ML20235H849
| ML20235H849 | |
| Person / Time | |
|---|---|
| Site: | Haddam Neck File:Connecticut Yankee Atomic Power Co icon.png |
| Issue date: | 02/28/1989 |
| From: | NORTHEAST UTILITIES SERVICE CO. |
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| ML20235H847 | List: |
| References | |
| NUSCO-165, NUDOCS 8902240075 | |
| Download: ML20235H849 (180) | |
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,9 XUSCo 165 FEBRUARY 1989 XORTHEAST UTILITIES ..
SERVICE COMPANY Large Break LOCA Fuel Rod Response (NUFRAP-T6)
- and Core Oxidation Evaluation Models (NUCOM) o NORTHEAST UTILITIES '
THE CONNECTICUT LIGHT AND POWER COMPANY u
WESTERN MASSACHUSETTS ELECTRIC COMPANY HOLYOKE WATER POWER COMPANY NORTHE AST UTILITIES SERVICE COMPANY NORTHEAST NUCLE AR ENERGY COMPANY i
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h LARGE BREAK LOCA FUEL ROD RESPONSE (NUFRAP-T6) l AND CORE OXIDATION '
(NUCOM)
FEBRUARY 1989 l
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I j SAFETY ANALYSIS SECTION REACTOR ENGINEERING BRANCH NORTHEAST UTILITIES SERVICE COMPANY l
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e DISCLAIMER I
The information contained in this topical report was prepared for the specific requirements of Northeast Utilities Service Company (NUSCO) .
and its affiliated companies, and may contain materials subject to 4 privately owned rights. Any use of all or any portion of the informa-tion, analyses, methodology, or data contained in this topical report by third parties shall be undertaken at such party's sole risk. NUSCO and ,
its affiliated companies hereby disclaim any liability (including but not
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limited to tort, contract, statute, or course of dealing) or varranty (whether express or implied) for the accuracy, completeness, suitability for a particular purpose, or merchantability of the information.
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TABLE OF CONTENTS PAGE NO.
Table of Contents i-Abstract 111 List of Tables iv List of Figures v
1.0 INTRODUCTION
1 1.1 Relationship of NUFRAP-T6 and NUCOM to Other NU Codes 1 2.0 GENERAL DESCRIPTION OF THE NUFRAP-T6 CODE 4 2.1 Modification to FRAP-T6 Source for IBM Couversion 5 2.2 Addition of Stainless Steel Material Properties 6 2.3 Miscellaneous Changes and Error Corrections 9 3.0 NUFRAP-T6 H0DELS AND CORRELATIONS 10 3.1 Transient Thermal Conduc, ion Model 12 3.1.1 Heat Generation 15 3.1.2 Gap Conductance 16 I 3.1.3 Thermal Conductivity of Cracked Fuel 21 3.1.4 Fuel Rod Cooling 23 3.1.5 Heat Conduction and Temperature Solution 24 3.2 Fuel Rod Mechanical Response Model 25 3.3 Plenum Gas Temperature Model 35 3.4 Fuel Rod Internal Gas Pressure Model 36 3.5 Treatment of Fission Gases 40 I
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TABLE OF CONTENTS PAGE NO.
3.6 Material Properties 40 3.7 Clad 0xidation Model 41 4.0 NUFRAP-T6 VALIDATION 44 4.1 Simulation of TREAT Tests FRF-1 and FRF-2 45 4.2 Simulation of PBF LOC Tests 64 5.0 GENERAL DESCRIPTION OF THE NUCOM CODE 129 5.1 Purpose 129 1
) 6.0 MAJOR MODELS AND FEATURES OF NUCOM 130 6.1 Thermal Conduction Solution 130 6.2 Boundary Conditions 139 6.3 Clad 0xidation Model 139 6.4 Gap Conductance Model 142 6.5 Clad Rupture Model 145 7.0 NUCOM VALIDATION 150
8.0 CONCLUSION
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9.0 REFERENCES
163
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ABSTRACT NUFRAP-T6 DESCRIPTION NUFRAP-T6 is a FORTRAN computer program used to simulate the tran-sient mechanical and 0,xmal response of a nuclear fuel rod during a Loss of Coolant Accidua. The development of NUFRAP-T6 along with descriptions of the key models are provided. Comparisons with the results of tests simulating Loss of Coolant Accident phenomena are
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provided to demonstrate the adequacy of NUFRAP-T6.
NUCOM Description NUCOM is a FORTRAN computer program used to calculate the core-wide clad oxidation during a Loss of Coolant Accident. Descriptions of f the key models and correlations of NUCOM are provided. Comparison with the results of NUFRAP-T6 calculations are provided to demonstrate the adequacy of NUCOM.
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LIST OF TABLES Table No. Title Page No.
2.1 Stainless Steel Property Modifications 7 6.5-1 Rupture Temperature vs. Differential 148 Pressure 6.5-2 Rupture Strain vs. Differential Pressure 149
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LIST OF FIGURES
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Figure No. Title Page No.
3.0-1 Order of General Models (NUFRAP-T6) 11 3.1-1 Flowchart of Fuel and Cladding Temperature 13 Model f
3.3-1 Flovchart of Plenum Temperature Calculation 37 i 4.1-1 Schematic of TREAT Fuel Rod Failure Facility 46 4.1-2 NULAP5-LB Model of TREAT Tests 52 4.1-3 NUFRAP-T6, TREAT FRF-1 R0D H (EM), Clad 54 Surface Temperature
} 4.1-4 NUFRAP-T6, TREAT FRF-1 R0D L (EM), Clad 55 Surface Temperature
> 4.1-5 NUFRAP-T6, TREAT FRF-2 R0D 12 (EM), Clad 57 Surface Temperature, Node 3 I
4.1.6 NUFRAP-T6, TREAT FRF-2 R0D 12 (EM), Clad 58 5 Surface Temperature, Node 4 4.1-7 NUFRAP-T6, TREAT FRF-2 R0D 12 (EM), Clad 59
> Surface Temperature, Node 3, No 0xidation 4.1-8 NUFRAP-T6, TREAT FRF-2 R0D 12 (EM), Clad 60 Surface Temperature, Node 4, No oxidation 4.1-9(a) FRF-1: Measured vs. Calculated Strain 62 l
i 4.1-9(b) FRF-2: Measured vs. Calculated Strain 62 l 4.2-1 PBF LOCA Test System ' 66 4.2-2 PBF LOCA Fuel Train Orientation 67 4.2-3 Node Diagram for PBF Test LOC-11 74 4.2-4 Node Diagram for PBF Test LOC-3 and LOC-6 76 i
) 4.2-5 PBF, LOC-11C, Hot Leg Spool Flov 78 l
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l LIST OF FIGURES l
Figure No. Title Page No.
4.2-6 PBF, LOC-11C, Cold Leg Spool Flov 79 4.2-7 PBF, LOC-11C, Hot Leg Spool Density 80 j
4.2-8 PBF, LOC-11C, Cold Leg Spool Density 81 4.2-9 PBF, LOC-11C, Hot Leg Spool Pressure 82 4.2-10 PBF, LOC-11C, Upper Turbine Flov 83 4.2-11 PBF, LOC-11C, Lover Turbine Flov 84 4.2-12 NUFRAP-T6, PBF LOC-11C, Evaluation 86 l
Model, 12 Nodes, Clad Surface Temperature, Node 5 4.2.13 NUFRAP-T6, PBF LOC-11C, Evaluation 87 Model, 12 Nodes, Clad Surface Temperature, Node 6 4.2-14 NUFRAP-T6, PBF LOC-11C, Evaluation 88 I Model, 12 Nodes, Fuel Centerline Temperature
- 4.2-15 NUFRAP-T6, PBF LOC-11C, Evaluation 89 Model, 12 Nodes, Hoop Strains y 4.2-16 NUFRAP-T6, PBF LOC-11C, FRACAS /BALON2 91 Model, Clad Surface Temperature, Node 5 I 4.2-17 NUFRAP-T6, PDF LOC-11C, FRACAS /BALON2 92 Model, Clad Surface Temperature, Node 6
! 4.2-18 NUFRAP-T6, PBF LOC-11C, FRACAS /BALON2 93 Model, Fuel Centerline Temperature 4.2-19 NUFRAP-T6, PBF LOC-11C, FRACAS /BALON2 94 Model, Hoop Strains 4.2-20 NUFRAP-T6, PBF LOC-110, Evaluation Model, 95 l 12 Nodes, Clad Axial Displacement f
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LIST OF FIGURES Figure No. Title Page No.
4.2-21 NUFRAP-T6, PBF LOC-11C, FRACAS /BALON2 96 Model, Clad Axial Displacement 4.2-22 PBF, LOC-3, Cold Leg Spool Pressure 98 4.2-23 PBF, LOC-3,. Cold Leg Spool Flov 99 4.2-24 PBF, LOC-3, Lower Turbine Flov 100 4.2-25 NUFRAP-T6, PBF LOC-3, Evaluation Model, 101 12 Nodes, Clad Surface Temperature, Node 9 4.2-26 NUFRAP-T6, PBF LOC-3, Evaluation Model, 102 12 Nodes, Clad Surface Temperature, Node 10 4.2-27 NUFRAP-T6, PBF LOC-3, Evaluation Model, 103 12 Nodes, Fuel Centerline Temerature 4.2-28 NUFRAP-T6, PBF LOC-3, Evaluation Model, 104 12 Nodes, Rod Gas Pressure 4.2-29 NUFRAP-T6, PDF LOC-3, Evaluation Model, 105 12 Nodes, Hoop Strains 4.2-30 NUFRAP-T6, PBF LOC-3, FRACAS /BALON2 107 Model, Clad Surface Temperature, Node 9 4.2-31 NUFRAP-T6, PBF LOC-3, FRACAS /BALON2 108 Model, Clad Surface Temperature, Node 10 4.2-32 NUFRAP-T6, PBF LOC-3, FRACAS /BALON2
' 109 Model, Fuel Centerline Temperature 4.2-33 NUFRAP-T6, PBF LOC-3, FRACAS /BALON2 110 Model, Rod Gas Pressure 4.2-34 NUFRAP-T6, PBF LOC-3, FRACAS /BALON2 111 Model, Hoop Strains vil
l LIST OF FIGURES l
Figure No. Title Page No.
4.2-35 NUFRAP-T6, PBF LOC-3, Evaluation Model, 113 6 Nodes, Clad Surface Temperature, Node 4 4.2-36 NUFRAP-T6, PBF LOC-3, Evaluation Model, 114 6 Nodes, Clad Surface Temperature, Node 5 4.2-37 NUFRAP-T6, PBF LOC-3, Evaluation Model, 115 6 Nodes, Fuel Centerline Temperature 4.E-38 NUFRAP-T6, PBF LOC-3, Evaluation Model, 116 6 Nodes, Rod Gas Pressure 4.2-39 NUFRAP-T6, PBF LOC-3, Evaluation Model, 117
( 6 Nodes, Hoop Strains 4.2-40 PBF, LOC-6, Cold Leg Spool Pressure 118 4.2-41 PBF, LOC-6, Lover Turbine Flow 119 4.2-42 NUFRAP-T6, PBF LOC-6, Evaluation Model, 121 j 12 Fodes, Clad Surface Temperature 4.2-43 NUFRAP-T6, PBF LOC-6, Evaluation Model, 122 12 Nodes, Rod Gas Pressure i
4.2-44 NUFRAP-T6, PBF LOC-6, Evaluation Model, 123 6 Nodes, Hoop Strains 4.2-45 NUFRAP-T6, PBF LOC-6, FRACAS /BALON2 Model, 124 Clad Surface Temperature 4.2-46 NUFRAP-T6, PBP LOC-6, FRACAS /BALON2 Model, 125 Rod Gas Pressure
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! 4.2-47 NUFRAP-T6, PBF LOC-6, FRACAS /BALON2 Model, 127 Hoop Strains j 6.0-1 Order of General Models (NUCOM) 131 7.0-1 NUCOM, Boundary Conditions, Rod 151 f Linear Power l
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LIST OF FIGURES Figure No. Title Page No.
7.0-2 NUCOM, Boundary Conditions, 152 Surface Heat Transfer Coefficient
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' 7.0-3 NUCOM, Boundary Conditions, 153 Coolant Pressure l 7.0-4 NUCOM, Boundary Conditions 154
! Coolant Temperature i 7.0-5 Comparison of NUCOM and NUFRAP, 156 t Clad Temperature, Zircaloy 7.0-6 Comparison of NUCOM and NUFRAP, 157 0xidation Thickness, Zircaloy 7.0-7 Comparison of NUCOM and NUFRAP, 158 i Clad Temperature, Stainless Steel 7.0-8 Comparison of NUCOM and NUFRAP, 159 0xidation Th'ckness, Stainless Steel
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1.0 INTRODUCTION
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- NU has developed an Evaluation Model (EM) for performing Large Break LOCA analyses to te used in licensing support of Pressurized Vater Reactors f (PVRs). NUFRAP-T6 is a transient fuel rod behavior simulation program g ;
which is part of that Evaluation Model. Its purpose is to predict the transient thermal and mechanit al behavior of a nuclear fuel rod. The -
I results of NUFRAP-T6 vill be used to determine compliance with the Peak l
Clad Temperature (PCT) and Clad Oxidation Criteria stated in 10CFR50.46 -
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(Reference 1). The NUFRAP-T6 calculations vill also be used to provide boundary conditions for the core-vide oxidation calculation performed with the NUCOM program.
I 1.1 RELATIONSHIP OF NUFRAP-T6 AND NUCOM TO OTHER NU CODES l
The NU Evaluation Model consists of several computer programs and inter-facing procedures. The major components of this model are three FORTRAN computer programs which are maintained and executed on NU's system. The three main programs are NULAP5-LB (Reference 2), NUFRAP-T6, and NUCOM.
NULAPS-LB simulates the thermal and hydraulic response of the Reactor Coolant System, Nuclear Core, Secondary Systems, Emergency Core Coolant System, Control Systems, and Containment. It is a modified version of the RELAPS/ MOD 2 (Reference 3) computer program. The models,
! correlations, and verification of NULAP5-LB are described in Reference 2.
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The input to NULAP5-LB consists of dimensions, material properties, and I
control logic, which are representative of the facility being modeled, f
reactor kinetics parameters, power distributions and fuel performance data indicative of the state of the reactor core and input flags used to
- l l select among NULAP5-LB's optional features.
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The results of NULAPS-LB calculations define the boundary conditions and NUFRAP-T6 power history for the hot rod simulation with NUFRAP-T6.
provides a detailed calculation of the thermal and mechanical response of the hot rod. The 10CFR50 Appendix K (Reference 4) required models of clad swell and rupture and clad oxidation are included in this program.
Input consists of fuel rod dimensions, property descriptions, selection of optional features, power distributions (radial and axial), boundary conditions and power history from NULAP5-LB, noding and time step selections. The results of NUFRAP-T6 calculations provide the clad temperature response and clad oxidation thickness for comparison with the 10CFR50.46 PCT and peak clad oxidation criteria.
The NUCOM computer program provides a calculation of the total core clad oxidation for comparison with the 10CFR50.46 acceptance criterion. The NUCOM core-wide oxidatiori code is a multi-channel clad heatup program which calculates the transient cladding temperature and oxidation thick-ness for an array of nuclear fuel rods with user-specified power distri-butions, dimensions and initial conditions. NUCOM contains constituent models which calculate conduction heat transfer, cladding rupture and
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rupture strain, oxidation, and cladding temperature for Zircaloy and l
stainless steel clad fuel rods. Boundary conditions are provided either by user input or from the results of NUFRAP-T6.
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2.0 GENERAL DESCRIPTION OF THE NUFRAP-T6 CODE l
The NUFRAP-T6 computer program is a modified version of the FRAP-T6/ MOD 1 (References 5 and 6) code developed at Idaho National Energy Laboratory (INEL). FRAP-T6 is a FORTRAN program written for execution on CDC type computers. The modifications made to FRAP-T6 by NU consist of the I
following:
o Conversion to IBM compatible FORTRAN.
o Addition of stainless steel properties and correlations.
i o Miscellaneous changes.
o Error corrections.
} The details of these modifications vill be discussed further.
The modifications made to FRAP-T6 are relatively minor. The major models and correlations of FRAP-T6 have not been altered.
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2.1 MODIFICATION TO FRAP-T6 SOURCE FOR IBM CONVERSION 1
The VS-FORTRAN compiler (Reference 7) is the most current compiler for NU's IBM operating system. Therefore, it was chosen to process
! FRAP-T6/ MOD 1. The capability of handling character strings with VS-FORTRAN makes the conversion of character variables much easier. Also l
the ENC 0DE statements in the CDC coding could be replaced easily with internal read statements. ,
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Occasionally, subroutine or variable names are longer than six char-acters. This is not acceptable in the IBM operating system. All the I names which vere longer than six characters were trimmed to no more than a j six. -
The CDC computer allows the initialization of variables in COMMON block -
at any subroutine. However, this is not permitted in the IBM operating l
} system. Therefore, all data initialization statements for variables in COMMON block vere relocated to a Block Data subroutine, f Because FRAP-T6/ MOD 1 was created by combining several codes together,
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some of the argument lists were not consistent through the coding. This
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The entire code was expanded to double precision to compensate for the shorter words of the IBM machine. Also some portion of the coding which was originally coded with double-precision was expanded to extended precision. .
There are diffe+ences between CDC and IBM format specifications. All these differences were resolved to be acceptable by the IBM compiler.
FRAP-T6/ MOD 1 utilizes a dynamic storage scheme to optimize central core memory utilization. However, the required subroutines to perform the dynamic storage operations were not included in the transmittal package.
Therefore, a fixed dimension area was selected for the NU version'rather than dynamic storage. From the experience of running the sample problems, a storage area of 10,000 to 15,000 words was sufficient to handle these test problems. The NU version of FRAP-T6/ MOD 1 has a storage area of 50,000 words.
I 2.2 ADDITION OF STAINLESS STEEL MATERIAL PROPERTIES:
l NUFRAP-T6 vill be used to model the Haddam Neck Plant. This plant currently uses stainless steel clad fuel rods. In order to model these , ,
rods, a set of stainless steel material property routines were added to
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NUFRAP-T6. Also an input flag was added to enable selection of either Zircaloy or stainless steel cladding. Table 2.1 summarizes the changes made to NUFRAP-T6 to include stainless steel properties.
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TABLE 2.1 STAINLESS STEEL PROPERTY MODIFICATIONS Subroutines Change Modified Comments / Reference Material Selection INTIP Add cladding type flag, ICLD, to design input block Young's Modulus CELMOD Reference 8 EMCLEM .
Equation of State CKMN Reference 8 l
Thermal Expansion Coeff. CTHEXP Reference 8 EMCTXP l
Specific Heat CCP BAV-1411 (Reference 9)
EMCP i
Meyer Hardness CMHARD Reference 8 Shear Modulus CSHEAR Reference 8 Thermal Conductivity CTHCON Reference 8 EMCTON Surface Emissivity 20EMIS Set to 0.44 (Reference 8)
Metal Vater Reaction METVTB NUREG-0065 (Reference 10)
) CHIT 0X BAV-1411 (Reference 9)
Rupture Strain CSRUPT NUREG-0065 (Reference 10) /
Annealing CANEAL Bypassed - Not important for LBLOCA .
Clad Strain CSTRANI Bypass iteration use equation of state CSTRAN Remove temperature l dependence in strain cale Anisotropic Effects CANISO Model isotropic effects -SS Reference 8 Effective Stress CSTRESS Add stainless steel properties
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l Subroutines change Modified Comments / Reference Poisson's Ratio EMCPIR Reference 8 l
l Failure Models DETERM Set eutectic melt to high value FRAIL Set fatigue and stress l
corrosion cracking
. probability to zero
- Not considered for LOCA ,..
Rupture Strain EMSTRN NUREG-0065 (Reference 10) l l
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2.3 MISCELLANEOUS CHANGES AND ERROR CORRECTIONS Additional miscellaneous changes to NUFRAP-T6 included:
Adding the option in the power specification to read the power history from tape.
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Adding an edit of average fuel temperature at each axial node.
Adding an option to output boundary conditions for NUCOM at f
specified time intervals.
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Correction of the -all to subfunction EMFTON for the evaluation model fuel conductivity.
Corlection to tuning blouk gap conductance input.
Calculate stress using thin shell formula for prediction of Powers /Meyer rupture temperature.
I Allow selection of LACE deformation option only if LACE options 14 or 18 are selected.
Correct calculation of Baker-Just clad oxidation.
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3.0 NUFRAP-T6 MODELS AND CORRELATIONS i
NUFRAP-T6 contains several calculational models and various correlations which simulate the important phenomena of transient fuel rod behavior.
The most important of these models are those which calculate the tran-f sient heat conduction, mechanical behavior of the fuel and clad, and l
pressure response of the rod. Additionally for LOCA transients, models for determining the failure of the clad and the oxidation of the clad are r
important. Figure 3.0-1 shows the general sequencing of the models in NUFRAP-T6.
I As shown in Figure 3.0-1, the solution of the transient thermal and mechanical models is an iterative process, since these phenomena are closely coupled. The inner and outer loops are repeatedly cycled until two successive cycles calculate temperatures and pressures differing by
.ess than the user specified convergence criteria. The convergence of
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both the inner and outer loops are accelerated by use of the method of Newton (Reference 3).
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Fuel and cladding ]
= temperature model {
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.i p Plenum temperature model !
1r Fuel and cladding deformation model 1 r Failure probability l model 1 r Internal gas pressure model u
Cladding oxidation model 1r l
Cladding ballooning model if Fission gas release model
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l New timestep Figure 3.0-1 Order of general models (N'JFRAP-T6).
3.1 TRANSIENT THERMAL CONDUCTION MODEL The fuer and cladding temperature model applies the laws of heat transfer and thermodynamics to calculate the temperature distribution throughout ,
i the fuel rod. Either a one-dimensional (radial) or two-dimensional (radial plus circumferential) temperature distribution solution is performed, depending upon the user specification. The solution is performed in several steps by division of the dependent variables into smaller groups and then solving each group of variables in sequence.
A flowchart of the fuel and cladding temperature model is shown in Figure 3.1-1. First, the local coolant conditions (pressure, quality, and mass flux) are determined, either by a one-dimensional transient fluid flow model or from an input coolant boundary condition tape. Then the heat generation in the fuel is found by interpolation in the user-input tables of fuel rod power distribution and power history. Through
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use of the most recently calculated fuel-cladding gap size, the value of the fuel-cladding gap conductance is calculated. This calculation 1
obtains the gas properties from the MATPRO materials properties package (Reference 16). In addition, values of the fuel conductivity are also obtained from MATPRO or from the Licensing Audit Code Evaluation (LACE) routines (Reference 11) and, if specified, are modified to account for the effects of fuel cracking. Next, the surface temperature of the cladding is calculated either based upon the input boundary conditions or i
Enter-fue! and cladding temperature model' h
Determine local coolant conditions if Determine heat generation ,
in fuel
- if Calculate gap conductance if l
Modify fuel conductivity for cracking if Calculate surface temperature i
If Calculate 1
temperature distribution if Return f'
Figure 3.1-1 Flowchart of fuel and cladding temperature model.
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a determination of the mode of convective or boiling heat transfer and an evaluation of the surface heat transfer coefficients. Finally, the temperature distribution throughout the fuel and cladding is determined l by the solution of a set of simultaneous equations.
1 The models used in the temperature calculations involve a number of assumptions and limitations, the most important of which are:
- 1. No heat conduction in the longitudinal direction
- 2. Steady state critical heat flux correlations are assumed to be valid during transient conditions (the EM uses NULAP5-LB heat transfer calculations)
- 3. Steady state cladding surface heat transfer correlations are assumed to be valid during transient conditions (the EM uses NULAP5-LB heat l transfer calculations)
- 4. Coolant is water I
- 5. Cladding oxidation does not influence the cladding thermal f properties l
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3.1.1 HEAT GENERATION The total heat generation is typically input to NUFRAP-T6. Alternative-ly, only the heat generation due to fissioning is prescribed by input, and heat generation due to radioactive decay is calculated by the ANS decay heat model within the code (Reference 5). If the reactor is scrammed at the initiation of an accident, so that no heat is generated by fissioning durfng the accident, the latter option can be used. The i
NUFRAP-T6 EH uses the power history calculated by NULAPS-LB.
The heat generation input consists of three sets of tables: (a) rod power versus time, (b) normalized power versus elevation, and (c) normalized power versus radius. The power distribution tables are l
part of the input data deck. The normalized power versus elevation data, which prescribe the axial power profile, are assumed not to change with time. The normalized power versus radius data, which prescribe the
(
) radial power profile, are assumed not to vary with elevation or time.
Heat is generated in the cladding by oxidation. The amount of heat J generation is negligible for cladding at a temperature less than 1000 K,
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but is significant for cladding at a temperature greater than 1300 K.
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The amount of heat generation is calculated by the cladding oxidation correlation specified by the user. The NUFRAP-T6 EH clad oxidation models are the Baker-Just correlation for Zircaloy clad and the White correlation (Reference 9) for stainless steel clad.
3.1.2 GAP CONDUCTANCE l
l The gap conductance model is taken from the GAPCON-THERHAL-2 code (Reference 13). The model has different forms depending upon whether the i fuel-cladding gap is open or closed. The model for the open gap is described first, then the model for the closed gap is described.
Open Gap. The open gap conductance model consists of two terms:
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-h gave +h (3-1) h - Conductance of open gap (V/m2 ,g) gp b = average conductance through gas in the gas gap (V/m g) 2 l gave h = conductance by radiation from fuel outer surface to cladding to inner surface (V/m 2 .K)
The conductance through the gas in the fuel-cladding gap is inversely proportional to the size of the gap. The NUFRAP-T6 Evaluation Model assumes the pellet is located concentrically within the rod. It is also possible to model the pellet as being offset within the rod. This l
j modeling option is described in detail in Reference 5.
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.The average.conductanc'e, hga'n, is computed by the equation:
y h gave - g/ [tg'+
- I f+ c ) + (gi + C2 )] (3-2) where K = thermal conductivity of gas (V/m.K) g a t g
= width of fuel-cladding gap (m).
R f
= surface roughness of the fuel (m)
R c
=. surface roughness of the cladding (m) gl'g2 = temperature jump distance terms for the fuel and cladding (m). '
If the denominator of the above equation is less than 6.349 x 10-7 m, the denominator is set to 6.349 x 10-7 The temperature jump distance terms account for the temperature dis-continuity caused by incomtlete thermal accommodation of gas molecules to surface temperature. The ter.,s also account for the inability of gas molecules leaving the fuel and c.' adding surface to completely exchange their energy with neighboring gas molecules, which produces a nonlinear temperature gradient near the fuel and cladding surfaces. The terms are calculated by the equation:
K 'f 0gas
.5 (3-3) gg + g2 = 0.024688 gas P
gasff"j'"0.5 j j vhere T ,- temperature of gas in fuel-cladding gap (K)
P gas
= gas pressure (N/m 2)
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= mole fractions of j-th component of gas i f) ag = -accommodation coefficient of the j-th component of gas
! M = molecular- weight of j-th component of gas 3 (gram-moles) l The accommodation coefficients for helium and xenon are calculated by the ;
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equations:
a He = 0.425 - 2.3 x 10-4 Tgas (E*1I"")
(3-4) a (Xenon)
Xe = 0.740 - 2.5 x 10-4 T gas l If T gas is greater than 1000 K, T is set equal to 1000 K.
Eas The~ accommodation coefficients for gases of other molecular weights, such as argon and krypton, are determined by interpolation using the equation a) = aHe +
He (ay, - aHe) (3-5)
Xe _ He l
I The radiation term in Equation (3-1), h,, is usually only significant when cladding ballooning has occurred. Then the gas conductance term is small because of the large fuel-cladding gap vidth. The radiation term is calculated by the expression:
hy =
cF,(T)+Tf) (Tp+T} C ( ~0)
, ,.-1 p, 1 f 1 1
'f c s c .. (3-7)
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- where h = radiation gap conductance'(V/m2 ,g)
- a. = Stefan-Boltzmann constant
- 5.6697 x 10-8 V/m2 .K4 F, = _ emissivity factor
- e = ' emissivity of fuel surface f ]
1 e = emissivity of cladding surface rg - outside radius of fuel (m) i r - inside radius of cladding (m)
Tp = temperature of outside surface of fuel (K) l l T c
= temperature of'inside surface of cladding (K).
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Closed Gap. The closed gap conductance model consists of four terms:
I' h y=h gase + h, + h +h oc (3-8) where I
h cy = conductance of closed fuel-cladding gap (V/m ,g) 2 h
gase
= c nductance through gas in fuel-cladding gap (V/m ,g) 2 h, = conductance through points of contact (V/m 2 ,g) h = conductance by radiation from fuel outer surface to cladding inner surface, which is calculated by the same expression (Equation (3-6)) as used for an open gap (V/m 2 .K).
h e
= adjustment t'erm to force continuity of conductance as transition from open to closed gap occurs (W/m 2 ,g),
The gas conductance is calculated by the equation:
h -k g (f* c}
- El + g2 - 1.3969 x 10-6] (3-9) aase
'where C - a coefficient which is dependent on the interface pressure between the fuel and cladding
- 3.6 exp (-1.2746 x 10-9 P) 3 2
- interface pressure (N/m ),
P)
he contact conductance is calculated by the equation:
P h -X 4.5579 x 10-3 K, ( )" (3-10) s R exp (5.738 .528 In (3.937 x 107R,)]
where A -
coefficient dependent upon P)/H
- 0.01 ; 0.0001 f b f 0.01 H
1 ; h<0.0001or H
b>0.01 H
K
- fc Kg+K l Kg - fuel thermal conductivity (V/m.K) k K
c
- cladding thermal conductivity (V/m.K)
H - Meyer hardness of cladding (N/m 2)
R - g) 39.37(R)+R2)0.5 I n - exponent dependent upon Pj /H I
- 0 ; 0.0001 3 ( b ) f 0.01 H
l
- 0.5 ; (I) < 0.0001 H
= 1 ;
(b) H
> 0.01
l k
The adjustment term, h , is calculated by the equation:
h oc
=h opo .- h clo (3-11)
I where !
, i h = conductance calculated by the open gap' conductance l p
model with the fuel-cladding gap vidth, T , equal to zero 8 ]
(.
h - conductance calculated by the closed gap conductance el model with the interface pressure, P), equal to zero L
If cladding collapse or cladding yielding has not occurred, the interface pressure betveren the fuel and cladding is assumed to vary with circum-l ferential position. The interface pressure is assumed to vary from P3-l 3.45 x 106 N/m2 to P3 + 3.45 x 106 N/m2 ,
l 3.1.3 THERMAL CONDUCTIVITY OF CRACKED FUEL l
The EM does not consider the effects of fuel cracking and relocation in
)
the thermal or mechanical models. However, the code does contain a cracking model which is used in some of the data comparisons. The effects on fuel conductivity of this model are described below. The thermal conductivity of fuel with circumferential cracks is less than that of uncracked fuel. In order to calculate the thermal conductivity of cracked fuel, a correction factor, R, is applied to the uncracked fuel
{ conductivity. The correction factor is only applied when either the fuel 1
I r
1 relocation model or the FRACAS-II deformation model is selected by the
. code user. This correction. factor is not used for EM calculations. The correction factor is applied as follows:
I (3-12) k,ff = R kf where k - thermal conductivity of fuel with circumferential cracks (V/m.K)
R = correction factor to account for fuel circumferential cracks kg = fuel thermal conductivity (V/m.K)
The correction factor R is computed by an empirical correlation. This correlation was developed from fuel centerline and offcenter thermocouple data taken as part of the Gap Conductance test series (Reference 12) performed in the Power Burst Facility at the Idaho National Engineering Laboratory. The equation for R is:
R = 1.0 - 0.30 C ,1 [1.0 - kg /kg ] (3-13) where C = V rel 4r p (0.8 x 10-4) k . nductivity of gas in fuel-cladding gap (V/m.K) g V = void fraction produced in the fuel by fuel relocation in the radial direction r = as-fabricated pellet radius (m).
p
NOTE: The FRAP-T6 manual incorrectly lists a multiplier of 0.48 instead of 0.30 which is used in FRAP-T6.
C,,1 is a measure of the instantaneous volume available for cracking.
i i This term decreases as the fuel-cladding gap size decreases. Recognizing that cracked fuel can never fully reconsolidate, this term is never allowed to be less than 0.~125. The 0.30 factor was chosen to best fit the experimental data base for rods containing He, Xe, and Ar.
Instantaneous crack healing is assumed when the local fuel temperature reaches or exceeds the user-specified fuel sintering temperature. Crack healing is enforced as:
R = 1.0 when T y > T sint (3-14) where T = 1 cal fuel temperature (K) r T = fuel sintering temperature (K).
sint l
3.1.4 , FUEL R0D COOLING
[
The fuel rod cooling model calculates the amount of heat transfer froa the fuel rod to the surrounding coolant. In particular, the model calculates the heat transfer coef ficier.t, heat flux, and temperature at the cladding surface. These variables are determined by the simultaneous 1
solution of two independent equations for cladding surface heat flux and !
surface temperature.
l The first equation is the appropriate correlation for convective heat l
transfer from the fuel rod surface. This correlation relates surface heat flux to surface temperature and coolant conditions. Different correlations are required for different heat transfer modes, such as nucleate or film boiling. The Evaluation Model uses heat transfer.co-efficients and sink temperatures calculated by NULAP5-LB.
The second independent equation containing surface temperature and surface heat flux as the only unknown variables is derived from the finite difference equation for heat conduction at the mesh bordering the fuel rod surface. The derivation of this equation and the simultaneous solution for surface temperature and surface heat flux are described in Appendix C of Reference 5. Neither of the two equations solved simul-taneously contains past iteration values so that numerical instabilities at the onset of nucleate boiling are avoided.
1 3.1.5 HEAT CONDUCTION AND TEMPERATURE SOLUTION _
i Once values for the heat generation, gap conductance, cracked fuel I
conductivity and surface temperature have been obtained, the complete temperature distribution in the fuel and cladding is obtuined by applying l
.the-law for heat conduction in solids. The FRAP-T6 Code Description
.(Reference 5)-provides a detailed description of the solution technique.
This solution has not been altered in NUFRAP-T6.
l 3.2 FUEL R0D MECHANICAL RESPONSE HODEL i
l . .
l An accurate analysis of the fuel and cladding mechanical response is y
necessary in any fuel rod response analysis because of the fact that the I i heat transfer across the fuel-cladding gap is a strong function of the 1 l gap size. In addition, an accurate calculation of stresses in the l l-cladding is needed so that an accurate prediction of the extent of l
l cladding ballooning.and failure (and subseciuent release of fission products) can be made.
t j In analyzing the mechanical response of fuel rods, two physical 1
situations are encountered. The first situation occurs when the fuel pellets and cladding are not in contact. Here, the problem of a cylindrical shell (the cladding) with specified internal and external pressures and a specified cladding temperature distribution must be solved. This situation is called the "open gap" regime.
l The second situation encountered is when the fuel pellets (which are considert.bly hotter than the cladding) have expanded so as to be in contact with the cladding. Further heating of tho fuel results in
" driving" the cladding in.an outward direction. This situation is called j- .
_ = _ _ _ _ _ _ _ _ _ _ _ _ -. - _ _ __
the " closed gap" regime and results in pellet-cladding mechanical interaction (PCHI). Alternatively, this closed gap regime can occur due to the collapse of the cladding onto the fuel pellets due to elevated cladding temperatures and a high coolant pressure.
There are three models in NUFRAP-T6 for calculating the mechancial response of the fuel and cladding. Two models are mechanistic (FRACAS-I and FRACAS-II), and the third is part of the Licensing Audit Code Evalua-tion (LACE) model. The more simplified mechanistic model, named FRACAS-I, neglects the stress-induced deformation of the fuel and is called the rigid pellet model. The model includes the effects of the thermal expansion and relocation of the. fuel and thermal expansion, plasticity and high temperature creep of the cladding. The more complex 1
model, named FRACAS-II, includes all the effects of FRACAS-I, plus stress induced deformation of the fuel.
After the cladding strain has been computed by the FRACAS-I or II models, the strain is compared with the value of an instability strain obtained from MATPRO. If the instability strain has been exceeded at any point along the rod, then the cladding cannot maintain a cylindrical shape and local ballooning occurs. For the local region at which instability is predicted, a large deformation ba]Iooning analysis is performed. This analysis allows for nonaxisymmetric large deformation of the cladding and can take into account local axial and circumferential temperature 1
Q-_____-____ . _ _ ._
- 6 h
. variations. Modification of the local heat transfer is calculated as the-
~
')
cladding ballooning progresses and additional surface area is presented
~
to the coolant.
l.
! A third mechanical response model is used for Evaluation Model calcula-tions. This model is part of the Licensing Audit Code Evaluation (LACE)'
l package of FRAP-T6 (Reference 11). The LACE Deformation'and Failure >
- models consist of the subroutines LACEDF, LCDFDV, PRSINF, and EMSTRN.
LCDFDV is the driving routine for the LACE Deformation model. IliCEDF performs fuel and cladding thermal expansion'and stress and strain calculations. Subroutine EMSTRN predicts cladding failure, plastic ;
. strain and flow block' age. Subroutine PRSINF calculates the interfacial pressure betveren fuel and clad if pellet-clad mechanical interaction .. ;
occurs. ,
l n
l-In the LACE deformation model, fuel relocation is riot considered. Fuel y i
thermal expansion'is calculated using the FRACAS-I method (Reference 5). l l
l l !
L LACEDF calculates cladding thermal expansion'and material properties from-the average cladding temperature. Cladding hoop stress and axial stress are calculated as for a thin cylinder using the equations:
L l
- a = PRj-PECo g (3-15)
H (Rg-Rj)
L p
i ' t _l
,G@u
.# n
- - .. p u.
i . 'L ,
m n
, m, _ P(Rj)2 g - P C(Rg )2 ' (3-16) z' 2 '
(R 2 -<g- Rj )
- y. g where i ]
i a H
- j 1
a- .= axial stress
.P g = . fission gas pressure P
C
= coolant pressure.
0
.Rj = new inside cladding radius as calculated at'the last-calculation step.
R'. - new outside' cladding radius as calculated at the last j calculation step.
l' l The cladding strains are computed by the equations: ]
c H
= H - v(T) 'Z +c + c p (3-17)
E(T) E(T) c 3
= Z .- v(T) 'H . (3-18)' "
E(T) E(T) s 4
j i: where .I c
H
= hoop strain c = axial strain 3
i' -j c - plastic strain calculated in EMSTRN ,
P E(T) = temperature dependent Young's modulus i T = average cladding temperature v(T) = temperature-dependent Poisson's ratio l
I e = creep strain (a quantity initialized from steady-state calculations).
- l. .
L The new cladding dhuensions are calculated as:
- ., Rj - R' - g (3-19) t 2 b
R' = R' + ott (3-20) 2 1
i
,. .u 3_
gr :i
- id ,. ,
- ?'
N..I ; i ,
s
..; s ,
t ? ; j. ,
.R'=. ii+ (~ )
- p;; '2 o ( 1 '+ c.H + *TH) i t
1 !
ot--- (R g -R) g (1 + cTH)~ (3-22),
[ '
L (1 + .c) H ,
7 '
. where- 1 Rj = new inside cladding radius R' .= new outside cladding radius Rg = ' cold inside cladding radius R = cold outside cladding radius o-i E
- TH
= a(T) (T Tr ) !
j j-
= . thermal strain ;
T = strain-free reference temperature, r
~
a = coefficient of thermal expansion-
)-
l- - If the deformation of the fuel and the cladding is such that PCHI has l
occurred,.an interface pressure is cellculated in subroutine PRSINF. The !
I new cladding coordinates are then' calculated from:
i i' R R'
= (3123)
P I R' = R' + ot o p (3-24)
I where' R' = new fuel pellet radius. l P
i I
L.
h
l After failure has been predicted to occur, the rod internal pressure is 4
assumed to equal the coolant pressure.- The LACEDF calculations of cladding deformation subsequent to failure utilize Equations 3-21 and 3-22 but with the following change. The hoop strain, : c. ,a is now defined l ast .j T c *+U 1;
H" p c ,
where e, is the plastic strain predicted at failure (by subroutine
-EMSTRN) and'c, is the creep strain defined earlier. c, is multiplied by four because EMSTRN limits the plastic strain to one-fourth'the strain at
, failure found in the Radial Expansion versus 6P table.
l l
Subroutine PRSINF calculates the interface pressure due to pellet-L cladding interaction. "The interface pressure due to interference is calculated as: l
- - IE c P g= k (3-25)
R' +
R{ . y . c E I1 - "f)
R' - R' f o i where I = cladding-fuel interference (the overlap between the new fuel radius and the new cladding inside radius, i.e.,I-Ry)-R{.)
Rj = new inside cladding radius
)
I
m - . , .. ,
v-l R' = new outside cladding radius q.
v = . volume averaged Poisson's ratio of the fuel ,
f 2n'fr (3-26)
,. "f (T) rdr, l 2 l f r = fuel outside radius f.
rg = fuel center, radius (i.e., r = O gfor solid. fuel pellets)' )
vf(T) = temperature dependent value of v at radius r-f and at T(r)
T(r) = temperature at radius r v
C
= volume averaged Poisson's. ratio of the cladding (calculated similarly to v ' calculation in f
!' Equation 3-26)
E f
=. volume averaged Young's Modulus of the' fuel (calculated similarly.to v in Equation 3-26) f E'
= . volume averaged Young's Modulus of the cladding (calculated similarly to vg in Equation 3-26).
Since the P calculation uses the deformed radial coordinates the total i
interface pressure must also include the contribution from the fission gas pressure so that:
P = total interface pressure
- P gas
+P g (3-27) where P = fission gas pressure gas l
Pg = interface pressure due to interference calculate.d above i.
Y l'
u If the calculated total interface pressure would cause the cladding stress to exceed the yield stress, then the interface pressure is set equal to the pressure required for the cladding stress to equal the yield i stress.
I i
Subroutine EMSTRN computes cladding failure, plastic deformation and flov 1 l
blockage by comparing the cladding pressure differential against
, tabulated data of cladding failure behavior data. The data are supplied in the form of three tables:
I 1
(a) Rupture Temperature versus aP i
l (b) Radial Expansion versus AP (Singl( Rod Data) 1 (c) Assembly Average Flow Blockage versus 6P (Multiple Rod Data) ]
l l The prediction of plastic deformation and flow blockage depends upon the l-pressure differential aP across the cladding where:
l j
AP = P as
-P eool I~ )
The EMSTRN subroutine calculates failure and plastic strains only if the rod internal gas pressure is greater than the coolant pressure, that is, aF > 0. If AP is greater than zero, the EMSTRN subroutine determines the rupture temperature (T,upt) corresponding to the 6P value. This rupture I temperature is calculated by interpolation from the user input table of I
rupture temperature versus aP or from the Powers /Meyer correlation l i
(Reference 15). EMSTRN defines the differential in rupture temperature and cladding temperature as:
oT - T rupt ~ clad (3-29)
The plastic strain and flow blockage predictions are then calculated for the following three possible cases:
(a) oT > DTPLAS For this case there is no plastic strain or flow blockage. Failure
- is not predicated.
(b) 0 < AT f DTPLAS A value of plastic hoop strain is calculated as:
l I
g, F exp (-0.0153aT) (3-30)
P 4 I
l where F is the value of failure strain corresponding to 6P inter-polate) from the Radial Expansion versus 6P table. There is no blockage in this case and failure has not occurred.
l DTPLAS = 93.3*C if Table input is used, I
l or i
DTPLAS = 70'C; T rupt < 700*C (3-31)
= 70 + 0.14166 x (Trupt - 700) ; 700 f Trupt f 1300'C
- 155'C; Trupt > 1300'C if the Powers /Meyer correlation (Reference 15) is specified.
(c) First timestep when 6T f 0.
Failure is predicted, and the total plastic hoop strain is defined as:
l e = F/4 (3-32)
P.
The flow blockage is predicted and calculated by interpolation from the assembly average flow blockage versus 6P table.
l (d) All timesteps after failure.
l After the first timestep at which failure is predicted, the plastic strain is set equal to the experinnental failure strain; 3.e.,
i cp = F.
f l
l 3.3 PLENUM GAS TEMPERATURE H0 DEL l
.i I
To calculate'the internal fuel rod pressure, the temperature for all gas volumes in the fuel rod must be calculated. Under steady state and I transient reactor conditions, approximately 40 to 50 percent of the gas i
)
in a fuel rod is located in the fuel pellet expansion chamber (plenum)
>- provided at the top and sometimes at the bottom of the fuel rod. The plenum temperature model computes the temperature of this gas. This model includes all thermal interactions between the plenum gas and the top pellet surface, hold-down spring, and cladding vall. ;
The transient plenum temperature model is based on three assumptions:
f
- 1. The temperature of the top surface of the fuel stack is independent of the plenum gas temperature.
- 2. The plenum gas is well mixed by natural convection.
- 3. Temperature gradients in the spring and cladding are small.
I I
)
1 F,
b The first assumption allows the end pellet temperature to be treated as an independent variable. The second assumption permits the gas to be
- i. modeled by one lumped mass with average properties. The third assumption I
allows the temperature response of the cladding and spring to be
( represented by a small number of lumped masses.
The plenum temperature model consists of a set of six simultaneous first order differential equations that model the heat transfer between the
)
plenum gas and the structural components of the plenum. These equations involve heat transfer coefficients between the various components. A detailed description of the plenum temperature model can be found in Reference 5. A flovchart of the calculations is shown in Figure 3.3-1.
3.4 FUEL R0D INTERNAL GAS PRESSURE MODEL l
The pressure of the gas in the-fuel rod must be known in order to j calculate the deformation of the cladding and the transfer of heat across the ftrel-cladding gap. The pressure is a function of the temperature, L volume and amount of gas. Since the temperature is spatially nonuniform, the fuel rod must be divided into several smaller volumes, so that the temperature in each small volume can be assumed to be uniform. In particular, the fuel rod is divided into a plenum volume and several fuel-cladding gap and fuel void volumes. The temperature of each volume i
I f
Enter plenum temperature model k
Calculate natural convection heat transfer coefficients l
Calculate conduction heat transfer coefficients t
Calculate radiation
) heat transfer coefficients l'
> t Calculate 7
heating of spring and cladding l Solve plenum temperature equations k
Return Figure 3.3-1 Flowchart of plenum temperature calculation.
}
is given by the temperature model, the size of the volume by the deformation model and the amount of gases by the fission gas release i model, or by user input.
The internal gas pressure can be calculated by either a static pressure model (which assumes that all volumes inside the fuel rod equilibrate in pressure instantaneously) or by a transient pressure model which takes into account the viscous flow of the gas in the fuel rod. The transient model 'is an input option. Unless the fuel-cladding gap is small
(<25 microns) or closed, the static and transient models give identical results. The transient fuel rod gas pressure model is described in Reference 5. The NUFRAP-T6 Evaluation Model uses the static model.
) Static Fuel Rod Internal Gas Pressure Model The static fuel rod gas pressure model is based on the following assump-tions:
) 1. The perfect gas lav holds.
- 2. The gas pressure is the same throughout the fuel rod.
- 3. The gas in the fuel cracks is at the average fuel temperature.
i f l
The static pressure in the fuel rod is calculated by the perfect gas law,
{
modified to include volumes at different temperatures as follows:
P g= , Y , (3- W
"(# cn ~#
}+ cn + Dn + pn + rfn + ren AZ h + "7 ""1 f
T p i Gn aven Dn aven fsn esn ,
where P
g
- internal fuel rod pressure (N/m 2)
)
M = moles of gas in fuel rod, which is the sum of the 8 moles of fill gas and released fission gases, (gram-moles)
R = universal constant (N m/K gram-mole)
V = plenum volume (m3 )
p T
p
- temperature of gas in plenum (K) n = axial node number
\
N = number of axial nodes r = radius of inside surface of cladding at axial C"
l node n (m) r = radius of outside surface or fuel at axial I"
node n (m)
I T = temperature of gas in gas gap at axial node n (K)
GN AZ - fuel rod length associated with axial node n (m) n V = fuel crack volume per unit length at axial node n en
(,3j,)
T = temperature of gas in fuel cracks at axial node n (K) cn V = y lume f fuel pellet dishes per unit length of fuel Dn stack at axial node n (m 3/m)
T = temperature of gas in fuel dishes at axial node n (K)
Dn V = v lume f gas in fuel open pores per unit length at Pn axial node n (m /m) 3 f _ _ -
T = v lumetric average fuel temperature at axial node aven n (K)
V - volume of gas in voids due to fuel surface roughness l
- f" per unit length at axial node n (m 3 /m) l T = temperature of fuel surface (K) fsn V - volume of gas in voids due to roughness on cladding ren inside surface per unit length (m 3 /m) l T
esn
- temperature of cladding inside surface (K) 3.5 TREATMENT OF FISSION GASES The quantity and makeup of fission gases in a NUFRAP-T6 simulation are l typically specified through user input or from a FRAPCON-2 tape. The EM calculations will use input to specify the gas composition based on a steady state fuel performance code.
I The user also has the option of allowing NUFRAP-T6 to calculate the l production and release of fission gases using the PARAGRASS subcode (Reference 6). This option vill not be invoked for eve.luation model I calculations.
3.6 MATERIAL PROPERTIES There are three sets of Material Property routines employed in NUFRAP-T6.
The MATPRO (Reference 16) subroutines are used for calculating material properties of UO 2 , fission gases, and Zircaloy clad.
)
Stainless steel properties have been added for simulating' fuel rods with Type 304 stainless steel clad. These correlations were taken from the NUFRAP code (Reference 8) and from Reference 9 and 10 (see TABLE 2.1).
-l A set of LACE material properties for UO2 , fission gas and Zircaloy are 1 available if selicted by the user. These LACE material property routines are described in Reference 11.
3.7 CLAD OXIDATION MODEL l
NUFRAP-T6 contains three oxidation models. The CATHCART correlation (Reference 17) is available for best estimate calculations of Zircaloy.
This correlation has been recommended if the clad temperature is not expected to exceed 1800K (Reference 6). The Baker-Just correlation is also applicable for Zircaloy clad fuel. This correlation is considered-conservative for clad temperatures less than 1800K and is required by 10CFR50 Appendix K.
l The White correlation (Reference 18) is used for calculating stainless steel clad oxidation. The Baker-Just correlation (Reference 19) for Zircaloy oxidation and the White correlation for stainless steel oxida-tion have the same form.
V2 = t K exp (-6E/RT)
}
l
l I
where i V = mass of metal reacted per unit area (mg/cm2 )
l K = rate constant (mg2 /cm4 -s) f E = activation energy (cal / mole) l R = universal gas constant (1.987) cal /(mole "K) i I
l T = temperature (*K) t -
time (s) i
)
The reaction coefficients for Zircaloy-4 and AISI Type 304 stainless steel are:
5 Metal K(mg 2 /cm 4 -s) E (cal / mole) Reference l Zirconium 33.3 X 106 45,500 Baker-Just (Reference 19)
Stainless Steel 6.28 X 1012 84,300 White (Reference 18)
(
The reaction heat values are taken from Reference 10 and are 3880 cal /gr-mole H2 0' reacted for Zirconium and 410 cal /gr-mole H 2O reacted for stainless steel.
Oxidation calculations are extended to th'e inside of.the clad at the node l
of rupture and at nodes within 6 inches above or below the rupture node after rupture occurs during EM calculations. This logic exceeds the requirements of 10CFR50 Appendix K. -NUFRAP-T6 also includes the effeet of' clad' thinning on oxidation due to swelling of the clad.
1 l
l 1
)
[
p i __ _
c f
L l
4.0 NUFRAP-T6 VALIDATION In order to demonstrate the adequacy of the NUFRAP-T6 code in simulating l ..
transient fuel rod behavior, comparisons with several LOCA conditions.
tests are provided. In these comparisons, the NUFRAP-T6 calculations of j
the thermal response, mechanical behavior and oxidation of the test rods are shown to adequately simulate the actual behavior as indicted by the test measurements. Also, the thermal-hydraulic calculations of NULAPS-LB are shown to provide the appropriate boundary conditions for NUFRAP-T6.
l The Two sete of tests have been selected for NUFRAP-T6 validation cases.
Fuel Rod Failure tests 1 and 2 (FRF-1, FRF-2) performed by the Oak Ridge National Laboratory at the TREAT facility (References 20, 21) provide rapid fuel rod heatups and failures in the alpha and beta phase tempera-ture ranges. The test conditions were representative of the late blov-down period of a LOCA. The PBF LOC test series (References 22, 23, 24) were chosen because of their simulation of the blowdown phase of a LOCA and because the failures in these tests occurred in the alpha, alpha plus beta, and beta phase temperature ranges of Zircaloy. The ability of NUFRAP-T6 to adequately simulate the thermal, mechanical, and failure behavior of these tests demonstrates its adequacy as a part of the NU large break LOCA evaluation model.
I; 44 -
l 1
L
\
l 4.1 SIMULATION OF TREAT TESTS FRF-1 AND FRF-2 l
4 A fuel rod failure study program was initiated at Oak Ridge National Laboratory in July, 1968 to determine the characteristics and extent of fuel rod failure under LOCA conditions. This program included two high temperature rupture tests of clusters of fuel rods in a steam atmosphere in the Transient Reactor Test (TREAT) Facility. The simulation of the TREAT FRF-1 and FRF-2 tests provides the opportunity to compare the evaluation model (EM) predictions of clad temperature, onset of plastic l l deformation and rupture to test data of UO2 fuel rods in a late-blowdown type steam environment. Specifically, the steam cooling heat transfer calculations of NULAP5-LB and the thermal / mechanical models of NUFRAP-T6 can be tested. Reported measurements include clad su: face temperature, pin pressure, and average diametral strain.
Facility Description - A schematic of the test facility is shown in Figure 4.1-1. The circular test section of Fuel Rod Failure tests FRF-1, FRF-2 contained a cluster of seven Zircaloy clad UO 2 fuel rods. The rods were nominally 27 inches long and the test section inner diameter was nominally 2-3/16 inches. The rods were exposed to a flowing steam / helium atmosphere. The center rod in each test contained fission products from a previous irradiation of 650 MVD/MT (FRF-1) and 2800 MVD/MT (FRF-2) to test the effect of irradiation on rupture characteristics. By using
.\
,p>
l
-n, O r h 8 4 1__ [flLTER PACNS Cosetalm osf Fulsose coils Amo fiLTEn Papgas A u
'~
l
--e 3 g 37 tau Y ' Low FL0s ~
w(itR I,n' a FFLutut Gas CominELEns - - l g
- t rission-encouct (#Los utste cas ,,,,, g ,
tJ ptees/ men tee
- GEsst4Af0A l U ll /
COLLECYtom UNaf es0. 2 Sg/mem, g 3 6 ps6g i N.
[*
"L"
(
l
-/ 1! CONDE hlt R taaP F0n M(TMYL IOOe0E Ek,,"[# 3 l I guPPLY. 4 19 3 *Cl D
- "'* l f ly
- we i i i
i l._j uo C
~
~
PA(
TY,PICAL.00,$.S.u.
um f AlIE0,ll ,_,,,,
Or PaiuAar vessco ,
i i raap. _ ._ _
i *5 ,,u n l . ,...0,<
...P ,,
. ,. .a.CP - ,. .C .s
, s-i- ----- J C 'a'a"J"i.i"*,'0. .
en-n( ACf04 CoasP08stlett l
1-l .
\ l' l
i 1
FIGURE 4.1-1 SCHEMATIC OF TREAT FUEL ROD FAILURE FACILITY l
1
fissioning in the UO2 pellets as the heat source, the heat transfer conditions between pellet and cladding are similar to ,those expected in a LOCA. The maximum measured clad temperatures during the tests were approximately 1800'F in FRF-1 and 2400'F in FRF-2.
EXPERIMENT DESCRIPTION FRF The test section contained seven 26-7/8 inch long Ziracloy clad fuel rods. Three rods were made with Zircaloy-4 clad and four were made l
vith Zircaloy-2 clad. The rod plenum lengths and gaps were varied to examine the effect of these parameters on rupture deformation. One rod (C) was previously irradiated to a peak burnup of 650 MVD/MT. Two rods (H and L) were instrumented with surface thermocouple and pressure i transducers. The rods were placed in an equilateral triangular spacing with 0.75 inches betveren centers. The fuel bundle was placed within a 2-3/16 inch ID Ziracloy sleeve. Steam flow of 9 gr/ min and helium flow i of 1.8 1/m (STP) were provided to the rod bundle during the test. The
)
test section pressure was approximately 22 psia. -
The transient proceeded according to the following schedule:
)
1 l
l Time Event 4
-14 m Steam flow, helium flow started (preheat temperature 130 C) 0s Start of TREAT transient l 8s TREAT power = 30 MV (estimated bundle linear heat rate = 6.3 l
kV/ft) 28 s Reactor power decreasing from 30 MW. Maximum cladding tempera-ture reached was 1770'F. Primary pressure increased from 21.6 l
l to 24.5 psia due to helium released from rods.
l 28.4 s Rod H ruptured at 172 psia 28.7 s Rod L ruptured at 162 psia FRF The second fuel rod failure experiment was performed with a seven
) rod bundle of 27 inch long Ziracloy-4 clad fuel rods in a flowing steam / helium atmosphere. The TREAT reactor power was held approximately constant for 30 s to cause the cladding temperature to rise at a rate of 80*F/s to 2400'F. The center rod was pre-irradiated to a peak burnup of 7800 MVD/MTu. The fuel rods were initially pressurized with helium to l
between 65 and 75 psia. Two rods (11 and 12) were connected to pressure transducers to measure pin pressure during the transient. Two rods (12 and 13) were provided with clad surface thermocouple. The Zircaloy bundle sleeve used in FRF-1 was replaced with a thin gold plated reflective sleeve.
l l
1
p n
L The sequence of. events 1for the FRF-2 te'st were as follows:
4 Time Event-l; L -2.h . Steam system electrically preheated; helium flov --1.8 1/m .
(STP)
-8 m Steam flow started -8 gr/m
.0s TREAT transient started.
I l' 6s Reactor power' reached 30 MV, power held o'.veen 20 and 40 MV l- 30.3 s iCladding temperature 2190'F; first rod ruptured 1
30.8 s Cladding temperature 2220'F; rod 11 ruptured 31.0 s Third rod ruptured
~
32.9 s Cladding-temperature 2300'F; rod 12 ruptured l'
i 33.8 s Fifth rod ruptured 34.7 s' Sixth rod ruptured' 35 s Reactor scrammed 37.5 s Cladding temperature;2400'F; seventh rod ruptured 15 m Heat to steam generator turned off -
l 31 m Flow stopped i
l l
l~
ANALYTICAL MODEL The methodology used.to predict the FRF-1 and FRF-2 TREAT data made use of the NUFRAP,'NULAPS-LB and NUFRAP-T6 codes. NUFRAP, which is described i in Reference 8, was used to obtain the fuel rod radial power distribution and to determine the' fission gas inventory of the center irradiated rod.
1 NULAP5-LB, which is described in Reference 2, was used to simulate the thermal-hydraulic transient and to obtain the heat transfer, sink temperature and coolant pressure boundary conditions to be passed to '
( NURAP-T6. Finally, NUFRAP-T6 was used to simulate the thermal and mechanical behavior of the various fuel rods in the test section.
l l
NUFRAP Model - The fuel rod was simulated using 6 axial nodes of unequal ;
length, chosen to be consistent with the NUFRAP-T6 model. The inputs to NUFRAP included physical dimensions of the fuel pellet and cladding, fuel i' l
density and enrichment, stack height, plenum volume, fill gas composition i
and initial pressure, axial power distribution, physical properties, coolant temperature, power history, etc. NUFRAP was used to calculate f- the radial power distribution, fission gas composition, fuel / cladding l
dimensional changes and oxidation thickness as a function of burnup.
These parameters are used as initial conditions for NULAP5-LB and NUFRAP-f T6. The FRACAS-II mechanical model and the ANS 5.4 (Reference 26) i fission gas release model vere used in this analysis.
I f
NULAPS-LB Model - As indicated above, the fuel rod and coolant channel vere simulated using 6 axial nodes of unequal length, chosen to be consistent with the NUFRAP-T6 model. The node diagram, shown in Figure 4.1-2, consists of two time dependent volumes and junctions supplying steam and helium at prescribed flow rates and temperatures to a node representing the lover plenum. The lover plenum, containing the mixed steam and helium, is connected to the six axial segment node repre-senting the fuel rods and the coolant channel. The outlet of the top segment of the test section node is connected to a time dependent volume, representing the upper plenum, which controls the test section pressure.
Three heat structures were modeled to represent (1) the hot rod, (2) the remaining 6 fuel rods, and (3) the cylindrical Zircaloy test section.
The radial heat conduction from the fuel pellet, gap and cladding was modeled using seven radial nodes in the fuel pellet, one node for the gap and two nodes for the cladding. The radial heat conduction through the Zircaloy test section was modeled using three radial nodes.
NULAP5-LB calculates the heat exchange between the heat structures and ;
the coolant and the effect of the heat transfer on the momentum and energy of the coolant. The results of the NULAP5-LB calculation that are l passed to NUFRAP-T6 consist of a set of tables of coolant pressure, 1
J 300 ;
20s 206 k 205 k l.
k I
204 24.- Heat Structure i i
1 203
/ /
202 201 I . ins l 10 '///// 100 ///// 20
- ~ - -
l Steam 12 22 Helium i
i Figure 4.1-2 NULAP5-LB Model of TREAT Tests l
1 I
.g 1,
coolant temperature and the heat-transfer coefficient for each axial node as a function'of' time. This information~provides_ boundary conditions for the more detailed thermal-mechanical calculations performed by NUFRAP-T6.
l l- NUFRAP-T6 Model - As indicated above, the fuel rod and' coolant channel vere simulated using 6 axial nodes. The node lengths were chosen such that the location of the temperature measurements coincided with the center of the respective nodes. Inputs to NUFRAP-T6 include the appro-( .
I priate initial conditions from NUFRAP and the heat transfer and mechanical boundary.conditio'ns from the NULAP5-LB. Cases were run using a best estimate model (FRACAS-I/BALON4), and the Evaluation Model (LACE). j Since NUFRAP-T6 models one fuel rod at a time, separate cases were run for several of the fuel rods. Two of the fuel rods were connected to L :
b pressure cells via lengths of unheated tubing. Since NUFRAP-T6 cannot
.l model unheated volumes, the measured pressure responses were input when these rods were modeled.
COMPARISON OF NUFRAP-T6 RESULTS TO DATA Cladding Temperature - Figures 4.1-3 and 4.1-4 show comparisons of the FRF-1 thermocouple data to the predicted cladding surface temperature rods H and L using the LACE model to predict clad swelling. The com-parison is excellent until the time of rupture. After rupture, the test data indicate an immediate cooling of the clad and NUFRAP-T6 continues to NUFRAP-T6
?
j TREAT FRF-1 ROD H (EM)
CLAD SURFACE TEMP (P)
NODE =5-2000 '
1900-l 1890 1700- ,
l'600-1500-1460-1300-1 '
l n 1200-b
'g 1100-W 1000-I' 900-800-700-600-d 500-400-300- i i i i
i e i i i i i 0 5 10 15 20 25 30 35 40 45 50 TIME (SEC)
CURVE CODE * *
- TEST FIGURE 4.1-3
3l.
l ,
( ).
1 NUFRAP-T6 ,
TREAT FRF-1 ROD L (EM)
ClJ.D SURFACE T2MP (F)
NODE =4 2100-
- a l 2000- )
i 1900- l 1800-f * *
- 1700-1600-l 1500-l j 1400- ,
1300-n -
D 1200-l S I
w 1100 -
l 1000-900-
/
l l
800-700-600-500- /
/
/
400- /
300- . . i i T- . i i i i i 0 5 10 15 20 25 30 35 40 45 50 TIME (SEC)
CUF VI CODE * *
- TEST FIGURE 4.1-4
}
calculate increasing clad temperature until the stored energy in.the rod f
pellet is redistributed. The apparent cooling of the clad in theitest is probably due to the clad swelling and rod bowing which would close the gap between the rod and the Zircaloy shroud. Radiation cooling would then be effective in cooling the rod. Nota that the thermocouple were L attached to the clad surface that faced the shroud.
Figures 4.1-5 and 4.1-6 show comparisons of the FRF-2 thermocouple data ,
i to the predicted cladding surface temperature of nodes 3 and 4 for rod -)
- 12. The measured and calculated temperatures match until about 2000'F at which point the oxidation calculation in NUFRAP-T6 (Baker-Just) becomes dominant. The test section was apparently prevented from oxidizing significantly by the' low steam flow and the presence of Helium. .
1 Figures 4.1-7 and 4.1-8 present the cladding temperatures calculated without oxidation. In this case, the comparison is axcellent. This test was different than FRF-1 in that a reflective sleeve was used inside the l test section which resulted in more uniform temperatures and less 1
radiation cooling. Also the thermocouple faced toward the center of the test section.
)
l l
l
E,- ,1 NUFRAP-T8
) TREAT FRF-2 ROD 12 (EM)
CLAD SURFACE TEMP (F)
' NODE =3 I
4000-
) 4 4
)
I r
3000-I m
b 2000- .
sw -
H' 4
4 I-1000-I' ,
l a
l.
- J <
I 0, , , , , , , , , , ,
, 0 5 10 15 20 25 30 35 40 45 50 TIME (SEC) l CURVE CODE * *
- TEST FIGURE 4.1-5 l
l
J l
l i 1 NUFRAP-T6
CIAD SURPACE TEMP (F) .1 1
NODE =4 L
E 4000-
, f 3000-
).
i
\
) C v 2000-N ,
f
- 1000-
/
i
- L 0-b ,5 10 15 20 25 3O 35 4O 45 50 TIME (SEC) :l l
C ur4 VE CODE * *
- TEST i F1GURE 4.1-6 j
1
NUFRAP-T6 i TREAT FRF-2-ROD 12 (EM)
CLAD SURFACE TEMP ($
NODE =3 I
3 00-F .
1 l' -
p
- 4. '1
! 2000c
)
1 l
~
y C
v
~
l f -1000- p
/
/
/
9'
/
I l
f /
0- ,
i t i 1 i i e i i i 0 3 10 15 20 25 30 35 40 45 50 TIME (SEC)
CURVI CODE * *
- TEST l NO OXIDAT!ON FIGURE 4.1-7 I -
3.
NUFRAP-T6~
L TREAT FRF-2 ROD 12 (EM)
C1AD SURFACE TEMP (F)
NODE =4 b
I 3000-l-
)
l i
) , , i 2000-J
, 'C v
I
- i i 1000-
)
L f
t 4 0- i i - i i i 6 i e a i i
.-- 0 5 10 15 20 25 30 35 40 45 50 TIME (SEC)
CURVE CODE * *
- TEST NO OXIDAT10N
)
FIGURE 4.1-8
1
[..
.)
I 1
l Clad Svelling - For NUFRAP-T6, the prediction of clad swelling is 1 t- !
I
'important in how it affects the thermal response of the fuel rod. The
> onset of clad swelling vill affect the thermal response of the fuel rod by reducing the gap condnetance. However, after the gap has opened significantly, the magnitude of the. strain is less important.1 Two i
models were examined in these test comparisons. The first was the best i estimate' deformation model (FRACAS-I/BALON2). FRACAS-I is a multi-axial l model for small deformations. BALON2 is a large deformation model performed at the hot spot. The second was the LACE deformation model - a simplified empirical approach based on NUREG-M30. In this approach, the 4 engineering hoop stress is correlated to a rupture temperature and f strain. As the rupture temperature is approached, the plastic strain is calculated as a fraction of the rupture strain. The measured strains (based on the average of the maximum,diametral strain and the diametral strain 90' from maximum) and the calculated strains (based on the predicted increase in circumference) are compared in Figures 4.1-9(a) and (b). As shown, both models show good agreement for small strains.
l However, for large strains. there is considerable scatter between the measured and predicted values. One reason for the scatter is that these I were multi-rod tests and NUFRAP-T6 models the deformation of only one i
rod. Therefore, ruptures which occurred early due to rod-to-rod interaction in the tests would have had larger strains if this
)
)
- 1. Note that for the purposes of NU's Evaluation Model, flow blockage effects are determined in NULAP-LB and do not rely on NUFRAP-T6 results.
l
)
)
1-l; i
I' 40 , , , , , , .
I 35 - -
- ~ 30 - * -
8 40 i 74 3 25 - - -
_)
5 20 - m m-l-- 1 15 - -' -
3 m FRACAS g 10 -o 5 ,,
- LACE
~
l .._ .
, c. 5 ma "
l O'
' 0 5 10 15 20 25 30 35 40 Measured Strale %
Figure 4.1-9(a) FRF-1: Measured Versus Calculated Strain f_
)- !
' 70 , , , , , ,
a i
7 60 - a N CAS .
- LACE *
> 1 50 -
e -
l s **
- i
! 40 - -
5 '
30 - -
! 7 i 5 3 20 - -
N Om "
o 10 -
g* g -
0 O 10 20 30 40 50 60 70 Measured Strain - %
Figure 4.1-9(b) FRF-2: Measured Versus Calculated Strain
) !
I
interaction did not exist. A second reason for the scatter is that the calculated and measured strains were determined differently. A third reason for the scatter is that the occurrence of rupture cannot be deter- .
1 mined precisely, and once it occurs the swellirig st' ops.
t Oxidation - The reported Zirconium - steam reaction was 0.2 percent for FRF-1. NUFRAP-T6 uses the Baker-Just (Reference 19) correlation to determine the rate of reaction. A comparison of the measured to l predicted overall reaction is shown below: l CATHCART/ !
l Test Measured FRACAS-1 LACE l FRF-1 0.2% 0.66% 1.26%
I I As indicated, the measured reaction was less than the predicted extent of reaction. However, the presence of helium in the test section was not modeled in the NUFRAP-T6 oxidation calculation and it is expected to have l inhibited the oxidation process. This probably accounts for the lov f.
f measured values.
l k'
Conclusion - The comparison of the predicted and measured cladding temperatures, particularly for test FRF-2, indicate that the combination of the NULAP5-LB and NUFRAP-T6 can accurately predict the thermal l
. L response of'a nuclear fuel rod to conditions similar to those expected during the late blowdown phase'of a large break'LOCA in a PVR.
4.2 SIMULATION OF PBP LOC TESTS t
The PBF LOC test series.vas designed to examine the transient behavior of fuel rods during a blovdown. Of the LOC test series, LOC-11 and 6 were t
(. de' signed to reach maximum' cladding temperatures in.the alpha phase' range i L
of Zircaloy (1070K). LOC-3 was designed to reach the transition phase f i
i I temperature (1190K), and LOC-5 was designed to peak in the beta phase range of temperatures (1350K). The rods used during these tests included
)_ fresh and irradiated fuel with low and high pin pressures. The LOC-5 test'is not included in these simulations because of the many hardware k
problems experienced during that set of tests. These problems included failures of the isolation valves and check valves. The test facility consists of an In Pile Tube (IPT) connected to a blowdown system residing )
within the PBF reactor. Only the IPT was depressurized during the tran-sient. Four fuel rods were contained within the IPT, each encased in a fluted shroud. Initial conditions and rod dimensions were typical of a
( ' commercial PVR.
I 1
The tests began after running the system at power to build decay heat and 4 to stabilize test conditions. The primary coolant loop system was isolated from the IPT to start the test. High speed blovdown valves in cold (and hot) legs were opened to start the depressurization. The r
reactor.pover was controlled in each test'to attain the desired peak clad temperature. After a blowdown and heat up period, a quench valve vas-opened to quench the rods.
1 The test rods were well instrumented with external thermocouple, center-line thermocouple, and plenum temperature and pressure sensors. Also,
' detailed post test measurements for the fuel rod conditions provide data i with which to verify the calculations of NUFRAP-T6.
1 FACILITY DESCRIPTION A diagram of the PBF test facility is shown in Figure 4.2-1. Figure 4.2-2 shows a cross section of the IPT. The fuel rods used in the tests were similar to commercial design rods, but were approximately 0.9 m in length.
(active fuel). The fuel enrichment was 9.5 to 12.5 percent, which is significantly higher than commercial rods.
f Several modifications were made to the IPT after the initial LOC-ll I- tests. These consisted of adding check valves seen in Figure 4.2-1 to L the top of the fuel rod shrouds to control the _colant conditions around i
the rods, and adding additional filler blocks in the upper plenum and downcomer regions to provide a closer approximation to the relative r
p b
X l
84owdown vei e t x
Aeflood velves
,g F ' Hot
- 'I Hot seg flupture W at s enchangers instrumentation 60008 piece teoisi.on valve Hea'[
nozzies (4)
Oi ; I i e-in-pile tube LOCA 0
] "' in piie tune bypass eme warmup I i bypass
*"' Thermas swesi , , Pressur Jer h" O gg,h,"', n 8 verve ' accumulators A l Loop pump velves (4) Core i .
~ -
- 1 i '"*t sotation i
"' I e instrumentation ,,,,, pio, g,,,,,
Cold 6e0' i 8000'D*Ce "' '
1 i . CONI 9 alve =
- snstrumentabon Blowoown p _~_ ,j Demenersiirec wster ten" maaeup tana Heeger Quench waive Quench
' tank
) f _
Cold leg rootation g .
IPT valve during quench upperhead y Demineralized Demineralized d $
water water storage pump Q tank Ftitor p>ece ,
Hefiood system
% Upper plenum
- [1
- INEL 21057 Outlet e
{ R h b Metered flow bypass
- upper particie
[ screen Center hanger Fslier piece rod g'g,/ e N
f i
Check valve #,e c ( ) '
3 Fiow tube L
- -- Fuel rod Bypass volume#-]" and flow f Faller piece 4 [ f %
shroud Lower support x Q plate Catch basket l
Lower plenum Lower particle screen I FIGURE 4.2-1 PBF LOCA TEST SYSTEM l
1 _
N ,
1 Flow shroud Flux shaper (stainless
\180- steel,3 mm thick) j .
~
90* - 9
,, 270*
- m. --'
, g, 61.09 mm i f ; 55.09 mm ,
270- l 90*
O 180*6; 12 '
-0*- 10 6180*y t
iS3 N
i 14.29 mm N/34.93 mm - l Test train hangerrod k I' ,'
270*- ) '
11 .
90*
Fluted
', shroud i
'd 13'0*
l NN\
\%W y
Rod to-rod pitch 49.39 mm O Flux wires
) o Cladding thermocouple e Inside shroud coolant X Self powered neutron detectors thermocouple
@ Self powered gamma detectors o Outside shroud surface thermocouple
$ Zircaloy 4 support tube -
10,7 mm outer diameter
- Differential thermocouple a inlet / outlet thermocouple f IN EL 3 0314 FIGURE 4.2-2 l
PDF LOCA FUEL TRAIN ORIENTATION
volumes in a PVR. Also, a metered bypass path shown in Figure 4.2-1 was added between the upper plenum and the downcomer to control the depressurization of the upper plenum and hot leg.
DESCRIPTION OF LOC-11C l The LOC-11C test cas performed with four, separately shrouded, fresh fuel rods of PVR 15X15 design. The initial plenum pressures ranged from atmospheric to a pressure representative of end-of-life (4.83 MPa). l l
The sequence of events during the test is as follows:
Time Description of Event 1
0.0 sec Reactor Scram 0.15 sec Isolation of IPT from loop l
0.25 see Hot Leg blowdown valve opened 0.4 see Cold Leg blovdown valve opened i >50.0 see Blowdown valves closed, Quench valves opened The blowdown of the hot and cold legs was measured by turbine flow i
j meters, drag disks, and gamma densitometers in the spools which were up-stream of the Henry nozzles. The Henry nozzles formed the choke plane during the test. These converging / diverging nozzles had throat diameters of 14.22mm. Turbine flow meters were also used to measure the flow at the inlet and outlet of the fuel rod flow shrouds. Additional instru-mentation vas-used to measure the pressure response in the hot and cold leg spools,.the fuel rod surface temperature and centerline temperature and the axial growth of the fuel rods.
l DESCRIPTION OF LOC-3 This test was performed with two fresh fuel rods and tvo rods irradiated in the Saxton reactor for a burn-up of approximately 16000 MVD/Mt. For !
each type of. rod, both lov and high plenum pressures vere used.
t' The sequence of events during the test is as follows:
Time Description of Event
-20.0 see Varm up line closed, shroud flow. reset to 1.0 1/s 0.0 see Isolation if IPT from loop
( 0.1 see Cold Leg blowdown valves opened i
<0.5 see Reactor power held at 100 percent 0.5 see Reactor power reduced to 25.5 percent in 0.3 sec 0.8 see Reactor power reduced to 14.45 percent in 1.2 sec 2.0 see Reactor power reduced to 9.77 percent in 2.8 sec 4.8 see Reactor power reduced to 6.80 percent in 5.2 see 10.0 see Reactor power reduced to 6.30 percent in 1.5 see
>50.0 see Blowdown valves closed, Quench valves opened Reactor scram f
)
P j_ , .
,7 7:
i In addition a the measurements provided in the . LOC-11C, test data was *
. . J taken measuring the fuel rod plenum pressure'and temperature. ,
I d
DESCRIPTION OF LOC i The LOC-6. test'vas very similar to the LOC-3 test in configuration and I
test sequence. The major difference betveren the tests was the power 1
~
history used. The' LOC-6 test sequence was as follows:
L Time Description of Event j .-20.0 see Varm up line closed, shroud flow reset to 1.0 1/s ;
7
-1.5 see Reactor. power reduced to 30.7 percent in 0.5 sec ;
I-
-1.0 see Reactor power reduced to 23.3 percent in 0.5 sec l -0.5 see Reactor power reduced to 17.8 percent in 1.0 sec 0.0 see Isolation of IPT from loop 0.1 see Cold Leg blowdown valves opened
}
0.5 see Reactor power reduced to 13.2 percent in 1.5 see i 2.0 sec Reactor power reduced to 10.1 percent in 3.0 sec 5.0 see Reactor power reduced to 7.60 percent in 4.0 sec 9.0 see Reactor power held at 7.60 percent for 90.9 sec
>100.1 see Blowdown valves closed, Quench valves opened Reactor scram t
L
ANALYTICAL MODELS The system response of the IPT and blowdown system was modeled using NULAPS-LB. The four test rods were lumped into one equivalent rod. The heat transfer boundary conditions of the rod were then provided to NUFRAP-T6 for the more detailed rod calculations. NUFRAP-T6 cases were run using both the FRACAS-I/BALON2 and LACE deformation options.
The initial stored energy of the fuel rods was determined by comparison with the fuel centerline and clad temperatures. The initial stored energy of the fuel is an important parameter in the calculation of transient fuel behavior. The stored energy calculated by NUFRAP-T6 is primarily controlled by the choice of the fuel relocation model and can be tuned by multipliers on gap conductance. In a typical EH calculation, the stored energy would be determined by an approved steady state fuel performance code. The test results presented later demonstrate that the l NUFRAP-T6 EM (no relocation, concentric pellet) provided fuel centerline temperatures and clad temperatures which compared well with the test data I
for tests LOC-llc and LOC-6. The LOC-3 fuel centerline temperature, however, was more consistent with the FRACAS-II relocation model calculation. Since the purpose of these test comparisons was to
)
determine how well the EM predicts the thermal-mechanical response of the fuel rod during a transient, it was necessary to use the gap conductance
's multiplier to adjust the initial stored energy of.,the fuel for test LOC-3. A multiplier of 2.5 was found'to approximate the relocation model results and provide good agreement with the fuel centerline temperature.
j System conditions from NULAPS-LB vere compared to test data to assure.
the adequacy of the system model. Fuel centerline and clad surface temperatures were compared to test riata for validation of the thermal response calculations of NUFRAP-T6. Clad deformation strains were 1~
compared for the mechanical model validation. i l
The fuel rods modeled for these tests are the rods which were described
- in detail in the reports. These rods were the fresh, high. pressure rods designated 611-3, 603-3, and 606-11.
I LOC-11 MODELS The description of the LOC-11 test is given in Reference 22. This report provides a description of the test transients and results, as well as I
I descriptions of the RELAP4 and FRAPT-4 models used in pre- and post-test simulations.
Appendix C of Reference 22 contains a description of the RELAP4 model used in the pre- and post-test comparisons. This description was used to set up a NULAP5-LB model. All volume dimensions, heat structure dimensions, and nodalization vere based on this description.
l
-Figure 4.2-3 shows t'he nodalization used in the NULAPS-LB model for test LOC-11. The test rod nodalization was selected to center nodes at the locations of thermocouple. The Henry-Fauske and Moody critical flow models were used to calculate the break flow. Discharge coefficients of 1.0 for single phase and 0.8 for two-phase flow were used. The NULAPS-LB EM heat transfer options were used in all cases.
Appendix E of Reference 22.contains a FRAP-T model description. This was L
used as the basis for the NUFRAP-T6 input model. The NUFRAP-T6 input is based on the data reported in Appendix E of Reference 2. The Test rod simulated is the 611-3 rod. One of the important mechanisms for heat 1
I transfer late in these tests was radiation to the fuel rod shrouds.
NUFRAP-T6 contains a shroud radiation model for this purpose. This model was used with the temperature history for the shrouds reported in l Reference 22.
LOC-3, LOC-6 MODELS Several changes were made to the PBF IPT internals after test LOC-11.
The major changes are described in Reference 29. These included: adding check valves to the outlet of the fuel rod flow shrouds, adding a
' controlled bypass from the downcomer to the upper plenum and adding relatively massive filler pieces in the upper plenum and downcomer. In addition to these modifications, both fresh and irradiated fuel rods were used in these tests. In order to equalize the relative power of the rods
2Z , .41 2 0-2 '
,12:1, ,12:2, - 22:1, l 58 i i 19 i , 20 p I 22 i i 23 Sa:1 l 22:2 l 22-1 EE 1 31 ! '
n d 21 h 2R s
18- Loop d 46 l Henry gl 29 Isolation Valves _
344 l 99 Nozzles 50 f
g j
I 0
A5 1 2 3h g 32 ,gi 21:1 I yg 1 ell T 32 ,
l 56 l g l 5 -4 4 H I 25 l 24 EE:1 I if ' A:2 33 l dQ 17 5 34 4
to 21:2 I I 1Z:1 3 28 16 21:1 I I 11 g '
7 7 2
[
6 6 8 5 ** 5 N 4 4 U 3 e ,gg 3 3 2 2 1 1 1 l
2fd l l 10 1 l12Z, 26 10 2 l
O ! I Ed 1m 9
l a:2 a:1l 8
Figure 4.2-3 Node Diagram for PBF Test LOC-11 l
! f P i piip p q immimmwa
3, stainless steel flow shrouds were used for the fresh fuel rods. . In order !
to flatten the power distribution in the center of the. rod, a stainless steel " flux shaper" cylinder was added within the IPT shroud. #
Figure 4.2-4 shows the nodalization used in the LOC-3 and LOC-6 tests .
1 which included the test modifications. The new volume information was l
taken from Reference 24. The active length of the fuel rods is taken to be 0.88 meters. This length is modeled as six equal size nodes of length 0.1467 m.
The power history for LOC-3 was taken from Figure F-1 of Reference 23.
The initial rod average linear heat rate was 44.7 kW/m. The radial power profile was assumed to be the same as in LOC-11. The axial power profile was taken from Figure F-3 of Reference 23.
The power history for LOC-6 was taken from Figure B-7 of Reference 24 with decay heat (ANS79 Standard) added in. The axial and radial profiles were the same as in the LOC-3 simulation.
l l
l s
180 al i 41 I 20-2 '
, .1]L1 ,11:2 i . - 22:1, l 170 , i, 19 , , 20 p l 22 , i 2S 121h1 l 221h21 120.h2 El 31 ! ,
d 21 h af d E E .
150 g
a R
- Loop lsolation d 46 l 39 Henry Nozzles 50 E HQ l Valves y 144 l f*
l d1l2l3h g 22 , g T'
~
200-1T T 2011 g :11T 32 ,
l 56 l l5 M 4 f ! 25 l 24 140 EE:1 I 11 k2 33 l
.4Q 5 34 ' ;
i 121 I I 122 4
- 131 132 130-
- 12Q.1 1 1 l 130 l 3
28 31g all i 12 i
6 6 5 5 g 4 4 7
l 3 @ 3 2 2 1 1 2E1 l l 10-1 l1QZ 26 10 2 i s 83 I IM 1 9
l a-2 a.1 l 8
Figure 4.2-4 Node Diagram for PBF Test LOC-3 and LOC-6
CALCULATION AND RESULTS Comparison with LOC-11C Tests Results
.i In order for an accurate assessment of NUFRAP-T6, it is important that the boundary conditions provided by NULAP5-LB be accurate. Therefore, several system' parameters are examined to demonstrate the adequacy of.
NULAP5-LB. Figures 4.2-5 through 4.2-8 show a comparison betveren the aeitsured and calculated flows and densities in the hot and cold legs.
The code simulation is excellent, except for the cold leg density. This parameter was reported to be suspect in the test results report.
Figure 4.2-9 shows a comparison betveren the measured and calculated pressure in the hot leg. Again, the agreement is excellent. Figures 4.2-10 and 4.2-11 show the measured and calculated upper and lover shroud turbine meter flows. The comparison is very good for the first four seconds of the transient. Af terwards, NULAPS-LB shows an early flow re/ersal. This was also seen in the post-test calculations with RELAP4.
The trends of the flow and the absolute magnitudes are approximately correct. Therefore, the heat transfer boundary conditions should not be significantly affected.
NUFRAP-T6 was run modeling the 611-3 rod and using the heat transfer
'oundary o conditions from the case described above. Two runs were made.
The first run used the code options which vill form the Evaluation Model.
. Specifically, the LACE deformation and Powers /Heyer clad swell and l
I - . i
PBF l LOC-11C HOT LEG SPOOL FlhW 10- 1* ,
9-8-
7-n
- h 6-5 W
a: 5-3 w
$ L1 -
5 .
3- O+
+
2-
+
+
l- +
+
+ + + +
0 + ,,,, , , ,,, , ,, ,
5 10 15 20 25 30 0
TIME (SEC)
CURVE NULAPS + + + PBF I
l FIGURE 4.2-5
l PBF LOC-11C C0th IRG SPOOL F14W i
1 10- + l 9-1
, 8-l 7-i :
i . ^ t l M J d 6-5 w l Q +
a: 5-
, 3:
O k
1 m
m 4 k l
5 I
)
3-4(
+
+
2-
+
+
l- +
+
3
+ +
+ + + +
+
+ + +
0-+ ,
0 5 10 15 20 25 30 TIME (SEC) l CURVE NULAPS + '+ + PBF FIGURE 4.2-6
PBF LOC-11C HOT LEC SPOOL DENSITI 800- .
k 700-
+ + t-
.+-
l 600- 1 1
500- l f ,,
N O 400-s.
D b
C 300-en Z
uJ Q
200- +
+
100-f
- - - _+ + + +
0-l t
l
-100 ,. . ;, ., ,
-5 0 5 10 15 20 25 30 TIME (SEC)
CURVE NULAP5 + + + PBF FIGURE 4.2-7
\
h PBF LOC-11C
- cois tra spooi.omsrn j 800-700-J-
+
r
+.
+
+
600- :
)
500-i 3 400-s +
5 l >-
) h 300- ,
5 a
200- +
+
++
100 -
+ +
+ _
+ t + +
0 -
-100 ,, ,,,, ,
, , , ,,, ,i., , ,,. ,, ,,,,
3 10 15 20 25 30 L
-5 0 5 TIME (SEC)
CURVE NULAPS + + + PBF FIGURE 4.2-8
PBF LOC-11C Hof IJlG SPOOL PRESSURE 16-i 15-14 -
13- ;
l.
12-
- 11-10-
^ -t 9-v w 8 e
o m
m y 7-c.
6-5-
y.
) 3-
+
2-
+
)
1- +
+
+ +
0,i , . . . , ,, ,,
- i. , ,, ,,,. ,
i TIME (SEC)
CURVE NULAP5 + + + PBF FIGURE 4.2-9
PBF LOC-11C UPPER TURBINE F14W j l
) 2-h l
'1
). -
I
' +
1- + +
+
+
1 .
++ +
+ ++
, 4 +
g +
h v
++
3: [ +
0 e ,
\ ++
m f
5 :
p u.
+
h (-k.: =
+
}
_i.
)
t I
-2 ,,,,
i TIME (SEC)
CURVE -
NUL fiP 5 + + + P8F F1GURE 4.2-10
I I
l PBF {
LOC-11C 1DWER RIRBINE FLOW 1
2 a
+
l-t 1
) +
.+
^ + ,
m + ++
++ ++
j h
+
++
3
) o a
" !- +
0 2 'I 0
x W h n i O
/
I f +
+
+ +
+
) l
-2 ... . . ...., ,, ..... ,, ,
.... .i
-5 0 5 10 15 20 25 30 1
TIME (SEC)
CURVE NULAP5 + + + PBF FIGURE 4.2-11 l I
)
i rupture model, the. Baker-Just clad oxidation mode, and the concentric pellet gap-model were used. The second run used the more typical FRAPT-6 code options, such as the FRACAS-I and BALON-2 mechanical deformation I model, the FRACAS-II gap relocation model and the Cathcart oxidation
- model. This second case is included to provide a comparison between the EM model and the more mechanistic model.
The results of the EM case are presented in Figures 4.2-12 through 4.2-15. Figures 4.2-12 and 4.2-13 present the comparison of the measured
) and calculated clad temperatures at 0.53 meters and 0.62 meters. The code calculations show that NULAPS-LB correctly calculated the time to f CHF and that the post-CHF heat transfer was a good representation of the test conditions, The shroud radiation model was effective in simulating the heat transfer late in the test so that the calculated clad temperatures were close to the measured temperatures. The fuel centerline temperature calculated by NUFRAP-T6 is compared to the f measured temperature of 0.53 meters in Figure 4.2-14. The initial temperature was close to the measured value. The NUFRAP-T6 fuel temperature response shows a similar decrease in temperature but a higher value late in the transient.
I
)
i
- -l o
NUFRAP-T6 PBF LOC-11C CIAD SURFACE TEMP (K)
NODE =5 1200-i 1100-
+ +
1000- + +~
\ +
p+ +
++
f-
- +7+e m 900- j .>
6 l cL $+
D
?A Q 800- !,
d !
\ I j.
700- f i
I .'
+ . I 600- t".."
f' 500- . . . " . ... ,,. .,
f i- ... ... ... . .
-5 0 5 10 15 20 25 30 TIME (SEC) f.URVE - CODE + + + DATA EVALUADON WODE1,12 NODES l
nouRe 4.2-is l
(+'
NUFRAP-T6 PBF LOC-11C CLAD SURPACE TEMP (K)
NODE =6-l '.
1200-
\
1100-I 1000- -
s i
+M + +
, 900-(
l i
[ ++
.,+
- + +
+
6 f f %e p+
y >
} n.~
j,
)
s '
600
@ g" d i+
l' l
700- l I
I l
! I' 600 I I. ;
1
) l I
5 0 0 -', , ,,, ,,, ,
-- S C 5 10 15 20 25 30
/
TIME (SEC)
CU;vE CODE + + + DATA EVALUATION WODE1.12 NODES F1GURE 4.2-13
i 1
NUFRAP-T6 l l
~ PBF LOC-11C 1 1
FUEL CENTERUNE TEMP (K) I t 2500- ---...------ ,
\
- 's, i'
1 t
1 i
\,
I \
20004 i
\ t, x I.', ,
v a ',
s +
w \ '
~ \ ,
t w i ',
_z_
i ,
I a ',
a:
w ,
w ',.
2 w \,
o ,
1500-t ,
\,
4 ',
1 ,
l
)- '.,
) . . . , "
1000- ... ,,. .,
-5 0 5 10 15 20 25 30 TIME ISEC)
C'Jhv E CODE ------- DATA EVALUATION WODE1.12 NODES FIGURE 4.2-14
' /
NUFRAP-T6 PBF LOC-11C HOOP STRAINS 1 1
I l
CSTRN O.17 4 ,
0.16- 1 0.15- ,
O.14 O.13-O.12-0.11 ,1 0.10-l 0.09-!
0.08-0.07- ,
0.06-0.05-0.04-0.03-0.02-0.01s 0.00- ' ~ ~ ' ~ ~
s i e i i i i e i i 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Z
CURVE * *
- CODE DATA LTALUATION WODEL,12 NODES FIGURE 4.2-15 i
i The calculated and measured clad circumferential strains are shown in Figure 4.2-15. NUFRAP-T6 did not predict clad rupture which is consistent with the test. The clad strains calculated by the EM are much greater than the measured strains.
The results of the FRACAS-I/BALON2 case are presented in Figures 4.2-16 through 4.2-19. The fuel thermal response is very similar to that of the EM. However, the initial fuel temperature was substantially lower as are the clad temperatures early in the heat-up.
The results of these tests demonstrate the difficulty of modeling fuel rod behavior. Figure 4.2-20 shows the comparison of the measured and calculated clad elongation for the EM case. The EM model does not include fuel relocation effects and therefore was unable to match the initial clad contraction. This contraction was caused by the following behavior. During the initial heat-up, the fuel radial expansion caused clad Jock up and the axial expansion elastically stretched the clad. At the start of the transient the power was reduced causing the fuel to cool and contract. This allowed the clad to release and resume its normal length. Figure 4.2-21 shows the comparison of the measured and calculated clad elongation for the second case. The FRACAS-II relocation model predicts the clad behavior with remarkable accuracy. In spite of this apparent correctness of the relocation model on mechanical phenomena, the prediction of the thermal effects was poor. The cases run without the relocation model provided much better agreement with the fuel
NUFRAP-T6 i' PBF LOC-11C CIAD SURPACE TEMP (K)
N00E=5
)
1200-I
/ l 1100-I
++ + +
1000- +
/ ++* I
. / #+A+
s n 9008 .,.
u +
v Si /*
}
l+
Q 800- f,4 a.
<) i I
I 700-i I
.___ g. ,e 600- #O l-500 4,. .-.,. .,. ... ..
-5 0 5 10 15 20 25 30
)
TIME (SEC)
! CURVE CODE + + + DATA 1
FRACAS /BALDH2 WODEL FIGURE 4.2-16 ii a r e a i inse a
'.t-I t
~
[. <
NUFRAP-T6
. PBF LOC-11C CIAD SURPACE TEMP (K) l NODE =6-i 1200-
)
l .1100-I 1 1000- y !
++* + l
,,+ .
+
I
., 900- ++- !
U , 84+ ++
l S '
+
% + i
@ 900-1 700- j
.i .
600- ,
1
)
500 , , . .,
}
L -5 0 5 10 15 20 25 30 TIME ISEC) l CURVE CODE + + + DATA FRACAS /BALON2 WODEL FIGURE 4.2-17
4 1
1 l
i i
i 1
.i 1
NUFRAP-T6 "
PBF LOC-11C
."JEL CENTERUNE TEMP (K) 2500- ....- - ---- ,
, 's,
. i
+
\
\
'2000- > '.
e
\ .
s y- 1 i v i i
\
oe i . ,
w
- i p t w , .
a '.
c:: .
y .
e-z .
\ '.
w r U ,
1500-a g g .
r ~
's, t
?
y
..... ~~-- -........
1000
... ., 1
-5 0 $ 10 15 20 25 30 TIME (SEC)
I CURVE CODE ------- DATA f
FRACAS /BALO:12 WODEL F1GURE 4.2-18
\ . . _ _ = - - _ - _ _ - _ - _ - - _ _ - _ _ . _ _ -
NUFRAP-T6 PBF LOC-11C HOOP $3 AIMS CSTRN 0.17-1 0.16
- 0. , o 0.14
) O.13 ]
1
) 0.12 $. ,
=
1
- 0. ! ! 1 i
) 0.10 4 i 4
0.09 d
~
i 0.08 ,
-1 0.07s 0.06-0.05)
) 0.04 -
0.03-0.02-
- 0.01-
) ,
' - ' ' ' " ~ ' * "
0.00-
) 7- ' . i i i e i i i i
) 0.G L. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2
f f. U c.V E * *
- CODE DATA FRACAS /BALDN2 WODEL FIGURE 4.2-19
NUFRAP-T6 PBF LOC-11C -
CIAD AX1AL DhSPIACMENT (WETERS) 0.002J '
l 4
1 0. 00 L '
,***----~~~~~,,_,,,
,,..o ....
4 I I ,
l ;
l , . . '-
1 I I
l l
/
ce >
- ,/
> g-0.C00-]
w 3
s" t l
\ l 1
l l
- i 1 . .
i l
) l
- l
). - 0. 0 01 -). ;,-
[ }
i l
).
-0.002 ,
-5 0 5 10 15 20 25 30 TIME ISEC) l l- CURVi CODE -------
DATA 1
EVALUATION MODEL.12 NODES FIGURE .4.2-20 NUFRAP-T6 PBF LOC-11C 1 01.AD AX1AL DISPLACEMENT (WETERS)
O.002J J,
i n
i i !
f 0.001- ,
__,..r
.i
'~
4 a'
m m 1
/
y ~ 0. 000 .'-
w
] -
l r_
! / /
,.'f i l 1 .I
- r
-G.001<.
i ,
l 8 i,,..
I
- k. r.
l
- L,!
\>
J f
) ',
-0.002- ,,. .,
.- .i- .i. ... ... ...
-5 0 5 10 15 20 25 30 TIME ISEC) f C U F '! F CODE -------
DATA
(
FRACAS /BAlhN2 MODEL F1GURE 4.2-21
temperatures. This apparently contradictory information seems to indicate that fuel relocation and PCHI occurred at the high power region below the fuel centerline thermocouph. However, the fuel in the region of the centerline thermocouple apparently did not crack and relocate, which resulted in a relatively low gap conductivity and a high centerline temperature.
Comparison with LOC-3 Test Results 1
Figures 4.2-22 through 4.2-24 present the system response as calculated by NULAP5-LP and measured during the test. The pressure response shown
- in Figure 4.2-22 demonstrates excellent agreement with the test data.
Likewise, the cold leg spool flow shown in Figure 4.2-23 indicates that the critical flow calculated by NULAPS-LB is reasonably accurate. The calculated and measured flow at the inlet of the fuel rod flow shroud is presented in Figure 4.2-24. The initial dovnvard surge is predicted well f by NULAP5-LB. The subsequent flow decay is calculated to be more rapid than the test data indicates. The overall prediction of the system t
response is very good, and thus, provides reasonable boundary conditions
! for NUFRAP-T6.
)
The comparison of the NUFRAP-T6 EM calculations with test data is presented in Figures 4.2-25 through 4.2-29. The NUFRAP-T6 cases used 12 equally spaced axial nodes. Additional cases were run with the EM using six equal sized axial nodes to determine the sensitivity of the results l
)
PBF LOC-3 l CND MC SPOW. PMS 16-1 i 15-4 14-13-t 12- -
11-10-i
=C 9-g +
y 8- +
o m
W +
w 7 x
1 +
6-e 5- +
4-
+
1 r
+
3-
)
2-1-
r
- 0. i .
-5 0 5 10 15 20 25 30 TIME (SEC)
CURVE CODE + + + DATA FIGURE 4.2-22
4 PBF LOC 3 l Colb 12G SPOOL F1hv i
i
.60-1 l
.l 50- -
l.
I I
40-n s
e 5
w, m 30-E o
d m i 1'
I 1-20- +
! +
I 10-
+
+
++
+ +
.+ 4
+ ,
4 +
,,. ,,, ,, ,, ,, . t,
i,, ,
[ ,3 , , ,i,
-5 0 5 10 15 20 25 30 TIME (SEC)
CURVE CODE + + + DATA F1 CURE 4.2-23
PBF ,1 LOC-3 l LovsR Tuname Flow !
2-
).
1-t i n
) ,.
so o
J Ls. '
0-- - -.
+ '
+
, 4+* ++%+++++
+
y / +. ++ .
=. ..+
$ 4 O ',
f t
-j. f I
) l
+
-2 '
i i-8' 15 20 25 30
-5 0 5 10 TIME ISEC)
CUP,vE CODE + + + DATA FJCURE 4.2-24
- 100 -
)
i a
NUFRAP-T6 i PBF LOC-3 CIAD SURFACS MP (K) '
. NODE =9 1500-i 1400-1300- ,
i 1200-1100-n -
x f 1000- ,,++ +++ ++++ +
+
W +
i a
+
d 900-
+
l-800- +
) I I
700 - !4 I
3'%
600i 500 ,,.. ... ... .. ,,
-5 0 5 10 15 20 25 30 TIME (SEC)
CU R'/ E CODE + + + DATA EVALUATION WODEL 12 NODES FIGURE 4.2-25
- 101 -
1
.t ,
l i
3 f
l NUFRAP-T6 !
PBF LOC-3 .
CLAD SURPACE TEMP (K)
NODE =10 i
1500l t
i j.
1400-
)
)
1300-
)
- 1200-1100- __
n
.5
+ + +
1000- , , +
4,
< +
c at
+
d 900- l i*
800- /
I 700 i
- c 6
.- I 600- .Q 500 ... ... ... ... ... .,
10 15 20 25 30
-5 0 5 TIME (SEC)
.URVF CODE + + + DATA I
l EVALUATION WODEL 12 NODES FIGURE 4.2-26
- 102 -
'k.
i
)
NUFRAPT6 PBF LOC-3 FUEL CENTERUNE TEMP (K) 2500'
) l 2000-n ..............
x v
I
- a. i; 2 \,
w
~ \,
w z ',
m '.
w C '
O .
o . ,
1500- i, i
\ '.,
N(\,
i
( '
/ -
1000 ,, ... ... ... ... ... ... . ..,
10 15 20 25 30
-5 0 0 TIME (SEC)
CURVF. CODE ------- D A T A EVALUATION MODEL 12 NODES f
FICIJRE 4.2-27
- 103 -
NUFRAP-T6 PBF LOC-3 !
R0D GAS PRESS (WPA) ,i 1
16- ,
j l
+ + +
\ ,
u.
gy. 'g .'N, i
s 4 '
A
+
i- 12-
. L-e 10 i -
0- +
2.' .
w +
a:
M 6' w.
'is' ..
' i C
O c: 6-I t 4- >
l l
+
+
t
+
2 *1 * +
+
1
+
j +
+
0 ,. . m, . .
2
-5
^
.. 5 10 15 20 25 30 TIME (SEC) s li' VE CODE + + + DATA EVALUATION MODE 1,12 NODES t
FIGURE 4.2-28
- 104 -
NUFRAPT6 PBF LOC-3 HOOP STftAINS CSTRN 0.8-1
- 0.7-O.6-i O.5 3 i
r i 5
' 0. 4 -
0.3-l O. 2 -
) 0.1 -
- 4 4
r
,/
0.0-i . e i i i e i i .
0.0 0. i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Z
CURVE * *
- CODE DATA EVALUATION WODEt,12 NODES FIGURE 4.2-29
- 105 -
to node size. . Figures 4.2-25 and 4.2-26 present the. clad temperature
. response at two locations,(0.62' meters and 0.67 meters). It can be seen j
that NUFRAP-T6 bounds the data. Figure 4.2-27 shows the fuel centerline i
comparison. Note that a multiplier of~2.5 on the gap conductance was used. The transient response is fairly good but again exhibits a more j rapid decrease than the centerline thermocouple. Figure 4.2-28 presents the pin pressure response and indicates the time of rupture. NUFRAP-T6 l demonstrates excellent agreement with the data on this parameter.
. Finally, Figure 4.2-29 presents the calculated and measured clad strains.
The figure indicates that the EM provides a very good model of the clad swell and rupture. Only the rupture node strain is significantly different from the data and the code predicts more strain.
Similar plots are included in' Figure 4.2-30 through 4.2-34 for the FRACAS case. Again, the clad temperature response shown in Figures 4.2-30 and 4.2-31 is good. The sharp rise in temperature at 14 seconds in
-Figure 4.2-31 is caused by the beginning of oxidation calculated with the Cathcart correlation. Figure 4.2-32 shovs'even better agreement with the l
i' rod pressure measurements. Note that a failure probability of 0.6 was used to set the rupture time. Figure 4.2-33 shows the measured and
)
calculated fuel centerline temperatures. The relocation model was very accurate in this case indicating that the fuel preconditioning was effective in cracking and relocating the fuel. The transient response is similar to that seen in the EM case. The hoop strain comparison is
- 106 -
t
NUFRAP-T6 PBF LOC-3 .
CLAD SURFACE TEMP (K)
N0DE=9 ;
j 1500-1400-1300-1200-1100-2
. , + + +
+++ + +'
@ 1000- ,+++
w +
" ++
e /
d 900-
[*
i 800- I-
~
l 700- l4
.I I
600- --._ _ __1g'f 500 ,, ,
-5 0 5 10 15 20 25 30
)
TIME (SEC)
CUhvE CODE + + + DATA FRACAS /BAIDN2 WODEL, FIGURE 4.2-30
- 107 -
NUFRAP-T6 PBF LOC-3 CLAD SURPACE 11!XP (K) ,
NODE =10 1500
1400-1300-1200-1100-Q v
@g 1000- ,, , + +'+ +
+
W .++++
+
g
+
d 900-
. +
800-
.s 700- f
+
600- (l
[
500, .,
- i. ... ... .
-5> 0 5 10 15 20 25 30 TIME (SEC)
CUPVE CODE + + + DATA FRACAS /BALDN2 WODEL ncURE 4.2-S1
- 108 -
NUFRAPT6 PBF LOC-3. i I
FUEL CENTERLINE 1TMP (K) {
i 2500- i i
l n
N d
2000-n x ,
- \ '
\ ',
o.
- s ,
w t. ,,
w i z \ ',
- , g, a
(E i$
w -
P- -
z -
w o 1 i, 1500- I\ \,
's a
l t
\\ ,
t .
l f
1000 ,. ... ... ... ... .n.... ...- . ,
-5 0 5 10 15 20 25 30 TIME (SEC)
C 'J R '! E CODE ------- D A T A
! FRACAS /BAIDN2MODEL naURE 4.2-32
- 109 -
r L
NUFRAP-T6 I PBF LOC-3 ROD CAS PRESS (WPA) 16-
+ F +
T 14 - \"
\+
f \
~:
12 -
n 10-
+
W 5 8-0
- 5. .
8 a: 6-4-
+
+ l
+ 1 2- +
+
+ )
. + i
+
0- + ,
i- - -
-5 0 5 10 15 20 25 30 '
TIME (SEC) j CUFVE CODE + + + DATA TRACAS/BAlhN2 MODEl, ncURE 4.2-33
- 110 -
1 i
NUFRAP-T6 .i PBF LOC-3 4 J ROD CAS PRESS (WPA) 16-
+ > +
6 kN " \
\+
s.
\ \
12-K
,., 10 -
- z w.
I
+
x R 8-0 i .
8 m 6-l 4-
+
+
+
2- +
+
+
+
0- . .,. ,. ... ... ...
2
-5 0 5 10 15 20 25 30 TIME ISEC)
CUFVE - CODE + + + DATA PRACAS/BAlhN2 MODEL F1 CURE 4.2-33
- 110 -
<? '
e
~('
s NUFRAPT6 ,
. PBF LOC-3' HOOP STRAlNS -l C S T.RN 0.20 }
0.^ 19 -
0.18-O.17-t O.16- I 0.15- I s 1 0.14 -
O.13-4 0.12] ,
- 0. !! d l i
0.10 d, j l
- 0. 09 J( ,
0.08 : I 0.07 , /.
- 0. 06 j l,,l e i .
0.05k l 4 /
0.04 i /
- 4 /
0.03 ,
O.02- }
/
0.01- /
0.00- - i i i i - i i i- a i 0.0 L. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 7
C f!s'* ? * *
- CODE DATA FRACAS /BAlhN2 WODI2.
FIGURE 4.2-34
- 111 -
-I' t I
t presented in Figure 4.2-34. The FRACAS-I calculated-strains chov very good-agreement with the measured strains.
L Figures 4.2-35 through 4.2-39 present the results of the EM case using ;
i six axial nodes These figures indicate that there is no significant effect of using the larger nodes for this test. The rupture time is '
! 1 l increased slightly but the effect on clad and fuel temperature and clad strain is minor. Note that the node 5 clad temperatures are almost identical to the node 9 temperatures from the 12 node case.
Comparison with LOC-6 Test Results The results of the LOC-6 test simulation are discussed next. The cold leg spool pressure comparison with the LOC-6 test data is presented in Figure 4.2-40 and shows excellent agreement. The fuel rod shroud inlet flow comparison is shown in Figure 4.2-41. This' flow shows the same i
trends as the LOC-3 data and the code comparison is considered to be reasonable. No cold leg spool flow data is available for comparison but since the system and valve sequencing were similar to the LOC-3 test, the system response is expected to be similar to LOC-3. The NULAF5-LB l
prediction of CHF occurred at approximately 2.5 seconds and traveled from top to bottom. Note that the data report (Reference 24) assumes the CHF to occur first at the bottom and travel up the rod. The first CHF indication from the data was the measured clad elongation that occurred at 1.0 seconds. The clad thermocouple indicated CHF at 4 seconds.
{
l - 112 -
NUFRAP-T6
. PBF LOC-3 )
CIAD SURFACE TEMP (K)
NODE =4 l 1500- I 4
1400-4
.1300-1200- i 4
!!00-2 1000- ,+++ +++ ++++ +
W +
4 e
d 900- +
l q+
800- +
700- +
l
^
600- Q 500 ,. ,. ... ... ... ... ... .,
-5 0 5 10 15 20 25 30 TIME (SEC)
CURVE CODE + + + DATA EVALUATION MODEl. 6 NODES FIGURE 4.2-35
- 113 -
1 NUFRAP-T6 PBF LOC-3 CLAD SURPACE TEMP (K)
NODE =5 1500-1400-1300-1200-1100-n -
5
+ + +
i @g 1000 - ,, + +
+
- *++++
+
q
+
I d 900-
+
I 800-
+
f-700-l 600- }
500- ..
l 25 30
! -5 0 5 10 IS 20 TIME (SEC)
CURVE CODE + + + DATA EVAWATION WODEL,6 NODES F1GURE 4.2-36
- 114 -
1
--_x________-____-__--
, _ , _ . . _ . . .. - - - - - - - - ~ - - - -
NUFRAPT6.
PBF LOC-3 )
FUEL CENTERUNE 1TMP (K) 2500-2000-m ..............,
- a. ,,
2 's ka.J '
i P= ',
w '.
z 4 1 w i.
C '.
o '.
4 1500- \,
i, e g 1
l '
) .
~,
a.g
- m 1000- ... .... ... .. .,
-5 0 5 10 15 20 25 30 TlHE (SEC)
CURVE CODE ------- DATA EVALUATION WODEL,6 NODES FIGURE 4.2-37
- 115 -
NUFRAP-T6 PBF LOC-3 ROD CAS PRESS (WPA) 16-c . .
\
14 -
+
-H
+
12- ,
+
m 10-g +
) @ 8-
!0 '
8 a:: 6-l 4-
'k t 2- +
+
+
+
+
0 ,, , ,, ,,, ,,, ,,, , ,
2
-5 0 5 10 15 20 25 30 TIME (SEC)
CURVE CODE + + + DATA EVALUATION WODEL,8 NODES
{
FIGURE 4.2-38
- 116 -
NUFRAPT6 PBF LOC-3
- HOOP STRAINS CSTRN 0.7-4 0.6-1 I
0.5-0.4 0.3-0.2-
) *
/ 0.1- ,
s
,m
- 4 0.0 , , , , , , , , , ,
a O.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Z
f
( CURVE * *
- CODE DATA
[ EVALUATION WODEL. 6 NODES l
F1GURE 4.2-39
- 117 -
fT-i
. 'i PBF LOC-6 CO2 WG SPOOL, MS ,
1 16-
\ .\
15- 1 14-13-i' 12-11-10-
.+
- e
[
2-9
+
u e- .
o m
m y 7-c..
6- ,
.5-
+
4-
. 3-2-
+
+
1-4+ + + +
l-0 ,, . ., , ,
10 15 20 25 30
! -5 0 5
\ TIME (SEC)
CUR'!E CODE + + + DATA P1GURE 4.2-40
- 118 -
4
)'
p.
PBF LOC-6 LOWER WRSINE F1.DW 2-
)
l I
1 1
'1
! I i
J l
l 1
f.
1- + + 1 1
)
n '
i d
a o
)
?
M [ ++%++ +*+#
i C ;>+4
$ r, +
8 +
+
[.
e I. I l-
+
-2 ; ,
,,. ., . ... ., . . .. - 4
-5 0 5 10 15 20 25 30 TIME (SEC)
CURVE CODE + + + DATA F1GURE 4.2-41 11e .
)
Therefore, NULAP5-LB's prediction at 2.5 seconds is considered 4 reasonable.
The results of the first EM, 12 axial nodes case are presented in Figures'4.2-42 through 4.2-44. There is no fuel centerline thermocouple i
data available for this test. Therefore, the uncertainty in the initial stored energy in much greater. The NUFRAP-T6 simulation with the FRACAS-1 and relocation models showed very low clad temperatures for rod i
11 and a late rupture time. The clad temperatures for this case were similar to those reported for rod 12 which had been previously irradi -
ated. Figures 4.2-45 and 4.2-46 show the clad temperature and pin pres-sure response or this case. Because of this response, it is assumed that the fuel preconditioning was not sufficient to crack and relocate the i fuel in rod 11, and therefore, the no relocation, concentric pellet option is correct. The EM calculations presented in Figures 4.2-42 through 4.2-44 vere made using a gap conductance multiplier of 1.0. The j predicted clad temperature response is excellent in comparison with the data. The early CHF and over prediction are consistent with tt" assumed fin effects of external thermocouple. The pin pressure response is also very good, although the EM ruptured approximately one second early I
(Figure 4.2-43).
I
}
The hoop strain calculation of the EM underpredicts the data. Only the rupture node was calculated to have significant strain. The magnitude of the calculated strain is consistent with most of the rod data near the
- 120 -
)
l NUFRAP-T6.
PBF LOC-6 CIAD SURFACE 1EMP (K) 1500-
\
t 11100 -
l 1300-l .
1200-1100-n l 5 1 g 1000- [, + +
+
2
[j 900- ,
i f 800-
+
700-1.
600- +
+
500- ..
i-
] -5 3 5 10 15 20 25 30
/
TIME (SEC)
CURVE CODE + + + DATA EVALUATION WODEL 12 NODES FIGURE 4.2-42
- 121 -
I NUFRAP-T6 i PBF LOC-6 !
ROD CAS PRESS (WPA) 30-
+
25- +
a
- \,,_,
+
20-2 ei I +
E 5 15 l '
l0
? ,
8
= :
+
10-
, N 5- +
+
+
+
+
0 ,, ,,, ,,, , ,,, ,,, ,,, ,, ,,
-5 0 5 M 15 20 25 30 TIME (SEC)
CUAVE CODE + + + DATA EVALUATION WODEL 12 NODES FicVRE 4.2-43
- 122 -
NUFRAP-T6 PBF LOC-6 HOOP STRAINS CSTRH 0.31 0.30, O.29-0.28-0.27- ~
0.26-0.25 ,
0.24 ,
0.23p 0.22-0.21-
- 0. 20 g 0.19 j 0.16 1 (
0.17f 0.16- ,
) 0.15-0.14-0.13 ,
0.12-0.11- f J
0.10 1 0.05-0.08-0.07-0.064 0.05-7 l 0.04- l 0.03 j f 0.02 ,
3 0.01
- 0. 00 l#g * * * * * * '*
e i i i i e l i e i i i
)- 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Z
CURVE = *
- CODE DATA EVALUA110N WODEL 12 NODES F1GURE 4.2-44
- 123 -
NUFRAP-T6 q PBF LOC-6 i C1AD SURFACE TEMP (K) 15008 I
l 1400-1300-1200-
!!00-
"i v
+ +
g 1000- #
- +
d 900- 3 f
f 800-
+
700-I
- ._ 7 600- q! ++
)
500-_.. . .-
15 20 25 30
) -5 0 5 10 TIME (SEC)
CURVE CODE + + + DATA PRACAS/BAlhN2WODEL F1GURE 4.2-45
- 124 -
i NUFRAP-T6 PBF LOC-6 ROD CAS PRES (WPA) 1 30-4 t
25 S .+
\
+t ,
\ .s 20- s
. \
n s.'s Si .
4 S.15-0 x -
3.
8
= .
. +
10- .
+
k l +
5- +
l
+
+
t
+
+
i
- 0. . . ., m . ... ... ..
-S U 5 10 15 20 25 30 TIME (SEC)
CORVE CODE - + + + DATA FRACAS /BA14N2 WODEL ricURE 4.2-46
- 125 -
~
rupture location, however, the maximum rupture strain is almost twice the calculated value and'the rupture location is slightly belov the calculated location. The discrepancy in the strain calculations is apparently due to the calculation of the CHF slightly early. The early prediction of CHF caused the clad temperatures to increase rapidly while 1
the pin pressure was still very high. The high clad stresses resulted in
{
a low rupture temperature in the lov alpha range and therefore low rupture strains. The FRACAS-I case shows in Figure 4.2-47 the strain prediction for a later rupture and demonstrates very good agreement with the data.
CONCLUSION The res-1ts of comparing the EM calculations for system response and fuel j rod response with three sets of test data from the PBF LOCA test series demonstrates that the EM provides excellent simulation capabilities. The
, NULAP5-LB system response and heat transfer calculations were generally in very good agreement with the test data. This is significant in that
) these tests are essentially integral tests. The NUFRAP-T6 EM showed excellent agreement with the measured clad and centerline temperatures as long as the initial condition of the fuel (cracked or solid) and the I
associated stored energy were correctly modeled. The sensitivity of the I
fuel rod calculations to initial stored energy is not surprising but it does emphasize the need for using initial fuel performance data from an approved, conservative steady state code. Given the correct stored
- 126 -
m NUFRAP-T6 PBF LOC-6 HOOP STRAINS 'q l
CSTRN ]
0.31- 1 0.30- .)
O.29 '~
O.20-0.27-0.26 2 0.25-0.24-0.23-'
0.22.
- 0.21- ~
0.20-0.19 2 0.16-0.17-0.16-O.15-0.14-
) 0.13-O.12-O.I1- ~
0.10-0.09-0.08- 4 0.07-
)
0.06 0.05- r
[
I 0.04 - /
[
- 0.03- y/
0.02- *
)- 0.01 0,00!? '
i i i i i i i i i i i 0.0 .1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2
CURVE * *
- CODE DATA FRACAS /BAthN2 WODEL I ricURE 4.P,-47
- 1:7 -
energy and appropriate boundary conditions from NULAP5-LB, NUFRAP-T6 can
. calculate the mechanical' deformation of the clad. These clad swell and rupture' calculations tend to be accurate over most of the rod and !
conservative at the' node of rupture.,
i i
A limited sensitivity study with NUFRAP-T6 on axial noding indicated that l, nodes of.approximately 0.15 meters (0.5 ft) provide adequate modeling.
)
i L
)
I-l - 128 -
g 1 stig i
5.0L GENERAL DESCRIPTION OF THE NUCOM CODE '
5.1. PURPOSE NUCOM is a multi-channel clad heat up simulation program which is part.of
~
the Northeast Utilities large break LOCA Evaluation Model. Its purpose ,
is to predict core-vide clad oxidation. The results of NUCOM will be used to determine compliancefwith the maximum hydrogen generation (clad oxidation) criterion in 10CFR50.46.
L I
u g.
t h
)
)
}
h - 129 -
i i..-
i 6.0' MAJOR N0DELS AND FEATURES OF NUCOM ;
I NUCOM contains calculational models and correlations to simulate tran-sient fuel rod behavior and to enable the calculation of core-wide.
oxidation. The most important of these are the calculations of heat conduction, clad oxidation and clad failure. Figure 6.0-1 shows the general sequencing of the models in NUCOM.
NUCOM allows for the modeling of multiple radial zones of the core. This allows for modeling of the radial power profile of the core and cores containing both stainless steel and Zircaloy clad fuel assemblies.
6.1 THERMAL CONDUCTION SOLUTION
'In NUCOM, each axial segment of the fuel rod is divided radially into three regions: the pellet region, the gap region and the cladding
. region. The pellet region and the gap region are represented by their region-average temperatures. The gap region is considered only as a
. resistance to heat conduction. The pellet and cladding temperatures are calculated as follows.
h l
[
l~
)- - 130 -
) !
Fuel and Cladding Temperature Model V
Local Oxidation Model V
Clad Rupture Model V
i Core-Wide Oxidation i
New Timestep I
Figure 6.0-1 Order of general models (NUCOM).
I y
- 131 -
f
}
L
.r The' general heat conduetion equation is.
^ pC h = q ' ' ' + - V kVI (6-1) where p is the material density j
C is the material heat capacity.
t k.is the material thermal conductivity.
q is" the volumetric internal heat generation rate i.
/ and T is the temperature distribution within the material.
An energy balance for the fuel. pellet region is obtained by integrating this equation over a volume element at each axial elevation and each radial zone. The resulting equation is pC f (t)Af d [Tf(I,J, t)]' = _ q'(I,J, t) - 2 it Rg q"(I,J, t) (6-2) d t' vhere:
pC, = pellet volumetric heat capacity A, = fuel pellet cross-sectional area l T, = pellet mean tempe ature q' = linear heat generation rate I'
R, = pellet outer radius q" = heat flux at pellet surface t = time I,J = spatial indices 1
- 132 -
/-
The linear heat generation rate'is assumed to be constant over the volume j element and is equal to 1
q'(I,J,t) = q',y,0 t (t)0,(I) 0,(J) (6-3) where:
q',y, = initial average linear heat rate Qt - heat generation rate normalized to initial 0, = axial peaking factor 0, = radial peaking factor Similarly, an energy balance is determined for the cladding region by integrating the general heat conduction equation over the volume element of cladding.
pC (t)A [Tc (I,J,t)) = q'x(I,J,t) + 2nRf q"(I,J,t) (6-4) c c -
dt
-2nR q"(I,J,t) 9 where:
l
)
pC, = cladding volumetric heat capacity Ac = cladding cross-sectional area T, = cladding mean temperature q',, - linear heat generation due to oxidation
- 133 -
R, = pellet outer radius q" = heat flux at pellet surface q ", = heat flux at cladding outer surface R, - cladding outer radius In order to determine the heat flux across the gap (q"(I,J,t)), it is assumed that the temperature profile within the pellet has the general parabolic form of the steady state temperature profile with a uniform heat source and uniform material properties. This assumption is valid after the initial pellet stored energy has been dissipated and the total temperature drop across the pellet.is relatively small. Since this is the period of time during which most oxidation occurs, this is a reason-able assumption for the NUCOM fuel rod temperature solution. Similarly, it is assumed that the temperature profile across the thin cladding region is linear. This is a reasonable approximation at all times.
Vith these approximations, the heat flux at the pellet surface can be related to the difference between the mean pellet temperature and the mean clad temperature.
- 134 -
I
(
q"(I,'J,t) = h,,,,,(I,J,t) [ T,(I,J,t) - T c (I,J,t) ] (6-5) where 1/h,,,,,(I,J,t)'= [R,/4Kr (t) + [1/h,,,(J)] (6-6)
+ [R e (R,-R i )/(2 R ic K (t))]
and h,,,,, = effective gap conductance Re = pellet outer radius K, = thermal conductivity of the pellet h,,, = gap conductance R, = cladding outer radius Ri - cladding inner radius Ke = thermal conductivity of the cladding i
In the expression for h,,,,,(I,J,t) the left-hand side represents the effective resistance to heat transfer between the pellet and the
> cladding. The first term on the right-hand side represents the 7
resistance due to conduction within the pellet itself. The second term is the resistance of the gap. The last term is the resistance due to conduction within the cladding.
L 1
- 135 -
?
N hl '
a
'U A similar expression is solved.for'the cladding-to-coolan.t heat flux,
- i. .
1
+ q",(I,'J,t).= h,,,re(I,J,t)[Te (I,J,t) - T,(I,t)] -(6-7) i
..where
.u ,
i 1/h,,,,,(I,J,t) = [l/h(I,t)] + [(R, - R )/2K,(t)] i (6-8) 1 and '
hs ..cr - effective surface conductance T,. . cladding mean temperature 4
, T, = coolant temperature-h - surface heat transfer coefficient R,- = cladding outer radius Ri - cladding inner radius K, = thermal conductivity of the cladding s
L The pellet and cladding energy balances are written as two simultaneous linear equa'tions which are solved for the mean pellet temperature
)
, Te (I,J,t) and the mean cladding temperature T,(I,J,t). Pellet and cladding material properties are temperature dependent and are evaluated L
L
- 136 -
l
k at the temperature.from the previous time step. Also, the heat addition to the cladding from oxidation is the value calculated at the previous 1
time step.
The pellet and cladding energy finite difference equations are:
Pellet energy equation:
A 3 (I,J,t) T,(I,J,t) - A 2(I,J,t) T e(I.,J,t) (6-9)
- A 3 (I,J,t)
Cladding energy equation:
-B3 (I,J,t) T,(I,J,t) + B 2 (I,J,t) T c (I,J,t) (6-10)
= B 3 (I,J,t) where A1 (I, J , t ) = pC, ( t ) A, / ot + 2 n R r hy ,,,, (I,J,t) (6-11)
A2 (I,J, t) = 2 n R, h,,,,, (I,J, t) (6-12)
A (I,J,t) = q' (I,J,t) + pC,(t) A, T, (I,J,t - ot)/ot 3 (6-13)
Bt (I, J , t ) = 2 n R, h, ., , , , - (I, J , t ) (6-14)
B2 (I,J, t) = ' pCc ( t) Ac /ot + 2n R, h,,,,, (I,J, t) -
(6-15)
+ 2 n R, h, , ,,, (I , J , t )
B 3 (I,J,t) = q',, (I,J,t - ot) + pC (t) e A, T e (I,J,t - ot)/ot (6-16)
+ 2 n R, sh , . r t (I,J,t) T, (I,t) l l - 13, -
1
4
.r -
and' T, := . pellet'mean' temperature T, -- = cladding mean temperature pC, = pellet volumetric heat' capacity A, = pellet cross-sectional area
, 4 .
.ot - time step size
,. ' R-e = pellet outer radiu's h,,,,, =. effective gap conductance q'- = linear heat generation rate
.([ "
pC_ = cladding volumetric heat capacity A, = cladding cross-sectional area R. = cladding outer radius h,,,,, - effective surface conductance q',,, = linear heat generation rate due to oxidation T, = coolant temperature These equations are solved at each time step'for each axial elevation within each radial zone. If clad rupture occurs, the expanded cladding dimensions are used along with a different gap conductance in the above
)
equations for the rupture elevation.
p
- 138 -
6.2 B_0UNDARY CONDITIONS NUCOM does not perform transient determination of core power, core fluid conditions or clad to core fluid heat transfer coefficients. These are supplied as boundary conditinns to NUCOM. The boundary conditions used by MUCOM are:
o normalized core power, o core pressure, o fuel rod surface heat transfer coefficient, as a function of axial elevation, o local coolant temperature, as a function of axial elevation.
These boundary conditions can be generated directly by NUFRAP-T6 or provided by the user.
6.3 CLAD OXIDATION MODEL NUCOM calculates the rate cf cladding oxidation using a parabolic rate equation. In all cases, the reaetion is assumed not to be limited by the amount of steam available for reaction. The form of this equation is:
d 2 K eXP [-E/(RTc )l g [X (I,J,t)) =
p 2 (30.48 cm/ft)2 (6-17)
} - 139 -
where K is the reaction rate constant in gm2/cm -sec i
E is the activation energy in cal /gm-mole o is the cladding density in gm/cm3 X(I,J,t) is the oxide layer thickness in ft Te is the clad temperature in degrees Kelvin R is the universal gas constant in cal /gm-mole-deg.K If it is assumed that the temperature remains constant over one time step, then this equation can be integrated to determine the change in local oxide layer thickness over that time step.
X2(I,J,t) = X2(I,J,t-at) + Kot exp[-E/RT c]/p2(30.48)2 (6-18)
At the start of the problem, the initial oxide layer thickness is specified by the user.
1
! The heat generated due to this chemical reaction is calculated as follows and is added as a cladding heat source at the applicable axial elevation and radial zone.
2 rt R, o X phr (112375.4 Btu-cm /Kcal-ft )
q'gx (I,J,t) = (6-19) f At ot
- 140 -
l
where q'o,(I,J,t) is the heat addition to the cladding due to oxidation h, is the heat of reaction in Kcal/gm-mole Ae is the atomic weight of the cladding in gm/gm-mole AX = X(I,J,t) -.X(I,J,t-At)
The same equations are solved for oxidation on the inner surface at the rupture elevation, if rupture is calculated to have occurred. In this case the expanded cladding inner radius is substituted for the radius R, in the above equation. The heat generation due to oxidation on the out-side surface of the cladding at the rupture elevation is calculated using the expanded cladding outer radius instead of R o
. The inner surface oxide layer thickness is calculated beginning at the time of rupture.
The heat generation due to this inside surface oxidation is added to the heat generation from the outside surface oxidation in computing the total cladding heat source at the rupture elevation.
l i The above equations are general and are applied for either Zircaloy or stainless' steel cladding. The constants appearing in these equations
{
are:
l
- 141 -
o -
l
)
] Zircaloy Stainless Steel Parameter Units (Reference 19) (References 27 and 28) l K gm2/cm -sec 4
33.3 6.28E6.
p gm/cm 3 6.6 7.9 Ag gm/gm-mole 91.22 55.85 E cal /gm-mole 45500 84300 h, kcal/gm-mole 140.5 10.0
} 6.4 GAP CONDUCTANCE MODEL The gap conductance within each radial zone is specified by the user.
This value is used at all axial locations (except as noted below) and is held constant during the transient. A more dynamic treatment of the gap is not necessary since (i) the oxidation transient is relatively slow and insensitive to short-term variations in the gap conductance, and (ii) most of the oxidation occurs during reflood when the fuel pellet initial stored energy has dissipated and there is relatively little temperature drop across the gap, regardless of the gap conductance.
The one exception to this modeling of the gap conductance is at the axial elevation of rupture (if any) within each radial zone. At the rupture location, the expanded cladding dimensions are used to calculate the large reduction in gap conductance. This calculation accounts for two heat transfer mechanisms: radiation from the pellet to the inside surface of the ruptured cladding and conduction across the steam-filled gap region. This calculation is as follows.
- 142 -
l 3
i h
gap, rupture ( ) " gap, conduction.+ h8ap, radiation (6-20) l vhere h
gap, conduction " v I ci, rupture ~ f) (0~ 1) y = conductivity of steam at the gap temperature R
ei, rupture = cla M ng inner ram us at rupture elevation Rf = pellet outer radius gap temperature = [ Tr (I,J,t - 6t) + T, (I,J,t - 6t ]/2 and h
gap, radiation " "*ff (Tg - T )/(Tf - Tc ) D where Tg and T care the fuel and cladding temperatuers in degrees Rankine a = Stefan-Boltzmann constant in BTU /ft 2-hr-deg.R4 1/ c,,, = 1/ c, + (R, /Rei,ruptur.) II/Ec -1] (6-23) c.,, = effective gap emissivity c, = pellet emissivity ce = cladding emissivity
- 143 -
~
!- l p
. .j . -
The : fuel emissivity c, is calculated as a function of. fuel temperature.
(
Reference:
16),
1: ,
c, - 0.7856 + 1.5263 x-10-5 T, (6-24) i -l l
vhere T,.is the fuel temperature in degrees Kelvin l
a I
The cladding emissivity c, is taken as 0.44 if ' the cladding material is !
stainless steel (Reference 8). If the cladding is Zircaloy, the emissivity is calculated as a function of cladding oxide thickriess and ;
cladding temperature (Reference 16).
For Zircaloy cladding temperatures below 1500'K, ;
t ce = .325 + 1.246 x 105X insid. if X io,ia, <3'88 x 10-sm (6-25)
= .808642 - 50X io,ia, if Xin,ia, p.88x10-8 m (6-26) !
l l
vhere Xio,ta, is the cladding inside oxide layer thickness in meters.
I f I
, b e ;
q l
l
- 144 -
- - - _ = __ = _ =_:. _ - - _ ______ - _ - - _ - _ __ _ _ _ _ _ _ _ _ __ _ _ - - _ _ _ _ __ -_-_-__:________ ._-. - _ _ _ _
For cladding t.emocratures above 1500"K, l
l cc = eXp((1%0 - T ) 00) c c c,T <1500 (6-27)
Where cT is th'e cladding temperature in degrees K and c c,T <1500 e
is the clad 31ng emissivity calculated by equation 6-25 or 6-26. The ainimum value of c used is .325.
c 6.5 CLAD RUPTURE MODEL NUCOM checks for the occurrence of clad rupture within each radial zone at each time step. This check is performed independently for each radial zone; i.e., all zones do not necessarily rupture at the same time. In fact, all zones do not necessarily experience rupture. Once a zone has ruptured, the fuel rod is assumed to depressurize and no further tests for rupture are performed for the fuel rod representing that radial zone.
NUCOM has two options for calculating the occurrence of rupture within each radial zone. Rupture may be specified to occur within a zone at a particular time. (Thir option can be used to force one or more zones to rupture at the time of the hot rod, as calculated by NUFRAP-T6.) In this option, the rupture is assumed to occur at the specified time at the elevation containing the highest clad temperature.
- 145 -
l Alternatively, NUCOM can test for rupture during the transient based on the current fuel rod-to-coolant differential pressure and the current cladding temperature. Curves of rupture temperature versus differential pressure are contained in NUCOM. (Separate curves are provided for
- Zircaloy cladding and for stainless steel. These are listed in tabular form in Table 6.5-1.) In this option, the axial elevation with the current highest clad temperature is tested. If the clad temperature exceeds the rupture temperature, then the cladding is assumed to rupture at this elevation.
In either model, if rupture is calculated to occur, the rupture strain is determined by curves of rupture strain versus fuel rod-to-coolant dif-ferential pressure. Again, separate curves are provided for Zircaloy and for stainless steel. These are listed in Table 6.5-2.
At the time of rupture, the cladding outside radius, R eo,ruptur., is assumed to increase by the following:
R eo,ruptur. = R, (1+ c, ) (6-28) where R, = cladding outer radius c, = cladding rupture strain
- 146 -
The cladding inside radius, R ei,ruptur., is also assumed to increase so as to conserve cladding mass, i.e.
R ei,ruptur. = [R2 eo,ruptur. - R,2 + Ri z) 1/2 (6-29)
The cladding outside oxidation layer is thinned by the amount X(IMAX(J),J,t),e rupto,, = X(IMAX(J),J, t)be r o r. rupture /(1+Cs) (6-30) where IMAX(J) is the axial index of the highest clad temperature in zone J at the time of rupture.
Oxidation on the inside surface of the cladding is calculated at the rupture elevation, beginning from the time of rupture.
Inside surface oxidation of the cladding is assumed to occur over the entire inside surface of the axial segment. The number of axial segments modeled will assure that inside oxidation extends at least one and one-half inches each way from the rupture location.
- 147 -
4 q.
1 TABLE 6.5 RUPTURE TEMP 2RATURE VS. DIFFERENTIAL PRESSURE
- Zircaloy (Referen>ce 15)
Rupture Temperature (deg.F.) Differential Pressure (psia) 2060.6- 0.0 )
2060.6 173.6 l 1880.6 283.3 1700.6 483.9 1610.6 639.0 1520.6 847.0 1430.6 1123.8 1340.6 1488.8 Stainless Steel (Reference 27)
Rupture Temperature (deg.F.) Differential Pressure (psia) 2500.0 0.0 2369.0 100.0 2300.0 200.0 2162.0 400.0 l 2025.0 600.0 1820.0 800.0 1770.0 1000.0 1680.0 1200.0 1610.0 1400.0 1560.0 1600.0 1510.0 1800.0 1470.0 2000.0 1430.0 2200.0 1400.0 2400.0 l
I' Differential pressure is defined as fuel rod internal pressure minus core coolant pressure.
)
- 148 -
TABLE 6.5-2 RUPTURE STRAIN VS. DIFFERENTIAL PRESSURE
- Zircaloy (Reference 15) q
\
Rupture Strain Differentia 1 Pressure (psia) 0.35 0.0 0.35 173.6 0.75 201.1 0.80 228.5 0.75 255.9 0.40 323.4 0.27 383.6 0.25 433.7 0.27 483.9 0.82 742.9
, 0.90 847.0 0.90 1123.8 0.82 1306.4 Stainless Steel (Reference 27)
Rupture Strain Differential Pressure (psia)
) 0.01 0.0 0.10 100.0 0.22 200.0 0.38 400.0 0.43 600.0 0.27 800.0 l 0.20 1000.0 0.13 1200.0 0.11 1400.0 .
0.09 1600.0 O.08 1800.0 0.06 2000.0 i 0.06 2200.0 f 0.05 2400.0
- Differential pressure is defined as fuel rod internal pressure minus core coolant pressure.
l - 149 -
)
'l 7.0 NUCOM VALIDATION 4
In' order to demonstrate the adequacy of the NUCOM code in simulating clad oxidation, comparisons with NUFRAP-T6 predictions are provided. The i
) NUCOM calculations of clad temperature and oxidation are shown to adequately match the NUFRAP-T6 predictions. Also, the thermal-hydraulic !
conditions used by NUFRAP-T6 are shown to provide the appropriate boundary conditions for NUCOM.
l l
Two cases were run in order to demonstrate the adequacy of NUCOM for both Zircaloy and stainless steel cladding oxidation predictions. The
, NUFRAP-T6 model and parameters used were selected to adequately simulate the expected modeling and behavior for a large break LOCA. The NULAP5-LB model used to provide the boundary conditions to NUFRAP-T6 was similarly selected. T,he NUCOM boundary conditions generated by the NUFRAP-T6 run with Zircaloy cladding are shown in Figures 7.0-1 through 7.0-4. The f boundary conditions for stainless steel cladding were essentially the same since the only NUFRAP-T6 input modifications were related to the f
( change frm Zircaloy to stainless steel cladding and initial power. The
- power was adjusted to provide approximately the same peak clad f
temperature for both clad materials.
The NUCOM model was based on the NUFRAP-T6 model. The same number of axial nodes and fuel and clad dimensions were used. The inputs to NUCOM vere also chosen so that the initial conditions for both NUCOM and
- 150 -
L
w-----,.-_,--___- . - . - - . . - _ _ . _ _ . _ _ _ _ _ _ _ _ _ _ _
)
NUCOM-BOUNDARY CONDITIONS ROD UNEAR POWER 14 -
12 ,
t 0
8 l
l 10- <
a 4
e n
4 0-
[
n x
6-e s d
4-n 2.
d
.0-j 0 10 20 0 40 50 60 70 80 90 100 110 10 130 TIME (SEC)
FIGURE 7.0-1
- 151 -
i
NUCOM~
BOUNDARY CONDITIONS SURFACE HTC (BTU /HR-SQ.FT-F) 5-4 d
4 I '
\
.4-4 4
3-i n 0
5 o
? ,
2- '
}
i j }
i l
)
) .
~
H
\/ i G
4 0- ' '
b ' 1O PO 3O 40 50 6O 7O 8O 9O lb0 110 1$0 130
{
I TIME (SEC)
I FICURE 7.0-2
- 152 -
NUCOM BOUNDARY CONDITIONS COOLANT PRESSURE
~2200- .
0 2000- , l l
)
1800-1600- ,
1400- ,
\
r 4
- - 1200-5
$ 1000-800-600-f 400-200- \
l 0-Y , ,
0 10 20 30 40 50 60 70 80 90 100 110 120~ 130 TIME (SEC)
FIGURE 7.0<-3
- 153 -
NUCOM l BOUNDARY CONDITIONS COOLANT TEMPERATURE 2200- ;
2000-1800-1600-1400-1200-I
~ . ;
O l
$ 1000- ! '
,J
! t 800-l.
k/
i 600- h i
! 400-L I f _- lA) >J _ ___
200-0 -
, 1
- s u . , .
0 '10 20 30 40 50 60 70 80 90 100 110 120 130 TIME (SEC) f I
FIGURE 7.0-4
- 154 -
NUFRAP-T6 were the same. This results in NUCOM and NUFRAP-T6 starting with the same initial power level, average fuel temperature, clad temperature and axial power shape. Figures 7.0-5 and 7.0-6 show comparisons of clad temperature and clad oxidation predictions by NUFRAP-T6 and NUCOM for Zircaloy cladding. Figures 7.0-7 and 7.0-8 show comparisons for stainless steel cladding.
The NUCOM and NUFRAP-T6 comparisons show that NUCOM can adequately simulate cladding oxidation. In addition, the NUFRAP-T6 generated boundary conditions are appropriate and result in good agreement between the NUCOM and NUFRAP-T6 predictions. Based on the comparisons, it is concluded that the NUFRAP-T6 and NUCOM combination can adequately calculate the clad oxidation following a postulated large break LOCA in a l
PVR.
i l
1
- 155 -
COMPARISON OF NUCOM AND NUFRAP CLAD TEMPERATURE ZIRCALOY NUCOW
.NUPftAP 2500-I i
20004 Zone 4
.............................,'~.. ...
l
......~~
7 l, .;;..........................
's e f ',,'-
i
,, ,'.5 Zone 7 M
p 4*... ,, -
1 E g5g9 j
- R '=. ,
g T ; 't U
/
Zone 2l y A 1 E \.
ll ' '. . ,
- f .......
0 1000.)j E
G J, F
j
/
n
/
i 500 1 E
I 1
1 0-i i i i i i i i i i , i , i 0 10 20 30 14 0 50 60 70 80 90 100 110 120 130 TIME ISEC)
FIGURE 7.0-5
' - 156 -
COMPARISON OF NUCOM AND NUFRAP OXIDATION THICKNESS ZIRCALOY MUCOM
NUPRAP
- 1. 5 -
0 X
I D ,
y1,0 J l
0 N
T H
I C
K N '
E j *... ,,, -
i s .
c*
- j. . ,,*', f
,e Zone 4 I
l H
I J
L .<'
1 S ..
I ,,*** .* ***,,......................
,.* , , .. ' '. ****,,,.... ***Zone 7 c,
Zone 2 0.0- i i i i < i i i ; i i i ,
0 10 20 30 40 50 60 70 80 90 100 110 120 130 TIMEISEC)
)
FIGURE 7.0-6
- 157 -
COMPARISON OF NUCOM AND NUFRAP CLAD TEMPERATURE STAINLESS STEEL NUCOM
NUFRAP 2500- .
t Zone 6 l I
2000 -
- ::::::::::.... W' ...,
Zonef4 4
......... ........ ----- w .
l 3 Zon,f 8 -
c r
a .
, /.. ,-
E 1500 -) I,/
P
{ >//
) %.
b' '] I R 1 E i l 1
k D 10001 ':
E 1, G i i
F 1 i
4 Ji
)
I SCO -
l l
C -1 60 YO 90 lbo 110 12^ ! b^
b 10 20 3O 40 5O 8O T IME ISEC) t l
)
FIGURE 7.0-7
- 158 -
l COMPARISON OF'NUCOM AND NUFRAP OXIDATION THICKNESS STAINLESS STEEL MUCOW
NUFRAP
- 0. 4 - ,
i 1
1 J
i 0 0.3 ,,.
... t
- ' Zone 6 0
A
/
T
/
C k , , ' ,Zone , . , *4* * . f i
H l f0,2-4 n
E 2
1 i *
../
S 1 ..'. *',..,...'..
..-- =
Zone 8 f I I
5 0'l' I 1 l
l
)
0.0- i . . i i i i ; , , i , i 0 10 20 30 40 50 60 70 80 90 100 110 120 I F.
TIME!5EC) l l
FIGURE 7.0-8
- 159 -
8.0 CONCLUSION
S The NUFRAP-T6 and NUCOM computer programs have been developed for the l
purpose of simulating the fuel rod thermal and mechanical response and l l
the core oxidation of a PVR during a Large Break LOCA. These codes, along with the NULAP5-LB system and response code, form the major components of the Northeast Utilities Large Break W A Evaluation Model.
NUFRAP-T6 is a modified version of the FRAP-T6 Modl transient fuel rod behavior code. The modifications included: conversion to IBM Fortran, addition of stainless steel properties, error corrections, and input / output modifications. The Evaluation Model consists of the use of selected options in NUFRAP-T6. These options are the LACE deformation and oxidation models and the concentric pellet option. The LACE deformation option consists of a simplified thin shell approximation for elastic deformation and the Powers /Meyer or Coffman clad swell and rupture models for plastic deformation of Zircaloy or stainless steel cladding.
7 The LACE oxidation model option results in the use of the Baker-Just I
oxidation correlation for Zircaloy or the White correlation for stainless steel. Oxidation occurs inside the clad for all nodes within six inches of the rupture node. These models meet the requirements of 10CFR50, Appendix K.
I - 160 -
In order to d'emonstrate the performance of NUFRAP-T6, comparisons were made with test data consisting of 1.4 fuel ~ rods'from the TREAT tests FRF-1 and FRF-2 and three fuel rods from the PBF tests LOC-11C, LOC-3, and i LOC-6. The TREAT tests were representative of the late blowdown, early 3 refill period in a Large Break LOCA. The PBF tests simulated the' full l
' blowdown period of a LOCA. Code to da** comparisons included fuel l centerline and clad surface temperittrec, clad strains, time to rupture I and fuel rod gas pressure.
The results of the test comparison demonstrate that the EM adequatelv j simulates the transient response of a fuel rod during a LOCA.
The calculated thermal response of the fuel and the clad were generally in good agreement with the test data. The calculated mechanical response of the fuel rods typically resulted in greater than measured clad strains. Overall, the combination of boundry conditions calculated by NULAP5-LB and the transient fuel rod calculations from NUFRAP-T6 provided very good simulations of the system and fuel rod responses.
[
The NUCOM computer program was written to provide conservative calculations of the total core oxidation. NUCOM uses a simplified thermal conduction solution and thin shell deformation calculation.
Oxidation calculations are made using the Baker-Just correlation for 1
) Zircaloy and the White correlation for stainless steel. Much of NUCOM's conservatism is caused by the use of the hot-pin boundary conditions from l'
I - 161 -
NUFRAP-T6 as the boundary.. conditions for the entire core. NUC0H's
- capabilities include the. ability to model multiple core regions with differing powersLand clad materials.
NUCOM's verification consisted of comparisons with NUFRAP-T6 to '
i
~
. demonstrate the adequacy of the thermal conduction' solution in NUCOM and 1 the oxidation calculations. Based on these comparisons, NUCOM does adequately calculate the clad temperature and oxidation response during LOCA conditions.
L l
p - 162 -
I t-
9.0 REFERENCES
- 1. Title 10 Code of Federal Regulations, Part 50.46 l 2. Large Break LOCA Analysis System Evaluation Model (NULAPS-LB),
NUSCO 164, January 1989.
- 3. V. H. Ransom, et al, "RELAP5/ MOD 2 Code Manual Volumes 1 and 2,"
NUREG/CR-4312, August 1985
- 4. Title 10 Code of Federal Regulations, Part 50, Appendix K
- 5. L. J. Siefken, et al, "FRAP-T6: A Computer Code for the Transient i
Analysis of Oxide Fuel Rods," NUREG/CR-2148, May 1981 i
- 6. L. J. Siefken, et al, "FRAP-T6: A Computer Code for the Transient Analysis of Oxide Fuel Rods," NUREG/CR-2148, Addendum, June 1983 i
/. " IBM VS-FORTRAN Language and Library Reference, 3C26-4119-0" I
- 8. "NUFRAP: Northeast Utilities Fuel Rod Analysis Program," NUSCO 135-P, August 1, 1983
- 163 -
g'; ' q g: A H
- 9. A...- L. Love,. Jr. , "Haterial Properties and Acceptance Criteria for'
'LOCA Analysis of Stainless Steel PVR Core," BAV-1411, February 1.975 I
- 10. Franklin D. Coffman, Jr., 'LOCA Tempera ture Cri terion . for S tainless - '
[
r Steel Clad Fuel," NUREG-0065, June 1976
- 11. M. P. Bohn, et al, "The Licensing Audit Calculation Evaluation (LACE) Models in the,FRAP-T4 Code - Description and Developmental.
Assessment," EGG-CDAP-5144, April 1980 l I
- 12. R. V. Garner, et al, " Gap Conductance' Test Series - 2 Test Results I Report for Tests GC 2-1, GC 2-2 and GC 2-3," NUREG/CR-0300, TREE-1268, November 1978
- 13. 'C. E. Beyer et al,."GAPCON-THERMAL-2: A Computer Program for Calculating the Thermal Behavior of an Oxide. Fuel Rod," BNVL-1898, November 1975
. i.
- l
- 14. C. R. Hann, C. E. Beyer, L. J. Parchen, "GAPCON-THERHAL-1: A y Computer Program for Calculating the Gap Conductance in Oxide Fuel Pins," BNVL-1778, September 1973 l^
- 15. D. A. Powers and R. O. Meyer, " Cladding Svelling and Rupture Models for LOCA Analysis," NUREG-0630, 1980 l .1 l
i
- 164 -
l
u
- 16. D. L. Hagrman, G. A.-Reymann, and R. 2. Mason, "MATPRO ' Version 11 (Revision 2) A Handbook of' Materials Properties for Use in the a
Analysis of Light Vater Reactor Fuel Rod Behavior," NUREG/CR-0497, TREE-1280, Revision 2, R3 and R4, August 1981 .i 3
.s
.j.
- 17. J. V. Cathcart,." Quarterly Progress Report on Zirconium Metal-Vater .
Oxidation Kinetics Program" sponsored by the NRC Division of Reactor Safety Research for April-June 1978, ORNL/NUREG/TM-41, August 1976
- 18. J. F. White, "Physico-Chemical Studies of Clad UO2 Under Reactor Accident Conditions," Eighth Annual Report, AEC Fuels and Materials Development Program, GEMP-1012, 1969
- 19. Louis Baker, Jr. and Louis C. Just, " Studies of Metal-Water Reactions at High Temperatures III. Experimental and Theoretical Studies of Zirconium-Vater Reactions," ANL-6548, 1962
- 20. R. A. Lorenz, et al, " Final Report on the First Fuel Rod Failure l
l Transient Test of a Zircaloy - Clad Fuel Rod Cluster in TREAT,"
URNL-4635, March 1971
- 21. R. A. Lorenz, G. V. Parker, " Final Report on the Second Fuel Rod Failure Transient Test of a Zircaloy-Clad Fuel Rod Cluster in TREAT," ORNL-4710, January 1972 1
- 165 -
. l;r ir
- 22. 'J. R. Larson,'et al, "PBF LOCA Test Series Test LOC-11 Test Results i Report," NUREG/CR-0618, TREE-1329 R3, April 1979
- 23. J. M. Broughton, et al, "PBF LOCA Test Series' LOC-3 and LOC-5-Fuel Behavior Report," NUREG/CR-2073, EGG-2094, June 1981 i n ,
1 in :
- 24. nJ. M. Broughton, et al,."PBF LOCA Test LOC-6 Fuel Behavior Report,"
NUREG/CR-3184, EGG-2244, April 1983 1
'l
- 25. M.1P. Bohn, et al, "The Licensing Audit Calculation Evaluation (LACE) Models'in the.FRAP-T4 Code, Description and Developmental Assessment," EGG-CDAP-5144, April 1980
- 26. V. N. Rausch and F. E. Panisko, "ANS 5.4: 'A Computer Subroutine for Calculating Fission Gas Release," NUREG/CR-1213, PNL-3077, August 1979
.27. F. D. Cof fman, Jr. , "LOCA Temperature Criterion for Stainless Steel l'
Clad Fuel," NUREG-0065, 1976-
- 28. A.-L. Love, Jr., " Material Properties and Acceptance Criteria for LOCA Analysis of Stainless Steel PVR Core," BAV-1411, 1975
- 29. D. J. Varacalle, Jr., et al, "PBF/ LOFT Lead Rod Test Series Test Results Report," NUREG/CR-1538, EGG-2047, July 1980 f.
I - 166 -
i.,,, - . . . -