE 7-8 CRBRP E0EC LOF NO FISSION GAS PARAMETRIC TIMING AND SEQUENCE OF EVENTS u

 .                                           U RU S                       +        s                  0*

a a e a d $ E5 W = 59 5e =N E5 $ E O dG SG PG Et et 5 $ 80 90 da d5 E5 1 A 11.203 11.726 12.713 14.104 14.080 = B 11.888 12.469 13.551 15.628 15.355 = C 11.581 12.086 13.091 14.077 14.024 = 2 A' 13.502 13.758 14.147 14.147 14.129 = B 14.479 15.067 15.653 15.660 15.657 = C 13.646 14.015 - 14.101 14.100 = 3 A 12.984 13.291 14.047 14.135 14.097 = B 13.626 14.099 14.994 15.651 15.623 = C 13.146 13.408 14.021 14.093 14.020 = 4 A 13.316 13.641 14.148 14.148 14.132 = llh B 14.547 15.297 - 15.667 15.669 C 13.239 13.685 14.094 14.100 14.076 5 A 12.170 12.646 13.532 14.129 14.097 = B 13.300 13.680 14.669 15.653 15.619 = C 11.627 12.242 13.316 14.086 14.020 = 6 A 13.580 14.056 - 14.153 - B 14.508 15.306 - 15.662 15.671 = C 13.522 14.021 14.125 14.102 - 7 A 13.614 14.157 - - 14.157 8 14.141 14.741 - 15.661 15.662 = C 13.101 13.479 14.096 14.100 14.077 = 8 A 11.073 11.541 12.575 14.084 - B 11.711 12.249 13.341 15.605 15.549 = C 11.435 11.862 13.004 14.028 13.967 = 9 A 13.651 13.973 - - 14.153 B 14.484 14.928 15.660 15.662 = C 13.973 14.060 14..'31 14.102 - 10 A 14.112 14.159 - - 14.159 9 14.246 14.880 - 15.663 15.663 = C 13.968 14.105 14.128 - 14.105

*- Stable bubble penetrates core region.
=  Burst pressure criteria met in voided channel.

A Revised flow case, August 1975. B E0EC base case carametric C Revised flow, DJcencer 1976. 7-42

TABLE 7-9 EVENT SEQUENCE FOR ROEC LOF BASE CASE Channel Relative Average Voiding Cladding Fuel Number Power Burnup Initiation Solidus Temp. Motion (Subassemblies) (Power / Flow) (f L'D/f1T ) (Sec) (Sec) (Sec) 1 (6) 1.271 (1.103) 1,700 11.46 13.05 14.506 2 (18) 1.157 (1.010) 53,600 13.16 14.36 14.526 3 (6) 1.261 (1.100) 1,700 11.55 13.13 14.506 4 (18) 1.049 (0.984) 60,500 14.12 tt 14.550 5 (18) 1.104 (1.034) 1,500 12.98 14.24 14.535 6 (36) 0.865 (0.906) 45,300 14.48 tt' 14.562 7 (18) 1.107 (1.041) 1,500 12.89 14.20 14.529 1.012 (0.948) 54,100 14.20 t 14.549 8 (24) 9 (18) 1.070 (1.265) 1,400 9.99 12.34 14.513 10 (36) 0.795 (0.929) 42,600 14.46 ttt 14.569 tPeak cladding temperature was 1270 C at fuel motion initiation. ttPeak cladding temperature was 1340 C at fuel motion initiation. r+tFuel-coolant interaction.

TABLE 7-10 EVENT SEQUENCE WITH CLAZAS AND LIMITED INITIAL FUEL HOTION Channel fiumber Voiding Clad Clad fuel (Subassemblies) Initiation Solidus Motion Motion 1 (6) 11.46 13.05 13.72 14.13 2 (18) 13.16 14.14 - 14.21 3 (6) 11.55 13.13 13.67 14.12 4 (18) 14.05 - - 14.22 5 (18) 12.98 14.09 - 14.21 6 (36) - - - 14.23' 7 (18) 12.89 14.07 - 14.21 8 (24) 14.10 - - 14.22 9 (18) 9.99 12.34 13.21 14.15 g 10 (36) 14.16 - - 14.23 tFuel Coolant Interaction. O 7-44

TABLE 7-11 EVENT 3EQUEf4CE FOR B0EC LOF CASES WITH fl0 AXIAL EXPAtiSION REACTIVITY CHANNEL NUMBER V01DIf4G INITIATION FUEL fiOTION (Subassemblies) (Sec) (Sec) 1 ( 6 ', 10.54 12 93 2 (18) 12.09 12.954 3 (6) 10.67 12.93 h 4 (18) 12.79 12.975 5 (18) 11.92 12.962 6 (36) 12.98 12.980 7 (18) 11.87 12.956 8 (24) 12.90 12.971* 9 (l8) 9.39 12.944 10 (36) 12.98 12.984* tFuel-coolant interaction

O 10 2 2.0 Z LOF EDEC BASE CASE ANL NEUTRONICS _~. POWER + RE ACTIVITY VS TIME 1.0 m i T ,r,bt- $' \ i -... m m 10' _ - - - - - - - - - - - - - - - - - - - - - > ] - 0.0 < w  : I a 5: ._.  ; o o -- o

              ~

l 2 o _ i

                                                                                                        -1.0 N                                                                                I                              >

3 - b $ 100 __

                                                                                                        -2.05 o            -
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                                                                                                        -3.0 y
                                                                                    ,2 I        I                                                      -4.0 10 '

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 ilME IN SECONDS 10 2 2.0 5 LOF EDEC BASE CASE ANL NEUTRONICS Z POWER + RE ACTIVITY VS TIME 1.0 m

                                                    '                               /
               ~                                                g                                                 1
                              ~~_-_--       -#'                                   I                             m

} _,, l m 1 t a 10' -- t / - 0.0 $ $  ? V $ o _ o

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                                                                                                         -3.0 E l [\r 3 SI
                       !        I        I        I          I              I                 I 10                                                                                               -4.0 14.90      15.05    15.20   15.35     15.50       15.65        15.80             15.95      16.10 TIME IN SECONDS Figure 7-1            Power and Reactivity Traces for E0EC LOF Base Case O

7-46

0.6 LOF E0EC BASE CASE ANL NEUTRONICS 4 COOLANT RE ACilVITY VS TIME g 0.4 -

                                                                       )n           -2
                                                                                   ~3 j'

s i m ' ~

            ~ LINES NUMBERED O                   BY CH ANNEl.

5 0.0

                                                        - - - ~    ~
?

sp a -0.2 - E

    - 0.4    -

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    -0.6 0.6 LOF EDEC BASE CASE ANL NEUTRONICS COOL ANT RE ACTIVITY VS TIME 7

0.4 - v 6 E

 }    0.2       -
                                                                               ]8 o                LINES NUMBERED 9

a BY CHANNEL j

 ;     0.0                -                                  .

y t-2 h-0.2 - E

    -04     -

10 I I I I I I I

    -0.6 0.0       2.5      5.0      7.5         10 0       12.5      15.0            17.5 20.0 TIME IN SECONDS Figure 7-2           Coolant Reactivity by Channel for E0EC LOF Base Case 7-47

O 5 LOF EDEC BtSE CASE ANL NUETRONICS RE ACTIVITY VS TIME 3 - m NET 5 1 - AXIAL EXPANSION 3 a \ z

                                               ~\              m          a

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u_ u _.. _ _ _ _ w = = za2m m EE r - o m -= g _g3= = _n ~= ass = s==a  %) / e -E=EEH=: l - - s-a+2 u w_-. -- f o  :: #p cs { l I i o l I I ci o o o o o o o = ~ o e o -r - m m ~ - (*W3) IUN19 'P!I'/V UlM01.iG U0 t t03 330SV 1H9I]H 7-49 O 1.2 3900 LOF E0EC BASE CASE ANL NEUIRONICS FUEL CONDITt0NS VS TIME a 3300 r 41 1.0 - CHANNEL NUMBER 8 POSITION = 82 9 b 1 = CENTER LINE , " 2700 - 2 = MASS AVERAGE \ 0.8 b o 3 = SURF ACE ,3 C g 4 = FR ACTION g y w 2100 - 0.6 z B \ e n - G a 1500 - 0.4 "- m u. 0.2 900 - ,  ! I I I  !  ! 300 0.0 1.2 2800 LOF E0EC BASE CASE ANL NEUTRONICS CL AD CONCITIONS VS TIME 4 2300 - CH ANNEL NUMBER 8 FOSITION = 82.9 "1 - 1.0 g 5 1 = CL AD w 1800 - 2 = COOL ANT - 0.8 b $ 3 = STRUCTURE [ $ 4 = FRACTION y 3 - 0.6 z 1300 -

• 2 g o 800 -

0.4 e a o p 0.2 300 - 0.0 -200 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 0.0 TIME IN SECONDS Figure 7-5 Core Midplane Temperatures E0EC LOF Base Case O 7-50 ~ 135.00 TEMPER ATURE PRESSURE MELT (DE G R E E S-C) ( A T M) F R ACTION 130.00 2721.1 3.758 g% g 0.000 0.000 2750.0 3.781 '"!E  ; ?;.i. ;As 0.048 125.00 - 2767.0 4.047 afd 0. IIB 2767.0 4.355 E3 , , . , _._ 8"'"q ~ --------a 0.I84 2767.0 4.352 = - 4.3'43 E -- - -yf 0.239 120.00 2707.0 - - - - 0.313 2767.0 4.322 ' he~~ ~n-men ess.f ~ 0 4'49 2767.0 4.270 ~ " ' IL5.00 0 613 2767.0 4.173 - GERG Jag =m O.746 27ti7. 0 4.092 0.860 110.00 2767.0 3.927 Y ((N.q [dh[h2Nzj[qif4gg]! 0.995 2767.0 3.037 1 000 28'11. 4 3 703 105.00 1.000 2837.0 3.635 2 _ 2E88. 2 3. 5 70 3 000 $ 100.00 2955.0 3.515 =- - IM 3 l.000 2 o 2m 9 3.492 3.460 1.000 o o 3007.1 ~ 3018. 7 3 431 ,

l. M $m

~~ l MO 3025.6 3. 3D

90. m 3334.4 3.JS1 2 -

1.003 5 -~~~ ~ ~ 1M " = 3041.5 3.337 [ T' - a o 3941 4 3 291 - N $ B5.00 3.243 ~ ~ ~ ~ ~ ~ ~ " ~ l 000 -- 3058.0 3067.0 3 194 1.0'20 g 3 " - - - l.000 $" g 80.00 3374,3 3.103 w w x lM s-3025.1 3.137 3 000 75.00 2T47.6 3.132 3.1g7 1.000 m =ma 2878.8 2801.0 3.343 3 000 E 70'00 'K'TC'/'%g!'i&YNdjf O  ??.N .0.913 @ILg;F 2767 0 3.633 2767 0 5.OrG .vjNilksdQhtf  % 0.865 g 65.00 - 2767.0 C.483 b%T .JOejhg' b"' O. f45 7 3= M2&i 0 858 5 60.00 - 2767.0 2767.0 2767.0

6. 9<'s 5.9?S E.4JS h{k[ff,@'[v dilji),di%$6pgg

-* Mt ikA U>dQ 3 232 Ei D.591 0.533 2767.0 5.454 4.948 r.j? U dg$. g 4.B k g,%.G quGranW 0.5 11 2767.0 ec 55.00 - 2767.0 4.5?S IN. )i, ? IN$ D,g M

0. 3 75 d 'i. wM;Q~W D.199 2757.0 4.000  % s up.;fv.ii  :

0E 50.00 - 2700.9 4. 50L' I".w:n/ W Yeh kf km.b.h,.h u wF d: ' . 0.000 2652 6 5.I11 K-'~" Ta'uz~;;..ca - 45.00 - 2835.1 5.670 ( h[ff k(([ 0.000 26'40.1 _e015 m.czow.. gne, Aw& p- A, 0.000 0.353 0.000 2701.4 .00 - S . fE 0.000 273'4.9 -

6. 74 3 _. : 0.000 2709.4 .

_ = - - - - 35.00 - Figure 7-6 Early Expansjor o' .e..h ' sum a Fuel in E0EC LOF Casc Case />l - TEMPE R AT URE PRESSURE MEti 135.00 (DEGRE ES-C) ( A T M) F R ACil0N 130.00 ~ 2563.3 6.832 mmN 0.000 2502.1 6.905 3? w?W 0.000 2618.0 6.914 } k @yg @ M 6 fd A 0.000 2677.9 6.926 [51[hEMM5-[- M Y- 0.000 -@7MCRS$h45!M: 120.00 2767.0 6. 9M gg-m.-ggga=gy 0.354 fy Y $?bWONN?M i15.00 2830.5 6.951 ~ N D # # '" % - j.000 2926.1 6.956 kkk' _ l.000 110.00 3011.0 6.962 1.000 rs - _ . - .-= -w_ - = , . - . . . .- - = - = _ 3095.3 6.971 E]- %Ii-]{f;?hh=l 1.000 3157.9 6.963 -]~g Q l.000 100.00 32iB.4 6.996 gg:_;_3 = ; f 1.000 a "d 95.00 - 3298.B 7.013 Z _2ETE_ l.000 . - - = _ . - = _ x 3348.0 7.028 ==_i= := "= " - =: t-- s 1.000 m ~ 33f,8.9 7.036 ((_ . 1.000 h !5 m.* - 'is:' 3390.5 Mr

7. m o MBER __ _ Mh[-- [5

 !"" P 1.000 S cI 00.00 - -- - ag 3372.4 7.m3 pyg ' "'g,3 ~ 1.000 m g 00 - 33il' 7 7' 3 m 1.000 y 3224. 7 7.043 ==== 1.000 , 3099.2 7.043 " 1.000 *" 70.00 - 2969.8 7.042 1.000 2949.I 7. m2 ~ 1.000 d N .9 .m3 - 1.000 g= - 65.00 - 7.044 28 % .4 1.000 < 2783.4 7.m5 1.000 5 60.00 - 2767.0 7. m 7 0.858 2787.0 7.050 - O.796 2767.0 7.053 0.699 55.00 - 2/67.0 7.057 0.y08 2767.0 7.001 0.044 2590.7 7.066 0.000 M. 00 - 2528.0 7. 0 72 D.000 '2490.9 7.079 I. 0.000 45.00 - 2416.3 7.065 . D.000 2303.3 7. 09J 0.000 2

• O.000

[q.yyy ~- 40.00 - 2212:0 7.I15 e 0,000 2209.9 7.I24 .m O.000 30.00 - Figure 7-7 Later Settling of Peak Channel Fuel in E0EC LOF Base Case 7-52 110.00 - TEMPERATURE PRESSURE MELT 107.50 - (D E G R E ES-C) (ATM) F R ACTION 2757.0 3 031 u .y mm O. El 105.00 - 2757.0 3.000 p 0 MS 2757.0 3.0C0 1RMit bJ 0.3B6  !? $ 3 $$8%I5h 100.00 --- 2767.0 3.000 t=g=. = -se ~ e = o = =- 4 0.330 2767.0 3.000 0.392 9 .50 - 2787.0 3. 0(T7 _- 0. 3 12 2767.0 3.032 - - 0.333 g5,00 - 2767.0 3.039  ??4qq J% ee/4' qngy v$%m!p y - 0.333 2767.0 3.102 4 MI .g'hij$)ky) w; . w@p y ~ ~ 0.334 0.333 27S7.0 3.125 ~ 82.50 - 2767.0 3.131 0.399 G 2787.0 3 157 he-j- -_={ ,- s c+ er-@ +-j{ 0.400 y 90.00 - 2767.0 3.I84 . D.401 Pg 0.401 ~m c5 2767.0 3.209 ' - 2767.0 3 229 0.338 a 87.50 - ~ 0.387 z 2767.0 3.243 0.391 " - - ' ~ 2767.0 3.253 05.00 - 2767.0 3.259 ~ _1 . _ _ f_ _ __ J_7 0.392 g _ 2767.0 3.262 T.1, _ _ _ . - - ~ ~ ~_ 7 -~ _ Z_._T 0. M 3 e$ 3 82.50 - 2767.0 3.264 T ~f 9 i ~ - -XM hi~ 0. 38 3 a cf [- 2767.0 3.255 MT.) -_ l--M M8136 g 0.384 $ 0.333 g I 80.00 - 2767.0 2767.0 3.376 3.667 Eg g.g] +>QD{gpT- **3

• 0.372 w E 2767.0 3.926 &N ~ O 351 UE 77.50 -

2767.0 4.223 $  ; dib$kNAq/gsv3?j 0.336'g-y0 75.00 - $181:8 2767.0 4:$ 4.567 inidNINM9hF~ 8: M - M - t & = = _= n h i 0.333 $. 2767.0 4.552 - ===.;=== 0.332 MS 72.50 - 2767.0 4.605 g; pg- 0.329 p ug 0.260 y 2167.0 3.093 2767.0 4.058 q;;@M%gypEAMM qjise g;yg 0.220 z c, 70.00 - 2767.0 3.533 == in- a =.; w =a-f @gEY~ 0.207 g 67.50 - 2767.0 2767.0 3.555 3.568 N_Ei[fhhN3hkk~ qm 't ~ O.177 0.170 2 P'Q2.0 '3.Geo NO 9k"kh $r* Y4 ciig 0.Ipk 6.aso 55.00 - 4 o 1. 0 ptgy g gg 2767.0 3.449 gnemfdyw}, jhi&g.y _ 0.043 62.50 - 2767.0 3.323 -_j 0.043 2767.0 3.000 NEM5 f-25NTN E55A ' ~ = " 25 %="*55-5 O.046 00.00 -- O.039 2797.0 3 000 g_. _-- _ g ap=g 57.50 - 2767.0 3 000 Y -l_.c -~ [.Ddf_ _ _ _ 0.039 55.00 - 2767.0 3.000 0.011 52.50 - 50.00 - Figure 7-8 Fuel Configuration in Channel 3 at Initiation Of Collapse of Upper Sevent t:0EC LOF Base Case 7-53 TEMPER ATURE PRESSURE MELT (D E G R E E S-C) (ATM) FRACTION 110.00 2167.0 3.001 0.249 2167.0 3.002 0.236 2767.0 3.002 0.221 I

• I 2767.0 3.004 -

0.201 102.50 2767.0 3. rxN h b .- 0.217 100.00' - 2767.0 3.00/ 0.235 ~~ 97.50 2767.0 3.006 0 255 ~ D.23t 2161.0 3. r105 . <.; 92.50 4 . ,%. g. ,,5 , v.%. _ ~- 0.192 2767.0 J.008 _ 00.00 2767.0 3. OrJ7 0.I85 2767.0 3.007 7-.=a=a ===;= 3Ew ==#s==I - 57.50 - 2787.0 3 006 i== _= t = == = = == = . jl - 0.199 0 197 $ ~ 2767.0 3. Um = 0.189 5 85.00 2.67.0 3 006 __MWWalIM:igT= 0 156 $ 2767.0 3.005 E-~~=- R -- M M E ==I2 0.139 w a 62.50 2761.0 "*' #-~filhM5CR;EKM 0.I'40 9 3 00ci -

00. m -

M8 3.881 8:141 5 77.50 - 5 2767.0 3.112 - D.104 SN mM g 75.00 _ 2167.0 2787.0 3.000 3.03t me-- ev vs -n i--_. M h .m_- 0. C89 e e 0.092 g ' s' 72.50 - 2707.0 3.032 0.074 E 00 - x wy 07.50 0 077 E~ ~~ 2787.0 3.034 - , m . 65.00 - .] - 2 - 62.50 - p } 60.00 - N3 2567.5 3'f$f 3.065 .. ). k'm g :.; NM .E 36,4M-_ bM h ' 0.000 z e . a< ~}tgg ~ 57.50 - s5.00 - 2553.2 3.070 [s Eg O.000 { 2546.2 3.050 _ _ _ 0.000 52.50 - 50.00 - 2515.0 3.075 0.000 47 50 - 45.00 - a 90.2 3.iO2 Ef_- 7- 0.0c0 42.50 - a50.ta 3. n 2 0.000

40. m - --

37.50 - 35.00 - Figure 7-9 Fuel Configuration During Slumping of Upper Segment in E0EC LOF Base Case 7-54 110.00 - TEMPERATURE PRESSURE MELT 107.50 - (D E G R E E S-C) LATM) FR ACTION 102.50 $R1:8 2767.0 3:899 3.036 g K N ~ 8.ilt 0.259 100.00 - 2767.0 3.048 0.231 -5?l~" 87.50 - 2761.0 3.072 $g?$- g  :{ig 0.246 95.00 - 2767.0 3.085 0.267 92.50 - 2767.0 3.091 - - - - - 0.308 00.00 - V y"W B7.50 - 2767.0 3.102 - ' -.. ' P- - O.307 G 2767.0 3.106 t' .[ _ 0.260 M 85.00 - 2767.0 3.1C8 ================= 0. 2 f'4 b B2.50 - 2 .l0 i ~ = ' ~ ~ ~ 0$2S 6 2767.0 3.112 - E - ~~ 0.255 $ " ~ 2767.0 3.111 h=:-s- e=va=_r r==a=-i- 0.220 77.50 - 2767.0 3.112  ;;;ff] ]sy[g E:-]=fi-E~ = - -v_; 0.200 g g70 0'7. 0 g~. we== n== t x - .. g.2g 'E Sg  ? 75.03 - 8 ,?$ V 'T *$ " ~ 0 z 72.50 - - - 0.!S4 w a 2787.0 3.118 "i oi  ; 2761.0 3.122 , -,+ ~ 0.146 C; 30'og 0.137 gd * ~ 2767.0 3.120 _ _{___- __~ 67.50 - 2767.0 3.119 0.122 C s2 f. 6-HB  ? 8:888i Stim ' 2578.8 3.100 } 0.000 o 57.50 - } . ~ 2562 5 3m tz o* 55.m - 52.50 - 2539.1 3.229 0.000 50.00 - O.000 2504.2 3.222 -- 47.50 - 45.00 - 2474.5 3.227 0.000 42.50 -  ! 2424.7 3.231 0.000 yo,gg _ 1 37.50 - 35.00 - Maximum Slumped Configuration in Channel 3: E0EC LOF Figure 7-10 Base Case 7-55 115.00 TEMPERATURE PntSSURE MELT 112.50 - (D E G R E E S-C) ( A T M) FRACTION 2557.S 4.760 Mfgi gg 0.000 2658.tt 5.002 g y g -; g g g g 0.000 2859.1 5.248 E=J ~  ;-i- =__M 0.000 107.50 2659.0 5.629 0.000 2560.5 6.266 Ew&em e 0.000 105.00 2661.1 6.737 E d* ="" 0.000 Erwu., - 3 7. .0 IM* 50 2763.0 7.99i ~ 0.000 ~ 2783.B 9.I77 . 6h ' O.000 100.00 2764.2 0.302 0.000 2764.7 B.365 0.0C0 U ~ )$ 97.50 - 2765.1 0.395 5 - 0.000 3 2765.4 0.410 5% - 0.000 o (*- o i

95. M 2765.8 B.382 0.000 $

0.000 E 27E6.1 0. 795 , 3 2767.0 B.343 0.132 5" 92.50 - 2767.0 0.338  : 0.133 2767.9 8.281 - '.,eS- ~ 0.I34 5 2767.3 0.299 O.I34 2 8 h M*W 2767.0 ~ 8.226 0.134 $= Z 2767.0 B.219 ~ N ~ 0.135 = 07.50 - 2767.0 0.195  % 0.135 G g 2767.0 D.167 N 8.201 . I 2767.0 8.189 0.167 C5 ~ 85.00 - 2757.0 8.208 D.I68 3" '~ 2767.0 8.200 E., 0.168 2737.0 8.230 0.188 $ ~ 02.50 . -j O.I68 00 2767.0 B.220 ' 2767.0 0.250 O.169 s M. 00 ~ 2767.0 8.232 Y ~ '; 0.167 y* 2757.0 B.252 e 0.092 z 77.50 - 2767.0 2767.0 B. D4 8.234 0.092 5 0.092 2767.O B.I95 7 0.092 75.00 - 2767.0 B.143 ~ 0.09t 2767.0 B. 04 '. 0.031 72.50 - 2757.0 7.081 r,g.t. 0.030 2736.9 7.642 Oha ' ~ 0.000 70.00 - 273S.8 2735.3 7.312 8.870 f$MfCMTMW-M 0.000 E C 5"F m m wx m Q 0.000 , 2736.0 6.362 E gy.gJg q. 0.000 67.50 - 2735.6 5.830 _ _ _ _ 0.C00 2735.1 5.365 gg gg'ran""" ~ 0.000 85.00 - 2734.6 5.047 ==;=r ~~= ====pisisy 0.000 l 62.50 - 60.00 . Figure 7-11 Representative Break-up of tool in the Second Barst: E0EC LOF Base Case O 7-56 135.00 - TEMPERATURE PRESSURE MELT (D E GR E ES-C) ( A TM) F R ACil0 N 2431.8 7.510 0.000 } 125.00 - 2439.1 6.890 _ _ _ _ _ _ 0.000 2446.1 6.701 =_ - - - - - - _ _ _ _ 0.000 120.00 - 2472.4 6.278 0.000 'O *IO 0.000 115.00 - 2613.9 6.055 _ _ __.. .- 0.000 "5 - 2317.2 5.849 _[ggggj g-ifM 0.000 250s.4 s.639 i; = # s :i E spis M 0.000 2715.9 5.436 ==a=%tziji inicq-r= =.=_=EO=3 0.000 105.00 - 2737.2 5.253 ~5 2- N_ $2.. M N._ - __D M E50.003 _ - _ - - . - W S 2730.6 5.065 5fi'EE55?=21=:=== ~M D.000 $ IN W ~ 2731.0 4.900 Y -= A & =s M 5Mi A s sh fK5;-MM %N @li- U ML E- k 0.000 c3 h 2767.0 4,761 g_gsipjM4+p3 =;Zj- =EF-ishj 0.050 4 g$,gg _ w-- =__.- w_=;= u . 2= = w I 2761.0 4.64L m =cesr=;22 d*1fi;-- -as 3 0.I12 'd M &=T~2:4== M=2:=G;-T & 2767.0 4.544 yg-m=_= g-_g===ggpg O.114 5 - 90'00 -- g, 3 2767.0 4.413 Mii-7jl@-[M_~{}~2dQ] [ _ 0.136 o5 2751.0 4.419 [-[ hi'(h [ k M N 0.149 _ o 2767.0 4.397 = = -3 m mz=- ====== 9 0.151 S C E+3=- #E-~5s-- MiEii=Fi- - 12 ;;;

• 2767- " 3'" . 50 e0.00 -

55-9M 3;i= == 5 ? M g :q 2767.0 4.384 E +E=3=-5-iMy===1; ..- T _ZJis 2 0.083 ;- 75.00 - 2767.0 4.415 [hh-hh_h-hh5!_ 0.041 $ 5 ~g 2787.0 4.483 $ $_ h ih ~=_5 M M Y 0.041 70.00 - 2767.0 2745.9 4.549 4.663 y- _h [ E=E ==5= ; 2__ ._ -izz _ (( 0.048 D.000 h 65,00 - 2600.8 4.028 EEs3igi i F da ==sgig 0.000 G 2S 78.9 5.124 M.I. TY[ Y 0.000 g,g _ 2622.6 2534.6 5.546 5.978 "" MM } 0.000 0.000 ~ 2439.7 8.363 - 0.000 55.JO - 2490.2 6.683 0.000 2413.5 6.958 . ._ _ _. Am 0.000 50.00 - 2348.7 7.226 {-(( ~ ~ ~ ~ ~*[-y] 0.000 uS.00 - 2324.7 0.048 -- 0.000 40 M -~ 2318.G 9.131 __. 0.000 35.00 - Figure 7-12 Representative Expansion of Lower Power Fuel in the Second Burst E0EC LUF Base Case 7-5' C 9 8 1 0 I 6 1 0 e I 4 s 1 a C e s a B 0 F I 2 O 1 L E S C A E C 0 E E S A 0 ) B I 0 S e: S 1 D c C E N a I O r S R C T Y U E H S S e P S L N A E R P ' 0 8 ( E M I r u s s e 9 P T T E r R L P B N RI t C e l C n E 0 I D I 6 E F O 3 L 1 7 0 e ' r 4 u g i F 0 2 - - - - - - - 0 0 0 0 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1 1 G5g_EESE e S E 3 2.0 10 _ z LOF E0EC CLA0 MOTION PLUS LIMITE0 INITIAL FUEL MOTION POWER + REACTIVITY VS TIME 1.5 2 10 _ 7 i ~ MI - 1.0 $ }

c s'

~~~_.._--- g t ] a y "' l 5 ~ ~, y e 5 N i o w 10 1 '~~~~~~~. . - 0.5 [ i _ $ 5 __ i 2 i ' Y a -- - c-0.0 [ t z i 0 t 10 _ Z t I _ g -0.5 .- l 12 i I ' ' I I I 10-1 -1.0 14.88 14.93 14.98 15.33 15.08 15.13 15.18 15.23 15.28 TIME IN SECONOS Figure 7-14 Power and Reactivity Traces for the Burst Phase of the CLAZAS and Limited Fuel Motion Case 4.0 O LOF EDEC CL AD MOTION FLUS LIMJTED INiilAL FUEL M0710N RE ACTIVITY VS TIME 3.0 - E 2.0 - o" Q g NET 3 1.0 - FUEL k U 0.0 ' I AXIAL EXPANSION - 1.0 - DOPPLER I I I I I l ll4 - 2.0 2.0 LOF E0EC CLAD MOTION PLUS LIMITED INIT' . FUEL MOTt0N 1 RE ACTIVITY VS TIME COOLANT yq _ E F $ 1.0 - /' NET a  ; 0.5 - e s CLAD 3 } y 0.0 - - - PRO G R AMM E D -05 - 1 I I I I I I i - 1.0 14.93 14.98 15.03 15.08 15.13 15.18 15.23 15.28 14.88 TfME IN SECONDS Figure 7-15 Reactivity Components for the Burst Phase of the CLAZAS and Limited Initial Fuel Motion Case O 7-60 SUV1100 NI AliAll3V38 M S S M S N E, S, n o o o o o e o o o o o I d I I - E - E =

j. l 1 jijir, ( at r tIf I ll '

.F $ gi x N EE p g li i - 5 iji tig il H ji i -- li p_ ' 3 h N" I i 0 i ! l *"}}$s- b +o um!diff!Fiinr ij ni li 'it i ti l  :: {! = i, sj[ititrp[!I a h b's, ti ud t li, . ) f rij"# il lih ~,5 E

e Mil la 1

= - _i ni s.IB]-g i;yrarms;p! c5 ir  !! gi lig ,5 =_ i c eg;i sn ,Pi""m tf o ae g 1. litIl lih i.inplht: E t li f sig{E = ES 5 an""32dpi p P = Uliniz!ntl imiil!!illiiGi! $ramm mnid!" d"if " th m }ihll i j,i!!!ils ilni: lH *d lji !!:p$'il'l' nH !!'i! m l a ii' n- 'I! H i t M_ - o $ o ~g 5x a%  !! U I=gg E .rg TO FTii il;fllbni If*Ilid >

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if  !. g lil !! i 11 ?! ift = il i i =__] ti { 1!!l llf *' #  ! a w n. 1 iii la !IHiU }j,,jll!!!!!!!,l li; lidlDi n 'l i l }g"[=-==sL= $ * = <,q n h"It =f f E =E$lilii!!!!ili!!Lhhit,i!,3 f , I; g -- - - e mt i n - - - ud :3t,}p in tng wiiiam.'* }i at iE lilii IFi >- ~ " $ * *- 4 a

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E "~ E 'E Ea '12 IDEA! iiiillii@@} buy!ilithisl [.l! i; fi!!! illii 3 ,,m yigr;igisiiEli !m m liiki! !!T! [iI!Ilh $ Di M sl_o _ magm7 gg=- y!l vI!!ibiil! 13 5 = 33 "55 ~~E!I fin @!lh F  !!  !;ilz=s- $ >" 585 pa m I j !! $ll 4k"k::(!! m!!!Mt ilii ij Hi litiliHMin hadanta m n;igilit;ttP=t l-yU[ u =-.__ niEisiEHi dEMM$kT g ,2; g - , , , ' -- ~ 55 x ;- u;g uu f 4 m ei a y a w n = .,= - _af _- = . = = o e a a u-g a __:=_- j d '_- # o l I a R R R R m n M - - (~W3) 13E V10 lVIXV B3M01 30 WO1109 3A09V IH913H 7-El CHANNEL 1 CHANNEL 1 CHANNfL 1 TIME 14 % 57 Tiut 143924 TIME 14 6170 170 00 - STEP 542 STEP 497 SifP 507 160 00 - -- 975'C -- 974*C -- 9 73*C 150 00 - 985*C 988*C -- 985*C -- -- -- 990*C -- 991*C 123s*C --- 1371*C 140 00 - -- 1021*C 1163 C --- -- 1351*C 1271 C 130 00 -. -- 1371* C 13710C -- -- 1371* C 1416*C 120 00 - -- 1311 C -- 1371*C ] -- 1371*C I454*C -- 1314*C 0000 ~ -- 1311oC 1613*C ~~ 1331 C I a - 90 00 - -- 13 71* C N g - g3ygog -- 13 71*C 1414*C - 80 00 - E -- 1170*C -- 1170*C -- 1311*C 70 00 - 1017"C -- 1146*C -- 1034*C -- -- 1041 C -- 10 35*C -- 1250*C 60 00 - -- 974"C 1017'C -- 1098 *C 54 00 - 897'C -- 99s*C -- 1006*C 40 00 - -- 311*C - 927 C -- a7s*C -- 703*C -- 810C -- 89 2"C -- 62 3a C -- 7 20C - 776*C 2000 - t000 - -- 519*C -- '285*C -.- *616"C I ' I I ' I I ' I 0 00 -0 10 0 00 0 10 0 23 -0 10 0 00 0 10 0 20 -0 10 0 00 0 10 0 20 R40luS(CMI R A DIUS (CMI R A DIUS (CMI Figure 7-17 Early Cladding Relocation Showing Formation of the Upper Plug via CLAZAS. 'O O O G CHANNEL 1 CHANNEL 1 CHANNEL 1 170.00 - TIME 14 8619 TIME 15 2162 11ME 15 1315 STEP 572 STEP 612 STEP 687 160 00 - -- 9 7 3*C -- 974*C 1068"C - 1371*C IM M ~ 991*C ~ - -- 99 6* C 1371*C - - 140 00 -13E2*C 1371*C 1368*C - - 3 1371oc 1371*C - - ,,,p -- 1316*C - 1309" C 1560*C - - 130C3 - 1445"C 120 00 - 1994*C 1707*C 110 00 - J 1994 C 100 00 - 4 O S0 00 - ? ' 2CD7"C Ch W h 53 00 -. g -_ , 143F C 10 00 - ~ ~ 7 151 TC 1710 C i.0 00 - - 1371*C d - - 1250*C 13 71*C - 14 06C 1371*C 50 00 - I -- 1110*C -- 1174*C 1327 C M 00 - - - 966*C __ ig33oC 1216*C 30 00 - 8 36* C -- 899"C ~~ 3 74* C 737*C -- 807*C -- 917'C 2000 - 10 04 - - - 59F"C - - 653"- -- ?39*C I I  !  ! I ' I 0 00 -6 10 0 00 0 10 0 20 -0 10 000 0 10 020 -n 10 0 00 ato 0 20 R ADIUS ICM) R ADIUS (CMI R ADIUS (CM) Figure 7-18 Later Cladding Relocation Showing E fects of Fuel Vapor Pressure Development 145.00 - TEMPERATURE PRESSURE MELT 140.00 - F R ACTION (DEGREES-F) (ATM) 2767.0 3.562 0.609 135.00 130.00 - 2667.3 13.49? . 1.000 3032.6 10,544 ' W l J. 1.000 3277.0 2L.620 .:  : .- 1.000 '~ 125.00 - 31 74.5 22.842 . ' . ' - ? .: k *.. l.000 3559.9 23.279 )  ?' '? #1  ? 1.000 't.000 3808.4 22.784 -J - '. - 4 120.00 ~ 3956.0 20.935 .'.. ~" . l.000 4053.4 20 928 ..- .. 1.000 115.00 - 4139.0 2 .566 gg , $, c,g .. j.l ., , .) 1.000 4227.2 20.337 .g______j 1.000 S 110 00 NE i . ~ = = - E 4283.3 19.253 _ _ ;-~ _- ~ ~~ _ 1.000 a o = - - - - - _ . . _ - - . - = . _ . - m. 4320*7 10 307 fAAA575 ==~Iiii32 iM;5- ;;gga 1.000 w o 105*00 -- ms==i.a= + = = -_. ==_ a Z 100.00 - 4342.7 18.253 _ l.000 [ m

o=

 ? 6 95.00 4364.3 19.333 _ _ . _ _  !.000 $ 5 90.00 - S m z en m wi 05.00 - g-4352.1 18.721 1.000 , 00.00 - wa w* a w 75.00 - 5~ ~ 4337.1 18.825 1.000 85.00 - 4335.4 J9.675 y g;pjgg3 g 1.000 60.00 - 4158.4 20.920 _EM==rE= Mi-ysrggf = l g g 1.000 ==== = 2= =:== = :: _ 55.00 - 4023.4 23.513 S_5M?is 5 9-N 1.000 n == = -- : ---- ~~~ ~ 3302.2 26.592 1.000 50.00 - 3728.0 29.736 1.000 3570.I 33 782 ,, p*l " N. ' ,g $ p. . , ,. ., . - 1.000 45.00 ~ 3311.0 38.507 ' b. ,h. I '..*,- 1.000 3l46.2 ';3. 7 t S . . . N~~ 1.000 ' "5 s[ ~ ~ 40.00 - 2891.0 47.805 ' 1.000 2787.0 49.414 '.. . ..' ' 3* -t,q: " ' ,y' . ."' y . : . - 0 789 Figure 7-19 Final SLUMPY Configuration Channel 1 7-64 TEMPERATURE PRESSURE MELT jg FRACTION - (C E G R E ES-C) ( AT M) l 1.000 107.50 - q201.3 33.883 ~ 1 MG 4248.3 33.684 1.000 105.00 - 4296.3 33.632 ~ 1.000 ~ 4476.3 33.990 1.000 102.50 - '4572.3 34.391 - 4618.2 36.?99 - f.000000 4644.1 38.487 100.00 - 1.000 4620.3 36.426 97.50 - 1.000 4604.0 35.133 95.00 - 3.00 92.50 - 4B05.0 35.155 90.00 - S 5 o 87.50 - 4590.5 35.371 1.000 g "o 05.00 - 3N 5 4577.5 34.535 hMNN$$$$hMksN x:: == gmmyg;gm_ - b2.50 - 45G7.5 32.170 I.000 yg c s -Ss 80.00 _ 30.823  !.000 4 i 4533.2 450'4.1 30.513 1.000 [ E 77.50 _ 29.178 1.000 g o 4526.9 E 75.00 - 4511.9 28.128 FFissa=JsMiliti d Fsa 1 000 "h 1-28.781 1.000 g 77,$g _ 4491.9 . bm  !.000 g8 70.00 - 4471.9 25.480 _ _ _ 67.50 - 4414.5 24.478 MQWQ . 1.000 { I 85.00 - 3 2 62.50 - & $5 gin;j}19;55 - 1.000 4102.B 19.671 = = - _==-g g /i g g - .a. k . 57.50 - 1.000 3725.8 14.945 55.00 - l*000 52.50 - 3944.4 14.247 ~ == 1.000 3584.0 13. 8'n 47.50 - 45.00 - Figure 7-20 Final SLUMPY Configuration Channel 8 7-65 5,. 5 1 e I 0 5 1 g n i d i 5 o I V 4 1 g N n i O w IT o O l M l L o E F U F 0 e D E I 4 ) r E 1 S u T R D s U N s ~ I MSS O e I L E C r R E P S P U S L T ( m P E E u n S L A N Z A L I I 5 3 1 M I T l P e 9 C t C e l E D n I E F O L 1 2 0 - I 3 7 1 e r u g i F 5 I 2 1 ~ 0 _ - - - - - - - - - - - 2 1 5 5 0 5 0 5 0 5 0 5 0 5 0 8 7 7 6 6 5 5 4 4 3 3 2 2 Go3g E= Yg Z--SBV1100 NI AllAll3V3813N = m - T 7 i 7 = a 1 I I I ~ o E r m 6 s - _ _ ~ - a y a u )) - a x u g l E 5-w- m k - ~ o a1 1 - a-op f o= ' m E> l o z o z >- m - I o e e5 a " oc i e w EE g - s" ~E m I E dE a; s m I I l yE p o E S5 o' I m e l - W

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I li t l l 1 1 I ill!!!I I I IlII I I I I o o o a o - - a ~ t--U3M0d 03Zl1ViNBON 7-67 O 5 EDEC LOF CLAD ORAINING CASE REACTIVITY VS TIME 3 - 2 $ l5 4 lY 3 0 E -1 - "} a C 5 REACTIVITY IN DOLLARS u -3 - 1 = NET d 2 = TOTAL COOL ANT

• 3 = PROGRAMMED

-5 - 4 = SCRAM 5 = TOTAL CLAD I I I I I i ' i 1 I _ J - 3 E0EC LOF CL AD OR AINING CASE RE ACTIVITY VS TIME / < RE ACTIVITY IN 00LLARS d 1 = NET U 2 = DOPPLER -5 _ 3 = DENSITY [ 4 = TOT AL FUEL 5; P o -7 - e _g _ 4 _g i l i I I I l 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.9 TIME IN SECONDS Figure 7-23 E0EC LOF Clad Drainir.g Case: Reac',ivity vs Time O 7-68 0 60 E0EC LOF CL AD UR AINING CASE ^ ' 0.45 - s m 3 ;INES DUMBERED 3 0.30 - BY CHANNEL ' S s 0.15 - 1 b 2 f 12 U 0.00 4 cc }q,bi 1 -0.15 - 6 I I I I I I I -0.30 0.60 -- E0EC LOF CL/.0 0R AINING C ASE A0 RE ACTWIT VS TWE 0.45 - e LINES NUMBERED $ BY CHANNEL 8 3 0.30 -- f 8

• }

0.15 -

e > ? 0 0.00 - (, 9 10 m 8 -0.15 - I I I I I I i -0 30 0.0 2.5 5.0 7.5 10 0 12.5 15 0 17.5 20 0 TIME IN SECONOS Figure 7-24 E0EC LOF Clad Draining Case: Clad Reactivity vs Tirie 7-69 O <da s $2$<E Ca 2 0 E. 6 4 2 0 2 4 1 1 0 0 0 0 0 0 0 9 e - - 6 m i - - - - - - - 5 1 T s v 8 y 6 t = 5 i 1 v i t c a e 3 I 7 6 5 R - 1 d n a - I 6 6 5 r e w 1 o P S  : 5 O Y 6 N P I 5 O M 1 C UL 4 E S N n I i S O I 5 6 E s 1 M I a T G n 3 o i I 6 s 5 s 1 i F 2 o 6 N I 5 F 1 O L C E 1 6 0 I E 5 1 5 0 2 6 - - - - - - - - 5 7 1 e 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 r 8 7 6 5 4 3 2 0 u 1 g i cw$ c owB$=c@ F e yL g a U_3~$* 0 0 0 0 0 0 0 0 4 2 0 8 6 4 2 0 2 2 2 1 1 1 1 1 9 6 5 T - - - - - - 1 y N t A i L v O i O 8 t C 6 c I 5 a - 1 e R f o 7 s I 6 t 5 n 1 e n o p m 6 o I 6 C 5 1 Y P S M 5 D U -- I 56 ON LS 1 L C E E n i U S F N s I a 4 E G I 6M 5 I n 1 T o i s s i 3 F 6 I 5 o 1 N F O f 2 L 6 C I E 5 0 / 1 E 6 1 2 N 6 - D 3 I 5 7 3 1 L N e A r - I X P A_ X u g A E i 0 F - - - - - - 6 5 0 c 0 0 0 1 0 0 0 8 0 2 0 2 4 6 4 1 j8 - a U_2,yy ?s~ e ~8! mc<$aoz_ c ,_t2+NwcWwz - c 0 0 0 0 0 0 0 2 3 4 2 1 O 1 6 1 e i m T t 2 s l\ ' . I ' ,eE e 3 i I 4 v ul 1 A y 8'. t #e,'- i , v i l - t c - a - 2 e . e I 1 R ' d - n - a - r - e w 0 o - I 1 P - S y - D t N i Y - O v T i - C I t V I T C A E ' 8 S E N I R c a e G E M I - E R T M n N S - I i o O V - T I s S Y - n N T a A I - ' 6 p P V X T I - x E C - E L A - l A ER a I X i A + - x O R - A E N o W - I 4 N F O - O P L - F C - O E - L 0 - E C - E - 0 I 2 E 7 2 7 - e ~ .. __ . __ - - -~--__ - _ i 0 r u o -- g 2 0 '01 0 1 0 1 i F 1 - 'ic cwgoa.o" 3<2:coz _ G 7~" 0.5 LINES NUMBERED BY CHANNEL 2 0.0 1 ca $ EDEC LOF NO AXt AL . XPANSION RE ACTIVITY i3g d -0.5 - FUEL RE ACTIVITY VS TIME E a >. - 1. 0 - t~ 2 r y -1.5 - E -2.0 ' - 4 ' I I I I I I -2.5 0.5 LINES NUMBERED BY CHANNEL 79 10 0.0 y EDEC LOF NO AXIAL EXPANSION REACTIVITY FUEL RE ACTIVITY VS TIME 8 $ -0.5 - o o E - 1. 0 - C 5 5 -1.5 - cc 6 -2.0 - I I I I I I -2.5 O 2 4 6 8 10 12 14 16 llME IN SECONDS Figure 7-28 E0EC LOF No Axial Expansion Reactivity: Fuel Reactivity vs Time 7-73 O (1) BASE CASE (2) DOPPLER COEFFICIEf1T PLUS 505 g2_ (3) DOPPLER COEFFICIEt1T f1IfiUS 501 \ hl ,i ' d It ' ~ 'l  : I' / ;i 2 j l sti < 2 10 i' i li , ai a _ ey i il ,  : d - l j G  !) tiy'8  !(i g - -  ! :1 : a - ' i g ' i (: 1. O - s ll .' : :$: 'f - i ,%., l g . I i ji :: r*1 *: o ,!  ! y: o t' i ! i

J-I{

i o tj i ,,,,p,'  !' l .,(2) 0 - - '-*  ?.' 10 --.m...,,- i  ; ,(3) M1) I I I I 3 8 11 12 13 14 15 16 TIME IN SECONDS Figure 7-29 E0EC Core Doppler Coefficient Variations: Power vs Time O 7-74 l_ , ' !^' ^ , il!i ni '^ , X rd . . i ;;fk_;f 0- , '~ --.'_,.'~~~.. _} .! ~ ': , 2 i , / I . 8  ! i 0  : . $ -l - 1 i .(2) 8 a i a ni 7 5 8 5 -  ; i b i  ! C i C ' 5 x [ 1) BASE CASE l z ((2) DOPPLER COEFFICIENT PLUS i 50% i (3) DOPPLER COEFFICIENT MINUS l' 50% l/3) (1) i i i i . 12 13 14 15 16 17 TIME IN SECONDS Figure 7-30 E0EC Core Doppler Coefficient Variations: Reactivity vs Time O (1) BASE CASE (2) VOID COEFFICIEf4T PLUS 50% (3) VOID COEFFICIEtlT MIfluS 50% i ) 2 10 -  ; . G c ., t !F ' e - Er uJ ti -g o . ' . ..

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I $ !c-!" l, e ., in ji ! [. 9~ 3' !iAl ;v .- .:

l:.(3)

(  :) , ,', e ~ l(2) ,/ ..~. , ~ 0 10 - .;_-a..__,,,.. _ N(1) 11 12 13 14 15 16 17 18 19 20 TIME IN SECONDS Figure 7-31 E0EC Core Sodium Void Worth Variations: Power vs Time 7-76 A  % t/0;;>, sh'Af? +f)+ ,mAeE E A<e 1,em TEST TARGET (MT-3)  %'*4 1.0 E IE  !!m e gu em I,l [* llI!!M 1.8 l 1.25 I l.4 1.6 I < 6~ > MICROCOPY RESOLUTION TEST CHART #4 *kA4% +4%

1. v.,4/M i____ __ . . ._ - ---

4 4 $+f>4>%%4 _E e A<eA1,e~ $<#h TEST TARGET (MT-3) 1.0 52HEH y @ ILE u s?' HM ^ 1.8 1.25 1.4 1.6 4 6" > MICROCOPY RESOLUTION TEST CHART #4 +4%

• ?W

& hf _ . s%<;%, 77777 4 4

1. b%

9'++ ,m e ev <e 1,em $& %4te TEST TARGET (MT-3) 1.0 19mMa i ? ele I.l [j[EEM l.8 1.25 1.4 1.6 4 6" MICROCOPY RESOLUTION TEST CHART #4 <$ 4 b,yh s. o it - - '% a'///h ss T 4e i 44 t ]* .

1  : '

m //1.,/ " [ 'fl,(3) @ n. . . . . . . . g 2- ,[ _ _ . . . _ . .'. . . . --. . . . a a ' ~ '- \[j ' ~' ' ' * * ' ~ . . "- ~ ^ - f5 E ? - i ~ y O . 5 cr  !(2) s La = (1) BASE CASE -3_ (2) VOID COEFFICIENT PLUS 50% (3) VOID COEFFICIENT MINUS 50% l(1) -4 12 13 I4 15 l'6 17 18 19 TIME IN SECONDS Figure 7-32 E0EC Core Sodium Void Worth Variations: Reactivity vs Time ,(2)

0. 6 - /

(1) SAS + PLUTO ~

0. 5 - .

m

• x .

a

• 8 0.4. .

(1) t- .' ~ e h { o 0.3-5 .- x

• 0.2-0.1-

0. 0 - , , , , , ,

4 6 8 10 12 0 2 TIME IN MILISECONDS Figure 7-33 VENUS Driving P,eactivity: No Fissian Gas Parametric Case

• O e

5 102 _ Z LOF BOEC BASE CASE ANL NUETRONICS Z POWER + REACTIVITY VS TIME - 3 i i vs K <t l 3 1 o e 101 _ - a w g -_ _ _ _ _ ____ _ _ _ _ _ _ _ _ _ _ _,-- ' y z m _ _ .- 1 e_ o _ w - S - u 1 5" - -3 m y 100 _ r S 2 .i. w 2 '2 -5 I I 10-1 I I I I I -7 8 10 12 14 16 0 2 4 6 TIME IN SECONDS 5 102 _ ~ g LOF BOEC BASE CASE ANL NEUIRONICS i POWER + REACTIVITY VS TIME - 3 i m x <T 1 ~8 l ~ 5 10' i'~---__._-___- -~~_ h \ , D Z U 2 - \ t \ -1 t-  ? \ d _ \ U d \ < s K 100 -- \ - -3 y r z 2 y - \ 1 \ -5 - '2 - ' I I I I I I -7 10-' 14.26 14.36 14 46 14.56 14.66 14.76 13.96 14.06 14.16 TIME IN SECONOS Figure 7-34 Power and Reactivity Traces: BOEC LOF Base Case 7-79 O g.01 S3W11 SUV1100 NI AllA113V38 % o S W 5 $ R e 6 6 6 6 6 s i l l l l w t" " " =irry ' rii 7l11J1W i E .. . _ _-_d 4 e i n gg T tl_ _t'l! ' . 1 g' ".- --- == J e ij t tm a i i, I - -<.: y,,7 ~ *5 t e i,1 o d;I a nw, 4 q t-j j Jj ogh- - # Ii! b b EE "- d ~a~--- # S -Elif*H B M!h IE!! [$da li ll!l , {i $djBt!!!!f ~ ~ ~ ~ , . g. gg_ d;4 -  ;- 1J2=- S y 1' 9 a 7 J, J25 8 aire ' =- = =- t - i nl e _i - n m = P1!ig i. t.t b E. 1 t  ; {,  ; j a -_ ~Nki, g d v ~ j dh h(IB)  !" (a - I e m =z nd i 4 i q ts ;g B)b .a a =msen i,Ls. " - g g;  ; j n; ==_= m m e , "r ~ ,(N, '!L $ = n,~ = 3 c -=6212!! h,  !! al s,iitg de up " } IS lj i i 1$,h g  ; 4 =- _== J 371$ti [1$7 Il Wililr' I U ' I V- ~ ~ E E Ll}d usui l j lth INd i  ! l r 1 11 /. u!3  : m y em d[dii!!NU , mi' 31 l($ riJ dhl - i; u I k=N .= u > m m ., =- - m o f , m .. J p=m mn /.h j: 1 , n m m o- - . _ _ . _ L '! hh, ""'E""] 'f I!f j' f I - f2 A j' ills _a__ _i ~ ": s . al I 1rJI!rs_ ~ a_ , e., ,o_ ~ -- F- ~M.9E . u. ws-m_ 1 pj.__ , m a u3 u ;____ _.__ _ __ d_ . s-ag:  : -= ==v2 m =m == x a o =a x en ==4 _. I NN { p f .- . . -  : i 8; o r _ __ .- 6 i = = g -: I =- : o, ,,, / __. -= e' o f I I '1-I o N ~ - m ~ - (*W3) 13'ANV79 7VIXV B3M07 30 WO1108 3A08V IH9I3H O 7-80 S8V1100 NI AllAll3V3tf S S S S S S S o = m n. m o n o o o o o o 00 I I - m e O m M k N O z oW >_ p W ,_ ca J ~ h U p C e8 Sm~ z>m o 4 o# a zW W D zo" " z k 4 P$ ' o O =$z ' _ " QT $3d =e= i 2 e

e to w "Z O

• U C

U E 55 _ e. ~ 55 m S

u.  %

C O e m ~ - 4 m C .l O &C4 .c C g g h ' ~~ 5 n#m =semmnffEg}@W@k%Y[f;#'"jilif' 1"11 e*. n, "h"" i [*k i. . - "" 'm ~ ".- e _= E__ fi_Ill n! c t n Yd! $ l!!!!l } !! Il } n. tj jij{ h, j h f @ e"inb8 ~ El 3 " P M 4 =JMIM WJ$lii t F~lst p t Bil tt 1 it i 1 h0rh a end _.__ - 1_e nei ah f_- '- e x*F_s - ~_7_' adl e o CD y _ _ _ _ _ .~Mra_ . _i=es? '_ _ _ _ /, 3 c - .-=_- =_ = - ===ei = . _ - s o ) e 5_T-_ __ .3-s I  !~"' l l  ! o l l l - o m ~ ~ - - ('WJ) 13'iNVl9 lVIXV H3tt01 JO WO1109 3A00V IHDI3H 7-81 O 1p LOF BOEC BASE CASE ANL NEUTRONICS FUEL RE ACTIVITY VS TIME 0 - p LINES NUMBERED , 4 BY CH ANNEL 3 .1 8 E -2 - t~ 2 u < -3 - E -4 - I I I I I I I -5 I LOF BOEC BASE C ASE ANL NEUTRONICS F UEL RE ACTIVITY VS TIME 0 a y LINES NUMBERED < _; _ BY CHANNEL so E -2 - C b 10 s y -3 - W -4 _ 6 I I I I I I -5 13 96 14.06 14.16 14.26 14.36 14.46 14.56 14.66 14.76 TIME IN SECONOS Figure 7-37 Fuel Motion Reactivity by Channel: BOEC LOF Base Case O 7-82 400 CH Attli 6 (R BmP 10f 80ft IAll (All 350 - 300 - b , 250 - UPPER ivTERFM E 5 o [ 200 X E U 150 - E u 9 100 CORE 50 towtRINitRfAct I I I I I 0 60 80 100 120 140 O 20 40 TIME (MSEC) Figure 7-38 Voiding Profile for Channel 6 Following an FCI: BOEC LOF Base Case 7-83 \ 2500 LOF 80EC CHANNEL li g CALCULATED BY PLUTO 2000 - TIME

• O 15 14.562 SEC U

$1500 - "s

u 3

^ ~ $ UPPER INTERF ACE a cc g 500 - $ \ 12 g a z -500 - LOWER INT ERF ACE I I I I I I -1000 O 20 40 00 80 100 120 140 TIME (MSEC) g 5000 G 4500 LOF 00EC CilANNEL 6 y 4000 - CALCULATED BY SAS/FCI 3500 - 3 3000 - e  ; 2500 - $ 2000 - cc D 1500 - UPPER INTERF ACE

u. 1000 -

h 500 $ 0 - 2 LOWER INT ERF ACE 500 - I ' ' ' ' ' ' -1000 14.56 14.58 14.60 14 62 14 rd 14.66 14.68 14.70 14.72 TIME (SECONDS) Figure 7-39 Sodium Mass Flow-rate Comparison Following Pin Failure: B0EC LOF Base Case $ 7-84 1000.0 _. 2 LOF BOEC CHANNEL 6 5 100.0 - E  : E  : g ,. x - 8 10.0 -- 0 2 - E  : I I I I I I 1.0 1.0 LOF BOEC CHANNEL 6 0.8 - _ SODIUM w 0.6 - d z 0.4 - Q x u e TOTAL e 02 - m x * ~ 0.0 p 3 -0.2 - p y - 0.4 - FUEL w x - 0.6 - I I I I I -0.8 O 20 40 60 80 100 120 140 Time from FCI (msec) Figure 7-40 PLUTO Pressure and Reactivity Histories Following Pin failure: BOEC LOF Base Case 7-85 F i g u a$,uy a L U D> 2u$s 5 h z d eN~ a 3"z fdo Eb>E 5m5<zt @d_ r 2 2,. e 0 0 1 1 2 2 0 0 1 1 0 5 5 0 5 0 5 0 5 0 5 0 7 O - 4 - - - - - - 1 - I T I N I 2 M S I I TI N PI I E D S 0 = E M I Ln C C E D Ui C C 3 P H O = E Tt 0 I H O N A O P Oi 4 A O M N L I N 1 0 I N a 0 I N L N I S I N A E f l N A E N M o E N C L T S 7 r F L T A E - u F C te 6 T 8 ' I A L 6 hl A 0 E L O F O e X R T F I F M A F E E Bo A .B R 0 L l 0 Ot 8 I L E I F E Ei P 0 U A C / C Co O R C I L C n S I E i U H L l A T A R Of I 1 0 I N E N Fo O 0 N N l E Bl N E L L ao ( C T 6 sw M 1 2 6 I O ei T n ) 0 T A Cg O L a T s P 1 A I ei 4 I L n 0 F ' a 1 I i l 6 I 0 t u r e 1 i 8 0 n 2.5 LOF BOEC CHANNEL 6 5 TOTAL P S 2.0 - d z z = M 1.5 - INSIDE PIN S E TIME = 60 MSEC AFTER F AILURE tg1.0 - 8 d IN

u. COOLANT 0.5 -

= CHANNEL I I - I I 0.0 2.5 LOF BOEC CHANNEL d TOTAL u $ 2.0 - r  % d z 5 m g 1.5 - INSIDE PIN S E b TIME - 100 MSEC AF T ER F AILURE a I.0 - 5 Q ' lN \ 0.5 - C ANN \ E a I  ! I ' I 0.0 O 20 40 60 80 100 120 140 160 180 AXI AL POSITION (CM) Figure 7-42 Later Fuel Motion Following Pin Failure in PLUTO for the BOEC LOF Base Case 7-87 11.0 h INLET PRESSURE 10.0 - LOF BOEC CRBRP ANL PHYSICS BASE CASE 9.0 ? R.0 - 7.0 E o 6.0 - M { 5.0 - 4.0 - 3.0 - Ne I I I I I I I 2.0 O 2 4 6 8 10 12 14 16 TIME (SECONDS) 11.0 INLET PRESSURE 10.0 - LOF BOEC CRBRP ANL PHYSICS BASE CASE _ 9.0 - E

s y8.0 -

E U$ 7.0 - 0 E 6.0 - 5.0 ' ' I I I ' 4.0 14.56 14.58 14.60 14.62 14.64 14.66 14.68 14.70 14.72 TIME (SECONDS) Figure 7-43 Inlet Pressure History: B0EC LOF Base Case O 7-88 1.6 LOF BOEC BASE CASE ANL NEUTRONICS N A 0 HOW VS TWE = int ET CHANNEL NUMBER 1 - - - - - - = O UTL ET jy _ 0.8 - 3: o a " i l l ,", i f y Cf a 0.4 - , .s

s. a

,'i i j .m:: s g ,i = s o i ,, I ', i , g t , i s 8, , , c ' '. ' < 0.0 i ,' 'I , ,' ,' ' ' ,' , 'h ',' u , , - ' ,, , , ,, ; v i. 2 i, , f La u l' i -0.4 - l ,1 I I I I I I I -0.8 9.0 9.8 10.6 11.4 12.2 13.0 13.8 14.6 15.4 TIME IN SECONDS Figure 7-44 Chugging Dynamics Channel 1: BOEC LOF Base Case 105.00 - - TEMPERATURE PRESSURE MELT 102.50 (DEGREES-C) (ATM) FRACTION 3.J00 0.754 100.00 - E767.0 3.000 0.758 2767.0 ' 3.000 O.751 M. 50 - 2767.0 3.000 0.755 2767.0 3.000 0.768 2787.0 ~ 95.00 3.000 0.771 2787.0 ~ 3.000 0.791 2787.0 ~ 3.000 0. 061 92.50 - 2787.0 3 000 0.086 2787.0 0.800 ~ ~ 2787.0 3 000 90.00 - 2767.0 3.000 ~ 0.894 G 0.897 $ 2787.0 1 00 - 2787.0 3.000 0.e99 gg 87,50 - ' O.902 w ci 2787.0 3.000 O.906 E 2767.0 3.000 e5.00 - 2707.0 3.000 0.912 5 2707.0 3.000 ' 0.914 O.917 u g= 2767.0 3.000 - 82.50 - ' O.918 g*i 3 2787.0 3.000 0.918 m ~ ~ 2787.0 3.000 z 80.00 - 2707.0 3.000 0.907 G* 0.857 m $ 2767.0 3.000

• 2767.0 3.000 0.790 gg 77.50 -

0.791 g 2787.0 3.000 ' 3.000 O.792 i 2767.0 75.00 - 2767.0 1 000 ~ 0.792 m[- 0.791 ~ 2767.0 3.000 2767.0 3.000 O.785 y 72.50 - 0.7'45 z-2767.0 3.000 0.657 $ ~ 2767.0 3.000 ~ " 70.00 3.000 0.656 2767.0 3.000 0.656 2767.0 ~ 3.000 0.656 67.50 - 2767.0 3.000 0.654 2767.0 3.000 0.652 2767.0 ~ 65.00 3.000 ~ 0.625 2767.0 3.000 0.516 2767.0 3.000 0.515 62.50 2767.a 3.000 0.514 2767.0 3.000 0.513 2767.0 ' O.511 60.00 - 2767.0 3.000 3.000 0.510 2767.0 3.000 0.508 57.50 - 2767.0 . . 55.00 - Figure 7-46 Initial Movement Of Frmh fuel: BO[r. LOF Base Case O 7-90 TEMPERATURE PRESSURE MELT (D E G R E ES-C) (ATM) FRACTION 115.00 llli EM 112.50 - 2761.0 3.002 _ 0.414 2767.0 3.001 _ 0.426 110.00 - 0.417 ~ 2767.0 3.000 . . ,. ~.4...., . gs r* ~ " 107. 'WI 2767.0 3.000 .- _ 0.587 0.819 - ~ ~ - 2767.0 3.000 - 105.00 - _. _ . _ . _ _m _ 3 - 3.000 _.-Z= "" - 6: 0.923 2767.0 102.50 - Ma_= O r =rd-st-s=3-2767.0 3.000  ; =-;- ._g =..____ _gg  ;-zg=g;= 0.075 = _ 2813.5 3.000 1.000 97.50 = - - = - - - = 95.00 - 2929.1 3.000 _WM_Ti MMM5MMM 1.000 G u ~.m _ _ _ _ _ . . . . . _ 92.50 - 2940.7 3.000 2 1.000 3 90.00 - 2773.3 3.000 _' ^__l__~ l 2_[ 1.000 y 3013.7 3.000 == =--=9= = = - 1.000 E 87.50 - -- .- x 3033.1 3.000 _ _ _ _ __ 1.000 85.00 - 3042.3 3.000 7 1.000 g 82.50 _ 3046.0 3.000 _ . _ _ _ . . . _ 1.000 g <y

E 8 80.00 "

- 3043.9 3.000 _ _ 1.000 N 3057.tt 3.000 __ 1.000 G r 3341.2 3.000 . I...'.~. 3 Y ' 1.000 **5 '~ ' ' k'{. '. '.l' : 9.l*.*h'#-1.000 y~ 7$*00 ~ 2977. Il 3.000 - 72.50 ' " .-' .+.:.. d 137 : MM. 1.000 r , . ,.;.. ; 2036. Li 3.000 70.00 - 2940.0 3. 0F g i .S ,/ .,f' - 1.000 y.R m. 2855.5 3.000 ' W W . *' M ' d . ' ' i 1.000 67.50 - *I. ".. ,sv.f. ~ 2778.2 3.009 1.4 5 M- . #3, .'9 .J'i '.' 1.000 $ - - 65.00 - 2778 2 3.051  ;;. 1.000 , ,g ' M'sp ~ -' '. 'E%* 1.000 I 2700.1 3.136 1: . ~ 62.50 - 2767.0 3.000 "M.' 0.874 2707.0 3.003 . T ': (' 'e?._..4  % y$03 f. c % ' O.748 M. 00 - 2767.0 3.000 D.737 . d .c .' ' N ..-('!.T;':  : ..,2 w $ s f.j 57.50 - 2767.0 3.000 1 : . . t -# , .- 0.591 2767.0 3.000 a Ud:y .- O.384 55.00 2767.0 3.000 O.301 ~ 0 ~ 270'I.0 3 000 . O.285 50.00 - 2767.0 J.000 _ . D. Orn T ~ 2655.6 3.000 0.000 47.50 - 1.6 3 000 0.000 45.00 - 2647.2 3.000 -- O.000 42,50 - 40.00 - Figure 7-46 Start of Significant Slumping of Fresh Fuel: BOEC LOF Base Case 7-91 115.00 - TEMPER ATURE i RESSURE MELT (DE G RE E S- C) ( A T M) T R ACTION ggp,39 _ l c' / b i . U . 3.001 1 U. 2b 110.00 2767.0 3 000 0 in i 27f,1.0 3.000 n.31H 107.M - 2767.0 3.000 F2NW -- 0.4 74 105.00 - 2767.0 3.000 _ [ 0.721 Q ~ 102.50 _ 2767.0 3.000 _ 0 e37 . . = e .=- 100.00 _ 2767.0 3.000 i . _ = . _. =_ ._ . .J J.25 0.770 ._.l_._. ^ _ - _ : X =: 97.50 _ 35.00 _ 2787.0 3.000 ___ 0.985 g 9 0 _ 3 90.to _ e 37.50 - E E n5.00 _ e8ss.2 3.000 11. . E- i . 0m m ~ - FR6'4 3 3 tiu .. 1 Ono C. b 00.00 2893.6 3.000 -( . , 1.000 mE7 2935.3 3.000 ,,.. . ,, < . ; 1.000 .+ N 77.50 2958.7 3.000 '1 r.gf. 1.000 G g 2972.3 3.000 *} ; '? 7 1.000 M-1.U00 ;C y 75.00 2976.7 3.000 O f...t. 2980.4 3 000 SN' l.000 s" 72.50 2989.6 3 000

9. p./ L. 1.000 C 2972.4 3.000 y, . ., f ;.jv6' ; . 1.000 g, 70.00 2897.5 3.000 ' ,. y , ., 1.000 "s a 0850.3 3. 0'10 .- ' ', a 1.000

'6 , , . 67.50 _ 28s9.4 3.0v0 E 4 1.001 ;;j 2767.0 3.000 ~,,' y I '*: 1: 0.993 8' 65.00 _ 2767.0 3 000 i 'j '  : , ,[l. ~' O.850 $~ 2767.0 3.000 d. J,. s . ' j., ' ' / . c - 6 0.857 5 62.50 - 2767.0 3.000 3A ~ , ~ . , , p.* / ~ ' O.858 3.000 ~$. ,k'*. tg'Jg 4' 0.708 2767.0 S'2.00 - P767.0 3.000 t .. ") i . 0 559 2767 0 3.001 3.W - t '.'- " 0.557 57.50 * ~ 2767.0 3.000 'I $.x i uG.'W' I' . ac. t O.389 55.00 __ 2767.0 3.000 mg 0.149 2767.0 3.000 a gy,4f m cig m A & 0.053 52.50 _ -""'-"# b *" - 2767.0 3.000 , 0.037 50.M ~ 3 000 - - 0.000 2608 9 47.50 - 2483.0 3.000 ~ ~ * ~' - 0.000 us.00 _ 29as.2 3 000 0.000 298i.0 3.000 - 0.000 4 .50 _ 40.00 ._ llll Figure 7-47 Final Observed Slumpmi tr .it ion of Fresh Fuel: 80EC g LOF Base Case W 7-92 115.00 - TEMPERATURE PRESSURE MELT - (D E G R E ES-C) (ATM) FRACTION 2721.7 3.081 E ==== g_ = 0.000 110'00 ~ 2722.'l 3.I37 g} g O.000 107.50 - 2723.4 3.207 0.000 105.00 - 2727.4 3.302 0.000 102.50 - 2731.0 3.411 I.- ___ 0.000 2734.4 3.330 Z---__m_s__. D.000 - - ~ ~ F -~ 0.000 100.00 - 2737.5 3.380 - 2739.3 3.360 D.000 , _ . . I. . 1"" -~ _ S* 2747.4 3.332 . b'ca .[ 0.000 0 2767.0 3.286 ~ ' . i f.'. f [ g,fei?g 0.039 3 2767.0 3.210 ~. 3 f .i ' hhM, ',] f)...{} 0,170 $o 85.00 - --Z~~~~-- 0.184.x5= 2767.0 3 177 2787.0 3.188 - 0.188 y, 2767.0 3.160 f-ZTE_ j_n,g ~ ~ ~ ~ ~ 0.188 g 2767.0 3.142 0,189 8o 5 W.00 -- y } S 2767.0 3.111 0.190"$o  ; 2787.0 3.073 0.214 g 87.50 2787.0 3.032 _ m 0.272 9 E 2767.0 3.003 _. _Z_ __ ' O.333 50, ~ 2767.0 3.000 h == = _ assa 0.304"h3 2767.0 3.000 h+E :ca=cas sss=#5 0.305 82.50 - 2767.0 3.000 isAI$5NNANYdMY 0.306 S? ' 2707.0 3.000 5 M5 N- O.306 00.00 - 2767.0 3.016 # 0.32 d 27S7.0 3.038 _ 0.304 2 , 767.0 3.298 0.002 g 77.50 - 2767.0 3.326 a.c .n 0.301 u 75.00 - 2767.0 3.359 EE EE53t[aM_ Fri am -- 0.299 2787.0 3.389 _ 0.295 2.50 - 2787.0 3.277 E= = = 0.23t 7-70.00 ~ 2767.0 3.000 0.287 67.50 - 2767.0 3.000 0.284 85.00 - - 67 .50 - 60.00 - Figure 7-48 Initial Expansion of Irratiiatec Fuel' B0EC LOF Base Case 7-93 TEMPERATURE PRESSilRE MEET 120.00 - (D E G R E E S-C) (ATM) F R ACTION 117.50 - 2606.4 3. M M ~E 0.000 2600.9 3.000 0.000 t15.00 - " ~ 2603.3 3.001 0.000 110.00 - 2612.0 3.010 0.000 1U7.50 - 2823.7 3.027 Gj M*C; 0.000 105.00 - EF+==1- . = - = - 2833.7 3.047 l-h70=@ [2El3 0,000 ~ " ' ~ ' ~ 102.50 - 2611.3 3.011 _.~- ~ 0.000 2655.3 3.071 - 0.000 100.00 - 2106.5 3.028 . 0.000 - 2767.0 3.014 , . . , . . . 0.016 y 97.50 - 2761.0 3.007 - - ~ - - ' - ~ ^ ~ 0.064 E o g$ _ 2767.0 3.000 0.068 ]oy 2761.0 3.000 0.012 E Z 02.50 - 2767.0 3.000 0.015 " D0.00 - 2767.0 3.000 0.017 boo B .50 - 2 3 000 1 ' ~' z 2767.0 3.000 O.193 ;3 o B5.00 h 2767.0 3.000 0. ISS " y 02.50 - 1- . D. H6 p 80.00 - 2107.0 3.003 0.197 ig 77.50 - 2767.0 3.006 0.197 0~ 3 030 2767.0 ~'~ ~ ^ ^ . 0.189 s 75.00 - 2767.0 3.000 0.178 E, ,li z 2787.0 3E0 _,yy . ,; 0.184 g 72.50 - ~~- 2787.0 3.00L 0.143 67.50 -, 2707.0 3.023 . O.120 [ - 05.00 - - 2/67.0 3.000 D.100 62.50 - 00.00 - 2761.0 3 000 Idh-j [5 0,090 s7.50 - 2787.0 3.017 0.102 55.00 - 52.50 - 50.00 - Figure 7-49 Beginning Of Irradiated fuel Collapse: B0EC LOF Base Case 7-94 TEMPER ATURE PRESSURE 120.00 - (DEGRE ES-C) (AIM) 117.50 - 2415.5 3.000 M i15.00 - 2390.S 3.000 112.50 - 110.00 - 2385.6 3 001 _ 1U7.50 ~ 2y02.4 3.001 105.00 - 2919.9 3.00t lyg)) kWM ==# ~-a- ^

-D r=n-102.50 -

2138.5 3.001 M =2 grg 2455.7 3.001 we_ gf== g-100.00 - -' ~ '~- 2477.9 3 00L

• 97.50 2538.1 3.001 1 - O 3.001 Y. ' ' .i 5,,I~ 3 2637.1 2648.8 3.001 -

31 :  %-- e.A e c, 95.00 - ~~ 2650.5 3.001 " ' ~ ~ - ~ ~ - - - CO o 92*50 - 2652.0 3.000 a di 90.00 - 2652.8 3.000 87.50 - $R s a7 S B5.00 - 2654.0 3.000 $ a - h 82.50 2BG7.6 3.002 p g=? f==y g g;3 g ~ g 3 3 g $, E 80.00 - 2699,9 3.008 T i W E M M 5 {~Z- i- @ d  ? 2717.9 3.007  ;- 77 _ 18 .018 $, g 75.00 - - v 72.50 - 2702.9 3 000 $ 70.00 - 2685.0 3.000 [h ==== ==== h" 7 u 67.50 - 2861.2 3 023 65.00 - 2636.0 3.010 62.50 - 60.00 - 2610.2 3.012 ]-_] _ _ _ _ _ _ _ 57.50 - 2586.7 3.012 55.00 - 2565.8 3.003 52 50 - X== - - = = 3 CT' T--= S0.00 - 2564 1 =F --~==-- E ._ 47.50 - 2500.3 3.005 45.00 - Figure 7-50 Irradiated Fuel Slumping: BOEC LOF Base Case 7-95 4 4.0 10 = _ LOF BOEC CLAZAS PLUS LIMITED INITI AL FUEL MOTION POWER + REACTIVITY VS TIME 3.0 3 -- 10 = = - ~ l 2.0 g i < c: g 10 2 -- g" a a

o. -

a m *s y w - 1.0 >. g ~ ___________ _ p _ ____ --- , g $ 103 - ', h 8 5 i e l - 0.0 - _ i l t 0 r , 10 l- 8 - -1.0 - I 32 t I I I ' ' I I 10-1 -2.0 13.88 13.93 13.98 14.03 14.08 14.13 14.18 14.23 14.28 TIME IN SECONOS Figure 7-51 Power and Reactivity Traces: CLAZAS and Limited Initial Fuel Motion O O O 3.0 LOF SOEC CL AZAS PLUS LIMITED INITI AL FUEL MOTION REACTIVITY VS TIME 2.0 - 1 = NET 2 = DOPPLER g 3 = DENSITY < 4 = TOTAL FUEL d 1.0 -- / NET f 8 z DENSITY TOTAL FUEL ) 0.0 N ' DOPPLER y -1.0 - 2 e 1 -2.0 - 4 I I I I I ' -3.0 4.0 , LOF BOEC CL AZAS PLUS LIMITED INITI AL FUEL MOTION RE ACTIVITY VS TIME 3.0 - 1 = NET 2 = TOTAL COOLANT y 3= PROGRAMMED d 5 = TOTAL CLA0 a 7 z C 1.0 - f_ ~ NET f 3 TOTAL CLAD y 5 p - 3 Q 0.0 - 4 E -1.0 - 1 -2.0 13.88 13.93 13.98 14.03 14.08 14.13 14.18 14.23 14.28 TIME IN SECONDS' Figure 7-52 Reactivity Components: CLAZAS and Limited Initial Fuel Motion 7-97 04 h LINES NUMBERED llY Clf ANNEL ~ LOF BOEC CLAZAS PLUS LIMiiED INITI AL FUEL MOTION m F UEL FIE ACTIVITY VS TIME cc 3 0.0 $ 4 a E s > -0.2 - 1-2 U -0.4 - 2 <t E - 0.6 - 3 I I I I I I - 0.8 0.4 LINES NUMBERED I BY Cll ANNEL ~ LOF BOEC CL AIAS PL US tlMITE D INiil At IUEL M0110N g F UEL RE ACTIVITY VS IIME 8 J a 0.0 - a 2  ; -0.2 - e E s y -0.4 - 7, 9 E -0.6 - I I I I I - 0. 8 13.88 13.93 12 14.03 14.08 14.13 14.18 14 23 14.28 TIME IN SECONUS Figure 7-53 Fuel Reactivity per Channel: CLAZAS and limited Initial Fuel Motion O 7-98 800 1.08 700 - NORMAltZED POWER f - 1.06 -== NET RE ACTIVITY l 600 - I 1.04 m I  % 5 500 f 1.02h sl: o 2 / E o >- ?  % 400 - / 1.00 t s 2 $ 4 # C 2 / 5 5 300 - / - .98 : / C - a / 200 - .96 / / 100 - .94 / / I ' I 0 .92 14.50 14.51 14.52 14.53 14.54 14.55 14.56 TIME (SECONDS) Figure 7-54 BOEC LOF No Fission Gas in SLUMPY: Power and Reactivity vs Time 40 NOTc: COOL ANT V010 LNG REACTIVITY 35 - IS S1.935 AT 14.50 SEC. 30 - NET FUEL m 25 - 5 NET COOLANT ~ [ l a g 20 - u3tgypy o 5 P w 15 - \ UNO SAS/FCI FUEL SAS/F CI 5 g , l -COOLANT l 14.51 14.52 14.53 14.54 14.55 14.56 14.50 TIME IN SECONDS Figure 7-55 BOEC LOF No Fission Gas in SLUMPY: Coolant Voiding and Fuel Motion Reactivity vs Time O O O 10 2 _ 1.25 = ~ 1.00 ) 10 2 _ , I a 0 E r,e 0.75 m x il 4 _a g C g 5 l E o 3 z 7 a 10' - 8 - 0.50W[ ~' w  : 8 - ~_ 0 a s I C 2 - a q cc I w 0.25 * ,. A ; O - ~ POWER 10  : s I ,t - 0.00 -________________________________________,,'"~'# RE ACTIVIT Y +- 10-' ' -0.25 0 2 4 6 8 10 12 14 16 TIME IN SECONDS Figure 7-56 B0EC LOF No Axial Expansion Reactivity (15 cm Rip): Power and Reactivity vs Time O mIh<2 oC z >t>- a$cc "z 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 y 1 t - - - - - i v i t c a e R i 4 1 d n a 2 i i1I1lI r 0I4 EIIgI1Illll li e f w 1If / o P 2 W I 1 ) p f /- i R - m c - I 0 1 0 3 - ( - S - O y N t - O i - C v i E O - t '~ S c 8 - N a I e E R - M n - I T o i - s - n 6 a - p - x E l - a i - x - A - 4 o - N - F e Om - Li - T C - E 1 2 Os - B v 7 - 5 7 _--~_-- - - ~ _- - 0 e r 2 1 0 1 u 0 0 0 - g 1 i 1 1 0 1 ~

. cm:aa2Ez 7i55oc f O

ye 2 0.4 / 15 CM RIP / ~~ 30 CM RIP 0.3 - / / / COOLANT < n.2 - d / 8 E / C / E / $ / w 0.1 FUEL 0.0 N N . \ I I l I I I I - 0.1 12.980 12.984 12.988 12.992 12.996 TIME IN SECONOS Figure 7-58 B0EC LOF No Axial Expansion Reactivity: Channel 6 Reactivity vs Time f 7-103 .14 .12 - LANT ~ 15 CM Rip '0 ' " ~ ~ 30 CM RIP .08 ~ e 3 ' .06 - a ~ E i .04 g o s i': # .02 - e 0 p- g /  % / \ p .02 - N FUEL g \ - 04 \ \ .06 12.970 12.974 12.978 12.982 12.986 17.590 12.994 12.998 TIME IN SECONOS Figure 7-59 BOEC LOF No Axial Expansion Reactivity: Channel 8 Reactivity vs Time O O O l.0 (1) BASE CASE (2) DOPPLER COEFFICIEtiT PLUS 50% (3) DOPPLER COEFFICIEtlT MIt1US,,, . 50% i  :. 0.8 , ' ' , l,  : ,I , ,1 . ,,,,. 3 *s'. :s 0.6 - - / ,  ;  : - t .,  ;. m , i ,. x * , .t. s j , . . d o 0.4 i ',  : i 5 s' $ = { 0.2 - , . . ,, , [v ', r ..i d - u, , x 1 ..

e. i .

g , , . 'i,.*  ; us 0.0 ------L- . ,- e

i  :

. s - '- i  : ,(3) i -0.2 _ l -0.4 -

• II) i(2) 10 11 12 13 i4 15 TIME If4 SEC0f(0 Figure 7-62 00EC Core Doppler C3 efficient Variations t

7-107 -(2) (1) BASE CASE 3 g,7 (2) VOID COEFFICIFitT PLUS 50% 1 3 (3) VOID COEFFICIEilT MIf4US 50%  ! i 1 l :l  ; ,i . 5 IO7 ? 8 G. -d* I . --e I' 8 a kj l1 . 3 . s22 ,I i i ... - . S ' - s .-  ! .  !(3) 3 10 _.] -- 2  ! (1) i i 1 10 _ 3 9 10 11 12 13 14 15 16 17 18 TIME Ifi SEC0tIDS Figure 7-63 B0EC Core Sodium Void Worth Variations O O O .10 .08 - - 15 CM RIP - - 30 CM filP .06 - .04 -- m FUEL $ .02 d 8 E ~~ ~ - 00  % b N $ \ w Ns w .02 - N cr .04 - N N N COOLANT  % .06 - N \ N .08 - N .10 12.982 12.986 12.990 12.994 12.998 TIME IN SECONDS Figure 7-60 BOEC LOF No Axial Expansion Reactivity: Channel 10 Reactivity vs Time 7-105 102 l (1) BASE CASE  ; I

(2) -DOPPLER COEFFICIENT PLUS 50$ ,

- (3) i DOPPLER COEFFICIENT MINUS 50% 'i . l a j .. I . 1 I ,. .' : i i I 101 _.) ..' - - I s '. I x W , ,' . .: V .  ; ~.. -a 2 1 . '. .- . t i _i i a , 7 5 g /* -( 3 )  ;, l(2) ! m -  ; a . --)1-- E l g, I _- , = 103J . i, ~ ' l i i(1 ) i l i l 1 8 9 10 11 12 13 14 lS TIME IN SECONDS Figure 7-61 BOEC Core Doppler Coefficient Variations O O O

1. 0 ~

t'!(2) } i e I f 0.8 ' ll 'l If 0.6- ,'. e 8 g < .~. . , > 0.4- . -'.l.. .,* c a  :: . .e ~ . . e ~ . . ca ...-  : , . *; '.f. l . 's o ! p -- .. .  : .: s i - ' > 0.2- l V I . .o n.-. i s l r u , g 0.0. .:..' . . . a: . , g -............. ... . b' ' -0.2. l -0.4 (1) BASE CASE 4 (j) l (2) VOID COEFFICIEf1T PLUS 50% l (3) VOID COEFFICIENT MIllVS 50% -0.6 i 1., (3) 11 12 13 14 15 16 17 TIME Ill SEC0t1DS Figure 7-64 BOEC Core Sodium Void. Worth Variations 7-109

8. Initiating Phase Analysis of Unprotected, Combined Step Reactivity Insertions and Loss of Flow Events (STEP /LOF) at Full Power.

The initiating sequence evaluated in this section is based upon the occurrence of a step reactivity event combined with pump trip and simultaneous failure of both primary and secondary shutdown systems. The probability of this segaence is believed to be of much lower magnitude than either the LOF or TOP <equences and is evaluated here only to assure that accident consequences do not differ significantly from those for equivalent probabi-lity LOF and TOP's. The physical mechanism with highest probability for causing such a sequence is believed to be an earthquake which causes a radial compaction of the fuel assemblies coupled with a common mode mechani-cal failure of the two redundant shutdown systems (Ref. 60). The magnitude of the reactivity insertion from such motion is extremely complex and because of the many degrees of freedon, may be negative, positive or zero, but certainly small. For analysis purposes an arbitrary magnitude of thirty cents was chosen to be both significant with regard to its impact on the reactor and conservative from the standpoint of likelihood of occurrence. Becaus' of these combined phenomenological assumptions STEP /LOF events were assigned to probabilistic category three. 8.1 Effect of Thirty Cent STEP /LOF in 80EC Configuration As a result of the 30 cent step reactivity increase, the power level rises 40 percent during 40 milliseconds. Doppler and fuel expansion reacti-vity feedbacks respond and gradually reduce the net reactivity and power. By the time sodium boiling begins in the highest power-to-flow fresh fuel assemblies (Channel 9) at 7.52 seconds, the net reactivity has decreased to 2.4c supercritical and the power to 1.18 x nominal. (Table 8-1 sunmarizes the sequence of events during the SAS analysis.) Because of its location in the outer core zone, Channel 9 introduces negative void feedback, further reducing power. Power and reactivity do not increase until 9.20 seconds when fresh fuel Channels 1 and 3 begin to introduce positive sodium void reactivity. At this time, the net reactivity is 1.4c subcritical and the power is only 1.12 x nominal. 8-1 Channels 1 and 3 introduce significant positive feedback. By the time they have completed the voiding process, the net reacti.vity has risen to sl.5 x nominal. Conditions remain approximately constant until 10.42 seconds when Channels 7 and 5 begin voiding. These two channels complete their voiding by 10.70 seconds, driving the net reactivity to 69.7d superrritical and the power 4.4 x nominal. Again, there is a short delay during which Doppler and expansion feedbacks lower net reactivity before Channel 2 voiding becomes effective. Net rr,ctivity and power drop to 63.2d supercritical and 2.99 x nominal respectively, at 10.80 seconds. Channel 2 r:.pidly introduces substantial void reactivity driving .the net reactivity to 87.7c supercritical and the power level to 14.7 x nominal by 10.99 seconds. Again chere is a delay during which temperature driven negative feedbacks partially reduce the net reactivity. By 11.08 seconds, when voiding in Channels 4 and 8 significantly affect the core, the net reactivity and power have fallen to 69.9c and 7.1 x nominal respectively. The sodium void reactivity introduced by Channels 4 and 8 provides the driving reactivity for the following fuel slumping and FCI events. Figure 8-1 shows that the initial step insertion of 30 cents is sufficient to hold g the power near or above the design level until gross boiling takes place. This causes the fuel temperature to increase and causes the compressed time scale of events when compared to the 80EC LOF scenario (Section 7.2). - Figure 8-2 shows in more detail how the voiding history affects the reactor power and net reactivity. The rapid subprompt critical excursion due to Channel 4 and 8 voiding results in the 50 percent melt fraction criterion for slumping in fresh fuel pins being exceeded. These pins have little or no fission gas accumulated to continually disperse the fuel and so introduce positive reactivity as the fuel in the upper segment and molten region slump. Slumping is initiated in Channel 1 at 11.133 seconds with Channel 3 slumping at 11.135 seconds. Slumping begins in Channels 9 and 7 at 11.166 seconds and 11.178 seconds respectively. During this period of rising reactivity, voiding in Channels 4 and 8 provides the major share of the driving reactivity with total fuel motion reactivity providing 30 to 40% of the driving ramp. O 8-2 Because of the rapidly rising temperatures, the Doppler and fuel expansion feidbacks overcome the combined effects of voiding and fuel slumping and temporarily turn around the reactivity and power pulse. The net reactivity peaks at 11.181 seconds at 98.5c supercritical and the power peaks 4 milliseconds later at 124.3 x nominal. The Doppler and expansion feedbacks are reinformed by Channel 2 slumping at 11.179 seconds. Channel 2 is the highest power irradiated fuel assembly and is strongly dispersive on failure. The fission gas driven dispersiun introduces strong negative fuel motion reactivity, but not enough to overcome the slumping of the near fresh fuel pins. It does, however, stop the increase in cumulative fuel motion reactivity and hold it approximately constant for a period of several milliseconds. Channel 8, consisting af 24 irradiated fuel assemblies, also fails during this period at 11.184 seconds. It also exhibits a dispersive type failure; however, the failure occurs high in the flow channel and part of the fuel is disnersed downward toward the core midplane. The net effect is a slight but positive increase in reactivity. Channel 4, another irradiated assembly, fails at 11.185 seconds in the same location and manner as Channel 8. It introduces a slight but negative change in reactivity which offsets the positive change in Channel 8. Channel 5, the last fresh fuel assembly, fails at 11.182 seconds and exhibits the same type failure as the other unirradiated assemblies. The combined fuel motion reactivity effect of these three channels is basically zero during this period. The period of semi-equilibrium is ended at 11.191 seconds when internal pin pressure built up by the sustained high power operation causes a pin rupture at the core midplaae in Channel 6, the last chanr:el entirely filled with liquid sodium. At this point, the net reactivity is only six cents sub-pranpt critical and decreasing at the rate of 3 $/sec with the power at 80 x nominal. (When the similar event occurred in the 80EC LOF base case, the net reactivity was approximately 64 cents and decreasing at the rate of 26 $/sec with the core at 9 x nominal power.) The midplane failure in Channel 6 generates both positive fuel and sodium void reactivity responses upon ejection of the fuel fission gas mixture. Initially, the dispersive 8-3 effect of Channel 2 offsets the fuel motions in 6. However, the very strong sodium void effect (330 $/sec) in Channe? 6 is sufficient to drive the h reactor superprompt critical for the first time at 11.199 seconds at a rate of 11.4 $/sec. A pin failure similar to that in Channel 6 occurs in Channel 10 at 11.192 seconds. Although sodium boiling in Channel 10 had initiated at 11.169 seconds, it was limited to a small region at the core outlet. The cladding rupture occurs just above the midplane causing initial fuel motion to be slightly negative. As the sodium void worth at the core outer boundary is negative, Channel 10 introduces approximately eight cents of negative reactivity at the occurrence of prompt critica'ity. Following prompt criticality, the rate of energy generation in the fuel increases exponentially. Based on the behavior of Channel 6, a hydrodynamic disruptive event is judged to occur. The PLUTO code was employed to examine fuel-sodium responses in Channels 6 and 10. Since PLUTO does not allow for continued generation of molten fuel, it is necessary to conservatively account for the growing cavity by running pLUT0 with cavity sizes larger than those predicted at pin failure by SAS3A. In order to provide conservative voiding rates and fuel velocities $ within the pin (relative to SAS/FCI predictions) the pressure and fission gas inventories present at the time of pin failure are assumed. Such an assumption is conservative, since the pressure decays very rapid 1/ following pin failure, with consequent rapid movement of molten fuel toward the pie center. It was seen above that the sustained superprompt critical burst predicted in SAS3A was due primarily to the reactivity effects in Channel 6 followiag failure at midplane. The sodium voided very rapidly, and the fuel moved toward the midplane in such a manner as to cause increasingly positive reac tivi ty. To ensure a conservative PLUTO calculation, a cavity size was chosen that would be present at a time when reactor disassembly should be well underway. For this case, the conditions existing 8.157 millisec af ter Channel 6 pin failure wolld be a good first estimate. At this time, SAS3A predicted superprompt critical conditions (n = 1.055, P = 285 Pg . o = 35 $/sec and increasing). The internal pin pressure predicted by SAS/FCI at this time was 58 atm; however, the value at the start of the g 8-4 FCI (238 atm) was used for the PLUTO calculation, in order to move the fuel in a conservative manner. The cevity sizec M4 for conditions at the time of initial pin failure in Channel 6 and at 8.1 msee beyond failure are listed in Table 8-2. Note that the cavity has not. grown axially during this time period, although the ends c he cavity contat.: much more molten fuel after the 8.157 msec has elapsed. The reactivity generated by motion of molten fuel in these segments provides the necessary conservatism in the analysis of this time interval. (There is also slightly more sodium voiding due to more fuel being ejected earlier from the nodes in the central portion of the cavity causing a slightly more energetic FCI). For purposes of comparison, PLUTO calculations were done assuming cavity sizes that existed at failure and 8.16 msec afterward, the results are shown in Table 8-3 and Figure 8-3. Comparison of PLUTO and SAS/FCI generated results shows that the solutions cross at about 11 usec for the original cavity and at 11.6 msec for the larger cavity, which are times well into the disassembly phase. It is therefore concluded that a driving reactivity for VENUS which contains Channel 6 results from a PLUTO calculation with the larger cavity is conservative: that is, axial growth of the cavity and motion of this newly formed molten fuel does not occur on a fast enough time scale to influence the driving reactivity for disassembly. The SAS/FCI predicted reactivity consequence from failure in Channel 10 is shown in Figure 8-4 and is mildly negative (-5 cents in 8 msec) until the superprompt excursion generates rapid fuel melting at the axial ends of the pin cavity. Then, based on the SAS fuel reactivity feedback model a strong positively accelerating fuel effect is predicted (same as in Channel 6). The SAS/FCI reactivity feedback model is non-physical in that momentum, inertia and compressible flow effects are ignored and is most in error during high power conditions. To bracket the time dependence of the SAS pin cavity, PLUTO was used to examine the original failure cavity conditions (a valid assumption until significant additional melting in SAS) as well as a hypothetical cavity condition which would exist without material ejection in the SAS solution S-S at 7.3 msec af ter failure. This time is just past prompt-critical conditions, prior to when Channel 6 fuel 1 tedback occurs, and approaching hydrodynamic conditions. Table 8-4 preserts the conditions in the Channel 10 fuel pin cavity in SAS/FCI as well as the PLUTO initial and hypothetical cavity models. The net reactivity feedbacks are compared in Figure 8-4. Up to about 8 msec, the feedback in the SAS solution is about equally contributcd from sodium and fuel. Beyond 8 msec, it is almost entirely fuel reactivity. The PLUTO solution indicated that the sodium responds about twice as fast (compressible effects) and dominated the total feedback beyond the first two milliseconds. The PLUTO initial cavity case, which is a more realistic treat-ment for this short time after failure, indicates that sodium feedback is always dominant in Channel 10. Figure 8-5 demonstrates th the PLUTO model of the 7.2 msec cavity is conservative with regard to fuel reactivity feedback during the first eight msec of the failure. It can be seen that the PLUTO cavity is defined to be somewhat longer and does remove more fuel from the cavity ends to the failure site thereby providing more positive fuel relocation within the pin. At the same time PLUTO ejects more fuel and allows it to accumulate at the failure site in the flow channel, again a conservative result. Al - though fuel is moving inward (i.e. , toward the core midplane) from the axial ends of the pin cavity, preferential removal from the cavity ends as in the SAS/FCI treatment is non-existent. Thus, for the purposes of establish-ing the effect of the channel 10 failure on the reactor as it enters the hydrodynamic disruption phase, the PLUTO hypothetical cavity results are considered the most appropriate up to about 9 msec. An assessment of the energetics consequences of this event is provided in Section 11.2.3. 8.2 Effect of Thirty Cent STEP /LOF in the E0EC Configuration This case has the same basis for assumptions as the analysis presented above for the 80EC configuration. The general accident progression is summcrized by Table 8-5 and Figure 8-6. g 8-6 The thirty cent step insertion results in a forty percent step power increase. Doppler and axial expansion effects act to offset the insertion and the sodium reduced density feedback (15c) such that in about nine seconds the reactor has returned to just critical with a thirteen percent overpower condition (i.e. ,1.13 x nominal) and a flow of i7 percent. At about this same point sodium boiling initiates in the eighteen peak power-to-flow assemblies (Channels 1 and 8). Voiding and dryout progress in a mild manner such that when cladding melting starts in Channel 8 at 10.094 seconds the reactor power is 1.4 x nominal and the net reactivity is at 19 cents supercritical. Continue boiling and voiding (Channels 1, 3, 5, 8, 10) slowly (1-3 $/sec) bring the reactor to 4.5 x nominal and a relative peak net reactivity of 68 cents at 11.2 seconds. Sodium re-entry in Channels 3 and 5 then combine with voiding in Channel 10 (negative effect) to reduce the power and net reactivity to 2.4 x nominal and 37 cents in 140 msec. Fuel malting has just now initiated in Channels 1 and 8. The cladding in both of these assemblies has become fully molten above the midplane and cannot offer restraint. Fission gas release fractions are on the order of thirty to forty percent. Voiding in Channels 2 and 9 combine with re-voiding of 3, 5 and 7 to drive the reactor to about 75 cents supercritical and a power level of 8 x nominal by 11.900 seconds when fuel disruption occurs in Channel 8 with a melt fraction of 0.53 just above the midplane. The sodium void pattern (Figure 8-7) shows that only Channels 4 and 6 have significant sodium above the core midplane and thus represent potential LOF-d-TOP failure regions. Positive sodium v.id worths associated with these regions (56 and 41 cents, respectively) ar sufficient to initiate and sustain a superprompt critical transient from the current reactivity state. Thus the behavior of the lead disrupting fuel channels (8 and 1) constitutes a branch point in the accident progression. Fission gases initiate a mild (-2 $/sec) dispersal of Channel 8 fuel away from the midplane which overcomes the positive effects of continued voiding and lets the core reactivity slowly decrease. At 11.983 seconds 8-7 Channel 1 initiates fuel disruption just above the midplane with a melt fraction of 57 percent. The power and net reactivity at this time are h 6.6 x nominal and 66 cents with reactivity decreasing at -0.9 $/sec. Gases have slipped by the fuel in Channel 8 and the disrupted region is now experiencing a slow collapse. Dispersal of fuel toward the midplane in Channel 1 results in a very mild reactivity increase. Flow reversal and voiding in Channels 4 and 6 now lead to a mild (10-20 $/sec) superprompt excursion which results in disruption of the remainder of the core fuel . During the power burst to about 900 x nominal, only fuel motions in Channel 8 are significant. Initially, rapid axial disruption below the midplane leads to fuel negative reactivity effects as the new fuel merges with that already collapsing. liowever, the imediately released fission gas pressures rapidly start to move fuel up toward the midplane. This actually drives the core (m15 $/sec) through the super-prompt burst whcn sodium voiding effects are falling off. Doppler feedback terminates the 6.6 msec superprompt excursion. Generation of fuel vapor pressures in Channel 8 and fission gas effects in Channel 10 combine to rapidly move the reactor away from prompt critical. Thirty msec af ter the g prompt critical burst (12.109 seconds) general fuel disruption throughout the core has rendered the reactor 3.1 $ subtritical, decreasing at 44 $/sec with a power of 1.4 x nominal . A LOF-d-TOP event did not occur since voiding of Channels 4 and 6, which initiated the prompt burst, occurred prior to significant cladding loading. The initally mild fuel dispersion of Channel 8 was significant in that it kept the power and reactivity under control, such that time became available for the voiding in 4 and 6 to occur. The hex can walls in Chennels 1 and 8 were molten and the SAS calculation terminated. The fuel vapor pressures were on the order of 15 and 30 atmospheres, respectively with large quantities of intennixed steel near its boiling point. Peak fuel temperatures of 4700 K exist near the midplane of Channel 8. The average core fuel specific energy was 1366 joule /gm corresponding to a temperature of 66 K above the melting point. Thus formation of a boiling molten fuel-steel pool without significant fuel vapor expansion would terminate the event without energetics of significance. g 8-8 8.3 Summary and Conclusion on Combined Reactivity Step Insertion and Loss-of-Flow Event The initial positive reactivity insertion does increase the likelihood of overpower failures in sodium filled low power-to-flow fuel assemblies above that of the straight LOF. Based upon the magnitude of the step insertion and the behavior of disrupted fuel in earlier sodium voided assemblies (i.e. , compactive or dispersive), these LOF-d-TOP events can result in either hydrodynamic or hydraulic disruption pressures. Thus, in the BOEC configuration the voided fresh fuel assamblies initially compact and accelerate the failures in Channels f and 10. For the E0EC configuration initial dispersal of Channel 8 fuel allows the net reactivity to decrease and sufficient sodium voiding of the lower power assem-blies such that overpower failures are avoided and the excursion terminates very benignly. Nominal STEP /LOF sequences appear to be similar to less probable LOF sequences with respect to their enhanced sensitivity to early fuel disrup-tion and LOF-d-TOP phenomenology. Since the STEP /LOF sequence is of much lower probability and the phenomena of interest are identical with those of less probable LOF events, the assessment of STEP /LOF events can be considered a subclass of LOF events. .a Table 8-1 SEQUENCE OF SIGNIFICANT EVEf1TS BOEC STEP /LOF EVENT g TIMING ')F EVENTS (I) - THIRTY CENT STEP /LOF IN BOEC CONFIGURATION 5"j 88 E gg b es 38 EVENT rx8 Em EE EE 025 a5 EH 'N tge $S Sgb Geb CHANNEL 1 8.686 9.986 11.133 --- 2 10.143 11.095 11.179 11.070 (3) 3 8.899 10.084 11.135 11.133 (3) 4 10.799 --- 11.185 --- 5 9.925 11.015 11.182 11.177 (3) 6 --- --- 11.186 (2) 11.191 7 9.920 11.004 11.178 --- 8 10.978 --- 11.184 --- 9 7.524 11.135 11.166 11.147 (3) 10 11.169 --- 11.186 (2) 11.192 (1) SINCE LOSS OF FLOW  ! (2) SLUMPING CRITERION MET WITil SODIUM PRESENT (3) FCI CRITERION MET WITH VOID PRESEilT O 8-10 TABLE 8-2 CROSS SECTIO!1AL AREAS IN CHAf4NEL 6 FOR PLUTO CALCULATIONS (FROM SAS3A) flode Axial location Initial Cavity Cavity at 8.157 msec (cm) (cm ) (cm ) 5 46.72 .023155 .087840 6 53.98 .085887 .116623 7 61.24 .108669 .146829 8 68.50 .109205 .165422 9 75.76 .118455 .153875 I .165404 10 83.02 .135986 11 90.28 .099521 .160084 12 97.54 .080468 .112110 13 104.80 .018795 .083020 I Failure at node 10 (core midplane). 8-11 TABLE 8-3 CHAtit4EL 6 PLUTO RESULTS IfilTIAL CAVITY CAVITY AT 8.157 MILLISEC Time O fuel P sodium net fuel " sodium " net (millisec) 7 7 ) g 7 7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.040 0.027 0.067 0.053 0.032 0.085 m 4.0 0.065 0.077 0.142 0.087 0.090 0.177 C 6.0 0.090 0.136 0.226 0.125 0.158 0.283 8.0 0.115 0.197 0.312 0.156 0.227 0.383 10.0 0.120 0.254 0.374 0.164 0.291 0.455 12.0 0.123 0.314 0.437 0.167 0.357 0.525 14.0 0.122 0.371 0.493 0.174 0.421 0.596 16.0 0.122 0.429 0.551 0.168 0.480 0.649 18.0 0.112 0.481 0.593 0.160 0.533 0.693 20.0 0.102 0.528 0.630 0.141 0.581 0.723 # 9 e TABLE 8-4 CHANNEL 10 CAVITY CONDITIONS IN SAS/FCI AND PLUTO BOEC 30 CENT STEP /LOF SAS/FCI Cavity PLUTO Model At Failure 7.3 msec SAS Later Initial Hypothetical Cavity Variable Unit At Failure 4.50 7.06 4.49 7.17 Volume cc 254. 66. 254. 245. Pressure atn ca 38.2 53.c 37.9 60.2 Fuel Mass gm 2. w 3040 3047 3040 3050 Fuel Temperature K 2.69E-4 3.9E-4 2.69E-4 3.9E-4 Gas to Fuel Mass --- Ratio 0.62 0.62 0.69 0.69 Cavity Length to -- Core Length 0.102 0.102 0.102 0.142 Ejection Flow sq cm Area Ejected Fuel gm -- 6.14 - - - Ejected Gas gm --- 2.26E-3 --- TABLE 8-5 - TIME SEQUEt1CE FOR E0EC THIRTY CEf4T STEP /LOF SODIUM CLADDING SLtJiPY SAS/FCI SAS BOILIt1G MELTIt4G It4ITI ATI0tl If1ITI ATIO!1 CHAtitlEL (SEC) (SEC) (SEC) _ (S EC) 1 9~.07 10.38 11.983 (11.709)* 2 11.19 11.97 12.076 (l1.934) ca 3 10.46 11.50 12.073 (11.868) 4 11.24 ----- 12.077 (12.057) 5 10.22 11.29 12.071 (11.783) 6 11.21 ----- 12.077 (12.040) 7 10.78 12.07 12.076 (11.983) 8 8.88 10.09 11.900 (l1.595) 9 11.19 11.99 12.076 (11.945) 10 10.85 12.07 12.076 (12.013) *(Time) indicates satisfaction of burst pressure failure criteria but voided sodium region prevented model execution. O O O 200 1.2 g - 1.1 g 2 - 1.0 < N 0.9 d cn - o O o - 0.8 = F 3 - 0.7 h H N 3 0.6 5 $ 100 NET REACTIVITY - 0.5 h x < O - 0.4 W ? cc m m 0.3 g 0.2  % g 0.1 ~ - - 0 POWER 0 2 3 4 5 6 7 8 9 10 11 12 O 1 TIME (sec) Figure 8-1 50EC Thirty Cent STEP /LOF - Power and Net Reactivity NOTE: ARROWS INDICATE INITIATION Of SIGNIP1 CANT SOOtuM YOIDING IN INDICATED CHANNELS 200 , n 9 + - 1.2 m e; w - + - 1.1 cc 1.0 d r o 5 - U - 0.9 O 2 "

c. -

OE o - NET REACTIVITY 07 3 c DE e 5 i $ 100 - [ 05 g j *

• 0.4 lF F cc o

n + v - 0.3 $ z - - 0.2 h - - 0.1 5 a. o POWE R % 0 9.0 9.4 93 10.2 10E 11.0 11.4 TIME (sec) Figure 8-2 BOEC Thirty Cent STEP /LOF - Power, Net Reactivity and Voiding Sequence Detail O O @ 0.70 - 0.60 - BOEC STEP /LOF: f1ET REACTIVITY ADDITIOri - IN CHANNEL 6 FOLLOWING PIN FAttURE 0.E4 - - E 5 g PLUTO: CAVITY 8.157 micc o AFTER FAILURE ~ E PLUTO: CAVITY AT h PIN FAllt :5E 2 U 4 - - 't>E 030 SA$NCl 0.20 - - 0.10 - - 1 i i f f i e i 1 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20 0 TIME AFTER CHANNEL 6 PAttuRE (nact Figure 8-3 PLUTO and SAS/FCI Channel 6 Reactivity Histories 8-17 O 0.08 i i i ' ' O.06 - SAS/PCI _ PLUTO INITI AL 0.04 - C 9 (7.3 msec SAS CAVITY) PLUTO _ 0.02 - - 2 4 6 3 10 12 e ,x i i i i o TIME FROM CHANNEL 10 FAILURE (miec) 0.02 - - D_ me . U 5 e 4D6 - - 4.00 - - 4.10 - - -0.12 - - 4.14 - - 4.16 - - l l 4.18 I Figure 8-4 B0EC STEP /LOF Channel 10 FCI Reactivity feedbacks l l 8-18 ~ PLtJTO HYYOTHETICAL CAVITY C 0 PLUTO AFTER 8 me.c BLOWDOWN 6 - c a SAS AT 7.3 msec BLOWDOWN w 5 . z 5 e 4 - 5 3 - O a s / \ 2 - FAILURE SITE d I ~ SAS AXf AL CORE NODES \ / - s \ W 4 8 9 12 13 1 2 3 5 6 7 y' 11 8  : . l l l ,  := w:  : , l  ! 5 v%

• 1 - M --t+ - -g+- l UPPE R Z BLANKET

om S m ta mox tie!z aox CHAfif1EL s 1 6.98s 7.976 8.598 --- 2 7.980 --- 8.616 8.613 (3) 3 7.004 8.i13 8.598 --- g 4 8.409 --- 8.61 9 (2) 8.628 5 7.821 8.61 3 8.618 8.603 (3) 6 --- --- is.621 (2) 8.617 7 7.800 8.601 8.61 3 8.598 (3) 8 8.612 --- 8.618 (2) 8.628 9 5.961 7.434 8.607 8.598 (3) 10 --- --- P.621 (2) 8.627 (1) FOLLOWING LOSS OF FLOW INITI ATION AT 12.05 SEC0f1DS. (2) SLUMPlflG CRITERI A MET WITil SODIUM PRESENT. (3) FCI CRITERI A MET WITil VOID PRESEf1T. O 9-14 TABLE 9-2 FUEL PIf1 CAVITY C0flDITIONS IN SAS/FCI and PLUTO B0EC T0P/LOF BASE CASE: CHAfif4ELS 6 and 10 UTO Cavity Variable lini ts #6 #10 #6 #10 Volume cc 6.01 4.60 8.66 7.13 atm 254 291 255 290 Pressure Fuel Mass gm 51 . 0 39.1 73.5 60./ Fuel Temperature K 3044 3040 3044 3040 Gas to Fuel Mass --- 2.717 2.620 2.704 2.62 4 Ratio (x 10 ) Cavity Length to --- 0.69 0.62 0.85 0.77 Core Length Ejection Flow Area sq. cm 0.124 0.100 0.164 0.142 9-15 TABLE 9-3 h EVENT SEQUENCE FOR BOEC 20c/SEC T0P/LOF E0il!NG CLAD MELTING SLUMPING CRITERION FAILUPE CPf *;"EL OCGirls (1) BEGINS MFi CRITERION MET f;'J"C E R (SEC) (SEC) (SEC) (SEC) 1 5.17 5.64 5.810 5.75 (2) 2 5.55 ---- ----- 5.80 3 5.18 5.68 5.808 ,5.73 (2) 4 5.68 ---- ----- 5.872 5 5.33 ---- ----- 5.78 (2) 6 -.-- ---- ----- 5.77 7 5.36 ---- ----- 5.79 (2) h 8 5.76 ---- ----- 5.876 9 4.98 5.60 ----- 5.78 (2) 10 ---- ---- ----- 5.77 NOTES (1) LOSS OF FLOW 8EGINS AT 1.218 SECONDS (2) FCI CRITERION MET AT A VOIDED LOCATION O 9-16 TABLE 9-4 SEQUENCE OF EVENTS IN BOEC T0P/LOF WITH MOLTEN CLADDING GRAVITY DRAINAGE TIMING OF EVENTS (1) - INITIATING PitASE OF T0P/LOF PARAMETRIC - CLAD HOTION WITH GRAVITY DRAINAGE 8 e b C e4 3< EVENTS gm gm pm =g gg 35 a5 c5 EW 'W BS $$ $$ um 3Eb wuz uEQ auz CHANNEL mm um 1 6.985 7.969 8.353 8. 61 9 --- 2 7.979 --- --- 8.639 8.635 (3) 3 7.004 8.042 8.41 5 8. 621 --- 4 8.437 --- --- 8.642 (2) 8.650 5 7.824 8.635 --- 8.641 8.625 (3) 6 --- --- --- 8.642 (2) 8.64 8 7 7.800 8.625 --- 8.636 8.621 (3) 8 -- --- --- 8.641 (2) 8.649 9 5.980 7.434 7.948 8.626 --- 10 -- --- --- 8.643(2) 8.648 (1) FOLLOWING LOSS OF FLOW INITIATION AT 12.05 SECONDS (2) SLUMPING CRITERIA MET WITH S0DIUM PRESENT (3) FCI CRITERIA MET WITH VOID PRESENT 9-17 TABLE 9-5 h SAS SEQUENCE OF EVENTS IN 80EC T0P/LOF WITH MOLTEN CLADDING-SODIUM VAPOR COUPLING TIMING OF EVENTS (1) - INITIATING PHASE OF T0P/LOF PARAMETRIC - CLAD MOTION WITH SODIUM VAPOR COUPLING 5 W D e em Se em tw ?w 59 ~e 55 c5 a5 kW W BS $S $S Seb G e ta CHANNEL \ 1 6.985 7.959 8.342 8.528 --- 2 7.981 --- --- 8.539 --- 3 7.004 8.032 8.393 8.528 --- 4 8.292 --- --- 8.542 (2) 8.547 5 7.824 --- --- 8.541 3.533 (3) 6 --- --- --- 8.543 8.547 7 7.800 8.539 --- 8.538 8.531 (3) 8 --- --- --- 8.541 (2) 8.547 9 5.980 7.434 7.948 8.532 8.531 (3) 10 --- --- --- 8.543 (2) 8.547 (I) FOLLOWING LOSS OF FLOW INITI ATION AT 12.05 SECONDS (2) SLUMPING CRITERIA MET WITH SODIUM PRESENT (3) FCI FAILURE CRITERIA MET IN V0IDED CHANNEL 9 9-18 TABLE 9-6 SEQUENCE OF SIGNIFICANT EVENTS, E0EC T0P/LOF EVENT TIMING OF EVENTS (1) - INITIATING PHASE COMBINED REACTIVITY INSERTION AND LOSS OF FLOW U EVENT g, m Sh h 35 a5 kW "W CHANNEL 5$ #$ d $5h bbh(3) 1 7.971 9.102 9.934 9.636 2 9.409 --- 9.970 9.931 3 9.037 9.780 9.966 9.762 4 9.568 --- 9.971 9.960 5 8.858 9.700 9.963 9.797 6 9.544 --- 9.970 9.948 7 9.287 --- 9.970 9.922 8 7.856 8.915 9.884 9.554 9 9.403 --- 9.970 9.939 10 9.205 --- 9.974 9.936 (1) FOLLOWING LOSS OF FLOW INITIATION AT 12.80 SECONDS. (2) SLUMPING CRITERIA MET WITH SODIUM PRESENT. (3) ALL FCI CRITERIA MET WITH VOID PRESENT. 9-19 200 - 1.5 1.0 9 = 9 10 $ m 8 a e - NET REACTIVITY g = b b 100 - - 0.5 C

p 5 5 i

' e e w dk - 0.0 POWER 0.0 - 0. 5 =f 19$ '. 0 20.0 21.0 TIME (SEC) Figure 9-1 Combined Reactivity Insertion and Loss of Flow in B0EC Configuration- Power and Reactivity vs Time e O * ---__ SAS/ FCI PLUTO CHANNELS 6 AND 10 , 60 - I I i 50 - I # CHANNELS 6 AND 10 t t 40 - p m I *^ z  ! C / o o r } ~ 30 -

- I C /

O / = , i 20 ,' ,' NEGATIVE OF e CHANNEL 10 / a' s 10 - e' o' 0 _. 2 4 6 3 10 12 14 16 TIME FROM #6 FAILURE, MSEC Figure 9-2 BOEC T0P/LOF Base Case: PLUTO & SAS/FCI Results for Channels 6 and 10 O DJ 10' nI I

m a _

m I _ _dC ._J I N- J & a w 2 do 10- -. I 3 }h o  : Z Q_ - H M y o - - I p w _ - N H H ~ D & J 1 m H T o c 10_ _ i F r  : o E - E o  : w z _ 1 Nm - l 2 w Z 1 (B 10- - i  ! I I I l 4.0 4.4 4.8 5.2 5.6 6.0 6.4 TIME IN SECONDS Figure 9-3 BOEC 20c/sec 10P/LOF: Power and Reactivity Traces O 9-22 m L1HES NunBERED w BY CHANNEL 29 a - J J Ov 0 - p z 3 H N 1 t.- - + u "n-e 1 I I I I I i 4.0 4.4 4.8 5.2 5.6 6.0 6.4 tit 1E IN SECONOS m LINES Nun 8ERED g BY CHANNEL Q m9 G - I J a a o v Z 4 H N 3- ' F H i 3 0 r m ' f ['- R_ _ _s SN 0 w t - e i i i I l l l 4.0 4.4 4.0 5.2 5.6 6.C 6.4 T I t1E IN SECONOS Figure 9-4 BOEC 20c/ set iOP/LOF: Coolant Reactivity Comporents by Channel 9-23 LINES Nun 8ERED g o BY CHANNEL y cx c,- /s J aJ cn . O i _ ZO H

• v4

>- t _ t-H T

• 3 H N p i _

N9 7_ o . v i 1 1 1 I 1 4.0 4.4 4.8 S.2 S.6 6.0 6.4 T I f1E IN SECONDS CD O LINES HUMBERED g o BY CHANNEL T

• i~

7 J .1 (p h ok .1 a . oi_ ZW H = e-4 >- i_ s Hv y ' H N r 8 - $9 ' E 7-o v ' i i i i i 1 4.0 4.4 4.8 S.2 S.6 6.0 6.4 I I t1E IN SECONDS O Figure 9-5 B0EC 20c/sec T0P/LOF: Fuel Reactivity Components ]y Channel 9-24 90 - a e 80 - SAS/FCI RESULTS FOR ,' CHANNELS 6 AN] 10 70 - # d i 60 - # / m / E 50 - PLUTO RESULTS FOR CHANNELS . 40 . 6 AND 10 e / c C s' $ 30 - ,e' h 20 _ ,# ,,- UPTURN MOSTLY DUE TO SAS 10 . ~, FCI ANOMALY IN 4 AND 8 0 - '~~ -10' . SAS RESULT FOR REPAINDER 7 0F REACTOR 1 2 3 4 5 6 7 8 9 10 TIME AFTER CHANNELS 6 AND 10 FAILURE, MSEC Figure 9-6 B0EC T0P/LOF with Molten Cladding Gravity Draining: Comparison of FCI Feedbacks in Channels 6 and 10 with SAS/FCI and PLUTO O # (1) 70 - (1) SAS/FCI 50LUTIO'4 FOR 6 + 'O , I SAS SOLUTION FOR REACTOR MINUS (6 + 10) , ll FLUTO SOLUTION FOR EXTENDED CAvlTY (6 + 10) # 1 PLUTO SOLUTION FOR INITIAL CAVITY (6 + 10) ' 1 VENUS CRIVER FOR EXTENDED PLUTO CAVITY 60 _ (6) VENUS CRIVER FOR INITIAL PLUTO CAVITY * . '"IN (5) 6 I ,- f (3) t ,s I/ 50 - ' . s t' s I / q y ' / I w s u r i / C 40 ~ , 5 . I (6) / g C u / 6" # 1 / ' *(4) 30 ~ r t , ,,,.. q ,. s ']t. . ' 'a. / ' ' , . ' ' ,, ~ ' s 20 - s f .. r / '. s ',. **..' / / / ,.. y r  ; . / ...',,..' f .' ,e ' *** ' 10 - , ._ s .. ,a (2) .sf ,, , _ _ , y I F 3 5 y 5 1 2 3 4 5 6 7 TIME FROM CHANNELS 6 + 10 FAILURE, MSEC Figure 9-7 VENUS Ramp Estimate for B0EC T0P/LOF with CLAZAS O 9-26

10. Non-Energetic Reactor Core Disruption Phase Evaluations The mechanistic SAS analyses in Sections 6, 7, E, and 9 have indicated that a reduced reactivity state is accomplished by removal of fuel from the reactor core via one or more processes. The physical processes by which the reduction in reactivity takes place have been broadly classified as either energetic or non-energetic. An energetic classification is employed to specify the development of fluid pressures and mechanical forces which are of structural significance to the reactor internals and the primary heat transport system boundaries.

The current section deals with non-energetic progression paths to which a large fraction of the initiating phase analyses proceeded. 10.1 Potential for Partial Core Damage with In-Place Haat Removal 10.1.1 Reacfivity Insertion Events These events involve an increase in the net reactivity and power gen-eration of the core while the primary coolant flow remains unchanged. Mechanistic descriptions of the reactor response and mode of neutronic termination (i.e., fuel removal) were provided in Section 6. The most prebable fuel removal mode was non-energetic and locally confined by the fuel assembly can walls. The extent of damage was typically limited to less than fifty percent of the fuel pins. The primary uncertainty in these events is the efficiency of the fuel removal process and the restoration of heat removal to damaged fuel assemblies. The coolability of the partially damaged E0EC core was discussed in detail for the base case (6.1.1) and can be further assessed from the parametric analyses of Appendix A. The SASBLOK evaluations indicated that the damaged core regions in Channels 5 and 8 were coolable for very large degrees of flow region blockages (>90% areal blockage) existing above the reactor core. Blockages of up to 45 areal percent were found to be coolable within the core region. It was also shown that temporary two phase sodium conditions can occur within the blocked regions without fuel melting. If the blockage mat? rial cannot be cooled below the melting point, the reloca-tion would be strongly biased upward due to the pump head, and fuel would 10-1 be swept further up the channel by flow or, for locally small values of flow, to slowly move downward. This would take place until the material g sufficiently dispersed to reach the coolable configurations discussed in Appendix A. The reactivity effects of core fuel melting and compaction in Channel 8 (most susceptible) have been estimated to provide a bound on the probability of entering a transition phase. These estimates are based upon expulsion of 25% of the fuel from Channels 5 and 8 and then assaming sodium boiling, steel removal, and meltdown of the Channel 8 core region into its most rea, :ve configuration. For these conservative assumptions the reactor is still com-puted to be -60 cents subcritical. At decay heat levels, the molten fuel contained within the Channel 8 assemblies would be readily cooled by the surrounding non-damaged assemblies. If this were not the case, at some point the radially propagating melt front would be subjected to the full pump head and flow shear forces leading to axial dispersal. Thus, it is concluded that the potential for in-place heat removal occurring in the E0EC TOP event is high. g In the BOEC TOP base case (6.2.1) initial shutdown occurs after Channel 10 failure at approximately 12 seconds followed by a return to overpower conditions and permanent shutdown at 33 seconds by Channel 2 failure. A larger degree of uncertainty exists that for the E0EC configuration due to the nature of the B0EC transient. At the time of initial failures in Channel 10 all the fuel pins in the reactor have suffered some degree of damage, including gas release, pellet cracking, and plastic cladding strain. Thus, for the second overpower phase it becomes increasingly less certain to predict the location and degree of fuel failure leading to ultimate termination. For additional irradiated fuel assembly failures the potential for in-place cooling is expected to remain high. However, if fresh fuel assembly failures occur as a result of boiling and disruption (similar to a LOF event) the potential for extensive core damage would be increased. Since the pump head is available and a degree of fuel incoherence exists, it is believed that energy released from a partial core meltdown following a TOP would be bounded O 10-2 by those events which could follow termination of the initiating phase of the 80EC LOF accidents which are considered in the following sections. As concluded in Section 6 3 less probable path of energetic, hydro-dynamic core disruption exists for reactivity insertion sequences. Tnis termination process is considered in Section 11. 10.1.2 Loss-cf-Flow Initiated Events These events encompass loss of primary sodium pumping capacity and may be accompanied by reactivity insertions (Sections 7-9). In contrast to the post-TOP initiating phase termination situation, every assembly in the core is predicted by SAS3A to be disrupted by the time that the initiating phases of the LOF accidents terminate. In nearly every case considered, conditions in the core are not such that a true hydro-dynamic disassembly calculation is justified as a means of continuing the analysis to permanent shutdown. In these less energetic LOF cases, the power level at SAS3A termination is below nominal ps ver and the reactor is several dollars subcritical due to fission-gas-and/or fuel-vapor-induced fuel dis-rersal. Although the dispersed fuel may start to slowly settle back into the low-density regioi, at the core midplane, the core average temperatures are either above or rapidly approaching the fuel melting point. Heat is rapidly being transferred to the entrained steel by radiation, convection, and fuel vapor condensation; substantial amounts of steel vapor should start to form, retarding, arresting, and reversing the settlire process. Thus, for the CRBRP design, unprotected LOF events are considered to most probably result in whole core involvement without significant in-place heat removal potential. The remainder of this section therefore examines the evaluation of the core mel tdown. Several of the physical processes which could occur are examined in order to define a most probable path to permanent shutdown by fuel removal, as well as explore the consequences of deviations from this nest probable path. The most probable path is judged to be one of early removal of large amounts of fuel by ejection of a molten-steel-fuel mixture into the sargely intact pin structure above and below the core. The potential for plug 10-3 formation preventing this early fuel removal is assessed, as well as the alternative paths the system could take to shutdoen should fuel and steel g cladding plugs form. 10 2 Transition to Molten Pool 10.2.1 Potential for the Existence of Steel Blockages The formation of thick complete steel blockages at the axial ends of disrupted fuel assemblies prior to significant fuel removal could have a significant impact on the course of the accident. Such blockages would limit the degree of initial expulsion of fuel from the core into the axial blankets. It is presently believed that such blockages do not form or are incomplete in almost all assemblies (Ref, SI). A key assumption in the base case, discussed in Section 7, was that the probable effect of cladding relocation was minor (Ref. 57). The arguments may be sunmarized as follows:

a. Only a short time exists, for most assemblies, between the inception of clad melting and fuel melting, for about 75%

of the assemblies, this time span is less than 0.2 sec. Any upward cladding relocation in the hottest assemblies would shorten this time by adding positive reactivity and increasing the reactor pcwor. Results from the initiation phase of the accident suggest that the cladding in only about 10% of core assemblies has significant thie (i.e. , 0.5 sec or more) or cladding relocation. Results from these cases where cladding motion was considered suggest that under pessimistic clad relocation assumptions even the assemblies that do form blockages only have time to form a blockage in one direction, whether at the top of the core in the cases where sodium vapor effects were considered, or at the bottom of the core in the clad draining case. Thus, complete blockage at both ends of an assembly to preclude fuel removal from the core region appears highly unli' ely.

b. Large sodium vapor velocities will cause flooding of a molten cladding film leading to wave formation and concentration of the sodium vapor pressure gradient. However, cladding melting O

10-4 is not ccherent across an assembly, Since a flooded subchannel must see the same pressure gradicnt as an unflooded subchannel, molten cladding films initially flooded must very quickly un-flood because of vapor flow diversion to other subchannels. On reestablishment of vapor flow, the flooding process will be quickly repeated; i.e. , the molten cladding may " slosh" around with the net result of relatively little upward or downward movement.

c. Because of the two dimensional flow patterns described in paragraph (b), any clad relocation which does occur, either upward or dowrward, will consist of a series of "ratcheting" oscillations rather than a smooth uni-directional flow. As a result, mass displacement will occur in a much slower and piecemeal manner than suggested by the one dimensional CLAZAS model. This further decreases the probability of net clad displac ment as discussed in paragraph (a) and penetration of the biar ,et/ plenum region will be irregular and intermittent

= further decreasing the likelihood of plugging.

d. Cladding that moves into the blanket could freeze as a planar blockage, but once frozen would stop flow. Any planar block-age would therefore tend to be thin. Th py wnuld offer sig-nificant impedance to sodium vapor due to a large surface area and a low hydraulic diameter. Hence, any flooding process will tend to terminate. However, the blockage as formed will of fer little resistance to the meltout properties of a hot fuel-steel mixture. Such a mixture being driven through holes in the blockage or against the complete block-age will melt and ablate away the steel it is in contact with, destroying the blockage. This behavior has been observed in experimental tests in which molten fuel, fonted by a thermite reaction at 3200 C, was driven through hot steel tubes.

Hence, the vast majority of assembly cladding blockages will not form prior to significant fuel removal. Cladding will move with the oxide as a fuel-steel mixture. For the purpose of this analysis, it will be assumed that, at worst, only 10-5 incomplete or temporary blockages form at both the bottom and top of the assemblies over most of the active core. Since such blockages will be immediately melted out when molten fuel-steel mixtures attack them, these blockages can be neelected in the analysis. Experiments have been performed which substantiate the general picture of two-dimensional flow effects on cladding relocation in CRBRP. A detailed discussion of the tests results is pre-sented in Appendix A of Reference 3. 10.2.2 Extended fuel Motion 10.2.2.1 Fission Gas Effects When no clear transition to a purely hydrodynamic disassembly is evident, the initiating phase is terminated when:

a. Net reactivity is several dollars subcritical and continuing to decline.

Power is near or below nominal. b. O

c. Core channel geometry is clearly disrupted in a substantial volume of the core by melting structure and/or pressures clearly exceed-ing probable can wall strengths.

At this time there may still exist intact substantial masses of solid un-restructured fuel in the cooler regions of the core. This remaining solid fuel contains significant quantities of fission gas which is released upon heating and melting, if and when the solid fuel is added to the growing molten pool. The gas then released is a dispersive mechanism which can act immediately during the transition phase to disperse fuel long before temperatures reach the point when steel vapor becomes significant. Because no calculational model is currently available to describe this transition phase nechanism, it has been neglected in the transition phase analysis to follow. 10.2.2.2 Steel Vapor Pressure Effects At the termination of the SAS3A calculation, fuel and steel in the highest power fuel assemblies are on the verge of vigorous boiling. The development of fuel and steel vapor pressures strongly suggest that the 10-6 fuel mction will be monotonically dispersive. In particular, the presence of clad material will play an important role since the saturation tempera-ture of the clad is approximately equal to the melting temperature of the fuel. Entrainment of clad could arise from three sources: (1) as a result of molten clad wetting the fuel, capillary forces will lead to clad pene-tration in fuel cracks fonned by the thermal transient, (2) cladding steel sloshing will lead to loss of interface stability between molten fuel and steel and subsequent entrainment, and (3) vigorous mixing of fuel and clad by fission gas during the fuel disruption process. Entrainment is predicted to occur for a velocity differenc or less than sl5 cm/sec, using stability criteria provided by (Ref. 58). Post-test metallurgical examination of in-pilt. loss-of-flow meltdown experiments indicates that steel entrainment in molten fuel can take place (Ref. 59). Heat transfer from the fuel to the clad will result in rapid clad vaporization and dispersal of fuel. Only a small fraction of the available clad material is necessary, since the liquid-to-vapor density ratio is in the order of 10 . Furthermore, because of the above entrainment processes and since molten steel is known to wet oxide fuel, the local heat transfer between fuel and clad can be approximated by equilibrium conditions. The vaporization rates are therefore more than suf ficient to fluidize and to maintain a dispersed fuel-steel system. The potential for fluidization of fuel and steel droplets can be assessed in terms of a characteristic vaporization time and a characteristic fuel di-mension (Ref. 60). For CRBRP conditions, one finds that the required time to produce vapor corresponding to the fluidization void fraction (s50%) (Ref. 61) is only of the order of 1 msec at nominal power, and 10 msec at 10% power. Furthermore, the fuel dimension necessary to exceed the fluid-ization velocity is 0.5 cm at nominal power and s5 cm at 10% power. The above dispersal process will start toward the center of the fuel assembly because of the effect of the power profile, and because of the direct effect of the power density, will lead to sustained bidirectional movement of a molten fuel-steel-vapor mixture with penetration into the upper and lower core structure. 10.2.2.3 Fuel / Steel Penetration of Blanket Structure Since steel blockages will be incomplete or thin as discussed in Section 10.2.1, fuel which is driven to the axial ends of the assemblies 10-7 will ablate away the steel it is passing through including the cladding material in the axial blankets. The likelihood of complete fuel plugging depends upon power level as well as the mode of freezing that may take place. Two limiting models have been proposed to describe the freezing process. The " Bulk-freez.ing Model" (Ref. 62) considers a fully turbulent flow of a liquid slug through a circular tube that is initiaily at a temperature lower than the freezing point of the liquid. It assumes complete turbulent mixing up to the wall so that no stable frozen layer is formed at the wall and freezing begins when the bulk liquid temperature reaches the freezing point. The effect of the heat of fusion is accounted for by adding an equivalent temperature difference to the initial liqaid temperature. This model is highly idealized and does not include effects such as steel ablation which can have a significant effect on blockage formation. The " Conduction Model," on the other hand, considers a stable frozen layer forming at the wall. Freezing begins at the wall and the frozen layer grows as long as the heat flux to the wall exceeds that from the bulk liquid to the frozen layer. The heat flux to the wall is controlled by conduction h through the frozen layer. Where simultaneous solidification (of fuel) and melting (of steel) can occur (this is the case where molten fuel first enters the upper axial blanket), the turbulent model may be more appropriate. Because the bulk material for these assu.o,tions will contain solidified and molten material together, a slurry of solid fuel and molten steel is formed which may not provide significant containment capability. For con-ditions satisfying tube flow approximations and contact temperatures between cold solid surface and hot fluid below the melting temperature of the cold material, the conduction model is recommended, based upon experimental veri-fication using simulant materials. This is the case following ablation and melting of the cladding material in the upper axial blanket where molten core fuel is coming in contact with cold blanket fuel. Here the conduction model suggests that complete freezing and plugging of molten fuel in the axial blankets will not occur since the freezing becomes limited by a solid fuel layer which again is smaller than the equivalent CRBRP coolant channel dimen-sions. Since the lower axial blanket is s500 C colder than the upper blanket O 10-8 early ablation and melting of cladding material in the lower blanket is less likely and the possibility of fuel freezing can therefore be based on the conduction model. At high core power levels, fuel blockages are less likely to fonn in the axial blankets. For the conduction model, simple calculations of the maximum stable solid fuel layer thickness that can exist, 6 max = /2 k ( FM T -TSM) 4

• where k is the fuei thennal conductivity, T and T are the melting temper-FM SM ature of fuel and steel, respectively, and q is the internal heat generation, illustrate that if the power generation is equal to or above the nominal power, 6 is less than the equivalent CRBRP coolant channel dimension, which max implies that complete plugging is impossible. Power levels of this magnitude may exist since voiding of the sodium in the core adds about 3$ of reactivity so that even with some fuel removal the power level may tend to remain high.

For a core average power level of 10 times nominal, core fuel relocated to the top of the axial blanket would generate heat roughly equivalent to nominal power which is sufficient to prevent complete plugging. However, the bulk freezing model would still predict blockage formation due to fuel freezing. Should blockages form under such conditions, the ' :n power level would rapidly melt them out. Thus, a supercritical core condition cannot be sustained or lead to any significant pressure generation. Based on the above considerations, molten fuel under sustained pressure can probably travel distances which exceed the dimension of the CRBRP axial blankets. Beyond the axial blankets, fuel plugging again appears unlikely because (1) the heat capacity in the fission gas plenum region is too small (for an initial fission plenum temperature of 1000 C the fuel layer thick-ness required to bring the steel tubes to melting is about half the cladding thickness), and (2) the flow passages below the lower axial blanket are larger than the axial blanket itself. The above considerations suggest that the fuel can penetrate the entire blanket region and the fission gas plenum. Fuel will ' leave the core as it is disrupted, and be ejected into the sodium above and below the core, leaving the reactor core in a permanent subcritical state within tens of seconds following initial core disruption. Even if fuel blockages should form over most of the core, the net result will be almost the same as no 10-9 i blockage formation at all. The reason for this is that even small openings are sufficient to allow an almost complete core expulsion. This will occur once the hexcans are melted through which should take place in only a few seconds after fuel disruption. 10.2.2.4 Fuel / Steel Ejection from Core Region During the. ejection of hot materials (fuel and steel), th two-phase flow pattern in the core region is believed to be a dispersed sy..em; i.e., continuous vapor phase containing liquid fuel and liquid steel droplets. The droplets are carried out of the core through openings because the vapor velocity exceeds the velocity required for fluidization. This process can continue since experiments (Ref. 63 & 25) (with both simulant materials and reactor materials) suggest that the mixing between a hot dispersed system and a cold liquid is unlikely to result in sustained interaction pressures larger than the vapor pressure or system pressure of the hot fluid. This rule. out the possibility for any fuel reentry and fuel compaction during the ejection phase. Basically, dispersal of the hot fluid largely prevents liquid-liquid contact and favors the film boiling regime, since the dis-persed size is likely to be an order of magnitude smaller than the wave h length as determined by Taylor stability criterion. Furthennore, the vapor pressure which provides the driving force for impact of the hot droplets with sodium tends to be self-canceling since the rate of vapor production (which will tend to prevent contact) is proportional to the vapor pressure. Solidification of fuel droplets may occur in the film boiling regirre (which may result in further fragmentation due to thermal stresses) (Ref. 64) followed by quenching in the liquid sodium pool. A more detailed descrip-tion of the entrainment process and subsequent dispersal throughout the above-core region due to convective effects is not possible at this time. However, these processes are not believed to significantly affect the accident energetics but may be important in assessing initial conditions for post-accident heat removal and radiological consequence evaluations. 10.2.3 Disruption of Fuel Assembly Structure Initially, at the termination of the initiating phase the core will consist of several molten " blobs" of fuel and steel mixture separated by assembly can walls. These " blobs" are likely to be in a highly dispersed, h 10-10 turbulent condition due to still evolving fission gas and steel vapor pressure depending on the local power level. Energy will be transferred to the cold surrounding structure from the hot " blobs" by turbulent con-vection. An analysis of boiling pool initiation and propagation through the structure has been done for FFTF (Ref. 65) with similar fuel assembly geometry to CRBRP. At nominal power, melt through of the can wall was pre-dicted to be of the order of 3 seconds. It should be anticipated then that a large pool of molten " boiled up" fuel and steel mixture would form in a matter of seconds following the termination of the initiating phase. It is further anti;ipated that a " floor" of solidified steel and fuel would form below the pool which would only slowly melt through the lower blanket and core support structure. Estimate of melt through times range from tens of minutes to several hours depending on assumptions made. The upward heat flux is considerably greater than the downward flux from the molten pool and the upper plug, if any, will be thinner and probably porous. Fuel will leak out through openings in the upper plug and melt out or relocate actual plugs. Melt through of a S cm thick plug of frozen fuel / steel mixture is estimated at about 8 seconds. The resultant disparity in melt rates between upward and downward motion will result in a preferentially upward ejection of fuel from the boiled up pool . Eventually, ejection of material from the pool through openings in the upper core structure will result in a non-critical geometry leading to decay heat power levels and post-accident heat removal. In summary, the most probable path to termination of this transition phase which the core is entering is that of substantial fuel removal from the core by ejection through the pin structure remaining both above and below the core. The work potential involved in such a monotonic fuel dis-persal would be minimal. However, because prototypic experimental data are not yet available to verify this most probable path,'the formation of substantial and complete fuel-steel blockages in the upper and lower blankets following an initial ejection of these materials from the core cannot be precluded. The ejected material may not be sufficient to assure permanent shutdown. To examine this possibility, it will be assumed that steel and fuel freeze ana form complete blockages which temporarily prevent further fuel ejection. 10-11 10.3 Behavior in a Bottled-Up Molten Pool Region if complete core plugging due to early clad and fuel relocation is postulated, assessment of heat losses takes on considerable importance to show that:

1. rapid pressurization leading to a significant work potential does not occur, and that

2. collapse of the pool, thereby leading to a recriticality event will not occur.

The disruption of fuel in different assemblies in relatively coherent across the core due to the high power levels in the initiating phase of the accident. All of the assemblies experience fuel disruption within a few seconds of each other. The boiled-up and fluidized fuel in individual assemblies will begin to melt out the hexcan walls, as well as the postulated axial blockages. The hexcan steel will melt away in a short period of time (or the order of 5 sec). If this is assumed to be faster than renoval of the postulated frozen steel-fuel blockage above the core, a large fraction of the core can become a single coherent boiling region. 10.3.1 Boiling Flow Regimes A prerequisite to any analysis describing the heat transfer and material motions in such a bottled up system is a definition and description of boil-ing flow regimes. In the evaluation of boiling flow regimes, use can be made of the model of a liquid with vanishingly small viscosity. This enables one to eliminate consi trations of laminar and turbulent flow regimes and to focus attention of the structural changes caused by the presence of the interfaces. As ponted out by Kutaleladze (Ref. 58) the above statement of the problem impl.c that the stability of the overall flow structure can be determined by examining the stability of the elements of the phases comprising it - droplets, bubbles, films. Generally, the interaction at the interface between two phases of different densities results in wave formatiom. The character of this disturbance (stable vs unstable) depends upon the ratio of dynamic and surface tension forces, and in most cases of interest, the stability statement takes the fonn (Ref. 63). u* t/p c g 4 go (og - oL) 10-12 where u* is the critical superficial velocity of the lighter phase, o c is the density of the continuous phase,a is the surface tension of the heavy fluid, and pH and pL are the densities of the heavier and the lighter fluid, respectively. The values of the stability parameter k for two fluid-fluid flow processes of particular relevance to understanding flow regimes with internal heat generation are given in Table 10-1. Table 10-2 illustrates some key properties for boiling pool considera-tions in addition to numerical values for the important flow regimes bound-aries. The superficial vapor velocity is defined as U = Q/Aphfg, where Q 9 is the total power going into vapor formation (10 watts at nominal power, 2 A is the core area available for vapor flow (27,800 cm ) and phfg is the product of steel vapor density and heat of vaporization (1.71 J/cm at 2800 C). As seen from Table 10-2, at nominal power, the superficial vapor velocity is about 100 times greater than that needed for fluidization of the liquid fuel. The stability criteria summarized in Tables 10-1 and 10-2 lead to the boiling flow regime map illustrated in Figure 10-1 pre-sented as a function of the power level. Drop fluidization describes the transition from churn turbulent to a continuous vapor regime containing liquid fuel and steel droplets. The absence of the slug flow regime is directly related to the presence of internal heat generation. In order to avoid superheating, the fuel must be in a dispersed state for void fractions of interest (> 50%). 10.3.2 Heat Transfer at Boundaries Since churn-turbulent and fluidized droplet regimes dominate the boil-ing process, the fuel-steel mixture in the postulated " bottle" can to a first approximation be treated largely as a homogeneous system with heat transfer characteristics similar to that of nucleate boiling on a heated surface (q =aT ) (Ref. 66) . The heat transfer coefficient is up to two orders of magnitude higher than the single phase free convection coefficient. Resistance to heat transfer on the pool side is therefore extremely small if the pool is postulated to be in a boilirg state. Since at high power levels the structural material (melting point sl400 C) is likely to be in direct contact with the constantly impinging two-phase fuel-steel mixture ( N2800 C), the molten structure is rapidly entrained in the latter, there-by increasing the steel volume fraction in the pool. This entrainment process or 10-13 rapid removal of molten steel leads to continued renewal of fresh steel surface. This results in a high heat transfer coefficient together with a tempera- h ture driving force at least equal to 1400 C, which is maintained as long as a solid steel boundary exists, resul ting in a very small heat transfer resistance on the structural side. Therefore, for a surface-to-volume ratio corresponding to theCRBRP core, heat losses to the structures are likely to keep up with the internal heat generation, thereby preventing any significant pressure generation. Approximately 5 atm over-pressure in the boileu-up system would be enough to provide for sufficient mass transpo t to the cold structure as well as provide the necessary temperature drising force on the boiling side (in the order of 100 to 200 C according to nucle-3 ate bciling correlations of the form q aAT ) at nominal power. Other possible modes of heat transport including condensation and radiation, are discussed in Ref. 1. 10.3.3 Molten Fuel Pool Density Collapse of the void within the pool appears impossible except at extremely low power levels, if void collapse is postulated, a solid fuel layer must be formed at the boundaries of the bottle. The maximum stable h thickness of this layer is given by 6 max = dGT b - I sT/ii where T b is the boiling point for steel (*2800"C) and T s is the melting point for steel (11400 C), k is the thermal conductivity of fuel, and q is the internal heat generation. Since the saturation temperature for steel is approximately equal to the melting point for fuel, this is the maximum thickness of full density fuel that can exist, since a thicker layer implies temperatures above the steel boiling point. Nonboiling convective heat transfer cannot remove the available heat from the system without large temperature gradients in the liquid, which again implies boiling of steel. At full power, this layer thickness is only 0.2 cm, at 10% power 0.63 cm, and at 1% power 2 cm. A fuel crust 2 cm thick (stable at 1% power) on all surfaces around the fuel mass would account for only one-third of the core in/entory. The remaining two-thirds of the core material under the crust would boil thereby supplying heat by convection to the crust and reducing the crust thickness. The actual thickness of the crust must 10-14 therefore be less than that predicted by the equation for maximum stable thickness given above. It therefore appears that the postulated pool of boiling fuel and steel is self-regulating as a result of the fuel crust where neither significant pressurization or void collapse can take place. This picture is likely to be rather insensitive to the magnitude of internal heat generation even for power levels as low as 1% of nominal power. Two other possible sources that could lead to void collapse and recriticality are (1) cold material, such as above-core steel falling into the pool and quenching it, and (2) overpressurization above the pool. These mechanisms will be discussed in turn. If cold material such as hexcan steel falls into the p'ool from above the core, an instantaneous thermal equilibration could quench the pool causing a collapse and recriticality. However, the assumption of instantaneous thermal equilibration is nonrealistic. Cold steel falling into the pool should be instantly coated by a layer of frozen fuel, since the contact temperature is well below the freezing temperature of the fuel. While this layer will be rapidly eroded away as the steel heats up and the pool turbulence attacks the steel, the net effect should be a simple increase in effective heat transfer area. This will temporarily slow the melting attack on the boundaries of the core, but will not lead to any quenching of the pool. A pressure-driven collapse of the pool can be postulated, if hot fuel and steel being driven out the upper and lower core structure encounter sodium. A fuel-coclant or steel-coolant interaction generating high sodium vapor pressures has the potential for generating high pressures and possibly inducing high reactivity ramp rates. A series of experiments has been performed to investigate this effect (Ref. 25). Designated the " upper plenum injection" experiment, these tests did not find evidence of sufficient sodium vapor pressure; to reverse the flow of molten fuel and steel or to collapse a boiling pool. It is concluded that a recriticality caused by a collapse of the boiled-up configuration is not at all likely. Since melt-through of the structure would be anticipated well before the power level has dropped to 1%, a significant fraction of the fuel-steel mixture would probably be rapidly ejected. A 1% decay heat level, which is 10-15 reached about one hour following initial core disruption, the total energy that has been generated is more than suf ficient to have melted the above h core structure, therefore providing escape paths for the fuel, Fuel left in the core region at this time can be estimted by the existing fuel crust which is likely to represent not more than 10 to 15% of the fuel. With a one atmosphere overpressurization of the boiling fuel pool, a two-phase choked flow calculation (Ref. 65) indicates that the entire core can be expelled in the order of ten seconds through the flow area of a single assembly. In this length of time, permanent openings will develop in other subassemblies and speed up the core blowdown. 10.4 Reactivity Effects in a Disrupted Geometry The power level and thus the rate of melting of core steel, will be determined by the reactivity history of the accident. Insight into the power level was gained by reactivity calculations on a disrupted core. All calculations were performed using the two-dimensional FX-2 code in r-z geometry with a nine group cross section set. The isotopic content was the same as for the E0EC core discussed in Section 5.3. Reactivities were normalized for a multiplication factor of unity for a hot, operating core with sodium in. g The disrupted core is voided of sodium except for the bottom of the lower axial blanket, the lower reflector region, and the control subassemblies. This core, with fuel at 3200'K, has a reactivity of 2.38$. A similar cold core, at 1650 K, has a reactivity of 3.12$. The -74d from the Doppler effect cannot overcome the 3$ voiding reactivity. This result has signif'. cant implications for the transition phase, particularly for that period of time immediately following the second burst, as calculated by SAS3A. At the point of termination of the SAS3A calculation, the dispersed fuel is starting to settle slowly back into the lower density core midplane area. Since steel in the core, particularly in the higher power subassemblies, is nearing its boiling point, rapid production of steel vapor is imminent and should arrest the slumping of the dispersed fuel. Should the onset of steel vapor production be delayed for any significant period of time, the core would again reach criticality and another mild burst would follow. The burst would be mild because the dispersed fuel does not have to settle much for the O 10-16 system to reach criticality again, thus preventing the settling fuel from achieving any significant velocities and thus preventing significant ramp rates. Calculations were performed to determine the amount of reactivity which is lost when fuel is ejected into the blankets. As discussed in Section 10.2.2, there is a reasonable chance that fuel which is ejected into the blankets will travel through them without plugging. For these reactivity calculations, fuel and steel in their original proportions were removed from the core and substituted for the sodium in the upper axial blanket for the full length of 35.7 cm. The remaining fuel and steel were honogenized in the core. The amount of fuel relocated was 33.2% of the .otal core fuel . The reactivity of this system is ca'culated as -41.8$. prcetra-tion of the same amount of fuel and steel into bo;h blankets, a dn. 2nce of about 20 cm should have about the same reactivity effect as penetration into one blanket, a distance of 36 cm. Following such a fuel ejection, the reactor would be substantially subtritical. By employing the promat jump approximation, it can be seen that a reactivity insertion of -40$ would cause the power level to drop to 5 to 10% of its value before the reactivity insertion. This power is higher than the expected level (2.4%) because additional delayed neutron precursors have been produced by previous high power levels. However, the power level is still relatively low once sub-stantial amounts of fuel have been removed. Fuel that penetrates into the blankets is almost totally lost from the core as far as reactivity is concerned. This is demonstrated by the fact that removing one assembly worth of fuel and steel uniformly from the original intact core reduces the reactivity by 0.62$. Extrapolating this to a removal of 33.2% of the core yields a net reactivity of -38.5$, which is in good agreement with the -41.8$ obtained when this fuel and steel is inserted into the upper blanket. Af ter melting of the hexcan walls, inner and outer core fuel will nomogenize. A calculation was performed to determine the concomitant reactivi ty change. Starting from an intact, hot, voided core, homogenizing the inner and outer core fuel raises the reactivity by 14.2$. Thus, bringing 10-17 higher enrichment outer core fuel into the higher worth region in the center of the core adds on the order of 14$ to the systen. g It is quite unlikely that any such complete homogenization of fuel remaining in the core would take place until well af ter a substantial quantity of fuel has been ejected upward and downward from the core. Thus, for the best-estimate path to temination of the transition phase, this result has little relevance. In the event that complete fuel blockages were to form and delay permanent removal of the core fuel, this reactivity is still small compared to the amount of reactivity that would be removed from the system in the form of the fuel which would be required to form blockages. As the boiling fuel-steel pool melts its way upward and downward, the reactivity will steadily decrease. This is due to the increasing neutron leakage and to the effect of adding poisonous blanket fuel to the boiling core. For the original core geometry, 1.3$ of reactivity is lost per centimeter of axial blanket melting and mixing with the core. As the accident progresses, the reactivity and the power will continue to decrease. Calculations were performed to determine the degree of fuel removal h required to produce a permanently subcritical dense pool in the core region. For these calculations, a layer of molten steel, 23 cm high, was floated on top of a fully dense pool of pure fuel. The control asserblies with sodium-in were lef t in the core for the E0E0 case. The critical pool height is 17.2 cm which represents 50.8% of the core fuel. This may be compared to FFTF where about 40% of the fuel is sufficient for criticality. This difference is due to the lower Pu enrichment of the CRBRP fuel. 10.5 Summary and Conclusions on Non-Eneraetic Disruption The potential for a reactivity insertion event leading to core meltdown and a transition phase is judged to be quite low. If a core meltdown were originated from a TOP the consequences should not be much different than transition phase phenomena associated with an LOF. In particular postulated recriticalities are likely to be mildly energetic if this occurs. At the end of the initiating phase of tne LOF accident, the entire core is voided of sodio.n. Some of this fuel has been slightly dispersed O 10-18 toward the axial ends of the core by fission gas. If there is insufficient stee! vapor pressure or fission gas pressure at this point to eject part of the fuel into the axial blankets, fuel may recompact as the fission gas escapes from the core. This would lead to a mild recriticality, insufficient to disassemble the core, or to a sub-prompt-critical high power situation. Af ter enough heat has been added to the fuel-steel mixture to generate significant steel vapor pressures, material will be injected into the axial blanket. The steel blockages that might form at the axial ends of the core would be incomplete over much of the core and flow of molten fuel through them would destroy their integrity. Molten fuel being driven out of the core would most likely penetrate deeply into tne blanket regions. Such fuel would De quenched by the sodium and structure with no destructive pressures being generated. It is possible but not likely, that fuel passing through the blankets will freeze and form blockages. If these blockages are complete over the entire core, the remaining fuel will be tcmperarily trapped or bottled-up in the core until a permanent opening can be melted out. The remainder of the fuel and steel in the core will boil in a churn-turbulent and a dispersed droplet flow regime, even for decay heat power levels. Rapid heat transfer will melt the hexcan stee.1 leading to formation of a single coherent boiling region. A continued melting attack on the surrounding steel is likely to lead to fuel penetration into the radial blanket assemblies. During this phase of the accident, core pressurization due to steel vapor would be prevented by high heat transfer to the corrounding steel. !cause of the very high negative reactivity induced by the ejection of fuel into the axial blankets the fission power level should drop to a few percent of nominal during the remainder of the accident. For lower power levels, collapse of the pool should be prevented by decay heating and the formation of an insulating fuel crust on the surrounding steel when the pool cemperature drops. Af ter the initial part of the transition-phase, the reactivity of the core will tend to be highly negative because of fuel expulsion into 10-19 the axial blankets prevents any further criticalities due to fuel rearrange-ment or fuel reentering the core. Af ter complete melt-through of the axial blockage in one assembly, O a core blowdown will be initiated. Additional blockages may melt through leading to simultaneous fuel ejection through several openings. This ejection could be in either direction, up or down, or it could be in both directions at the same time. Well over half the fuel should be ejected from the core region into the upper or lower reactor sodium plenum. Fuel remaining in the core region would continue to produce energy by decay heating and could, eventually penetrate the supporting structure and relocate downward. O O 10-20 TABLE 10-1 VALUES OF Tile STABILITY PARAMETER k flature of Process k B akdown of bubbly flow (Ref. 36) s0.3; pc"PH Breakdown of churn turbulent flow - drop 10.14; pC " PL fluidization of a heavier fluid by a lighter fluid (Ref. 73) 10-21 TABLE 10-2 POWER DE!;SITY A!;D FLOW REGIME CHARACTERISTICS (Boiling Fuel-Steel Pool) Superficial Vapor Velocity, cm/sec Power SV Level, a or* = 1, sec , , , Limit of Liquid L G "' fuel Fuel Pool Bubbly Flow Dispersion . 100 s10 10~ 2x 10 15 12 x 10 2 o -2 .h 10 s10 10 2 x 10 3 s5 12 x 10 2 -I 1 s10 10 2x 10 2 15 s2 x 10 2 * ( c.V g /AVfuel) = 1 indicates the tire required to produce equal volumes of 1 quid and vapor if all the neutron and decay heating goes into latent heat of vaporization. i 9 O O 100 8 - 6 - 4 - 2 - DISPE RSE D DROPLETS 10-1 - 8 - 6 - CHURN TURBULENT d 4 _ 3 E 2 - 8 $ 10-2 _ z 8 - 9 6 - C q 4 - SUBBLY FLOW 5 2 - 10-3 a 8 - 6 - 4 - 2 - ' ' ' ' I ' ' ' ' 10-4 10-2 2 4 6 8 10-I 2 4 6 8 10" REL ATIVE POWER Figure 10-1 Flow Regimes in a Boiling Fuel Dool in CRBRP 10-23

11. Energetic Reactor Core Disruption Phase Evaluation 11.1 Introduction All of the probability category one or two analyses presented, except for the BOEC 150% void worth case, terminate with virtually no associated recuanical damage potential . The category three and four scenarios in this section are based on assumed phenomenological behavior that is believed to be very improbable. These disassembly analyses include the more energetic accident sequences presented previously and recriticality configurations which were postulated during the transition phase. The events analyzed and the methods used are sunmarized below.

For LOF events in the 80EC core configuration, SAS analyses indicate that phenomenological assumptions which force the core into higher reactivity states result in the prediction of LOF-d-TOP failures. Thus, within category three, assumptions are separately treated which:

a. ignored the axial expansion of the fuel pins

b. allowed cladding to be massively and coherently relocated (CLAZAS module) by sodium vapor forces

c. allowed fuel disruption but not dispersal in sodium voided fuel assemblies.

The SAS analyses predict that the additional reactivity inserted by these mechanisms is sufficient to produce cladding failures in sodium filled dssemblies at a high power and reactivity state. flote that it is these latter failures which are primarily responsible for the energetics consequences. Autocatalytic ef fects can occur if the tailures are near the core midplane due to the motion of fuel within the pin to the failure site and the accom-panying displacement of liquid sodium. lhe resulting reactivity effects are usually sufficient to sustain a super prompt critical excursion and are utilized to drive a VEilUS hydrodynamic disassembly calculation. For E0EC LOF cases, pessimistic assumptions were .made regarding tne effects of fission gas either at the peak of the second burst in the refer-ence design or from initiation in the August 1975 design, to generate hydrodynamic disassembly. 11-1 For TOP events, unrealistic assumptions of core nidplane cladding failures or hypothetical control system reactivity insertion rates must be made to attain hydrodynamic disassembly. A significant characteristic of these TOP VENUS calculations is that a large amount of sodium is still in the core. The sodium-in condition is generally beneficial to reducing the power burst because of the disassembly feedback from high liquid phase pressure at low fuel energies. However, it is known (Ref. 67) that VENUS calculations can be sensitive to small amounts of homogeneously distributed void being introduced to the fully dense core. The distribution of the void is very non-uniform in the TOP cases and therefore both pointwise and regionally smeared void distributions were considered. For an accurate assessment of TOP consequences the reference cases consider the spatial void distribution that was present in SAS at the time of transfer to VENUS. Also a 600 KPa radial pressure gradient threshold was imposed to represent the assembly hexcan wall strength. Finally, where full sodium-in conditions existed the reference cases modeled the single phase departure condition as either the fuel liquidus temperature (core) or a one percent volume g compliance (blanket and control). Sodium voids in the blanket regions were regionally smeared. T0P/LOF or STEP /LOF events in the BOEC core configuration led to hydro-dynamic disassembly conditions using best estimate physical models. The improbable phenomenological events here are the failure mode of the protec-tion system and the amcunt of reactivity insertion involved. Additional phenomenological uncertainties were then included in the T0P/LOF sequence by considering pa 2 metric cladding relocation modes. Recriticality configurations during meltdown or in a homogenized fuel pool could be postulated if enough adverse assumptions are involved. Modes of fuel re-entry which could cause superprompt critical bursts are considered and conservative ramp rates at prompt critical are defined. Based on these analyses, disassembly calculations are performed to determine the consequences of certain recriticalities. In addition an evaluation of the effects due to bubble collapse in the homogeneous pool was performed. O 11-2 All of the disassembly calculations were done with the VENUS-I' code (Ref. 2), which contains a two-dimensional Lagrangian hydrodynamics model, coupled with point reactor kinetics and an appropriate equation of state. The point reactor kinetics model incl" des, in addition to the driving reactivity, terms to account for the feedback effects of Doppler broadenirg and material displacement. The VENUS-II code was modified (see Appendix C) to account for the reactivity associated with bubble collapse. Although these ef fects are not rigorously accounted for i .e. , the FX-2 (Ref. 39) code is not used, it is judged that the inaccuracies incurred are not serious (Ref. 68). There are several criteria which should be satisfied in order to justify a disassembly calculation. Primarily, the reactor must be undergoing a sustained superprompt critical burst. The reactivity must be at or near prompt critical, and must be increasing at a fairly high rate (s30$/sec or higher) which shows no signs of abatement. The fuel must be in a largely molten state (since VENUS-II assumes that the reactor materials behave as an isotropic, non-viscous fluid) and the fuel vapt. pressures must be fairly high (or will soon be 50). However single phase , essures at VENUS initiation are to be avoided as an underestimate of the energetics will resultf? All of the disassembly calculations presented below were done when the above-mentioned criteria were satisfied. In all cases, care was taken to begin the disassembly calculation early enough to ensure that conservative estimates of the energy generated were made in VENUS-II. The initial conditians for the SAS/ VENUS-II calculations were generated as follows:

1. The initial core configuration is the same as that of the FX-2 model, and is shown in Figure ll-1. The power density and material worths were computed with FX-2 on this grid, with the initial core isotopics but with sodium removed.

2. The time at which the important criteria for transition to VENUS were satisfied was determined. These criteria include -

a. Reactivity at or near prompt critical, with power level s100 times nominal.

ll-3

b. Highest power, voided channels contain molten fuel.

c. SAS3A predicts a sustained superprompt critical burst (s30 $/sec or O

greater for 4-10 milliseconds or more) following the time at which a and b are satisfied.

3. The average core temperature was computed in HOCUS, for conditions existing at the start of disassembly. Then, the AVTEMP option in VENUS wat used to obtain the temperature distribution corresponding to this average temperature. It should be noted that the heat of fusion was prope, ly accounted for, and that the power density used was character-istic of the initial core configuration, with sodium out. This inaccuracy is not judged to be significant.

4. The power level, precursor concentrations, and reactivity at the start of disassembly were obtainei directly from the SAS3A output.

5. Doppler coefficients and sodium volume fractions were made consistent by linear interpolation between sodium-in and sodium-out Doppler values for each region.

6. The driving ramp rates were taken from SAS3A output at the start of disassembly. When a major contribution to the driving reactivity was due to LOF driven TOPS, the values were obtained by carrying out PLUTO calculations for the channels in question. It should be noted that the driving reactivity is defined to be the sum of sodium voiding, fuel motion, and clad motion reactivities from all channels.

The consequences resulting from all of the cases below are cast in terms of comparison with the thermal source chosen for the SMBDB namely, an average core temperature of 4800 K. The isentropic fuel expansion work potential was obtained by an inaependent sum over all of the core nodes according to the expression (Ref. 69). VM = C (Tg - T) - L X + R X T M where C is the specific heat of liquid fuel, Tg is the initial fuel temperature T is the fuel temperature af ter expansion to a given pressure P. L is the e 11-4 latent heat of the vaporization of fuel. X is the final mass fraction of fuel vapor. R is the ideal gas constant for one gram of fuel vapor, and M is the :nass of fuel in the node. The fuel temperature ( K) and vapor 2 pressure (dyne /cm ) are related by the equation of state (Ref. 2): P = exp(-4.34 In T - 76800/T + 69.979) Thus, the work calculations were not based on the average core tempera-ture, but rather on the temperature distributions that exist at the termina-tion of tne VEfluS calculation. The total work-energy to any given end state is ti,en obtained by summing over the entire core fuel. Thus, those nodes which werc at a very high te.riperature contributed a much higher fraction than did those at or below the average core temperature. Finally, the perfect gas law is used to compute the volume occupied by the fuel vapor as the expansion takes place. Results are presented, both for expansion to 1 atm and for expansion to a volume which is the equivalent 7 of the inert cover gas (2.1 x 10 cc). The latter quantity provides a meaningful estimate of damage potential, if it is assumed that the sodium slug hits the reactor closure head when such an expansicr has occurred. 11.2 Hydrodynamic Disassembly During Initiating Phase These VEfiUS analyses are direct extensions of the SAS3A results reported in Sections 6, 7, 8 and 9. 11.2.1 Unprotected Reactivi ty_ Insertion Events 11.2.1.1 BOEC Design Ramp Rate l2.4c/sec) With Forced Midplane Failure Of all the BOEC TOP cases considered in Section 6.2, hydrodynamic dis-assembly conditions were predicted to exist only if the fuel pin cladding failure location for every failed pin was arbitrarily forced to occur at the core axial midplane during an unprotected recctivity ramp insertion at the design rate. Several VEfiUS calculations were perfonced to investigate the effect of the sodium void spatial distribution, the control region compliance, and finally a 50 uncertainty in the driving reactivity rate during disassembly. 11-5 The reference calculation modeled the actual spatial void distribution from the SAS3A result. When these voids were regionally smeared as the first @ parametric case, the single phase condition was delayed, resulting in increased consequences. Two additional cases examined the effect of increas-ing the annular control region (see Figure 11-1) volume compliance to ten percent instead of the reference one percent in the above calculations. For regionally smeared' voids the effect was insignificant while for pointwise distributed voids a small increase in consequences resulted. Thus, a large change in control region compliance was not significant on the energetic consequence. A final parametric on the reference case arbitrarily increases the driving reactivity rate by 50% to 75$/sec. This rate is considered to be a rational bound to uncertainties af fecting the energetics consequence of the TOP event. Table 11-1 presents a summary of the initial conditions, the VENUS results and the fuel expansion work potential for the above calculations. Significar.t margin is seen to exist between even the bounding case and the SMBDB energetics. h 11.2.1.2 E0EC 10c/sec Ramp Rate Forced Midplane Failure As discussed in Section 6.1.3.4, the 10c/sec E0EC TOP event also terminates by hydrodynamic disassembly when the fuel pin failure location in all channels is specified to be at the core axial midplane. The SAS calculation was repeated with the additional assumption of no fuel axial expansion. The VENUS initiating conditions were so similar that the resulting snergetics are cor.sidered to be adequately addressed by the follow-ing VENUS calculations. Table 11-2 presents the three calculations considered for this event. The reference case again used the spatial void distribution from SAS and results in a low energetics consequence. By regionally smearing the sodium void the consequences were increased proportionally similar to the results of Section 11.2.1.1. An additional two percent void was added to regions 3 and 7 (Figure 11-1) of the smeared case to investigate the sensitivity of energetics in the final case. However, the result was essentially insensitive to this additional increase. 11-6 The most important result is that all of the cases lead to consequences that are significantly less than energetics selected for the SM8DB. 11 2.1.3 E0EC llypothetical 3$/sec Ramn Insertion As stated in the predisassembly [ 1ase discussion in Section 6.1.2.3, this case represents a reactivity insertion rate that is two orders of magnitude greater than the design basis accident reactivity insertion rate of 2.4c/sec. An analysis of the 3$/sec ramp rate was performed to determine if an accident sequence different than that calculated for the E0EC TOP 10c/sec forced midplane failure would occur. The VEfillS case incorporated t n.: same reference modeling as the previous two sections. Based upon the previous results and the low probability of the initiating event hrobability category 4) only a reference VEtiUS calculation was performed. Pertinent information is compiled in Table 11-3 and the results demon-strate that the core average temperature and the work energy are well below the values associated with the SMBDB. The results of the SAS predisassembly phase calculations and the VEffUS-II disassembly phase calculations indicate that a generically different type of accident sequence does not occur at higher ramp rates. 11.2.2 Unprotected Loss of Flow Events 11.2.2.1 BOEC: f4eglect Fuel Axial Expansion As discussed in Section 7.2.2.3, the neglect of fuel axial expansion led to FCI failures in sodium filled channels and with a 15 cm rip length, a sustained superprompt critical excursion. Table 11-4 presents the initial and final conditions for the VEfiUS calculation. flote that results quoted herein for B0EC LOF disassenblies differ from earlier calculations (Ref. 4) because the present calculations more consistently accounted for sodium presence, its impact on the Doppler feedback and SAS temperature distributions. 11.2.2.2 BOEC: flegl ec t F i,s s i o n Ga s F,ue l D_i spe rs a l in SLUMPY Without ini'ial fu21 dispersal, continued downward reincation of fuel leads to a situation similar to neglecting axial expansion. Thus , LOF/ TOP's 11-7 occur in Channels 6 and 10. The VEtiUS results (Table 11-4) indicate that neglect of early mitigating mechanisms would lead tc prompt excursions followed by FCI events, and energetic consequences of a similar order. 11.2.2.3 BOEC: CLAZAS With Limited Initial Fuel Motion Allowing cladding to be coherently and massively relocated while re-stricting fuel dispersal results in a superprompt excursion. The VEfiUS calculation is indicated in Table 11-4 under the column heading "CLAZAS". The relocation of cladding in Channels 1, 3 and 9 lead to the attainment of driving ramp rates and core thermal conditions similar to the two previous cases with lower f.et reactivity and core power. A SOS /sec ramp conservatively estimated the early prompt critical driving function. The resulting calcula-tion (Table 11-4) indicated energetics consequences of the same order as the previous two cases. An additional calculation was perfonted which used the non-linear driving function produced by SAS/FCI. This function is, in part, non-physical (see Section 3.2.5 for discussion) and attained peak rates of 87$/sec. By an oversight the effective Doppler was ten percent lower in this case and somewhat g biased the energetics results upward. Thus, this result was considered to be a enveloping calculation and placed within category four, 11.2.2.4 E0EC: Arbitrary 40$/sec Ramp Insertion As was stated previously in Section 7.1.3, none of the SAS3A analyses of the E0EC LOF event in the reference core configuration produced a sustained superprompt critical burst that led into direct disassembly. All of the events would result in mild energetics and enter the transition phase. tieverthel ess , if fission gas failed to act as predicted at the peak of the second burst then it would be conceivable for the core to disassemble. Hence, an arbitrary case was run in which the driving reactivity ramp rate was 40$/sec. Table 11-5 presents the important initial conditions, the vet 1US-II results, and the fuel expansion work predictions for this case. It should also be noted that full sodium-out conditions were conservatively assumed in the core and upper axial blanket. O 11-8 The VENUS-II results and fuel expansion work are very similar to those of the 40$/sec BOEC LOF case. The differences in nonnalized peak power and duration of disassembly are due to the differences in initial power level. As was mentioned in the preceeding section a lower initial power enables the power to build up higher, and the disassembly to proceed over a larger time increment because the Doppler feedback does not enter strongly until the power level (and hence fuel temperatures) are sufficiently high. The average core temperature and the work energy are below the BOEC results. Although it should be stated again that such a disassembly was not predicted, this case weuld represent an upper bound to the E0EC LOF event. 11.2.2.5 E0EC: Aug. '75 Flow Orifice Scheme Neglecting Fission Gas Fuel Dispersal in SLUMPY The change in flow orificing, when combined with neglect of fission gas fuel dispersal, led to a greater degree of sodium in the core during the prompt burst. Additionally, Channel 10 suffered an autocatalytic FCI failure in the superprompt regime resulting in a nonlinear driving ramp (see Figure 7-33). The VENUS results indicated in Table 11-5 reveal the energetics sensitivity to LOF/TCP modeling and nonlinear ramps. The expansion work to slug impact and to one atmosphere both exceed the SMBDB, however, it should be noted that this result is arrived at by the basically inconsistent assumption of ignoring fission gas in some Channels while allowing failure and prompt time scale fuel motion due to fission gas effects in others. 11.2.3 BOEC: Unprotected Step Reactivity Insertion with LOF As stated in Section 8.2, the 30c step reactivity insertion with loss of coolant flow results in a superprompt critical excursion. The VENUS-II code is used to calculate the resulting energetics and core temperatures for the hydrodynamic disassembly phase beginning at the time the pin failures occur in Channel 6. At this time the normalized power is 80 and the reactivity is 0.9445. The driving reactivity is a composite of SAS and PLUTO (Channels 6 and 10) fuel motion and sodium voiding contributions. The resultant tabulated driving reactivity is such that it is about 505/sec for 0-4 msec and less 11-9 rapid thereafter. The AVTEMP option in VENUS-II (with proper treatment of the melting transition) is used to obtain the initial fuel temperature dis-tribution. Input values for the AVIEMP option were iterated upon until the desired average core tempeioture of 2883"K wu obtained. Results of the disassembly calculation are presented in Table 11-6. The average core temperature and work-energy at slug impact are both noderate compared to the structural margins. The consequences are greatly different from the B0EC LOF event discussed in Section 7.2.1. since negligible energetics were predicted for its base case. The consequences are similar, on the other hand, to the BOEC LOF analyses when pessimistic assumptions were made in treatment of phenomenological uncertainties in these latter analyses. In this respect both cases show similar consequences for category three assump-tions. 1s.2.4 BOEC: Unpratected Reactivity Ramp Insertion with LOF SAS analyses of these category three events were presented in Section 9. The base T0P/LOF case was similar to the STEP /LOF just discussed. Table 11-7 presents a summary of the disassembly calculations for the base and two ciadding parametrics performed for T0P/LOF events. Employment of the CLAZAS model coupled with the scram system phenomenological failure assumptions placed this parametric event into a probabilistic category four. The reactivity ramp rate inputs for these cases were input in a piecewise linear fashion based on results from both SAS3A and PLUTO. In the clad-sodium vapor coupled case these ramp rates were calculated neglecting nonphysical fuel motion reactivity feedbacks due to FCI events in Channels 4 and 8.* Both the clad gravity draining case and the clad-sodium vapor coupled case resulted in increased energetics compared to the base case. The base case and the clad gravity draining case were within the Structural Margin Beyond the Design Base; however, the sodium vapor coupled case exceeded the SMBDB. 11.3 Hydrodynamic Disassembly During Transition to a Molten Pool During the transition phase of the accident sequence, assuming that plugs form in the axial blanket, fuel which has been ejected into the axial blankets mi#c fall back into the core, leading to a recriticality. There G

• See Section 3.2.5 for a discussion of the nonphysical modeling.

11-10 are several reasons for believing that such a recriticality is unlikely. First, the pressure from vapor generation in the boiling material in the core would tend to support the blockages. Any material re-entering the core would most probably not come in as coherent slugs but rather come in gradually as the upper blockages are melted and " washed" out by the boiling turbulence below. Material injected into the blankets would tend to have a temperature profile that is steadily decreasing away from the core. That is, the further the material is from the core, the colder it would be. This is due to three factors. The first nuterial ejected will be material from near the core axial extremities and therefore the coldest. Further, the material that has penetrated deeper into the blanket has flowed over more cold steel and has lost more heat. Finally, the fission heating will be higher for material closer to the core. For example, at the core radial centerline, the power level at the top of the upper axial blanket is 8% of the power at the core-blanket interface, and at the radial core edge it is 16%. Thus, any material which has penetrated the axial blanket and plugged there would re-enter the core gradually as progressively colder material is melted and washed out of the blockage. Several improbable assumptions are made in order to proceed with this analysis:

1. Fuel blockage will form in the upper axial blanket.

2. While fuel blockages remain in :he blanket, other fuel in the same assemblies has begun to re-enter in such a way that this behavior is simultaneously occurring in 36 assemblies 'n the innermost ring of the outer enrichment zone of the E0EC core.

. Re-entry velocities can equal or exceed those of a gravity collapse. If assumptions equivalent to the above are not made, then core disassembly from fuel re-entry cannot reasonably result from this scenario. Consioer the E0EC core following shutdown from fuel dispersed in any of the SAS3A cases presented in the E0EC LOF analysis in Section 7. Assume that, in 3/4 of the assemblies in the innermost ring of the outer core zone, blockages form in the lower portion of the upper blanket. Further, assume that the 11-11 remainder of the fuel which was originally above the core midplane in these channels has moved upward, and is in contact with the fuel in the blankets $ which has formed the blockages. At this point, the reactor is 1.59$ subcritica. and the bottom of the slug is about 23 cm from the core cer,ter. This calculation, as were all of the others discussed below, was made with the FX-2 code, using the same E0EC geometry and cross section set that was described in Section 5.3. Once the slug starts downward, the reactivity begins to increase. At 11.5 cm above core center, the reactivity is 0.64$ super-critical, and would be 2.63$ supercritical if it could reach the core center. When these points are plotted, a smooth curve can be drawn between them, as is shown in Figure 11-2. To obtain ramp rate estimates as a function of velocity at prompt critical, it is necessary to determine the slope of the curve at prompt critical . This value is found to be 17.3c/cm and cccurs when the slug is about 9.5 cm from the core center. Although a gravitational fall could be expected the following arbitrary increases in gravitational forces were also considered: Acceleration, "9's" Disassembly Ramp Rate (at Prompt Critical), $/sec 1.00 28 1.25 37 2.60 45 5.00 63 No means of obtaining such accelerations have been identified but are included here for purposes of a parametric study. The important initial conditions and the VENUS-II results are presented in Table 11-8. Also note that full sodium-out conditions were assumed for the core and upper blanket. One interesting aspect of this calculation is that an implosive effect is evident in the low-ramp-rate regime, because of the high fuel concentration in the slug. The power gradient, and hence the temperature gradient, allows for a large inward fuel motion during the early states of the disassembly. The trend is soon reversed, however, without causing very much positive 11-12 reactivity to be added. At higher ramp rates, the effect is not seen as much because pressures build up more rapidly to cause shutdown. As noted previously, there are three improbable assumptions required to produce this type of recriticality. In particular, the assumption of coherent re-entry and the observation that small incoherencies rapidly reduct the ramp rate for a given re-entry velocity, place this sequence in category 4. Considering these assumptions and the fact that no mechanism has been identified to cause significant initial velocities, ramp rates greater than 285/sec are considered extreme cases even for probability category 4 sequences of recriti-cality from immediate re-entry, 11.4 Hydrodynamic Disassembly of a Homogenized Molten Pool 11.4.1 Pool Initial Conditions and Effect of Initial Power Recriticality of a homogenized molten pool is considered unlikely for this system since the net reactivity of the system would probably be too low for fuel re-entry to return the systeu to critical. If fuel has been injected half way into the blankets over the entire core and the remaining inner and outer core fuel is homogenized, the reactivity is on the order of -305. Nevertheless, possible ramp rates for such postulated material re-entry have j been examined. k n A core model was used where the control assemblies are gone, the sodium is removed from the core and the upper blanket, and the inner and outer core ' fuels are homogenized. Fuel and steel have been expelled to a distance of 17.9 cm into the upper axial blanket, filling the available space in the voided sodium flow channels. Some 17% of the core fuel is located in the blanket. The fuel and steel which has been expelled is then postulated to fall out of the blanket in rings two and three. This is a total of 18 assemblies behaving coherently in the highest worth radial position in the core. Since the phenomena discussed above tend to limit the spatial and temporal re-entry coherence, it was felt that this amount of fuel would form a conservative upper bound for re-entry reactivi ty ramp rates. The material is allowed to interpenetrate the material already in the core. Reactivity is a function of penetration distance is shown in Figure 11-3. This yields the reactivity 11-13 gradient shown in Figure 11-4. Note that the highest reactivity gradient is where the fuel is entering the core. The last two points are for fuel h which is completely in the core and yield gradients only half that of fuel which is still entering the core. The highest gradient in this figure, 15.25c/cm, is a reasonable upper bound for a re-entry reactivity gradient for an 18 assembly re-entry. If fuel is allowed to fall a distance of 20 cm, without any impedance into the pool material below it, it attains a velocity of 200 cm/sec. This yields a reactivity ramp rate of 30.5 dollars per second. While higher gravity driven velocities are possible, the speed of f all depends on the square root of the distance. Doubling the ramp rate would require a fall of 80 cm. If the impedance of the material below the falling slug is taken into account, a velocity of 200 cm/sec is still a conservative re-entry velocity. Therefore, it is believed that 30 dollars per second is a reason-able upper bound for the ramp rate from a postulated re-entry in the transi-tion phase of the accident. To obtain initial conditions for a disassembly calculation for such an event, a boiled-up pool, with an initial uniform temperature of 3100 K and at nominal full power, was brought from delayed critical to prompt critical with a 30$/sec ramp. This was done using a point-kinetics model. The Doppler coefficient, power distribution, and the material worth distri-bution were determined for the boiled-up homogenized core. The resulting initial conditions for the disassembly calculations are given in Table 11-8; the initial power was 21 times nominal. The VENUS-II and fuel expansion work results are also given in Table 11-8. The work-energy predicted for this case is larger than for the direct-disassembly LOF cases for several reasons:

1. The initial power is lower, thus leading to a larger energy release for a lower ramp.

2. The outer core, which has a large pressure gradient which disassembles the core for a lower energy input, has been homogenized with the inner core. This region of the core was a major contributor to negative reactivity in the initiating phase.

O 11-14

3. The initial temperature dist,'ibution is almost flat. Thus, more energy must be input in order to reach the pressure gradients necessary for displacement.

4. The Doppler coefficient for the homogenized core is lower, because there is less U-238 where the flux is high.

Since the initial power level is uncertain, two additional cases were run where vet 4US-II was initiated at 2.1 and 210 times nominal f ull power. These results are also given in Table 11-8. For the calculations presented in this section, the low power case results in the largest work-energy. 11.4.2 Consideration of Bubble Collapse (Behren's Effect) Appendix C discusses in detail the results of exploration of the Behren's effect (Ref. 70) as it applies to the molten homogeneous fuel / steel pool. Behren's effect is based in the premise that the rate of neutron leakage from the system has a significant dependence upon the presence of bubbles or voids in the boiled-up pool, and that loss of neutron streaming paths due to the collapse of these bubbles could result in a significant positive reactivity feedback. Although the magnitude of the reactivity feedback is small, if introduced in the neighborhood of a few cents above prompt critic 1, it would augment the energetic release. Using the VEf1US-II Code with appropriate modifications, this phenemenon was investigated to determine its significance during hydrodynamic disassembly. Conclusions from this investigation are that the energetic consequences of a hydrodynamic disassembly are increased somewhat, but when the "best estimate" equivalent bubble radius is chosen, this effect is not large. The increase in work-energy to one atmosphere, for example, is on the order of 15%. 11.5 Summary and Conclusions on Energetic Core Disruption Evaluations Based on the pessimism involved in the assumptions. related to phenomeno-logy or initiating faults, hydrodynamic disassembly is a highly improbable termination path for core disruptive accidents Within the framework of hydrodynamic disassembly analyses attaining sustained disassembly ramp rates greater than 50$/sec requires combinations of pessimistic assumptions for the - physical processes that are considered unrealistic. However, hydrodynamic 11-15 disassembly calculations have been perfonned for disassembly ramp rates to 100$/sec to show that the consequences from these improbable sequences are not discontinuously different from the results of the more probable ramp rate range (30$/sec to 50$/sec). Disassemblies from TOP events resulted only when core midplane cladding failures or unrealistic initiators were assumed in the SAS3A analysis. The energetic consequences of such disassemblies do not exceed the consequences of LOF events in similar probability categories. The 80EC LOF event was judged to be the most likely to leak into core disassembly. Ramp rates from 40$/sec to 1005/sec were considered, mainly to account for the uncertainties in ramp rate from LOF/ TOP phenomena. The resulting average core temperatures ranged between 4150 K and 4533U K. Only one direct-disassembly calculation was run for the reference orifice scheme E0EC LOF event, since no SAS3A cases predicted a direct dis-assembly. For an arbitrary driving ramp rate of 40$/sec, an average core temperature of 4277 K was obtained. Calculations for an alternate flow orificing shceme which neglected fission gas dispersal in SLUMPY while allowing fission gas to fail fuel and g move fuel in other parts of the calculation indicated enhanced sensitivity to LOF/ TOP phenomena. Energetics consequences were calculated to exceed somewhat the Structural Margin Beyond the Design Base. Accidents involving unprotected step reactivity insertion with loss-of-flow or unprotected reactivity ramp with LOF resulted in disassemblies similar in nature to the 80EC LOF cases that utilized pessimistic phenomenological assumptions. Final average core temperatures and work-energy to slug impact are within the SMBDB, and are bounded by the conservative 80EC LOF cases. Only when the CLAZAS module is used in the T0P/LOF analysis is the Structural Margin Beyond the Design Base exceeded. Disassemblies resulting from early fuel reentry in the LOF transition phase are judged to be very mild, i.e. , average core temperatures should not exceed 4200U k. Only when unreasonable assumptions are made abcut initial re-entry velocity do more severe consequences result. rc en these, however, do not exceed 4800 K in average core temperature. g 11-16 If rapid r3criticalities could occur in a homogenized fuel pool, the consequences could be severe if the power level at prompt critical is low enough. For 21 x nominal power, an average core temperature of 4540 K is attained; for 2.1 x nominal power, the final average core temperature is 4652 K, and the work-energy at sodium slug impact is 99 MJ. Uncertainties associated with vapor bubble collapse during pool dis-assemblies were addressed and considered to be within the uncertainty range of estimating a driving ramp function for VENUS. Based upon this analysis, it is concluded that direct disassemblies in the CRBRPwould leak to consequences which are enveloped by the SMBDB. Only when unrealistically pessimistic assumptions are made with regard to fuel behavior under fuel-coolant interaction conditions, can sufficiently high ramp rates be attained to approach energetic consequences comparable to the SMBDB. 11-17 Table 11-1 Sumary of BOEC TOP 2.4c/se: Forced Midplana Failure Disassembly Calculations Initial Conditions VENUS Results Pef. With Smeared 10. Control Arbitrary Pef. o . i 2

• Co pliance 755/ sec h,p Raw Rate. 5/sec 50 Fuel Peak Temp, K SJ31 5452 5134 5511 Fuel Avera;e Te perat.re. K 2600 Fuel A<erage Temp, K 3789 4050 3853 4034 Normlized Power 70 Energy in v olten fuel, MJ 433v 5262 4565 5400 i Net Pea;tivity, 5 1.03 ,4cr-alized Peak Pcaer 2408 cc 2500 2407 4050 Pointasse Sodium Distribution Duration of Disasse.mbly, msec 7.9 3.7 7.9 6.6 W0ri-Energy to Na Slug Irpact, MJ 25 49 31 53 Wors-Energy to One At , MJ 129 257 157 281
• Resul ts for a Case Tr.at Included Both 5 earej Vaids and 10'. Control Compliance Were Essentially Identical With Smearec Void Case, See Text Page 11-6.

e G G Table 11-2 Summary of E0EC TOP Midplane Failure Disassembly Calculations Reference Smeared Additional Initial Conditions Case Voids 2% Void Ramp Rate, $/sec 50 Core Average Temperature, K 2545 same same Normalized Power 155 Reactivity, $ 1.06 Sodium In Core Pointwise Smeared Smeared VENUS-II Results Core Average Temperature, K 3490 3666 3654 Maximum Temperature, K 4654 4905 4936 Energy In Molten Fuel, MJ J220 3763 3830 Normalized Peak Power 1530 1565 1565 Duration of Disassembly, msec 8.7 9.4 9.7 Fuel Expansion Work, MJ Work-Energy to Na-Slug Impact 12 19 20 Work-Energy to 1 Atm 47 87 94 11-19 Table 11 3 Disassembly Calculation for A 3 $/Sec Insertion in E0EC Configuration Initial C6nditions Ramp Rate, 5/sec 70 Core Average lemperature, K 2670 Normalized Power 79 Reacti vi ty , 5 1.04 Sodium In Core Pointwise VENUS-1I Results Core Average Temperature, K 3717 g Maximum Temperature, K 4828 Energy in Molten Fuel, MJ 4122 Normalized Peak Power 3220 Duration of Disassembly, msec 6.2 Fuel Expansion Work, rg Work-Energy to Na-Slug Impact 18 Work-Energy to 1 Atm 91 11-20 TABLE 11-4

SUMMARY

OF J0EC LOF DISASSEMBLY CALCULATIONS No Axial No Fission CLAZAS Initial Condition Expansion Gas CLAZAS Tabular

• Ramp Rate, $/sec 40 50 50 ----

Core Average Temperature, K 2937 2991 2992 2992 Core Peak Temperature, K 3241 3826 3712 3712 flomalized Power 240 529 194 194 Reactivity, $ 1.06 1.07 0.99 0.99 VENUS-II Results Core Average Temperature, K 4194 4043 4084 4196 Maximum Temperature, K 5647 5724 5690 5858 Energy in Molten Fuel, MJ 5759 5182 5330 5713 Nomalized Peak Power 1942 1572 1459 1491 Duration of Disassembly, msec 6.8 5.5 7.9 8.8 " Effective" T dk/dT .0036 .0036 .0036 .0033 Fuel Expansion Work, MJ Work-Energy to Na-Slug Impact 64 65 64 78 Work-Energy to 1 atm 340 303 309 379

• Doppler s10% low 11-21

TABLE 11-5 h

SUMMARY

OF E0EC LOF DISASSEMBLY CALCULATIONS Neglect Fission Gas Arbitrary Ramp Dispersal Aug. '75 Initial Conditions On Base Case Orifice Scheme Ramp Rate, $/sec 40 Figure 7-33 Core Average Temperature, K 2903 2788 52 106 Normalized Power Reactivity, $ 0.99 0.98 VENUS-II Results Core Average Temperature, K 4277 4843 Maximum Temperature, K 5787 6166 Energy in Molten Fuel, MJ 6060 7974 O Normalized Peak Power 3400 4594 Duration of Disassembly, msec 8.0 11.26 Fuel Expansion Work, MJ Work-Energy to Na Slug Impact 74 132 Work-Energy to 1 atm 397 767 O 11-22

TABLE 11-6

SUMMARY

OF BOEC THIRTY CENT STEP /LOF DISASSEMBLY CALCULATION Initial Conditions Ramp rate, $/sec S0 $/sec for 0-4 msec Tabular Function for > 4 msec Core Average Temperature, K 2883 Normalized Power 80 Reactivity, $ 0.944 VENUS-II Resu'ts Core Average Temperature, K 4225 Maximum Temperature, K 5678 Energy in Molten Fuel, MJ 5870 Normalized Peak Power 2280 Duration of Disassembly, msec 9.1 Fuel Expansion Work, MJ U) Work-Energy to Na-slug impact s68 Work-Energy to One Atm. s340 c Note (1) Estimated from similar analyses. 11-23

TABLE 11-7 h

SUMMARY

OF BOEC T0P/LOF DISASSEMBLY CALCULATIONS

                                                      ' Cladding Gravity    CLAZAS Initial Condition                      Base Case             Drainage        Motion Ramp rate, $/sec                     44 (0-5 msec)         52 (0-0 msec)   63 (0-4 msec) 33 (5-9 msec)         61 (8-10 msec) 113 (4-6 msec) flormalized Power                            7F                  128           180 Core Average Temperature, K               2883                 2883           2883 Core Peak Temperature,   K                3041                 3041           3041 Net Reactivity, $                           .95                  .97            .99 VENUS-II Results Core Average Temperature, K               4253                 4453           4935    h Core Peak Temperature,   K                 5720                6020           6717 Energy in Molten Fuel, MJ                 5960                 6643           8255 Normalized Peak Power                      2492                3067           4533 Duration of Disassembly, msec               8.8                  7.5           6.8 Fuel Expansion Work, MJ (1)

Work-Energy to Na-slug Impact s70 ~93 sl70 Work-Energy to One Atm. s380 s520 s850 Note (1) Estimated from similar analyses. O 11-24

TABLE 11-8 SUtttARY OF DISASSEMBLY CALCULATIONS FOR TRANSITION PHASE RECRITICALITY Disassembly Calculations for the E0EC LOF Immediate Reentry Case Initial Conditions _ 28 37 45 63 Ramp Rate, $/sec Core Average Temperature, K J034 3034 a034 3034 100 100 100 100 Normalized Power Reactivity, $ 0.97 0.97 0.97 0.97 VENUS-II Results Core Average Temperature, K 4173 4108 4158 4468 Maximum Temperature, K 5527 5442 5511 5955 Energy in Molten Fuel, MJ 6070 5840 6020 7110 1710 1450 1600 2550 Normalized Peak Power Duration of Disassembly, msec 10.1 10.3 10.1 8.4 Fuel Expansinn Work, MJ Work-Energy to Na-Slug Impact 55 50 53 94 Work-Energy to 1 a tm 330 300 315 537 Homogenized Core Reentry Disassembly Calculation Summary Initial Conditions Ramp Rate, $/sec 30 30 30 Core Average Temperature, K 3130 3130 3130 Normalized Power ?1 2.1 210 Reactivity, $ l.0 1.0 1.0 Core and Axial Blanket Tdk/dT -0.00275 -0.00275 -0.00275 VENUS-II Results Core Average Temperature, K 4540 4652 4138 Maximum Temperature, K 5902 6111 5120 Energy in Molted Fuel, MJ 6980 7340 5593 Normalized Peak Power 1910 2310 800 Duration of Disassembly, msec 9.6 10.3 8.9 Fuel Expansion llork, MJ Work-Energy to Na-Slug Impact 80 99 30 Work-Energy to 1 atm 473 568 193 11-25

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11-26

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12. Definition of Pressure - Volume Relationship Used to Specify the Structural Margin Beyond the Design Base A very large amount of fission energy is generated during the course of a core disruptive event. This results from the fact that tihe CRBRP coolant and fuel systems are designed to normally handle large power dcnsities and

                                                                   ~

energies with margin. In addition, the design of the reactor core and primary heat rejection system affords an enonnous thermal energy sink beyond its operating range prior to core disruption. This section provides a basis by which the structural margin requirements for the reactor coolant taundary can be specified for events beyond the design base. 12.1 Definition of Thermal Source The state-of-the-art does not allow for a continuous, mechanistic deter-mination of the primary boundary mechanical and thermal loads which result from a hypothetical core disruptive accident. Therefore, to develop a rational basis to define the mechanical load margin requirements for the reactor coolant boundary, a consideration of the system state at the end of the mechanistic determination is appropriate. The analyses and engineering considerations presented in Sections 6 through 10 indicated that the nominal end states of an HCDA in the CR8RP. (resulting from probability category 1 and 2 assumptions) would be a partially damaged, coolable reactor or a fully molten reactor core for TOP and LOF initiated events, respectively. The thermal consequences of LOF events con-sistently envelope those of TOP events. However, even for the larger LOF thermal consequences no intermediate state in the nominal progression path (Section 10) could be identified as producing structural damage due to dynamic mechanical loads. Therefore, the nominal events could not be used as a basis for defining the structural margin requirements. It is only for the less probable category 3 and 4 events that thermal conditions are predicted which have the potential for substantial structural loadings. Thus, the remainder of this Section will focus on these lower probability category 3 and 4 energetic events. Section 11 quasi-mechanistically defines those system states which represent the largest energy potential for performing mechanical damage. The reactor state is defined by the VENUS code at a point where the net reactivity is subcritical, 12-1

the power generation is rapidly falling toward decay generation levels, and the core materials are expanding from their approximate steady state spatial positions (except, perhaps for the sodium). An inventory of the total fission energy generated from the initiation of an energetic LOF transient indicates that about 50 percent of the energy has been transported away by the sodium flow. This energy is stored as a temperature increase (still below 800 C) of the sodium in the outlet plenum and outlet piping between the reactor vessel and IHX's. Approximately 40-45 percent of the remaining fission energy is associated with the core fuel internal energy. Characteristically, some 5000 to 6000 MJ will be stored in fuel at temperatures both above and below the fuel solidus temperature of 2767 UC. The remaining five to ten percent is associated with temperature increases of the upper blanket region (s970 C), the fuel assembly steel structure ($1000 C) and the core cladding (1100 C). Less than one percent (<200 MJ) is stored in steel above its melting point of 1371 UC. Thus, when the amount and thermodynamic characterization of excess energy in the system are considered, the fuel becomes the only significant thermal energy source for potential mechanical damage to the reactor coolant boundary. h Due to the very rapid energy addition and the volumetric constraints, the fuel is essentially at a. low quality, saturated liquid condition. Although U peak temperatures and vapor pressures are on the order of 6000 K and 30 MPa, the average conditions are typically less than 4300 K and 0.75 MPa. Thus, very large physical gradients will exist within the fueled core region at the tennination of a VENUS calculation. In detail, VENUS provides the thenno-dynamic state (pressure, temperature specific volume, volume) and kinetic energy (axial and radial) of each core node. From SAS, the detailed distri-butions and state of the sodium and steel are also known at VENUS termination. A discussion pertinent to selection of initialization criteria for the SAS-VENUS switchover was presented in Section 11. The final thennal conditions, as calculated by VENUS, are subject to several types of uncertainties. The initially defined distributions of sodium mass and fuel temperature are not mapped on a one-to-one basis from SAS to VENUS due to modeling constraints. These distributions will affect the VENUS calculations of the thermal end state. O 12-2

In particular, the VENUS code has an input option (AVTEMP) which will inter-nally compute the initial fuel temperature distribution based on the input power distribution and two input parameters. This method is a useful option but can, if not properly applied, introduce a bias in the computed energetics in the following manner. The VENUS energy deposition is neutronically termi-nated by small, inertia constrained motions of fuel material which are driven by gradients in fuel vapor pressure.* Since the fuel vapor pressure in turn is an exponential function of temperature, the VENUS results are sensitive to the spatial distributions of fission power and initial fuel temperature peaks. As several SAS channels often are mapped inio one VENUS annular region, fuel temperature peaks which represent sources of early disassembly pressures are degraded. Selection of the AVTEMP parameters will additionally smooth and affect the peaking of fuel temperatures with respect to the core average conditions. A flat distribution should generally result in higher final average temperatures and it is part of the reason that homogenized core recriticalities (Section 11.4) are more sensitive to ramp rates than are direct disassemblies. This shape sensitivity may be as great as any reasonable variation in the Doppler or net reactivity. It is thus important to reflect the temperature peaking which has occurred in the SAS calculation. Hence, the initial temperature distributions which result from using the AVTEMP input option in VENUS should be compared with the SAS termination fuel temperature distributions to assure that the results are not unduly biased. Besides the initial conditions, the VENUS results are also sensitive to variations in Doppler magnitude, initial core power and the driving reactivity function. Sufficient parameter studies of these effects have been performed (Ref. 68) to allow a conclusion for CFBRP that the major uncertainty lies in the driving reactivity function. This function is calculated by the SAS code for direct disassembly events and should be modified as necessary to reflect engineering judgements on the important physical processes. Linear

• This is not true for "hard" systems (i.e. , full sodium-in) where single phase pressures are important. However, such systems readily disassemble at low specific fuel energies and are not of significance to the definition of the SMBDB.

12-3

representations in VENUS of concave nonlinear driving functions will generally underestimate the energy release. Either parabolic or piecewise linear functions should be employed in cases such as LOF driven TOP defined ramp rates. For the purpose of specifying a thermal source for the definition of the SMBDB, the variations in ramp rate afforded in the calculations of Section 11 were considered to adequately encompass the other uncertainties. The thermal source was chosen, based upon the absence of energetics in the nominal progression paths and engineering judgements on the probability of event occurrences, to encompass a wide spectrum of core disruptive initia-tors and phenomenological assumptions. With allowance for a range of reasonable uncertainties, the calculated energetics associated with LOF or combined TOP-LOF events in the CRBRP (Section 11) result in core average and peak temperatures less than 4600 and 6000 K, respectively. The most energetic calculations within this range resulted from hypothesized recriticalities on a homogenized, molten core. Energy storage in the liquid fuel was approximately 7000 MJ for these cases. h Only two cases resulted in thermal conditions which exceeded the above values. One calculation was an arbitrary category four T0P/LOF event with CLAZAS modeling in the 80EC configuration. The other represented a LOF event without fission gas dispersal in SLUMPY for an E0EC configuration. The orifice scheme employed in the latter calculation (not reference design) pro-moted LOF driven TOP conditions leading to enhanced energetics. Therefore, the thermal source for the SMBDB was specified to be charact-erized by an average core temperature of 4800 K with a power and temperature distribution based upon molten, homogenized core. This results in a peak fuel temperature of 6030 K and a distribution which is flatter (peak / average = 1.26) than nominally expected in a direct disassembly (P/A3 1.35). The resulting distribution of temperature with respect to the core fuel mass is depicted in Figure 12-1. The above information constitutes a definition of the thermal energy source available for conversion to mechanical loads on the reactor coolant boundary. 12.2 Uncertainties in Thermal - Mechanical Energy Conversion O Mechanical energy can be extracted from a thermal source at reasonable L2-4

efficiencies as clearly evidenced by modern heat engines. The ability to predict apriori the efficiency of a real conversion process is highly dependent upon the physical complexity of the process since available work is a thermo-dynamic path function. In a practical sense, thermodynamics describes the upper limits of conversion efficiencies and provides guidance on how to effect changes in the process efficiency. The major uncertainty in mechanis-tically calculating the conversien efficiency for a core disruptive event is simply that the physical process is not well known due to its complexity. Essentially all of the uncertainties in the real expansion process would degrade the thermodynamic potential of the fuel to perform work. Examples are: heat transfer to steel and sodium, turbulent internal mixing of the liquid fuel, viscous dissipation, shock wave formation, etc. One exception has been proposed which could increase the conversion efficiency. The exception results from an idealized, efficient transfer of the fuel thermal energy to sodium, thus making sodium vapor the working fluid (Ref. 71). For a specific range of initial conditions, more work could be extracted since for the same internal energy sodium has a much higher vapor pressure than fuel. The case for such large scale, rapid conversions has been theoretically and experimentally considered for the CRBRP design and found to be most unlikely (Ref. 20). This is particularly true for the LOF initiated events for which liquid sodium is not initially associated with the higher tempera-tore fuel . However, even for TOP of LOF/ TOP conditions, such as the Sll and S12 TREAT reactor experiments in which intimate proximity of liquid sodium was assured, no evidence of an efficient, nondissipative, fuel to sodium heat transfer process could be found (Ref. 72). Thus, the situation is that the mechanisms for significant work product-tien, if they exist at all, are not defined sufficiently well for mechanistic computations. Many energy dissipative mechanisms are identifiable. The process based on transfer of fuel energy to sodium is not a likely or effici-ent one in a reactor environment. With this situation, the most reasonable approach was considered to be the adoption of a thermodynamic upper limit for mechanical work extraction from the fuel, This is very likely to be an extremely conservative process for defining work potential relative to real processes (including fuel to sodium heat transfer) that would exist. 12-5

12.3 Thermodynamic Work Potential for Structural Margin Assessments To calculate the maximum thermodynaaiic work potential of the fuel an isentropic expansion process was applied independently to each VENUS defined fuel mass and the total work sumed over all the fuel. For an isentropic process the path integration of work becomes equal to the change in internal energy, (including phase transitions) which is readily evaluated (Ref. 69) for a specified pressure endstate. Based on a perfect gas rela-tionship to define the fuel volume, a pressure-volume relationship was constructed for the core expansion to a specified pressure. This pressure-volume relationship (Table 12-1) was then used as the source term for avail-able work in a two-dimensional structural dynamics model of the reactor surroundings to calculate the mechanical loadings on the reactor coolant boundary. The available work for expansion to sodium slug impact on the vessel closure head, to the equilibrium pressure attained at the end of the dynamic loadings (20 bar), and to atmospheric conditions are 101, 140, and 661 MJ, respectively. O O 12-6

TABLE 12-1 PRESSURE VOLUME RELATIONSHIP FOR STRUCTURAL MARGIN BEYOND THE DESIGN BASE P(bar) V(m ) 273 2.558 203 2.6179 147.3 2.878 103.8 3.595 86.09 4.309 70.77 5.415 57.6 7.228 46.47 10.098 37.08 14.748 29.25 22.01 22.8 33.13 17.55 49.54 13.32 75.38 9.96 115.26 12-7

20 - 100 Fuel Mass 7500 Kg 18 -

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13. Re ferences

1. F. E. Dur.n, et al. , "The SM 1A LMFBR Accident Analysis Computer Code," f,rgonne National La aratory, 1975, (ANL/ RAS 75-17).

2. J. F. Jackson and R. E. Nicholson, "VEf4US-II: An LMFBR Disassembly Program," Argonne National Laboratory,1972 ( ANL-7951).

3. W. R. Bohl, J. E. Cahalan and D. R. Ferguson, "An Analysis of the Unprotected Loss-of-Flow Accident in the Clinch River Breeder Reactor with an End-of-Eqt.ilibriut. Core," Argonne National Laboratory, May 1977, (ANL/ RAS 77-15).

4 W. R. Bohl, et al., "An Analysis of Unprotected Transient Under-Cooling and Transient Overpower Accidents in the Clinch River Breeder Reactor," Argonne National Laboratory, 1975, (ANL/ RAS 75-29).

5. D. S. Dutt, et al. , "A Correlated Fission-Gas Release Model for Fast Reactor Fuels ," Trans. Am. Nucl . Soc. , 15,198,(1972).

b. R. G. Stuart and G. R. Thomas, "Ef fects of Fission Gas on Transient Overpower Fuel Rod failure," Trans. Am. Nucl . Soc. , l_3_, 654-56, (1970).

7. L. L. Smith and M. G. Stevenson, "Effect of Reactivity Insertion Rate on Fuel Pin Failure Threchold," Trans. Am. Nucl . Soc. , ~17, 284-85, (1973).

8. O. D. Slagle, C. A. Hinman, and E. T. Weber, " Experiments on Melting and Gas Release Behavior of Irradiated Fuel," Hanford Engineering Development Laborctory, 1974, (HEDL-TME 74-17).

9. E. E. Gruber, " Transient Gas Release from 0xide Fuels: Parametric Representation of FRAS Results." 'rgo,'ne National Laboratory, flarch 1975, ( ANL/ RAS 75-7).

10. E. E. Gruber, "A Generalized Parametric Model for Transient Gas Release and Swelling in Oxide Fuels," Argonne National Laboratory, 1976, (ANL/ RAS 76-20).

11. L. W. Deitrich, et al., "Modeling the Response of Fast Reactor Fuel to Hypothetical Accident Transients," ( ANS CONF-76-1007), Chicago, October 1976.

12. G. Bandyopadhyay and J. A. Buzzell, " Microstructural Investigation of Mixed-Oxide Fuels Subjected to Siir.ulated Thermal. Transient Conditions,"

Ceramic Microstructures 76, " Proc. of the Sixth International Materials Symposium," Berkeley, Ca. , August 1976. 13-1

13. L. L. Smith, et al., "SAS/FCI: The SAS3A Fuel-Coolant Interaction Model," Argonne tJational Laboratory, October 1975, (ANL/ RAS 75-33). g

14. C. W. Hunter, G. D. Johnson, and R. L. Fish, " Mechanical Properties During Simulated Overpower Transients of Fast Reactor Cladding Irradiated from 700-1000"F," Hanford Engineering Development Laboratory, June 1975, (HEDL-TME 75-28).

15. R. W. Tilbrook, " Coolant Voiding Transients in LMFBRs," in P oc.

Conf. on New Developments in Reactor Mathematics and Applications 1, (CON F-710302) , Idaho Falls, Idaho, March 29-31,1971, pp. 215-40.

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Argonne National Laboratory, June 1972, (ANL-7947).

17. P. G. Lorenzini and G. F. Flanagan, "An Evaluation of Fuel-Coolant Interactions During Disassembly of an LMFBR," in Proc. Conf. on New Developments in Reactor Mathematics and Applications 1, (CONF-710302),

Idaho falls, Idaho, March 29GlD971, pp. RF7B.

18. D. H. Cho, R. O. Ivins, and R. W. Wright, " Rate-Limited Model of Molten-Fuel / Coolant Interactions: Model Development and Preliminary Calculations," Argonne National Laboratory, March 1972, ( ANL-7919).

19. E. T. Rumble, Ill, et al . , " Fuel Movement Investigations During LMFBR Overpower Excursions Using a New Model," Proc, iim. Nucl. Soc. Fast Reactor Safety Conf. , (CONF-740401 ) , BeverWliills , Ca. , April 2-f, TW4, pp. 1M6-71,

20. H. K. Fauske, "An Assessment of Thermal Interactions in Sodium-Cooled Oxide-Fueled Fast Reactors," Argonne National Laboratory, August 1974, (ANL/ PTS 74-19).

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(CONF-740401-P3), Beverly Hills, Ca. , April 1974, pp.1541-55.

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June 1975.

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Soc. Fast Reactor Safety Conf. , (CONF-740401), Bever O IIlls, Ca., 1974, pp. 220-38.

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O 13-2

25. R. E. Henry, E. G. Erickson, G. T. Goldfuss, J. J. Heiberger, D. J.

Quinn, R. L. Roth, L. A. Splehu, and I. O. Winsch, " Experiments on Pressure-Driven fuel Compaction with Reactor Materials," Proc. Intl. Meeting on Fast Reactor Safety And Related Physics, Chicago, Illionis, October 5-8, 1976.

26. F. E. Dunn, G. Hoppner, T. J. Heames, and G. J. Fischer, " Comparison of SAS2A Sodium Boiling Analysis with Experiment," Trans. Am. Nucl.

Soc., 15, (1), 340, (June 1972).

27. F. W. Peppler, "Experimentelle Untersuchungen der Siedevorgange mit Matrium in engen Kanalen and deren Anwendung auf schnelle Reaktoren,"

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Sci. and Engr., 44, 320-44, (June 1971). 30 F. E. Dunn, et al., "The PRIMAR-2 Primary Loop Module for the SAS3A Code," Argonne National Laboratory, March 1976, (AtiL/ RAS 76-5).

31. W. R. Bohl and T. J. Heames, "CLAZAS: The SAS3A Clad Motion Model,"

Argonne National Laboratory, August 1974, (ANL/ RAS 74-15).

32. G. Hoppner, "SAS3A Analysis of R-Series Experiments," Argonne National Laboratory, August 1974, (ANL/RA: 74-14).

33. P. J. Persiani, et al., "Some Considerations on the Meltdown Problems for FARET," Argonne National Laboratory,1964, (ANL-6935).

34 W. R. Bohl , "SLUMPf: The SAS3A Fuel Motion Model for Loss-of-Flow," Argonne National Laboratory, August 1974, (ANL/ RAS 74-18).

35. C. E. Dickerman, L. E. Robinson, F. L. Willis, W. Stephany, and C.

August, " Status of Recent Meltdown Studies," Proc. Conf. on Safety fuels and Core Design in_ Large Fast Power Reactors, TANL-7120),

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13-3

38. Reactor Development Program Progress Report, October 1975, (ANL-RDP-42),

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Proc. Conf. Mathematical Models and Computational Techniques for Analysis of Nuclear Systems 2, (CONF-730414),1973, pp.1X-59. 40 R. Kumar, L. Baker, Jr. , and M. G. Chasanov, "Ex-Vessel Considerations in Post-Accident Heat Removal," Argonne National Laboratory, October 1974, (ANL/ RAS 74-29).

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U. S. Steel Corporation,1964.

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Argonne National Laboratory,1974, ( ANL/ RAS 74-24).

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21, (June 1975).

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64. A. W. Cronenberg, T. C. Chawla, and H. K. Fauske, "A Thermal Stress 3 Mechanism for the Fragmentation of Molten UO2 Upon Contact With W Sodium Coolant," Nucl. Eng. and Design, 30, 434-43, (1974).

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McGraw-Hill', 1973.

67. R. B. Nicholson and J. F. sockson, "A Sensitivity Study for Fast Reactor Disassembly Calculations," Argonne National Laboratory, 1974, (ANL-7952).

68. W. T. Sha, T. A. Daly, A. J. Lindeman, E. L. Fuller, D. A. Meneley, and G. K. Leaf, "Two-Dimensional Fast-Reactor Disassembly Analysis with Space-Time Kinetics," Proc. Conf. on New Developments in Reactor Mathematics and Applications 1, (C0hF-710302), Idaho Falls, Idaho, March 29-31, 1971.

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70. D. J. Behrens, "The Effect of Holes in a Reacting Material on the Passage of Neutrons," Physical Society of London Proceedings, Section A, Vol. 62, 1949, pp. 60/-16.

h

71. E. P. Hicks and D. C. Menzies, " Theoretical Studies on the Fast Reactor Maximum Accident," Argonne National Laboratory,1965, ( ANL-7120).

72. M. Epstein and D. H. Cho, " Fuel Vaporization and Quenching by Cold Sodium; Interpretation of TREAT Test Sll," Proc. Am. Nucl. Soc. Fast Reactor Safety Conf. , USAEC Report (CONF-74TT401-P2), Beverly Hills , Ca. ,

April 1974. O 13-6

Appendix A SASBLOK Summary This Appendix surranarizes how SASBLOK calculations were made using SAS. SASBLOK is not a coded subroutine in SAS. Instead it represents a set of code modifications to existing subroutines which allow a simulation of SAS/FCI predicted hydraulic and neutronic effects on the reactor. This allows the FCI module to be bypassed and an accident calculation continued beyond difficulties which often occur during the latter stages of an FCI in subroutine TSC8. Additionally, the modifications pennit the simulation of post-FCI fuel blockages and power reduction (fuel loss) to be considered. All calculations of the blockage configuration and stability are performed external to the SAS code. A.1 SAS Modifications and Input Requirements A SASBLOK evaluation starts by simulating the results of a SAS/FCI, PLUTO calculation or an analysts estimate. The SAS calculation is restarted prior to the original failure with the SAS/FCI module turned off for the failure channel (s) and a flag set to indicate that a SASBLOK evaluation will occur. This is accomplished by setting NT0TFL(ICH)=0 and 10PFC8(ICH)

 > 1, fixed locations 601-610 and 751-760, respectively.

The FCI zone growth and pressure are simulated with the nonnal SAS . ;ular fission gas release option. The initiation time is input via floating point location 2271-2280 as XLOR(ICH), in seconds. The SAS TSCl subroutine was modified to test on IOPFC8 and XLOR and then initiate the fission gas release option. A printed message will occur to notify the user. Based upon normal e SAS user instructions, one specifies the pressure and bubble interface posi-tions as a function of time since gas release. The maximum time (seconds) that the tabular release option is to be employed is set with variable TMAXFS (IFUELV), loc 2651-2655. At the end of this time, subroutine TSCl will tenninate the tabular option and test the value of IOPFC8(ICH) again. If IOPFC8 >l, the fission gas bubble will be lef t alone and if IOPFC8 = 1, the

f. - 1

bubble will be re-indexed such that it Fecomes a sodium vapor bubble. (The g switch to sodium often causes a considerable degree of internal SAS coolant dynamics re-initialization). The effects of failed channel fuel motion reactivity components on the reactor net reactivity is accounted for by modifying the programmed reactivity (PREATB,- locations .5767-5786) and corresponding time (PREAM, locations 5787-5806) as follows. Prior to initial pin failure, input values of PREATB and PREATM are specified to produce the initial reactivity insertion rate, if applicable. From the time of initial channel failure until the time of SAS/FCI termination, table values for the programed reactivities PREATB are: PREATB (PREATM) = PROGRAMMED REACTIVITY + SAS/FCI CALCULATED FUEL MOTION REACTIVITY Af ter the termination time for the SAS/FCI calculations, values of PREATB and PREATM a' e elected such that reactivity insertion is continued at the initially specit ed (pre-failure) ramp rate. The above reactivity and hydraulic simulations should always be com- g pared to the original solution for adequacy. Following the FCI event, modifications were made to SAS subroutines TSCl, PRIMAR and SHAPE to provide a simulation of hydraulic impedence (fuel blockages) and fuel loss (power reduction), respectively. The hydraulic impedence is substituted for the normal expansion loss coefficient (XKE, location 5943) and is specified as variable DHOR(ICH), location 2281-2290. To smooth the solution, the minor loss value is ramped from XKE to DHOR over a period of time equal to twice TMAXFS. Special precautions are taken to keep the loss coefficient associated with the fuel assembly upper outlet region in case of flow reversal. Since the assessment is focused on ade-quate heat removal from the core region over a long period of time (compared to the FCI event), neither the ramp delay in the blockage effect nor the outlet location of the hydraulic blockage seriously impacts the results. The power reduction affected by the fuel renoval from the core to the blockage region is determined by the user input value A0R(ICH), location 2391-2400. A0R uniformly reduces the axial power distribution in the pin g A-2

in a sir.gle step at the time that the blockage coefficient reaches its maximum value DHOR. It is also necessary to set JRUPT(ICH) > 0 to prevent multiple power reductions. A statement is printed to notify the user when the power reduction takes place. Table A-1 summarizes the input variable definitions utilized in the SASBLOK modifications. A.2 External Calculations The objectives of the external calculations were to relate the physical accident conditions in which blockages have occurred to either computer code input values or scoping the magnitude of the problem. In an FCI event, blockages formed could be porous or solid and could be spread over various locations and cross sections. The fuel mass and the stability of the core region fuel was determined and simulated in the SAS code. Because of the limited ability of SAS to simulate blockages, the hydraulic effects of the complex blockage configurations had to be reduced to one input parameter which was DHOR, the blockage loss coefficient. The porous blockages were simulated both with a simple parallel resistance network and a more elaborate computer flow network. A study was made comparing both networks with block-age test data. For a porous blockage with liquid sodium flowing through the blockage, the resistance through the blockage was calculated using a fraction factor correlation which agreed well with tests of upward flowing water through a uranium dioxide particle bed (Ref. A-1). The same mean particle size (420 u) used in the experiments was employed for these calculations, since the particulate beds were formed by acal fuel coolant interactions typical of an accident. Void fractions used in the Reference A-1 tests and these calculations are also comparable (0.45 versus 0.5). The blockage was located in the fission gas region of the fuel assembly and occupied the volume normally filled with sodium coolant. By knowing the mass of ejected fuel from the original SAS/f CI calculations, assuming the channel geometry is preserved and using a void fraction of 0.50, the length of the blockage was ascertained. Using the Leva correlation (Ref. A-1) for friction factor, A-3

an equivalent pressure loss coefficient was calculated from the following equations: KBloc.k = 4In L (1-E) '" D 3 p E where K = AP / (G 2/2p) Block Block f n

                                  =   Lev friction factor L    =   length of blockage D      =   mean particle diameter p

E = bed void fraction n = leva factor on void fraction G = mass velocity based upon unblocked area p = sodium velocity Once the loss coefficient due to the blockage was determined, a core average loss coefficient representing both the blocked and unblocked flow channels within an assembly was calculated to simulate the blockage for the SAS code which can simulate only overall or average resistance effects. The assem-bly average loss coefficient was obtained from the following equation for parallel fuel assembly flow channels: 1 = 1' k + n-k

              # AVG CHAN                 bl0CKCHAN            UNBLOCK CHAN  .

where K

                                   =   average flow channel loss coefficient AVG CHAN K
                                   =   blocked flow channel loss coefficient 8 LOCK chaff K                      =   unblocked flow channel loss coefficient UNBLOCK CHAN n =      number of flow channels in a fuel assembly k    =   number of blocked flow channels in a fuel assembly O

A-4

The SAS reactor model includes an exit cxpansion loss coefficient, (XKE) so the non-blockage loss coefficients were subtracted from the average channel loss coefficients to obtain the equivalent exit loss coefficient. The above equations are valid for a steady state analysis; however, for TOP's the primary pumps remain operating and a constant pressure head is maintained across the reactor, the steady state loss coef ficients can be applied to a long term evaluation of the reactor a. d blockage condition. Using the above relationships, the blockage coefficient was calculated for various area blockage fractions and amounts of ejected mass. The amount of fuel mass in the blockage did not have a significant effect below 401 blockage. A HAFMAT (Ref. A-2) flow model was constructed similar to the SAS model and this model without blockages was checked against the SAS BSEC and E0EL steady state flow, pressure and temperature solutions. The blockage model consisted of a parallel flow path through the fission gas plenum region of SAS Channel 8 with the blocked flow path having the friction factor calculated from the leva correlation for packed beds while the unblocked flow path used the project design friction factor. A contraction loss coefficient was applied to the inlet and an expansion coefficient was applied at the exit of the unblocked flow. These coef ficients accounted for the area changes due to the blockage. To compare the results of this model to test data or previous calcula-tions, an equivalent loss coef ficient was calculated by replacing the blockage model with a loss coef ficient that produced the same flow in the blocked channel. By this method, a curve of area blockage ratio versus loss coefficient was generated. Figure A-1 compares the data for an orifice (Ref. A-3), plate blockage (Ref. A-4) for the 19 rod assembly, the porous blockage generated by the Haft 1AT model, and the curve for the parallel flow network. The HAfMAT curve agress with the orifice and 19 rod data; however, the parallel network model is somewhat conservative (smaller blockage area for the same loss coefficient). For a solid blockage or a porous blockage without flowing sodium, a simple heat conduction model was used to detenaine coolable blockage sizes. These blockages are assumed to form as a contiguous mass of material located A4

in the fission gas plenum region where either the original geometry has been destroyed or in the coolant channel where the geometry has been main- g tained. The major uncertainties in the calculations are the shape and the composition of the blockages. The shape of the blockage determines the heat conduction equation used while the composition affects the thermal conductivity used. For this analysis either spherical or cylindrical shapes were assumed and the conductivity was either that of solid fuel or a volume weighted value dependent upon the blockage composition assumed. The conductivity equations used were, for a sphere: AT = q"'r /6 k s eff and for a cylinder: AT = q" r /4 k c eff where AT = conduction temperature difference for a sphere s AT = Conduction temperature difference for a cylinder c q"' = volumetric heat generation rate g r = radius of the sphere or cylinder k = effective thermal conductivity eff The effective thermal conductivity was calculated from the following equation: n k eff

                              =

kg V j [y j i=1 i=1 where k = thermal conductivity of iS component of the blockage 4 V 4

               =   volume of i S component of the blockage For the fuel, a mean conductivity (kmean) w s calculated from the following equation:

O A-6

r2767 k = k dT mean fuel J T g where Tg = temperature at outer surface of solid ( C) kfuel = c0 + c)T + c2 +cd 3 c = 6. M -2 0 cj = -7.51E-5 c = 3.66E-8 2 c3= -5.56E-12 Average conductivity values were also employco for the clad, sodium vapor ana fission gas. For the convective temperature drop across the film in a spherical geometry, a correlation for a packed bed (Ref. A-5) was used, while for the cylindrical geometry the CRBRP project core design correlation was employed. Specifically, these correlations were: Nu = 0.33 Re0 .6 (sphere) Nu = 4.48 + 0.0144 (Re Pr)0.86 (cylinder) where Nu = Nusselt no. Re = Reynolds no. Pr = Prandtl no. The centerline of the blockage was maintained at 2767 C (melting point for the fuelJ and a blockage size vs power was calculated for a range of coolant temperatures (600 to 1200 C) which covered the range of. sodium boiling tempera-ture at the expected pressure of the blockage. With the above equations and values, parametric curves were generated for blockage size, coolant tempera-ture and blockage composition. Figures A-2 and A-3 show the parametric curves. A-7

For uncooled blockages or blockages that have insufficient cooling, the h decay heat generation can eventually lead to a melted configuration that can be relocated due to external or gravity forces. The rate and direction . of this relocation will determine an ultimate stable configuration. The forces available to cause this relocation are the forces due to the coolant, if present, or those due to gravity. Elementary methods have been applied to the gravity effects; however, the coolant effects have not been analyzed. For the gravity effects, the rate at which the molten fuel moves downward has been estimated from a simplified falling film analysis along with a molten fuel penetration analysis to determine freezing distances. Also, the magnitude of the molten fuel droplets that could form and fall due to gravity has been estimated. For the falling film analysis where the molten fuel has been assumed to drain down the fuel pins, the following equation (Ref. A-6) for the fuel flow rate was used which is valid for laminar flow with straight streamlines. 3 2 9/3p r=6 g where r = the mass flow per unit width 6 = the film thickness p = the fuel density p = the fuel viscosity To maximize the mass flow while maintaining a film flow model the film thickness has been taken as half the minimum distance between fuel pins. Because the viscosity of the melted fuel can vary through the melting tempera-ture range, the lowest viscosity can exceed the upper Reynold's number limit (s2000); however, the equation is still applicable for an order-of-magnitude. analysis. The calculated mass velocity was 244 g/cm2 -sec with a corresponding film velocity of 28 cm/sec. This is a relatively high velocity, however, freezing will limit the distance traveled. O A-8

For the penetration or freezing distance that the molten fuel can achieve when it drains down the structure, a calculation using the techniques developed in Ref. A-7 resulted in a freezing length of 8 centimeters. As discussed in Section 10.2, molten fuel penetration predictions, both experimental and analytical, involves considerable uncertainties. However, the above equation is considered reasonable for preliminary analysis. An alternative possibility for downward relocation is the falling of the liquid drops from the melted blockage. The size of the falling drops has been estimated from an equation based on the appromimate relation (Ref. A-6) between the weight of the drop and the surface tension that retains the drop in the surface. The following equation was used to determine the drop size. D=2Y3c/pg where D = fuel drop diameter o = surface tension p = fuel density g = acceleration due to gravity Using the above equation, a diameter of .63 cm with a corresponding mass of 1.1 g was calculated. This indicates that relatively small drops will be formed. A-9

TABLE A-1 O SASBLOK INPUT PARAMETER DESCRIPTION FIXED POINT INPUT LOCATIONS FORTRAN LOCATION SYMBOL DEFItilTIONS/COMMEllTS 139-43 IFIZ NUMBER OF EllTRIES IN FCI ZONE UPPER AND LOWER INTERFACE TABLE, BY FUEL TYPE, L. BY TABLE LOOKUP. 1 < 1 < 5 (SEE INPUT LOCA-

                                                   ~

TIONS 2171-2630) ~ 199 IPREAN NUMBER OF ENTRIES IN PREA VS TIME TABLE. (IPREAN < 20) NOTE: IF NEITHER TABULAR VALUES NOR PREA SUBPROGRAM ARE SELECTED, THE CODE DEFAULTS TO STEADY STATE C0dDITIONS (I.E., POWER = 1.000; PROGRAMMED REACTIVITY = 0.0). (SEE INPUT LOCATIONS 5767-5806) 200 IXX 0,FORSASBLOKTABLELOOKUPFCIZONEVOID 1, FOR EXPLICIT FISSION GAS VOID MODEL. 601-610 NTOTFL 0, IFSASBLOK OPTION IS USED: 0THERWISE AS IN SAS3A INPUT DESCRIPTION 751-760 IOPFC8 TRANSFORM SASBLOK FCI ZONE INTO

1. SODIUM VAPOR BUBBLE

2. FISSION GAS BUBBLE AT TIME TMAXFS (SEE INPUT LOCATIONS 2651-2655) 820 IFLOSS 0, IF POWER REDUCTION IN FAILED CHANNELS IS DESIRED (SEE INPUT LOCATIONS 2391-2400).

                          >0,   NO POWER REDUCTION.

O A-10

TABLE A-1 (Continued) SASBLOK INPUT PARAMETER DESCRIPTION FLOATIf4G POINT INPUT LOCATIONS FORTRAN LOCATION SYMBOL DEFINITION / COMMENTS UNITS 2271-2280 XLOR TIME AT WHICH SASBLOK INPUT TABLE FOR FCI ZONE UPPER AND LOWER INTER-FACE LOCAT10fiS BEGINS, BY CHANf1EL, l < ICH< f1CHAfi SEC 2281-2290 DHOR VALUE OF EXIT LOSS COEFFICIENT WHICH REPRESEllTS FUEL BLOCKAGE l1YDRAULIC EFFECT, BY CHANNEL, l<ICH<NCHAN TS 2391-2400 A0R VALUE OF f40RMALIZED POWER IN BLOCKAGE CHANNEL RESULTING FROM FUEL LOSS, 0.<A0R<l.0, BY CHANNEL, l<ICH<NCHAN 2171-2270 TFIS (I,L) TIME SIf1CE INITIATION OF SASBLOK FCI ZONE SIMULATI0ft, BY FUEL TYPE, L. l < I< 20, l <L< 5. SEC 2291-2390 PFIS (I,L) SASBLOK FCI ZONE PRESSURE AT TIME TFIS (I,L). ATM 2411-2510 ZFISU SASBLOK FCI ZONE UPPER IflTERFACE (I,L) POSITION AT TIME TFIS (I,L). CM 2531-2630 ZFISD SASBLOK FCI ZONE LOWER IflTERFACE (I,L) AT TIME TFIS (I,L). CM 2651-2655 TMAXFS(L) MAXIMUM TIME FOR USE OF SASBLOK FCI ZONE SIMULATION TALLE, BY FUEL TYPE L. l<L<5. SEC 5767-5786 PREATB(L) PROGRAMMED OR DRIVING REACTIVITY If1PUT TABLE l<L<lPREAll (INPUT LOCATI0ft 199)T ~ D0LLARS VERSUS 5787-5806 PREATM(L) TIME SIf4CE IllITIATION OF TRANSIENT. SEC A-il

1. 0 -

         "O'
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                                                                                                            ,    .r i                        10                       100                       1000               10,000 LCSS COEFFICIENT Figure A-1    Relationship Between Blockage Configuration and Equivalent Loss Coefficient O                                                         O                                               O

100 . 1 DIA 100% POWE R = 128 W ATTS/GR AM FLOW P 60 - COOL ANT Tf MP.~8C 600 cc 800 E 1000 E 1200 40 g - e 20 - w I I I I 0 O 1 2 3 4 5 6 SPilERIC AL BLOCK AGE DI AMETER FOR INCIPIENT MELTING ~CM Figure A-2 Power, Blockage Diameter and Coolant Temperature Required for Incipient Mel ting of fuel A-13

0 1 G D A L g ' 9 C N E 3 h(E_ 2 )

                  + E                L E

R M U O LU F I 8 P F A O O - e V (V M g M C a S A a N A R ~ k Y. G G G cl 2 2 N / S N oe L + O I l u E I T 7 T BF LS T s I L U E S A F U F I W s E &f

            % F 0 %3     %             0 2

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                                     =

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References A-1 L. Baker, et al . , " Post Accident Heat Removal Technology," Argonne National Labord tory, July 1974, ( ANL/ RAS 74-12). A-2 L. H. Wunderlick and D. R. Dolk, "HAFMAT - Steady-State Flow Distri-bution Program," Knolls Atomic Power Laboratory, July 6,1970, (KAPL-M-7123). A-3 NASA Technical Memorandum 952, National Advisory Committee for Aero-nautics, September 1940. A-4 M. H. Fontana, et al. , " Thermal-flydraulic Effects of Partial Blockages in Simulated LMFBR Fuel Assemblies with Application to the CRBR," Oak Ridge fiational Laboratory, July 1975, (0Rf4L-TM-4779). A-5 W. H. McAdams, " Heat Transmission," McGraw-Hill, New York,1954. A-6 G. B. Wallis, "One-Dimensional Two-Phase Flow," McGraw-Hill,1969,

p. 331.

A-7 F. B. Cheung and L. Baker, " Downward Fuel Relocation in the Below-Core Structure Following an LMFBR Hypothetical Core-Disruptive Accident," Argonne National Laboratory, June 1975, (AtiL/ RAS 75-21). A-15

Appendix B Summary of Experimental Bases Employed in SAS LOF Modeling Unprotected loss-of-flow associated sequences are considered to be bounding events for an energetics assessment for the CRBRP. Two key phenomena which must be modeled in SAS are the relocations and interactions of steel and fuel in a sodium voided assembly. This appendix will provide a suninary of the experimental data which was available (1975) to select the modeling approach for the SAS calculations presented in this report. The status of technology is rapidly progressing in these areas. The most recent modeling judgements and analyses (Ref. B-1) which have had the benefit of further experiments and interpretations indicate that the fundamental sudgements employed in 1975 have not been substantially altered. The experimental evidence on the subject phenomena of cladding and fuel relocation during loss of flow events will be discussed separately. However, these phenomena can be rather tightly coupled through the reactor thermal hydraulic and neutronic design characteristics. Thus, to address this topic for the CRBRP additional experimental information related to sodium voiding and two-phase phenomena, as well as physics measurements on material displace-nant, neutronic effects will be introduced. Cladding relocation experiments had been performed both in and out-of-pile for a range of thermal-hydraulic conditions. These experiments consist of the TREAT reactor L (Refs. B-2 through B-5), R (Refs. B-6 through B-8) and F (Ref. B-9) series and the out-of-pile Argonne flooding and entrainment measurements (Ref. B-10). Of equal importance are the complementary set of OPERA (Ref. B-10) and TREAT R series sodium voiding and two-phase flow regime measurements. These experiments are continuing to substantiate the general conceptions of one and two-dimensional sodium voiding behavior under U1FBR thermal-hydraulic conditions and their representation within the SAS code (Refs. B-ll, B-6, B-10) for accident analysis. Thus, the initial conditions and forces which affect cladding relocation can be reasonably established. B-1

Results from most of these experiments have been documented in the open literature and specifically described at the DOE sponsored Base Technology Briefings (Ref. B-12, B-13) during 1974. Tables B-1 and B-2 list those experiments considered pertinent to cladding relocation dynamics and indicate new data which were not covered in the 1974 Base Technology Briefings. To maintain a perspective on the modeling employed for this report the tables have been left to indicate that several experiments were incomplete at the time. Although not specifically addressed herein, it should be noted that a large field of experimental data on material properties, flow dynamics and stability criteria, sodium superheat and boiling phenomena, etc., is being drawn upon to support and form the basis for interpretation of the experi-ments. This supportive literature is documented in the primary references used herein. Further, the ongoing experiments in foreign countries (e.g. , Ref. B-14, B-lS) are not being addressed to a lack of detailed knowledge of their experimental conditions and results. Such information will be applied within the CRBRP as possible. ,g The key tests and conclusions which were drawn in regard to cladding motion in theCRBRP are discussed in what follows. The impact of these conclusions is best represented by examples from Section 7 which provides a best estimate scenario of these events. In compliment with the conclusions he' rein, the ANL staff have recently reviewed the question of cladding relocation and have concluded that (Ref. B-l) cladding relocation uncertainties do not contribute significantly to the overall uncertainty regarding the consequences of the LOF accident in the CRBRP. The OPERA seven pin experiments and supporting calculations are employed to conclude that the characteristics of sodium voiding in an LMFBR 217 pin fuel assembly will be (Ref. B-10): o Initial vapor formation at low or zero bulk superheat (< 10 C) near the assembly outlet, in its interior subchannels. o Inlet flow reversal will occur with limited upstream voiding of the assembly due to pressurization of the vapor producing region (even with subcooled flow channels existing at the assembly radial boundary). - B-2

o Upstream voiding of the assembly is related primarily to heat capacity constraints. o A liquid sodium film remains on the cladding with an average subchannel void fraction of approximately 85-90 percent. o At LMFBR power densities, liquid sodium is not expected to re-enter the flow channel af ter voiding in the LOF sequence. Comparisons of the OPERA results with R series measurements and SAS calculations are quite satisfactory (Refs. B-6, B-16). The SAS analytic model has been shown to employ an incorrect two-phase flow regime prior to inlet flow reversal but the effects of this on a 217 pin assembly void progression will be quite minimal. Additionally, the experiments and three dimensional calculations show that at the time of sodium voiding (for pump coastdown rates similar to FFTF and CRBRP), a radial distribution of cladding temperature exists due to over-cooling in the outer three rings of pins within a fuel assembly. Quantita-tively, approximately half of the cladding, radially, will be some 100-?00 C colder than the central assembly pin cladding (Ref. B-10). Thus, these basic sodium voiding experiments, calculations with SAS and other codes (Ref. B-10) provide confidence in predicting the initial conditions in the fuel assembly at the time of cladding melting. Another basic factor, which is reactor dependent, is the neutronics effect of sodium voiding the active core region. fleutron leakage and spectral effects will affect changes in the Doppler coefficient and the net multiplication factor. Thus, a change in reactor power is indicated, downward for FFTF and upward for CRBRP. A substantial experimental and analytical effort was being made to verify the neutronic effects due to sodium voiding, steel, and . fuel relocations in the CRBRP core (Ref. B-17). The reactor power is important since it determines the axial location of initial clad melting and the time interval available to ot:tain substantial fuel melting at the same location. For the CRBRP, the reactor power is f rom one to four times nominal during cladding melting (0.5 to 2 seconds) prior to significant fuel melting. The basic L and R series experiments (12, 3, 4, 5, 6) were performed at approxi-mately nominal power (150 190 watt /gm of fuel). Experiments L5 and R7 were B-3

conducted with power bursts to 5 and 16 x nominal at the SAS precalculated occurrence of clad and substantial fuel melting, respectively. Ttese tests $ are more applicable to combined fuel and cladding motions. Post-test analyses and examinations were still in progress such that detailed conclusions could not be drawn at the time. The Argonne experiments on gas-liquid film interface flow stability are key results in extending available information from traditional engineer-ing fluids (e.g. , air-water) to LMFBR materials. These experiments resulted in physical models for criteria and quantitative data on inception of flooding and entrainment in a liquid metal film-gas flow system, which by dimensional similitude, can be applied to the liquid steel-sodium vapor flow system (Ref. B-18). These physical ideas were incorporated into the CLAZAS subroutine of the SAS code and successfully applied in pre and post-test analyses of the R series experiments to predict cladding relocation (Ref. B-16). The principal error in the calculations was to overpredict the upward plugging capacity of steel. The principal experiment with regard to steel relocation is RS, in which the TREAT energy was terminated af ter clad melting but prior to signi- g ficant fuel melting; based upon SAS pre-test predictions. Post-test examina-tion revealed some upper steel blockage and deposition in the unheated section, but not as massive as the SAS prediction (Ref. B-19) and confirmed a large pretest predicted steel blockage below the heated section. Bearing in mind that the R-series test section is designed to reflect a flat radial temperature profile (modes inner region of LMFBR fuel assembly), it was concluded from these R-series tests, the flooding experiments and the SAS calculations that the basic phenomena of clad relocation in a one-dimensional, radially coherent, test section could be adequately described with SAS. A final conclusion relative to CRBRP which is made from all of the above relates to a prior statement that the CRBRP fuel assembly is not radially coherent at the inception of cladding melting, and that the flooding process is considered to result in a large concentrated pressure drop. Thus, at the onset of cladding flooding in the central region, the local pressure drop 9 B-4

is greatly increased and the sodium vapor flow will be divertea to the outer assembly regions, leading to an unflooding of the central region. This process is considered to result in an axial oscillatory motion of cladding until additional radial melting occurs. The time interval for the latter to occur is equivalent to the onset of fuel motion. Therefore, in the Section 7 base ca'se analyses, the cladding and fuel were considered to relocate together. Additional experiments have run out-of-pile with a 28 pin, full length pie sector representation of a full fuel assembly with radial melting effects and verified these basic conclusions on cladding relocation (Ref. B-1). Because these supporting experiments were not yet concluded, analyses are presented in Sections 7 and 9 to reflect possible nonconfirmatory experi-mental results. The CLAZAS one-dimensional model was allowed to relocate steel based upon sodium vapor drag forces. Additionally, the sodium vapor and steel were purposely coupled and the steel allowed to drain under gravity fo rces . These cases resulted in increased thermal energy generation relative to the base cases, but were still within the Structural Margin Beyond the Design Base. As previously stated, the motions of cladding and fuel are coupled via the reactor design thermal hydraulic and neutronic conditions. Thus, the experiments discussed in regard to cladding relocation (and listed in Tables B-1, B-2) all contribute toward establishing the thennal hydraulic and neutronic conditions at inception of fuel relocations. Most of the experimental measurements already discussed continued into the fuel relocation regime. iwo out-of-pile information sources, not yet discussed, are the HEDL tungsten heated capsule (Ref. B-20) and the Argonne Direct Liectrical Heating (DEH) apparatus, described in Reference B-22. The key test results and conclusions which were drawn upon for analyses are discussed in what follows. Again, Section 7 a: alyses best reflect the conclusions drawn from the experiments. The HEDL tungsten capsule irradiated fuel test series demonstrated physical effects of gas release and resulted in the following HEDL conclusions (Ref. B-20): B-5

1. Significant fission gas release occurs from solid fuel at temperatures of approximately > 2000 C.

2. Fuel fragmentation can occur in high gas content regions during rapid heating (250 C/sec).

3. Extensive gas bubble precipitation and coalescence can occur between 2500 C and melting for time periods on the order of 1 to 2 seconds.

U

4. Gas release between 2000 C and melting can produce fuel motions which can be characterized as dispersal for high heating rates and/or high gas concentrstions, and fuel swelling and foam formation for low heating rates and/or gas concentrations.

The impact of the above on the CRBRP analyses and the SLUMPY subroutine (Ref. B-23) was the explicit representation of time-dependent gas release estimates (correlated, in part, to experiment FGR-15) and the drag forces resultino rrom the slip of the gas past fuel particles, in irradiated fue! channels, 'he mechanism tends to predict dispersal of the fuel af ter

" slumping" initiation from its original location.

The ANL DLH apparatus is being employed to determine the factors influenc-ing the onset of fuel relocation. pellet column integrity and cladding effects (Ref. B-24). These experiments are expected to have a continuing impact on verification of current CRBRP modeling and interpretation of in-pile experiments. The slow collapse of fresh fuel modeled for the CRBRP is based in part ou out-of-pile observations and more directly on hodoscope data from the TREAT L2 experiment. At the inception of fuel motion (hodoscope), the experimental data were interpreted to indicate an upper steel blockage with fluted-tube mel ting. The hodoscope shows a " plastic" (i.e., slow, 10 cm/sec) complete collapse of the upper third of the fuel. A quiescent period of approximately four seconds was abruptly ended by an eructation of fuel upward and outward (s50cm/sec). The upward displaced material partially fell slowly back down to be followed by another eructation some two seconds af ter the first and before TREAT power termina tion (Ref. B-2). O B-6

Such eructations have not been seen during out-of-pile experiments with fresh fuel, in the R6 hodoscope data, nor in the R4 test data (Refs. B-6, B-7). However, these R-series experiments were still in post-test destructive examination and conclusions on the mechanisms of such eructations could not be inferred. TREAT experiment R7 examined the effect of a pov:er burst (16 x nominal) during the LOF sequence. The burst was set by SAS pre-analysis and R6 data to occur during fuel melting but prior to fuel relocation. Preliminary results (Ref. B-8) indicated an inlet blockage formation during the burst and fuel dispersal into the upper reflector region. This is in constrast to the preliminary hodoscope data from R6 (constant power) which indicated a gradual downward collapse of fuel. The primary experiments on irradiated fuel relocation are the TREAT L and F series. In particular, L3, L4 and F1 are at constant power, while L5 and F2 include power bursts. The exoerimental conditions and fuel employed are characterized in Table B-1. Only L3 and L4 were considered to be complete at the time. These experiments have been employed in conjunction with the conclusions stated earlier from the HEDL tungsten capsule experiments to model the fuel behavior for the CRBRP. Hodoscope data from L3 and L4 indicate very sudden, rapid fuel dispersal (eructations). In contrast to L2, prior downward slumping was not seen in the irradiated fuel and material did not fall back down after dispersal. It was the opinion of the experimentors that the mecharism for fuel eructations is the entrapment and vaporization of steel. Howev er, rapid fuel dispersals were seen in the HEDL tests where steel was not present (Ref. B-20) and eructations were not indicated in either the R series or the F1, single pin, experiment. The L5 and F2 experiment results, where steel and fuel are in proximity during rapid fuel melting, were considered too preliminary for inference on this subject. For the CRBRPmechanistic analyses, steel vapcr pressures were not modeled to play a significant role in fuel relocations. Temperature calculations with SLUMPY supported these judgments. B-7

Analyses of experiments with the SLUMPY model have been perfonned by g the SAS code developer (Argonne) with limited success. Dissimilarity of boundary conditions between the HEDL tungsten capsule experiments and the analytic models frustrated the results of a joint HEDL/ANL attempt to calculate the FGk-lb fuel response (Ref. B-23). SAS post-test analyses r# the L-series experiments are sparsely documented with respect to cladding and fuel motions. Again, the radial incoherencies (power / flow), short-heated section, and tight flow loop coupling make the L-series test vehicle a difficult analysis for the SAS-SLUMPY assumptions. The R-series test vehicle provides a cleaner analysis capability and post-test analysis documentation shows good agreement with the R4 post-test neutronradiograph of fuel location (Ref. B-16). Since the R4 (and R6) post-test destructive exam were not available, conclusions on the appropriateness of the SAS analysis would have been premature. It is expected that pre-test analyses of the F series experiments (Ref. B-23), and the DEH apparatus provide the most definitive test and development opportunity for the SLUMPY module, g Resolution of fuel relocation modes and significance to theCRBRP will rely on the following:

1. Continued reduction and analysis of current data

2. Future R, F and P in-pile experiments

3. ANL DEH and HEDL out-of-pile experiments

4. ZPPR measurements of reactivity effects

5. SLUMPY correlations with the TREAT P, R, and F series and DEH experiments.

In conjunction, parametric analyses will be continued to provide insight into feedback mechanisms, identification of important parameters, and quanti-tative evaluation of the safety implicativ Ef these parameters. O B-8

TABLE R-! EXPERIMEllTS PERTINENT TO CLADDING AND/OR FUEL RLi.0CATl0f4 (IN-PILE)

                                                                 l ' FL       fM.                f ; P R r.E f.rfP!" INT /

FAL! Lily irrJ0it.Tinn pt5tr.cy I s tr.'r f uor Pirs t [ '.',1 u settific f r Lis ( Cit'( NT S ('< t c ! ) (en) ('4 s t t/ m)('e t c ?! L2 Pt'ir !! A

                .                    Fresh                         ---          7       31              190               fl so lina i' lor.h A.)c irellr ted OFIQr IO f ec l rei' i ce.

itper and Ir.cr el44fini llu959et. -r e L3 f@ar !! A l't.l .17 in I M t l  ! 1 31 155 fuel ateve ntrer insor ple te t loclage. 1.11 rJ/f t to 3. 51 P'J

                                                                                 ;                      g y;              gr,g , ,rt i al ste a l bi er vges c . t r ant f tf erc.f L4 furK !! A            fvT"[r.r in [Nt t[                        H                 33 to esis t a t time of f uel c r.,< t a t ion.

11-12 A'//ft to 4. 3: L" e6 190 live t ia m r3. e t, tr . t tir J to occur at ts Pt.r A 11 C i+[ft-51 in r.FfR I 3 (fWe .1) f4 Il L./F t to h1 Alj SAS ri otic tc f cia f ricitin i. P3 R t rop Fresh --- I 91 I r;l lo t se tica dep oned for ri fial tert ri 4-ture (r+ r r e er y . GMt ent ial In "' s teel bloct age - no F4 P teop Ircsh --- / 91  !!0 bed 1s(c;'e i t'%I ts.

    #5 R toop                        f r..sh                        ---          7      91              170               5m r i fi c ill r 4 tr r.1 a t e li t tica ac t iom tra..ir,       r      'c t t t e

• e ,6> n ' % pretast pr rilit t iori of rio f ael rut ion.

110 ter at nf r a n- t p. imrer e result , e J L '. A loop Fresh --- 7 91 dr i c rm e a e r vi n<1sc ate i l i t y , (f. ate 3) rl R lona fresh --- 7 91 l' 0 5 i' . n 'em i>. o't ri it in ott ur at %I,"> rr t u t r t 0,e l r e i t t e n. (thte 3) Il F fassute 'P "iC f la ffR !!

                                                          '           It        1       31            7 .1               Try capsule - cal, or clir inar v results.

(rante 3) 12. 7 PJ4/ f t t o 7. M P' f/ F r.'e'.ule t ill. 17 ?, i .i 100 !! ll 1 34  ??S Iie rir" ole ' n: t t li ir o f actults.

                                                                                                                                                                    *   <1ta ru..          4t ti t.,                        1 .< - r

('ic t e 3) II.h C4/8 t to 0.31s i.w.. 5 Ai g ri s i c ' I sm . '. r i ir t ureil fuel e'Itinq __-~~-i - .. - _ _ ~ _ _ _ _ . _ , _ _ _ _ . , Pi1Tl 5 (1) l

• i e . , n. A o f a . r ei s e r 1r qr.iiri. b. t W t hem t rentral sof.f; H i t i e.S . full re* t :ir.t ..r i n, w i t h <1act ored e c it r al soiel.

(7) Flat t:3 rower; c1uivslent rewer for out-of-pile esper f r ents. f)) I .tcr u e,t ont cnver e 1 in 1911 Ecquiarsr y Driefinris (i) Estinted eviruri of 17.s n/rt. B-9

TABLE B-2 EXPER:MENTS PERTINENT TO CLADDING AND/0R FUEL RELOCATION (0UT-OF-P I L E) l AVE UCE - E/PER:"X C'dECTI'.E TEST C0'.0 " ! M.5 CM'IUS lSoi:.:CDOWER

    !                                                                                            I

(.s!./;-;P.0!e 14

    !                                                                                                                                                                                                                              l i F[4                                         Sedit toil tan charic t fris t ?:s             { bli       Ieeeth a ee 1 ay rs;Tf:                      ,,; 7 0       WeII insteu-emtej f:r excee -catal and two-:Pase f!:4 re:' es in                    5 "' s ei a't- *rt*         3; re:':n                      e, e-*=ve. Snare; .uil3rity with prata! :i: cec etry.                             of C' :17 7 8.e                 *  .-4y.                                 ,

p.s,.ies test se: tion. Ce-*-strates (Seven ein tr:3. :ar s e e.i y }  ;;, to zero oalk surerret , anrular-sle: flow tra-s:t'en s* fled rave' sal. art averste aid fricticr. of 30-33

er:c-*

I Claf 2et:!: tion I Dete-ine t-0-D%se f!:odire and Si cie sad " ult O'" ce:-^* y, (s:te 3) visible, omt::rscaie record of t.:- C3  ! ea te s ir-9 t : tari s l a us- Irte aa l s t ai- ** n P ' o f :):s P *s* ft:= :ordittens. Or 3

• s t rJ I M 8 -

I t ;,' ! i m sf*te . 8re t a . "C l l f f ' 'll" *** '09s witn Cr4<ltf drain 3- fioedle sej entrate. p ,e Aro:n 35 > < 13 . ent fla- recaitions. h.e-t<-eica- pie o test Olave' ta verif f r31tal ron-CChere9t CIsfjing (10001*3 - fl3w effe.13.

     .l,-*.

- . -er r e ee %3 i

eis;re ..,:. v..,ty... ..gs. 7,,o pa..r c ri "e '" -31 <i"'iit . Mi""i"* I C ' ' ' * . . [ *C ' - 2.'. ' ", t :s s' *?20 dass:3 ,as rg. 3

                                                                                                       '                                                     ~~~
                                                                                                                                                                        "              271 e*d o f e7 Jil'bric* Cf:1?
                                                                                                 '                                                                                  5 M* " 'PflJe": s re3re;e'*
      ' PMie 2'                                   3. -: 2 r.13         ; g;ss.3.~..j;'

[ m"*"01

                                                                                                                                                                        .,r      cis    m ee-ert of s: ius c;,p:

e nati:3-e-ts. ver,<, , - *- Sed fuel to sw:: Ort PS*R dej C542 ;3':,. 1 rose l'aly! r ?!"335 e Olof*f IJt'O's. '9&l< sis Of da!3

• n p rc1r* 5 5.

I In de*3 la d 5 3 fe t/ r:2: t ' v i '. (410ulaI'C*s. e ry!,-c.:ue :c e- ,- ef,x . g ,u e ,e, . Sir,ie s u. n ta::. ne; :c,. p.u a m t-ste: fiss m m -e.3se <- l tai 09 fr- ci' tai #a f f , irc'td. faca t s I 2 i nt- e

• ni 6, .-e sal'd *gai and ef'ects c' tjs o'l fue!

-, nssie, c3: r-ie r., .-: re2t e sf rae eue- < , t . cn :re . e oos. eit ma. rs:

Pt: t *:"s . t#C' tea .all 4! C' -'* 3 '*.[$ e: . F a l C 3 t ' T1 c o rt t i a y 3 ,s if obser.'ed vi3 Static fla n eav:r:--*

• c.: 3 refiOtr5:af.

5.., er. w

                          ,2)                    ".**        ra ;a - ~- 4*- a s 1' ' r aa i' 5:**Ie 'Jef :?ll *t '"

• s w i ". '

                                                                                                 '                                                       103 75:            ;J!*. P0 0?J;*?C W0r J '8 'I S! s

I e-d 'ersfiate? 'sel t3.. h< i . 1  ::..'N;* ..F*.. ~'* **

• O' 'J'l c -di t on ; Caw n;trate?

                                                      <3:;get'                                     nett f S, eie *r

• d

      !                                                                                                                                r. ar r "i '                     TOI F                     J ' 'b7 Y D5 3 W i
                                             ;                                                     wt c3: gi- c: -                 '.r        -ii,-                     w ier,'r! ra  W m'
                                                                                                                                                                                              . " :t e ri m i cl -

I l ei , r-stront

      .                                      }                                                   .

(!) F;> to) ?:,e ; ewiv:1. ! M..f- fc- : 3r-21:e e :--i+c , (2) E s:e- %- . ac t ce v---d f n t 'J's deo.:3!.cf Or'e' m (3) Est W !et -s.' .- c ' 12.9

                                                            ~

O O O

References B-1 Bohl, Cahalan and Ferguson, "An Analysis of the Unprotected Loss-of-Flow Accident in the Clinch River Breeder Reactor with an End-of-Equilibrium-Cycle Core," Argonne National Laboratory, June 1977, (ANL/ RAS 77-15). B-2 G. Eberhart, et al . , " Final Report on the L2 Loss-of-Flow Experiment,"

        ,rgonne flational Laboratory, July 1974, ( AfiL/ RAS 74-10).

B-3 E. W. Barts, et al . , " Fuel Dynamics Loss-of-Flow Test L3 (Final Report)," Argonne flational Laboratory, January 1975, ( ANL/ RAS 75-2). B-4 J. G. Eberhart, et al. , " Final Report on Test L2, A Loss-of-Flow Experi-ment," Argonne flational Laboratory, August 1975, (ANL/ RAS 75-16). B-5 R. Simms, et al . , " Loss-of-Flow Test L5-Type Irradiated Fuel (Interim Report)," Argonne flational Laboratory, August 1975, (ANL/ RAS 75-30). B-6 M. A. Grolmes, et al . , "R-Series Loss-of-Flow Safety Experiment in TREAT," Proc. Am. Nucl . Soc. Fast Reactor Safety Conf. , (CONF-740401), Beverly Hills, Ca. , April 1974, p. 279. B-7 B. W. Spencer, et al . , " TREAT Loss-of-Flow Safety Experiment R6," ANS Transactions 21, June 1975, p. 287. B-8 B. W. Spencer, et al . , " TREAT Loss-of-Flow Safety Experiment R7," Alls Transactions 22, November 1975, p. 424. B-9 R. G. Palm, et al . , " Loss-of-Flow Test F1 on a FFTF-Type Fuel Element," ANS Transactions 22, flovember 1975, p. 427. B-10 H. K. Fauske, et al. , "An Assessment of Voiding Dynamics in Sodium-Cooled Fast Reactors," Argonne flational Laboratory, August 1974, (ANL/ RAS 74-20). B-li F. E. Dunn, et al . , "The SAS3A LMFBR Accident Analysis Computer Code," Argonne National Laboratory, April 1975, (ANL/ RAS 75-17). B-12 Regulatory Briefing, Safety Technology Meeting on TREAT Fuel Behavior Experiments, Argonne National Laboratory, August 1,1974. B-13 Regulatory Briefing, Safety Technology Meeting on Coolant and Cladding Dynamics and Thermal Interactions, Bethesda, Md., September 24, 1974. B-14 H. Kwast, "The Behavior of Fast Reactor Fuel Pins Under Loss of Coolant Flow Conditions - (RCN)," Proc. Am. Nucl. Soc. Fast Reactor Safety Conf. , (CONF-740401), April 1974, p. 550. B-ll

Re ferences h B-15 A. Alexas, et al. , "Out-of-Pile Simulation of Fuel Pin Behavior in Sodium Cooled Fast Breeder Reactors by U02 Rods Heated by Electrical Current - (KFK)," ibid, p. 535. B-16 G. Hoppner, "SAS3A Analysis of R-Series Experiments," Argonne National Laboratory, August 1974, (ANL/ RAS 74-14). B-17 " Critical Experiments and Analysis," Thirteenth Quarterly Report, General Electric Company, January 1975, (GEAP 13371-13). B-18 Ishii and Grolmes, " Inception Criteria for Droplet Entrainment In Two-Phase Cocurrent Film Flow," Argonne National Laboratory, October 1974, (ANL/ RAS 74-25). O O B -12

Appendix C An Analysis of the Reactivity Effects of Bubble Collapse _in a Boiled-Up Molten Puol in CRBRP C.1 Introduction It has been proposed by several authors (Refs. C-1, 2 & 3) that, in a power excursion terminated by hydrodynamic disassembly, positive reactivity feedback due to loss of streaming paths must be considered. The physical reasoning behind such a proposal is clear; loss of streaming paths reduces neutron leakage, thus making more neutrons available to cause fissions. Al-though the magnitude of this effect is small, it can, in theory, augment the energy release if it is introduced in the neighborhood of a few cents above prompt critical. Accordingly, the phenomenon has been the object of some study over the past few years (Refs. C-3, 4 & 5). It has been studied in two contexts: that of the " exploding" fuel pin (Ref. C-5) into channels voided of sodium, and that of collapse of bubbles in a boiled-up pool (Refs. C-3 & 4). In each case the neutron behavior can be adequately modeled with Monte Carlo calculations; the validity of diffusion theory, or even neutron transport theory is still being established. Nevertheless, such calculations have been attempted Sud their results used in analyses of disassembly of boiled-up molten pools. In these studies, it was shown that prompt collapse of bubbles added positive reactivity in such a manner as to delay somewhat the negative displace-ment reactivity. The pool sizes used in these studies have tended to be small, and hence have significant neutron leakage. The loss of streaming paths would be more significant in these systems. The pools also were envisioned to consist of bubbles that were uniform in size and evenly dispersed throughout the volume. As will be seen below, such a continuous-liquid regime is not envisioned to arise in hypothesized CRBRP accidents. Instead, a continuous vapor regime is expected, in which the pool would be fully boiled up. The reactivity effect of bubble collapse was, therefore, not expected to be as largo in CRBRP as in the smaller systems. Nevertheless, the analysis was dnoe to determine the magnitude of the effect. The VENUS-II code (Ref. C-6) was modified to account for the reactivity effects of bubble collapse, and various parametric calculations were performed. C-1

This appendix begins with a discussion of the domains of applicability of the Behrens model (Ref. C-7), followed by a discussion of the derived model g used to calculate the reactivity effect of bubble collapse. The modifications made within VENUS-II are identified, and the results of a homogenized pool, recriticality analysis in CRBRP, with consideration of the reactivity effects of bubble collapse, are presented. Finally, conclusions are drawn, based upon the information contained in this study. C.2 Domains of Applicability Both Nicholson (Ref. C-3) and Gelbard (Ref. C-2) agree that Monte Carlo methods are required to do an adequate analysis of the consequences of closing streaming paths in reactor lattices. More specifically, the " exploding" fuel pin problem cannot be solved using the Behrens method which is based on one-group diffusion theory. The relatively accurate results obtained by Webb (Ref. C-1) when he applied the Behrens method to such a situation may be fort-uitous, since he was applying it to a geometric configuration for which the Behrens theory breaks down. On the other hand, the Monte Carlo calculations of Dunn and Lell for CRBRP led to uncertain results (Ref. C-5); the uncertainty in the reactivity was of the same magnitude as was the calculated reactivity - each about one dollar. The upper bound was, therefore, judged to be about 2 g dollars. More recently, Lell (Ref. C-8) has obtained more conclusive results from a newly developed Monte Carlo method to compute the eigenvalue (and hence reactivity (in an infinite lattice. He found that homogenization of the rods increases the eigenvalue by 0.005 + 0.006, (equivalent to about 1.5 dollars). To date modeling modifications to VENUS-II have not been proposed to account for the effect of cuttir,g off streaming paths in reactor lattices by exploding fuel pins. In any case, since the effect is rather small compared with that predicted for btbble collapse using Behrens' theory (as will be seen below), it is judged that a realistic model would predict negligible differences. In contrast to the " exploding" pin case, the Behrens model has been shown to be appropriate for the analysis of bubble collapse in molten pools contain-ing dispersed bubbles and undergoing recriticalities. Previous analyses have been for pools with relatively-low void volume fractions, such that the system could be well-defined as a continuous liquid, in which vapor bubbles were interspersed. The types of systems actually envisioned for CRBRP, on the other hand, tend to be characterized more as continuous vapor regimes (Section 10) h in which liquid droplets of fuel, steel, or fuel-steel mixtures would be interseprsed in a sea of vapor. C-2

Compared with an equivalent continuous-liquid system containing bubbles (that is, the same materials, with the same void volume fractions), it would seem that the reactivity in a continuous vapor should be lower, since more long streaming paths should exist, particularly near the pool boundaries. However, since no quantitative estimates of this are known at present, it is only possible to treat the reactivity ef fects of the continuous-vapor system in a manner similar to the treatment of continuous-liquid systems by defining " equivalent" bubbles. One may do this by analogy with the continuous-liquid system, as follows. The maximum diameter of a stable liquid droplet before breakup of the droplet (due to aerodynamic forces from the relative motion between the phases) was calculated to be on the order of m0.5 cm. Since the volume fraction c. the liquid in the system considered below is m0.5, the volume fraction of vapor is also s0.5. An " equivalent bubble", therefore, would also have a dia-meter of about 0.5 cm. However, in order to account for the uncertainties involved in treating the continuous vapor phase system with a continuous liquid phase bubble model, a range of equivalent bubble diameters (from 0.3 cm to 6.5 cm) were used in the calculations described in the following sections. C.3 The Goldsmith-Nicholson Model C.3.1 The Behrens Theory Goldsmith and Nicholson (Ref. C-9) developed expressions for the reactivity effects of bubble collapse based upon a one-group diffusion theory model and a theory developed by Behrens to account for the reactivity effects of loss of streaming paths in a reactor. The theory assumes that first-order perturbation theory is valid, and that the reactivity effect can be related to changes in the diffusion length. Behrens derived equations for the root mean square distance travelled by a neutron in non-porous material and a similar equation equation for material with voids in it. The ratio of these equations is expressed as follows: For widely-spaced voids, 2 k = 1 + 2t + 9"Y + , II) L" o and for closely spaced voids, 2 h=1+24+$ 2 + Qr 4 , (2) Y L o C-3

where, 2 L = root mean square distance travelled by a neutron in material h containing voids. L! = root mean square distance travelled by a neutron in nonporous ma te rial . 4 = ratio o'f void volume to material volume r = hydraulic radius of the void; for a spherical bubble this equals 2/3 of the bubble radius. A = neutron mean free path in the non-porous material. Q = ratio of mean square chord length to the square of the mean chord length through a void. For a spherical bubble, Q = 9/8 = 1.125. Behrens also developed an expression that he called the " general lengthening formula," because it reduced to eqs. (1) and (2), respectively, when in the region of applicability of each. The formula, however, has a very limited domain of applicability, since it assumes that s neutron will enter either n or n+1 holes (no more, no less). Sur.h a situation can only arise when voided regions are regularly spaced, and fairly far apart (i.e. , g considerably more than one mean free path apart). The fact that +he formula, given by 2 2 L 2r 2 = 1 + 24 + exp(/ g )12r/ AT --lA ,' _Qr i (3) L reduces to eqs. (1) and (3) is fortuitous. Since it is not applicable for the boiled-up pool configuration, it will not be discussed further. Behrens defines "widely spaced" to mean that a neutron has a finite probability of passing through at most one void during its free flight, and " closely spaced" to mean that the probability of the neutron passing through a void is independent of any voids it may have already passed through during its free path. Obviously, the widely-spaced-holes formula has only a limited range of validity. Behrens defines this to be suun that the criterion V sA it, satisfied, where V is the volume of fuel in a cell, s is the surface area O C-4

of the void in the cell, and A is the mean free path in the liquid. Thus, the voids must be very far apart. The only criterion for the validity of the " closely-spaced-holes" formula is that the dis 'jution of voids be relatively random. Behrens quotes the domain of applicability to be when Vas A. In reality, the domain is much greater than that. Only when it is not possible to write an expression for the probability of entering n holes (in which the probabilities of entering the previous n-1 holes are also included) is the expression invalid. The restriction V sA exists only when a highly regular array of voids exists. Such a geometry is not expected in boiled-up pool configurations, even when in a continuous-vapor phase. Therefore, use of this fonnula is considered to be appropriate, and the ensuing development will be based upon its validity. C.3.2 The Goldsmith-Nicholson Bubble Collapse Formula Consider a bubble with radius r, surrounded by liquid multiplying medium (characterized by k,) with a mean free path . Goldsmith and Nicholson show that the total reactivity available from bubble collapse, when the voids are closelyspaced,isgivenby![k-lb h p =I I; 0.75r j 4 (4) V '

                          -/(A / (1+t)2 '

It can be similarly shown that, for widely-spaced voids, [k-lb[0.75r;

                          =

h t 7j (5) 1+24 '

                %.=(k, / (A /

It is instruct've to compare the two expressions as functions of the void volume fracticn Fy ; t = F /(1-F y

                                        ).y Table C-1 shows such a comparison for r = 0.5 cm (the "best-estimate" value), k, = 1.445 (which was obtained from FX-2, 2-D diffusion theory calculations with a zero current (no leakage) boundary condition), and A = 4 cm. Note the very close agreement for small values of Fy. The formulas agree to within 35% even when yF = 0.5 (where the widely spaced formula is particularly invalid).

C-5

In order to use the closely-spaced-holes formula to compute the reacti-vity effects of bubble collapse during the disassembly process, it will be necessary to evaluate the change from one time to the next. The reactivity added from t = gt to t = t) is given by the difference between the values Namely, available at t = gt and at t - t). vpB *P vo -P yl IO) To evaluate eq. (6), it will be useful to express the quantities appearing in eq. (4) as functions of Fy . Turning first to , note that the liquid density decreases as it expands into the bubbles fromo t to t). Since the mean free path in the liquid is inversely proportional to the liquid density it is directly proportional to the liquid volume. Hence, the mean free path at time t = t) is A) =A g Vg/VLo " A o II ~ fvl)/(I-fvo) , (7) if it is assumed that the total volume of the system is unchanged. Turning next to r, note that the total void volume is given by 3 g V y = h nnr , (8) where n = total number of bubbles r = average bubble radius. If it is assumed that the total number of bubbles does not change as the liquid expands and that the system volume is constant, then r V F

                        =

VI v1 (9) y F r g vo vo or 0.33 r) = rg [7v1 )1 , (10) (fvo/ O C-6

Since this variation is small, the bubble radius will be assumed - The ratio t is explicity given by cons tant, i .e. , rj = rg. (11) 4 = Fy /(1-Fy) , so that (12)

                          = Fy(1-Fv)

(1+t)2 Substituting Eqs. (4), (7) and (12) into eg. (6), and assuming rj=r, g one obtains

                         !k-l\[0.75r\                                        (13)

I (1-Fyg) (F yg-F y )) apB"kk * /k O/ Equation (13) yields the reactivity change resulting as one bubble in To obtain the a surrounding liquid reduces from volume fraction F yg to Fy ). total contribution from collapse of all bubbles, one must sum, with an Thus, appropriate weighting factor, over the entire reactor. II N SP

• W ap Bn n V (I4) v n n n=1 n=1 where N = total number of volume elements (Nodes),

W = weighting function in node n, n

           = contribution to reactivity change from node n ap8n                                                                  .

V volume f node n n If the definition k - -l \!0 75ro j (1-Fyg) (15) A y =l  ; Y~ ) N A o / is made, then equation (13) can be rewritten as (16) apB = A y (F yg -Fyj) C-7

i The total available reactivity (if geometric weighting is neglected) is given by eq. (16) when all of the voids have been filled, i.e. , when g F yj = 0.0. It is, therefore, possible to compute a value of the proportion-ality constant Ay, and reactivity from bubble-collapse py as functions of

he values of the parameters. The results of pne such computation are presented in Table C2. The values of k,, and A; chosen are those character-istic of the boiled-up pool configuration on wifich the VENUS-II calculations were performed. In addition, it should be noted that F yg = 0.47 for the same cases. Note that, for F =g 0.47, and r = 0.5 cm, that A = 0.0153 and the total available reactivity is about two dollars. Note, in addition, that the value. of A y is nearly twice as great if F yg = 0.1. Thus, the effect of bubble collapse on the parameter A is smaller, y is greater in cases where Fyg as long as reactivity remains available.

C.3.3 Comparison With Monte Carlo Calculations Lell (Ref. C-8) has recently developed a Monte Carlo method for computing the eigenvalue, as a function of buckling in an infinite lattice. The method has been used to test the accuracy of Webb's application of the Behrens theory to the " exploding pin" problem, and the Goldsmith-Nicholson g extension of the Behrens theory to the bubble collapse problem. For the

" exploding pin" problem, Lell shows that his Monte Carlo calculations are accurate to within 10%. They are, in addition, considerably lower than Webb's predictions, which are based on exter. ding the Behrens theory into a regime where it is not strictly valid.

The criginal Webb work, and Lell's Monte Carlo calculations, were for calculation of void worth in the Fenni and EBR-II reactors. Since it was desirable to determine the effect for CRBRP,Lell performed a multienergy, Monte Carlo calculation in a simplified CRBRP-type lattice cell geometry. He found that homogenization of the rods (i.e. , closing of f the streaming paths) increased the lattice eigenvalue by : 0.005 + 0.0006 (about 1.5 dollars). Such a finding suggests that treatment of the Behrens effect in direct-disassembly analys;s would lead to energetics augmentation of the same order as (or slightly less than) the augmentation found in the calculations presented below for boiled-up pool recriticalities. O C-8

For the bubble collapse problem on the other hand, agreement between the closely-spaced-holes formula and Monte Carlo calculations for random cubes (with spherical bubbles enclosed) was very close (to about 10%) for A = 4 cm, Fy = 0.25, and r = 1 cm). Lell also considered regular bubble lattices, in order to assess the validity of the " general lengthening fo rmul a . " Agreement here was not good, except for very small values of the mean free path (m 1 cm or less). Agreement was close, throughout the range of A, between Monte Carlo calculatioss for random cubes and Monte Carlo calculations for regular cubes. In fact, these values bracketed those computed with the closely-spaced-holes formula throughout the range, further verifying its validity. Lell also performed a multienergy Monte Carlo calculation for a regular critical bubble lattice, with parameters typical of a molten pool in CR8RP (with Fy= 0.25, r = 0.8 cm, k , = 1.5719 1 0.0031). The resulting eigenvalue change is 0.011 ! 0.001. Corresponding one-group calculations yielded 0.014 + 0.002. These values compare very well with the Behrens-theory-based values (see Table C-2, for F yg = 0.2 and 0.3, and r = 1 cm). Finally it should be noted that some Monte Carlo calculations have been done (Ref. C-10) to detemine the appropriateness of applying the Behrens theory to bubble collapse in a boiled-up pool. As McLaughlin (Ref. C-ll) has observed, hoaever, they were for configurations for which the closely-spaced-holes formula does not apply. Since the void arrays were highly regular, the general lengthening formula is more suitable. Indeed, agreement is quite good becween these Monte Carlo calculations and the use of the general lengthening fomula. C.4 VENUS-II Modifications Nichcison and \an Diemen (Ref. C-3) modified VENJS-Il to include a treat-ment based on Goldsm-lth and Nicholson's extension of the Behrens theory; the modifications are dis:ussed on pp. 93-97 of their report. These modifications were adopted for the present study as well, such that eq. (14) is used to compute the incrementa! reactivity feedback from bubble collapse. C-9

The basic modifications involved computing the change in void volume fraction from the temperature increase of the liquid fuel. The following h equation of state (which is basically the single-(liquid) phase of the ANL equation of state in VENUS-II) is used in each node (i,j):

                                           -4                         for T f
                                                                            <Tm
                 ' 11.2892 - 5.1013 x 10       T 7
                                          -4                          f r T <T pf =       fl.2892 - 5.013 x 10      Tm - 0.36223(Tf-Tm)           m f<Tm
                                           -4
               ,    10.9277 = 1.7169 x 10      Tm - 6.8182 x 10-4 T7 for T >T f m where T y= fuel temperature                                         (17)

T = fuel melting temperature m of = fuel density The fuel density change is related to the change inyF in node (i,j) by Fy =1-F ss

                                  -I na -I f,                                (18) where F ss = Mss /Pss/Vjj                                                 g F

na =Mna/Pna/Vjj F f = Mf /pf/V jj The subscripts ss, na, and f stand for steel, sodium (if present) and fuel, respectively, and V jj is the volume of node (i,j), which changes with time. Note that the changing value of of causes Ff to change, which, in turn, causes Fy to change. It should also be noted that these modifications in no way change the equation-of-state algorithm, which is coupled with Lagrangian hydrodynamics to ccmpute the displacement reactivity. C.5 Application to Homogeneous Pool Recriticality Analysis C.5.1. VENUS-II Model Used The VENUS-II model is the same as that used for the homogenized core re-entry disassembly calculations reported in Section 11. The control O C-10

assemblies are gone, sodium is removed from the core and upper blanket, and the inner and outer core zone fuels are homogenized. The model mesh structure is 40 x 40; the regionwise input quantities are given in Table C-3. The core regions are 2 and 5. Note that the initial void fraction in the regions is 0.47. It should also be noted that, due to the homogenization process, the value of keff for this system is computed to be 1.061, and k , was found to be 1.445. The reference case for the series of calculations reported below is that shown in Table 11-8 of Section 11, for which the initial power is 21 times nominal, and the driving reactivity is inserted at 305/sec. The quantity Ay was treated as a parameter, ranging from 0.0 to 0.10. As stated above, its most probable value is about 0.015. Two types of weighting functions, W(r,z), were considered. Each was used by Nicholson and van Diemen. A constant value of 0.7024 was one choice, and a 1.near variation with power, i.e. , W(r,z) = l-P(r,z)/P max (I9) was the other. The latter choice is considered to be a better representation, since it accounts for the fact that the reactivity change due to the collapse of bubbles is proportional to the neutron flux gradient, i.e. , neutron current. Equation (19) therefore satisfies the zero current boundary condition at the core center, which is the point of maximum power and maximum neutron flux. The fact that the constant weighting provides an overestimate of the inner-core behavior can be seen by examining Figs. C-1 through C-4, which show the variation in W(r,z) at the radial centerline, axial centerline, the top of the core, and at the outer edges of the core. The dashed lines represent the constant weighting, and agree much more closely with the linear-variation with power weighting at the core edges than in the central regions. Note that the blanket regions have a very high weighting. The void volume fraction changes very little in the blankets, however, and then only in the latter stages of disassembly, due to the rapid expansion causing shutdown. C.5.2 Influence of Bubble Collapse During Disassembly Figure C-5 shows the reactivity behavior for Ay = 0.025. The bubble collapse reactivity enters in a manner similar to the displacement reactivity, C-ll

but with oppr: ite sign. While the power is still rising its magnitude exceeds that of the displacement reactivity. This behavior is to be expected, since the same rechanism, expansion of liquid fuel as its temperature increases, is the ca ise of both rei2ctivity effects. Once past peak power, the displace-ment reactivity 6 ninates, since by this point the fuel vapor pressures have increased sufficiently to disp ~se the molten pool. The effect of using a corstant weighting function, instead of one which reflects the influence of the neutron current, can be seen by comparing the temporal variations of the bubble collapse reactivity for each case, flote that it builds up neare quickly for W = 0.7024. Since the weighting functions do not differ too much from one another at the pool edges (see Figs. C-3 and 4), the difference directly reflects the overestimate of the reactivity effect of bubble collapse in the internal regions of the core when the constant weight-ing is used. C.5.3 Energetic Consequences Table C-4 lists the results of varying Ay from 0.0 to 0.1. Both linear-with power and constant weighting are considered. These results are also plotted on Figs. C-6 through C-8. flote that, for A = 0.015, and W = l-P/Pmax' Q the average core temperature is 4615 K, the work-energy to sodium slug impact is 97 MJ, and the work-energy to one atmosphere 545 MJ. These represent the best-estimate values when the Behrens ef fect is considered. Also plotted on the same set of figures are curves showing the effect of varying the driving ramp rate from 30$/sec to 60$/sec, with no consideration of the Behrens effect. flote, for example, that the work-energy to one atmosphere varies from 473 MJ, whenb=30$/sec,upto1242MJwhen5=60$/sec. Such an increase corresponds very closely to that obtained when using yA = 0.1, and linear weighting, or using Ay =0.065andconstantweighting,when$=30$/sec. Indeed, such comparisons provide a good measure of the relative degree of sensitivity of the results when the Behrens effect is considered. For a given Ay , an " equivalent" ramp rate can be determined which would lead to the same energetic consequences in the absence of the Behrens effect. Thus, for A y = 0.015, W = l-P/Pmax, the equivalent ramp rate to obtain 545 MJ to one atmosphere is about 345/sec. This increase of 4$/sec in ramp rate is well within the degree of uncertainty involved in choosing a ramp rate for recriticality analysis. O C-12

It should be recalled that the 30$/sec ramp rate was chosen based on the hypothesis that fuel from 18 assemblies was re-entering coherently under gravi ty. Such a hypothesis is highly arbitrary and nonphysical, chosen only to access the degree of pessimism necessary to obtain energetic consequences sufficient to challenge the structural integrity of the plant. A different number of assemblies (either more or less) could have been chosen for the assessment. In this case the corresponding ramp rate at prompt critical would also have been different and the variation could exceed the variation associated with the Behrens effect. In this context, augmentation from the Behrens effect seems superfluous. Energetic recriticalities are deemed highly unlikely in the first place - no means for obtaining them can be rigorously identified - and, if they are postulated, then the driving ramp rates chosen are necessarily judgmental. Another point of interest can be made with the aid of Fig. C-9. That is, only a very small portion of the available reactivity (s 2%) from bubble collapse is actually added. Indeed, in the best-estimate range (A y y 0.015), the added reactivity is only a few cents. As was noted above, it is added at a rate of 4-5 $/sec, over a period fo a few milliseconds. Hence the slight augmentation of the energetics before hydrodynamic displacement effects terminate the transient. It is clear, then, that it is not the total reactivity addition, which is reflected in the value of A y, mostly from the choice of the initial bubble radius and initial void volume fractions. C.6 Conclusions The important conclusions emerging from this study can be sunmarized as follows:

1. The Behrens closely-spaced-holes formula is applicable, the Goldsmith-Nicholson formula based upon it is valid, and the Nicholson-van Diemen application of it to VENUS-II is appropriate for assessing the reactivity effects of bubble collapse.

2. Comparison of the Behrens theory with Monte Carlo calculations further establishes the validity of the Behrens theory.

C-13

3. The energetic consequences increase somevthat when the bubble collapse reactivity is accounted for in transition-phase-recriticality analysis in CRBRP. The increase is not large, however, when the "best-estimate" value of the equivalent bubble radius is chosen. An increase of effective ramp rate from 305/sec to 345/sec results, with a 15% consequent increase in work-energy to one atr,1osphere.

O O C-14

llk TABLE C-1 C0!TARI50:10F TOTAL AVAILABLE CUliBLE COLLAPSE REAC1 PiiTIES PREDICTED BY Tile CLOSELY-SPACED A iD WICELY-5 PACED FOR"ULAS WHEll r = 0.5 cm, k ,= 1.445, AND A= 4 cm Fy p y.close p y, wide 0.1 .00256 .00263 0.2 .00462 .00481 0.3 .00607 .00666 0.4 .00693 .00825 0.47 .00719 .00923 0.5 .00722 .00963 C-15

IABLE C-2

      ' ARI ATIOT10F THE PR0t nRTIOilALI TY C0i!STA!if A,,

TOTAL AVAILABLE BUBBLE COLLAPSE l'EACTI'lITY nv AS Ai') ll!E $ FllitCT10ilS OF F g and r g, llHEll k,= 1.44b END i g = 4 an F,/ 0 r A ov(.9.) p (i)' o y v 0.10 0.25 0.01299 0.00130 0.37 0.50 0.02598 0.00260 0.74 1.00 0.65197 0.00520 I.48 2.00 0.10394 0.01039 2.97 0.20 0.25 0.01155 0.00231 0.66 0.50 0.02310 0.00462 1.32 1.00 0.04619 0.00924 2.64 2.00 0.09239 0.01848 5.28 0.30 0.25 0.01010 0.00303 C. '7 0.50 0.02021 0.04606 I /3 3 16 g 1.00 0.04042 0.61213 2.00 0.08084 0.02425 6.93 0.4 0.25 0.00866 0.003:6 0. T:i 0.50 0.01732 0.00E93 1 'M 1.00 0.01465 0.01:86 3.'M 2.00 0.06929 0.02e72 e- '- U.4/ 0.25 0.00765 0.00360 I.03 0.50 0.01530 0.h0719 2.6 1.00 0.03060 0.01433 3.II 2.00 0.06121 0. 02 f' 7 7 3.22 0.50 0.25 0.00722 0.00361 1 O.50 0.01444 0.00722 ' ' 'd 1.00 0.n2E87 0.01142 J .- l 3 2.00 0.057/4 0.02837 'I.15

                       * $1.00 = .0035 C-16

TABLE C-3 REGIO::',7ISE INPLT QU.UT!ITIES FOR VE:iUS-II CALCULATIO:;5 Region Radial Dimensions (c:) ,tclal Di=ensicus(cm) Volume Fractions Lauer Upper Fuel Sodiun Steel Void No. Inn er du:er 1 0.3 60.911 0.0 35.711 0.3475 0.41S9 0.2336 0.0 137.75 0.3183 0 . 2 ' '. 0 0. 4 6 6 ~; 2 0.0 60.911 35.711 0.0 3 0.0 60.911 lJ7.75 163.46 0.3475 0.0 0.2336 0.4159 4 60.911 94.061 0.0 35.711 0.3475 0.4189 0.2336 0.0 a ' 5 60.911 94.061 35.711 137.75 0.3183 0.0 0.2140 0.4567 6 60.911 94.061 137.75 163.46 0.3475 0.0 0.2336 0.412'. 7 94.061 122.32 0.0 81.73 0.5572 0.2546 0.15S2 0.0 8 94.061 122.32 S1.73 163.46 0.5872 0.2546 0.1532 0.0

TABLE C-4 SUteMRY OF RESULTS OF DISASSEMBLY CALCULATIOtt$ Weighting A

                         # Initial Bubble     Average Core     Wc,k to Slug   !! ark to One Void Reactivity Function                 Radius (cf     Toperature ("K)     Impact (MJ) Atmosphere (MJ)    (dollars)
      .7024       0.0         0.0                4540               80            473            0.0 (I )
      .7024       0.005       0.163              4582               88            503            0.014 n

1 .7022 0.01 0.327 4621 95 541 0.030 co

     .7024        0.025       0.817             4758               12]            664            0.002
     .7024        0.05        1.634              5032             185             938            0.194
     .7024        0.10        3.263             59C0              503           2009             0.511 1-P/P        0.0         0.0               4540                80           473             0.0 1-P/P ma     0.005       0.163             4563                84           492             0.012 1-P/P    ,

0.01 0.327 4590 90 514 0.025 1 -P/ P. d id X 0.0:5 0.817 4670 107 600 0.066 l-P/P , 0 . C '. 1.634 4030 14e 741 0.147 1-F/P 0.: 3.268 5 '5 , 251 1135 0.276 (1) Section 11 Base Case O O 9

1.0

0. 8 - W(r,z) = l- P(r,z)/P y -__________ _____________ .______.__.._______ _ _ _ _ _ _ _ _ . . . . .

0. 6 - W = 0.7024 o

a w e 0.4 - 9

0. p . 5

                                                                   = .

o x 0.0 i - J./ - i i e i - =

0. 20. 40. 60. 80. 100. 120. 140. 160.

Z(cn) Figure C-1 Weighting Function vs Height at Core Center

1. 0 -

0. 8 -

W = 0.7024 y 0.6 - '? N o 0.4 - W(r,z) = l- P(r,z)/P max

0. 2 -

0.0 , , , , , 0.0 20. 40. 60. 80. 100. 120. R(cm) Figure C ? Weighting Functirn vs Radius at Core Midplane

  #                                                       #                                                 e

U 2 1 e r _ . o

           .                                  'O             C

_ 0 1 f o _ p o T

            .               x
            .               a                                t
            .               m                                 c P                           .

_ / '0 s _ ) 8 u _ z, i d r m a ( c R

             .         P                                   S

_ O s

                          -                                    v
             .         l                               )

0

             .                                          m6     n
                         =                                     o
                                              '0       (

c1 i

                       )                         6
              .                                        R =    t z,                                    c r                                 Z   n

( u 0 F _ W _ g

               .                                                n
                                                    .         i
               .                               '0              t 4            h

_ g

               .                                              i e

W 4 . 3 2 - 0 _ C 7 . e 0 . 2 r u

         = .                                                    g

_ i W _ F _ 0 0 6 4 2 0 8 . 0 0 0 0 1 - W O n,N-

9 0 6 1 4 2 0 7,. 0 . 0

           *-                                     . 4
               -                                      1 W-                                                        e r
   /           -
               -                                                  C o
               -                                                  f
               -                                                   o
               -                                  . 0 2             e x                          1             g
              -           a                                       d
              -           m                                       E P
                     /                                             r
                     )                                             e z,                                          t r                                           u
              -      (

O 0

              -      P                            . 0             t 1             a l                                            t
               -                                                 h
                       =                                           g
              -                         wz$8 E :'              m i
              -      )                                         c   e
              -      (

z, r . 0 6

                                                           )

m0 c (3 H s v G W Z8

              -                                                    n
              -                                                =   o i

R t

              -                                                    c
              -                                                    n
              -                                                    u F
              -                                      0             g 6             n
              -                                                  i t

h

              -                                                    g i

e

              -                                                  W 4
             -                                    . 0               -

4 C

              -                                                    e r

u

              -                                                    g
              -                                                  i F
                                                  . 0 2
 "    -            -              -   .              0 0     8           6              4   2           0 1     0           0              0   0           0 W
                            ?NN

0.08 ... M = 0.1024 W = l-P/P* et'Det E 0.04 - - COLLAFSE 7' 0.00 - - 1.32 DISPLACEMENT

       - 0. 0.; -                DOPPLER                                                     .1.28 0.08.                                                    [                            l.24 f40T E : PEAK P0'4ER AT 0.0078 SEC
       -0.12                                                                                   1.20 $
   >                                                                                                9 t:                                                                                               0 a:
   !3 1.16
   $ -0.16 -
       -0. 20 -                        DRIVING                                                 1*12 (305/EEC)
       -0.24                                                                                  -1.08
       -0.28 -                                                                                -1.04
       -0.32                                                                       ,           1.00

0. .002 .004 .006 .003 .010 TIME, SEC Figure C-a Components of Reactivity When ,v=0.025 C-23

O DRIVING PAMP RATE $/SEC 30 40 50' 60 1300 ' I DRIVlfiG PA!'P RATE , 1200 (r o Behrens effect) , t I

              ---      -Av(30$/sec Rrrp with                                 #

Behrens ef fect)  ! I 1100 i I

                                                                     , W = 0.7024                            s
                                                                    ,                                     eo
                                                                                                          /

1C20 - /

                                                                                                      /

8 / / 4 i

                                                                                                  /

E I / 9 ' Jx 900 -  !

                                                                                           /

s f I

                                                                                       /

g oc i y E

                                                                                /

Es0 p j 'W = 1-P/P 6 / / ? #

                                                            /

v  ! / $ / / a 700 - i /

                               /
                                       )
                           #        /
                                 /

600 - ,','

                    / /
                   / /
                  / '
                /

500 . / s e s 8 0.0 .02 .04 .06 .08 .10 ,12 Av Figure C-6 l',,rk to One Atmosphere vs Av g C-24

ORIVINS P/dP RAlf. S/SEC 30 40 50 60 260 - o I I 240 - DRIV!'.G RA'T PATE I I (No Behrens Effect) i / I W = 0.7024 /

                 - - _Av(303/sec Ran p                                                                              /

220 with Behrens Effect) ' l ' t l I I I y 200 - # , 8 I 9 I E # / 180- , f h I o I

3 , /

                                                                                   /

5 160 - #vl 4 g Sl t

                                                 /
                                                                         /
                                                                             /
                                                                               /

o a

                                                                     / W = l-P/P mx P

f j a 140 - , I o

                                    /             ,

l

                                             /
                                          /

120 i f p /

                         /
                                /

p / 100 - ,#

                     ,/
                   /
                 /
             /,'

80 - / 0.0 0.02 0.b4 0.05 0.03 0.10 0.12

                                                                           /v Figure C-7 Work to Sodium Slug I.apact vs Av C-25

DRIVI% Pf,MP FATE,1/SEC 3'a 40 50 45 0 5400 ' ' 5300- CR!yJNG RAMP RATE (No Behrens Effect) 1 i

                 - - - Av(30$/sec Ramp                                          p 5200                     with Behrens Effect)                            ,
                                                                            / W = 0.7024'                   f I

r I / u 5100- , o I , w' i 5 / r

-r,                                                           t                            e g 5000-y                                                         ,                         !

0 w , i 0 t  ! 4900- s / W = 1-P/P j / / '5 n # # C 4800- # [ t l

                                                       /4
                                   /
                                 /
                              !            l 4700-                  i           /
                                    /
                                 /
                             /
                          /

4600 - /

                   /

s 4500 - - - - - 0.0 0.02 0.01 0.06 0.08 0.10 0.12 Av Figure C-8 Final Average Core Temperature vs Av g C-26

11.0-10.0 9.0 - 10TAL REACTIVITY AVAILABLE

8. 0 -

7.0 - C.0 - m e

  '3
    ,  5.0 -

4.0 -

3. 0 -

2. 0 - .

1.0 T01AL REACTIVITY USED

                                                              ,-      W = 0.7024
                                                             - y , j,pjp
                                           .                                   ran

_m .. . .

0. 0 n,9, 0.d5 o,63 g,yg Av h Figure C-9 Utilization of Total Available Bubble Collapse Reactivity When the Initial Void Volume Fraction is 0.47 C-27

References p C-1 Richard E. Webb, "Some Autocatalytic Effects During Explosive Power Transients in Liquid Metal Cooled, Fast Breeder, Nuclear Power Reactor (LMFBRs)," Ph.D. Dissertation, The Ohio State University,1972. C-2 Ely M. Gelbard and Richard Lell, " Role of the Migration Area in Lattice Reactivity Calculation," Trans. Am. Nucl . Soc. , 2_1_, p. 222, (June 1975). C-3 Richard B. Nicholson and Paul van Diemen, "The Effect of Neutron Stream-ing in Voids on Hypothetical Core Disruptive Accidents (HCDA)," Design Basis Accident Studies, Final Report, Richard B. Nicholson, The Ohio State University, June 22, 1974, pp. 81-103. C-4 Thomas P. McLaughlin, " Effects of Neutron Streaming and Geometric Models on Molten Fuel Recriticality Accidents," Los Alamos Scientific Laboratory, 1975,(LA-6127-MS). C-5 F. E. Dunn and R. Lell, " Heterogeneous Neutron Streaming Effects in the Clinch River Breeder Reactor," Trans. Am. Nucl. Soc. , 2_2,2 p. 373, (1975). C-6 J. F. Jackson and R. B. Nicholson, " VENUS-II: An LMFBR Disassembly Program," Argonne National Laboratory,1972, (ANL-7951). C-7 D. J. Behrens, "The Effect of Holes in a Reacting Material on the Passage of Neutrons," Physical Society of London Proceedings, Section A, Vol. 62,1949, pp. 607-16. h C-8 R. M. Lell, " Neutron Streaming and Anisotripic Diffusion in Partially Voided Lattices," Ph.D. Dissertation, The Ohio State University,1976. C-9 Gerald Lee Goldsmith and Richard B. Nicholson, " Reactivity Due to ~ Neutron Streaming in the Voids of a Bubbly Pool Core," Design Basis Accident Studies, Final Report, Richard B. Nicholson, The Ohio State University, June 22, 1974, C00-2286-3, pp. 104-71. C-10 T. J. Hoffman, " Informal Letter Report on Monte Carlo Estimation of Bubble Collapse Reactivity," Attachment 1 to May 19,1976, letter from W. O. Harms to Director, RDD, "Effect of Bubble Collapse on Reactivity of a Molten Core." Also R. A. Little, " Informal Report on Bubble Collapse Reactivity Effects Using Discrete Ordinates," April 30, 1975, Attachment to May 19, 1976 letter from W. L. Haines to Director, RDD, "Effect of Bubble Collapse on Reactivity of a Molten Core," Oak Ridge , National Laboratory. C-ll Letter LASL R-7-76-148, Dr. T. P. McLaughlin (LASL) to Dr. Harry Alter (RDD), with Addendum, dated August 3, 1976. O C-28}}