Text

Non-proprietary Version of Rev 4,in Form of Replacement Pages,To WCAP-14808, Notrump Final Validation Rept, Vols 1-3
	ML20151Z114
Person / Time
Site:	05200003
Issue date:	02/28/1998
From:	Fittante R, Gagnon A, Halac K; WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:	;
Shared Package
ML20138L015	List: ML20151Z097; ML20151Z109; ML20151Z114; ML20151Z122; NSD-NRC-98-5754, Forwards non-proprietary Versions of Revs 3-5 to WCAP-14808 & Proprietary Version of Rev 5 to WCAP-14807, Notrump Final Validation Rept for AP600, in Form of Replacement Pages. Proprietary Encl Withheld;
References
	WCAP-14808-ERR, WCAP-14808-ERR-R04, WCAP-14808-ERR-R4, NUDOCS 9809210164
	Download: ML20151Z114 (450)
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r q WCAP-14808 l

C/ REVISION 4 l

I NOTRUMP Final Validation i Report for AP600 l l

February 1998 l

R. L. Fittante A.F.Gagnon K. E. Halac L. E. Hochreiter J. Iyengar R. M. Kemper v D. A. Kester K. F. McNamee P. E. Meyer F. A. Osterrieder R. F. Wright M. Y. . Young 9809210164 900913 PDR ADOCK 05200003 A PDR Westinghouse Electric Company Energy Systems Business Unit P.O. Box 355 Pittsburgh, PA 15230-0355 C 1998 Westinghouse Electric Company All Rights Reserved o:\4025w\4025w-tm.wpf:1b-031098

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, - WCAP-14808 l REVISION 4 l l

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1 NOTRUMP Final Validation Report for AP600 I

February 1998 R. L. Fittante i A.F.Gagnon )

l K. E. Halac L. E. Hochreiter J. Iyengar 7 R. M. Kemper is D. A. Kester K. F. McNamee i P. E. Meyer R. A. Osterrieder R. F. Wright M. Y. Young l

Westinghouse Electric Company l Energy Systems Business Unit P.O. Box 355 Pittsburgh, PA 15230-0355 l

01998 Westinghouse Electric Company

WCAP-14808 d,o REVISION 4 l I

NOTRUMP Final Validation Report for AP600 i i

I 4

February 1998 R. L. Fittante A.F.Gagnon ,

K. E. Halac I

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L. E. Hochreiter J. lyengar I

R. M. Kemper s D. A. Kester K. F. McNamee P. E. Meyer R. A. Osterrieder R. F. Wright M. Y. Young Westinghouse Electric Company j Energy Systems Business Unit

'. P.O. Box 355 Pittsburgh, PA 15230-0355

') @ 1998 Westinghouse Electric Company

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4 o TABLE OF CONTENTS ld Section Title Eage ACKNOWLEDGEMENTS . . . . . . . .. ...... ........ ............. ..... .. i EXECUTIVE

SUMMARY

. . . . . . . . . . . . . . . . . ................................ I 1 CODE AND ASSESSMENT OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1-1 1.1 Introduction .. .... . . . . . .. ... . ... .. .. .. .. .. .. .. ... .. ... .. . . 1.1-1 1.2 NOTRUMP Code Description . . . . . . . . . . . . . .. ................. 1.2-1 1.3 Small-Break LOCA Phenomena Identification ard Ranking Table . . . . . . . . . 1.3-1 1.4 Selection of Tests for Validation of NOTRUMP for the AP600 Phenomena Identification and Ranking Table Phenomena . . . . . . . . . . . . . . . . ..... . 1.4-1 1.5 Basis for Code Assessment . . . . . . . ............................. 1.5-1 1.6 Key Models Identified by the PIRT . . . . . . . . . . . . ..... ...... ... 1.6-1 1.7 Two Phase Flow Model . . . . . . . . . . . . . . . . . . .. ... ....... .... 1.7-1 1.7.1 Model Description . . . . . ............................. 1.7-1 1.7.2 Constitutive Relationships . . . . . . . . ...... . ....... .. 1.7-5 1.7.3 Vertical Flow Models . . .............. ................ 1.7-6 Q l.7.4 Horizontal Flow Models . ..................... ....... 1.7-13 V 1.7.5 Effect of Neglecting Momentum Flux Terms . . . . . . . . . . . . . . . . . 1.7-18 1.7.6 Conclusion . . . . . . . . . . . . . . . . . .......... ... ..... . 1.7-32 1.8 Mixture Level Tracking Model . ............ .. ...... ........ 1.8-1 1.8.1 Model Description . . . . . . . . .................... . .... 1.8-1 1.8.2 Assumptions and Range of Applicability . . . . . . . . .... . .... 1.8-3 1.8.3 Conclusions . . . . . . . . . . . . . . . . . ...... ........ ....... 1.8-7 1.9 Hydraulic Resistance Model . . . . . . . . . . . . . . . . . ...... .... ...... 1.9-1 1.9.1 NOTRUMP Model Description and Applicability . . . . . . . . . . . . . . 1.9-1 1.9.2 Conclu sions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ 1.9-2 1.10 Core Makeup Tank Model ..... . ............................ 1.10-1 1.10.1 Core Makeup Tank Behavior Observed from Tests . . ......... 1.10-1 1.10.2 NOTRUMP Core Makeup Tank Model (Recirculation Phase) ..... 1.10-1 1.10.3 Hot Layer Model . . . . . . . . . . . ......................... 1.10-1 1.10.4 Model Comparisons . . . . . . . . . . . . . . . . ...... . . ... . 1.10-2 l 1.10.5 NOTRUMP Core Makeup Tank Model (Draining Mode) .... . 1.10-4 1.10.6 Conclusions . . . . . . . ....... .......... .......... 1.10-4 1.11 Passive Residual Heat Exchanger Model . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11-1 1.11.1 Behavior Observed from Tests . . . . . . . . . . ............. 1.11-1

, 1.11.2 NOTRUMP Model Description . ....... ............... 1.11-1 p

1.11.3 Conclusi ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... 1.11-2 U'-

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TABLE OF CONTENTS (Cont.)

Section Title _P_ age 1.12 Critical Flow Model . . ....... ... ... ... ................ 1.12-1 l

1.12 1 Critical Flow through Automatic Depressurization System Valves . . 1.12-1 1.12.2 Break Flow Model . . . . . . . . . . . . . . . . . . . . . . ............ 1.12-1 f

1.12.3 Conclusion . . . . . . . . . . . ... .. .... .. .......... .. 1.12-1

1.13 Overview of Single Effects Tests Assessment ............. ... .... 1.13-1 1.13.1 Two-Phase Flow Model . . . . . . . . . . . . . . ..... .......... 1.13-1 1.13.2 Level Tracking Model ......... ...................... 1.13-1 1.13.3 Hydraulic Resistance Model ....... .......... ......... 1.13-2 1.13.4 Core Makeup Tank Model ... ........... .... ....... 1.13-2

! 1.13.5 Passive Residual Heat Removal Model . . . . . . . . . ... ....... 1.13-2 1.13.6 Critical Flow Model . . . . . . . . . . . . ...... ..... .... 1.13-3 l 1.14 Overview of Integral Effects Tests Assessment .... ....... .. .... 1.14-1 1.14.1 SPES Tests .... . ..... .. ... .......... ..... 1.14-1 l 1.14.2 Oregon State University Tests ..... .. .. ........... . 1.14-5 1.15 Impact of Assessment on AP600 Analysis Methodology . ..... .. 1.15 1 1.16 Noding Selection . . . . . . . . . . . . . . ..... . ......... . ....... 1.16-1 1.17 Key Features of the AP600 Analysis Methodology . . ............ . .. 1.17-1 l

i 1.18 Limits of Applicability . . .. ........ ...... ... ... .. .... 1-18-1 1

i 1.19 References ...... ..... . . ......... . ...... . . 1.19-1 1

2 MODEL IMPROVEMENTS ..... .. .......... ... ... ...... . .. . 2.1-1 2.1 Introduction ........... ... .... ........... . .... . . . 2.1 -1 '

2.2 SIMARC Drift Flux Methodology ... .. .. .... . . . . ..... .. 2.2-1 2.3 Modifications to Drift Flux Correlations . . . . . . . . . . . . . . . . ......... 2.3-1 2.4 Net Volumetric Flow-Based Momentum Equation .. ........... ... 2.4-1 2.5 NOTRUMP EPRI/ Flooding Drift Flux Model . . . . . . . . . . . . . . . . . .. .. 2.5-1 2.5.1 EPRI Correlation Parameters .. ... .. ............. . 2.5-1 2.5.2 Flooding Correlation Parameters . ... . .. .. ...... .. 2.5-4 2.5.3 NOTRUMP EPRI/ Flooding Correlation Parameters . . . . . . . . .. . 2.5-6 2.5.4 Implementation of the Model . . . . . . . ...... .. ..... . 2.5-6 2.6 Contact Coefficients . . .............. ....................... 2.6-1 2.7 Internally Calculated Liquid Reflux Flowlinks , , . . . . . . . .............. 2.7-1 2.8 Mixture Level Overshoot .. ... ...... ........... .......... 2.8-1 2.9 Bubble Rise ................. .............. ... ....... 2.9-1 l

2.10 Pump Model . . . . . . . ... ............. ....... ........ .. 2.10-1 l 2.11 Implicit Treatment of Gravitational Head .. . . ...... .. . ... . 2.11-1 )

2.12 Horizontal Flow Drift Flux Model (Levelizing Model) ................. 2.12-1 1

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February 1998 oM025w-toc.wpf:Ib-022798 iv Rev.4

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2.13 -- Revised Unchoking Model . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . 2.13-1 2.14 Condensation . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14-1 2.15 Critical Heat Flux .......................................... 2.15-1 i 2.16 Two-Phase Friction Multiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16-1

~ 2.17 Henry-Fauske/ HEM Critical Flow Correlation . . . . . . . . . . . . . . . . . . . . . . . 2.17-1 ,

2.18 Fluid Node Stacking Logic - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.18-1 2.19 Implementation of Transition Boiling Correlation . . . . . . . .. . . . . . . . . . . . . . 2.19-1 2.20 Modifications to NO'IRUMP Central Numerics for Application to AP600 : . . . . . . . . . . . . . ........................ ......... 2.20-1 2.20.1 Modifications to Momentum Conservation Equation for Non-Critical Flowlinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.20.1-1 2.20.2 Modifications to Fini:e-Differencing of Mixture Region Energy Conservation Equation for Interior Fluid Nodes . . . . . . . . . . . . . 2.20.2-1 2.20.3 Modifications to Finite-Differencing of Mixture Region Mass Conservation Equation for Interior Fluid Nodes . . . . . . . . . . . . . 2.20.3-1 2.20.4 Modifications to Finite-Differencing of Vapor Region Energy Conservation Equation for Interior Fluid Nodes . . . . . . . . . . . . . 2.20.4-1 2.20.5 Modifications for Finite-Differencing of Vapor Region Mass Conservation Equation for Interior Fluid Nodes . . . . . . . . . . . . . 2.20.5-1 2.20.6 Modifications to Central Matrix Equation . . . . . . . . . . . . . . . . . 2.20.6-1 2.20.7 Finite-Differencing Notation and Conventions . . ............ 2.20.7-1 2.20.8 Summary of Thermodynamic Properties, Related Quantities, and Panial Derivatives Used in the Modified Central Numerics . . . . 2.20.8-1 2.20.9 - Summary of Interfacial Energy and Mass Exchange Rates for Interior Fluid Nodes Used in the Modified Central Numerics . . . . 2.20.9-1 2.21 References ..............................................2.21-1 3- MODEL VERIFICATION AND VALIDATION USING BENCHMARK TEST CASES 3.1 -1 3.1 Introduction . . .. .. . .. . . . . . . .. . . . .. . . .. . .. . . . . . . . .. . . . . . . . . 3.1-1 3.2 Vertical Flow Drift Flux Model Benchmarking ........ .............. 3.2-1 3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 3.2-1 3.2.2 NOTRUMP Drift Flux Model and Flooding .................. 3.2-3

- 3.2.3 NOTRUMP Vertical Pipe Model . . . . . . . . . . . . . . . . . . . . . . . . . 3.2-3 3.2.4 - NOTRUMP Vertical Countercurrent Flow Limit Results . . . . . . . . . 3.2-4 3.2.5 Conclu sion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2-5 3.3 Levelizing Drift Flux Model Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . 3.3-1 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3-1 3.3.2 - NOTRUMP Horizontal Stratified Model and Flow Transition ...... 3.3-3 February 1998 eM025w-toe.wpr:Ib 031098 y. Rev.4

TABLE OF CONTENTS (Cont.)

Section Title Page 3.3.3 NOTRUMP Horizontal Pipe Model . . .... ........ ..... ... ... 3.3-3 3.3.4 NOTRUMP Horizontal Flow Results: Leveling Drift Flux . . . . . . . . 3.3-3 3.3.5 Conclusion . . . . . . . . . . . . . .. ...................... . 3.3-4 3.4 Implicit Treatment of Gravitational Head ................. ........ 3.4-1 3.5 Net Volumetric Flow-Based Momentum Equation . . . . .. ......... 3.5 1 3.6 Implicit Bubble Rise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..... 3.6-1 3.7 Main Coolant Pump Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7-1 3.8 Fluid Node Stacking Logic . . . . . . . . . ........................... 3.8-1 3.8.1 Single-Phase Oscillating Manometer Problem . . . . . . . . . . . . . . . . . 3.8-1 3.8.2 Two-Phase Constant-Pressure Boil-Off Problem . . . . . . . ........ 3.8-3 3.9 References ...... .. .................................... 3.9-1 4 TWO-PHASE LEVEL SWELL ANALYSIS ...... ...................... 4.1-1 4.1 Introduction ... ........ . ....... ............... . ... 4.1-1 4.2 General Electric Small Blowdown Vessel Test Simulation . ......... . . 4.2-1 4.2.1 General Electric Small Blowdown Vessel Test Facility . . . . . . . 4.2-1 4.2.2 NOTRUMP Model of the General Electric Small Blowdown Vessel Tests . .. .. .. ......... .. ........ ....... 4.2-2 4.2.3 NOTRUMP Comparisons to the General Electric Small Vessel Blowdown Tests . . . . . .. . .... ....... ..... 4.2-3 4.2.4 NOTRUMP Comparisons to the General Electric Small Vessel Blowdown Tests Using the Data Mass Inventory .......... .. 4.2-7 4.2.5 Noding Sensitivity Study .... .. .... ........ ... ., 4.2-10 4.2.6 Conclusions . . . . . . . . . . . . ..... ............ . . . . . 4.2- 11 4.3 ACHILLES Low-Pressure Level Swell Tests . . . . . . . .. .. . .. 4.3-1 4.3.1 ACHILLES Test Description . . . . . . . . . . . ..... ..... .. . 4.3-1 4.3.2 NOTRUMP Model of the ACHILLES Facility . . . . . . . . . . . . 4.3-4 4.3.3 NOTRUMP Comparison to the ACHILLES Data . . . . ..... . . 4.3-4 4.3.4 Noding Sensitivity Studies on the NOTRUMP ACHILLES Model . 4.3-6 4.4 G2 Test Simulation ..... ..... ......... ................ . 4.4-1 4.4.1 Introduction . . . . . . . .. .. . ...... ... ....... 4.4-1 4.4.2 G2 Test Facility Description . . . .... .... ... . ... .... 4.4-1 l 4.4.3 Method of Testing . . . . . . . . . . . . . .. . . .... . . .. . 4.4-4 4.4.4 Test Matrix . . . . .... ... .. . .. . .. .. ....... . 4.4-4 4.4.5 Selection and Tests for NOTRUMP Validations .......... 4.4-5 4.4.6 NOTRUMP Modeling of G2 Test Facility . . . . . . .. ... . . 4.4-5 4.4.7 Modeling of Test Boundary and Initial Conditions ... ... . 4.4-11 4.4.8 Analysis Results and Comparisons . . . ............. .. 4.4-12 Febmary_1998 oM025w. toc.wpf:lb-022798 yj gev. 4

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l Section Title Page a

i 4.4.9 Conclusions ............ .............................. .. 4.4-16 l

t 4.5 Summary of Level Swell Comparisons . . . . . . . . . . .................. 4.5-1 l 4.6 Assessment Against the Small-Break Loss.of-Coolant Accident Phenomena Identification and Ranking Table . . . . . . . . . . . . . . . . . . . . . . . . 4.6-1 I 4.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7- 1 1

5 NOTRUMP ANALYSIS OF THE AUTOMATIC DEPRESSURIZATION SYSTEM TESTS . . . . . . . . . . . . ......... .......... .............. 5.1-1 5.1 Introduction .. . . . ....... .. . . .. .. . .. .. ... .... .. .. . .. . ... .. 5.1-1 5.2 NOTRUMP Automatic Depressurization System Validation Approach ....... 5.2-1 5.2.1 NOTRUMP Model of the Automatic Depressurization System Phase B Test Facility . . . . . . . . . ..... .................. 5.2-1 5.2.2 Method Used to Simulate the Automatic Depressurization System l

Phase B Tests . . . . . . . ........................... .. 5.2-1

j. 5.3 NOTRUMP Analysis of the Automatic Depressurization System Test Data ... 5.3-1 5.3.1 Test Description . .. ......... ....................... 5.3-1 i ('N 5.3.2 Possible Locations for Critical Flow . . . . . . . . . . . . ......... 5.3-1 i t,v) 5.4 Comparison of NOTRUMP to the 200-Series Automatic Depressurization System Tests . . . . . . . ...................................... 5.4-1 5.4.1 Test 210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ . . 5.4-1 5.4.2 Test 212 . . . . . . . . . . . . . . .. .......... ............ . 5.4-1 5.4.3 Test 220 . . . . . . ................. .................. 5.4-2 5.4.4 Test 240 . . . . . . . . . . .......... ..................... 5.4-2 5.4.5 Test 242 . . ..... ........................... ..... 5.4-3 5.4.6 Test 25 0 . . . . . . . . . . . . . . . . . . . . .... ..... .......... 5.4-3 5.4.7 Test 3 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ .. 5.4-3 5.4.8 Test 34 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............. 5.4-4 5.5 ~ Overall Comparison of NOTRUMP to the Tests ...................... 5.5-1 5.5.1 Critical Flow . . . . . . . . . . . . . . .................... .... 5.5-1 5.5.2 Pressure Drop Predictions . . . . .. . ................ . . 5.5-1 5.6 Assessment of the Automatic Depressurization System Phenomena Identification and Ranking Table . . . .......................... ............ 5.6-1 5.7 Conclusions ........... . ........... ........ ..... ...... 5.7-1 l 5.8 References .......................... ..................... 5.8-1 i

6 NOTRUMP ANALYSIS OF THE CORE MAKEUP TANK TESTS . . . . . . . . . . . . . 6.1-1

/m Introduction . . . .. .... .. .. .. . . . ... . .. ... .. ... . ... . ... .. . .. .

O' 6.1 6.2 AP600 NOTRUMP Core Makeup Tank Model for 500-Series Tests . . . . . . . .

6.1-1 6.2-1 i

FebruarE 1998 oM025w-toc.wpf;1b-022798 vii K CV. 4 l

TABLE OF CONTENTS (Cont.)

1 Section Title Eage 6.2.1 Core Makeup Tank Noding Description ...... .. .. . .... . . 6.2-1 6.2.2 NOTRUMP Representation of the Core Makeup Tank . . ... .... 6.2-1 6.2.3 NOTRUMP Modeling of Core Makeup Tank Operation . . . . . . ... 6.2-1 6.2.4 Specific NOTRUMP Models to be Verified . . ......... .. ... 6.2-3 6.3 NOTRUMP Comparisons to the 500-Series Core Makeup Tank Tests . . .. . 6.3-1 6.4 NOTRUMP Circulation Behavior Comparisons with the 500-Series Core Makeup Tank Tests . . . . . . . . . . . . ........ .......... .... . . 6.4-1 l 6.4.1 NOTRUMP Comparisons to Core Makeup Tank Tests C059502 and l C066501 . ....... .... .... .. . .. ... 6.4-1 l 6.4.2 NOTRUMP Comparisons to Core Makeup Tank Tests C061504 and C068503......... ....... ......... ..... .. ..... 6.4-2 6.4.3 NOTRUMP Comparisons to Core Makeup Tank Tests C064506 and C070505 ... .. . .. . . . . ............... 6.4-3 6.4.4 Comparisons of the NOTRUMP Circulation Behavior with the 500-Sedes Core Makeup Tank Tests at 1835 psig (1850 psia) . . . . . 6.4-4 l

j 6.5 Comparison of NOTRUMP to the 300-Series Core Makeup Tank Tests . .. . 6.5-1 6.5.1 Introduction . . . . . . . . . . . . ... ..... .. .. ..... . 6.5-1 6.5.2 NOTRUMP Comparisons to the 10-psig (24.7-psia) Core Makeup Tank Tests 6.5-2 l . .. ........ .... .. ... ... . .. . .

i 6.5.3 NOTRUMP Comparisons to the 1085-psig (1100-psia) Core Makeup l

Tank Tests . . ... ..... ....... . .. .... .. .. . 6.5-3 6.5.4 Overall Comparisons of the NOTRUMP Core Makeup Tank Model to the Core Makeup Tank 300-Series Tests . . .. . . . . 6.5-3 6.6 Assessment of the NOTRUMP Comparison Results Against the AP600 Phenomena Identification and Ranking Table . . . . . . . .... . . . .... 6.6-1 6.6.1 Assessment of Core Makeup Tank 500-Series Test Comparisons . . 6.6-1 6.6.2 Assessment of Core Makeup Tank 300. Series Test Comparisons . 6.6-1 6.6.3 Assessment of Core Makeup Tank Phenomena Identification and Ranking Table Phenomena . . . .. .......... .. ...... 6.6-2 6.7 Conclusions . ....... .. . . .......... .... ..... . 6.7-1 6.8 References .... . . .. ....... .. . ... ... . . . 6.8-1 APPENDIX 6A NOTRUMP COMPARISONS TO THE 300-SERIES CORE MAKEUP TANK TESTS . . .. ..... .. ... .. . . 6A-1 7 NOTRUMP COMPARISONS TO THE SPES-2 INTEGRAL SYSTEMS TESTS . 7.1-1 1 7.1 Introduction .. .... .. . . ..... . .. .. .... . . ... 7.1-1 7.2 NOTRUMP Modeling of the SPES-2 Small-Break Loss-of-Coolant Accident Tests . . . .. .... . .... . ...... . . ..... .. . 7.2-1 Febru 1998 eM025w-toe.wpf:lb.022798 viii ev 4

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h Title Page 7.2.1 SPES-2 Test Facility DescHption . . ........... ... .... .. . . 7.2-1 7.2.2 Description of '.a "' UMP SPES-2 Model . . . . . . . . ..... . . 7.2-5 7.2.3 Selected SPES-2 Tests for Analysis . . . . . . . . . . . . . . . . . . . . . 7.2-20 7.3 Comparisons of NOTRUMP to the SPES-2 Integral Systems Tests . . . . . . . . . 7.3-1 1 7.3.1 2-in. Cold Leg Break (S00303) . . . . . . . . . . . . . . . ... ... .. 7.3.1-1 7.3.2 1-in Cold Leg Break (S00401) . . . . . . . . . . . . . . . . . ... ... . 7.3.2-1 7.3.3 2-in. Direct Vessel Injection Line Break (S00605) . . . . . . . . . . . . 7.3.3-1 7.3.4 Double-Ended Guillotine Direct Vessel Injection Line Break (S00706) 7.3.4-1 7.3.5 2-in. Cold Leg Balance Line Break (S01007) . ......... .... 7.3.5-1 7.3.6 Double-Ended Guillotine Cold Leg Balance Line Break (S00908) . 7.3.6-1 l 7.4 Assessment of NOTRUMP Comparisons to SPES-2 Integral Systems Tests . . . 7.4-1 7.4.1 Introduction . . . . . . . . . . . ....... ....... .......... 7.4-1 i 7.4.2 Comparisons of the NOTRUMP Predicted Event Timing . . . . . . . . . 7.4-1 7.4.3 NOTRUMP Comparisons to the Measured Flows in the ;

SPES-2 Facility . . . . . . . . . . . ..........

..... .. . 7.4-2 7.4.4 Comparison of NOTRUMP-Calculated System Mass at IRWST Injection Time . . . . . . . . . . . . . . . . . ..............

7.4-3 7.5 References .............................. .. ........... . 7.5-1 8 NOTRUMP COMPARISONS TO THE OREGON STATE UNIVERSITY INTEGRAL SYSTEMS TESTS .. . . . . . . . . . . . . . ...... ............... ..... .. . 8.1-1 8.1 Introduction .......................................... .. . 8.1-1 8.2 NOTRUMP Modeling of the Oregon State University Small-Break Loss-of-Coolant Accident Tests . . . . .. ... .............. .. . 8.2-1 8.2.1 Oregon State University Test Facility Description . . . . . . . . .... 8.2-1 8.2.2 Description of NOTRUMP Oregon State University Model ... .. 8.2-6 8.2.3 Selected Oregon State University Tests for Analysis . . . . . .. 8.2-17 8.3 Comparisons of NOTRUMP to the Oregon State University Integral Systems Tests . . . . . . . . . . . . . . . . . . . . ....... ... . .... 8.3-1 8.3.1 - 2-in. Cold Leg Break (SB18) . . . ... .... ............ 8.3.1-1 8.3.2 0.5-in Cold Leg Break (SB23) ... ... ... .. . .. . .. .. . ... 8.3.2-1 8.3.3 2-in. Direct Vessel Injection Line Break (SB13) ......... .. . 8.3.3-1 8.3.4 Double-Ended Guillotine Direct Vessel Injection Line Break (SB12) . 8.3.4-1 8.3.5 2-in. Cold Leg Balance Line Break (Sb09) . . . . . . .... . . . . . 8.3.5- 1 8.3.6 Double-Ended Guillotine Cold Leg Balance Line Break (SB10) . . 8.3.6-1 8.3.7 Inadvertent Automatic Depressurization System Actuation (SB14) . 8.3.7-1 3- 8.4 Assessment of the NOTRUMP Comparisons to the Oregon State (V University Integral Systems Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4-1 Februaq 1998 oM025w-toc.wp(:Ib-022798 ix Key.4

TABLE OF CONTENTS (Cont.)

Title .P.agg Section Introduction . . . . . ..... ... . ......... ...... .. 8.4-1 8.4.1 .

8.4.2 Comparison of the NOTRUMP-Predicted Event Times and Flows for Oregon State University . . . . . . . . . . . . . . . . . . . . . . . ...... 8.4-1 8.4.3 Comparison of NOTRUMP-Predicted System Mass for Oregon State University . . . . . . . . . . . . . .. ... . ..... .. 8.4-2 8.4.4 Assessment of Oregon State University Test SB23 (0.5-in. Cold Leg Break) .. ........ ............ ...... ........ . 8.4-2 ;

8.5 References . . . ............ ... ......... ...... ........ 8.5-1 9 CONCLUS:ONS ....... . ... ... ....... . .... ....... ..... 9-1 APPENDIX A LIST OF NRC REQUESTS FOR ADDITIONAL INFORMATION AND WESTINGHOUSE RESPONSES . . . . ......... . . .. ...... . A-1 O

i l

l

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I f ebruary 1998 ovo25w-toc.wpr:Ib-022798 X Rev.4

L I

l l 1 f LIST OF TABLES i A .

! .T.altit .Tius P.ast

1.3-1 Phenomena Identification and Ranking Table for AP600 Small-Break L

Loss-of-Coolant Accident . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3-5 l- 1.4 Method of Addressing Highly Ranked PIRT Phenomena . . . . . . . . . . . . . . . . 1.4-2 l- 1.6-1 . AP600 Small Break Loss-of-Coolant Accident Phenomena and -

!- NOTRUMP Models . . . . . . . . . . . . . . . . . . . . ..................... 1.6-4 1.6-2 Original Model Descriptions in Reference 1-1 ....... ............... 1.6-6 1.6-3 NOTRUMP Code Modifications for AP600 . . . . . . . . . . . . . . . . . . . . . . . . . 1.6-7

? 1.6 Key Model Validation Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6-8

'l.7-1 Figures Depicting Results from Vertical and Horizontal Flow Models . . . . . . . 1.7-26

! 1.7-2 Water Saturation Properties and Derivatives . . . . . . . . . . . . . . . . ........ 1.7-27 1.7-3 Acceleration Effects in ADS 1-3 Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7-28 1.7-4 Acceleration Effects in ADS 1-3 Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7-30

.1.7-5 Acceleration Effects in ADS 4 Piping . . . . . . . . . . . . . . . . . ........... 1.7-31 1.8-1 Figures Depicting Results from the Level Tracking Model .............. 1.8-8 1.10-1 Figures Depicting Results from the Core Makeup Tank Model . . . . . . . . . . . . 1.10-5 1.11-1 Figures Depicting Results from the Passive Residual Heat Exchanger Model . . 1.11-3

[ 1.16-1 1.17-1 Assessment S ummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.16-3 Assessment Summary . . . . . . . . . . . . . . . . . . . . . . . . . ............ 1-17-3 l

l -3.2-1 Vertical Countercurrent Flow Limit Model Cases Analyzed . . . . . . . . . . . . . . 3.2-6 3.2-2 Figures for Vertical Flow Drift Flux Model Benchmarking Cases . . . . . . . . . . 3.2-7 l; 3.3-1 Horizontal Countercurrent Flow Limit Model (Levelizing) Cases Analyzed . . . 3.3-5 3.3-2 Figures for Levelizing Drift Flux Model Benchmarking Cases . . . . . . . . . . . . 3.3-6 3.4-1 Figures for Implicit and Explicit Treatment of Gravitational Head Cases . . . . 3.4-4 3.5-1 Figures for Net Volumetric Flow-Based Momentum Cases . . . . . . . . . . . . . . 3.5 2 3.6-1 Figures for Implicit Bubble Rise Model Cases . . . . . . . . . . . . . . . . . . . . . 3.6-2 3.7-l' Figures for Main Coolant Pump Model Cases . . . . . . . . . . . . . . . . . . . . . .. . 3.7-2 L 3.8-1 Summary of the Stack Draining and Filling Events for the

First 1.5 Seconds of the Single-Phase Oscillating Manometer Simulation . . . . . 3.8-6 3.8-2 Plots for Fluid Node Stacking Logic Cases . . . . . . . . . . . . . . . . . . . . . . . . . 3.8-7 t;

4.2-1 Summary of Test Parameters for Small Blowdown Vessel Steam Blowdown Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . ......................4.2-12 l: 4.2-2 Figures for General Electric Small Blowdown Vessel Test Cases . . . . . . . . . . 4.2-13 4.3-1 ACHILLES Level Swell Test Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.3-8 4.3-2 Data for Run A1 LO66 at Zero Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3-9

f '

4.3-3 Data for Run ALLO 69 at Zero Time . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.3-10

. 4.3-4 Figures for ACHILLES Low-Pressure Level Swell Test Cases . . . . . . . . . . . 4.3-11 g

r.

Februart 1998 l oM025waoc.wpr:Hm98 xi Rev.4 l1 i

LIST OF TABLES (Cont.)

Table Title Eage 4.4 1 Comparison of 17 x 17-XL Pressurized Water Reactor Rod and Test Rod B undle . . . . . . . . . . . .......... ............. .. .... . . 4.4-17 4.4-2 G2 Loop Core Uncovery Test Vessel Flow Areas ............... . . 4.4-18 4.4-3 G2 Loop Core Uncovery Test Parameters ... . ....... .......... 4.4-19 4.4-4 Figures for G2 Test Simulation Cases . . . . . . . . .. . ........ ...... 4.4-20 4.5-1 Figures for Level Swell Comparisons . . . . . . . . . . . ........ ....... . 4.5-2 5.2 1 Figures: Automatic Depressurization System Phase B Test Facility . . . . . . . 5.2-3 5.3-1 Automatic Depressurization System Phase B1 Test Matrix . . . . . . . . . . . . . 5.3-3 5.3-2. Automatic Depressurization System 1-3 Tests Analyzed with NOTRUMP, Configurations ... . . . ........ ........ ...... 5.3-5 5.4-1 NOTRUMP Comparisons to 200-Series Automatic Depressurization System Tests . . ... ................ ............ . . . . 5.4-5 5.5-1 Occurrence of Critical Flow ... ................. . ....... . . . 5.5-2 5.52 Figures: Overall Comparisons of NOTRUMP Predictions to Automatic Depressurization System Performance Data . . . . . . . . . . . .... .. . 5.5-3 6.1-1 Phenomena Identification and Ranking Table for the AP600 Core Makeup Tank . . . . . . . .... ........ ... ...... ......... 6.1-3 6.1-2 Plots From AP600 SSAR 2-in. Cold Leg Break Calculations . . . . . ... . . 6.1-4 6.2-1 Figures Illustrating the AP600 NOTRUMP Core Makeup Tank Model for 500-Series Tests . . . . . . . . . . . . . . . . . ... . . ........... 6.2-4 6.3-1 Core Makeup Tank Matrix Test Program - 500 Series ........... . . .. 6.3-2 6.4-1 NOTRUMP Comparisons to the 500-Series Core Makeup Tank Tests ...... 6.4-5 6.5-1 Figures Illustrating NOTRUMP Comparisons to the 300-Series Core Makeup Tank Tests . . . . . . . . . . . . . . . . ........ ......... . . 6.5-5 6A-1 NOTRUMP Comparisons to the 300-Series Core Makeup Tank Tests . . . .. 6A-2 7.2-1 S PES-2 Test Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2-22 7.3.1-1 S00303 Sequence of Events ..................... ....... ..... 7.3.1-9 7.3.1-2 Figures for SPES-2 2-in Cold Leg Break (S00303) . .. ... .......... 7.3.1-10 7.3.2 1 S00401 Sequence of Events .................. ... ........... 7.3.2-10 7.3.2-2 Figures for SPES-21-in Cold Leg Break (S00401) . . . . . . . . . . . . . . . . . 7.3.2-11 7.3.3-1 S00605 Sequence of Events .. .. .................... ... . 7.3.3-9 7.3.3-2 Figures for SPES-2 2-in Direct Vessel Injection Line Break (S00605) . .... 7.3.3-10 7.3.4-1 S00706 Sequence of Events ... ............. ............. . 7.3.4-9 '

7.3.4-2 Figures for SPES-2 Double-Ended Direct Vessel Injection Line Break (S00706) . . . . . . . . . . . ........ ..................... .. . 7.3.4-10 Februarr 1998 oM025w-toc.wpf:Ib o22798 gij gey,4

i i.

I 1

l n LIST OF TABLES (Cont.)

I \

U/

l Tab,l.e Title Eage a

7.3.5 1 S01007 Sequence of Events ..... .................... .. .. . 7.3.5-9 ,

7.3.5-2 Figures for SPES-2 2-in. Cold Leg Balance Line Break (S01007) . . . . . . . 7.3.5- 10 1

l 7.3.6-1 S00908 Sequence of Events . ....................... .. .. . . . . 7.3.6-9 7.3.6-2 Figures for SPES-2 Double-Ended Cold Leg Balance Line Break (S00908) . 7.3.6-10 7.4-1 NOTRUMP Comparisons to the SPES-2 Integral Systems Tests . . . . . . . . . . 7.4-5 i

8.2 1 Oregon State University Summary Matrix . . . ...................... 8.2-18 8.3.1-1 SB18 Sequence of Events . . . . . . . . . . . . . . . . . . . . .. . ... . .. . . .. . . 8.3.1-8 8.3.1-2 Figures for OSU 2-in. Cold Leg Break (SB18) ...... . . . ... .. ... . . . 8.3.1-9 8.3.2-1 SB23 Sequence of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2-10 8.3.2-2 Figures for OSU 0.5-in. Cold Leg Break (SB23) . . . . . . . . . . . . . . . . . . 8.3.2-11 8.3.3-1 SB13 Sequence of Events . . . . . . . . ............ .. .. ... .. . . .. . 8.3.3-8 8.3.3-2 Figures for OSU 2-in. DVI Line Break (SB13) ........ . . ... .. . .. . . 8.3.3-9 8.3.4-1 SB 12 Sequence of Events . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . . . . 8.3.4-8 8.3.4-2 Figures for OSU Double-Ended Direct Vessel Injection Line Break (SB12) . . 8.3.4-9 8.3.5-1 SB09 Sequence of Events . . . ....................... ... .. . . 8.3.5-9 8.3.5-2 Figures for OSU 2-in. Cold Leg Balance Line Break (SB09) . . . . . . . . . . . 8.3.5-10 v 8.3.6-1 SB10 Sequence of Events . . . . .............. .... . .. . . . . . . . 8.3.6-9 8.3.6-2 Figures for OSU Double-Ended Balance Line Break (SB10) . . . . . . . . . 8.3.6-10 8.3.7-1 SB14 Sequences of Events . . . . . . . . . . . . . . . . ... . ... .... .. . . .. . 8.3.7-9 8.'k'-2 Figures for OSU Inadvertent ADS Actuation (SB14) ....... . . . . . . . 8.3.7- 10 8.4-1 Figures for Section 8.4 . . . . .. .... ....... ... . . . . . . . . . . . . . 8.4 -4 9-1 Assessment Summary . . . . . . .. . . ............ .... ............ 9-5 A-1 SDSER Confirmatory Items ................. . . . . . . . . . . . . . . . A -5 A-2 SDSER Open Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-7 A-3 NOTRUMP RAI Responses . ............. . ........ ...... . A-11 l'.

l oM025w. toc.wpf;1b-022798 Februarr 1998 xiij Rev.4

}

LIST OF FIGURESW Figure -

Title Eage a

1.2-1 NOTRUMP Noding Scheme for the AP600 Plant ....... . ... .. 1.2-4 1.3-1 AP600 Small. Break LOCA Scenario ...... ................ . .. 1.3-9 1.9-1 Comparison of Martinelli-Nelson Correlation (P.HIL(1)) to Chisholm Two-Phase Multiplier with Two Values of C (PHIL(2): C=2; PHIL(3): C=10) . . 1.9-3 1.16-1 AP600 Pressurizer Pressure Comparison . ..... ............. .... 1.16-7 1.16-2 AP600 Pressurizer Mixture Level Comparison . . . . . . . . ... .. ...... 1.16-7 1.16-3 AP600 Core / Upper Plenum Mixture Level Comparison . . . . . . . ....... 1.16-8 1.16-4 AP600 CMT-1 Mixture Level Comparison .. .............. ...... 1.16-8 1.16-5 AP600 CMT-2 Mixture Level Comparison . . . . . . ....... ...... . . 1.16-9 1.16-6 AP600 Integrated ADS 1-3 Flow Comparison . . . . . . . . . . . . . . . . . . . ... 1.16-9 1.16-7 AP600 Integrated ADS 4 Flow Comparison ....... ... ...... 1.16-10 1.16-8 AP600 RCS System Inventory Comparison , .. . ......... ..... 1.16-10 1.16-9 AP600 Integrated PRHR Heat Rejection Comparison . . . . . . . . . . . . 1.16-11 1.16-10 AP600 Core Inlet Temperature Comparison . . ... ... .. ..... . 1.16-11 1.16-11 AP600 Core Outlet Temperature Comparison .... .. ...... ... 1.16-12 1.16-12 OSU DEDVI Break, Pressurizer Pressure Comparison .... ....... .. 1.16-12 1.16-13 OSU DEDVI Core / Upper Plenum Mixture Level Comparison . . ... . .. 1.16-13 1.16-14 OSU DEDVI Downcomer Mixture Level Comparison ... ..... . .... 1.16-13 1.16-15 OSU DEDVI Integrated Vessel Side Break Flow Comparison . . . . . .. . 1.16-14 1.16-16 OSU DEDVI Integrated DVI Side Break Flow Comparison . .......... 1.16-14

'l.16-17 OSU DEDVI Integrated ADS 1-3 Flow Comparison . . . . . . ... ....... 1.16-15 1.16-18 AP600 Pressurizer Pressure Comparison . . . . . . ...... . .. .. 1.16-15 1.16-19 AP600 Pressurizer Mixture Level Comparison . . .. .............. 1.16-16 1.16-20 AP600 Core / Upper Plenum Mixture Level Comparison . . .. . ..... 1.16-16 1.16-21 AP600 Downcomer Mixture Level Comparison . ............... .. 1.16-17 1.16-22 AP600 Integiated ADS 1-3 Flow Comparison .... .. ............ 1.16-17 1.16-23 AP600 Integrated ADS 4 Flow Comparison ...................... 1.16-18 1.16-24 AP600 Integrated Vessel Side Break Flow Comparison . . . . . . . . . . . . 1.16-18 1.16-25 AP600 Primary System Inventory Comparison . . . . . ......... ...... 1.16-19 1.16-26 AP600 Pressurizer Pressure Comparison . . . . . . . . . . . . . . .... ..... 1.16-19 1.16-27 AP600 Core / Upper Plenum Mixture Level Comparison . . . . . . . . .... 1.16-20 1.16-28 AP600 Downcomer Mixture Level Comparison . . . . . . . . .. ......... 1.16-20 1.16-29 AP600 Primary System Inventory Comparison . . . . . . . . . . . . . . . .. .. 1.16-21 2.4-1 Sunple Situation for Use of Length Weighting . . . . . . . . . . . . . .... .. 2.4-10 5.3-1 Test A037210 Pressure Variation in Facility at Time 20 sec. . . ..... .. 5.3-6 Iebruary 1998 oM025wec.wpf.It422798 xiv Rev.4

?

- ~ . _- ~ _. . - - - . - ~ ._. - - - - - .- .- --.- ..-.- - --. .-

l l

I LIST OF FIGURES (Cont.)W Eigyte - Title Page i

l 6.6-1 Summary Comparisons of Average Core Makeup Tank Drain Flow from '

the 500-Series Test . . ............................. ......... 6.6-3 7.2-1 SPES-2 Test Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2-24 1 7.2-2 NOTRUMP Noding Diagram (Fluid Nodes) for SPES-2 Facility . . . . . . . . . 7.2-25

{ 7.2-3 NOTRUMP Noding Diagram (Metal Nodes) for SPES-2 Facility . . . . . . . . . 7.2-26 i

8.2-1 Isometric Drawing of the Oregon State University Test Facility . . . . . . . . . 8.2-20 l

- 8.2-2 NOTRUMP Noding Diagram (Fluid Nodes) for Oregon State

! University Facility . . . . . . ................................... 8.2-21 l 8.2-3 NOTRUMP Noding Diagram (Metal Nodes) for Oregon State I University Facility . . . . . . . . . . . .............................. 8.2 22

)

I l

M9E: l l r (1) Most of the figures for Sections 1.7,1.8,1.10,1.11, and Sections 3.2 through 8 are listed in tables l k preceding each set of figures in each subsection.

l l

l l-fx i

l Februarv 1998 eM025w-toc.wpr:Ib-022798 xv "Rev.4

I LIST OF ACRONYMS l

l ADS Automatic depressurization system AICC adiabatic isochoric complete combustion l AOV air-operated valve ASME American Socie.ty of Mechanical Engineers i l CCFL countercurrent flow limit I

CHF critical heat flux ,

CL cold leg CMT core makeup tank l CNS containment system l COL combined operating license l CRDM control rod drive mechanism CRT core reflood tank CVCS chemical and volume control system l

DAS data acquisition system DCP design change proposal DEG double-ended guillotine DECLG double-ended cold leg guillotine DF decontamination factor ;

DG diesel generator DNB departure from nucleate boiling DOE United States Department of Energy DSER draft safety evaluation report DVI direct vessel injection ECCS emergency core cooling system EPRI Electric Power Research Institute ESF engmeered safety feature HL hot leg HT heat transfer HVAC heating, ventilation and air conditioning HX heat exchanger IASCC irradiation-assisted stress corrosion cracking I&C instrumentation and control ICAP International Code Assessment and Application Program IIS incore instrumentation system IRWST in-containment refueling water storage tank ITAAC inspection, tests, analysis and acceptance criteria IJD length over diameter LBLOCA large-break LOCA LOCA loss-of-coolant accident oM025w-toc.wpf;It> o22798 xyj Februartgey,4 1998

6

(.

r LIST OF ACRONYMS (Cont.)

L L-LTC long-term cooling l- MFWIV - main feedwater isolation valve

, _ MSLB ' main steam line break MSLIV - main steam line isolation valve

. MSS main steam system NRC- Nuclear Regulatory Commission -

NRHR normal residual heat removal system NSSS - nuclear steam supply system -

i PAMS post-accident monitoring system P&ID piping and instrumentation diagram

.PBL~ pressure break line.

PCS passive containment cooling system i

PCT peak clad temperature PIRT phenomena identification and ranking table PLS plant control system

! PMS protection and safety monitoring system PORV power-operated relief valve (p PRAi probabilistic risk assessment V .PRHR passive residual heat removal

PWR pressurized water reactor.

PXS passive core cooling system QDPS_ qualified data processing system RAI: request for additional information RAM reliability, availability, and maintainability RCDT reactor coolant drain tank RCP reactor coolant pump D

RCS. reactor coolant system RHR. residual heat removal RTD resistance temperature detector SBLOCA small-break LOCA SCC. stress corrosion cracking

'SER- safety evaluation report

-SFS spent fuel cooling system h 'SFWS startup feedwater system j ._ SG steam generator

!- -.SGS steam generator system o SGTR steam generator tube rupture

. ' SI ' safety injection Iv SIMARC simulator advanced real-time code l

February 1998 oM025w4oc.wpf:Ib-o22798 Rev.4

. xvii l

l LIST OF ACRONYMS (Cont.) !

SMS special monitoring system SPS passive containment spray system SSAR standard safety analysis report STD standard UET unfavorable exposure time UPTF upper plenum test facility URD utility requirements document USC utility steering committee '

VBS non-radioactive ventilation system VES passive control room ventilation system VFS containment air filtration system 1

l

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l l l l l 1

l l

9 Febntary 1998 c:wo25w-toc.wpf:Ib-022798 xv111 Rev.4

g NOMENCLATURE

'tQ i A =. flow area, ft.2 i Ap- = flowlink area (ft.2)

[

ja.c BDFL = flowlink downstream end mixture fraction, b (1)J d BUFL = flowlink upstream end mixture fraction, bua)J c = user-supplied constant default valve = 0.13 (Co)g = discharge coefficient CFDFL =

flowlink downstream liquid flow fraction, Ch)3

CFUFL = flowlink upstmam liquid flow fraction, Chg),i CGDFL ' =

flowlink downstream gas flow fraction, Ch)3 I CGUFL = flowlink upstream gas flow fraction. C,Li

[

.ja.e C, = drift flux distribution parameter CONV- = 10-6 8

C i'.k,C ik = contact coefficients for liquid and vapor flow between fluid node i and flowlink k D- = diameter, ft.

DCONTFL = continuous contact flowlink diameter, ft.

DELWFL = flowlink change in either W or Q state variable, Ibm /sec. or ft.3/sec.

D g. = hydraulic diameter, ft. .,

. DWFFL = .flowlink partial derivative of liquid mass flow rate with respect to either W or Q state variable, Ibm /ft.3 Dfyior - = Taylor instability diameter, ft.

E = elevation, ft.

EBOTFN = fluid node bottom elevation, Ebot, ft.

EDFL = flowlink downstream elevation, Ep , ft.

EMIXFN = mixture elevation, Eg, ft.

ETOPFN = fluid node top elevation, E,op, ft.

-EUFL = flowlink upstream elevation, Eg , (ft.)

FULRFL(I,L) - =- Fraction of liquid flow througt link IULRFL(I,L) that is contributed to the flow in internally calculated liquid-n flux flowlink L

.g = gravitational acceleration, ft/sec.2 ge . = conversion factor, 32.174, Ibm-ftflbf/sec.2 G = total mass flux, Ibrn/sec/ft.2 h = specific enthalpy, Btu /lbm h = film heat transfer coefficient, Btu /secift.2.pf Februaq1998 oM025w-soc.wpf:lb-022798 xix Kev. 4

NOMENCLATURE (Cont.)

H = pump head, ft.

h,f

= latent heat of vaporization, Btu /lbm

= heat-transfer coefficient assuming all the mass flowing is liquid, Btu /secift.2 fop hr IDRNFN = fluid node mixture level overshoot drain flag IFILLFN = fluid node mixture level overshoot fill flag IREDOFL = flag for redoing certain flowlink calculations ISMFN = fluid node mixture region state flag ISTAKFN = node stack and mixture level backing flag ITYPEFL = flowlink type flag ITYPEFN = fluid node type flag IULRFL(I,L) = Identification number of the Ith link that can potentially contribute to the flow of intemally calculated liquid-reflux flowlink L j = total volumetric flux, ft.3 -seel l/ft.2 = ft/sec.

J = Joule's constant, 778.156, ft.-lbf/Bru JFLUXON = local logical flag (if true, drift flux is done on a volumetric flow bases; othenvise on a mass flow basis)

JREDOIT = local flag to cause drift flux to be done twice, first on a mass flow basis and second on a volumetric flow basis jf ,js = dimensionless form of the liquid and vapor component volumetric flux J pg = denominator of the liquid and vapor component dimensionless volumetric flux expression, ft/sec.

K = drift flux / flooding parameter, ft/sec.

kf = conductivity of saturated liquid, Btu /secift1 F L = length, ft.

[ ja.e M = mass, lbm NULRFL(L) = Number of flowlinks that potentially contribute to the flow of intemally calculated liquid-reflux flowlink L P = pressure, psia Pi = interfacial area per unit length ft2/ft.

Prt = Prandtl number of liquid P,,i = wall surface area in contact with liquid, ft.2/ft.

Q = volumetric flow rate, ft.3/sec.

Q = time rate of change of Q, ft.3/sec.2 M

Q = mass heat rate V

Q = volumetric heat rate R = radius of continuous flowlink Re = Reynolds number s = entropy, Btu /lbm/*F Februart 1998 oM025w-toc.wpf:lb 022798 xx Kev. 4

. _ . _ _ _ . . _ _ _ . . _ . _ . . . _ _ . . _ . _ . - . _ _ . ~ _ _ _ . _ . . _ _ _ _ . . . _ . _ . . . _ . - _ . _ _ _ _ _ _ . _ . _

l': - .

-t .

NOMENCLATURE (Cont.)

-(

\

! t = time at beginning of time step, sec.

! At = time step size, sec.

T- = temperature *F L TMMFN ~= fluid node mixture region mass, Mg, Ibm

TMMOFN = fluid node mixture region mass from previous time step, Mdd, Ibm TMVFN = fluid node vapor region mass, My, Ibm TMVOFN old

= fluid mode vapor region mass from previous time step, My , Ibm

'U- = internal energy, Btu V = volume, ft.3 Vg = drift velocity of vapor relative to the total volumetric flux, ft./sec.

W. = net mass flow rate, Ibm /sec.

L 4 = time rate of change of W, Ibm /sec.2 IW/, IW,1 = absolute value of liquid and vapor flow, Ibm /sec.

l WFFL = flowlink liquid mass flow rate, W , fIbm /sec.

(Wh)M -gy , (Wh)V i3 = net energy flow rate to or from the mixture and vapor regions of fluid node i for flowlink k, Bru/sec.

X = quality AZ- = characteristic liquid level difference term, ft.

.Zu = overall height of flowlink, ft.

(x = void fraction o = surface tension, Ibf/ft.

pg, pr = saturated vapor and liquid viscosities, Ibm /ft. sec.

p = density, Ibm /ft.3 o V = specific volume, ft.3/lbm t = shear stress, Ibf/ft.3 Subscripts:

ber = critial bubble rise bot : = botom end of flowlink or bottom node BR = bubble rise l [ P' i D = downstream y

! donor = donor -

f,1 = liquid phase j

[' g,v = vapor (gas) phase .

E k = flowlink k Februa~ 1993 eMo25..ioc.wpr:Ib-o:279s - xxi hev. 4

NOMENCLATURE (Cont.)

M = mixture region mix = mixture elevation recipient = recipient top = top end of flowlink.or top node U = upstream

[< :]Se V = vapor region w = w all Superscripts:

Cdt = CddCd donor = donor recipient = recipient stag = stagnation Q = volumetric flow-based t = throat ,

W = mass flow-based l

l l

4 O

February 1998 oM025w-toc.wpf;1t>O22798 xxii Rev.4

- .-- .. ... ~. -- . . . - - . ~ . - _ - . .- . . .. - . - . . - ~..

i ACKNOWLEDGEMENTS

\

Producing a repon of the magnitude of the NOTRUMP validation report requires the help and support of several individuals to make it a success. The authors would like to recognize and thank B.E. Rarig for his project management of the program and for developing attemate methods to complete the report. The authors thank E.H. Novendstern for his management and resource leadership on the project as well as his technical review of the repon. The authors also thank B.A. McIntyre for his technical review of the repon.

There were several individuals who panicipated in several of the code benchmark models and

l. assessments. Thanks are due to S. Blair and K. Muftuoglu from Penn State and P. Garner and C. Chu from the Argonne National Laboratory, who helped and supported validation of several of the NOTRUMP models and wrote and reviewed calculaticas and calculation documentation.

The r.uthors would like to thank R. J. Lucia. L. G. McSwain and N. Gibbs for the editing and coordination effort to complete this report and all the individuals in word processing for their effons on the repon. 'Ihe authors would also like to thank Dale Morgan for his preparation of many of the figures.

l s

i-1 i

l l

I O

V i

Febru a:w25ww25w.a& ibm 269s ;

t

1.9 Hydraulic Resistance Model d

The AP600 system consists of several interconnected pipes of varying diameter. These can be divided into the following components:

RCS loops CMT balance line

DVIline

Accumulator line

ADS 1-3 piping ADS-4 piping Typically, each component consists of a constant area piping run each with several bends and valves.

The most significant sources of pressure loss are therefore primarily due to friction and form loss.

1.9.1 NOTRUMP Model Description and Applicability he NOTRUMP model of the AP600 uses the Martinelli-Nelson correlation for the two-phase 2

multiplier @io in Equation 1.7-3. The resistance of each segment of pipe modeled as a flowlink is supplied to the code as an overall resistance coefficient K based on single-phase flow tests or

-e handbook calculations, therefore it includes both friction and form loss.

t The Martinelli-Nelson correlation is based on low-pressure boiling data in small diameter tubes, in ;

which the pressure drop is dominated by friction. In the NOTRUMP model, these multipliers are I applied in flow paths where form losses due to orifices, branches, and tees also exist. To establish whether this model remains applicable under these conditions, more recent correlations and models were examined.

Collier (Reference 1-22) reviewed available correlations for two-phase pressure drop across orifices, bends, and large diameter pipes. One of the more successful formulations was that by Chisholm (Reference 1-29) in which the two-phase multiplier @i2 is given by:

$2 ,3 ,C Q (j,9,3)

-x_,,

x2

. where X is the Martinelli-Nelson parameter (ratio of liquid to vapor pressure drop), and C is an

- empirical constant. De constant C varies from 2 to abom 10, depending on the component involved.

The liquid-only multiplier and the liquid multiplier are related by:

~

b Q 2

$ , ,4 (3.

3 2

x)2 (1.9-2)

February 1998 eManwwnsw.ic.wpf: Ibm 269s 1,9 1 Rev.4

l where x is the steam quality. The Chisholm equation is compared with the Martinelli-Nelson correlation for two values of C in Figure 1.9-1. It can be seen that the Martinelli-Nelson correlation generally overpredicts the two-phase multiplier.

In general, a large degree of uncertainty must be accepted in the prediction of pressure drops in two-phase flow regardless of the models used. Typically, even the most sophisticated correlations can only predict the pressure drop to with 30 or 40 percent. For this reason, it was decided not to incorporate one of the newer models into NOTRUMP.

1 1.9.2 Conclusions 1

It is concluded that the model used in NOTRUMP for two-phase pressure drop is applicable, although l it is subject to substantial uncertainty.

1 l

t i

e l

l l

l 9

.:u934wu934w.lc.wpf.lb 111297 },g.2 y,

l f

1.10 Core Makeup Tank Model G

1.10.1 Core Makeup Tank Behavior Observed from Tests Both single and separate effects tests have characterized the following behavior of the CMT during a small-break LOCA:

1) After the isolation valve opens, but before significant voiding occurs in the RCS, hot RCS water from the cold leg flows into the CMT while cold CMT water flows into the DVI line and into the vessel. The hot water collects as a stable layer at the top of the CMT, cooling slightly as heat is transferred to the cold CMT walls. The recirculation rate is relatively low due to the low gravitational driving force.

2) After significant voiding occurs in the RCS and these voids are propagated into the balance line, a bubble forms in the CMT and the CMT begins to drain. Draining may be affected by condensation of vapor in the colder CMT water.

The physical processes occurring in the CMT during recirculation are illustrated in Figure 1.10-1.

Tests indicate that three layers form: a cold layer (the original CMT water), a hot layer (most of the water entering from the RCS), and a warm layer (water next to the CMT walls that cools and sinks to the hot-cold interface).

V 1.10.2 NOTRUMP Core Makeup Tank Model (Recirculation Phase)

The NOTRUMP model of the AP600 CMT is illustrated in Figure 1.10-2. It consists of four fluid volumes, each representing the indicated fraction of the total tank volume. The basis for the choice of volumes is discussed in Reference 1-30. The key volume is felt to be the top-most volume, since its rate of heat-up and subsequent saturation would detcrmine the onset of draining of the CMT.

Any warm water entering the CMT mixes completely with the water in the top volume, ar.d this warming propagates to the other volumes as time passes. In addition, a simple lumped parameter (single temperature) model is used for the CMT wall.

This model ignores several potentially important phenomena identified in the PIRT, the main one being that it does not recognize the fact that stable (hot fluid over cold fluid) stratification is likely to occur in the CMT.

l 1.10.3 Hot Layer Model l

r l To examine the implications of this modeling of the CMT, a more accurate " layer" model was

! developed for comparison. "Ihe basic features of the model are illustrated in Figure 1.10-1. Assume

~

( that the hot water entering the CMT collects in a volume Vh(containing both the hot and warm February _1998 ouo25wwo25w.ic.wptib-022698 1.10. ] Key,4

i l layers), which displaces the volume of cold water V,. The flow rate entering the CMT is W,, and the water leaving is W,. Since the volumetric flow is conserved, the following relationship holds:

W,=bW ,

(1.10-1) p,,

where p, and p , (Ib/ft.') are the incoming hot fluid density and the initial CMT fluid density, respectively. A mass balance on the hot volume gives:

p,V" = bW* (1.10-2) dt p,,

where p, is the density of the fluid in the region V,.

An energy balance on the hot region V , assuming constant pressure, yields:

dh .

M, ". = _p"iW,(h,- h,) + Q, + Q,

. (l.10-3) dt p,,

where h is the fluid enthalpy (Bru/lb.), Q is the heat flow (Btu /sec.) from the wall to the fluid, and Q, is the heat flow across the interface between the hot volume and the cold volume.

As the hot volume expands, initially cold wall area is exposed to the hot fluid. The heat flux from the freshly exposed area is initially high, then decays as a thermal boundary layer builds up. The total heat flow to V, is therefore given by:

Q(t),=fP,(z)q dz (1.104) o s mc s Where P (Z) is the wall perimeter at location Z, and the heat flux function q (Btu /secift.2) is the heat flux at location z after an exposure time equal to (z - z)/Uw, where Uw is the rate (ft/sec.) at which the hot / cold interface travels. Since the heat transfer coefficient is relatively high (500 to 700 Btu /hr/ft.2/ F based on the CMT single effects tests), the heat flux is close to that from a semi-infinite solid early in time.

1.10.4 Model Comparisons The two models described above were coded as simple stand-alone models. In each model, the recirculation rate is calculated assuming equal pre:sures at the balance line entrance and the DVI line O

November 1997 c:\3934w\3934w-Ic.wptib-120397 1.10-2 Rev.3

.-.- - - . - , - . - - - - . - - . - . - . ~ . . -. .-._ .

I (p) exit, and using a momentum equation consistent with the model used. For the layered model, the recirculation rate is calculated as* I l

i 2p,g[(Zoy+ Zre)Pc + ZmPm- Z,tp,)

W, = A (1.10-5)

OK,t+ Koy

$ P, l

where W, is the mass flow (Ib/sec.) out of the CMT, DV denotes the DVI line, BL denotes the

- balance line, TC denotes the cold layer in the CMT, and TH denotes the hot layer in the CMT.

For the NOTRUMP model, the recirculation rate is calculated as: !

2gp, Zov p,+ Z,p,- Z,tph

' (1.10-6)

W=A ,

b K,t+ K oy 3 Pi V The NOTRUMP model was tested with the original 4 cells,10 cells of equal size, and 20 cells of equal size. Figures 1.10-3 to 1.10-7 compare some important variables from the two models. '

Indicated rJong the time axis in these figures are the times at which the CMT is observed to begin draining in the SPES tests. Figure 1.10-3 compares the fluid temperature in the top volume of the NOTRUMP model with the temperature of the hot layer in the layer model. Until about 300 seconds, !

the NOTRUMP model temperature is significantly lower. This may result in excessive steam condenntion onto the liquid when steam enters the CMT in the larger size breaks, leading to a delay l

in draining. For smaller breaks, the upper cell temperature reflects the predicted actual temperature reasonably well.

4 Figure 1.10-4 compares the exit fluid temperature for both models. It is evident that the thermal propagation inherent in the NOTRUMP model leads to substantial differences in the exit fluid l temperature for transients in which the draining phase is delayed by more than about 800 seconds for the base model. Increasing the number of cells mitigates the problem to some extent. For smaller size ;

breaks, the warmer water entering the vessel may impact the overall transient.

Figures 1.10-5 and 1.10-6 compare the calculated fluid energy in the tank and the metal energy.-

While the simple lumped parameter model results in a different metal energy, this component is a l relatively small fraction of the energy change due to inlet and outlet flows. As the lowest cell heats i up in the NOTRUMP model, the rate of energy accumulation decreases. Figure 1.10-7 compares the

!k CMT flows, which agree closely.

November 1997 c:U934w\3934w.lc.wpf:lb-120397 } ,l0-3 Rev.3 l

1.10.5 NOTRUMP Core Makeup Tank Model(Draining Mode)

The NOTRUMP CMT model assumes that draining begins when the top-most volume becomes saturated. The tests (Reference ,-30) indicate that the processes leading to bubble formation are more complex than a simple heatup of the upper-most CMT fluid to saturation. For the high-pressure tests (most representative of conditions in AP600), when the balance line drains and steam enters the CMT, time delays no greater than 50 seconds were observed, with draining beginning while the CMT upper region fluid was still subcooled.

'Ihe delay observed in the CMT tests occurs because steam is allowed to enter the CMT without an initial recirculation period. For more realistic situations where a recirculation period occurs, these delays would be expected to be even shorter. As indicated in the previous section, the NOTRUMP model would also be expected to produce a short delay, even though the volume must heat to saturation because the initial temperature of the volume is high for relatively small breaks. Longer delays could be expected for larger breaks, but the more rapid depressurization rate of these transients quickly brings the saturation temperature down to the fluid temperature to begin draining.

1.10.6 Conclusions This assessment indicates that the lack of a thermal stratification model could lead to high-energy fluid being injected into the RCS from the CMT for the smaller breaks, affecting the transient. Lack of other detailed models, such as a transient thermal conduction model and a detailed conder sation model, are not expected to have a significant effect on results.

O

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l-r i

r TABLE 1.101 FIGURES DEPICTING RESULTS FROM THE CORE MAKEUP TANK MODEL Figure No.' Title i

j 1.10-1 Stratified Layer Model of the AP600 Core Makeup Tank i

1.10-2 NOTRUMP Model of the AP600 Core Makeup Tank i

1.10-3 Fluid Temperature at Top of CMT during Recirculation: Layer Model vs. 4 ,10, and 20- Node NOTRUMP Model 1.10-4 Fluid Exit Temperature during Recirculation: Layer Model vs. 4 ,10, and 20- Node NOTRUMP Model l

1.10-5 CMT Fluid Energy during Recirculation: Layer Model vs. 4 ,10 , and ,

20- Node NOTRUMP Model 1.10-6 CMT Wall Energy during Recirculation: Layer Model vs. 4 ,10, and 20- Node NOTRUMP Model 1.10-7 CMT Flow Rate during Recirculation: Layer Model vs. 4 ,10, and 20- Node NOTRUMP Model l

November 1997 0:09Mwu9Mw-Ic.wpf:Ib-III297 1.10-5 Rev.3

1 Wall Heat Transfer Model:

I 7 .

i Wall Exposure j j Time: l Zh Vh,Th x

_ (Z h- Z .J ) / U he

g l \

\ -0 l U he " b l

1

! I l

l Vc ,Tc l

I 1

l l

l 1

I I

i l I i

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Wc , p c ,Tc v

Figure 1.10-1 Stratified Layer Model of the AP600 Core Makeup Tank Q

l a:u99wu99w.ic.wpr.:b-120397 3,j o.6 ev.3

I O Wu,pg,Tg Wall Heat Transfer Model:

y.

10 % T4 Tm l Volume 4 15%

Volume 3

-= -NOTRUMP

. . . . . ..... . . . . . ............. . ......... . . . . . . . ..... Volumes 15%

i Volume 2 n

U i

60 %

Volume 1 l

i t

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.t W c, p 3 ,T 3 Figure 1.10 2 NOTRUMP Model of the AP600 Core Makeup Tank November 1997

! o:0934wu934w.lc.wpf.lb-120397 1.10-7 Rev.3 l

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1.11 Passive Residual Heat Exchanger Model V 1 1.11.1 Behavior Observed from Tests i During a small-break LOCA, the PRHR removes some heat from the RCS. Typically, the amount is small relative to the energy removed by the break and the ADS. As the break size becomes smaller, l

however, the PRHR may have a more significant effect. Prior to significant voiding in the RCS, the primary (RCS) side of the PRHR is liquid solid, and the flow is driven mostly by the density difference between the hot fluid approaching t!'e PRHR and the colder fluid leaving the PRHR. The pressure difference between PRHR inlet (at the hot leg) and the outlet (at the steam generator outlet plenum) is small during most of the small-break transient because the pumps are tripped soon after the break. Consequently, the gravity-driven PRHR flow is relatively low. After the RCS voids, vapor flows in the primary side of the PRHR, and the overall volumetric flow rate may increase.

Single effects tests indicate that the physical picture in the IRWST can be qualitatively described as follows. Figure 1.11-1. Hot water initially at approximately 500*F flows in the primary side, and the IRWST water is at 90*F to 120*F. The large overall temperature difference causes boiling to occur on the secondary side, and a thermal plume surrounds the PRHR tubes. Single effects tests indicate that I

the secondary-side heat transfer follows a typical boiling curve, with natural convection heat transfer when the tube wall temperature is less than about 40*F superheated and nucleate boiling heat transfer l

at higher wall superheats. When a variety of nucleate boiling correlations are compared with the bA PRHR data (Reference 1-31), the heat flux for a given wall superheat is overpredicted by all the i models. 'Ihis is attributed to the action of the thermal plume suppressing the boiling process. I 1.11.2 NOTRUMP Model Description The NOTRUMP model of the PRHR and IRWST is illustrated in Figure 1.2-1. No attempt is made to model a thermal plume or stratification in the IRWST. This is considered acceptable for two reasons:

1) The NOTRUMP calculation is terminated at the beginning of IRWST injection, before thermal layers can play an important role in the process. Since there is no net flow in the IRWST prior to draining as occurs in the CMT, the propagation of higher temperatures from the upper cell to the lower cell is not a concern as it is in the CMT model.

2) The thermal plume is observed to affect the value of the heat flux, but not the basic boiling l process.

l m

Februart 1998 oM025wwo25w.id.wpf:Ib-022698 1,*l 1 -1 Kev.4

l l

T lieat transfer models used by NOTRUMP are:

Primary side:

a) Single-phase flow Dittus Boelter (Reference 1-32) b) Two-phase flow Shah (Reference 1-33)

Secondary side:

maximum of:

i natural convection using the McAdams correlation (Reference 1-34), or nucleate boiling using the Thom correlation (Reference 1-35)

On the primary side, the Dittus Boelter correlation is applied within its range, even though fluid velocities are relatively low (about I ft/sec.). The Shah correlation is used within its claimed range of l applicability.

On the secondary side, the Thom correlation is applied well outside its range of applicability since the correlation pressure range is 760 to 2000 psia. However, the Thom correlation, even when extrapolated, exhibits the same characteristics as other correlations that were examined in Reference 1-36, as shown in Figure 1.11-1. There is, therefore, no better correlation to use except one developed from the data. In addition, for the conditions expected during a small-break LOCA, the heat transfer on the secondary side is not expected to be limiting. This is illustrated in Figure 1.11-2, which shows the temperature drop from the primary fluid through the wall to the secondary side for various fluid velocities. Velocities of about I ft/sec. are typical of those occurring during the natural circulation period. Even when the secondary-side heat transfer coefficient is reduced by a factor of 10, the highest resistance under these conditions remains on the pnmary side (it has the largest temperature drop). This also indicates that the details of the secoridary-side heat transfer are not important for small-break LOCA. For higher primary fluid veloci:les, the heat flux across the PRHR tube rapidly increases (see Figure 1.11-3), and the discrepancy between predicted and actual heat transfer is likely to become larger.

1.11.3 Conclusions It is concluded that the NOTRUMP PRHR model contains a model deficiency that needs to be monitored to assure that excess PRHR heat transfer is not calculated.

oM025wWO25w-Id.wpf;1b-022698 Februart 1998 1,1]-2 Key,4

1.12 Critical Flow Model Critical flow occurs at the break and at the ADS valves when they open.

1.12.1 Critical Flow through Automatic Depressurization System Valves he geometry of the ADS valve package is relatively simple, consisting of gate valves and squib valves, both of which open quickly and present a single, sudden area change in the pipe. De ADS valves open while the system is two-phase, so the flow conditions are either single-phase vapor or a two-phase mixture. j A recent survey of critical flow data (Reference 1-37) compared several critical flow models to j available data. It was found that none of the simpler analytical models, such as the homogeneous equilibrium model (HEM), performed satisfactorily against all the data, while some of the more sophisticated space-dependent models performed somewhat better.

A more successful application might be expected, however, for a specific geometry such as the ADS I valves. Since conditions are expected to be two-phase, the HEM was chosen to calculate critical flow through the ADS valves. In Section 1.7, the effect of ignoring momentum flux terms was evaluated.

. It was determined that fluid velocities were low enough, such that these terms had a minor impact on

- the pressure gradient in all cases except for the ADS 4 piping, when both valves are open. In this case, comparison'with attemate calculations indicated that the predicted vapor flow was not significantly mispredicted. Section 5 compares the model to single-effects tests, and the resulting comparisons are shown to be acceptable.

1.12.2 Break Flow Model he critical flow through the break is subject to considerably more uncertainty due to the unknown geometry of the break. . It is expec*ed, however, that the HEM is reasonably applicable during the most significant portions of the transient when the conditions at the break are two-phase. Since the break area is ranged in the AP600 analysis using the Moody model as required by Appendix K, the most important issue is to ensure that the model predicts the integral test data reasonably well, so as

, not to introduce significant compensating error into the calculation.

1.12.3 Conclusion The critical flow model used is applicable and has been verified against tests that simulate the ADS valve geometry and the flow conditions upstream of the valves.

s February _1998 o:wo25.wo25w.id.wpub.o2269s 1.12-1 Rev.4

.___ _ ~ _ _ _ _ _ _ . _ . - _ _ _ _ . _ _ _ . _ _ _ _ . _ . _ _ . _ _ . . _

1 CODE AND ASSESSMENT OVERVIEW t

1.1 Introduction i

This repon documents the final validation of the NOTRUMP small-break loss-of-coolant accident (LOCA) computer code that is used for the calculation and assessment of the AP600 passive core cooling system (PXS). NOTRUMP has previously been approved by the United States Nuclear Regulatory Commission (U.S. NRC) for performing safety analysis calculations of the small-break LOCA transients for operating plants (Reference 1-1). The early portion of the AP600 small-break LOCA transient is similar to current operadng plant transients. However, with the inclusion of the automatic depressurization system (ADS), the reactor coolant system (RCS) is depressurized in a controlled manner to the containment pressure, resulting in the behavior being different from operating plants. The addition of the AP600-specific passive safety-related systems, which include the core '

makeup tanks (CMTs), ADS, accumulators, passive residual heat removal (PRHR) heat exchanger, and the in-containment refueling water storage tank (IRWST), and the application of NOTRUMP down to atmospheric pressure have required several model and coding enhancements to the original ;

NOTRUMP code.

The validation of the coding and model enhancements for NOTRUMP is contained in this report. This report is comprised of three volumes and a schematic of its organization can be found on Figure 1-1. ;

p A written description of the report sections is found below, b

Each of the model changes described in Section 2 has been verified and validated for use in AP600 plant analyses. Once the coding changes were developed, reviewed, and tested, one or more of three verification and validation methods were applied, including: 1) performance of simple benchmark test cases,2) simulation of separate effects tests, and 3) simulation of integral facility tests.

Section 3 describes the benchmark test cases that were performed. Simulation of separate effects tests is described in Sections 4,5, and 6 for each separate effects test facility, and the simulation of integral facility tests is described in Sections 7 and 8 for each integral facility.

During the extensive rem ,y the NRC, requests for additional information (RAls) were generated by the Staff. The RAls and Westinghouse responses are contained in Appendix A.

Because the documentation supporting NOTRUMP's application to AP600 spans several documents, a summary was also prepared to describe the key models and correlations, the physical basis for these models, and the conclusions drawn from the assessment studies performed in this report.

O February 1998 c:\4025wS40251.wpf.It422698 1,1-1 Kev. 4

The main objectives of this summary are to:

. Identify the key models required to simulate the important phenomena identified in the AP600 small-break LOCA phenomena identification and ranking table (PIRT) and describe their bases in summary form.

O l

l l

! O February 1998 ovo25wwa25-1.wpf:1bm2698 1.1-2 kev.4

O O O i O

i

b. ;

h .

i j !!!~ :!!

j Figure 1-1. XOTRUMP Report Organization ageJ;;

i i

W CAP-14807 !

NOTRUMP V&V Report i i I i i

[ Model Single integral Code RAls 4, improvements Effects Systems Assessment DSER Ols :

Validation Validation & Overview (Appendix A)

(Ch.1) l I I I I Description Level Swell (3 tests) OSU PIRT Relationship Responses (C h. 2) (Ch. 4) (Ch. 8) l I I I I Benchmarks CMT SPES 2 Areas of Good Agreement Road map i (Ch. 3) (Ch. 6) (Ch. 7) j l l ADS 0eficiencies (Ch. 5) 2 ___

I l '

Appendix K App!ication EE m :

s co

_ . _ _ _ _ _ ._-__ _ ________ _ ___ __ ________________ _____________ _ ___________\

l 1.16 Noding Selection '

\

he following paragraphs describe the basis for the noding utilized for AP600 analyses using NOTRUMP l The basic reactor coolant system (RCS) noding utilized is an evolution of the standard plant

! NOTRUMP Evaluation Model (EM). Specific noding was added for new passive safety system components, such as the passive residual heat removal (PRHR) heat exchanger, core makeup tanks (CMTs), in-containment refueling water storage tank (IRWST), and automatic depressurization systems (ADS). The noding bases for these individual components were generated by analysis of individual separate effect tests (SET) for each component. The noding for the individual components obtained from the SETS was then applied to the integral effects test (IET), i.e., SPES-2 and Oregon State University (OSU), and eventually the AP600 plant model itself.

The basic rule applied was to preserve the number of fluid volumes utilized in each main component utilized in the IET and SET facility simulations. The exceptions to this rule and these items will be

discussed next.

1,16,1 Deviations From Base Noding Rule The following section discusses the various deviations from the IETs and SETS and the basis for these l- decisions.

Reactor Vessel And Coolant Loops l

The noding utilized in the SPES-2 and OSU IETs consider atypicalities of the specific facilities versus ,

the full scale AP600 plant design. Differences in the SPES-2 facility will be discussed first, followed by the OSU test facility.

l-One SPES-2 difference is the region which models the hot leg to steam generator inlet piping. The SPES-2 facility is comprised of [ ]a.b different piping sizes in this region, and thus the SPES-2 NOTRUMP model contains [ ]' C separate fluid nodes to best represent this geometry difference.

Neither the OSU or full AP600 facilities have varying piping sizes in this region and do not require the additional noding detail.

i Another SPES-2 geometry difference is the region between the steam generator outlet plenum and the cold legs. The SPES-2 model is atypical of the AP600 design in that it utilizes a single traditional shaft seal reactor coolant pump (RCP) followed by piping which splits the flow to the two cold legs, whereas the AP600 design utilizes dual canned motor RCPs which feed the individual cold leg pipes.

Due to this physical difference, the SPES-2 model includes [ ]* C to represent

the RCP and inlet pipe region which is not required for either the OSU or AP600 facilities.

February 1998 oM025wWO25-116.wpf:lb-022698 1,16-1 Rev.4

. . - ~ . _ , , . .

Another SPES-2 specific area which requires different modeling is the downcomer region. The SPES 2 test facility consists of two distinct downcomer regions: an upper annular downcomer which represents the region from the upper head bypass connection (i.e. spray nozzles) to below the direct vessel injection (DVI) port elevation, and a lower tubular downcomer which connects the upper annular region to the lower plenum. To accurately reflect this configuration, [ ]* C fluid nodes were utilized for the SPES-2 NOTRUMP model with [ ]* C representing the annular region and [ ]* C representing the tubular region. Bob the OSU and full AP600 facilities are constrteed with a continuous annular downcomer region modeled as a [ ]*'C. The results of downcomer noding sensitivity studies on these two facilities will be discussed later.

Another region where the SPES-2 facility deviates from the OSU and AP600 NOTRUMP models is the power compensation and ambient heat loss modeling. Specific models were added to the SPES-2 NOTRUMP model to account for compensatory power addition which is included at the facility to offset the distonions related to ambient heat losses. Additional details regarding the facility features can be found in the SPES-2 Facility Description Repon (FDR), Reference 1.16-1; the metal nodes used in the SPES-2 NOTRUMP model are shown in Section 7.2 (Figum 7.2-3) of this report. Since the OSU facility is scaled differently, it is [ ]*

and power compensation modeling is [ ]* C. The OSU and AP600 models also [ ]*#

ambient heat losses due to the power and size of the facilities. Metal heat is considered in the [

]*# components only for OSU and AP600.

'Ihe OSU model deviates from the SPES-2 and AP600 NOTRUMP models in the core region.

The OSU model utilizes a [ ]**C core node representation, whereas the SPES-2 and AP600 models utilize [ ]* C core nodes. The basis for the core noding is the SET testing performed using the GE Blowdown, ACHILLES and G2 tests as documented in Sections 4.2 through 4.4 of this document.

The NOTRUMP simulations performed for these facilities suppons the use of [ la.c core nodes.

As such, with OSU being 1/4 height scaled, using [ ]* C core nodes meets the [ ]*# node requirement. Since both SPES-2 and the AP600 plant are full-height facilities, the [ ]* C core node requirement results in [ ]*# core nodes for each facility.

Direct Vessel Injection (DVI) Piping Different nodalization in the DVI line piping is utilized in the AP600 plant model due to physical hardware differences. The AP600 design was revised subsequent to the test programs, and an elevated loop piping section was introduced adjacent to the vessel in the DVI line arrangement to enhance plant maintenance capabilities. Neither the OSU or SPES-2 test facilities have this feature. As a result,

[' ]*'C were added to the AP600 model to model this physical layout.

PRHR Heat Exchanger The nodalization utilized for the PRHR heat exchanger region differs from facility to facility. Due to the scaling utilized for each of the facilities, the AP600 model represents a combination of the two test February _1998 o.WO25wW025-Il6.wpf;1b 022698 1.16-2 Rev.4

. _.m_ .....__m. _ __.. _ _ _ _ _ _. _._ _.._._..___ _ _..___

facilities which best represents the full-scale design (see Table 1.16-1). The SPES-2 facility PRHR is full-height (i.e. vertical noding) with an atypically short horizontal length. Only [

]** is utilized for the SPES-2 upper and lower PRHR heat exchanger regions, whereas (four

]*# are utilized to represent the vertical region. The OSU facility, on the other hand, utilizes

[ . ]*# horizontal nodes on the upper horizontal portion of the PRHR, with [ Ja# nodes on the vertical portion due to 1/4 height scaling. The OSU facility and AP600 plant model both utilize only

[ .]*# to represent the lower PRHR heat exchanger region consistent with the SPES-2 facility. Noding study results will be discussed later. '

. Table 1.16-1: PRHR Noding Comparison Segment SPES-2 OSU AP600 l Inlet Horizontal - -

Vertical Outlet Horizontal l

ADS Piping Downcomer Of Stage 1,2,3 Valves

- The specific noding utilized downstream of the ADS stage 1-3 valves depends on the facility involved.

I ne test facilities are equipped with break separators with which the ADS flow discharge can be measured. Detailed noding of the separators is [. ']*# with the NOTRUMP models of the IETs. The AP600 model of the ADS 1-3 piping is validated by simulating Phase B ADS tests l performed at the VAPORE facility (Reference 1.16-2) and documented in Section 5 of this report.

The VAPORE facility is a full-scale representation of the AP600 ADS stage 1-3 configuration. The

! noding utilized during the simulations of these (VAPORE) tests forms the basis for the full scale AP600 NOTRUMP model.

Sensitivity Studies Performed To address the effect of varying nodalization on specific regions of the IET, SET, and AP600 facil-ities, sensitivity studies were performed. The specific sensitivity studies performed were as follows:

Core Noding Sensitivity Studies: Two Phase Level Swell

! Sensitivity studies were performed for the GE small vessel blowdown SET tests by varying the number of core nodes utilized in the NOTRUMP simulation from [ ]*# nodes. A

summary of the results can be found in Section 4.2.5 of the Final Validation Report (FVR). De simulations indicate that the [ ]*# node core model (i.e., [ ]*# core nodes) results in a significant February 1998 c: wo25wwo25116.wpf:1b-022698 1.16-3 Rev.4

improvement in mixture level behavior compared with the [ ']* C core node model. However, subsequent increases in core noding to [ ]a.c nodes respectively resulted in only minor improvements in mixture level performance.

Core noding sensitivity studies were also performed with the NOTRUMP model of the ACHILLES SET test. Analogous noding variations were performed with this model as with the GE SET tests.

Noding studies utilizing [ ]*** nodes, were examined with this model. The results of these simulations are discussed in Section 4.3.4 of this repon. The results support the [ ]*'C node height, as observed in the GE SET noding studies, as providing sufficient detail to result in a conservative prediction of average level swell.

PRHR Noding Sensitivity Studies:

The results of the calculations presented in the NOTRUMP Preliminary Validation Reports (References 1.16-3 and 1.16-4) for various break sizes for both the SPES and OSU test facilities showed underprediction of the PRHR heat transfer and a corresponding overprediction of the PRHR outlet temperature. To understand the differences between the test and NOTRUMP simulations, PRHR nodalization studies were conducted using the SPES-2 PRHR model.

The SPES-2 PRHR model is extracted from the full SPES-2 IET test facility NOTRUMP deck. This model was driven, using available test boundary conditions, in a stand-alone fashion, with variations in both horizontal and vertical section noding, as well as the introduction of an influer.ce zone model.

The influence zone model includes more detailed nodalization of the PRHR secondary side (i.e.,

IRWST tank side) which accounts for recirculation flow effects resulting from buoyancy effects within the IRWST. The detailed results of this study are reported in the response to RAI.440.339, which is 1

included in Appendix A of this report. The conclusions reached by this study are that the SPES-2 model is relatively insensitive to the number of inlet horizontal section PRHR nodes. Additional noding in the vertical ponion of both the primary and secondary side of the PRHR did not significantly improve the PRHR heat transfer prediction. It was concluded that the main reason the PRHR heat transfer is underpredicted is the underprediction of the PRHR primary flow rate, and that additional noding on the PRHR secondary side is not required.

In addition to the SPES-2 sensitivity study, a study was also performed with the full AP600 Safety Analysis Report (SAR) model which varied the number of vertical PRHR nodes from the base model of [. ]***. This was done to demonstrate the effect of utilizing the OSU facility NOTRUMP PRHR noding in its entirety, as opposed to the hybrid of the SPES-2 and OSU IET PRHR nodings.

Select transient plots for a 0.5-inch cold leg break simulation can be found in Figures 1.16-1 through 1.16-11. The results indicate that for the first 4000 seconds of the simulation, the transient results are vinually indistinguishable. Following this time point, however, deviations begin to appear between the

[ ja.c PRHR simulations. The most notable difference is in the behavior of the CMT !

draining and RCS inventory. With the PRHR performance being slightly degraded with the [

]* C vertical PRHR model, system saturation and draining stans sooner. As a result, the CMTs February 1998 oM025w\4025116.wpf.lb-022698 1.16-4 Mcv. 4

___ _._ - _. __ . ~_. .. _ . _ .____ _. _ ._ _ __ _ _ _ _ _ . _ _ _

l !

L begin draining earlier with the [. ]alc PRHR model, resulting in higher system inventory when

]

. (/ compared to the base [ ] *'C PRHR simulation. Although CMT draining begins earlier, the l drain rate is reduced relative to the base case, due to the PRHR degradation, such that the [

]*# PRHR model results in delayed ADS actuation. In terms cf margin-to-core uncovery, no significant differences are observed between the [ ]* C and[ ]*'C PRHR model results that are not directly attributable to the changes in ADS-1 actuation timing. De minimum system J

inventory values (Figure 1.16-8) are virtually identical.

CMT Noding Sensitivity Studies:

Sensitivity studies were performed to assess the impact of varying the CMT noding from a [ ]* C L

node model, as developed during the CMT SETS, to a [ ]*** node CMT model based on the OSU IET L NOTRUMP model. The transient event analyzed was the 0.5-inch cold leg break (Test SB23), due to l' the sensitivity of this model to CMT thermal stratification / mixing effects. The detailed response to this sensitivity study can be found in the response to RAI.440.339, located in Appendix A of this report.

The results indicated that the temperature increase in the bottom CMT node was delayed significantly relative to the base [' ]C node model (200 seconds base vs. 800 seconds [. -]C model).

However, the NOTRUMP model still predicts the bottom CMT node temperature increase to begin A carlier than observed in the test (800 seconds [. ]* C model vs. [ ]a b test). The V application of the [ ]*# CMT model eliminated the need to artificially adjust the base OSU NOTRUMP model for test SB23 in order to achieve reasonable ADS actuation times. It was concluded, however, that the continued use of the [ ]a# CMT model is conservative for AP600 analyses, since it leads to higher predicted core void fractions and delayed ADS actuation

- times.

Downcomer Noding Sensitivity Studies:

i Downcomer noding sensitivity studies were performed with both the OSU IET and full AP600 NOTRUMP models. For the OSU facility, the downcomer model was broken down into [ ]*#

discrete fluid nodes. 'Ihis noding was utilized in an attempt to further ref'me the NOTRUMP response to the double-ended direct vessel injection (DEDVI) line break (Test SB12) during the 130-250 second !

time frame. De DEDVI break was also selected since it represents a class of breaks that would be impacted by varying downcomer nodalization due to the location of the break and the expected

. phenomena. Breaks at locations away from the downcomer, such as small cold leg breaks, would not l be expected to be as impacted by downcomer nodalization. The DEDVI results indicate that

. increasing the downcomer noding from [- ]* C nodes had only a minor impact on th'e transient behavior. Figures 1.16-12 through 1.16-17 present a select set of plots demonstrating the impact. As a result of the sensitivity run, it was concluded that increasing the downcomer modeling detail does not O

Q significantly impact the transient and therefore downcomer nodalization is unimportant for OSU.

February 1998

. oM025wwo25116.wpf.1b-022698 1.16-5 Rev.4

For the AP600 plant model, sensitivity studies were performed utilizing [. Ja.C downcomer nodes per SPES-2 and OSU simulations, respectively. The studies were performed for the DEDVI and 2-inch cold leg breaks to determine the effect of the downcomer noding differences. The DEDVI results indicate that the [ .]a.c model, apportioned in the same manner as in the SPES-2 simulation, results in a more limiting transient response than either the [ ]a.c downcomer models. Figures 1.16-18 through 1.16-24 present transient plots for these simulations.

While very little difference is observed in the RCS pressure response, substantial changes are observed in the core and downcomer mixture level responses.

The [. ]a.c downcomer cases alter the downcomer void / drain behavior which result in core and downcomer mixture level depressions that are not observed in the base case ([ ]" C downcomer) simulation (Figures 1.16-20 and 1.16-21). These changes in mixture level behavior result in differences in ADS 1-3 and break flow behavior, respectively. The [ ]*

downcomer cases also result in a shift in the minimum system inven;ory time from the IRWST injection time to early in the blowdown period. The [ ]a.c results closely resemble the [ ]'* results, but are slightly less limiting in terms of core mixture level response; the differences are rather small.

Note, that the NOTRUMP code is known to lack multi-dimensional downcomer modeling capability, which may impact the phenomena predicted for the DEDVI line break.

The AP600 2-inch cold leg break results indicate no significant differences in transient response are obtained by increasing the downcomer noding from the base SAR [ ]8* model to a [

]* C model. Figures 1.16-25 through 1.16-28 present a few select transient plots for this simulation that support this statement. No [. ]* C model simulations were performed for this break size because of the agreement shown. Based on these results, the [ ]a.c downcomer is judged to be the most conservative nodalization for AP600 plant calculations of the DEDVI line break.

It should be noted, however, that core uncovery does not occur for this break even with the increased mass loss.

References 1.16-1. SPES-2 Facility Description, WCAP-14073, Revision 0 (May 1994).

1.16-2 Miselis, V. V., A. J. Brockie and J. S. Mitkiewicz, Facility Description Report AP600 Automatic Depressurization System Phase B1 Test, WCAP-14303 (Proprietary) (March 1995).

1.16-3 Meyer P. E., et. al., NOTRUkiP Preliminary Validation Reportfor SPES-2 Tests, PXS- GSR-002, Westinghouse Electric Corporation (July 1995) 1.16-4 Willis, M. G., et. al., NOTRUbfP Preliminary Validations Report for OSU Tests, LTCT- GSR-001, Westinghouse Electric Corporation (July 1995)

O omwmiis.wpr.ii>o22698 1.16-6 v

O V

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AP600 0.5 inch Cold Leg Break in FN 49 P r e p,s u r i z e r Mixture Level Vert. PRHR Vert. PRHR -

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February 1998 ,

oM025wWO25-116.wpf:1b-022698 1,16 7 Rey,4 1 I

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Figure 1.16 AP600. CMT-1 Mixture Level Comparison February 1998 o:%025wu025-il6.wptib-022698 1.16 8 Rev.4

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February 1998 eM025wV.025-116.wpf:lt422698 ],]612 Rev.4

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I February 1998 oMo25wwo25-116 wpf.lb-022698 1,16-15 Rev.4 l

O AP600 DEDVI Line Break Noding Sensitivities

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1 1

O I AP600 DEDVI Line Break Noding Sensitivities Two phase Downcomer Level Downcomer

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l February 1998 oM025ww025116.wpf:1b-022698 1.16-17 Rev.4 l

AP600 DEDVI Line Break Noding Sensitivities

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a 0 1000 2000 3000 4000 Time (s) ngure us-23 Ar600 intesrazed Aos-s now comparison q

AP600 DEDVI Line Break Noding Sensitivities hltegrated Break Flow Downcomer

Downcomer Oowncomer M.

? ,---- . - - - . - - - -

E 3 __.<---------- --------------

20 @ 0 5 i C 150000 m -

E :

g100000 e-0 * >

0 1000 2000 3000 4000 Ilme (S)

Figure 1.16-24. Ar600, Integrated Vessel Side Break Flow Comparison O

February 1998 o:\4025w\4025-116.wptIb 022698 1,16-18 Rev.4

n v

AP600 DEDVI Line Break Noding Sensitivities

_ _,., System Inventory Downcomer Downcomer Oowncomer 3y ,

~

3000r/a l

E

$ 250000 .

n :

g 200000

{

e :

e 150000 R j _ _ _ _ _ _ _

100000 ,g

j b

2 00 u 1000 2000 3000 4000 i

Time (s) l Figure 1.16 AP600, Primary System inventory Comparison O AP600 2 Inch CL Break In FN-49 DC-Noding Sensitivity Pressurizer Pressure Pressure (pslo)

Bose 2

[ ]Q49Downcomer 2in49 2500

, 30 2000 - 25 m

n 8 -

- 20 8 3 1500 3

~

V o_ .

10hm

-5 0 0 0 1000 2000 3000 4000 Time (s)

Figure 1.16 AP600. Pressurizer Pressure Comparison

\

February 1998 eM025wuo25-116.wpf:1b-022698 1.16-19 Rev.4

l l

l 1

AP600 2 Inch CL Break In FN-49 DC-Noding Sensitivity '

Two Phase Core / Upper Plenum Level Base 2 g49

' ----[ ]i'D o w n c om

- - - - - -- T o p 0f Activs Fue1 2in49 er 28 26 --

_ _ y t _-

5 : r"( N 7 '7 g i % 24 _

2 -

~

$ 22

.? :

= _

20 - -

1_______________ _______________________________________________.

18 ' '

O 1000 2000 3000 4000 Time (s)

Figure 1.16-27. AP600. Core / Upper Plenum Mixture Level Comparison APdOO 2 Inch CL Break In FN-49 DC-Noding Sensitivity Two Phase Downcomer Level Bo:e 2 g49

[ ][,D o w ri c om2in49 er

DVI Port Bottom Elevotion

-- O V i Port Top Elevation 32

^ 28 \ l

^

26 '

24

! I I" JWI 18 MI ,,

r-16 0 1000 2000 30'00 4000 Time (s)

Figure 1.16 28. AP600, Downcomer Mixture Level Comparison g

February 1998 oM025wwn5116.wpf.lW696 1.16-20 Rev.4

O .

AP600 2 Inch CL Break In FN-49 DC-Noding Sensitivity System Inventory Bose 2

[ ]Q49 Oowncomer 2in49 350000 300000 e :

e. :

m 250000 0 2 2 :

E 200000 150000 W

.* 100000 ~ '

u 1000 2000 3000 4000 Time (S)

Figure 1.16 29. AP600, Primary System inventory Comparison O

February 1998 oM025wwo25-116 wpf.Ib-022698 1.16-21 Rev.4

- -- -. - -- - . -~ .. - -

{

1.17 Key Features of the AP600 Analysis Methodology l

I O

De application of NOTRUMP as an Appendix K evaluation model to the AP600 must take into account the findings from the assessment described in this report. First, the following conservative features required by Appendix K are applied:

a) Appendix K requirements ANS 71 + 20 percent core decay heat Application of this model increases the core power by nearly 25 percent compared with the more recent 1979 ANS standard for decay heat, during the time period of most interest near the point of ADS-4 actuation. Since the mass inventory and system pressure is in large part determined by the steam generation rate, application of this model leads to significant conservatism.

Moody critical flow model at the break and break spectrum Application of the Moody model results in overprediction of the break flow by about 20 percent relative to data. The integral effects tests confirm that larger breaks tend to reduce p system mass to a greater extent than smaller breaks. This model therefore is also considered V to include additional conservatism, when combined with the required analysis of a spectrum of breaks.

b) Additional Conservatisms to Account for Plant Geometry Uncertainties he resistances in the DV1, IRWST, CMT, and accumulator lines are set at design upper bound values to reduce the flow rate from the passive components into the RCS. In addition, the minimum effective critical flow area is used in the ADS critical flow calculation, and maximum resistances are used in the ADS flow paths.

Minimum containment pressure (14.7 psia) is assumed.

c) Additional Confirmatory Checks and Assumptions to Account for Model Deficiencies

- The flow velocity through the PRHR primary will be confirmed to be less than 1.5 ft/sec in all AP600 simulations. In addition, the PRHR is removed from the model after ADS 1-3 actuation to further reduce the depressurization rate.

If the flow through the PRHR is higher than 1.5 ftisec. for any significant period of time, the i

Q D

calculation for the limiting case (minimum mass or highest PCT) is repeated with the PRHR heat transfer surface area reduced by 50 percent to account for the potential overprediction of heat transfer.

February 1998 c:\4025wu025w-Id.wpf:lb-022698 1,17 1 Rev.4

The IRWST flow will be delayed to account for potential nonconservatism in the prediction of system !

I pressure after ADS-4 actuation. This will be accomplished by reducing the IRWST level by 6 feet. 1 The basis for this value is described in the response to RAI 440.721(g).

In summary, the differences between predicted and actual integral test results can be attributed to one or more of the identified model deficiencies discussed in this report. Table 1.17-1 summarizes the highly ranked component phenomena from the PIRT (Table 1.3-1) and the results of the assessment in terms of the criteria established in Section 1.5. For those areas where the agreement was found to be minimal, specific steps have been taken to address the deficiency in the AP600 analysis.

O i

Ol 1

l February 1998 c:uo25wwo25w.id.wpr:ib-o2269s 1.17-2 Rev.4 l l

i N

T \

_u.{)

O

~

-I N

i TABLE 1.17-1 k ASSESSMENT

SUMMARY

i y Component Phenomenon Assessment Results 'AP600 Modeling Approach Comments W' ADS 1-3: '

Critical flow Reasonable Mini num critical flow areas used. Poor agreement in OSU tests 4~

due to pressurizer refill.. I Two Phase Pressure drop Reasonable No additional conservatism ADSI-3 in critical flow most of i required. the time.

l Valve loss coefficients Reasonable Upper bound loss coefficients - ,

used. ;

ADS 4: i i

. C Critical flow Reasonable Minimum critical flow areas used.

?

Two phase pressure drop Minimal Delay IRWST drain. Possible reason for poor '

prediction of ADSI-3 flow, !

pressurizer liquid holdup in OSU tests. l BRFAK: -

Critical flow Reasonable Break size, lor:'on is ranged.

i ACCUMULATORS: i Injection flow Excellent Upper bound loss coefficients. .

COLD LEGS: !

m Er Phase separation at tees Reasonable No additional conservatism Predicted excess entrainment 2

required. delays CMT drain, ADS.

J -

==

't

n a TABLE I.17-1 h ASSESSMENT SUh8'ARY (Cont.)

h Component Phenomenon Assessment Results AP600 Modeling Approach Comments 8

2 VFSSEllCORF; Decay heat N/A 1971 +20% ANS used.

S Natural circulation flow Reasonable No additional conservatism required.

Mixture level Reasonable No additional conservatism required. Mixture level underpredicted by Yeh correlation.

CMT:

Circulation Excellent No additional conservatism required.

Thermal StratiGcation Minimal Conservative Lack of model increases CMT exit

[ temperature, reduces core inlet a subcooling.

A Draining Reasonable No additional conservatism required.

DOWNCOMER:

Level . Reasonable No additional conservatism required. In cases where agreement is minimal, increased downcomer level delays CMT diain.

IIOT LEGS:

Stratification, phase separation at Minimal Delay IRWST drain. StratiGed model may overpredict tees vapor out ADS 4, reduce pressurizer CCFL.

I a

2 a

is e O O

'\

i

i i '

1

[

0!

TABLE 1.17-1 i ASSESSMENT

SUMMARY

(Cont.)

E Conoponent Phenomenon Assessenent AP600 Modeling Approach Conintents E, Resnits '

~

IRWST:

{

$ Gravity draining Reasonable Use upper bound line resistance.

PRESSURIZER AND SURGE LINE:

l CCFL Minimal No additional conservatism required. Poor agreement in PRZR drain due to low vapor [

now through surge line.

Entrainment Reasonable No additional conservatism required. l Level Swell Minimal Delay IRWST drain. Poor agreement is due to excess vapor content

! predicted in vessel. :

[ STEAM GENERATOR: :

r w 1

& Natural circulation Reasonable No additional conservatism required.

t l Heat transfer Minimal No additional conservatism required. Poor agreement in some tests due to t

underprediction in PRHR heat transfer, excess energy from CMT.

Tube draining Reasonable No additional conservatism required. l 1

PRilR:- L Heat transfer Minimal Check primary flow, reduce surface area if Heat transfer not overpredicted as long as primary necessary. side is limiting.- [

Recirculation flow Minimal during No additional conservatism required. Under predicted flow reduces PRIIR heat transfer.

two phase flow.

UPPER HEAD / UPPER PLENUM: '

m 6 8- Mixture level Reasonable No additional conservatism required.

2 !

2-4

== ,

t I

l l

1.18 Limits of Applicability Ba:,ed upon the NRC review of NOTRUMP (Reference 1-38), the following application restrictions apply for small-break LOCA analyses:

1. The transition boiling correlation, as used in the fuel rod heat transfer model, remains unchanged from the NRC approved 1985 Evaluatier Model NOTRUMP. Should

{

l Westinghouse change the fuel rod heat transfer transition boiling model, the NRC should be l

l requested to review the modification.

l 2. 'Ihe NRC noted that NOTRUMP cannot calculate the effects of noncondensible gases injected into the primary coolant system during the AP600 SBLOCA. The presence of noncondensible gases is a concern due to the possible degradation in performance of the PRHR HX.

However, the noncondensible gases generally enter the PRHR late in the transient, when the PRHR HX is no longer playing a significant role in heat removal. Thus, the noncondensible gases do not have a significant effect on the course of the event. The NRC staff accepted the NOTRUMP code for evaluation of the AP600 SBLOCA in spite of this shortcoming.

However, if scenarios are found which cause noncondensible gases to reach the PRHR HX while it actively removes heat from the primary system, the NRC should be informed and requested to re-evaluate this deficiency. j

(

3. The COSI condensation model (Reference 1-39) submitted for review to the NRC for operating plants, is neither applicable nor acceptable for evaluation of the AP600 SBLOCA.

O

__,.__s ,.,,., ee % n

1 1

1.19 References

v) 'l-1 1

i Meyer, P. E., et. al., "NOTRUMP - A Nodal Transient Small-Break and General Network Code," WCAP 10079 P-A, Proprietary, WCAP 10080-A, Non-proprietary (August 1985).

I 1-2 Kemper, R. M., Applicability of the NOTRUMP Computer Code to the AP600 SSAR Small Break LOCA Analyses, WCAP-14206, Westinghouse Proprietary Class 2, WCAP-14207,

. Westinghouse Proprietary Class 3 (November 1994).

i l

1-3 Lahey, R. T., "On the Various Forms of the Conservation Equations in Two-Phase Flow,"

listernational Journal of Multiphase Flow, Vol 2 (1976). l 1-4 Zuber, N., and J. A. Findlay, " Average Volumetric Concentration in Two-Phase Flow Systems," Trans. ASME Journal of Heat Transfer, Ser. C, Vol 87, p. 453 (November 1%5).

1-5 Sudo. Y.,

Estimation of Average Void Fraction in Vertical Two-Phase Flow Channel under Low Liquid Velocity," Journal of Nuclear Science and Technology,17(1), p.1-15 (January 1980).

i 1-6 Cunningham, J. P., and H. C. Yeh, " Experiments and Void Correlation for PWR Small-Break p

J LOCA Conditions," Trans. ANS,17, p. 369 (1973).

1-7 Chexal, B., and G. Lellouche, A Full-Range Drift Flux Correlationfor Venical Flows (Revision 1), EPRI report NP-3989-SR (1986).

18 Ishii, M., "One-Dimensional Drift Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes," Argonne National Laboratory, ANL-77-47 (October 1977).

1-9 Wallis, G. B., One-Dimensional Two-Phase Flow, McGraw Hill (1%9).

1-10 Bankoff, S. G., Lee, S. C., "A Critical Review of the Flooding Literature," NUREG/CR-3060 (1983).

1-11 Bankoff, S. G., " Countercurrent Air / Water and Steam / Water Flow above a Perforated Plate,"

NUREG/CR-1808 (1980).

12 Takeuchi, K., and M. Young, " Generalized Crift Flux Correlation For Vertical Flow," Nuclear Science and Engineering,112, p.170-180 (1992).

O l'13 Pushkina, O. L., and Y. L. Sorokin, " Breakdown of Liquid Film Motion in Vertical Tubes,"

Heat Transfer-Soviet Research, Vol.1, no. 5 (September 1%9).

February 1998 eM025=W125w.1d.wpf;1M122698 1.19 1 Rev.4

l l

l-14 Ohkawa, K., and R. T. Lahey, "The Analysis of CCFL Using Drift Flux Models," Nuclear I

Engineering and Design 61, p. 245-255 (1980).

l-15 Thom, J. R., " Prediction of Pressure Drop During Forced Circulation Boiling of Water,"

International Journal of Heat and Mass Transfer, Vol 7, p. 709-724 (1964).

1-16 Bankoff, S. G., "A Variable Density Single-Fluid Model for Two-Phase Flow With Particular Reference to Steam-Water Flow," Trans. ASME Journal of Heat Transfer, ser C, Vol 82, p.

265 (1960).

1-17 Dobson, J. E., and G. B. Wallis, "The Onset of Slugging in Horizontal Stratified Air-Water Flow," International Journal of Multiphase Flow, Vol.1, p.173-193 (1973).

1-18 Dukler, A. E., and Y. Taitel, "A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow," A/ChE Journal, Vol 22, No 1 (1976).

1-19 Bajorek, S. M., et al, Westinghouse Code Quahfication Documentfor Best Estimate Ixss of Coolant Accident Analysis, WCAP 12945-P, Volume 3, Section 15-1-4-1 (1995).

1-20 "NOTRUMP Final Validation Report for AP600," WCAP 14807, Revision 2,1997 1-21 Wallis, G. B., One Dimensional Two Phase Flow. McGraww-Hill,1969 l-22 Collier, J. G., Thome, J. R., Convective Boiline and Condensation, Third Ed., Clarendon Press, 1994 1-23 " Flow of Fluids Through Valves, Fittings, and Pipe," Technical Paper No. 410, CRANE Co.,

1973 1-24 Dukler, A. E., et al, "Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes," AIChE Journal, Vol 26, No 3, p. 345-354 (1980).

1-25 Grolman, Eric, et. al, " Wavy-to-Slug Flow Transition in Slightly Inclined Gas-Liquid Pipe Flow," AIChE Journal, Vol. 42, No. 4, (April 1996).

1 26 Ishii, M., and I. Kataoka, " Mechanistic Modeling and Correlations for Pool Entrainment Phenomenon," NUREG/CR-3304 (1983).

1-27 Schrock, V. E., et al, "Small-Break Critical Discharge-The Roles of Vapor and Liquid Entrainment in a Stratified Two-Phase Region Upstream of the Break," NUREG/CR-4761 (1986).

Februan 1998 ovo25wwo25..id.wpt:itw2269s 1,19-2 key. 4

fm 1-28 Mudde, R. F., et. al., "Two-Phase Flow Redistribution Phenomena in a Large T-Junction,"

\ International Journal of Multiphase Flow, Vol 19, No. 4 (l993).

1 29 Chisholm, D., " Flow of Incompressible Two-Phase Mixtures Through Sharp-Edged Orifices,"

Journal of Mechanical Engineering Sci., 9(1), 72-78 (l967).

1-30 Cunningham, J. P., et al., AP600 Core Makeup Tank Test Analysis, WCAP-14215 (December 1994).

1-31 Hochreiter, L. E., F. E. Peters, and D. L. Paulson, AP600 Passive Residual Heat Removal Heat Exchanger Test Final Report, WCAP-12980, Revision 3 (April 1997).

1-32 Dittus, F. W., and L. M. K. Bolter, University of California Berkeley Publ. Eng. Vol. 2, p. 433 (1930).

1-33 Shah, M. M., "A General Correlation for Heat Transfer during Film Condensation inside Pipes," International Journal of Heat Transfer, Volume 22 (l979).

1-34 McAdams, W. H., Heat Transmission, McGraw-Hill Publishers, p. 172 (1954).

p 1-35 Thom, J. R. S., et al, Boiling in Sub-cooled Water during Flow up Heated Tubes or Annuli,"

Q) Proceedings of the Institute of Mechanical Engineers,180, p. 226-246, London (1965-66).

1-36 Hochreiter, L. E., et al., Passive Residual Heat Removal Heat Exchanger Test Final Report, WCAP-12980, Revision 2 (September 1996).

1 37 Elias, E., and G. S. Lellouche, "Two-Phase Critical Flow," International Journal of Multiphase Flow, Vol. 20, Suppl., p.91-168 (1994).

1-38 NRC letter to Westinghouse, "Open Items Associated with the AP600 Safety Evaluation Report (SER) on the Applicability of NOTRUMP for Analysis of AP600 Small Break Loss-of-Coolant Accidents (SBLOCA)," December,1997.

1-39 Thompson, C. M., et. al., Addendum to the Westinghouse Small Break ECCS Evaluation Model Using the NOTRUMP Code: Safety injection into the Broken Loop and COSI Condensation Model, WCAP-10054-P-A. Addendum 2, Revision 1, July,1997.

r3 N.

ow5.wnsw.id.wpt:id-<n269s February 1998 1,19-3 Rev.4

- - _ - - . _ . - - ~ ~ - . - - . . . . - . - - - - _ . . - - - - - - _ - _ . . - . . _ _ .

l.

NOTRUMP model for ADS pioine and critical flow Figure 1.7-7 illustrates the noding used to model the ADS piping and valves in AP600. The piping from the hot leg or pressurizer to the valve is simulated with a fluid node. A portion of the overall line resistance is allocated to the flow link connected to the pressurizer or hot leg. The local static pressure and enthalpy in the ADS piping node, Po and h o, are used in the Henry-Fauske and HEM i critical flow models to calculate the critical mass velocity (Section 2.17 Reference 1-20). With this L modeling, the frictional pressure drop in the piping leading to the ADS valve is accounted for. ne l

HEM model is applied over the short remaining distance to the valve, where the effect of friction can be ignored. However, the NOTRUMP model contains two deficiencies:

a) ne model does not account for acceleration effects in calculating the pressure distribution up

~

to the ADS valve (previous sections).

_ I b) ne model does not account for the effect of significant upstream kinetic energy on the critical flow calculation.

As indicated in the previous section, lack of momentum flux terms in the momentum equation may result in an underprediction of the pressure drop to the ADS valves. In the next section, the effect of ignoring the kinetic energy terms in the calculation of critical flow is examined.

The HEM critical flow model assumes frictionless adiabatic, steady flow and begins with the following simplified mass, energy and momentum conservation equations:

dW = 0 2

.d h+"_ =0 s 2, dP + pudu = 0 1.7-72 r ,

2 dP u d +- =0 p 2, where h is the fluid enthalpy. Because the flow is asumed frictionless and adiabatic, the flow is isentropic. nerefore, either the momentum equation or the energy equation can be replaced by:

O ds = 0 i' Q February 1998 c:w125wwx25w-la.wpf:Ib-022698 1.7-23 Rev.4

-. -m~ _ . .._. . .. - ___. _,_ . _

In the HEM, the energy and entropy equations are used. The differentials are expanded to give:

2 2 u, uo 1.7-73 h, + =h o+7 s, = so where the subscript t represents the conditions at the throat, and the subscript 0 represents conditions at the lcration where the acceleration to the throat is assumed to begin. Usually this is taken as a location where the kinetic energy is negligible (uo is small). Given the stagnation enthalpy and entropy, the stagnation pressure and the conditions at the throat leading to the maximum mass velocity can be determined. In NOTRUMP, the Henry-Fauske and HEM models consist of a series of tables giving critical mass flux as a function of stagnation enthalpy, and stagnation pressure.

In the modeling of the ADS, the effect of a significant kinetic energy component at the start of the process must be examined. To determine what the appropriate stagnation pressure should be, retain the second form of the momentum equation, and expand the differential to yield:

2 2 P, dP u, -u o ,g 1.7-74 p 7 P.

Assume that an average density can be defined such that:

P, dP , P, - P0 1.7-75 P, p G R en:

i -2 -2 l

p . P"t 2 g P"O 2

1.7-76 l Dis indicates that the " reservoir" pressure should include the recoverable portion of the fluid dynamic pressure at the point where acceleration is to begin.

l O

Februarv 1998 oM025wWO25w.la.wpf.lb-022698 1.7-24 hev. 4 l

l

.__ . _.- _ _ _ _ _ _ _ . _ _ _ _ _ _ _ - - -_.m. . _ . _ _ _ . . . . _ __m . _ _

l he momentum equation can be written:

O

~ , ,

d j$+

,p

=-1 $ dz (1.7.72a) 2, p dz ,f where the term on the right-hand side represents the pressure loss due to friction. This can be approximated as:

e , , I d P + Y" 2,

=$ dz

, dz,g Assuming that a location can be found where the dynamic pressure is negligible (location where P =

Poo), then

.- 2 p0 . P "o ,p _ dP g (1.7-72b) 00 2 "d"z", ,

ub

~ De NOTRUMP procedure is to calculate the tqui pressure just upstream of the valve (P, + 2.P__

- u,)

2 from the hot leg or pressurizer (Poo, where dynamic pressure is negligible), then solve for the critical flow using the total pressure as the reservoir pressure.

Because of the energies and pressures involved, a significant velocity must exist at point 0 before significant error is introduced. For example, at 50 psia the enthalpy of steam is 1174 Btu /lb. For a 1

_ percent increase in the total enthalpy, the fluid velocity must be about 770 ft/s. This would indicate that ignoring the kinetic energy terms, as is done in NOTRUMP, would result in negligible error.

-To confirm this, an altemate flow calculation was performed on the ADS 4 piping system to compare witn the NOTRUMP prediction (as noted previously, the effects of compressibility were determined to j b6 most important for this component). For steam flow in a piping system, the effects of compressibility can be taken into account by the use of net expansion factors Y (Reference 1-23.

Dese factors are functions of the pressure difference through the pipe, and the loss coefficient in the

, pipe (Figure 1.7-8). De flow rate through the pipe is calculated by the following equation (Equation 1-11, Reference 1-23:

.bA) i l February 1998 eM025wWn5w.la.wpf:IbO22698 1.7-25 Rev.4

2 (Pgt - P,) p,at. 1.7-77 Wgo4 = 0.525Yd whe e d is the pipe diameter in inches. The calculated flow rate through both valves assuming compressible conditions is compared with the incompressible result (Y=1) in Figure 1.7-9. To compare with the NOTRUMP AP600 predictions, vapor flow is plotted against hot leg pressure for the ADS 4 pipe in Figure 1.7-10. The NOTRUMP values are seen to remain below the calculated value assuming compressible conditions.

1 A model of the ADS 4 piping from the hot leg to the valves was developed. 'Ihis model included integration of the complete momentum and energy equations (assuming steady-state, homogeneous j conditions). The NOTRUMP predictions were compared to this model (see response to RAI l 440.796F, part (a)). NOTRUMP predicts similar flows through ADS 4 when the hot leg pressure is high enough to result in choked conditions at the valve. At lower pressures, the flow rate predicted by NOTRUMP was about 20 percent higher. This was attributed to underprediction of two-phase i

pressure drop in some fittings, such as elbows, and lack of acceleration terms, which is still relatively important. In terms of the total vapor released from the time of ADS 4 opening to IRWST injection, l the effect was relatively small (about 5 percent).

I

Conclusion:

l It is concluded that NOTRUMP has compensating errors in regions where the fluid acceleration is significant. These errors become significant only in the ADS 4 piping where both valves are open.

The overall effect, however, is to produce a reasonable estimate of the vapor flow through ADS 4 l when compared with more detailed models.

l l

i l

l l

9 Febmary 1998 omwwo25..itwpr:ite.2698 1.7 26 Rev.4

i l c t

2.0 MODEL IMPROVEMENTS 2.1 Introduction Early simulations of the AP600 integral test facilities demonstrated the need to modify the NOTRUMP

]

code to correctly capture phenomena exhibited in the low-pressure regimes typical in AP600 small-break loss-of-coolant accident (SBLOCA) transients. These modifications, which are addressed in the following sections, allow for the new types of geometries introduced in the AP600 design.

Some of the modifications incorporated into the NOTRUMP code also changed the code numerics.

Net volumetric flow-based momentum equation, implicit treatment of bubble rise and droplet fall, and implicit treatment of gravitational head are the three model improvements having an impact on the numerics. Rese three changes are outlined in Sections 2.4,2.9, and 2.11, respectively. These modifications were described in Revision 3 of this report. In response to NRC and ACRS comments (See FSER OI 440.795F in Appendix A), additional documentation was added to Revision 4 of this report; these changes are also discussed in the context of code numerics in Section 2.20. Section 2.20 l documents the details of the new numerics affected by the modifications. If the reader is interested in the detailed numerics, it may be easier to read Section 2.20 prior to reading the more detailed l

discussions in the other Section 2.0 subsections.

O V

l l

O l

L)

February 1998 o 4025uo25w.2.wpt;Ib-022598 2.1 1 Rev.4

2.9 Bubble Rise The NOTRUMP code uses its bubble rise model to calculate the flow of vapor from a stratified fluid node's mixture region'to its vapor region. Appendix H of Reference 2-1 describes the existing model.

The model was modified in five ways for application to the AP600:

L The bubble rise mass flow rate was incorporated into the code's numerical scheme implicitly rather than explicitly.

; ['

ja,c l 'Ihe model was modified to prevent the bubble rise mass flow rate from going negative.

l An optional, user-specified override of the internally calculated interfacial area was implemented.

An option was implemented allowing the bubble rise to be based on the volume flow into a node rather than the mass flow into a node.

O ig NOTRUMP's existing bubble rise model was implemented into the code's numerics explicitly. At the beginning of each time step, the code calculates each node's bubble rise mass flow rate from the known propenies of the node, and then the code holds this mass flow rate constant throughout the time step. This in piementation of the bubble rise model makes it unstable if the model convects more liquid out of a regon during a time step than exists in that region at the bi. ginning of the time step, i.e., when it violates the material Courant limit.

1 The material Courant limit on bubble rise becomes prohibitively restrictive as mixture levels approach and cross node boundaries. For example, as a mixture level drops out of one node into the node below it, the mixture region in the upper node becomes infinitesimally small just before the mixture i

level leaves the node. If this infinitesimally small mixture irgion is voided, the material Courant limit I on the region's bubble rise restricts the time-step size to similarly infinitesimal values. As a result, the code has to expend a large number of time steps to simulate each level crossing. ;

i To circumvent this problem, the bubble rise model was implicitly implemented into the code's numerics. This implicit treatment does not affect the computation of the bubble rise mass flow rate from the properties of the fluid node. The implicit treatment estimates the change in the bubble rise mass flow rate corresponding to the change in the fluid node's state variables during each time step.

February 1998 oS4025=wn5-nspfdb.02M98 2.9 1 Rev.4

- ,. . - . - - - - =- - -, --

In the implicit treatment of bubble rise, the bubble rise mass flow rate in a node is given by:

O BW 3g

AU BW gg BW BR Wgg (t + At) = WBR (t) + g+g = AM y +

SUy (2.9 1) b

+ B R . AM y BMy where:

\V gg = bubble rise mass flow rate, Ibm /sec.

t = time at beginning of time step, sec.

At = time step size, sec.

U y,Uy = mixture- and vapor-region total internal energy, Btu AUg,AUy = change in mixture- and vapor-region total internal energy during time step Btu M y,My = mixture- and vapor-region mass, Ibm A Mg,A M y = change in mixture- and vapor-region mass during time step, Ibm A new input variable activates the implicit treatment of bubble rise. This input variable is fluid node-specific, and it is IMPBRFN(n) (Implicit Bubble Rise for Fluid Node n). If IMPBRFN(n) equals zero, the bubble rise in fluid node n is handled explicitly. If IMPBRFN(n) does not equal zero, the bubble rise in fluid node n is handled implicitly. The default value of IMPBRFN(n) is zero for all fluid nodes.

{

ja,c O

February 1998 oW25ww015 29 wpf.lb-02269s 2,9 2 Rev.4

Although the above two modifications enhanced the robustness of the bubble rise model considerably, Q'

the bubble rise mass flow rate still became negative under some circumstances. To prevent this, the

' bubble rise mass flow rate is simply reset to zero whenever it is negative. '

l l In addition to the enhancements described above for the bubble rise model, two improvements to the drop fall model were also made. First, the drop fall mass flow rate was modified to allow the use of.

the full range of drift flux correlations used by the bubble rise model. Previously, a simple mist fall calculation was used in all instances of drop fall. The drop fall calculation was also made implicit to the numerics as was the bubble rise model.

De derivations and the expressions for the partial derivatives comprising the implicit bubble rise t

model formulation of Equation 2.91 are now described. He current equation for the bubble rise mass flow rate with the modifications described above is:

A.C (2.9-2) where:

(x y = void fraction in mixture region

=Vg = = drift velocity, ft/sec.

C, = . distribution parameter v r,u, = saturated liquid and vapor specific volume, ft.3/lbm Ay g = mixture-vapor interface area, ft.2 When bubble rise is treated explicitly, the derivatives BW ag/8Ug, BWag/BM g, BWag/3Uy, and BWag/BMy in Equation 2.9-1 are assumed to be zero.

When bubble rise is treated implicitly, the derivatives DWeg/3Uy, BWBR/BMy, BW3g/8Uy, and BW3g/BMy are needed. Since Equation 2.9-2 uses several limits, there are special cases that must be treated when calculating derivatives. They are now presented as they are coded in subroutine p BEFORE. Equation 2.9-2 can be expressed as:

W3g = max BOT,0 (2.9-3) l I

. where:

.c (2.9-4)

February 1998 oMG25wWO25-29.wpf:1b422698. .2.9-3 Rev.4

_ .. ~

a.C (2.9-5)

)

If ( ]* 8, then:

i C

(2.9-6)

'a.C (2.9-7)

'a.C (2.9 8)

'a.C (2.9-9) a.C (2.9-10) where:

hiv = vapor region mass, Ibm If [ ]* C, then:

[ (2.9-11)

] a.C O

_ _ , ,, _ ,, 2.,4 e

_.. ._ , . 4 . __ . m . . _ . . _ _ _ _ . . . . _ . . . _ _ . . _ . . _ , . . . _ . . _ _ . - . . _ . . . . . _ . . _ _ . _ _ _ _ _ . . _ _ _ _ _ . _ . _

'a.c (2.9-12) a.c (2.9-13) -

i

'a.c (2.9-14) l

. a.c

, (2.9-15) 9 If [ Ja.c, then:

.c (2.9-16)

'a.c

. (2.9-17) a.c (2.9-18) l l

l 1

l February 1998 oM025=M025 29.wpf:Ib-02269s 2.95 Rev.4

.j

I 1

a i

a.c O

4 (2.9-19) la.c j

, (2.9-20) 5 J

! If [ j'8, then:

i c

(2.9-21) a 1

i

'a.c (2.9-22)

'a.c (2.9-23)

I l

a.c (2.9-24) l l

'a.c

, (2.9-25) l 9

oW125wWO25 29 wpf:1b-022698 February 1998 2.9-6 Rev.4

{

p .

i

]", then:

.. Q If l -

D.

[ ,f.c (2.9-26) l l

i n.C 1

(2.9-27)

I' I

j a.c l

, -(2.9 28) 1 1

'a.c

(

(2.4-29) .

1' a.c (2.9-30)

' If I ]**C, then:

[ pc (2.9-31) l t-i.

I' February 1998 oM025wwo25 29.wpf:Ib-022es 2,9 7 Rev.4

l i

'a.c

[ i (2.9 32) a.c (2.9-33)

'a.c (2.9-34)

'a.C (2.9-35)

If { .

] , then:

a.c (2.9-36) a.c (2.9-37) a.c (2.9-38)

O oM025wuo25-29.wpf:lb@.2698 February 1998 2.9-8 Rev.4

. . . . - .g ~, . . . . . . - .. . . - . ~ . - - . . - . - . - . - . - . - . - . - - - - . - - - . . . - . . . -

l-a.c (2.9-39) 4.C (2.9-40) t If [- )* c, then:

l l

l

[ {c (2.9-41) l

'a.c re n-42) ;

)

i t.C (2.9-43) l.

a.c (2.9-44)

I' t

I.

l l

I '

t.C (2.9-45) j i

i

(-

[ .

J I

19 oM025ww25 29.wpf:Ib422698 2.9-9 FebruNev.98 4

Finally,if Wgg > 0, the quotient rule fo differentiation:

TOP 1 (2.9-46) d( BOT) , BOT2 * [ BOT

dTOP -TOP

dBOT]

Or:

d

' TOP' 1 (2.9-47)

[dTOP - *dBOTl

, BOT, BOT s BOT, gives:

'a,c (2.9-48)

O 1a.c (2.9-49) gc (2.9-50)

~ '

a.c (2.9-51)

O February 1998 oM025ww025-29.wpf:Ib-022698 2.9-10 Rev.4

.--. -.-.-. . . - . = . _ .

i and if Wag = 0, then, f~

SW BR l-

"0 (2.9 52)

BU g,

\

8W 3g ;

(2.9 53)

BM g l

"O (2.9-54)

BU 8"

g

=0 (2.9-55) l The mixture region void fraction is calculated in subroutine FLUID as follows: I l

X u eV g au = min max '0 'j (2.9 56)

Xg*ug + (1 - Xy) a uf '

where:

XM = mixture region quality

'Ihe partial derivatives of the mixture region void fraction a swith respect to the nodal state variables Ug, M ,yU , yand My are now derived.

For 0 < ag < 1, ay can be written as:

(

l o:w25wwo25 29.wpr:ib4:269s 2.9-11 * "Tv)

i XM

u, (2.9-57) ag = XM

V, + (1 - xg ) . y, where:

vy - uI Xg a (2.9-58) u, - ur where:

ug = mixture region specific volume, ft.3/lbm Using Equation 2.9-58 in Equation 2.9-57 gives:

ug (uM - V f) a (2.9-59) y = vy * (ug- vg)

Therefore, using the quotient rule for differentiation (See Equation 2.947):

' Bug But au, ' Bu, But + an y u*s

- + * (ug - u g) - GM* DM* ~

(Da ~D)f i

OG M BU y BU y, BU y ,8U g BU g, BU g BU y ug (u, - uf) (2.9-60) bM b bg bD g bD f bD M Ba y V =

8 f

BM g,

+ = (ug -v) -ug= ug.

g

- + . (ua - vg) 2.M;,; BMg , BMg BM g, BM y BM y ug = (u, - uf) (2.9-61)

O February 1998 o:WO25wWO25-29 wpf;lb-o22698 2.9 12 Rev.4

, . .. - . - - . . . . - - -.... ---. - _ . .-.-. _ - - . . . . - . . ~ . -

(..

r i

l Bu y_ avr ' Bu g ' av8 Bug-

&u 3G u.-

8

- +

buy

. (uy -u) -as. um. g

- +

M . (u8 -u)r -

y, ,8U y -. 8Uy , ,0Uy BUy , BU y BU y u m . (u, - u g)

(2.9-62) r ,

bM bf OD g u.

s

- + . (u m - ug ) - ay . vy, OVs _ auf ~

.b M

, (U: - Vr)

Ba y

,8M y BMy , aMy .ag y ay y, ag y BMy- Vu . (u, - u f)

(2.9-63) these partial derivatives are calculated in subroutine FLUID.

The partial derivatives of the mixture region specific volume v u with respect to the ncdal state variables Ug, Mg, U , yand My are calculated in subroutine FLUID using:

U R.L (2.9-64) 1

. a.c (2.9-65) l i

l O

i February 1998 o.W25ww25-29.wpf;tb 022698 2,9 13 Rev.4 9- '.

(2.9-66) a.c (2.9-67) where:

P = pressure, psia hy = mixture region enthalpy. Bru/lbm The partial derivatives of the saturation specific volumes with respect to nodal state variables Ug ,

Mg, Uy, and My are calculated in subroutine FLUID using:

y.c O

, (2.9-68) a.c (2.9-69)

^

A.C (2.9-70)

O c:WO25wu02$-29 wpf.1b 022698 2,9.t 4 Ty)

/

( 'a.c (2.9-71) e

'a.c (2.9-72) a.C (2.9-73)

E.C

, (2.9-74)

(

l (2.9-75)

The derivatives du/dP and du/dP are calculated in subroutine SPEEDY using Equations L-7 and L-8 of Reference 2-1, respectively. !

The panial derivatives (Bv/8P)hu and (Bv/3hy)p are calculated in subroutine SPEEDY using Equations L-14 and L 15, Equations L 35 and L-36, and Equations L-38 and L-39 for subcooled, saturated, and superheated fluid states, respectively. "Ihe partial derivatives BP/3U y , BP/BMg ,

BP/ buy, BP/BMy,' are calculated in subroutine DCALCY using Equations L-%, L-98, L-100, and L-102, respectively.

j i

For ag = 0 or ag = 1, the panial derivatives of the mixture region void fraction ag with respect to the nodal state variables g U , Mg, U ,y and My are set to zero in subroutine FLUID.

l ovo25.w25 29.wptm269s February 1998 2.9-15 Rev.4

r The NOTRUMP energy and mass conservation equations are given by Equations 2-1 to 2-4 of MV Reference 2-1. W i and (Wh),@ in these equations are the net mass and energy exchange rates between the mixture and vapor regions. The sign convention for these two quantities is that positive means exchange from the mixture region to the vapor region. Currently, these exchange rates are comprised of three parts, interfacial mass and energy transfer, bubble rise, and droplet fall, i.e.:

W MV = W MIV + Wgg - WDF (g)MV = (Wh)MIV + WBR=h (2.9-77) g -Wpp

hf The exchange rates and their partial derivatives with respect to the nodal state variables are calculated in subroutine BEFORE using Equations 2.9-76 and 2.9-77 and:

MV MIV BWBR ,, b DF BW , SW . (2,9 78)

SU y BU y SUy buy BW MV

, BW MIV 8W 3g BW DF (2,9 79)

BMy BMy BMg SM y MV MIV BW , BW . 8WDR _ b DF (2.9-80) buy buy buy buy l

O February 1998 ow25wo25 29.wpr.Ib 022698 2.9-16 Rev.4

. -. - - - . - - . . _ . - - . - - . _ - - - - . - - . . ..- ~.. - . . .

4 BW MV =-

BW MIV BW gg SW DF

+ _,

(2.9-81)

BMy '8My BMy BMy (2.9-82)

B(Wh)MV 8( % )MIV Bh g BW Bhg BW BU g

= +W ag . + BR .h 8 -Wpp . -

DF .h I BU g BU g BU g BU y BU g l

- (2.9-83) 8(Wh)MV 8(%)MIV Bh g BW BW

=

+ Wag . + ag . h -W ap . . Bhr - op . h r BM y BMg BMg BM g 8 8Mg BM y i (2.9-84) ;

V 8(Wh)MV B(Wh)MIV Bh g 8W 8W

= +Wgg . + ag . h -W op . Bh g - op . h I

.BU y buy buy buy 8 buy buy l

(2.9-85)

~

8(Wh)MV 8(Wh)Mlv Bh g BW Bh g BW

=

+WBR . + ag . h -W pp a -

op

hr BMy BMy BMy BMy 8 BMy BMy l

1 4

WMIV and (Wh)MtV and their panial derivatives with respect to the nodal state variables y U , Mg, Uy, i and My are discussed in Appendix V (Interfacial Mass and Energy Transfer Model) of Reference 2-1.

Weg and its partial derivatives with respect to Uy, My, Uy, and My have been described above.

Wpp and its partial derivatives are done analogously to Wgg.

1 The partial derivatives of rh and hg with respect to Ug , M g, Uy, and My are given by Equations L 110 to L-117 of Reference 2-1.

,O

- NJ a

February 1998 c:WO25wWO25-29.wpf.!b-022698 2.9 17 Rev.4

The eight partial derivatives calculated according to Equations 2.9-78 to 2.9-85 are finally used in the central numerics in Equations E-92, E-94, E-96, E-98. E 100 to E-104, E-106, E-108, E-110 and E-112 to E-115 of Reference 2-1. This concludes the description of the addition of the implicit bubble rise (and droplet fall) model into the central numerics.

9 9

February 1998 oM025wM025-29.wpf;lb-022698 2.9-18 Rev.4

I l

l A 2.11 Implicit Treatment of Gravitational Head b

In NOTRUMP, gravitational head is accounted for within both fluid nodes and Howlinks as described in Reference 2-1. Within fluid nodes, the pressure calculated from the known state variables is assumed to apply to the top of the node. Using this convention, the code sets the pressure at the end of any flowlink connected to a fluid node equal to the sum of the pressure at the top of the fluid node and the gravitational head from the top of the fluid node to the flowlink-fluid node connection.

Within flowlinks, the code calculates a gravitational head term from the elevation difference between the upstream and downstream ends of the flowlink, using the density of the fluid within the flowlink.

However, the flowlink gravitational head model can lead to flow instabilities when the density of the l fluid within the flowlink changes rapidly. !

NOTRUMP's existing fluid node gravitational head model is incorporated into the code's numerics l explicitly. At the beginning of each time step, the code calculates the gravitational head between the top of a fluid node and the connecting end of adjoining flowlinks. The code then holds this gravitational head constant throughout the time step. This implementation of the fluid-node gravitational-head model could also lead to flow instabilities when the fluid node der.sity changes rapidly.

The fluid node gravitational head model was incorporated into the code's numerics implicitly to preclude flow instabilities resulting from the rapid density changes experienced by fluid nodes at low V pressures. This implicit treatment does not affect the computation of the fluid node gravitational head from the properties of the fluid node. The implicit treatment estimates the change in the gravitational head corresponding to the change in the fluid node's state variables during each time step.

This implicit treatment of gravitational head through fluid nodes is activated by the flowlink-specific input variable IMPGHFL. The gravitational heads through a flowlink's upstream and downstream fluid nodes are treated implicitly when IMPGHFL does not equal zero for that flowlink. The gravitational heads through a link's upstream and downstream nodes are treated explicitly when l IMPGHFL equals zero for that link. The default value of IMPGHFL is zero.

I Following is a mathematical description of the implicit treatment of gravitational head and its addition into the central numerics.

The flowlink upstream and downstream pressures are calculated in subroutine FLOW. If flowlink k has an IMPGHFL value not equal to zero, then the upstream and downstream pressures for either point contact or continuous contact flowlinks are calculated using Equations 5-3 and 5-4 (with a radius of zero) of Reference 2-1, i.e.:

O i 3

%/

February 1998 eM025wwo25-211.wpf:Ib-022598 2.11-1 Rev.4

8 *

(Emp), -max ((Emix),,(E u )g)+ max [$ mix)i-@U)L]-(Eu)k (2.11-1)

(Pg)g =P'. +

144g, (uy); (uy);

g (Emp);-max ((Emix)f,(Eo)g] + max ((Emix)),(Ep )g]-@p)k (2.11-2)

(Po)g=P.+

J 144g, (uy)j (uy))

where:

P = pressure, psia (Pu)g,@p)g = upstream and downstream pressures for flowlink k Equation 2.11-1 for continuous contact flowlinks is an approximation to using Equations 5-3 and 5-5 of Reference 2-1. Similarly, Equation 2.112 for continuous contact flowlinks is an approximation to using Equations 5-4 and 5-6 of Reference 2-1.

(Pu)g and (Po)g are then used in subroutine BEFORE to calculate the bracketed part of the right-hand side of Equation 2-33 of Reference 2-1. Then Wg is calculated using Equation 2-33. Finally if ITYPEFL(k) = 11 or ITYPEFL(k) = 21, then W gis modified according to Equation 2.4-3.

l where:

Wg = time rate of change of mass flow rate at flowlink k The addition of the implicit treatment of gravitational head is implemented in subroutine SETUP. The details are now presented. In Appendix E (Detailed Numerical Equations and Solution Technique) of Reference 2-1, additional terms representing the linearizations of the gravitational head for flowlink k with respect to the nodal state variables gU , Mg, Uy, and My for node i are added to Equations E-61 to E-64 if flowlink k has an IMPGHFL value not equal to zero.

If node i is an interior fluid node, is the upstream node of flowlink k, and the elevation of the upstream end of flowlink k is below the top of node i, then the gravitational head through the node can change with respect to the nodal state variables as follows:

If ( (Emix); > (Eu )g) or [(Emix)i = (Eu)g and ( y); > 0] where:

. BV BV y DV V

y = dug u.O g+d.M . My + BVy

. Uy + yBMy My (2.11-3) y 8Uy Februart 1998 oM025wuG23-211.wpf:Ib 022598 2.11-2 Kev.4

-~. - -. . . . . - . .. . .-~ ..

I p

't j where Oy, Ni ,gy and Niy are the time rates of change of the nodal state variables and the partial derivatives are given by Equations L-97, L-99, L-122, and L-123 of Reference 2-1. Then the l gravitational head through the vapor region and mixture region is given by:

GHVm- E . Mi ~ fbx i (2.11-4) 144ge (uy);

g (Emix); -(Eu)k GHMa , (2.11-5) 144ge (uy)3 The partial derivatives of GHV and GHM with respect to the state variables, obtained using the quotient rule for differentiation (see Equation 2.9-47), are then:

i 8GHV , 1

, -g , . B(Emix); , BVu, BuV (2.116)

BU y (uy); 144ge 8V u BU g BU g q -

8GHV , 1

, -g , 8(Emix): ,

DV M

_g, BuV M -7)

BM y (uy)i 144ge BV u BM g BM u, BGHV , 1

, -g , 8(Emix)3 , BV y , BuV (2.11-8) buy (uy)3 144g, 8V g buy _ buy I

&GHV 1 -g B(Emix)i . SV M Bu y (2.11,9)

= . . -GHV.

BMy (uy) 144ge BV u BM y BM y, i

l February 1998 o:WO25wWO25-2I1.wpf:1bc2598 2.11-3 Rev.4 I'

I l

8GHM , 1 g ,

B(Emix); , BV y , ,

bum (2.11-10)

BU g (u y ), 144gc BV y BU g BU g, 8GHM , 1 ,

g ,

B(Emix); , 8V y , ,

bum (2.11-11)

BM g (uy); 144g, 8V y BMg BM y Bu M 8GHM , 1 ,

g ,

B(Emix)i , OV M (2.11-12) buy (uy), 144gc BV y buy _ g , buy, 8GHM , 1 ,

g , 8(Emix)i , OV M bum (2.11-13) 8My (ug)i 144gc BV u BMy _ g , BMy-If [ (Emix)i < (Eu )g] or [ (Emix), = (EU)k and 9 y s0],then:

GHV = 8 . P)i ~ f U}k (2.11-14) 144gc (v y)3 GHM = 0 (2.11-15) so that:

BGHV , 1 "V (2.11-16)

= GHV .

BU y (vy); 8U p BGHV , 1 vy

-GHV = (2.11-17)

BM g (uy); BMy O

oM025ww025-211.wpf:lb-022598 2,.4 %,,

l~ L l . l D

    'h                                                   BGHV ,                   1
                                                                                          * -GHV

uv (2.11-18) ,

buy (uy)3 BUv-BGHV , 1 VV (2.11-19)

                                                                                            -GHV

SMy {

BMy. (vy)3 , BG W

                                                                                             =0                                          (2.11-20) buy GW =0 (2.11-21) dMy T

BG W

                                                                                             =0                                          (2.11-22) s                                                                            buy BG W =0 (2.11-23)

BMy in the above equations (starting with Equation 2.11-3), g, s y, Oy, and s y are given by Equations 2-1 to 2-4 of Reference 2-1.yBV /BU g , BV y /BM g , SV y /aUy, and BVg /BMy are given by Equations L-97 L-99, L-122, and L-123, respectively.g au / buy, Bu g /BMy, Bu g /aUy, and aug/BMy are calculated using Equations 2.9-64 to 2.9-67, respectively. Bu y /0Ug, Buy /aM g, Buy /0Uy, and Buy /BMy are calculated in an analogous manner. B(Eg)i/aVu is calculated in subroutine DIST. 'Ihe derivatives are added to Equations E-61 to E-64 as follows: l r , At

144ge BGHV BGHM (2.11-24) l (AwUu)k.i "(AwUu)k.i - (I UA)g , BU y BU g NJ February 1998 eM025ww)25-211.wpr:lt@22598 2.11-5 Rev.4

f BGHV BGHM 9 At a 144ge * + (2.11-25) (Awy,)g,; = (Awy )g,; - g g At = 144ge BGHV BGHM (2.11-26) (Awuy)g; = (Awgy)g,i - buy (EIJA)g , OUy , f % At

144ge (Awy y)g,i = (Awyy)g,i - a BGHV +BGHM (2.11-27) g where:

A = flow area, ft.2 E = elevation, ft. g = cceeleration of gravity, ft/sec.2 ge = 32.174 lbm ftllbf/sec.2 L = length, ft. M = mass, Ibm U = intemal energy, Btu V = volume, ft.3 u = specific volume, ft.3/lbm W = mass flow rate, Ibm /sec. and the subscripts: D = downstream i = upstream fluid node = U(k) J = downstream fluid node = D(k) k = flowlink k M = mixture region mix = mixture top = top of fluid node U = upstream V = vapor region If node j is an interior node and it is the downstream node for a flowlink k having an IMPGHFL value not equal to zero, then GHV and GHM and their derivatives are calculated in the same way as for an upstream node, i.e., using Equations 2.11-3 to 2.11-27. The only difference is that in February 1998 oM025w\4025-211.wpf:Ib-022598 2.11-6 Rev.4

2 Equations 2.11-24 to 2.1127, the subscript i is changed to subscript j, and the terms are added rather than' subtracted. 4 4 1 i 1 f i l l J j ( Febru

                      .: = - = .ui.+ i - ,                                2.ii.7

i 2.20 Modifications to the NOTRUMP Central Numerics for Application to AP600 The original NOTRUMP central numerics, that are documented in Reference 2-1, were modified for application to AP600. The main modification to the numerics was the change from the net mass flow-based to the net volumetric flow-based momentum conservation equation (described in ' Section 2.4). Additional modifications to the numerics were the implicit treatment of bubble rise and droplet fall (described in Section 2.9), and the implicit treatment of gravitational head (described in Section 2.11). In this section, all of these central numerics modifications are assembled in a cohesive fashion. The derivations that are required to modify the starting differential equations of

 ;       Reference 2-1, and then place them into finite-difference form for solution, are presented.

The changes to the NOTRUMP central numerics for AP600 directly affect the momentum conservation equation for each non-critical flowlink (i.e.,~ Equation 2 33 in Reference 2-1), and indirectly affect the energy and mass conservation equations for the mixture and vapor regions of each interior fluid node (i.e., Equations 2-1 through 2-4 in Reference 2-1). The modifications for the , volumetric flow-based momentum formulation of Section 2.4 are the most extensive. They affect the l structure of the starting momentum conservation equation, as well as the finite-differencing of all of ! the aforementioned conservation equations. The modifications for the implicit treatment of bubble rise l and droplet fall of Section 2.9 only affect certain implicit terms in the finite-differencing of the energy and mass conservation equations for the mixture and vapor regions of each interior fluid node. De modifications for the implicit treatment of gravitational head of Section 2.11 only affect certain implicit terms in the finite-differencing of the momentum conservation equation for each non-critical j flowlink. l Section 2.20.1 contains the modifications to the momentum conservation equation for the non-critical I flowlinks. The changes to the structure of the equation for the volumetric flow-based formulation are described in Section 2.20.1.1, and the finite-differencing modifications ere presented in Section 2.20.1.2. Sections 2.20.2 through 2.20.5 contain the modifications to the finite-differencing of the energy and mass conservation equations for the mixture and vapor regions of the interior fluid nodes. De modifications to the NOTRUMP central matrix and its elements (of Appendix E in Reference 2-1) which result from the changes described in Sections 2.20.1 through 2.20.5 are ' contained in Section 2.20.6. Section 2.20.7 describes the finite-differencing notation and conventions that are employed. A summary of the thermodynamic properties, related quantities, and partial derivatives that are used in the modified central numerics is presented in Section 2.20.8. Section 2.20.9 contains a summary of the interfacial energy and mass exchange rates for the interior fluid nodes that are used in the modified central numerics. 2.20.1 Modifications to Momentum Conservation Equation for Non-Critical Flowlinks The momentum conservation equation for non-critical flowlinks in the mc<lified NOTRUMP central 4

       - numerics is described in this section. Section 2.20.1.1 contains the modifications that were made to N

the starting mass flow-based momentum conservation equation (Equation 2-33 of Reference 2-1) to February 1998 oM025wwo25-220.wpf:1b.022698 2.20-1 Rev.4

obtain the volumetric flow-based formulation. Section 2.20.1.2 contains the derivations that were performed to place the modified momentum conservation equation into the finite-difference form to be solved, which also includes terms for ihe implicit treatment of gravitational head. 2.20.1.1 Modifications to Momentum Conservation Equation for Volumetric Flow Based Formulation In this section, the modifications to the momentum conservation equation for the volumetric flow-based formulation are presented. 'Ihe starting equation is the mass flow-based momentum conservation equation for non-critical flowlinks given by Equation 2-33 in Reference 2-1, without the momentum flux terms { ] dW k, 144gc w (pu)k - (PD)k -C k = lWk l Wk+Dg (2.20-1) dt (I UA)k for k = 1, .... K, where: Wk = mass flow rate in flowlink k, Ibm /sec. (Pu)g = pressure at center of upstream end of flowlink k, psia (Po)k = Pressure at center of downstream end of flowlink k, psia C* g = mass flow-based friction coefficient for flowlink k, lbf sec.2/in.2/lbm 2 Dg = gravitational head within flowlink k, psi (I UA)k = user-specified inertial length for flowlink k, ft.-l gc = gravitational constant, 32.174 lbm ft/lbf/sec.2 K = total number of non-critical flowlinks and the subscript: k = non-critical flowlink On the right-hand side of Equation 2.20-1, (Pg)g for both point-contact and continuous-contact flowlinks is given by Equations 5-1 and 5-3 (with a radius R of zero) of Reference 2-1 as follows: O February 1998 eM025wuo25-220.wpf:1b-022698 2.20-2 Rev.4

q Q (Pu)g = P; + g . (Egop); - max [(Emix)i, (Eu)g] 144gc (uy)j max [(E,;x)i, (Eu )g] -(Eu)k

                                                                .                                               (2.20-2)

(ug); so that the complication of using Equation 5-3 (with radius R) of Reference 2-1 in conjunction with Equation 5-5 of Reference 2-1, for continuous-contact flowlinks, is avoided (using Equation 2.20-2 for continuous-contact flowlinks is an approximation to using Equations 5-3 and 5-5 of Reference 2-1). In the above: Pi = pressure at the top of fluid node i, psia (Uy); = specific volume of the vapor region of fluid node i, ft.3/lbm (Ug); = specific volume of the mixture region of fluid node i, ft.3/lbm (Emix)i = elevation of the mixture-vapor region interface in fluid node i, ft. (Egop); - = user-specified elevation of the top of fluid node i, ft. (Eu)g = user-specified elevation of the center of the upstream end of flowlink k, ft. g = acceleration due to gravity, ft/sec.2 and the subscript: i = fluid node at the upstream end of flowlink k (= U(k)) I Tlae equations for Pi , (uy)i, and (uy); are discussed in Section 2.20.8. (Emix)i is given by the l following: (Vg)i (2.20-3) (Emix)i = (Eg); + [(Etop); - (Ebot)i] . where: (Vy); = mixture region volume in fluid node i, ft.3 g Vi = user-specified total volume of fluid node i, ft.3

(Eg); . = user-specified elevation of the bottom of fluid node i, ft. February 1998 eM025wwo25-220.wpf:Ib.022698 2.20-3 Rev.4 4

The equation for (V p), is discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). Returning to the right-hand side of Equation 2.20-1, (Pp)g for both point-contact and continuous-contact flowlinks is given by Equations 5-2 and 5-4 (with a radius of zero) of Reference 2-1, in a manner analogous to the way in which (Pg)g was defined, as follows: g * (Eyj - max [(Emix)j, (ED)kl (PD)k = P.J + 144ge (uy)j max {(E mix)j, (E p )g] -(ED)k (2.20-4) (ug)j where: (Eo)g = user-specified elevation of the center of the downstream end of flowlink k, ft. and the subscript: j = fluid node at the downstream end of flowlink k (= D(k)) All other terms in Equation 2.20-4 for fluid node j are the same as those defined for fluid node i in Equation 2.20-2. The term Cg* on the right-hand side of Equation 2.20-1 is the friction coefficient Cg ni Reference 2-1, with superscript "W" added here to denote " mass flow-based." Cg* is dependent upon fluid conditions and the specific models chosen. The details are contained in Equations 5-33 through 5-36, 5-39, 5-41, 5-43 through 5-45,5-50,5-51, and 5 55 through 5-57 in Reference 2-1, and in Section 2.16, and are not repeated here since they do not impact the central numerics modifications for AP600. However, the following familiar form for single-phase flow from Equation 5-33 of Reference 2-1 is shown for illustrative purposes:

                                 -                                                         =   4. C.

(2.20-5)

                                                                                            .i February 165 c:M025ww025-220.wpf:1b-022698                         2.20-4                                           Rev.4

l' where:

v. g = specific volume in flowlink k, ft.3/lbm Ak = user-specified flow area in flowlink k, ft.2 l

rg, , user-specified pointwise friction loss factor for flowlink k ) l $ D ,p.k l r 3 ' 1 user-specified average friction loss factor for flowlink k

                            , D ,a.k f                                 = friction factor L                                 = length, ft.

D = diameter, ft. j- In the above, ukis given by Equation 5-17 in Reference 2-1: L ' Uk* ak- + (1-G) k (2.20-6) (V8)k . (Uf)k l' g( D- where: l ug = average void fraction in flowlink k (Vg)k . = specific volume of the gas component in flowlink k, ft.3/lbm ! _(Vg)k = specific volume of the liquid component in flowlink k, ft.3/lbm The terms ag, (v,)g, and (vf)g are calculated by the drift flux model equations in Appendix G of Reference 2-1.

                 'Ihe last term on the right-hand side of Equation 2.20-1. Dg, is given by Equation 5-31 of Reference 2-1:

D 8 * ( U)k - @D)k (2.20-7) g = 144ge Vg

               . Ihe modification of the momentum conservation equation from the mass flow-based to the volumetric

.p flow-ba' sed formulation involves converting the non-critical flowlink central numerics variable from the O L l February 1998

               , oMo25wwc5-220.wpf:1M22698                                            2.20-5                                                 Rev.4

mass flow rate Wk to the volumetric flow rate Qg. As outlined in Section 2.4, this is ultimately accomplished by using the following approximation to relate Wg and Qg: Wk" N' Dk I i l where: j 1 l Qg = volumetric flow rate in flowlink k, ft.3/sec. ! 1 Recall that this relationship (Equation 2.20-8) is implied in the discussion in Section 2.4 which I explains the modification to the friction coefficient, in the generation of Equation 2.4-28. l Differentiating Equation 2.20-8 with respect to time and neglecting the temporal derivative of ug i l yields-i dW k d(Qk/g u) i dQg !

                                             =              = _ _  .                              (2.20-9) dt           dt          Uk      dt                                         i It is noted that Equation 2.20-9 is equivalent to Equation 2.4-6, whereg u = 11pfi, and pfi is given by Equation 2.4-7. Equation 2.20-9 epresents the modification of the left-hand side of the mass flow-based momentum conservation equation (Equation 2.20-1) for conversion to the volumetric flow-based formulation.

On the right-hand side of Equation 2.20-1, the only term which is possibly affected by the conversion to the volumetric flow-based formulation is the friction term "- g C *

lW k l . Wk." As explained in

Section 2.4, NOTRUMP has two options for the treatment of the friction term in the volumetric flow-l based formulation.

1 1 In the first friction option (ITYPEFL(k)=ll), the friction term is treated as volumetric flow-based. l Substituting in Equation 2.20-8, the friction term becomes:

                  - C *

lWk !
Wk=-Ck
l Dk j , Qk D

                                                                      = - C[ = lQk !*Ok (2.2N0) k        k O

February 1998 ovo25.w.5 220.wpt:1b.022698 2.20-6 Rev.4

I i where: O I V W k Cg 9= (2.20-11) (uk) Equation 2.20-11 is identical to Equation 2.4-28, where: CkQ = volumetric flow-based friction coefficient for flowlink k, Ibf sec.2/in.2/ft.6 ITYPEFL(k) = user-specified option flag for flowlink k. In the second fdction option (ITYPEFL(k)=21), the fdction term is treated as mass flow-based, such that it remains as "- C g W. l W k I

Wk ~

In either of the two friction options in the volumetric flow-based formulation, the volumetric flow rate Qg is the central numerics variable for non-critical flowlink k. j Incorporating the above modifications (Equation 2.20-9 for the left-hand side; possibly Equation 2.20-10 for the right-hand side) into Equation 2.20-1, the momentum conservation equation in the O' volumetric flow-based formulation becomes: dQk , , 144gc

                                                               , ((pU)k -(Po )g + Rg+D]    k             (2.20-12) dt             (I IJA)k for each non-critical flowlink k = 1, ..., K, where:
                       - Ch lQ !*Qk,k   in the volumetric flow -based friction option (ITYPEFL(k) 41 )

Rk"

                       -C gw .lW lkW , inthemassflow-basedfrictionoption(ITYPEFL(k)=21) k (2.20-13)
      'Ihis concludes the discussion of the modifications to the momentum conservation equation for the volumetric flow-based formulation.

t I l p l February 1998 oMo25wuc25 220.wpf.12698 2.20-7 Rev.4

2.20.1.2 Modifications to Finite-Differencing of Momentum Conservation Equation In this section, the derivations to place the modified momentum conservation equation for the volumetric flow-based formulation (Equation 2.20-12) into finite-difference form are presented. Refer to Section 2.20.7 for the notation and conventions that are employed for finite-differencing. Finite-differencing of Equation 2.20-12 yields: n AQk+1 1448c

                                 ,y n +1 ,             ,  (p    +1 _ (p
                                                                           +1
                                                                               + Rk"* + D k"+l       (2'20'l4) n At +1                 (I UA)g for each non-critical flowlink k = 1, ..., K. Each transient term in Equation 2.20-14 is now examined.

On the left-hand side of Equation 2.20-14, AQg"+1 is the new central numerics unknown variable for non-critical flowlink k to be solved for. The tenn At"+I is the time step size (= t"+I - t"), which is calculated by the NOTRUMP time step size selection method described in Section 10 of Reference 2-1. Note that the latter has not been modified for the application of NOTRUMP to AP600. On the right-hand side of Equation 2.20-14, the ug "+1 multiplier is treated explicitly. [ a .. - Thus, using the notation discussed in Section 2.20.7: v"*I =uk + AVn+1 . y (2.20-15) In the (Pu)g"+3 and (Po)g"+1 terms, it is noted that in the original NOTRUMP central numerics of Reference 2-1, only the nodal pressures (P i and P) j were treated implicitly, and the remaining terms for fluid node gravitational head were treated explicitly. However, as indicated in Section 2.11, the fluid l node gravitational head terms are now treated implicitly in the modified NOTRUMP central numerics l for AP600. The discussion that follows begins with the (Pu)g"+I term. Also see Section 2.11. First, Equation 2.20-2 is rewritten to more closely resemble the form discussed in Section 2.11: (Pg)k = Pi + (Pf"); + (POH); (2.20-16) O February _1998 o:wo25wwo25-220.wpf:1b-022698 2.20-8 Rev.4

where: l g (Etop); - max [(Egx)i,(Eg )gf I (PyGH); = * (2.20-17) 144ge (vy) ; (p GH , g max [(E gx)i, (Eu )k] -(Eg)k (2.2()-18) 144ge (Vg); 1 In the above:

(PyGH) = gravitational head through the vapor region of fluid node i (= GHV in the notation of Section 2.11), psi (PgGH) = gravitational head through the mixture region of fluid node i (= GHM in the notation of Section 2.!!), psi Next, it is noted that (Pu)k si only a function of fluid node i quantities, such that, in general it may be expressed ir. terms of the central numerics variables for fluid node i as follows f~) V l (Pg)k = P u ((Uy);, (M g)3, (Uy);, (My);) (2.20-19) so that: 4 (Pg)"*I = (Pg)g + A(Pg)g (2.20-20) where: g g A(Pgk )n+1 = B(P )k

A(U 8(Uy);

gi )n+1 + 8(P )k g;

A(M )n+1 8(M y ),

                                          +   B(Pg )g

A(Uy)n.i '

g

                                                                      + O(P )k

A(My)n+1 .

                                                                                          '             (2.20-21) 8(Uv);                    8(My);

I i 0 ' Q February 1998 o:\4025w\4025-220.wpf.!b-022698 2.20-9 Rev.4

l l 1 l where: l (Uy), = mixture region intemal energy in fluid node i, Btu (Mg)3 = mixture region mass in fluid node i, Ibm (Uy)3 = vapor region intemal energy in fluid node i Btu (My); = vapor region mass in fluid node i, Ibm Thus, differentiating Equation 2.20-16 with respect to the fluid node i central numerics variables yields: 8(Pg)g 8P; 8(PfH) g(pGH) _ (2.20-22) 8(Ug); 8(Ug); 8(Ug )i 3(Uy )i GH 8(Pg)k , BP 8(POH) g(pgt )i (2.20-23) 8(Mg); 8(My ) 8(Mg); 8(Mg); U 8(Pg)g BP; 8(Pf"); 8(P3g ")i _ (2.20-24) 8(Uy); 8(Uy); 8(Uy); 8(Uy); 8(Pg)g BP; (8POH) g(pGH)i (2.20-25) 8(Mv); 8(Mv); 8(Mv); 8( My)i

 'Ihe partial derivatives of the fluid node i pressure with respect to the fluid node i central numerics BP'.       BP'.        8P'-           BP*-

variables, 8(U g );, d.(M g );, 8(Uy);, and -8(My);, are discussed in Appendix L of Reference (see the Section 2.20.8 summary). It is noted that in the original NOTRUMP central numerics of Reference 2-1, in which the fluid node i gravitational head terms were treated explicitly, the second and third partial derivatives on the right- l hand side of Equations 2.20-22 through 2.20-25 were ignored. In the modified NOTRUMP central l numerics herein, these terms are retained. Equations 2.20-17 and 2.20-18 are rewritten as follows, to account for the two situations that may exist (as a result of the " max" in Equations 2.20-17 and 2.20-18): O o*5ww220 wpt;Im69s 2.20-10 ev. __ -- - - --___- ___- -_ _ _ -_____________ -_________- l

1 If [ (E mix)i > (Eu)g ] or [(E mix)i = (Eg )g and (i g); >0], then: (p GH , g (Ecop); -(Emix)i (2.20-26) 144gc (Vy); (p GH 'g (Emix); --(Eu)k (2.20-27) l 1448c (UM); i otherwise: (p yGH , g (Etop); -(Eg)k (2.20-28) 144ge (uy) 1 (PgGH) = 0 (2.20-29) , where: f % ( g)j = the time rate of change of(Vy )i = d(VM)I , ft.3/sec. t dt , l Equations 2.20-26 and 2.20-27 are the same as Equations 2.11-4 and 2.11-5, respectively, while t Equations 2.20-28 and 2.20-29 are the same as Equations 2.11-14 and 2.11-15, respectively, It is noted that the second portion of the above test accounts for the situation in which the mixture-elevation in fluid node i is currently equal to the elevation of the center of the upstream end of flowlink k, but the mixture region is growing (( g); > 0), such that the mixture elevation is increasing. As shown in Section 2.11 (Equation 2.11-3), ( g); is approximated as follows: f%

19 j eM025ww)25-220.wpf:Ib-022698 2.20-11 FebruNev.98 4

                                  .          8(Vg)                       g

( vy )' - 8(Ug); * (O ); + 8(M g g );8(V ); - (Ag);

                                          . 0( V M )i . ( G y)'. + D M h . ( s y),                                (2.20-30)

B(Uy); 8(My); where: d(Ug); (Oy); = the time rate of change of (Uy ); = , Btu /sec. 3 d(Mg);

                                                                                                    , Ibm /sec.

($M)i = the time rate of change of (Mg); = r , d(U y)3 ( y); = the time rate of change of (Uy); = , Btu /sec. dt d(My); (My); = the time rate of change of (My); = , Ibm /sec. t dt , i Equation 2.20-30 is based on the fact that (V y ); is expressed in tenns of the fluid node i central numerics variables, (Uy)i, (Mg)i, (Uy)i, and (My)i, as discussed in Appendix L of Reference 2-1 (see the Section 2.20-8 summary). The partial derivatives of (Vg ); with respect to the fluid node i central numenes vanables, . g(V ); 8(Vg); 8 B(Vg); 8(Vg);

                                                              ,and i                                                                              are discussed in Appendix L of d(Ug );, 8(Mg);, 8(Uy);                  8(My);

Reference 2-1 (see Section 2.20.8 summary). 'Ihe terms g (O )i,g (A )i, (Oy);, and (sy); are approximated by the right-hand side of the fluid node i conservation equations for mixture region energy, mixture region mass, vapor region energy, and vapor region mass, respectively, at the end of the previous time step. These expressions are given by Equations 2-1 through 2-4 of Reference 2-1, and are also presented in Sections 2.20.2 through 2.20.5. As explained in Section 2.11, the partial deri/atives of (Py")i and (P y "); with respect to the central numerics variables for fluid node i are obtained by using the quotient rule for differentiation on Equations 2.20-26 through 2.20-29. Thus: Februart 1998 o:wo25wwo25-220.wpf;)b-022698 2.20-12 Kev.4 i

1 If [(Emix)i > (Eu)k] or (E mix)i = (E u )g and (9g ); > 0 , then: 8(Pf"); 1 g b(UV)i B(Emix)i _V(p ,,GH)' (2.20-31) 8(Ug); (uy); 144gc 8(Uy); 8(Uy);. B(Pf"); B(Egx); 8(uy)i 1 g , _p Vog ' , (2.20-32) 8(Mg); (uy) 144gc 8(Mg); 8(Mg);' , l B(Pf"); 1 g 8(E b(VV)i mix)i _ (p V GH)'

                                                                                        ,,                  (2.20 33) 8(Uy);          (ny)             144gc         8(Uy)i                  8(Uy);,

8(PfU)i _ 1 g 8(E O(VV)i mix)i _ (pV GH)'

                                                                                        ,,                  (2.20-34)     l 8(My);           (uy);

144gc 8(My); 8(My);. 8(PgCH) 1 8 8(E 8(ug)i

                                     ,          ,              .        mix)i _ (p M og)'
                                                                                       .,                   (2.20-35) 8(Ug);          (uy),          144gc        8(Uu);                   8(Ug);,

8(P GH); g 1

                                                .              . 8(Emix)i _ (pGH      ,   C(DM)i         (2.20-36) 8(Mg);           (uy);                                    M '

144gc 8(Mg); 8(Mg )i, GH 8(Pg )i _ } . g . 8(Emix)i _ (pGH , O(VM)i (2.20-37) 8(Uy); (vu); M ' i 144gc 8(Uy); 8(Uy), B(P GH); g l 1

                                                .              . 8(Emix)i _ p GH          O(DM)i         (2.20-38) 8( My);         (ug);          144gc        8(Myi        M y',8(My)i, f3 LJ r

February 1998 l- eM025wwrs220.wpf:lt422698 2.20-13 Rev.4

1 othenvise: B(Py GH)i= 1 b(DV)i (2.20-39)

                                                        - (P y GH)i

8(U )

i 8(Ug); (uy); y; l 8(PyC"); 1 8(uy)i (2.20-40)

                                         =           .  - (PVog)'.*                                         1 8(Mg);       (uy);                   8(My)i, 3(PyU");                            8(uy)i 1
                                                      .  - (Pog)'

y .. (2.20-41) 8(Uy); (uy); B(Uy)i, 8(PyU"); 8(uy)i

                                                      , _p og    ,,

(2.20-42)

8(My); (uy i y 8(My) l 9

8(P3 $")i ,9 (2.20-43) 8(Ug); 8(PyU") (2.20-44)

                                                            ,9                                              )

B(Mg); 8(P gC")i ,9 i (2.20-45) 8(Uy); 1 1 8(P3$");

                                                            =0                              (2.20-46) 8(My)i l

Equations 2.20-31 through 2.20-38 are the same as Equations 2.11-6 through 2.11-13, respectively, while Equations 2.20-39 through 2.20-46 a.e the same as Equations 2.11-16 through 2.11-23, respectively. February 1998 i ovo25wwo25-220.wpf.lb422698 2.20-14 Rev.4 l

     . _   . _          m.    . _ _ _ _    ~ . _ , _ . _ _ - > . . _ . . - - . . . . _ _ _ _ _ . _ _ _ _ ...                                          .______ _. _ .

l ) .In the above, the partial derivatives of (Emix)i, with respect to the fluid node i central numerics L

    .-             variables are obtained by differentiating Equation 2.20-3, yielding:

3(Emix)i , B(E,;x) , B(Vh b (2.20-47) j- 8(Ug); d(Vg); 8(Ug); l B(E,;x); ., 3(E,;x); , B(Vy)i (2.20-48,' d(Mg); d(Vg); d(Mg)i l 3(E ,;x); , 3(Emix); , 3(Vy)i (2.20-49) B(Uy); &(Vy); 8(Uy); i B(E,tx); , 3(E,;x); , B(Vg)i (2.20-50) d(My); d(Vg); d(My); j where:

                                                                      ' 8(Emix);

(Ey; -(Ebot}i (2.20-51) 8(Vg); V; .

                ' Also, the partial derivatives of (vy); and (Vg); with respect to the fluid node i central numerics D(ny);      B(vy);           3(uy); - B(uy);                                      B(ug);     B(ug); B(uy);          3(ug);

p variables'g8(U );' yB(M ); 8(Uy); , 8(My); ,g and a(U g );, 8(My );, 3(U );, and d(M are discussed in Section 2.20.8. Returning to Equation 2.20-14, the (Po)g"+I term is treated analogously to the (Pu )g"+1 term. For

               - (Pp)g"+1, all of the expressions are identical to those for                                      u (P )g"+1 above, with the following changes:
              '=
,                          - Flowlink k' upstream terms (Pu)g and (Eu)g are replaced by flowlink k downstream terms (Po)g and (E p)g, respectively.

r February 1998 eM025wwo25 220s.wpf:IM22698 2.20-15 Rev.4

l l

Fluid node i (upstream node) subscripts are replaced by fluid node j (downstream node) subscripts.

f For brevity, only the following two " final form" expressions are shown for (P o)g"+1 (all others are given by the above (PU)t"* cxPressions with the aforementioned changes): 1 (PD) * = (P )g (2.20-52) o + A(P )n+1o l where: f l n.i 3(Po)g n.i 8(Po )g

A(U g. )J +

i A(Pog )n+1 = g. 8(Ug); 8(Mg);

A(M )J

D B(PD}k ,g +1 i 8(P)k*MUQ"*I 8(Uy);

a(My); (2.1.0-53)

    "Ihe Rg"+1 term in Equation 2.20-14 is described next. From Equation 2.20-13:

O

                                     - (Ck ) 'l

lQ"*'i l
Q *k , if ITYPEFL(k) = 11 (2.20-54)

R " *I =

                                    -(Ck )"*I = lW[* l

W[* if ITYPEFL(k) = 21

 -                                                                                                         .   . e. , c.

W

                                      .                                       . , a., c.

(2.20-55)

J i

l and j . . a., c. (2.20-56)

  -                                                                                                          ,  ,4,r
                                                                                                           ~

O omww.5-22kwpr:m69s 2.20-16 v

l l i

      /                                                                                                                     -  a,s.

t t

       %                                                                                                                                    l
                                                                                                                            ~

t

                                                                                           .%c (2.20-57) l where:

m=

                                                                        + 1. if Qk 2 0.                              (2.20-58)
                                                                        - 1., if Qk < 0.

i Note that with this definition of "m" from Equation 2.20-58, we have: m a Qk " !Qk l (2.20-59) Expanding the right-hand side of Equation 2.20-57 (and utilizing Equation 2.20-59 and ignoring the product of two A's) yields: l

                                              ~                                                              -
                                                                                                                 % C.

(2.20-60) Similarly, the "lW g"+3 l = Wk"+3" term in Equation 2.20-54 in the ITYPEFL(k) = 21 option becomes:

                                                                                                       . a., c.

I (2.20-61) , However, since Qg"+I is now the central numerics variable (and AQg"+I the central numerics l unknown), AWk"+ must be expressed in terms of AQg*+1. In general, we have: O omww220awietes 2.20-17 ev. l'

l ! BW g l AW[*I = k

AQl+1 (2.20-62) l dQL l l l l

t BW k where is given by Equatior 2.4-3,2: OQk l l i OWk ,d@f)k D )k g (2.20-63) SQk 8Qk BQ k where: l (W r)g = liquid mass flow rate in flowlink k, Ibm /sec. (W ,)g = vapor mass flow rate in flowlink k, Ibm /sec. B(W f)k 3(W 8)g and the partial derivatives and are calculated by the drift flux model equations of OQk OQk Appendix G of Reference 2-1, using the volumetric flow-based formulation as explained in Section l 2.4, i.e., Equations 2.4-22 and 2.4-23, respectively. l Substituting Equations 2.20-55,2.20-56, and 2.20-60 through 2.20 62 into Equation 2.20-54, the expression for Rg* becomes: 7 (2.20-64) n .c

This is placed in the following convenient form of: Rg " *I =Rk + AR "+1 (2.20-65) O February 1998 o:uo25wwo25-220awpf ltm2698 2.20-18 Rev.4

l l lg where:

    \                                                                                                                                                    l AR k          "

k *AQ"* k (2.20-66) ! 09 k i l and l

                                                                                                   . , aLC                                               i i                                                                                                                                                         i l                                                                                                                                                         I (2.20.67) l l

r

                                                                                                                                   . 4,f-l
      -                                                                                                                            J
                                                                                            -   A,c-(2.20-68)                i Thus, substituting Equations 2.20-15, 2.20-20, 2.20-21, 2.20-52, 2.20-53, 2.20-65, 2.20-66, and 2.20-68 into Equation 2.20-14 places the finite-difference form of the volumetric flow-based momentum conservation equation in terms of the (new) NOTRUMP central numerics unknown variables as follows:

l l AQ k 1448c 8(Pu)k 8(Pg)g .i g y '. + n At +1 = % * (I UA)g (P )k + 8(U y );

A(U )n+18(My);
A(M y)"8 l

l l l

                                                         +    8(Pg)k

A(U y '. )n+1 + 8(Pg)k
A(My)n+1 '

l 8(Uv); 8( My); l February 1998 l oM025ww025-220s.wpf:Ib-022698 2.20-19 Rev.4 [. I

D d(Po)k n+1 O

                                        - (PD )k - d(P )k

A(U g );n+1-g.

d(Ug); 0(Mg);

A(M )3 p

                                            - B(PD )k

A(Uy);n+1 - B(P )k y);n+1
A(M d(Uy); 8(My);

OR

+R

AQg"*I + D k (2.20-69) k+g for non-critical flowlink k = 1. ... K.

Multiplying both sides of Equation 2.20-69 by At"+3 and collecting all central numerics unknowns on the left-hand side yields: 144g 3R k n +1 I. - At"*I

U * ,

k (IUA)k EQ k k At " 4

U * , g(g )n+1 k * (I UA)k O(UM)i-b At "*1
V g * (I UA)k

                                                                         . A(My8 )"

8(Mg);- O omww22%um69s 2.20-20 ev, I l

n 1448e 8(Pu)g at +1 ug . -

A(Uy)n.1.

(I UA)k 8(Uy) . 144ge 8(Pu)k Atn 3 au =

A(My)n+1 .

g = (I UA)g 8(My);,

                                        + Atn +1 aua              I448c              =     3(PD)k g

A(U g);n+1 (I UA)k O(UM)j.

                                      +   At n+1

U I448c
8(PD)k
A(M g);n+1 k * (I UA)k 8(Mg)),

                                        + Atn +1

U I448c
3(Po)k n +1
A(Uy)J .

k * (I UA)k 8(Uy);,

                                      +   Atn+1 aVg a            1448e

8(PD)k n +1
A(My)3 .

(I UA)k 8(My)), 144g

                                = At "'I

Uk a (I UA)g = [(P u )k - (P o )g + Rk+D} g (2.20-70) for non-critical flowlink k=1, .... K.

This concludes the discussion of the modifications to the finite-differencing of the momentum conservation equation.

  \d o:WO25wWO25-220a.wpf:Ib-022698                                                                                          Februart 1998 2.20-21                                                        kev 4

? L 2.20.2 Modifications to Finite-Differencing of Mixture Region Energy Conservation Equation i O for Interior Fluid Nodes In this section, the modifications to the finite-differencing of the mixture region energy conservation equation for interior fluid nodes are presented. The starting mixture region energy conservation L . equation for interior fluid nodes remains the same as it was in the original NOTRUMP central I I-numerics of Reference 2-1, and is given by Equation 2-1 of Reference 2-1: M =- M d ai [ * (Wh)" - ai ,[

Qx ***

g.i x.

                                                        -(Wh)MY - I44 . P; e d(V )i g

3 Joule dt l l for i = 1, ..., I, where: (Uu); = mixture region internal energy in interior fluid node i, Btu Q; D a[ 3

incidence matrix element between interior fluid node i and flowlink k M (Wh)i,g = energy flow rate convected to/from the mixture region ofinterior

                                                  - fluid node i via flowlink k, Btu /sec.

ai ,[ = incidence matrix element between interior fluid node i and heat link A M A*" = Qx heat rate to/from the mixture region of interior fluid node i via heat link A (= Qx M of Reference 2-1, with " heat" added to the superscript to emphasize that this is a heat rate, and is not to be confused with a volumetric flowrate), Btu /sec. L (Wh);MV = energy exchange rate from the mixture region to the vapor region of interior fluid node i, Btu /sec. P3 = pressure at the top of interior fluid node i, psia 1 February 1998 oM025wuo25-220c.wpf:1b-022798 2.20.2-1 Rev.4

(Vy); = mixture region volume in interior fluid node i, ft.3 J = Joule's constant, 778.156 ft. Ibf/ Btu (= J in Equation 2-1 of Joule Reference 21, with subscript " Joule" added for clarity, and to distinguish it from other uses of J) K* = total number of flowlinks (non<ritical and critical) L* = total number of heat links (non-critical and critical) I = total number of interior fluid nodes and the subscripts: i = interior fluid node k = flowlink (non-critical and critical) A = heat link (non-critical and critical) On the right-hand side of Equation 2.20-71, the incidence matrix elements ai ,[ are calculated by Equations 2-5 and 2-6 of Reference 2-1, for fluid node i and flowlink k, as follows: w (2.20-72) a i.k , 3 .U(k) i - 3 .D(k) i where i = 1, . . I and k = 1, ... K*. The term 6 is the "Kronecker delta," whose elements S t.m are given by: l . if f " m (2.20-73) 6 t.m = 0., if f

m he result for a ,[i is that for each flowlink (column) k of the incidence matrix, the element for each fluid node (row) i is zero, except for the two nodes that are connected to flowlink k, wherein the element is "+1." if fluid node i is upstream of flowlink k (i.e., i = U(k)), and the element is "-1." if fluid node i is downstream of flowlink k (i.e., i = D(k)). De U(k) and D(k) fluid node /flowlink network information is user-specified.

Analogously, the incidence matrix elements ia ,k are calculated for fluid node i and heat link A by: O February 1998 oM025wuo25-220c.wpf.lb-022798 2.20.2-2 Rev.4

  . __      .          . . _ . . _ _      .     . _ - _ . _ ~ . ._ _ _ _ _ _ _ . _ _ _ .                        _ _ _ - _ . . _ . _ . _ _ _

l a}=S,gg,)-S,g) i i i (2.20-74) l where i = 1, .... I, A = 1, ..., L*, S .mt elements are given by Equation 2.20 73, and the U(A) and DC.) fluid node / heat link network information is user-specified. > I M The term (Wh)ik in Equation 2.20-71 is given by Equation 2-7 of Reference 2-1, which is: ('Whift - C[i = (W )gg = (hry)i.k + Ci g8 (W,)g * (hgy)i k where:

Cig .= contact coefficient for partitioning the liquid flow in flowlink k that 1 enters / exits the mixture region of interior fluid node i ' Cs ig = contact coefficient for partitioning the vapor flow in flowlink k that enters / exits the mixture region of interior fluid node i (W r)g = liquid mass flow rate in flowlink k, Ibm /sec. ' (W,)k = vapor mass flow rate in flowlink k, Ibm /sec. (hry)i.k = convected specific enthalpy of the liquid flowing in flowlink k that ; enters / exits the mixture region of interior fluid node i, Btu /lbm l (hgy)i,g = convected specific enthalpy of the vapor flowing in flowlink k that enters / exits the mixture region of interior fluid node i, Btu /lbm Tne contact coefficients C;'k and C;,8 g are dependent upon fluid conditions and geometry. The details are contained in Appendix F (Section F-5) of Reference 2-1 (see Equations F-39 through F-44 of Reference 21), and in Section 2.6, and are not repeated here, since they do not impact the central numerics modifications for AP600. j The component mass flow rates (W g)g and (W s}k are related through Equation 2-34 of Reference 2-1, which is: [ (Wr)g + (W,)g = Wg (2.20-76) l 1. February 1998 ovo25.wo25 220c.wpr;ib.02279s 2.20.2-3 Rev.4

and they are calculated by the drift flux model equations in Appendix G of Reference 2-1. The mixture region related convected specific enthalpies (hr y)i.k and (hg y)i.k that appear in Equation 2.20-75, as well as the vapor region related convected specific enthalpies (hy)i,g and (hgy)i,g that are discussed and used in Section 2.20.4, are given by Equations 211 through 2-26 of Reference 2-1, which are (the equation order is rearranged slightly here to present the form for positive component mass flow rate first): If (W f)k 2 0.:

                                                                                                                                             --] 0t (2.20-77)

(2.20-78) (2.20-79) (2.20-80) If (W f)g < 0.: _ AO (2.20-81) (2.20-82) (2.20-83) (2.20-84) If (W,)g 2 0.: February 1998 eM0'5.wo25 220c.wpr; ibm 279s 2.20.2-4 Rev.4 l

                                                                                                                  - 4r b l-(2.20-85)
                                                                                                        ~

(2.20-86) l (2.20-87) _ (2.20-88) if (W,)g < 0.:

                                 ~
                                                                                                                   ~

q, 6 (2.20-89) l i s (2.20-90) l (2.20-91) l (2.20-92) where: -

(hy)i.k convected specific enthalpy of the liquid flowing in flowlink k that enters / exits the vapor region of interior fluid node i (to be discussed and used in Section 2.20.4), Btu /lbm (hgy)i,g = convected specific enthalpy of the vapor flowing in flowlink k that i: enters / exits the vapor region of interior fluid node i (to be discussed ( and used in Section 2.20.4), Bru/lbm I' (hy); = mixture region specific enthalpy in interior fluid node i, Btu /lbm I February 1998 oMo25wwns 220c.wpr:itw2279s 2.20.2-5 Rev.4

(hy); = vapor region specific enthalpy in interior fluid node i, Btu /lbm h g(Pi ) = specific enthalpy of saturated liquid as a function of the pressure P; in interior fluid node i, Btu /lbm h,(P i ) = specific enthalpy of saturated vapor as a function of the pressure P in interior fluid node i, Btu /lbm The equations for Pi , (hy )i, (hy)i, hfP ),i and h (P;) g are discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). The heat rate term QxM. heat in Equation 2.20-71 is given by Equation 2-36 in Reference 2-1, (from both Sections 2-1-7 and 2-1-8 in Reference 2-1) which is: M I Q ' '(P;, (Tg)i, T)) , for A = 1,....L (2.20-93) OA. heat Q,ht(t) , for A = L +1,...,L

where:

(Ty); = mixture region temperature in interior fluid node i associated with non-critical heat link A, *F l-j Tj = temperature of metal node j associated with non-critical heat link A,

                                        *F L                   =        total number of non-critical heat links l

and the subscript: j = metal node h The heat rate function Q eat of Equation 2.20-93 for non-critical heat links is dependent irgon the heat transfer regime. The details are contained in Section 6 of Reference 2-1, and in Sec+. ions 2.14,2.15, and 2.19, and are not repeated here since they do not impact the centai numerics r'.odifications for AP600. The equation for (T y); is discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). As explained in Reference 2-1. T) is a NOTRUMP central numerics variable for interior metal nodes O February 1998 ou025mJ-220c.wpf:Ib-022798 2.20.2-6 Rev.4

f~j s

     - j = 1, ... J, or is given by a user-specified function per Equation 2-32 of Reference 2-1 for boundary metal nodes j = J+1, .... J , where:

i J = total number ofinterior metal nodes J* = total number of metal nodes (interior and boundary)

       'Ihe mixture-to-vapor region energy exchange rate (Wh);MV in Equation 2.20-71 is given by l       Equation 2.9-77:

(Wh)iMV = @)iMIV + (WBR)is = (h )i - (WDF)i f (h )i (2.20-94) where: (Wh);MIV = interfacial energy transfer rate from mixture to vapor region in interior fluid node i due to evaporation and/or condensation, Btu /sec. (Wag); _= bubble rise mass rate (from mixture to vapor region) in interior fluid j - node i, Ibm /sec.

(~% (WDF)i = droplet fall mass rate (from vapor to mixture region) in interior fluid O node i, Ibm /sec.

(hr)i = hfP), defined above, Btu /lbm (h,); = h,(P i), defined above, Btu /lbm The terms (Wh)iMIV '(Wag)i, and (Wpp)i are discussed in Section 2.20.9. As mentioned above, the terms (hf ); and (h,)i rea discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). The last term on the right-hand side of Equation 2.20-71 contains the temporal derivative of d(Vy)I (V y )i,~ . (V )iy is discussed in Appendix L of Referen < 2-1 (see the Section 2.20.8 dt summary). i em EU February 1998 ovo25vMo25-220c.wpr: iso 2279s 2.20.2-7 Rev.4

                                                                                   ._.         . ~ .

{ i Finite-differencing of Equation 2.20-71 yields: M =- a[ = (Wh)ff"4 - 3 a3 ,k = (Qx****)"*l At" kW A4 n +1

                                           - (Wh),MV,n +1 ,

144 , p n +1, O(YM)i (2.20-95) 3 Joule At"*3 for each interior fluid node i = 1, ..., I. Each transient term in Equation 2.20-95 is now examined. On the left-hand side of Equation 2.20-95, A(U )3y "+ 1 is one of the central numerics unknown variables for interior fluid node i to be solved for. The time step size At"+1 was briefly discussed in Section 2.20.1.2. f On the right hand side of Equation 2.20-95, (Wh)['"*I is (from Equation 2.20-75): (Wh)fi"d = (C ,'g)"*l = (Wr )"*3 = (hgg)[,[ + (C i ,[)"*3 = (W,)"*3 (hgy)n*l (2.20-96) _. - 0, L dib (2.20-97) (2.20-98) (2.20-99) (2.20-100) m w220c.wpfMJ798 2.20.2-8 Nev.

( l-l l- i j g In general, the new time component mass flow rates are expressed as: l l

(Wr)[d = (W r)g + A(W gg )"d C4% l (Wg)ld = (W g)g + A(Wg )l4 (2.20-102) i

!- mass flow rates are linearized only with re et to the net flow rate in the flowlink (i.e., all other

j. the original numerics with the net mass flow based

l formulation, this resulted in the following: 4,C (2.20-103) l l !p %J - (2.20-104) _ 1 3(W g)g 8(W8)k where the partial derivatives and were calculated by the drift flux model equations SW k OW k _ of Appendix G of Reference 2-1 (in particular, Equations G-34 and G 35, respectively, of-Reference 2-1; it is also noted that the latter are repeated as Equations 2.4-20 and 2,4-21, respectively). Similarly, in the modified NOTRUMP central numerics for AP600 with the net volumetric flow-based ( formulation, the component mass flow rate increments become: 0.S (2.20-105) l (2.20-106) 1 ( l February 1998 oM025wwo25-220c.wpt:1b-022798 2.20.2-9 Rev.4

8(W f)k 8(Wg)k where the partial derivatives and are calculated by the drift flux model equations of BQt SQg Appendix G of Reference 2-1, using the volumetric flow-based formulation as explained in Section 2.4, i.e., Equations 2.4-22 and 2.4-23, respectively. Thus, Equation 2.20-96 in the modified NOTRUMP central numerics becomes: A (. - (2.20-107) which is placed in the following convenient form of: (2.20-108) (Wh)$'"d = (Wh)" + A(Wh)M "4 where:

                                                                             - 05 (2.20 109) and 8(Wh)"
                               ' = C ,'g        I i

B(W )k * (hry)i,g + C sB(W

                                                                         , s k = (hgy);,g           (2.20-110) gg                                     ik Equation 2.20-110 is the same as Equation 2.4-16.

Equations 2.20-108 through 2.20-110 apply to all flowlinks, non-critical and critical, i.e., k = 1, ..., l K*. For non-critical flowlinks k = 1, .... K, AQg"+1 is the (new) central numerics unknown variable to be solved for. For critical flowlinks k = K+1, ..., K*,4Qg"+3 is discussed below. In the original NOTRUMP central numerics of Reference 2-1 with the net mass flow-based formulation, the mass flow rate of critical flowlink k was given by a user-specified function of the ovo25.wo25-220c.wpt;ib-022798 2.20.2-10 ev.

i pressure and region specific enthalpies of both the upstream and downstream fluid nodes (per Equations 2-35 and 5-9 through 5-15 of Reference 2-1) as follows: Wk= W (P 3, (hy ),, (hy),, Pj , (h y ),, (hy )j )' (2.20-111) for critical flowlink k = K+1, ..., K* in the mass flow-based formulation, where the subscripts: i = fluid node upstream of flowlink k (= U(k)) i j = fluid node downstream of flowlink k (= D(k)) Thus, in finite-difference form: i

Wg "4 =Wk + AWk

                                                                                                                                 ~
                . where:

sl n v (2.20-113) For consistency in the new NOTRUMP central numerics for application to AP600 with the net volumetric flow-based fonnulation, the volumetric flow rate of critical flowlink k is optionally (via user-specified ITYPEFL(k) = -11) given by the following analogous user-specified function of the pressure and region specific enthalpies of the upstream and downstream fluid nodes: Qg = Q (Pi , (hy )i, (h y)3, Pj , (hy)), (hy)) ) (2.20-114) so that: Qg"+1 = Qg + AQg"+1 (2.20-115) l l n l ( ,.) t

              . oM025wWn5-220c.wpf:Ib-022798 February 1998 2.20.2-11                                       -Rev.4-l-

l

where: Q, 6 (2.20-116) for critical flowlink k = K+1, ..., K* in the volumetric flow-based formulation. The pressure and region specific enthalpies of the fluid nodes are expressed in terms of the fluid node central numerics variables as discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary) so that for fluid node i: O l l (2.20-117) l l (2.20-118) h e oMo25wo25-220c.wpf:lt422798 2.20.2-12 *Nev. I

  . .    . . -      -         -          - . ~ . . , . - - . .         .- - - - - .   .. ..        - . - . . . . . ~ . . .

l OtD D V (2.20-119) The expressions for fluid node j are identical to Equations 2.20-117 through 2.20-1195ith subscript i , changed to j. Thus, AQg"+I for entical flowlink k is expressed in terms of the central unknown variables for both ! fluid node i and fluid node j, and Equation 2.20-116 becomes: l l l l O l l (2.20-120) 1 where, for the fluid node i partial derivatives: 4:0 (2.20-121) j

. O oM025wWO25-220c.wpf:1b-022798 February 1998 2.20.2-13                                      Rev.4

w

                                                                                                                       . Qh (2.20-122)                   O                        i (2.20-123)

(2.~20-124)

           ._                                                                                                         _1 The expressions for fluid node j are identical to Equations 2.20-121 through 2.20-124 with subscript i changed to j.

As was the case in the original NOTRUMP central numerics of Reference 2-1, the following approximation is then made to neglect the coupling between fluid nodes via critical flowlinks. The nodal unknowns for the downstream fluid node j in the upstream fluid node i conservation equations , which result from the critical flowlink k AQ k"+ expression are ignored (i.e., fluid node j terms are treated explicitly with respect to fluid node i equations), and vice versa. Thus, in the fluid node i conservation equations, Equation 2.20-120 is approximated as follows:

                                                                                                                ~ 0, l (2.20-125) and in the fluid node j conservation equations, Equation 2.20-120 is approximated as follows:
                ~
                                                                                                                  -00  1
                ~~

1 February 1998 omwe-220c.wpr.lW798 2.20.2-14 Rev.4

aA (2.20-126) for critical flowlink k = K+1, ..., K*. , M Retuming to Equation 2.20-95, the (Qx .hemyn+1 term is expressed generally as: I l P M M M O . heat + A(Qx . heat)n+1 , for A = 1,..., L (q . heat)n+1 ,< A (2.20-127) l ,Q $* (t"*I) , for A = L +1,..., L

I where, for non-critical heat link A = 1, ..., L :

                              ~                                                                                         ~

diO l0 (2.20-128) l where: 1 1 aj $.MNE = incidence matrix element between metal node i and heat link A (hence the "MN/HL" superscript) It is noted that while from the fluid node i perspective, the right-hand side of the fluid node i mixture L* M region energy conservation equation contains the term"- { aj ,[ . Qx #**" as shown in Equation A-1 2.20-71, similarly from the metal node j perspective, the right-hand side of the metal node i energy L* conservation equation contains the term "- { a}MNE j GAM.hea" as shown in Equation 2-31 in A=1 f] v Reference 2-1, where the clernentj a $#"" is from the metal node / heat link incidence matrix. This oM025wWO25-220c.wpf.lb-022798 February 1998 2.20.2-15 Rev.4 l

nomenclature differs slightly from that for ai ,[ for fluid nodes /flowlinks, because a flowlink always connects two fluid nodes, while a heat link always connects a fluid node to a metal node. In Equation 2.20-128, AP;"+1 is given by Equation 2.20-117, ATj "+I is the central numerics unknown variable for metal node j, and since (Ty)3 is expressed in terms of fluid node i central numerics variables as discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary), A(T )3y "+1 is given by: ,

                                                                                          "OL      f l

! (2.20-129) l The partial derivatives of QxMheat in Equation 2.20-128, which are dependent upon the heat transfer regime, are described in Section 6 of Reference 2-1, and are not repeated here since they do not impact the central numerics modifications for AP600. l Thus, for non-critical heat link A = 1, ..., L, Equation 2.20-128 becomes: O l l

                                                                                              ~
                   -                                                                              0, (.,

I (2.20-130) O o:w25.w25 220c.wpr:itm22798 2.20.2-16 "Sev.1

i j l i js where- I (): \

Qil

(2.20-131)

(2.20-132)

                                                                                                       -(2.20-133)

(9-N./ (2.20-134) For critical heat links A. = L+1, ... L*, Qf*,*/ (t"4) in Equation 2.20-127 is known at the new time 1"+ 3 M It is noted that all of the above for (Qx ***')"I (Equations 2.20-127 through 2.20-134) are the same as in the original NOTRUMP central numerics of Reference 2-1. As discussed in Section 2.20.9, (Wh);MV is only a function of fluid node i quantities, such that the (Wh); MV'"+1 term in Equation 2.20-95 is expressed generally as: (Wh),P'"*I = (Wh)MV qqMV "*l (2.20-135) l l O eMo25wws220c.wpr: b422798 2.20.2 17 ey?I

WESTINGHOUSE PROPRIETARY CLASS 2 where: 6tC (2.20-136) 4 The panial derivatives in Equation 2.20-136 are discussed in Section 2.20.9. Expansion of the last term on the right-hand side of Equation 2.20-95, ignoring the product of two A's, yields:

                                                                                         -    e,C-(2.20-137)
                  ~

As discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary), (Vy); is expressed in terms of the fluid node i central numerics variables, so that:

del l l l (2.20-138) Thus, substituting Equations 2.20-108, 2.'20-109, 2.20-125, 2.20-127, 2.20-130, and 2.20-135 through I 2.20-138 into Equation 2.20-95 places the finite-difference form of the mixture region energy conservation equation in terms of the (new) NOTRUMP central numerics unknown variables as follows: M V

=-

a,[ j = (Wh)$ 1-17.,j a j = Qx . heat , At "*I bl ow2sww.5 220c.wpt:1b.02279s February 1998 2.20.2-18 Rev.4

. .-..-.                                                                                                                                                                                 tr tg
    \                                                                         K 1

{ a,w ik

3(Wh)M* A9 k+1

                                                                                                           'k           n k =1                       k M Al Y '

I l

l. ,

l r i 1 l l 4 1 (- i~ -,

           ~
         . owns.wns-220s.wpfab 022798                                                                                                                                 February 1998 2.20.2-19                                                                              Ro, 4               '

t

  .    -                      . . . . , - . .v --
                                                       -        - ,..,                  , - , , . - .         ,      e    .    -r                ..,--. - - . - ., --      -        +   -m. w

1 I

                                                                                           ~ 01D I

l l (2.20-139) s for interior fluid node i = 1, ... I. l 1 l It is noted that the second term on the right-hand side of Equation 2.20-139 indudes the new time value of (Qf***)"+1 for critical heat links A=L+1, .... L* via Equation 2.20-127, whc-- the "n+1" superscript has been dropped to allow combination of the critical heat link terms with the explicit

. terms for non-critical heat links (A=1, ..., L) together with one summation term.

l Multiplying both sides of Equation 2.20-139 by At n+1 and collecting all central numerics unknowns on the left-hand side yields: At"*l . aj ,[ . 'k . A Q g"+1 l k =1 bQ k

                                                                                                ~
               --                                                                                     41 6 1

_. i l l Ol' e.

  . -              ,, _ ,s                           2.20.2 2,                                       y.,

1

l l l i f

                                                                                                                                                      &, L l.

i r-I I l L \ I r l L t i t - y 4

N W -220e wp u u 2279s

                                              .                                                                                           Febru     1993 2.20.2-21                                          ev.4

Qil O 4 ( M J K* L* [ a *g* (Wh),$ + { a ,ki = QxM #'" + (Wh)fiv (2.20-140) ?

                       = - At " 4

kW A -1 1 For interior fluid node i = 1, ..., I.

This concludes the discussion of the modifications to the finite-differencing of the mixture region energy conservation equation for interior fluid nodes. O o:wo25m5-2Ioc.wpf:Ib-02 79s Febru 998 2.20.2-22

l

r. 2.20.3 Modifications to Finite Differencing of Mixture Region Mass Conservation Equation for i

k, Interior Fluid Nodes l In this section, the modifications to the finite-differencing of the mixture region mass conservation equation for interior fluid nodes are presented. The starting mixture region mass conservation equation for interior fluid nodes remains the same as it was in the original NOTRUMP central numerics of l Reference 2-1, and is given by Equation 2-2 of Reference 2-1. i d(My) K*

                                                   ,_              ,w y    -W iMV                     (2.20-140) dt          k=1 for i = 1, .... I, where:

1 1 (My): = mixture region mass in interior fluid node i, Ibm

w l "i,k = incidence matrix element between interior fluid node i and I flowlink k 1 G (

 /)             Wi,k M
                                   =      mass flow rate convected to/from the mixture region ofinterior fluid l
                                                                                                                    )

node i via flowlink k, Ibm /sec. W iMV = mass exchange rate from the mixture region to the vapor region of interior fluid node i, Ibm /sec. i l K* = total number of flowlinks (non-critical and critical) I = total number of interior fluid nodes and the subscripts: i = interior fluid node l k = flowlink (non-critical and critical) ; w On the right-hand side of Equation 2.20-140, the incidence matrix elements "ik are discussed in

Section 2.20.2 (see Equations 2.20-72 and 2.20-73). The term i-in Equation 2.20-140 is given by February 1998 cuo25wwo25-220d.wpt; ibm 269s 2.20.3-1 Rev.4

Equation 2-8 of Reference 2-1, which is: 8 (2.20-141) Wi *k = C ,Ii g = (W f )g + Ci g = (W,)g where: Ci .'k = contact coefficient for partitioning the liquid flow in flowlink k that enters / exits the mixture region of interior fluid node i C ik

            .g
                             =     contact coefficient for partitioning the vapor flow in flowlink k that enters / exits the mixture region of interior fluid node i (W r)g              =     liquid mass flow rate in flowlink k, Ibm /sec.

(W,)g = vapor mass flow rate in flowlink k, Ibm /sec. I' As stated in Section 2.20.2 the contact coefficients are discussed in Appendix F (Section F-5) of Reference 2-1, and in Section 2.6. The component mass flow rates (Wg )g and (Ws)k are discussed in Section 2.20.2 (see Equation 2.20-76), and are calculated by the drift flux model equations in Appendix G of Reference 2-1. MV The mixture-to-vapor region mass exchange rate W3 in Equation 2.20-140 is given by I Equation 2.9-76: l W;MY = W;MIY +(Wag); -(WDF)i l where: WMIV i

                             =     interfacial mass transfer rate from mixture to vaper region in interior fluid node i due to evaporation and/or condensation, Ibm /sec.

(Wag)3 = bubble rise mass rate (from mixture to vapor region) in interior fluid node i, Ibm /sec. February 1998 eMo25wwo:5-220d.wpf:st422698 2.20.3-2 Rev.4

(Wap); = droplet fall mass rate (from vapor to mixture region) in interior fluid

                                                                       - node i, Ibm /sec.
                                                                                       ~
                                                                                                                                                                                       \

The terms WMIV (Wag)i, and (Wop)3 are discussed in Section 2.20.9. Finite-differencing of Equation 2.20-140 yields: 0 M =- I ai ,[

W;$'" - W MV.n +1 3 (2.20-143)

At"*I k=1 for each interior fluid node i=1,... I. Each transient term in Equation 2.20-143 is now examined. On the left-hand side of Equation 2.20-143, A(M )iy "+1 is one of the central numerics unknown variables for interior fluid node i to be solved for. 'Ihe time step size At"+1 was briefly discussed in Section 2.20.1.2. On the right-hand side of Equation 2.20-143, W;$.n+1 is (from Equation 2.20-141) : I Wi $'"*' = (C;,I)"*I g a (Wr)"*' + (Ciks)n+1, (w )n+1 g (2.20-144) D

                                                                                                                                                                         - a.,c.

i . Thus, Equation 2.20-144 becomes: s ,. Wj'"*I =W i3M+ AW;M.n+1 (2.20-145) l' i l- where: (

                                                                                                                                     . a,t (2.20-146) 1                                                                          ~                                                          ~

February 1998 4 o wo25.wo25 220d.wpt:1b 022698 2.20.3-3 Rev.4 l l- , , - - - . - . .- .- .. . - . - - . . ,- - . . - --

and' l l BW;,M g I 8 ( g)k (2.20-147) SQg Ci'k = SQg k+CI'k . BQ k l Equation 2.20-147 is the same as Equation 2.4-17. As explained in Section 2.20.2, AQg"+3 is the central numerics unknown variable for non-critical flowlinks k=1, .... K, and is given by Equation 2.20-120 for critical flowlinks k=K+1,... , K* The latter is approximated by Equation 2.20-125 in the fluid node i conservation equations, or is approximated by Equation 2.20-126 in the fluid node j conservation equations (where i = U(k) = upstream node, and j = D(k) = downstream node). As discussed in Section 2.20.9, W i MV is only a function of fluid node i quantities, such that the W;MV"+3 term in Equation 2.20-143 is expressed generally as: W iM V'" *I = W.MV i + AW;MV "+1 (2.20-148) where: O

                                                                                     - 4,c i

l (2.20-149) l l 1 l The partial derivatives in Equation 2.20-149 are discussed in Section 2.20.9. l Thus, substituting Equations 2.20-145,2.20-146 (with 2.20-125),2.20-148, and 2.20-149 into Equation 1 1 2.20-143 places the finite-difference form of the mixture region mass conservation equation in terms of the (new) NOTRUMP central numerics unknown variables as follows: i l O l 1 February 1998 omww.5 220iwpr;it>c22698 2.20.3-4 Rev.4 l

, ..... . . . . - - ~ ~ . . . _ . . . .

                                                     . . . ~ . . - . . . ~ .           . . . _ _ -            ~ . .        .                                              . . -      . . .

4 A(M Mi)"*I K* M At.4-

                                                                             - - E a,,W, . w,,,- w,MV                                                                                     ;

k.: w I 1- - { a ,g j . BW i. f .AQg n

                                                                                                                             +1 k =1                 SQk
                                                                                                                                        .-                     c.

1-r m J 4 4 4. f f i l . I l 1 (2.20-150) )- i , for interior fluid node i = 1, ,..., I. a a i 1 d 1 4 4

i. .

4 1 February 1998 oM025wwn5-220d.wpf:Iba9s 2.20.3-5 lley, 4 i i

  -                      ,y   . --.. ,              p    --.--b                      -    -,.s,_--
                                                                                                         %        .-----        . , - - . . . - , - - . . . - ~                 y- -

Multiplying both sides of Equation 2.20-150 by At"+1 and collecting all central numerics unknowns on the left-hand side yields: At"4 = I'" ai ,[ *

AQ"*I k =1 k

                                                                                          - . e., c.

O

K*

                                  = - At"+1     { a ,[i = W if + W,uv                       (2.20-151) k =1 for interior fluid na i=1, .... I.

This concludes the discussion of the modifications to the finite-differencing of the mixture region mass conservation equation for interior fluid nodes. O c:wo25wwo25-220d.wpr.1b-022698 2.20.3-6 ev. k

f p, 2.20.4 Modifications to Finite-Differencing of Vapor Region Energy Conservation Equation for l V Interior Fluid Nodes l~ In this section, the modifications to the finite-differencing of the vapor region energy conservation equation for interior fluid nodes are presented. The starting vapor region energy conservation equation for interior fluid nodes remains the same as it was in the original NOTRUMP central numerics of Reference 2-1, and is given by Equation 2-3 of Reference 2-1: d(Uy )i , _ [ , w , _ , v, heat dt k4 14 l

                                                 + (Wh),MV - I44 .P=               d(Vy)i (2.20-152) 3 3

Joule dl for i=1, . . I, where: (Uy); = vapor region internal energy in interior fluid node i, Btu

W a i.k = incidence matrix element between interior fluid node i and flowlink k V (Wh)i.k = energy flow rate convected to/from the vapor region of interior fluid node i via flowlink k, Btu /sec. Q

               *i A                =

l incidence matrix element between interior fluid node i ano s 'k A V 'h'*' Qx = heat rate to/from the vapor region of interior fluid node i via heat V link 1 (= Qx of Reference 2-1, with

heat" added to the superscript to emphasize that this is a heat rate, ed is not to be confused with a volumetric flow rate), Btu /sec.

MV = (Wh)3 energy exchange rate from the mixture region to the vapor region of interior fluid node i, Btu /sec. l February 1998 l eM025wuo25-220e.wpf:1b-022698 2.20.4-1 Rev.4

l P = pressure at the top on' interior fluid node i, psia j l (Vy); = vapor region volume in interior fluid node i, ft.3 I J w, = Joule's constant,778.156 ft. Ibf/Bru (= J in Equation 2-3 of Reference 2-1, with subscript " Joule" added for clarity, and to distinguish it from the other uses of J) K* = total number of flowlinks (non-critical and critical) L* = total number of heat links (non-critical and critical) I = total number of interior fluid nodes and the subscripts: i = interior fluid node k = flowlink (non-critical and critical) A = heat link (non-critical and critical) On the right-harn side of Equation 2.20-152, the incidence matrix elementsi a ,[ and aj ,f are discussed in Section 2.20.2 (see Equations 2.20-72 through 2.20-74). The term (Wh)# i.k in Equation 2.20-152 is given by Equation 2-9 of Reference 2-1, which is: (Wh)[k = (1. - Cik.I) . (W r)k * (hf y);,g + (1. - C;s) g * (W g)g (hgy)i,g (2.20-153) where: Ci .'k = contact coefficient for partitioning the liquid flow in flowlink k that enters / exits the mixture region of interior fluid node i Cik.8 = contact coefficient for partitioning the vapor flow in flowlink k th tt enters / exits the mixture region of interior fluid node i February 1998 c:wo25wuo25-220e.wpf:lt422698 2.20.4-2 Rev.4

  -     - - - . . -                .-       .~ - .                  . . . - . . . . - - . _ - -                . . - - . - - -                   . _ . .

l l l (W)k r = liquid mass flow rate in flowlink k. Ibm /sec. l (Ws)k = vapor mass flow rate in flowlink k, Ibm /sec. (hry)j,g = convected specific enthalpy of the liquid flowing in flowlink k that l enters / exits the vapor region of interior fluid node i, Bru/lbm (hgy)i.k = convected specific enthalpy of the vapor flowing in flowlink k that enters / exits the vapor region of interior fluid node i, Bru/lbm As stated in Section 2.20.2, the C;[ and C;j contact coefficients are discussed in Appendix F

          - (Section F-5) of Reference 2-1, and in Section 2.6. The component mass flow rates (W                               g   )g and (W,)g are discussed in Section 2.20.2 (see Equation 2.20-76), and are calculated by the drift flux model equations in Appendix G of Reference 2-1. The vapor region related convected specific enthalpies (hry)i.k and (h gy);,g are defined in Section 2.20.2 (see Equations 2.20-77 through 2.20-92).

l V The heat rate term Qx . heat in Equation 2.20-152 is given by Equation 2-37 in Reference 2-1 (from both Sections 2-1-7 and 2-1-8 in Reference 2-1), which is: I ' V. heat g heat (P ,(T y )i, T)), for A = 1, . . L (2.20-154) Q,h*'*(t)

                                                      ,,                     , for A = L + 1, .., L

where:

(Ty); = vapor region temperature in interior fluid node i associated with non-critical heat link A, 'F Tj = temperature of metal node j associated with non-critical heat link A,*F L = total number of non-critical heat links l' i l and the subscript: i j = metal node ) h The heat rate functicn Q eat of Equation 2.20-154 for non-critical heat links is dependent upon the heat transfer regime. The details are contained in Section 6 of Reference 21, and in Sections 2.14,2.15, February 1998 oMo25wwns 220e.wpr.1w22698 2.20.4-3 Rev.4

and 2.19, and are not repeated here sitce they do not impact the central numerics modifications for AP600. The equation for (Ty)3 is discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). As explained in Reference 2-1, T) is a NOTRUMP central numerics variable for interior metal nodes j = 1, ..., J, or is given by a user-specified function per Equation 2 32 of Reference 2-1 for boundary metal nodes j = J+1, ... J*, where: J = total number of interior metal nodes J* = total number of metal nodes (interior and boundary) MV in Equation 2.20-152 is presented in The mixture-to-vapor region energy exchange rate (Wh)i Section 2.20.2 (Equation 2.20-94), which is also equivalent to Equation 2.9-77. The last term on the right-hand side of Equation 2.20-152 contains the temporal derivative of (Vy )i, y d(V )' . (V y), is discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). dt Finite-differencing of Equation 2.20-152 yields: (UV) ,, W , n +1 , Q, V.hea n +1 O j At"*1 k -1 A -1 l 4

                                           .        MV,n +1 _ 144      , p n +1, A(Vy)f                  (2.20-155) 3 Joule               At " *I for each interior fluid node i = 1, ..., I. Each transient term in Equation 2.20-155 is now examined.

On the left-hand side of Equation 2.20-155, A(Uy);"+I is one of the central numerics unknown variables for interior fluid node i to be solved for. The time step size At"+I was briefly discussed in Section 2.20.1.2.

                                                                #'" 'I On the right-hand side of Equation 2.20-155, (Wh)i k is (from Equation 2.20-153):

O oMo25ww_5-220e.wpt:Ib-022698 2.20.4-4 v

                                                                                                                                                        'I ik .I) *. (Wr )['I *(hy)[i
                                                                                      =

(Wh)[i"'I 1. -- (C g

                                                                                      +    1. -(C s)n+1 g          , (w ){+1   g          * (hsV) .k V                         .
                                                                                                                                                                                                  . . = ,c.
                                                                           .-                                                                         . g, t.

(2.20-157) l (2.20-158) l .

                       '~
                                                                                                                                                                                                -   a., L a

b

%.)

Thus, Equation 2.20-156 becomes: ! (Wh)[f"*I = (Wh) k + A(Wh),V;n+1 (2.20-159) where: g (2.20-160) l and: l.- (2.20-161) r. t. 8(Wh)y i'k g

                                                                      = (1 - Cik .f )

B(W )g y* (h )i,g + (1.

i - C {)

B(W 8 )g

                                                                                                                                                                 . (h,y)i.k 39 l

l, J

   .                       Equation 2.20-161< is the same as Equation 2.4-18.

p U i : February 1998 oM025wwo25-220e.wpf;1b 022698 2.20.4-5 Rev.4

As explained in Section 2.20.2, AQg"+1 is the central numerics unknown variable for non-critical flowlinks k = 1, ... K, and is given by Equation 2.20-120 for critical flowlinks k = K+1, ... K* The latter is approximated by Equation 2.20-125 in the fluid node i conservation equation, or is approximated by Equation 2.20-126 in the fluid node j conservation equations (where i = U(k) = upstream node, and j = D(k) = downstream node). V The (Qx .heatyn+1 term in Equation 2.20-155 is treated analogously to the (QxMAcat)n+1 term in V Section 2.20.2 (see Equations 2.20-127 through 2.20-134). Thus, (Qx . heat)n+1 is expressed generally as: V

                                                                )"*I , for A = 1,...,L g , heat yn+1 , . OA

O(OA V (2.20 162)

Qf3,***(t"*l) , for A = L + 1,..., L

where, for non-critical heat link A = 1, ..., L:

                                                                                               - A., C-0 (2.20-163)
                    ~                                                                          ~

! where: Q,MNML "i A = incidence matrix element between metal node i and heat link A l (hence, the "MN/HL" superscript) In Equation 2.20-163, AP i "+1 is given by Equation 2.20-117 in Section 2.20.2, AT)"+1 is the central numerics unknown variable for metal node j, and since (Ty)3 is expressed in terms of fluid node i central numerics variables as discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary), A(Ty),"+1 is given by: i om3*ms-220e..rt:ib-o22698 2.20.4-6 ev.

    . - .  . _ ~ . - . . - . . . . .      . . - -   . .- __- _. - .__ - .- .. . - . . . - . . . . . - . . . . . - .                                  . . . --
                                        .                                                                                        a,c O

(2.20-164) V The partial derivatives of Qx 'h'** in Equation 2.20-163, which are dependent upon the heat transfer regime, are described in Section 6 of Reference 2-1, and are not repeated here since they do not impact the central numerics modifications for AP600. Thus, for non-critical heat link A=1, ..., L, Equation 2.20-163 becomes:

                                     -                                                                                             - 4,C O

(2.20-165) where:

                                                                                                                                   - R, '

(2.20-166) (2.20-167) l i February 1998 c:wo25wwo25 220e.wpf:1b-022698 2.20.4-7 Rev.4

                                                                                         -   q., C (2.20-168)

(2.20-169) For critical heat links A = L+1, ..., L*, Qf*,*/ (t"*I) in Equation 2.20-162 is known at the new time 1"+ I . It is noted that all of the above for (Qx .Vheat)n+1 (Equations 2.20-162 through 2.20-169) are the same as in the original NOTRUMP central numerics of Refercnce 2-1. MV "+1 The term (Wh)i in Equation 2.20-155 is given by Equations 2.20-135 and 2.20-136 in Section 2.20.2. Expansion of the last term on the right-hand side of Equation 2.20-155, ignoring the product of two l A's yields: l l

                                                                                              .    ,c (2.20-170)

As discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary), (V y)3 is expressed in terms of the fluid node i central numerics variables, so that: O ovo23wwo25-220e.wpr:tb-02269s 2.20.4-8 ev

l l 6., C O t L (2.20-171) L _ Thus, substituting Equations 2.20-135, 2.20-136, 2.20-159, 2.20-160 (with 2.20-125), 2.20-162, l 2.20-165, and 2.20-170 into Equation 2.20-155 places the finite-difference form of the vapor region energy conservation equation in terms of the (new) NOTRUMP central numerics unknown variables as , follows: K* L* A(Uy))M 3, , - 3 al * (Wh(aj -* Qx*" +(Wh)fV l l k, l [} v ua a ao, Q'n d

                                                                                                        -   s,c i

C d l 0:MN-220e.wptit>.022698 2.20.4-9 * *Tyfl t

n , c. O l 1 O, (2.20-172) for interior fluid node i = 1, ..., I. It is noted that the second term on the right-hand side of Equation 2.20-172 includes the new time V value of (Qx ,heatyn+1 for critical heat links A = L+1, ..., L* via Equation 2.20-162, where the "n+1" superscript has been dropped to allow combination of the critical heat link terms with the explicit terms for non-critical heat links (A = 1... L) together with one summation term. February 1998 c:wo25.wo25-220e.wpf:1b 022698 2.20.4-10 Rev.4

l. - - _ . _ .._.._ .-.__ _ -...._.._ ._ - . _ _ . . . _ . . _ . . _ ._ _ . _l

'.r j L Multiplying both sides of Equation 2.20-172 by At"+I and collecting all central numerics unknowns on the left-hand side yields: t 5 f At "*I ik aj ,[ .

AQ k"*I , l k.1 Mk j i

l

                                                                                                          .                             -- gL 1

i I i l t ! r. D l l L L l i t l i t. ( - I t

              *2eJ220c.wpf;lb-022698                                                                                                February 1998 l                                                                                     2.20.4-1i                                              Rev.4 i

l

                ..:,,.      -,   ,      ,.,+ - ..               ---

                                                                                                  .AN e

. ~

O i

K' L'

                        = - At " 4 =                                                            (2.20-173)

I a i,[ . (Wh)(k + 11E k =l i a f a Q[, heat - (Wh),1V for interior fluid node i = 1, .... I. This concludes the discussion of the modifications to the finite-differencing of the vapor region energy conservation equation for interior fluid nodes. e E

N

1 i i l i l 2.20.5 Modifications to Finite Differencing of Vapor Region Mass Conservation Equations for { Interior Fluid Nodes 1

In this section, the modifications to the finite-differencing of the vapor region mass conservation equation for interior fluid nodes are presented. The starting vapor region mass conservation equation j for interior fluid nodes remains the same as it was in the original NOTRUMP central numerics of l' Reference 2-1, and is given by Equation 2-4 of Reference 2-1: J l' 1 d(Mv)i , _ K (2.20-174) ai

W i,[ + W;MV dt kl l

for i = 1, ..., I, where : (My); = vapor region mass in interior fliid node i, Ibm w

                   *i k     =

incidence matrix element between .'nterior fluid node i and flowlink k v i.k l , = mass flow rate convected to/from the vapor region of interior fluid node i via ' flowlink k, Ibm /sec. W iMV = mass exchange rate from the mixture region to the vapor region ofinterior fluid node i, Ibm /sec. I K* = total number of flowlinks (non-critical and critical) l I = total number of interior fluid nodes 1 and the subscripts : i = interior fluid node k = flowlink (non-critical and critical) On the right-hand side of Equation 2.20-174, the incidence matrix elements a;[ are discussed in f l Section 2.20.2 (see Equations 2.20-72 end 2.20-73). The term wi,kV in Equation 2.20-174 is given by Equation 2.10 of Reference 2-1, which is: February 1998 omswwns-nor.wpr: b. oms 2.20.5-1 Rev.4

Wi,[ = (1. - C i,[) (Wr )g + (1. - C,g) g , (w g)k (2.20-175) where: C;,'g = contact coefficient for partitioning the liquid flow in flowlink k that enters / exits the mixture region of interior fluid node i C;8g = contact coefficient for partitioning the vapor flow in flowlink k that enters / exits the mixture region of interior fluid node i l 1 (W g)g = liquid mass flow rate in flowlink k, Ibm /sec. (W)kE

                  =           vapor mass flow rate in flowlink k, Ibm /sec.

As stated in Section 2.20.2, the C;,[ and C;8k contact coefficients are discussed in Appendix F (Section F-5) of Reference 2-1, and in Section 2.6. The component mass flow rates (Wr)g and (W,)g l are discussed in Section 2.20.2 (see Equation 2.20-76), and are calculated by the drift flux model l equations in Appendix G of Reference 2-1. The mixture-to-vapor region mass exchange rate W MV in Equation 2.20-174 is presented in Section 2.20.3 (Equation 2.20-142), which is also equivalent to Equation 2.9-76. l l Finite-differencing of Equation 2.20-174 yields: A(My)[ K*

                                               , _ E a ,[i a W [g'"*I                                                        +W Mv.n +1 3

(2.20-176) i At"*3 k-t l l for each interior fluid node i = 1, .... I. Each transient term in Equation 2.20-176 is now examined. l

                                                                                                                "+1 On the left-hand side of Equation 2.20-176, A(My)i                                                                 is one of the central numerics unknown variables for interior fluid node i to be solved for. The time step size At"+3 was briefly discussed in Section 2.20.1.2.

Y'" *I On the right-hand side of Equation 2.20-176, Wi k is (from Equation 2.20-175) : O February 1998 omSN-220f wrf:1b-022698 2.20.5-2 Rev.4

         . ..-.    ... ..        -            -   . . . - - _                  . - . . ~ . - . .       . ._.     .    . - - _ -

l ! /G (2.20-177) l (

  ')                   Wi {#*I =

1. - (Cik.I )"*I (W g)"*I

                                                *              + 1. - (C;8)"*I g       = (Wg )"4 D

D l ' ! hus, Equation 2.20-177 becomes: I W;{#*I =Wi,kV + A W ,V * +I (2.20-178) where :

                                                                                  -    s,c PP (2.20-179) and:

v 1.k g)k

                                          = (1. - Cik.I) ,           k + (1. - Cg' () ,                       (2.20-180)

OQu &Qg dQg Equation 2.20-180 is the same as Equation 2.419. As explained in Section 2.20.2, AQg"+I is the central numerics unknown variable for non-critical flowlinks k = 1, ..., K, and is given by Equation 2.20-120 for critical flowlinks k = K+1, .... K*. The latter is approximated by Equation 2.20-125 in the fluid node i conservation equations, or is

     . approximated by Equation 2.20-126 in the fluid node j conservation equations (where i = U(k) =

upstream node, and j = D(k) = downstream node). l The term W;MV"+I in Equation 2.20-176 is given by Equations 2.20-148 and 2.20-149 in Section 2.20-3. I 1hus, substituting Equations 2.20-148,2.20-149,2.20-178, and 2.20-179 (with 2.20-125) into Equation 2.20-176 places the finite-difference form of the vapor region mass conservation equation in terms of the (new) NOTRUMP central numerics unknown variables as follows: 'O February 1998 l ovo25wuo25 22or.wpt:1bm2698 2.20.5-3 Rev.4 w

A(My)[d K* g, y 3, n.i :-j,a,.,.w,,.w, I-

                                                 -Ia[. g           4Q,n +1 k =1       OQk
                                                                                            ~ > s,c O
                                 '                                                         J (2.20-181) for interior fluid node i = 1, ..., I.

Multiplying both sides of Equation 2.20-181 by At"+I and collecting all central numerics unknowns on the left hand side yields : O Febru 1998 ow.5m.22hpf:lb422698 2.20.5-4 ev. 4

       . ~ . .   . - - - . _ . . . . _ . . . . .       - . . _ . . . .-. . - . . ~ . - . . . . . . . - . - . - _ - . - - - . . . ~ . . . . _ -

r t ot "*1 Ia*. k -1 iy

                                                                                                                #1 SQg
                                                                                                                            . ggk n +1 e,, , c.

l M K* V

                                                             =   - At " 4                  I a ,W   ik . Wi,g                 - W;My             (2.20-182) g for interior fluid node i = 1. .... I.

This concludes the discussion of the modifications to the finite-differencing of the vapor region mass conservation equation for interior fluid nodes. O

   %J February 1998 om5wwo25-2w:.wpen,02269s                                                     2.20.5-5                                                 Rev.4

l 1 l 2.20.6 - Modifications to Central Matrix Equation In this section, the modifications to the NOTRUMP central matrix and its elements (of Appendix E in { Reference 2-1) that result from the changes described in Sections 2.20-1 through 2.20-5 are presented. f In Reference 2-1, for the origind NOTRUMP central numerics with the mass flow-based formulation, the final finite-differenced consenation equations that contain the central numerics unknown variables are assembled in central matrix fenn for solution in Equation E-5, as follows: OWW OWU m OWMg OWUy dWMy b N B, OUg W EUg Up hUuMu hUuUy bUgMy dUgT b M E Ug OMgW hMg Un EMgMy hMgUy hMuUy bwT

E M EMg (2.20-183)

OUyW bUyUn bUyMy EUyUy buyMy OUyT E V E Uy OMvw DMyUg DMvMy QMyuy EMyuy byT Ev Hu y b dTU g dTM g OTUv OTM y Q R B T-I where all double-underlines for the submatrices and all single-underlines for the subvectors are retained here for clarity. The known quantities in Equation 2.20-183 are defined with the following notation: A -= coefficient submatrix

Q square diagonal coefficient submatrix, with no zero elements on the diagonal Q = square diagonal coefficient submatrix, in which diagonal eler .ents may be zero Q = zero coefficient submatrix (all elements are zero) R = right-hand side subvector and the subscripts: W = non-critical flowlink mass flow-based momentum equation / unknown related (of order K) Uy = interior fluid node mixture region energy equation / unknown related (of order February 1998 oM025wwo25 220s.wpf;Ib-022798 2.20.6-1 Rev.4 r . __ . - - - -

1 l l l My = interior fluid node mixture region mass equation / unknown related (of order I) Uy = interior fluid node vapor region energy equation / unknown related (or order I) l My = interior fluid node vapor region mass equation / unknown related (of order I) l T = interior metal node energy equation / unknown related (of order J) l 4 where: l l K = total number of ion-critical flowlinks I = total number of interior fluid nodes J = total number of interior metal nodes Each submatrix in Equation 2.20-183 contains two of these subscripts. The first subscript denotes the applicable conservation equation, and the second subscript denotes the unknown subvector that the submatrix multiplies. The right-hand side subvectors in Equation 2.20-183 contain only one subscript, to denote the applicable conservation equation. The unknown subvectors in Equation 2.20-183 are defined by: O' AW j"d AW = i (2.20-184) AW " *I l l l l A(Ug )[4 AU g = ! (2.20-185) A(Ug)[*I l l A(My)[*I AM g = ! (2.20-186) A(My)f*I l Februars 1998 oM025w' 5025-220g.wpf.It> 022798 3,20.6 ., yey, 4

      .. ..-. ._ .___m                                                   _ _ _ _ _ _ _ _ _ . _ _ . . _ . _ _ _ _ _ _ _ . . _ _ _ . _ . . _ . _ . _ _ . _ . .

I I i l l

O V- d i

A(Uy)$

j. i .(2.20-187)

AU v = i A(Uy)[4 4 l. l l , !- j d L A(My)$ AM = 3 (2.20-188)

                                                                       -v A(Mv)[4 l

l 1 D AT"d i _AT = I (2.20-189) AT)"d where: ( AWg"+I = mass flow rate incremer.t unknown for non-critical flowlink k = 1, ..., K, Ibm /sec. l A(Uu);"+I = mixture region intemal energy increment unknown for interior fluid node i = 1 .... I, Btu

                                         "+1 A(Mu)i               =       . mixture region mass increment unknown for interior fluid node i = 1, ... I, Ibm
                                        "+1 A;Uy)i .              =         vapor region intemal energy increment unknown for intemal fluid node i = 1, ..., I, Btu l

A(My) "+I = vapor region mass increment unknown for interior fluid node i = 1, ..., I, lbm AT j"+1 = temperature increment unknown for interior metal node j = 1, ..., J, *F L A brief summary of the contents of Equation 2.20-183, including the applicable staning corarvation I equations in Reference 2-1, is provided in Table 2.20.61. The elements of the submatrices of ( Equation 2.20-183 for the original NOTRUMP central numerics, and the overall solution process for f February 1998 I oM025wuo25 ao .wpf:1b-022798 s 2.20.6-3 Rev.4 L

l l l l the central matrix, are described in Appendix E of Reference 2-1 (Equations E-60 through E-147), and l are summarized in Table 2.20.6 2. Table 2.20.6-3 contains a summary of the modifications to the NOTRUMP central matrix equation that l result from the changes to the central numerics for application to AP600, as described in Sections 2.20.1 through 2.20.5. As indicated in Table 2.20.6-3, the first through the fifth " rows" of the central matrix equation contain modifications, while the sixth " row" (for the finite-differenced interior metal l node energy conservation equations) is not modified. In the modified central matrix equation, as a result of the conversion from the net mass flow-based to the net volumetric flow-based formulation, j the unknown subvector AE is replaced by AQ, and all subscripts "W" are replaced by "Q". In addition, the first coefficient submatrix in the first " row" of the central matrix, which is from the final l finite-differenced volumetric flow-based momentum equation and multiplies the AQ unknown subvector, has its designation changed from A to 2, because it is now a square diagonal submatrix with no zero elements on the diagonal. Thus, the modified central matrix equation becomes: l OQQ 8UQy 8 QMy 8 QUy 8 QMy kT b EQ 8UgQ OUyUu bugMy bUyUy bUgMy 8UuT b M O Ug 8MyQ bMyU y OMyMy bMyUy bMgMy bT y b M OMg (2.20-190) 8UyQ bUvU g bUyMy EUyUy bUvMy 8UvT E V E Uy 8MyQ bMyU g bMvM y bMyUy OMyMy 0-MyT Ev O My SQ OTUg 8TMg 8TUy 8TMy bd B T-where: AQ g, ; (2.20-191) AQu" where: AQg"I = volumetric flow rate ir.crement unknown for non-critical flowlink k = 1, ..., K, ft.3/sec. O February 1998 ow25ww220s wpt:1b422798 2.20.6-4 Rev. 4

l p and the subscript: I V Q = non-critical flowlink volumetric flow-based momentum l equation / unknown related (of order K) The submatrix modifications in Equation 2.20-190 are presented in the following subsections. Section 2.20.6-1 contains the modifications to tne first " row" of Equation 2.20-190 for the volumetric flow-based momentum conservation equation for non-critical flowlinks. The modifications to the second l through fifth " rows" of Equation 2.20-190, for the mixture region energy, mixture region mass, vapor l region energy, and vapor region mass, respectively, conservation equations for interior fluid nodes are i described in Sections 2.20.6.2 through 2.20.6.5, respectively. ! 2.20.6.1 Submatrix Modifications for Volumetric Flow-Based Momentum Conservation Equation for Non-Critical Flowlinks I The modifind final finite-differenced volumetric flow-based momentum conservation equation for non-critical flowlinks, Equation 2.20-70 in Section 2.20.1.2, is placed in the following matrix form: l OQQ * $ + dQ Ug

b M #

bMO M M !

                             + dQUy

Ev + 8QMy
Ev + kT
AT = B q (2.20-192)

Equation 2.20-192 forms the first " row" of the modified central matrix equation, Equation 2.20-190. Coefficient submatrix Dqq as h only diagonal elements, which are given by (all other elements are zero): 144g 3R k (Dgq)k.k = 1. - At "4 =* (2.20-193) uk * (I l>A)k 00 k for k = 1 ..., K. Equation 2.20-193 replaces Equation E-60 of Reference 2-1. i The non-zero elements of coefficient submatrix 6Quy are given by (all other elements are zero): i i oMo25wuo25-220s.wpf 1b-022798 2.20.6-5 ev.1 l l

l l 144gC 3(Pu)k (A quM)g,i = - At[ . ug . (E UA)g . (2.20-194) d(Ug); and i 144g" (Aqu M)g,j = At "4 . ug . . B(PD)k (2.20-195) (I UA)g 8(Ug)) for k = 1, ..., K, where i = U(k) and j = D(k). Equations 2.20-194 and 2.20-195 replace Equation E-61 of Reference 2-1. The non-zero elements of coefficient submatrix 69 y are given by (all other elements are zero):

                                                                    #"            Uk (2.20-196)

(Any )g,; = - At "4 ug . . (I UA)g d(Mg); l I i O 144gC B(PD)k (AqMu )y = At "4 . ug . . (2.20-197) (I UA)g 0(My)) for k = 1..., K, where i = U(k) and j = D(k). Equations 2.20-196 and 2.20-197 replace Equation E-62 of Reference 2-1. The non-zero elements of coefficient submatrix 69uy are given by (all other elements are zero): C Uk ( Aqu y)g,i = - At "4 eu.g . (2.20-198) (E UA)k d(Uy); and C Dk (Aquv )y =At" .Vg. . (2.20-199) (I UA)k 8(Uy)) c wo25wuo25-220s.wpf.tw2279s 2.20.6-6 Nev.1

l 4

t f p for k = 1, ... K, where i = U(k) and j = Q(k). Equations 2.20-198 and 2.20-199 replace Equation E-(/ 63 of Reference 21. l l The non-zero elements of coefficient submatrix 6quy are given by (all other elements are zero): ! i i l I 144g* B(Pu)k ! (AQM)g,i = - At "4 . Vg. . (2.20-200) l

                                                                     - (I UA)k      d(My);                                            l i

! and l 1 ! 144g* B(PD)k (Aqu y)gg = At "4 . gv . i (2.20-201) (I UA)k 0(hlv)j i for k = 1. .... K, where i = U(k) and j = D(k). Equations 2.20-200 and 2.20-201 replace Equation E-64 of Reference 21. l 1 The elements of the right-hand side subvector Bq are given by: 1 t0 * (Eq)g = At "4 . Vg. . [ (Pu)g + (Po)g + Rk+D] g (2.20-202) for k = 1 .... K.

      "Ihis concludes the discussion of the submatrix modifications for the volumetric flow-based momentum conservation equation for non-critical flowlinks.

l l t V(D February 1998 uM025wuG25-22og.wpf:Ib-022798 ~ 2.20.6-7 Rev.4

2.20.6.2 Submatrix Modifications for Mixture Region Energy Conservation Equation for Interior Fluid Nodes The modified final finite-differenced mixture region energy conservation equation for interior fluid nodes, Equation 2.20-140 in Section 2.20.2, is placed in the following matrix form: dUgQ

N + OUyUy *b M +

UM g u *b M

bugUy

Ey + bUuMy
by +dUuT
bT = RUy Equation 2.20-203 forms the second " row" of the modified central matrix equation, Equation 2.20-190.

The elements of coefficient submatrix OUyg are given by:

                                                                       )M i.k                 (2.20-204)

(Au,q)i.k = At"4 *i a ,[ * ( for i = 1, ..., I and k = 1, ..., K. Equation 2.20-204 replaces Equation E-65 of Reference 2-1. e Coefficient submatrix Qe u, has only diagonal elements, which are given by (all othei elements are zero):

                                  .                                          - a .c                          l I

(2.20-205) l

                        ~
                                                                                                         -qp for i = 1, .... I. Equation 2.20-205 replaces Equation E-66 of Reference 2-1.

l O1 Februart 1998 o:v'".5wuo25-220s.wpf:Ib-022798 2.20.6-8 Kev.4

    .    - - . . . -          .      . . . . . ~ . - . . . - . . .- - .-            _-  .. .            .... _ .. -_._             .-.. - ~.

N Q v Coefficient submatrix Qu,y, has only diagonal elements, which are given by (all other elements are zero): Op (2.20-206)

                                                  -                                               _                                          l m Q, C          l a

for i = 1, ..., I. . Equation 2.20-206 replaces Equation E-67 of Reference 2-1. I Coefficient submatrix Quyuy has only diagonal elements, which are given by (all other elements are 1 zero): g - 0,0

  %                                                                                                                     (2.20-207)

J 4C

     - for i = 1, ..., I. Equation 2.20-207 replaces Equation E-68 of Reference 2-1.

Coefficient submatrix Qu y y has only diagonal elements, which are given by (all other elements are zero): 1 t 9 February 1998 oM025wwo25-220s.wpf:Ib-02258 2.20.6-9 Rev.4

i l , l

                                                                             ~
                                       ~

( 1 l (2.20-208) i m 0,C/ 4 l 1 1

                                                                                                     .J for i = 1, ..., I. Equation 2.20-208 replaces Equation E-69 of Reference 2-1.

The elements of coefficients submatrix 6uy7 are given by:

                                                                                         -.Q,C (2.20-209) for i = 1, ..., I and = 1, .... J. Equation 2.20-209 is the same as Equation E-70 of Reference 2-1.

The eternents of the right-hand side subvector B_g are given by: K* L'

M (2.20-210) (Bu )i = - At '"I I a i,[ = (Wh)fk + A=lIaf=Qx#*** i + (Wh)MV k =l for i = 1, .... I. This concludes the discussion of the submatrix modifications for the mixture region energy conservation equation for interior fluid nodes. i O February 1998 eM025wwo25-220s.wpf Ims 2.20.6-10 Rev.4

1 l s 2.20.6.3 Submatrix Modifications for Mixture Region Mass Conservation Equation for

 's                       Interior Fluid Nodes l      The modified final finite-differenced mixture region mass conservation equation for interior fluid i

nodes, Equation 2.20-151 in Section 2.20.3, is placed in the following matrix form: OMgQ * $ + bMgU g *E M + OMg My

E M

                              + bMg uy

Ey + hM gMy
My + b Tg= AT = B y (2.20-211)

Equation 2.20-211 forms the third " row" of the modified central matrix equation, Equation 2.20-190. The elements of coefficient submatrix 6y 9 are given by:

i. (2.20-212)

(Ay q)i.k = At " = ai ,{ . l o' q V for i = 1, .... I and k = 1, ..., K. Equation 2.20-212 replaces Equation E-71 of Reference 2-1. Coefficient submatrix Qg u has only diagonal elements, which are given by (all other elements are zero):

                                                                                             -QA (2.20-213) for i = 1 .... I. Equation 2.20-213 replaces Equation E-72 of Reference 2-1.

l l l f\ l V February 1998 c:wo25wwo25 220s.wpf:Ib.022798 2.20A-11 Rev.4

Coefficient submatrix Qg y has only diagonal elements, which are given by (all other elements are zero): (2.20-214) for i = 1, .... I. Equation 2.20-214 replaces Equation E-73 of Reference 2-1. Ceefficient submatrix Qg,uy has only diagonal elements, which are given by (all other elements are zero): _ ~ 9, C. (2.20-215) for i = 1, ..., I. uation 2.20-215 replaces Equation E-74 of Reference 2-1. Coefficient submatrix Qy y has y only diagonal elements, which are given by (all other elements are 1 zero): l - A iC-(2.20-216) l for i = 1, ... I. Equation 2.20-216 replaces Equation E 75 of Reference 2-1. The elements of the right-hand side subvector B g are given by: Ke (By ), = - At "

Ia[=W;,M i +W iMV (2.20-217)

                                                        ,k =1 for i = 1, ..., I.

February 1998 om ms.22% wpr.im79s 2.20.6-12 Rev.4

l l l This concludes the discussion of the submatrix modifications for the mixture region mass conservation l Q/ equation for interior fluid nodes. l 2.20.6.4 Submatrix Modifications for Vapor Region Energy Conservation Equation for l Interior Fluid Nodes The niodified final finite-differenced vapor region energy conservation equation for interior fluid nodes, Equation 2.20-173 in Section 2.20.4, is placed in the following matrix form: 6UyQ * $ + hUyU m *$ M

UyM u

bM

                                        + Duyvy

M y + buyMy
My + 6UyT = AT = B g y (2.20-218) l Equation 2.20-218 forms the fourth " row" of the modified central matrix equation, Equation 2.20-190.

      . The elements of coefficient submatrix 6uyn are given by:

O v i.k (Au vg)i.k = At "+I = aj ,[ = (2.20-219) for i = 1, .... I and k = 1, ..., K. . Equation 2.20-219 replaces Equation E-76 of Reference 2-1. Coefficient submatrix Quyu has only diagonal elements, which are given by (all other elements are zero):

G &

2 (2.20-220) m

                                                                                                                              -0$
    ^
  /

l i for i=1,I... I Equation 2.20-220 replaces Equation E-77 of Reference 21. .J February 1998 l, oM025wuo25-220s.wpf:1b 022798 2.20.6-13 Rev.4

Coefficient submatrix QuyyM has only diagonal elements, which are given by (all other elements are O i 1 zero)-

                                   -                                      ~Q&                                 l l

(2.20-221) l l l l O.L l for i = 1, ... I. Equation 2.20-221 replaces Equation E-78 of Reference 2-1. i i Coefficient submatrix Quyuy has only diagonal elements, which are given by (all other elements are zero): I Op l (2.20-222) 0, C. for i = 1, .... I. Equation 2.20-222 replaces Equation E-79 of Reference 2-1. l Coefficient submatrix Quy y y has only diagonal elements, which are given by (all other elements are zero): O February 1998 c:wo25wwo25-220s.wpt:tb.022798 2.20.6 14 Rev.4

l'.. l OL e ( l-(2.20-223) l - diC__ for i = 1, .... I. Equation 2.20-223 replaces Equation E-80 of Reference 21. The elements of coefficient submatrix 6UyT are given by: _ _ 0,6 (2.20-224) for i = 1, ..., I and j = 1, ..., J. Equation 2.20-224 is the same as Equation E 81 of Reference 2-1. O The elements of the right-hand side subvector B_g are given by: K* L* (Buy)i _ = - At "

M I a i,[
M)[g + 1=lEi a ,[
Q x * - @ ),N k =l for i = 1, ..., I.

This concludes the discussion of the submatrix modifications for the vapor region energy conservation equation for interior fluid nodes. i l 7 1 I February 1998 < f ovo25wwo25 220s.*P :1t>.022798 2.20.6-15 Rev.4 l.

2.20.6.5 Submatrix Modifications for Vapor Region Mass Conservation Equation for Interior Fluid Nodes The modified final finite-differenced vapor region mass conservation equation for interior fluid nodes, Equation 2.20-182 in Section 2.20.5, is placed in the following matrix form: OMyQ ' $ + hMyUm

E M MyMy *E M

                                                                                                                            ~
                                                 + hMyUy* by

OMyMy
by + OMyT
N " O My Equation 2.20-226 forms the fifth row" of the modified central matrix equation, Equation 2.20-190.

The elements of coefficient submatrix 6Myg are given by: l W , I (2.20-227) (Ag yq);y = At"*1 = a g for i = 1, ..., I and k = 1, .... K. Equation 2.20-227 replaces Equation E-82 of Reference 2-1. Coefficient submatrix Qg yu has only diagonal elements, which are given by (all other elements are zero): _ . _ - Q,c (2.20-228) for i = 1, ... I. Equation 2.20-228 replaces Equation E-83 of Reference 2-1. Coefficient submatrix Quyu has only diagonal elements, which are given by (all other elements are zero): O February 1998 ovo25ww25-22og.wpf:lbO22798 2.20.6-16 Rev.4

_ , , _ .- . -_ . .. - -~ . . . . - - - - . . l l i l i

i

 ' l
    \_.)

Qtb (2.20-229) l l l for i = 1, .... I. Equation 2.20-229 replaces Equation E-84 of Reference 21. i ; i

Coefficient submatrix Qg yuy has only diagorni elements, which are given by (all other elements are

            **')                                                                                         -

O g C_. (2.20-230) l 1 l for i = 1, ..., I. Equation 2.20-230 replaces Equation E-85 of Reference 2-1. I Coefficient submatrix Qg yy has y only diagonal elements, which are given by (all other elements are zero). -' [ f] _ d, C l V (2.20-231) 1 4 for i = 1, ..., I. Equation 2.20-231 replaces Equation E 86 of Reference 2-1. The elements of the right-hand side subvector B._y are given by: 1 1 K* (By y); = - At "*l

I a ,[i
W;,[ - W;MV (2.20-232)

                                                                    , k =1 for i = 1, ..., I.

This concludes the discussion of the submatrix modifications for'the vapor region mass conservation equation for interior fluid nodes. A

%)

i February 1998 ! ovo25ww)2s.220s.wpf:Ib 022798 2.20.6-17 Rev.4 l

l l l l l 1 Table 2.20.6-1 l 01 Summary of Contents of Central Matrix Equation for Original NOTRUMP Numerics (Equation 2.20 183) l

           " Row" of                             Applicable Starting Conservation Equation in i        Central Matrix              First                          Reference 21                               I

{ Equation Subscript on ! Equation in

2.20 183 Submatrices l Reference 21 Description I W 2-33 Mass Flow-Based Momentum Conservation Equation for Non-Critical l

Flowlinks k=1, ..., K l l 2 Ug 2-1 Mixture Region Energy Conservation Equation for Interior Fluid Nodes i= 1, ... I 3 My 2-2 Mixture Region Mass Conservation i l Equation for Interior Fluid Nodes i= 1, .... I 4 Uy 2-3 Vapor Region Energy Conservation l Equation for Interior Fluid Nodes i= 1, . ... I l I 5 My 2-4 Vapor Region Mass Conservation j Equation for Interior Fluid Nodes i= 1, .... I 6 T 2-31 Energy Conservation Equation for Interior l Metal Nodes j=1, ..., J l O February 1998 ow25wwo25 220s.wpr.lb-022798 2.20.6-18 Rev.4

i Table 2.20.6 2 Summary of Equations in Appendix E of Reference 21 That Express Elements of the Central Matrix for Original NOTRUMP Central Numerics Submatrix of Equation in Other Equations in Appendix E of l Equation E 5 of Reference 21 Reference 21 Indirectly Used Reference 21 Defining Submatrix Element dww E-60 none 6wg E-61 none l 6wy, E-62 none l i 6wvy M3 none i 6wMy M none

;                                                     E-65                                     none 69 w Qg g                               E-66          E-92 (E-116, E-117, E-118), E-93 (E-119, E-120) gg                                  E-67          E-94 (E-Il6, E-Il7, E 118), E-95 (E-Il9, E-120) gg                                 E-68          E 96 (E-116, E-Il7, E-Il8), E 97 (E-119, E-120) gg                                 E-69          E-98 (E-116, E-117, E-118), E-99 (E 119, E-120)

E-70 E-132 oc uT E-71 none OMy w g E-72 E-100 (E-121, E-122, E-123) gg y E-73 E-101 (E-121, E-122. E-123) E-74 E-102 (E-121, E-122, E-123) EMyUy February 1998 c:wo25wwo25-220gyr;t1422798 2.20.6-19 Rev.4

Table 2.20.6 2 (cont.) Summary of Equations in Appendix E of Reference 21 That Express Elements of the Central Matrix for Original NOTRUMP Central Numerics Submatrix of Equation in Other Equat'ons in Appendix E of Equation E-5 of Reference 21 Reference 21 Indirectly Used Reference 2-1 Defining Submatrix Element E-75 E-103 (E-121, E-122, E-123) g sammmmmmmmmmmmmmmmum E-76 none Ouy w E-77 E-104 (E-124. E-125, E-126), E-105 (E-127, E-128) g E-78 E-106 (E-124, E-125, E-126), E-107 (E-127, E-128) g gg g E-79 E-108 (E-124, E-125, E-126), E-109 (E-127, E-128) E-80 E-110 (E-124, E-125, E-126), E-111 (E-127, E-128) gg E-81 E-133 aug E-82 none 6My w g E 83 E-ll2 (E-129 E 130, E-131) g E 84 E-113 (E-129, E-130, E-131) g E-85 E-114 (E-129, E-130, E-131) gg g E-86 E-115 (E-129, E-130, E-131) 6g E-87 E-134 (E-142, E 143), E-135 (E-144, E-145) E-88 E-136 (E-142, E-143), E-137 (E 144, E-145) 6g 6g E-89 E-138 (E-142, E-143), E-139 (E-144, E-145) ovo25.wo25-220g wpf:lb422798 2.20.6-20 ev.

     )                                                      Table 2.20.6 2 (cont.)

Summary of Equations in Appendix E of Reference 21 That Express l Elements of the Central Matrix for Original NOTRUMP Central Numerics Submatrix of Equation in Other Equations in Appendix E of l Equation E 5 of Reference 21 Reference 21 Indirectly Used Reference 2-1 Defining Submatrix 1 l Element i 43g E-90 E-140 (E-142, E-143), E-141 (E-144, E-145) Qg E-91 E-146, E-147 i (

\j i

l l l l l

.t

't i o:uo25wwo25-220s.wpf:1b422798 2.20.6-21 ev. $ l t

Table 2.20.6 3 Summary of Modifications to NOTRUMP Central Matrix Equation for Application to AP600 wumm

           " Row" of                Section                                  Applicable Modified Final Finite-Differenced Central Matrix              Where                                               Corservation Equation Equation Being          Modifications Modified                   Are Equation                        Description Described 1                    2.20.1.2                               2.20-70       Volumetric Flow-Based Momentum Conservation Equation for Non-Critical Flowlinks k = 1, .... K 2                     2.20.2                               2.20-140       Mixture Region Energy Conser eation Equation for Interior Fluid Nodes i = 1,...,1 3                     2.20.3                               2.20-151       Mixture Region Mass Conservatica Equation for Interior Fluid Nodes i = 1, ...,1 4                     2.20.4                               2.20-173       Vapor Region Energy Conservation Equation for Interior Fluid Nodes i = 1 ..., I 5                    2.20.5                               2.20-182       Vapor Region Mass Conservation Equation for interior Fluid Nodes i = 1, .... I 6                     N/A                                    N/A          Energy Conservation Equation for Interior Metal Nodes J = 1, .... J w

N/A = Not Applicable (not rrodified) k O February 1998 oM025wwo25-220s.wnf:Ib-022798 2.20.6-22 Rev.4

                                      - . _ -         - ~ - -             .      _   - .-. -..            .       -    ..

2.20.7 Finite-Differencing Notation and Conventions In this section, the notation and conventions'that are employed for the finite-differencing in Sections 2.20.1.2, 2.20.2, 2.20.3, 2.20.4, and 2.20.5 are defined. In general, for a transient variable x: x"+3 m x" + Ax"+3 = x + Ax"+ 3 (2.20-235) where the superscripts: n = denotes a previous time level of a transient variable (typically dropped for brevity) n+1 = denotes a new time level of a transient variable and: A = indicates the change in a transient variable over a time step (from one time level (n) to the next (n+1))

 ,G      Thus, an expression of the following form for the temporal derivative of a transient variable x:
 \)

1 dx

                                                                     =y                                       (2.20-234) dt is approximated in finite-difference form as:

1

                                                              = y "+1 = y + ' y " *3                          (2.20-235)

At"* It is then the "A" quantities that are the unknowns to be solved for in the central numenes. l The following discussion applies in the event that a transient variable is to be treated explicitly in the ! central numerics (i.e., it is to be ap;,roximated at its previous time (t") value in the finite-differencing 1 of the central differential equations at the new time (t"+3)). For example, suppose a transient variable z is a function of transient central variables x and y as follows: f z = z (x,y) (2.20-236) { l February 1998 eM025 wr25 22ab.wptm2259s 2.20.7-1 Rev 4

Finite-differencing yields: l z"I = z + Az"I (2.20-237) where: eg*, rg*, n Az"*l =

Ax "'I + = Ay +1 (2.20-238)

                                                ,0x,             ,8y, If z is to be treated explicitly in the central numerics, then:

Az"1 = 0 (2.20-239) so that: z"I = z (2.20-240) This explicit treatment in the finite-differencing of the central di: erential i equations is not meant to imply that z is treated as a constant for the entire transient. Rather, it means that in the central numerics solution. the dependence of z upon central numeries unknown variables Ax"+3 and Ay"+1 is ignored. Later, at the end of the time step At"+3, once Ax"I and Ay"+3 are calculated from the central numerics solution and then used to update x"I and y"+1 as follows: x"+ 1 = x + Ax"+ I (2.20-241) y"I = y + Ay"I (2.20-242) then z"+1 is updated ^ from the function for z (Equation 2.20-236) with x"+I and y"I as follows: z"I = z (x"I, y"3) (2.20-243) In the event that transient variable z in the above example is to be treated implicitly, Equation 2.20-238 for Az"I is used in the central numerics. However, since z is a provisional variable expressed in terms of central variables x and y, Equation 2.20-237 (with 2.20-238) is not t sed to update z"I at the end of the time step. Rather, Equation 2.20-243 is used to update z"I, after x"+1 and y"I have been upda*.ed with Equations 2.20-241 and 2.20-242, respectively. ) This concludes the discussion of the finite-differencing notation and conventions which are employed in the NOTRUMP central numerics. O February 1998 oumswo25 220b.wpr.ib.022598 2.20.7-2 Rev.4

g 2.20.8. Summary of Thermodynamic Properties, Related Quantities, and Partial Derivatives

                               .Used in the Modified Central Numerics In this section, a summary of the thermodynamic properties, related quantities, and their partial derivatives that are used in the modified central nuraerics is presented. 'Ihe equations for almost all of

{ these quantities are documented in Appendix L of Reference 2-1, and since they have not been I modified for the application of NOTRUMP to AP600, they are not repeated here. Rather, three tables are presented that summarize the quantities and their corresponding equations from Appendix L of Reference 2-1. Table 2.20.8-1 summarizes this information for the general saturation properties and derivatives that

are functions of pressure (P) only. The general thermodynamic properties and derivatives that are functions of pressure (P) and specific enthalpy (h) are provided in Table 2.20.8-2. As described in j Appendix L of Reference 2-1, the general property and derivative equations of Tables 2.20.8-1 and 2.20.8-2 are utilized to calculate various fluid node properties as a function of the NOTRUMP fluid node central variables,gU , M g , Uy, and My, as well as the partial derivatives of these properties j with respect to the nodal central variables. Table 2.20.8-3 summarizes these fluid node properties and partial derivatives. { I Although the fluid node specific volumes are referenced directly in the equations of Appendix L of Reference 2-1 as "v(P,h y )" and "u(P,h y )" for the nodal regions, or as "ufP)" and "u (P)" for 5 g saturation, their partial derivatives with respect to the nodal central variables are not shown, since they were not needed in the original NOTRUMP central numerics. These specific volume partial derivatives ans discussed below. From Equations L-13 or L-34 or L-37 of Reference 2-1, the fluid node mixture region specific volume is given by: I l VM = u(P,hy ) (2.20-244) so that it may be expressed generally in terms of the fluid node central variables as follows: Vu=vu (Ug, Mg, U y, My) (2.20-245) j The partial derivatives of ug with respect to the fluid node central variables are obtained by differentiating Equation 2.20 245 as follows: 4,6 (2.20-246)

    . .,Q                                             -                                                         -

wozswo25 22an..pr;id-o2259: 2.20.8-1 *"%v$

                                     ~                                                 -.. a , C.

(2.20-247) O (2.20-248) (2.20-249)

                '&u'                                                                              dh y' where   y           is given by Equations L-14 or L-36 or L-38 in Reference 2-1, and '           P is given by Equations L-15 or L-35 or L-39 in Reference 2-1.

The above is analogous to what is done for Ty and its partial derivatives in L ppendix L of Reference 2-1. Similarly, from Equations L-13 or L-34 or L-37 of Reference 21, the fluid node vapor region specific volume is given by: vy = u (P, hy) (2.20-250) so that it may be expressed generally in terms of the fluid node central variables as follows: Vy = vy (Uy , Mg, Uy, My) (2.20-251) The partial derivatives of Vy with respect to the fluid node central variables are obtained by differentiating Equation 2.20-251 as follows:

%t.

! (2.20-252) m _ l February 1998 l eM025 4025 220b.wpf:1bo22598 2.20.8 2 Rev.4 '

i - - g 4., G.

-(

(2.20-253) l (2.20-254) (2.20-255) Bu' au where is given by Equations L-14 or L-36 or L-38 in Reference 2-1, and

                ,dP 4y                                                                                      is given by
                                                                                               ,hhy,p Equations L-15 or L-35 or L-39 in Reference 2-1.

V The above is analogous to what is done for Ty and its pr.rtial derivatives in Appendix L of Reference 21. , From E luation L-3 of Reference 2-1, the fluid node saturated liquid specific volume is given by: l ur = vfP) (2.20-256) i i so that it may be expressed generally in terms of the fluid node central variables as fol.'ows: I vf = vf (Uy , Mg, Uy, My) (2-20-257) ! The partial derivatives of Vfwith respect to the fluid node central variables are obtained by differentiating Equation 2.20-257 as follows: i . v- ! (2.20-258) ;

 ,                                                                              .                                            1
'sOg U

i h February 1998 i oMo25ww25 220b.wpt.Ib.022598 2.20.8-3 Rev.4 l

e

                                     .                            ~

N C. (2.20-259) (2.20-260) (2.20-261) du r where 7p is given by Equation L-7 in Reference 2-1. The above is analogous to what is done for hg and its partial derivatives in Appendix L of Reference 2-1. Similarly, from Equation L-4 of Reference 2-1, the fluid node saturated vapor specific volume is given by: u,= u ,(P) (2.20-262) so that it may be expressed generally in terms of the fluid node central variables as follows: u, = ug (Ug, M g, Uy, My) (2.20-263) The pc..I derivatives of u withs respect to the fluid node central variables are obtained by differentiating Equation 2.20-263 as follows: m 4, C 1 (2.20-264) (2.20-265) L February 1998 oM025wWo25 220b wpf.Ib-022598 2.20.8-4 Rev. 4

                                                                                   --    a , c.

(2.20-266) (2.20-267)

The above is analogous to what is done for hg and its partial derivatives in Appendix L of Reference 2-1. This concludes the summary of the thermodynamic properties, related quantities, and their partial derivatives which are used in the modified central numerics. O i ewus.wns.22m..prmn2as 2.20.8-5 Febmukev?

4 l i TABLE 2.20.81

SUMMARY

OF SATURATION PROPERTIES AND DERIVATIVES (=f(P)) FROM APPENDIX L OF REFERENCE 21 QUANTITY EQUATION IN REFERENCE 2-1 i i T,,t = T,,, (P) L-1 dT,,, L-2 dP i ur= vf (P) L-3 du r L-7 dP 1 t ug = u g(P) L-4 i du s L-8 , dP hr = hfP) L.5 dh r L-9 5 hg = hs(P) L-6 dh, L-10 dP O O M W M S U %.g'.] @ 98 {ggg,g

I O TABLE 2.20.8 2

SUMMARY

OF THERMODYNAMIC PROPERTIES AND DERIVATIVES (=f(P,h)) FROM APPENDIX L OF REFERENCE 2-1 EQUATION IN REFERENCE 2-1 SUBCOOLED SATURATED SUPERIIEATED u = u (P,h) L-13 L-34 L-37

                'Du'                          L-14                 L-36              L-38 sh rgy'                           L-15                 L-35              L-39 M, p T=T (P,h)                          L-16                 L-30              L-40
               '8T'                           L-17                 L 31              L-41

'd ,dP,h

               '8T'                           L-18                 L-32              L-42
                   >P oA4025wwo25-220b wpt:1b.02259a February 1998 2.20.8-7                                   Rev.4

O TABLE 2.20.8 3

SUMMARY

OF FLUID NODE QUANTITIES AND DEMVATIVES WIIICII ARE A FUNCTION OF NODAL CENTRAL VARIABLES (=f (Uy, M ,gU , yMy)) FROM APPENDIX L OF REFERENCE 2-1 FLUID NODE QUANTITY EQUATION IN REFERENCE 2-1 P = P (U g , My , Uy, My) 2-44 (and " pressure search" of Appendix L) BP L-96 BU g BP L-98 BM y BP L-100 buy BP L-102 3My by = hy (Ug, My, Uy, My) L-55 Bh g L-126 or L-130 BU g Bhy L-127 or L-131 8Mg Bhg L-128 or L-132 buy Bh y L-129 or L-133 aMy by = hv (Ug , Mg, Uy, My) L-56 Bhy L-134 or L-138 BU m ouo25wwo25-220b.wpr:li,.02259s 2.20.8-8 v. !

TABLE 2.20.8-3 (Cont.)

SUMMARY

OF FLUID NODE QUANTITIES AND DERIVATIVES WHICH ARE A FUNCTION OF NODAL CENTRAL VARIABLES (=f (Ug, M ,gU , yMy)) FROM APPENDIX L OF REFERENCE 21 FLUID NODE QUANTITY EQUATION IN REFERENCE 21 Bh y L-135 or L-139 BM y Bhy L-136 or L-140 buy Bhy L-137 or L-141 SM y Ty=T y (Uy, My, U y, My) L-16 or L-30 or L-40 STg L-142 BU g BTy L-143 OM y BT y L-144 8Uy BT y L-145 BMy Ty = Tv (Ug , My, Uy, My) L-16 or L-30 r L-40 BTy L-146 BU g BT, . L-147 omsim25-22%3pr.li>.o2259s 2.20.8-9 evN

TABLE 2.20.8 3 (Cont.) I

SUMMARY

OF FLUID NODE QUANTITIES AND DERIVATIVES WIIICII ARE A FUNCTION OF NODAL CENTRAL VARIABLES (=f (Uy, Mg, U ,yMy)) FROM APPENDIX L OF REFERENCE 21 FLUID NODE QUANTITY EQUATION IN REFERENCE 2-1 BTy L-148 buy BTy L-149 BMy Vy=V u (Ug, M g, Uy, My) L-94 BV y L-97 l

,                                BU y BV g                                     L-99 BMy                                                           ,

BV g L-122 buy BV y L-123 BMy Vy=V y (Uy, M g, Uv, My) L-95 BV y L-124 BU m BV y L-125 BM g BV y I,101 buy o:wo25wo25-220b.wpf::b-o2259s 2.20.8-10 Nev.

1

(] TABLE 2.20.8 3 (Cont.)

SUMMARY

OF FLUID I40DE QUANTITIES AND DERIVATIVES WHICII ARE A FUNCTION OF NODAL CENTRAL VARIABLES (=f (Ug, M ,yU , yMy)) FROM APPENDIX L OF REFERENCE 2-1 FLUID NODE QUANTITY EQUATION IN REFERENCE 2-1 BV y L-103 l BMy T,,, = T,,, (Uy , Mg, Uy, My) L-1 BT,,, L-118 8U g j BT,,, L-il9

BM y 4

BT L-120 (/ w BU BT,,, L-121 8My hr = hr (Ug , My, Uy, My) L-5 Oh g L-110 BU y Bh g L-lli OM y Bh g L-112 8Uy Bh f L-ll3 BM y

-~.

L hs = h, (Ug , Mg, U y, My) L-6 February 1998 ova 25wwus-2m.wpt:1b 022598 2.20.8-11 Rev.4

TALLE 2.20.8-3 (Cont.)

SUMMARY

OF FLUID NODE QUANTITIES AND DERIVATIVES WHICH ARE A FUNCTION OF NODAL CENTRAL VARIABLES (=f (Uy, Mu, Uy, My)) FROM APPENDIX L OF REFERENCE 21 FLUID NODE QUANTITY EQUATION IN REFERENCE 21 Sh L-lI4 a BU y / dh g L-115 DM y Sh g L-116 dU y Sh L-II7

                                                                                             .s E v~                                                   .

O 6 - - ~ _ ,, 2.2, .,2 mn 1

                          . . . _       _.      ..    -_  _    . ..       _-~ -           . .-       -        _.          .- -

p 2.20.9 Summary of Interfacial Energy and Mass Exchange Rates for Interior Fluid Nodes Used () in the Modified Central Numerics In this section, a summary of the interfacial energy and mass exchange rates for interior fluid nodes that are used in the modified NOTRUMP central numerics is presented.

     'Ihe mixture-to-vapor eurgy exchange rate for interior fluid node i, (Wh),MY , appears in the energy conservation equation for both the mixture and vapor regions of interior fluid node i, as discussed in Sections 2.20.2 and 2.20.4. (Wh)f# is given by Equation 2.20-94 in Section 2.20.2 (which is equivalent to Equation 2.9-77).

(Wh);# = (Wh),M# +(Wag), * (h,); -(Wap); e (h r); , (2.20-268) The mixture-to-vapor mass exchange rate for interior fluid node i, WMV i , appears in the mass conservation equation for both the mixture and vapor regions of interior fluid node i, as discussed in Sections 2.20.3.and 2.20.5. WMV i is given by Equation 2.20-142 in Section 2.20.3 (which is equivalent to Equation 2.9 76). W i# =W iMW +(Wgg)i -(WDF)i MV

     -(Wh)f and Wi                are only functions of fluid node i quantities, such that they are expressed generally in finite-difference form in terms of the fluid node i central numerics variables as follows:
                                                                                                                 %C (2.20-270)

I U February 1998 ovo25ww25-220i.wpt. bo2279s 2.20.9-1 Rev.4

and: (2.20-271) Equation 2.20-270 is equivalent to Equation 2.20-135 (with Equation 2.20-136) in Section 2.20.2. Equation 2.20-271 is equivalent to Equation 2.20-148 (with Equation 2.20-149) in Section 2.20.3. The partial derivatives of (Wh),MV in Equation 2.20-270 are obtained by differentiating Equation 2.20-268 with respect to the fluid node i central variables. B(Wh)f =O(Wh),M* B(hg); B(W

                                                                      +(WBR)8
                                                                                                                             ..           +       gg); = (hg )'.                             9 d(Ug);     0(Uy)3                                                                           8(Uy);         8(Ug )i (2.20-272)

B(hg)*. B(W

                                                                   -(Wpp)' =                                                              -       op)i = (hg );

8(Ug) , 8(Ug)i B(Wh)fV= B(Wh)f B(hs)i 8(W

                                                                       +(WBR)'. .                                                           +      gg)3 = (hg )'.

8(My); d(My)i 8(My)3 d(Mg)j (2.20-273) B(h g)'. 8(W _(WDF)' = 8(My); DF)i

r(h )'-

8(Mg); O Febsaary 1998 ovo25wo25-220i.wpubm2798 2.20.9-2 Rev.4 l

!A V 8(Wh),P B(Wh),M#

                                                 =
                                                                     +(W 8(hg)j
                                                                                                           +

B(W 3g);

l'h8 ~)8 BtUy); 8(Uy) -

BR)

8(Uy)3 8(U y)3 l

(2.20-274) 8(hr); B(W

                                                                     -(Wo g;.                            _

ap)i . (hf)*. B(Uy); 8(Uy); 1 l B(Wh),P 3(Wh),M# B(h8); B(W

                                                 =
                                                                     +(W3g)'. .                            +        3g)i . (h s):.

B(My)3 B(My); 8(My); 8(My)3 (2.20-275) 8(h f)'. B(Wap)'.

       -(j (~}                                                      -(Wap); .                            ~
                                                                                                                             .(h);f                              l 8(My)3           8(My);

The partial derivatives of W i MV in Equation 2.2G-271 are obtained by differentiating Equation 2.20-269 with respect to the fluid node i central variables: l l l BW iMY BW iM3V BQ By

i. 8(Uy); 8(Uy); 8(Uy)3 8(Ug)3 My BW 3 BW iMIV

                                                                 .                  . 3(WBR)i _ 3@DF)i                            (2.20-277) l                                                 3(My);            3(My);                  B(My);             B(My )i I

l l BW g# BW iM# B(W3g); , _B(Wo di _ (2.20-278)

B(Uy); B(Uy)3 B(Uy); d(Uy);

!                                                                                                                                   February 1998
!                eM025.wo25-2206.wp(:Ib42279s                                2.20.9-3                                                        Rey,4 l

4

                        -                                      ~                             -              -                                                 _-

BW;MV BW;MIY O(Wgg); ,, B(WDF)i _ (2.20-279) O(My); B(My); d(My); O(My); Equations 2.20-272 through 2.20 275 are the same as Equations 2.9-82 through 2.9-85, respectively, while Equations 2.20-276 through 2.20-279 are the same as Equation 2.9-78 through 2.9-81, respectively, i In the original NOTRUMP central nt.merics of Reference 2-1, the last four terms on the right-hand side of Equat. ions 2.20-272 through '.20-275, and the last two terms on the right-hand side of Equations 2.20-276 through 2.20-279, were ignored for the explicit treatment of bubble rise and droplet fall. In the modified NOTRUMP central numerics for AP600, all of these terms are retained, r.s bubble rise and droplet fall are treated implicitly. In the above, the saturated liquid and vapor specific enthalpies, (br), and (h,)i, respectively, and their partial derivatives with respect to the fluid node i central variables, are discussed in Appendix L of Reference 2-1 (see the Section 2.20.8 summary). The mixture-:o .ipor region energy and mass transfer rates, (Wh),MIV and W MIV, i respectively, due to evaporation and/or condensation, the bubble rise mass rate (WBR)i, the droplet fall mass rate (WDF)i' and their partial derivatives with espect to the fluid node i central variables are discussed below. (Wh),MIV and Wi MIV are discussed in Appendix V of Reference 2-1, and have not been modified for application of NOTRUMP to AP600. They were, and still are, treated implicitly in the central numerics. In the typical case of the mixture region subcooled or saturated ((T y ),5 (T,,)i) and the vapor region MIV are given by Equation V-12 and V-11, superheated or saturated ((Ty)i 2 (T,,1)3), (Wh),MIV and W i respectively, of Reference 2-1:

                                                                                                       ~
                                                                                                                   %L (2.20-280) and:

O February 1998 ov025wwo25-220i.wpf.1b.02279s 2.20.9-4 Rev. 4 l l

      . - . . - - .           -     .. . _ . . .   . .  . . - - . . = . .        _. ..-.-          -               - - - . - . - -
                                                                                                  ,      a,c

[D - V , (2.20-281)

                               +
           . where, from Equations V-1 and V-2, respectively, of Reference 2-1:

Q; = (UA)fI * [(Tg); -(T,,t);] (2.20-282) and: (UA)fI = Ui * (Agy); (2.24283) and where from Equations V-3 and V-4, respectively, of Reference 21: Qi = (UA)[I * [(Ty)i -(T,,t)i] (2.20-28 0 and: VI (UA)[I =U g = (Agy)i (2.20-285) where: i Q;* = heat rate from the mixture region to the interface in fluid node i, Btu /sec. Q VI 3

                                      =     heat rate from the vapor region to the interface in fluid node i, Btu /sec.

U*g = user-specified overall heat transfer coefficient from the mixture region to the interface in fluid node i, Btu /sec/ft.2.p f U3VI = user-specified overall heat transfer coefficient from the vapor region to the interface in fluid node i, Bru/sec./ft.2 fop l

February 1998 ow25 ms-2201.wpcib02279s 2.20.9-5 Rev.4

(Ayy); = mixture-vapor interface area in fluid node i, ft.2 In the not so typical opposite case of the mixture region superheated or saturated ((T y ),2 (T,,t)i) and the vapor region subcooled or saturated ((Ty), s (T,,t)3), (Wh);MIV and W MIV i are given by Equations V-20 and V-19, respectively, of Reference 2-1: L c-(2.20-286) and

                                                                                                                                                                                                  .  % c.

(2.20-287) _J In the case of both regions subcooled or both regions superheated, (Wh);MIV and W Mtv are given by Equations V-22 and V-21, respectively, of Reference 21: NC (2.20-288) (2.20-289) MIV As stated in Reference 2-1, the (Wh)i and W iMIV terms are treated implicitly, and their partial derivatives are obtained by neglecting the derivatives of (UA)iMI and (UA)3VI (i.e., treating (UA)i MI and (UA);VI explicitly). The details of all of these partial derivatives are not repeated here, since they were not modified for AP600. However, the following typical examples are shown for illustrative purposes. In the typical case of the mixture region subcooled ((Ty ); < (T,,1)i; (h y ); < (h )3) f and the vapor region superheated ((Ty)3 > (T,,t);; (hy); > (h g)3), Equation 2.20-280 simplifies to (with Equations 2.20-282 j and 2.20-284 substituted): O l February 1998 j oW25wW5220impf:1t422798 2.20.9-6 Rev.4

4

J (2.20-290) so that: 4,L O (2.20-291)

            'Ihe partial derivatives of (Wh)3 MIV with respect to the other nodal variables in this case are analogous to Equation 2.20-291, and are not shown here.

Also in this typical case of the mixture region subcooled and the vapor region superheated' , Equ 2.20-281 simplifies to (with Equations 2.20-282 and 2.20-284 substituted):

=

omm22m.wpr:liw2279s February 1998 2.20.9-7 - Rev.4

                                                                                                   . d, c (2.20-292) so that:

s c. I 0 1 i (2.20-293)

    'Ihe partial derivatives of Wi MIV with respect to the other nodal variables in this case are analogous to Equation 2.20-293, and are not shown here.

The bubble rise mass rate (W BR)i and its partial derivatives with respect to the fluid node i central variables in the modified NOTRUMP central numerics for AP600 are discussed in detail in Section 2.9, and no purpose is served by repeating them here. (WBR)i is given by Equation 2.9-2, and the B(W3g)i BMBR)i O(WBR)i BR)i partial derivatives * ' and are given by either Equations 2.9-48 B(Ug)i B(M J ' B(Uy)i B(My)i through 2.9-51, respectively, or Equations 2.9-52 through 2.9-55, respectively. 1 l 1

     'm25ms-2206.wpru279s                              2.20.9-8                                            Nev.

['} The droplet fall mass rate (Wap); (which was mentioned briefly in Section 2.9) and its partial

\v     derivatives with respect to the fluid node i central variables in the modified NOTRUMP central numerics for AP600 are discussed below. (W DF)4i s given by:

p - (, c. (2.20-294)

     - where:
             -                               -     4, c-(2.20-295)

(2.20-296; and: P O g (vg); e ((uy); -(uf)3] !g

'                               (ay); = min        max (uy);
                                                                                     . 1.

[(u,)3 -(ur )3] , O. (2.20-297) where: (n y)3 = vapor region void fraction in fluid node i (uy); = vapor region specific volume in fluid node i, ft.3/lbm (u f); = saturated liquid specific volume in fluid node i, ft.3/lbm Vg>> = drift velocity, ft/sec. Co = distribution parameter (Ayy)3 = mixture-vapor interface area in fluid node i, ft.2

,3              VFBRLIM            =      user-specified void fraction limit, discussed in Section 2.9 February 1998 oMo25 wns-220i.wpt: b.022798                         2.20.9-9                                            Rev.4

    <<V g >> and Coin Equations 2.20-295 and 2.20-296 are calculated by the drift flux model equations of Appendix G of Reference 2-1. Equation 2.20-297 for (ay); is analogous to Equation 2.9-59 for (GM)i-Several special cases exist for calculating the partial derivatives of (Wpp)3, due to the uses of " min" and " max" in Equation 2.20-294. In a manner analogous to what was done for (W3g); in Section 2.9, Equation 2.20-294 is expressed as:

TOP (Wop); = max _(2.20-298) BOT , O. where:

                                                                                         - <, c
                                                                                         ~

(2.20-299) aad:

                  '                                                                          -   a, c.
                  ~                                                                            ,

(2.20-300)

                                                                -   4. c.

Regarding the numerator (TOP), if

                                                                                             ~ % C-(2.20-301) i l                                                                                                     (2.20-302) 1.

l l l (2.20-303) i eMo25wo25-220i.wprJb.022798 2.20.9 10 *Nev. l

. . - . . ..- . . . . . - . = . . . _ . . . . . . . - . . - . . . . . . . . . - . . - .

                                                                                                            ~       (, c (2.20-304)

(2.20-305)

                             -                        -   , 4, c.

otherwise (if

                                                                                                                   . (, (

(2.20-306) (2.20-307) (2.20-308) I (2.20-309) (2.20-310)

                                                                                           . g c, Regarding the denominator (BOT), if
                                                  '~

O_ c:M62201 wpf:!WM 2.20.9-11 "$v',)

 . .    . ..          .-. _. . .      . _ . . . ~ . . . . - . . . . - . . . .      .-       . . . . .

I I < l f 1 no ese d (2.20-311) i l l (2.20-312) (2.20-3;3y l (2.20-314) O f ODNJ220i.wP :ll>C22798 February 1998 2.20.9 12 Rev.4

4 (2.20-315) J

                   .                   .s. n. c-Or,if e , (, C (2.20-316)

(2.20-317) O (2.20-318) (2.20-319) (2.20-320) es g otherwise (if e= , A, C. (2.20-321)

           . - - - - _ . .                          2.2e.,.,3                    --e:

                                               - Q,C (2.20-322)

(2.20-323) (2.20-324) (2.20-325) l Thus, if (Wpp)3 > 0. - I - , c-l (2.20-326) l (2.20-327) l l l l (2.20-328) 1 O c:WO25ww025 220i.wpf;1b.022798 2.20.9-14 Sev. N l

P

                                                                                                                                              -    e, c-(2.20-329) otherwise, if (Wop), = 0.:

O NDF)i = 0. (2.20-330) B(Uu); ONDF)i = 0. (2.20-331) O(Mg); DF)i

                                                                                                                              =0.                                  (2.20-332)

_d(Uv)i B(Wpp);

                                                                                                                              = 0.                                 (2.24333)

B(My) i ( Febru 1998 ow.5 .xr25 220i.wpuba1279s 2.20.9 15 "4 A

              ,-,y.---      ,     - - , - - , - , -        4.        -

n - .,-- - , , - . - ,,a--,. ,- ,_. , . , -

In the above, from Equation 2.20-297, for 0. < (ny)3 < 1. : 8(ay), = 3, ' 8(uy); 8(ug)i (u,)' - - B(uf)3 + . [(uy); -(uf);) B(Uy); (uy), . [(u,); -(uf)3] ,

                                                                   ,8(Uy)3       8(Uu)3,     8(Uu)3
                                                              ' B(u,)3      8(uf);
                                     - (ny)' . (uy)' .                                +   B(uy); . [(u8 ), -(uf)i]
                                                              ,8(Uu); - 3(Uu)i,          2;Uu);

(2.20-334) 8(ay)3 3' . ' B(uy)3 _ 8(uf); 8(u,)'. (u,)' . + . [(uy) - (uf)3] 8(Mu) (uy); [(u,), -(u )3] f ,8(M g ), 8(Mg)i, 8(Mg)3 O

                                                             ' 8(ug)3 - 8(u )3   f        8(uy)3                      ,
                                   - (ay)3     (uy); .                                +
                                                                                                  . [(u 8)8 - (uf)3]
                                                             ,8(Mg); 8(My);,             8(Mg)3 i                                                                                                                  (2.20-335) l l

i l i O eMo25wuo25-220i.wpr:lt 022798 2.20.9-16 ev. k

3n f , 8(ay); . 1. , ' 8(uy), D(ug);

                                     =
                      &(Uy),

(v8 )' - -

                                                                                                                                      +    3(u,); - [(uy )3 -(up3]

(uy); = [(v,)3 -(udi) ,0(Uy)i 8(Uy)i, a(Uy)i

                                                      -(ay); . (uy);. ' &(ug )3                        -    B(ud'.            +    B(uy), . [(u                  ); -(upi]       ,
                                                                                           ,8(Uy);                                 8(uy);                    s B(Uy )i,                                                           ,

t (2.20-336) i B(ay) 1, ' 3(uy)i

                                    =                                     *

(u,)' . + 3(ug)i

                    &(My)i             (uy); = [(u,); -(ud;]                   ,
                                                                                               , B(My),            8(M_    y ),,a(vf)i    8(My),
                                                                                                                                                            . [(uy), -(upi)                      .

L l I O

    \s                                                                                   ,                               ,

B(ug)'. - B(up'. 8(uy)'. +

                                                     - ( ay )i - (uy), .
                                                                                                                             +                      . [(u8); -(uf)i]
                                                                                         ,d(My);          0(My)i,                 30!v)3 (2.20-337)

In the droplet fall-related partial derivatives above, the partial derivatives g O(C 8(V o)I

                                                                                                                                                                     ).)i        are             i B(ny), and &(ay );
         . calculated from the drift flux model equations of Appendix G of Reference 2-1.                                                                                                        !

In all of the above, the partial derivatives of (uf); , (u,)3, and (vy); with respect to the fluid node i central variables are' discussed in Section 2.20.8. l t This concludes the discussion of the interfacial energy and mass exchange rates for interior fluid nodes . that are used in the modified NOTRUMP central numerics. p i () February 1998 c:wr25.wa25-220i.wpuw22798 - 2.20.9-17 Rev.4

2.21 References 2-1 Meyer, P. E., et. al., NOTRUMP - A Nodal Transient Small-Break and General Network Code, WCAP 10079-P-A (Proprietary), WCAP-10080-A (Non-Proprietary), August 1985. 2-2 U.S. NRC, Letter from Cecil O. Thomas to E. P. Rahe, Jr., Westinghouse Nuclear Safety Dept., " Acceptance for Referencing of Licensing Topical Repon," WCAP-10079(P),

                                              "NOTRUMP, A Nodal Transfer Small Break and General Network Code" (May 23,1985).

2-3 Chexal, B., Lellouche, G., A Full Range Drift-Flux Correlation for Vertical Flows, (Revision 1), EPRI NP-3989-SR, Revision 1. Special Repon, September 1986. , 2-4 Porsching, T. A., et. al., " Stable Numerical Integration of Conservation Equations for Hydraulic Networks," Nuclear Science and Engineering 43, pp. 218-225,1971. 2-5 Shah, M. M., "A General Correlation for Heat Transfer dming Film Condensation inside Pipes," International Journal of Heat and Mass Transfer, Volume 22, pp. 547-556,1979. 2-6 Zuber, N., " Hydrodynamic Aspects of Boiling Heat Transfer," USAEC Repon AECU-4439,

1959.

2-7 Collier, J. G., and 'Ihome, J. R., Convective Boiling and Condensation, Third Edition, Oxford University Press Inc., New York, NY, pp. 54 59, 1994. 2-8 Aerojet Nuclear Company, "RELAP4/ MODS , A Computer Program for Transient Thermal-Hydraulic Analysis of Nuclear Reactors and Related Systems," ANCR-NUREG-1335, i Volume 1, September 1976. i 2-9 Henry, R. E. and H. K. Fauske, "The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Shon Tubes," Transactions of the ASME Journal of Heat Transfer, Volume 93, pp.179-187, May 1971, i 2-10 Willis, M. G., NOTRUMP Preliminary Validation Reportfor OSU Tests, LTCT-GSR-001, Westinghouse Proprietary Class 2, July 1995. 2-11 Meyer, P. E., NOTRUMP Preliminary Validation Reportfor SPES 2 Tests, PXS GSR-002, , Westinghouse Proprietary Class 2, July 1995. j 2-12 Zuber, N., "On the Stability of Boiling Heat Transfer," Trans ASME, Vol. 80, pg. 711 (1958). I tb U ) February 1998 eM025wuo25-220swpf:6022798 2.21-1 Rev.4

                  , - . _ ,                                               _ _ 2 _ .-____.                       ,_

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O APPENDIX A LIST OF NRC REQUESTS FOR ADDITIONAL INFORMATION AND WESTINGHOUSE RESPONSES !O f oM025whatwpf:lb-022798 A-1 Februgl 98

         .        .       , - , . - -           ~ - - . - . - - _ . . _ . - . . -                 . . - . - . - . . . . . . - . . . . - -

l:

              'Ihis Appendix provides a road-map to all issues raised by the NRC Staff. The following tables define
      .O O       how the NRC issue has been dispositioned:

i Table'A-1 SDSER Confirmatory items Table A-2 SDSER Open items Table A-3 RAls Table A-4 FSER Open Items Where a formal written response was submitted to the Staff by Westinghouse, a copy is included for completeness. l l l l l l i l lo l I. l I

                                                                                                                                               '1 l

l l l'

V l-F

           . oM025wwax.wpf;tb-022698                                                                                   FebruRTY 1998 l-                                                                             A-3                                                      Rev 4

1 i'

I l l TABLE A-3 NOTRUMP RAI RESPONSES RAI # - Description of item Reference Where Answered RAI 440.325 Questions on NOTRUMP CAD Appendix A (WCAP-14206) related to PIRT, Section 1.3 contains final NOTRUMP modeling of SBLOCA PIRT noncondensible gases, and NOTRUMP l-D model. RAI 440.326 Should include an AP600 plant Appendix A nodalization and reference to SAR Section 1.2 contains AP600 calculations. plant noding diagram RAI 440.327 Provide a matrix of tests that will be Appendix A used for assessing each of tb PIRT Section 1.4 contains table of items. Also, identify the models that tests and parameters selected are to be validated for each test. for validation of NOTRUMP for highly ranked PIRT items RAI 440.328 Explain what analyses were perfonned Appendix A to determine the limiting failure. RAI 440.329 Describe the low flow correlations Appendix A' e applicable to the prediction of the ! (, i single and two-phase friction factors in NOTRUMP for AP600 and identify ) the test data that will be used for the assessment. RAI 440.330 Describe the enhancements made to Appendix A the NOTRUMP code for AP600. Section 2 contains the i NOTRUMP code changes for I AP600 calculations RAI 440.331 Provide the specific inputs for the Appendix A code extemals used to perform the analyses in the SSAR calculations done in January 1994. RAI 440.332 Provide a document describing the Appendix A methods and models comprising the long term cooling code and describe how the code is initialized from the NOTRUMP code. RAI 440.333 Justify the use of a fixed containment Appendix A

pressure boundary condition since the response of the safety systems depend
on containment pressure.

oM025w\ app-a.wpf:Ib-022598 A-11 ev

                                         -TABLE A-3 (Cont.)

NOTRUMP RAI RESPONSES RAI # Description of Item Reference Where Answered RAI 440.334 Provide a test matrix showing the Appendix A separate effects and integral tests to be Section 1.4 contains table of used in the validation of NOTRUMP tests and parameters selected for AP600. for validation of NOTRUMP RAI 440.335 Justification for using constant friction Appendix A factors, particularly at low flow, flow pressure conditions are needed. RAI 440.336 Describe if momentum flux is Appendix A included in AP600 analyses and justify its omission if it is not used. RAI 440.337 Demonstrate that the Macbeth Appendix A correlation is adequate for the low flow and pressure conditions expected for AP600. RAI 440.338 Demonstrate that the NOTRUMP Appendix A pump model can predict the AP600 pump coastdown. Describe and justify the use of the two-phase pump degradation curves for AP600 analyses. RAI 440.339 Provide time step and nodalization Appendix A studies to justify the AP600 Section 1.16 nodalization. RAI 440.340 Discuss the potential for boric acid Appendix A build-up and precipitation during long transients for AP600. RAI 440.341 Describe in detail the IRWST model Appendix A including how the sparger and plumes are handled as well as their influence on IRWST injection and PRHR heat removal. O February 1998 ov025wwaxcupf.lb422598 Rev 4 ) l A-12 4 l

 .. _-.           _. _._ m       ._ _ . _ . _ _ _ _ _ . _ . . _ _ _ . . _ _ _ _                            . _ _       _ _ _ _ _ _ _ _ _

I

   .tG                                                                   -TABLE A 3 (Cont.)

V NOTRUMP RAI RESPONSES RAI # Description of item Reference Where Answered RAI 440.721 (c) Provide a thorough explanation . Appendix A (Issue raised during regarding NOTRUMP's misprediction 7/29-780 ACRS of mass flow out of the ADS stage I, Meeting) 2, and 3 valves in the OSU experiments (and related pressurizer refill). Improve the justification as to why this deficiency is acceptable. h RAI 440.721 (d) Provide an explanation for Appendix A (Issue raised during NOTRUMP's mispred.'ctions when Section 8.3.4 7/29-7/30 ACRS compared to the OSU test results of Meeting) DVI line breaks. RAI 440.721 (e) Explain the significance and justify Appendix A (Issue raised during the bases for any differences in the 7/29-7/30 ACRS Nodalization between the two integral Meeting) test facilities (OSU and SPES) and the ' AP600. RAI 440.721 (f) Provide more details on NOTRUMP's Appendix A

  .D/Q      (Issue raised during 7/29-7/30 ACRS misprediction of pressurizer drainage       Section 1.16 in the OSU tests. Thoroughly explain        Section 8.3.4 Meeting) -                          the significance of this deficiency in .

the code, such as non-conservatively predicting IRWST flow, and how it ' will be treated in performing AP600 calculations. RAI 440.721 (g) Related to (f) above, Westinghouse is Appendix A (Issue raised during proposing to apply a penalty in Section 8.3.4 7/29-7/30 ACRS IRWST level. Provide a detr 3 Meeting) explanation of how the penary is determined via scaling from the OSU test data to the AP600. Justify why this is conservative. RAI 440.721 (h) Provide detailed justification for not Appendix A (Issue raised during including momentum flux in the Section 1.7.5 7/29-7/30 ACRS NOTRUMP models. Meeting) RAI 440.721 (i) Provide discussion on how (Issue raised during NOTRUMP treats entrainment Appendix A 7/29-7/30 ACRS (waterspout) in branch lines. l Meeting) i eM025wupp-ax.wpf;lb 022698 FeiEiary 1998 A-39 Rev. 4

l TABLE A 3 (Cont.) NOTRUMP RAI RESPONSES RAI # Description of Item Reference Where Answered RAI 440.721 (j) Justify and demonstrate why use of Appendix A (Issue raised during Henry-Fauske/ HEM rather than 7/29-7/30 ACRS Moody is conservative for calculating Meeting) break flow through the DS stage 1,2, and 3 valves and why this is appropriate for an appendix K type calculation. O O ow25%apr;ib 022598 A-40 *** [tev,993

TABLE A-4 NOTRUMP FSER OPEN ITEM RESPONSES FSER 01 # Description of Item Where Answered FSER O1440.749F Provide evidence to demonstrate that the use of Appendix A the Henry /Fauske and HEM models for the RAI 440.721 (j) calculation of discharge rate from ADS is Conservative FSER O1440.750F Provide root cause and strategy regarding Appendix A reliability of using NOTRUMP for analysis of RAI 440.721 (d) the double-ended guillotine breaks of a DVI line, considering the lack of good agreement for this transient in the verification. FSER O1440.751F The staff has not yet completed its review of Appendix A RAI 440.721. RAI 440.721 FSER Ol 440.725F Document application restrictions for Appendix A NOTRUMP in Final V&V Report Subsection 1.17 added FSER O1440.795F Document changes to code numerics, including Appendix A derivation of all difference forms of the Subsection 2.20 added equations being solved. In addition. every Subsections 2.1,2.9 and l equation altered or changed from the from that 2.11 modified exists in the original, approved NOTRUMP code must be provided with derivation complete to the level of the difference form in the code. FSER 01440.7%F Momentum Flux - Benchmark deficiencies Appendix A Part a against additional detailed calculations. Subsection 1.7 modified FSER O1440.796F ADS 1-3 review test data analysis report to Appendix A Part b assure data reduction correct. FSER 01440.796F Entrainment - considered as part of the overall Appendix A Part c scaling and level penalty development. FSER 01440.796F Level Penalty - perform multi-loop scaling Appendix A Part d analysis for time period of ADS 4 and IRWST Subsection 1.5 modified draining. Justify basis for ADS flow as affected by entrainment. FSER O1440.7%F Surg: Line Flooding - an effort similar to the Appendix A Past e above FSER 01 is to be made. FSER O1440.796F Noding - provide more justification for what Appendix A Part f was used for AP600 since it differs from Subsection 1.16 added i accepted CSAU work, especially for PRHR and downcomer. i oM02$w\ app-ax.wpf:t b-022798 Februarr 1998 A-41 Kev 4 ,

w=am;== \ NRC FSER OPEN ITEM m Question 440.795F (OITS - 6440) Westinghouse stated during the December 10,1997, ACRS Thermal / Hydraulic Subcommittee meeting l that changes had been made to the NOTRUMP code numerics. The code numerics must be described l in full detail, including derivation of all difference forms of the equations being solved. In addition, every equation altered or changed from the form that exists in the original, approved NOTRUMP code ' must be provided with derivation complete to the level of the difference form in the code.

Response

The original NOTRUMP central numerics, which are documented in Reference 440.795F-1, were modified for application to AP600. De main modification to the numerics was the change from the net mass flow-based to the net volumetric flow-based momentum conservation equation. Additional modifications to the numerics were the implicit treatment of bubble rise and droplet fall, and the implicit treatment of gravitational head. These modifications are described in Reference 440.795F-2 (in Sections 2.4,2.9. and 2.11). To address the above comments on documentation, a new Section 2.20 is being added to Revision 4 of Reference 440.795F-2. With this new section, changes to the NOTRUMP central numerics, which were made for AP600, are documented in one place, from beginning to end. The derivations, which are required to modify the starting differential equations of Reference 440.795F-1, and then place them into finite-difference form for solution, are presented. /3 The changes to the NOTRUMP central numerics for AP600 affect the momentum conservation V equation for each non-critical flow link (i.e., Equation 2-33 in Reference 440.795F-1), and indirectly affect the energy and mass conservation equations for the mixture and vapor regions of each interior fluid node (i.e., Equations 2-1 through 2-4 in Reference 440.795F-1). The modifications for the volumetric flow-based momentum formulation affect the stmeture of the starting momentum conservation equation, as well as the finite-differencing of all of the aforementioned conservation equations. The modifications for the implicit treatment of bubble rise and droplet fall only affect certain implicit terms in the finite-differencing of the energy and mass conservation equations for the mixture and vapor regions of each interior fluid node. The modifications for the implicit treatment of gravitational head only affect certain implicit terms in the finite-differencing of the momentum conservation equation for each non-critical flow link. In the new Section 2.20 in Revision 4 of Reference 440.795F-2, the modifications to the momentum conservation equation for non-critical flow links are documented. This includes the changes to the structure of the equation for the volumetric flow-based formulation, followed by the finite-differencing derivations. Next, the finite-differencing derivations for the energy and mass conservation equations of the mixture and vapor regions of the interior fluid nodes are documented. The section concludes with a presentation of the modifications to the NOTRUMP central matrix and its elements, which is analogous to what is documented in Appendix E in Reference 440.795F-1. iV' T Westinghouse 440.795F-1

p NRC FSER OPEN LTEM

References:

e 440.795F-1 Meyer, P. E., "NOTRUMP: A Nodal Transient Small Break And General Network Code," Westinghouse Electric Corporation, WCAP-10079-P-A, August 1985. 440.795F-2 Fittante, R. L., et. al., "NOTRUMP Final Validation Report for AP600," Westinghouse Electric Corporation WCAP-14807, Revision 3, November 1997. SSAR Revision: None e 440.795F-2 T Westinghouse

 .    . . -      .-         . . ~ . -     - . . -         . -      . . - - . -       . _ . .         .-         . . . . _ - - . _

NRC FSER OPEN ITEM E J]

   ]         Question 440.796F Part a (OITS - 6441)                                                                                  i The following commitments were made by Westinghouse at the conclusion of the December 10, 1997 ACRS T/H Subcommittee meeting and must be fulfilled.

a. Momentum flux - Deficiencies (in the NOTRUMP model) are to be benchmarked against additional detailed calculations using actual two phase flow equations that incl de the effects of compressibility, including the condition of constant entropy.

RESPONSE: . i In section 1.7.5 of the Final Validation Report for NOTRUMP', an assessment was performed of the effect ofignoring the momentum flux terms. This initial assessment indicated that while the ADSl-3 valves and piping would experience a small effect due to fluid acceleration, in the ADS 4 l piping the effect could be significant. To further evaluate whether the lack of momentum flux terms for this component in NOTRUMP could lead to erroneous results, a detailed pipe model was developed. The modelintegrates the momentum and energy equations along a detailed mesh representing the ADS 4 piping from the hot leg to the squib valves, where the minimum area occurs. First, the model of the ADS 4 piping will be described. A comparison will then be made with flows calculated by NOTRUMP. Detailed model of the ADS 4 oicine Figures 440.796f-l and 440.796f-2 show two views of the ADS 4 valves and their piping. A pipe ofinner diameter 10.125 inches (0.56 sq. ft area) is connected to the top of the hot leg. An elbow turns the pipe to a horizontal configuration. About 7 feet downstream, a horizontal tee diverts some of the flow into the 8.5 inch (0.39 sq. ft area) piping leading to one of the two valve packages (the pipe from the tee to the valves is designated " branch 2" in this response). Downstream of the tee in the main pipe, a reducer leads to the 8.5 inch diameter piping which will lead to the other valve package (the main piping and this valve package are designated " branch 1"). The flow resistance (irrecoverable losses due to friction and form loss) through this piping network has been conservatively established for incompressible flow. Bounding assumptions have been used for pipe lengths (about 46 feet total, in contrast to the typical configuration shown in Figure 440.7%f-1), and fittings (a total of 6 elbows are assumed in branch 1, and 7 elbows in branch 2, compared with the smaller number in the typical configuration). The total irrecoverable loss coefficient for this conservative configuration was estimated as 4.2, based on the nominal ' flow area through both branches (2*0.39 sq. ft), assuming complete turbulence (constant) friction factors. l l lO d (,/ 440.796F part a -1

                                                                                                           .~                     ..

                                  . - ~                               .                    .          -

p-

  !        d LU                                                                              NRC FSER OPEN ITFM This piping network was simulated with a total of 442 cells, as illustrated in Figure 440.796f-3.

Ol In this figure, each "+" represents one cell boundary or node. The cell length is 0.25 feet, with ' I smaller increments taken at area changes in the reducer and gate valve (there are also area changes at the tees from the hot leg into branch 1, and from branch I to branch 2, but these are treated with special models as discussed below). Momentum and Enerev Eauations "Ihe momentum and energy equations to be integrated along the piping network are simplified ! equations in which steady state, equilibrium, homogeneous, adiabatic conditions have been assumed. The assumption of homogeneity (zero slip) results in a high estimate of the effect of I acceleration on the pressure gradient, as pointed out in Section 1.7.4 of the NOTRUMP Final Validation report. The momentum and energy equations in this form are: l dP

             -=      fvf'W'       @2 W du dz        2D < A,          u - A dz 1(a,b) r       23 d

, h+u =0 l dz ( 2, where h and u are the mixture enthalpy and velocity, W is the mixture flow rate, viis the liquid 2 specific volume, G is the two phase multiplier, fis the friction factor and D and A are the pipe diameter and area. Since: W = uA 2 v where Vis the mixture specific volume, and W is constant, this substitution can be made into equations 1 and 2. In addition, since for homogeneous flow: 440.796F part a-2 3 Westinghouse

_S NRC FSER OPEN ITEM b' O G h = hf + xhg 3(a,b) v = vf + xvg where x is the flow quality WJW, equations 1 and 2 can be set up in terms of pressure and quality. After some manipulation, 21 1 dA 'Bh

                                           +Gv2 dv'dP dx_ G vA dz              <dP            BP>dz i          dz                   hg+ G'vvy                                                             4
              =

a 1 dA b dP c A dz c dz i

                         ' G @ ,+EW+G v-vg "

dP _ 2D v dz < c,A dz 5 dz b* 1+G 2 ' dv Q, uJ qdP- - vg c, where dy/dz is the elevation gradient. , Friction and form losses Friction 2 and form losses are calculated using two phase multipliers developed by Collier and others The two phase multiplier for losses in both pipes and fittings takes the basic form:

          @$, = (1 -x)24 2
          @2 = 3, _C , 1                                                              6(a,b)

X X where C is a value which depends on the fitting or pipe, and on the fluid conditions, and where X is the lockhart-Martinelli parameter, defined by: l l I 440.796F part o -3 o

l

7. - y I

tU NRC FSER OPEN ITEM O f gp> # dzs i 1-x 'vf X= m - 7 dP' x ') y g dz , , , l In equations 6 and 7 above,it has been assumed that the single phase loss coefficient and/or friction factors are independent of Reynolds number (mass velocities are sufficiently high rnch i that this assumption is reasonable). Tees l Tees require special treatment because flow splitting and phase separation will occur Methods j summanzed in Lahey (1984)' were used to calculate pressure losses. These methods attribute l pressure changes in the main pipe due to momentum change (modified by a pressure recovery l term Ki.2), defined by (equations [19] and [20] of Reference 2): M-2 i = ~(V6-VkG) 2 2 i 50 8(a,b) K 1-2 =.11 + y l G, D, 3 .,7 pf , where 1 denotes the main pipe upstream of the tee,2 denotes the main pipe downstream of the tee, and (assuming homogeneous conditions): i v; = vf + x,vy, l l . 9(a,b) v=v+xv, 2 f 2f l where xi and x2 are the flow qualities upstream and downstream of the tee (see below). l The pressure change into the branch (denoted as 1) consists of an acceleration change and a form loss. The form loss is calculated as described in the previous section. The acceleration change is 440.796F part a-4 1 3 Westinghouse l l

1 NRC FSER OPEN ITEM l t n 1

   ,._/

given by (equation [13] of Reference 3 for homogeneous flow): i i vG_32 10 AP_3 = 1 < 3V3 > The assumption is made that the flow is locally incompressible at the tee junction. The flow split at the tee is calculated using correlations recommended by Seeger (1986)'. These 1 correlations describe the quality into the branch (3) in terms of: f S 1 b=f b X1 g G, , 11 The functional form depends on the tee orientation. For the vertical tee (from the hot leg), equation [2] of Reference 4 is applied, while for the horizontal tee, equation [8] of Reference 4 is applied. _ Critical flow at the sanib valve By carefulintegration of the momentum and energy equation,it is possible to find the maximum N (d flowrate (choked flow ) in a pipe, by finding the point at which the denominator in the momentum equation approaches zero. Because the last valve in each branch is the mimmum flow area (a design requirement), choking is likely to occur at this valve (this was confirmed by later calculations). The HEM was applied at the last cell in each branch, using as reservoir conditions (for branch 1,for example): l 2 hoi =h + 2b ji 12 41 = St+XJtsf, where jl is the next to last node in branch 1. The flow was assumed to be adiabatic and frictionless from this point to the squib valve minimum area. A similar calculation was performed for branch 2. Calculated results l The equations above w re implemented in a small computer program; the flowrate through ADS 4 was calculated for a range of pressures (20 to 80 psia in the hot leg,14.7 psia at the exit) and O) (, wgg, 440.796F part a -5 r l

p l l f E NRC FSER OPEN ITEM qualities (20% to 100% in the hot leg). The model was benchmarked to the incompressible total O loss coefficient by runmng a case with a hot leg pressure of 15 psia and 100% quality. At this low pressure difference, effects of compressibility and acceleration are mimmal and the predicted loss ! l should agree with the incompressible value. An adjustment of approximately 10 percent in the overall resistance was required to achieve good agreement with the loss coefficient of 4.2. It was I also assumed that all the hot leg flow entered the ADS 4, for maximum acceleration. Figures 440.796f-4 and 5 show the static pressure and fluid velocity in the piping for a hot leg pressure of 50 psia and a flow quality of 100%. There is an immediate 5 psi pressure drop at the entrance, then a pressure loss followed by a pressure recovery at the tee, then additionallosses along the pipe and at each elbow. At the first valve, there is a pressure loss, then recovery, followed by a pressure loss (the irrecoverable loss due to the valve is applied at the valve exit). Figure 440.796f

-5 shows that the fluid velocity within the pipe is highest at the hot leg entrance, reaching nearly 800 ft/s. Most of the acceleration occurs, however, at the squib valve.

Figures 440.796f -6 to 8 show conditions when the flow quality is 20%. In this case, phase separation occurs at the tee, with a higher quality mixture flowing into branch 2 (Figure 440.796f

-8). Calculations assuming no separation occurs show that this phenomenon has a negligible effect on the amount of vapor which can be vented.

Vapor flow versus hot leg pressure for a range of flow qualities predicted by the model are shown in Figure 440.796f-9. The 100 percent quality data show good agreement with points estimated g from a handbook, shown in Figure 1.7-9 of Reference 1. At approximately 40 psia, critical flow is W calculated to occur at the squib valve, and the model and handbook data begin to diverge. The model calculated data were used to generate a response surface which were then used to calculate ADS 4 vapor flow, given hot leg pressure and quality from NOTRUMP. This comparison is shown in Figure 440.796f -10 for the time period between ADS 4 opening and IRWST injection. These figures show good agreement between NOTRUMP and the detailed model, as long as critical flow conditions exist prior to 3000 seconds. The good agreement during choked flow indicates that the flow resistance upstream of the squib valve has a minor impact on the flow, even with the relatively high fluid velocities noted. When the flow becomes sub-critical, NOTRUMP predicts a higher vapor flow of about 20 percent (corresponding roughly to a 35 percent lower flow resistance) . Overall, the total vapor vented is underpredicted by NOTRUMP soon after opening, then is overpredicted, as seen in Figure 440.796f-l1. However, the NOTRUMP total vapor released is only about 5 percent higher at the time the IRWST comes on. Comparbon of NOTRUMP and model details indicates that the difference during sub-critical flow can be attributed to: 440.796F part a-6 T Westinghot;se

l l NRC FSER OPEN ITEM rs b] a) Underestimation of the two phase pressure drop through fittings. The large number of elbows assumed in the ADS 4 piping, for example, contributes to a 20 percent increase in flow resistance. b) Underestimation of the acceleration terms. Even if the flow is no longer critical, fluid acceleration and expansion at low quality will contribute to increased pressure drop. Conclusion The over prediction by NOTRUMP of AD34 vapor flow near the end of the transient is not considered to be a significant problem because of the bounding nature of the ADS 4 piping which was modelled. As shown in Figure 440.796f-1, the number of elbows and lengths of piping in actual designs will be substantially less than what was assumed in the NOTRUMP calculation. In addition, pressure losses due to acceleration were maximized by assuming homogeneous fluid conditions.

REFERENCES:

          ' WCAP-14807, Revision 3.

2 Collier, J. G., Convective Boiline and Condensation,3'd Edition, Oxford-Clarendon press, ij

    '    3 1994.

Lahey, R. T., Nematollah, S., "The Analysis of Phase Separation Phenomena in Branching Conduits", Int. J. Multiphase Flow, Vol.10, No.1,1984.

         ' Seeger, W., et al., "Two-Phase Flow in a T-Junction with a Horizontal Inlet", Int. J. Multiphase Flow, Vol.12, No. 4,1986.

t i r~~s. I 1

    '#      [ Westinghouse                                                                    440.796F part a -7 i

l l

[ f a bl NRC FSER OPEN ITEM Figure 440.796f-1. Typical AP600 ADS 4 piping layout. View 1. heber c.0" 6' 6" 6* 9" a.Anr , saved

                                     <=i           i=i
                                     )                         s2 /

A C. M '.s.w.W.i-._f' r v y i 3 : v

                       /     %(2%

n

                                                                       ?-
                                                                            /
                                                                            //                         q A                 /              #         , M- hp,8 2
     ,   f
                       /     -,-,

y e oteston Eu. tar .1 kkpor us. g'. 10'6" g l 440.796F part a-8 Westinghouse l

j NRC FSER OPEN ITEM l tO V, 1 Figure 440.796f 2. Typical AP600 ADS 4 piping layout. View 2. I I 1 l l 1 B A I

                                        /                                 ;

RCS 10CBC U398 I , RCS 10CBC L1388 [ 7 l RCS 10 v0048 { RCS 10 v0040, [

                                                       . .       LL*.CW.

( l I 9 l RCS te 10140 l ACS 10 v0148 RCS 10BTA L1338

                                          ~       ~
           .C. ,e... m3,.#                                           j
                                   /        , ,,             ,

O gmi. 440.7,68 ., -,

L- J NRC FSER OPEN ITEM O Figure 440.796f-3. ADS 4 piping flow area distribution ADS 4 PIPING FLOW AREA AREA (SQ. FT) 2 -- , 1.8-- l 1.6-- 1.4 -- 1.2-- 1-- 0.8-- BRANCH 1 REDUCER 0.6- , . 0.4-- 1

                                          -" "":._.c       -:=:: ::=:::= -"'-'"-"                                                      ::::

0.2-BRANCH 2 TEE SQUlB vat.VES , . 0 : : : : : : - - 15 20 25 30 35 40 45 50 0 5 10 DISTANCE FROM HOT LEG (FT) 440.796F pod a-10 Westinghouse h

NRC FSER OPEN ITEM - 1 O Figure 440.796f-4. Static pressure in ADS 4 piping for hot leg pressure = 50 psia, quality = 100 %. STATIC PRESSURE IN ADS 4 PIPING (P=50,X=100%) PRESSURE (PSIA) 50 - BRANCH 1 REDUCER 45 - y

++

40-- ,v -

GATEVALVES ) ., 30 -- 25 -- SQUlB VALVES

++

20 : : : : : : : : : 0 5 10 15 20 25 30 35 40 45 50 DISTANCE FROM HOT LEG (FT) gg 440.796F part a -11

l. . . ..

1 I {- d NRC FSER OPEN ITEM O Figure 440.796f-5. Fluid velocity in ADS 4 piping for hot leg pressure = 50 psia, quality = 100%. FLUID VELOCITY IN ADS 4 PIPING (PO=50,X=100%) VELOCITY (FT/S) 1600 --

1400 -- + 1200 - - 1000 -- 800 -- ,,j f ...a 600 - I . . .. 7;; ::=:::Z:: ::Z:: Z~ ~ '"

                    *r 400 --            +

BRANCH 1 200 -- 0 : : : l l : : 0 5 10 15 20 LS 30 35 40 45 50 DISTANCE FROM HOT LEG (FT) 1 l 440.796F port a-12 T Westingh0use _A

l l .m =: 1 f ! 4 NRC FSER OPEN ITEM ti 2 V 1 Figure 440.796f-6. Static pressure in ADS 4 piping for hot leg pressure = 50 psia, quality = 20%. l 4 STATIC PRESSURE IN ADS 4 PIPING (P=50,X=20%) l PRESSURE (PSIA) 50 - - BRANCH 1 45 --

                                   +,,.

1 .

                                                .....g .

40 - t,, g

                                                                                                " N. .     .

N 35 -- ' i BRANCH 2 .. .. ;; j

h 30 --

)

v. . . ,,;;-

4 25 -- 4

20 --

15 -- 1 10 : : : : : : : : ; ;

O 5 10 15 20 25 30 35 40 45 50

. DISTANCE FROM HOT LEG (FT) I 1 y ggg 440.796F part a -13 h E

1 l l? '$ m .

^""

NRC FSER OPEN ITEM O1. Figure 440.796f-7. Fluid velocity in ADS 4 piping for hot leg pressure = 50 psia, quality = 20%. ll FLUID VELOCITY IN, ADS 4 PIPING (PO=50,X=20%) VELOCITY (FT/S) 900 - 1

                                                                                                   +       l 800 --

t 700 -- I i 600 -- , 500 -- + I 400 -- ..

                                                                    .... . 4:
                                                           ......+-

300 -- 4:: :*"

                                                    "                                                      1 j::                                                                                    l 200 --                                                                          '"

100 -- BRANCH 1

l 0 : : : : : : : : : : 1 0 5 10 15 20 25 30 35 40 45 50 DISTANCE FROM HOT LEG (FT) 440.796F part a-14 T Westinghouse

l 4 NRC FSER OPEN ITEM f

    %s Figure 440.796f-8. Flow quality in ADS 4 piping for hot leg pressure = 50 psia, quality = 20%.

QUALITY IN ADS 4 PlPilNG (PO=50, X0=20%) 1 QUALITY , l 0.4 - l 4

 ,      0.35 - .

l

                                                                                        ,          .             ...+              ,

O.3-- BRANCH 2 0.25 -- 1 0.2 :* 1 0.15 -- +

                             ;;;;:             :             : c a;;;; :        .

0.1-- i BRANCH 1 0.05 -- 0 : : ; ; ; ; ; ; ; ; O 5 10 15 20 25 30 35 40 45 50 DISTANCE FROM HOT LEG (FT) i O T Westinghouse , 440.796F part o -15

i b NRC FSER OPEN ITEM O Figure 440.796f-9. Vapor flow vs hot leg pressure and quality predicted by pipe model. ADS 4 VAPOR FLOW PREDICTED BY MODEL MASS FLOWRATE (LB/S) 80 - a 70 - - U

                   + MODEL aCRANE

EO - - +

A 0.2 TO 1.0 + . 50 --

                                                                          +           +           .     +

40 -- +

e .

30 --

. 4

20 -- + ,

                                                +.           +

10 -- I 0 : : : : : : : : 0 10 20 30 40 50 60 70 80 HOT LEG PRESSURE (PSIA) f i 440.796F part a-16 : T Westinghouse l l I I

        . . - . - -       _  ...             ..  . - - .      . . ~ . -    - - . . - . . .

l 7 NRC FSER OPEN ITEM E O Figure 440.796f-10. Comparison of NOTRUMP and pipe model vapor flows i ADS 4 VAPOR FLOW FLOWRATE (LBIS) 70 - - i j NOTRUMP 60 -- ., - MODEL i S0 - - : l l: 40 . f' O - I th 3[ 10 -- 0 : : : : : : : 2000 2200 2400 2600 2800 3000 3200 3400 3600 TIME (S) O W Westinghouse 440.796F part a -17 i l

El NRC FSER OPEN ITEM e Figure 440.796f-l1. Comparison of NOTRUMP and pipe model vapor flows (integral) INTEGRAL OF VAPOR FLOW MASS (LB) 25000 - NOTRUMP

                                                                            --- MODEL 20000 --

15000 -- MODEL e 10000 -- 5000 -- l 0 : : l l l l l 2000 2200 2400 2600 2800 3000 3200 3400 3600 TIME (S) l l 440.796F part a-18 Westinghouse 1 _ - - _ _ _ _ _ _ _ - _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - _ _ _ _ - _ - - - _ _ _ _ - - - _ _ _ _ - _

l NRC FSER OPEN ITEM O Question 440.796F Part b (OITS - 6441) l ' The following commitments were made by Westinghouse at the conclusion of the December 10,1997 l ACRS T/H Subcommittee meeting and must be fulfilled. l b. ADS 1 the test data analysis report is to be reviewed to assue that the data reduction was l performed correctly. 1

Response

Westinghouse has reviewed the methodology used in the data reduction and has incorporated several l ' modifications discussed at the December 10,1997 ACRS T/H Subcommittee meeting. Consideration of the source stagnation enthalpy used to determine the local fluid qualities and the velocity head of l the fluid upstream of components at choked flow conditions are the most significant items. These, ; along with other items, will be documented in the revised ADS Test Analysis Report (WCAP-14305, l l Rev. 2), expected to be submitted to the Staff by February 27,1998. ' l SSAR Revision: None V~\ v l l O E Westinghouse 440.796F Part b -1 1 l

                                                                                                          .g_.

NRC FSER OPEN ITEM ^ O Question 440.796F Part c (OITS - 6441) , The following commitments were made by Westinghouse at the conclusion of the December 10,1997 ACRS T/H Subcommittee meeting and must be fulfilled.

c. Entrainment - consider as part of the overall scaling and level penalty development 1

Response

Phase separation associated with the Hot Leg (HL)/ ADS-4 T-junctions is ranked as a High/ Medium phenomena during IRWST injection in the AP600 SBLOCA PIRT. While a general analytical method does not exist for predicting this complex two-phase flow phenomena, expedmental work by Seeger, et. al. (Reference 440.796F-c-1) and Mudde, et. al. (Reference 440.796F-c-2) with vertically- l oriented branch geometries at different scales (similar to AP600 HL/ ADS-4 T-junction) suggests that i this phenomena can be correlated with diameter and massflow ratios between the main run of a T-junction and its branch. l Based upon preservation of massflow ratio, bottom-up (i.e. diameter ratio) scaling indicates that both SPES-2 and OSU Hot leg / ADS T-junction diameter ratios are very well scaled to the full scale AP600 plant. Therefore, phase separation phenomena in the HUADS-4 T-junctions should also be well-l scaled. Further details on this subject can be found in References 440.796F-c-3. Since this 1

 ~N phenomenon is well scaled in OSU, the level penalty which is based on OSU data (see RAI 440.721 (V   (g} contained in Appendix A of Reference 440.796F-c-4), can be applied to AP600.

l References 440.796F-c-1. W. Seeger, J. Reimann, and U. Muller, "Two-phase Flow in a T-Junction with a Horizontal Inlet", Int. J. Multiphase Flow, vol.12, No.4, pp. 575-585,1986. 440.796F-c-2. R. Mudde, J. Groen, H. van den Akker, "Two-phase Flow Redistribution Phenomena in a Large T-junctiori' ',t. J. Multiphase Flow, vol.19, No. 4, pp. 563-573,1993. 440.796F-c-3. apt >; . scaling and PIRT Closure Report, WCAP-1472~,, Rev. 2. 440.796F-c-4. NOTRUMP V&V Report, WCAP-14807, Rev. 4 SSAR Revision: None b T Westinghouse 440.796F part c -1

NRC FSER OPEN ITEM O. U Question 440.796F Part d (OITS - 6441) The following commitments were made by Westinghouse at the conclusion of the December 10,1997 ACRS T/H Subcommittee meeting and must be fulfilled d. Level Penalty - a multiloop scaling analysis is to be performed for the time period of ADS 4 and IRWST draining. Justify the basis for ADS flow, ADS 4 flow affected by entrainment ofliquid and the corresponding effect on the pressure loss due to two-phase flow. This is to be described in sufficient detail that a step towards scaling to AP600 can be made.

Response

A multiloop scaling analysis has been performed for the time-frame between ADS 4 and IRWST draining. The technical areas described in the above FSER Open Item have been addressed and will be documented in the revised "AP600 Scaling and PIRT Closure Report" (WCAP-14727), expected to be issued by February 27, f998. SSAR Revision: None A

;d*

3 W65tingh00S8 440.796F Part d -1 I

l l l FNnn i NRC FSER OPEN ITEM n f

 \   J Question 440.796F Part e (OITS - 6441)                                                                      l The following commitments were made by Westinghouse at the conclusion of the December 10,1997 ACRS T/H Subcommittee meeting and must be fulfilled.

e. Surge Line Flooding - an effort similar to that applied to the level penalty is to be made.

Response

1. Introduction The AP600 pressurizer surge line is composed of various sections of vertical pipe, inclined straight pipes, and inclined helical elbows, as shown in Figures 1-1 and 1-2. An attempt was made to find the limiting section for the CCFL and the scaling effect so that the liquid downflow rate from the pressurizer can be determined.

Geometrical characteristics of the surge lines for AP600, OSU, and SPES test facilities are sum-marized in Table 1-1. Fluid properties in Table 1-2 are for saturated steam and liquid at 35 psia. This pressure is assumed when liquid draining from the pressurizer becomes important to regulat-ing IWRST liquid injection rate to the primary system. f')% c CCFL in Inclined Pipe vs. Vertical CCFL Wallis' model for CCFL in a vertical pipe')is given in terms of dimensionless volumetric fluxes by

                                   .            e (j,)1/2 + m(-jf )1/2 =C                                   (1-1) where j = j,jp,/(gDAp) with steam superficial velocity,j , gand similarlyji* is defined. C ranges from 0.75 to 1.0. This equation is for a small pipe; scaling effects will be discussed later.

The flooding in an inclined straight pipe is estimated by applying Taitel-Dukler's flow regime 2 transition from a co-current stratified flow ) to a counter-current stratified flow. It is composed of the Kelvin-Helmholtz critical flow condition for instability of stratified flow (Section 1.1) and the steady state flow balance (Section 1.2). 1 440.796F part e -1

NRC FSER OPEN ITEM e 1.1 Kelvin-Helmholtz Critical Conditian The Kelvin-Helmholtz critical condition can be expressed in terms of Wallis' dimensionless volu-metric flux,jg** 1/2 j[ > C 2 (1-2) da

                                   -D
                                 . 3-   g where D is the pipe diameter, hi is the liquid level of the stratified flow, a is the void fraction, and 0 is the pipe inclination. Various values are assigned to C2 by investigators but Taitel-Dukler pro-posed C2 = 1 - h/D. Eq. (1-2) is a function of the liquid level or the void fraction, Fig.1-3 for cos0
 - 1. It should be noted that this condition applies for both co-current and counter-current flows.

1.2 Force Balance Relations Steady state force balance for counter-current flow is Liquid

               %                                             dP
               ,o. s                                   -A f dx, IwgSf + t,Sj + pf Af gsine = 0  (1-3)
                         , Steam h

e - A,g'dP' + tw,S,-T,S, + p, A,g sin (1-4) 0=0 where tw and t iare the wall shear and interfacial shear and Si, Sg , and Si are the wall (for each phase) and interfacial surface areas per unit length. From the difference of these two equations the interfacial force balance is obtained. I Si <S S S

                                                  +   + g; + Apgsine = 0                      (1-5)          i
                      -Twig,+Tw,- 3 where the approxmation tw, = t, employed by Taitel-Dukler has been used. In addition, it is assumed that:

s p t wf = f' 9t(lt) 2 and tw,=fjg(Jg)'# 2 440.796F part e -2 3 Westinghouse l

NRC FSER OPEN ITEM B*5

 %J s       S wherefi andfg are the liquid and steam smooth wall friction factors except for the velocity in the Reynolds number, which is combined with j2. Eq. (1-5) is, therefore, a function of the superfi-cial velocities ji,j and g    the void fraction a. Elimination of the void fraction from Eqs. (1-2) and (l-5) gives a critical curve in the coordinate system of the superficial velocities. The obtained l      curve is translated to the dimensionless coordinate system (h ), and compared with the vertical CCFL in Figures 1-4 and 1-5 for OSU and AP600 'vge lines, respectively.

It is seen that the CCFL in the vertical section is more limiting than the inclined pipe section and controls the liquid downflow rate from the pressurizer, provided that centrifugal effects are small (Section 3.2).

2. Scaling for CCFL in A Vertical Pipe In terms of dimensionless pipe diameter, D = D g3ps 1/2 (2-1) l p &c0)

V the following dimensionless flux was defined3 )

                            .    .'p   0 /2 l, a j, 3                                                 (2-2)
                                   <K >

where 2-2

                                      = min K,                                    (2-3)

D . D_ where Ko = 0.645 and Ki = 3.2. Wallis' vertical CCFL equation is generalized to 1/2 1/2 (1,) + m(-l, ) = 1 (2-4) such that the critical Kutateladze number for liquid hold up is satisfied. In fact, for small pipes of D* < 25 [D <~2.5"), Eq. (2-4) l'ecomes 1/2 1/2 (1,) + m(-j, ) = 0.803 (2-5) while it becomes ! O V g 440.796F part e -3 a.__

r.maanni.1 NRC FSER OPEN ITEM e

                              = 1/2         e 1/2 (k,)     + m(-k, )     = 1.79                (2-6) for large pipes, D* > 25. When ki * = 0, Eq. (2-6) becomes kg * = 3.2, which is the Kutateladze lig-uid hold up conditioa, where Kutateladze number is J    2 Pr                                                        (2-7) ka#k88c009 Eq.(2-6) becomes (j )      + m(-jf )    =

(2-8) 2<0.8 This means that Eq. (2-6) is more restrictive than the Wallis flooding curve, Eq. (2-5). For example, at 35 psia: f ( Wallis D* = D (126. (1/ft)) [.*8 <

                            = 35.9 for OSU                                         U
                            = 151.6 for AP600.                                                      >

Figum 2-1 Scaling Effect in Vertical CCFL [ h In the previous section, it is concluded that the Wallis' CCFL is more limiting than the inclined pipe. Since larger vertical pipe is more restrictive, the conclusion that the CCFL in the vertical section is limiting still holds.

3. CCFL in An Elbow between the Inclined Pipes Assuming that the vertical section is controlling the CCFL in the pressurizer surge line, the steam flow rate required to hold up the liquid is estimated. With this magnitude of steam flow, what would happen in the elbows due to centrifugal force is studied in this section.

3.1 The Minimum Steam Flow Rate for Liauid Hold Up For SPES, the pipe is small so that Wallis' CCFL shows dj['") = 0.75, where g j *(*)is the steam 440.796F part e -4 & T Westinghouse W

NRC FSER OPEN ITEM \ {\ G' flow at ji = 0. On the other hand, the pipes of OSU and AP600 are large pipes so that the hold up point is defined as kg*(*) = 3.2. These values are converted to the superficial velocities; j g(*) = 28.17 ft/sec for SP.ES, j g(*) = 42.65 ft/sec for OSU and AP600. (3-1) ! Correspondingly, the dimensionless volumetric fluxes are: dj['"} = 0.75 for SPES I

                        = 0.731 for OSU                                                                                 l
                        = 0.510 for AP600                                (3-2)                                          l With this steam flow assumed in the elbow, it can be determined if a flow regime transition from l

stratified flow could take place inside the elbow, which would cause liquid hold up in the inclined I elbow sections. l 1 1 3.2 Centrifugal Force vs. Gravity (Reference 4) j 1 Banerjee (Reference 4) has shown that the liquid phase may ficw on the inside of the elbow as p illustrated below (flow inversion).

l pipe cross section p(u,)2 Centrifugal Force = pR($)2 R j Steam Location of Liquid R 2 2 T tans = P8gu - Piu s (3-3) Rhpg i 6 ui Figure 3-1 Centrifugal Force vs. Gravity If the elbow were the limiting CCFL, the critical situation would take place at high void fraction, when (x > -0.8. Therefore, the superficial velocities, Eq. (3-1), are approximated by j, = u, (3-4) When the liquid is being held up in the vertical section, the centrifugal force on the steam is esti-mated assuming the liquid is motionless. [*] 4

 \ )  T Westinghouse                                                                     440.796F part e -5

1 NRC FSER OPEN ITEM f e 1 2 tans = #P (j m))2 = (),(m)) (4.46 x 10~5) (3-5) Rbpg R

                                 = 0.092        (S = 5.3 deg) ....... OSU                                   '
                                 = 0.023        (S = 1.3 deg) .... .. AP600 Thus, the angle of flow inversion is small and the gravity effect is much more important than the       i l

centrifugal force if the liquid is still. l 3.3 Liauid in Motion - 1 When the liquid moves, the liquid phase may move on the outside of the elbow (S < 0) as indi-l cated below. l l 3.3.1 Balanced Centrifugal Force l Centrifugal forces exerted by steam and liquid can cancel each other resulting in S = 0. The liquid l velocity at S = 0 is estimated while the steam flow is holding up liquid in the vertical section. uf = j(*)

                                     ,                                                    (3-6)         h
                             = (0.0379)*(42.65) = 1.61 ft/see ... ..      OSU & AP600 3.3.2 Natural Fall ofI igid Now examine the natural flow of liquid in an inclined straight pipe
                                                   ~

l LPiut l pil gsine = f52 (3-7) with f = 0.015. Assume the smallest inclination: AP600 .. .. D = 1.2 ft and 0 = 2.5 deg. ........... ui = 15.0 ft/sec OSU ..... . D = 0.285 ft and 0 = 2.0 deg. ... .... ui = 6.5 ft/sec The corresponding effect of centrifugal force is tan S = -(l5.0)2 / (42/12)(32.2) = -2.0 ( 6 = -63 deg) . ... AP600

                  = -(6.5)2 / (10.5/12)(32.2) = -1.5 ( S = -56 deg) ..... OSU The draining liquid is therefore on the outside of the elbow for zero steam flow, as expected.

440.796F part e -6 T Westinghouse

===

NRC FSER OPEN ITEM

/)

V 3.3.3 Effect of Steam Motion on Liauid Flow When steam flow rate given by Eq. (3-2), liquid can flow through the inclined straight pipe at the rate of [ = 1.125 for AP600 from Fig.1-5

                    = 0.625        for OSU from Fig.1-4.

Conespondingly, ji = 7.88 ft/sec for AP600 ji = 1.183 ft/sec for OSU . Applying Eq. (3-2) to Figure 1-1, stratified flow void fractions are: a 2 0.63 for AP600 a 2 0.80 for OSU Therefore, the liquid velocity in the elbow becomes: ui = 21.3 ft/sec for AP600 ui = 5.9 ft/sec for OSU at least. These values are approximately the same as the natural flow rates obtained in the previous section and these are substantially larger than the equilibrium velocity for S = 0. Thus, the centrif-ugal force on the liquid phase is large for OSU and AP600 and the liquid phase will remain on the (nv) outside of the elbow, when the liquid is being held up in the vertical section of the surge line, When the liquid flow is on the outside of the elbow, the body forces exerted upon the liquid (vec-torial sum as shown in Figure 3-2) are stronger than in the straight pipe section. So, the Kelvin-Helmholtz condition in the elbow section is less likely to be reached than the straight section. Thus, the flooding condition in the straight inclined section is to be more limiting, and the conclu-sion that flooding in the vertical sections controls pressurizer draining remains valid. r3 - Q' W Wesikgiiuse 440.796F part e -7

M EE!

NRC FSER OPEN ITEM f R R V S<0 S>0 V Figure 3-2 Flow Inversion Effect to Centrifugal Force and Gravity 3.4 Vertical Elbow vs. Venical CCFL The vertical pipe section of the surge line is connected to the inclined straight pipe section via a venical elbow. h l I I l PRIZER Pipe

                                                                  \
                                                                    -7Y  .

Curvature Diameter l 1 ' AP600 42" 14.44" R I OSU 10.5" 3.55"

                                                        ~*~~~~                Vertical Elbow The CCFL in this section of the surge line is estimated by regarding the elbow as a series of inclined straight pipes. As the inclination angle 0 increases, Kelvin-Helmholtz condition is pro-440.796F part e -8 T Westinghouse       h

l E NRC FSER OPEN REM = l n _

 'b                                               .

portional to square root of cos0 so that the condition is nearly independent of the inclination for 0

      < 60 degrees or so. On the other hand, the gro..ty effect in the flow force balance makes liquid flow rate proportional to square root of sin 0 so that the effect becomes very large with increasing inclination. So, a large amount ofliquid can flow without disturbing the stability of the stratified flow, which can be seen in Figure 1-4 by the increasing limit lines.

The gravity body force acts to resist the instability caused by local depressurization due to steam flow. This effect is quickly reduced around 0 = 90 degrees and it is replaced by the surface tension as evident from the Kutateladze number. However, the effect of the surface tension is substantially weaker than the gravity so that the steam flow rate required for liquid hold up is observed to be small (see Figure 2-1). This should be the reason why the surface tension effects can be ignored for the flow regime transition in the nearly horizontal pipes. This implies that the flow instability and CCFL is the most limiting at 0 = 90 degrees when the gravity effect becomes zero. In addition, the centrifugal force and gravity force make the liquid flow take place on the outside of the elbow and this third force also acts to suppress the surface wave disturbance. Once again,it is concluded that the vertical section of the surge line is the most limiting CCFL. O

4. Conclusions It is concluded in Section 3 that the CCFL in the straight inclined pipe section of the pressurizer surge line is more restrictive than the elbow section. In Section 1, the CCFL for the vertical sec-t tion is more restrictive than the inclined pipe section. Scaling effect of the vertical CCFL is included in Eq. (2-4). It should be noted that Eq. (2-4) is more limiting than Wallis CCFL for larger pipes such as OSU and AP600. Therefore, it is concluded that the CCFL in the pressurizer surge line is limited by Eq. (2-4), and controls the liquid draining rate from the pressurizer.

References:

1. G. B. Wallis, "One-dimensional Two-phase Flow," McGraw-Hill, Inc., N. Y. (1969) l p

C T Westinghouse 4W96F pad e -9

l NRC FSER OPEN ITEM

2. Y. Taitel and A. E. Dukler, "A Model for Predicting Flow Regime Transitions in Horizon-tal and Near Horizontal Gas-Liquid Flow," AIChE J.,22,47 (1976)

3. K. Takeuchi, M. Y. Young, and L. E. Hochreater, " Generalized Drift Flux Correlation for vertical Flow," Nucl. Sci. & Eng,.112,170 (1992) l 4. S. Banerjee, E. Rhodes, and D. S. Scott, " Film Inversion of Co-Current Two-Phase Film in l Helical Coils," AICHE J., 13,189 (1967). l l

l I O l l l l i 440.796F part e -10 3 Westinghouse

l NRC FSER OPEN ITEM o O Table 1-1 Surge Line Characteristics of Test Facilities Inclination Cur ture I.D. D/R lig. flow A?600 13 deg inf, 54" *3 14.438" 0.267 2.5 deg*5 42" *2 1.203 ft 0.34 OSU 12.5 deg infinity . 4.8 deg 13.5" *3 3.548" 0.26 3 deg 10.5" *1 0.285 ft 0.34 1.8 deg SPES 24 deg ~6" 1.338" 0.223 13 deg 0.112 ft 2.5 deg Taitel- 1,5. .03, infinity 1.97"(5cm) 0 down Dulder .1 deg 0.164 ft Grolman -0.5, -1. deg infinity 5.1,2.6 cm 0 up p Whalley -6 deg 19.7"(.5 m) 0.80"(2cm) 0.041 up i . 0.066 ft Study 13 deg 1.203 ft down 7.7 deg 0.285 ft 2.5 deg Shown in the above Table are the scalings ofpressurizer surge lines ofAP600. OSU, and SPES testfacility. Flow regime transitionsfrom horizontal stratifedflow to intermittent or annular dispersedfow were investigated by Taitel Dukler, Grolman, and Whalley. The scalings of their test sections are also shown in the table. From these scalings, cases to be studied are selected; that is, the pipe inclinations are 13, 7.7, and 2.5 degrees andpipe diameters are 1.203 and 0.285 ft. The positive inclination means that the liquidflows down by that angle ofinclination. For example, Whalley's test section is a helically inclined pipe at 6 degrees and liquid is injected fmm the bottom of the test section (therefore the angle is given as negative). R and D are the curvature of elbows and the pipe diameter; respectively. D/R is a scalingfor the helical efect, etc. It can be seen that Whalley's test section has a smaller D/R compared to OSU and AP600 elbows. t (3) V 440.796F part e -11 3 Westk.gh00S8 1

\ NRC FSER OPEN ITEM

                                                 .                                                               l Table 1-2            Saturated Fluid properties at 35 psia                                               i 1

Density (Ib 3 Pg = 0.08406 pi = 58.54 m /ft ): Viscosity (Ibm/ft sec) : 4 4 g = 8.687 x 10 i = 1.533 x 10 Kinematic Viscosity (ft2 /sec): v s= 10.334 x 10-5 vi = 0.2619 x 10 5 Surface Tension (lbr/ft): o = 3.680 x 10-3 O NOMENCLATURE: subscripts: 1 Liquid phase g Steam phase superscripts: (m) Steam flow at liquid hold up (ji = 0). Dimensionless quantity As 2 Steam flow area (ft ) Ai Liquid flow area (ft2 ) C Flooding constant, Eq. (1-1) 440.796F part e -12 .

l l e l NRC FSER OPEN UEM [ /^T O l C2 Multiplier for Kelvin-Helmholtz, Eq. (1-2)

              = 1 - hi /D D      Hydraulic diameter (ft)

D* Dimensionless hydraulic diameter, Eq. (2 1) fs g Wall steam friction factor (except for phase velocity if Reynolds number) ((ft/sec)o.2) fs i Wall liquid friction factor ((ft/sec)o.2) g Acceleration of gravity (ft/sec2 ) ge Conversion factor (ib m ft /lb fsec) hi Liquid levelin the pipe (ft) j Superficial velocity (volumetric flux) (ft/sec) j* Dimensionless volumetric flux K generalized critical Kutateladze number, Eq. (2-3) Ko coefficient to the critical Kutateladze number for a small pipe Ki critical Kutateladze number for a large pipe k* Kutateladze dimensionless volumetric flux, Eq. (2-7) 1* Generalizes mmensionless volumetric flux, Eq. (2-2) m Flooding coefficient, Eq. (1-1) O (d P R Pressure (psia) Radius of curvature (ft) Si Wall liquid surface area per unit length (ft) Sg Wall steam surface area per unit length (ft) , S3 Interfacial surface area per unit length (ft) ui Liquid velocity (ft/sec) ug Steam velocity (ft/sec) x Coordinate along the pipe length (ft) Greek: a Void fraction S Pipe cross sectional angle for location of liquid film, Eq. (3-3)

      $       Angular velocity (rad /sec) v       Kinematic viscosity (ft 2/sec) 0      Angle of pipe inclination O

V 440.796F part e -13

E Westinghouse

E ! NRC FSER OPEN ITEM p Density (Ibm /ft3) AP Pi - Pg a Surface tension (lbr/ft) Twi Wallliquid shear (Ibm/ft sec2) 2 Ti Interfacial shear (Ibm /ft sec ) S Definition of friction factorsfjs andfg : The original definition of friction factors: 2 2 Plut p u' TWI

ll 2 T Wg " fg 2

                                  <Di up-0.2 l

fi = 0.046 < v; > ,o 8u' -0.2 1 fs = 0.046 ( y, D= ' Us i Si o s= S, + S g In terms of Superficial Velocity:

                           .l.8 T  W =f         2                             Tw, = f,#     8
                                                                          'gg 2

4A ff = (0.046) ' A_. 2(0.046)I f:3 = (A, 4A ~ ' I rSi vp

                                                                                    \(S, + Si )v, l

as a result of: fl uf = f; If

          = ( 'ui"^'(0.046)'"'"'l~" <v> g
          =
              / A'2              r 4 A 3 -0.2 (0.046)
              <Ap                 S y
                                 <gp l

440.796F part e -14 1 , I l l

NRC FSER OPEN ITEM . o , oo , ! P2 R

                                   $I'      i B
                                                                                    ~

i A *<k 4(~ '-

1 - V '

                                                                                              /
  ,                   h                              x       k[j(; , [

N % 1 l I,' /

/{

t I Figure 11 OSU Pressurizer Surge Line

                                                                                                 ?40.796F part e -15 Westinghouse

 .:#1etal f                                                                                   NRC FSER OPEN ITEM tttnas etausa.Ifue ae=
                                                                                                     -      t-e a- = .
                                                                           ,. / ,, p             
                                      %'-                                /
                                                                                                                *z=

s \ ../ r 7 --~~...

           }.                                  N                                              s:                    f*

Gq.gLq - A m.p. .-

          + - -. ~..,
                                       /         /s % ,                            .G    ...
          . ps:             7,               /                                         x             .mt-
                 \                             . - ....,              . . .                                   ..    . . ,
           -.) e,:                                                    ..

E' .. s ** lA

n. E

           & M*)                                                                 lEAMt a. Sal f E04 2.S* l o

a ne.se

                                                                                                        <n -  s...,

r d ov. !F".:. P. e Figure 1-2 AP660 Pressurizer Surge Line 440.796F part e -16 Westinghouse $

NRC FSER OPEN ITEM ! i i i i i 2 - l .5 -

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%) Question 440.796F Part f (OITS - 6441) . l The following commitments were made by Westinghouse at the conclusion of the December 10,1997 ACRS T/H Subcommittee meeting and must be fulfilled.

f. Noding - provide more justification for the basis used which differs from the accepted approach developed under the CSAU work, especially for the PRHR and downcomer.

Response

A description of the noding utilized for the AP600 analyses using NOTRUMP is included as , subsection 1.16 in Revision 4 of WCAP-14808, NOTRUMP Final Validation Report for AP600. Other subsection numbers of Section 1.0 will be chan.in appropriately. It should be noted that based upon this study, there was a sensistivity discovered for - ]" in the downcomer for AP600; OSU results were insensitive to the number of downcomer nodes. For AP600, this sensitivity i occurs for DEDVI and larger breaks. Use of the [ ]" node downcomer model results in a possible I increase of PCT; however, this PCT is well below regulatory limits. Westinghouse will update the l SBLOCA section of the AP600 SSAR for those breaks sensitive to the number of downcomer nodes. l SSAR Revision: Westinghouse will update the SBLOCA section of the AP600 SSAR for those /O breaks sensitive to the number of downcomer nodes. b O s

!                                                                                        440.796F part f -1

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NRC RE45EST FOR ABBIT18tAL INFORIRATitu Question 440.721 (OITS - 5646) (a) Provide additional explanation and significance of the consistent delay in NOTRUMP predicted commencement of CMT draining when compued to testing data. What is the significance of NOTRUMP's lack of a flashing model in failing to accurately predict start of CMT draindown.

Response

NOTRUMP's consistent delay in the prediction of the onset of CMT draining is due to two fa: tors: a) In most of the SPES and OSU tests, the CMT's begin to drain when sufficient mass has been depleted to drain the steam generator tubes and begin to drain the cold legs. Vapor then flows up the balance line, displacing liquid and causing the CMT to drain. NOTRUMP, in several tests, predicted a slowei-steam generator draining and initiation of vapor formation in the cold legs. In addition, while in the CMT test draining was observed soon after vapor entered the balance line, draining was not predicted in NOTRUMP until the upper volume of the CMT reached saturation temperature. Both factors led to consistent late prediction of CMT drain by NOTRUMP. , b) In some of the OSU tests, the CMTs began to drain before the steam generators drained (see below). His is due to flashing cf the liquid at the top of the balance line when the saturation temperature decreases to the liquid temperature. NOTRUMP did predict this mode of draining in some cases initially. For these cases, the CMT only slightly drained, and did not begin free drain until significant vapor began to enter the balance line. Figures 440.721a-1 and 440.72ta-2 show the fluid temperature and the saturation temperature at the top of the balance line and several elevations in the CMT for SPES test S00303 (2-inch cold leg break), respectively. Figure 440.721a-3 compares the collapsed liquid levels in the steam generator tubes, the CMT balance line, and the CMT. De fluid remains subcooled, and the CMT does not begin to drain, until the balance line begins to drain at about $50 seconds. For this test, CMT draining does not begin until the steam generators drain and the cold legs begin to fill with vapor. This occurred in all the SPES tests. In contrast, in some of the OSU tests the CMT began to drain before the steam generators and cold legs drained. Figure 440.721a-4 shows the collapsed levels in the steam generator, balance line, and CMT for OSU test SBl8 (2 inch cold leg break). The steam generator has not completely drained before evidence of vapor is seen in the balance line, and the CMT begins to drain at about 120 seconds, Figure 440.721-1 indicates that the difference between fluid temperature and Tsat at the top of the balance line can be quite small. Small inaccuracies in predicted system pressure could therefore be sufficient to initiate or prevent draining by this mechanism. The small difference also indicates that in the AP600 flashing of the balance line cannot be precluded (and for the smaller breaks is calculated). As in the test simulations, however, this mechanism does not initiate continuous draining because the initial temperature of the liquid in the balance line is well below the cold leg temperature (approximately 400*F), and the liquid at th> top of the balance line at the CMT entrance is close to the CMT temperature (ie, highly subcooled relative to Tsat), and therefore the amount of steam generated is small. The implications for NOTRUMP's application to AP600 are as follows: NOTRUMP does not contain a nonequilibrium flashing model, if the liquid remains slightly subcooled relative W Westirighouse

NRC ret 9EST E9R ABBm0NAL INFSRMATitN to the local saturation temperature, vapor will not be formed; therefore CMT draining will be delayed. On the other hand, the liquid cannot become superheated relative to the saturation temperature either. One scenario which has been suggested is that the liquid may remain superheated relative to Tsat. This metastable condition can be maintained, it is argued, to significant superheat levels because the cold piping walls do not provide nucleation sites. The liquid will therefore not Hash in the plant or test facility when predicted to do so by NOTRUMP. NOTRUMP would then predict early CMT draining for this scenario. However, heated walls are not necessary for the production of nucleation sites; minute particles or contaminants in the Huid are also sufficient to initiate Hashing. Even in the presence of cold walls and extreme care in water purity, metastable states of liquid water cannot be sustained beyond a few degrees above saturation (Reference 440.721a-1, page 138). Dere is no measured evidence of significant and sustained liquid superheat in any of the tests. In addition, assuming that such a state occurs, the RCS will continue to depressurize due to heat removal by the l steam generators (which have not begun to drain yet) and by the PRHR, as well as mass removal by the break. As a result, the saturation temperature will soon fall sufficiently below the liquid temperature to induce Hashing. l l It is concluded that a prolonged metastable state is not likely, and there is no need to include a model to predict such a state in NOTRUMP. a l References. l 440.721a 1 Collier, J. G., Convective Boiline and Condensation, nird Ed., Clarendon press,1994, 1 l SSAR Revision: NONE 1 1 1 1 1 1 1 1 448.7Ha 2 3 Westinghouse 1

l l l I' NRC Ri4OEST FSR A38m8HAL INFORMAT10N a

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1 1 4 l 1 1 l l i l Figure 440.721a-1 Fluid temperature in the balance line for SPES test S00303 l W Westinghouse 448 N t -

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NRC RE$5EST FSB AB0m8 MAL INittalATitN

                                                                                                        . . . c E

s 6, c. 1 I l l l l Figure 440.721a-3 Collapsed liquid Icvels in the steam generator (LSGBH), balance line, and CMT for SPES test S00303. l W westinghouse see m

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O e 6 e Figure 440.721a-4 Collapsed liquid levels in the steam generator, balance line, and CMT for OSU test SBl8. 1 1 M.D 4 T Westinghouse , 1

NBC REGOEST FOR ABBffitNAL INFtRNAT10N n

Question 440.721 (OITS - 5647) (b) Provide additionaljustification why adv:rse effects from non-condensible gases are not a concern for AP600 NOTRUMP small break LOCA calcule.tions. Explain where the non-condensible gases end up and why assumptions made for NOTRUMP calculations are conservative.

Response

As discussed previously in the responses to RAI 440.325 and RAl-440.499 (References 440.721(b)-1 and 440.721(b)-2 respectively), both the SPES-2 ar.d OSU test facilities simulated the injection of non-condensible gases following the completion of the ace'imulator discharge period. For the SPES facility, the non-condensible gas injected was air, whereas nitrogen was utilized for OSU A detailed discussion of the non-condensible injection process and migration is provided in Reference 440.721(b) 3 Section 4.4 for SPES and Reference 440.721(b)-4 Section 6.1.4 for OSU. The test results indicate that the most likely non-condensible gas collection points would be the PRHR Heat Exchanger and Cold Leg Balance Lines /CMT tanks with no significant degradation in system performance being observed. The potential collection points for non-condensible gases are as follows:

                   -        Upper Downcomer Region f
                   -        Upper Head (via the Upper Head Cooling Nozzles)

(3 ' - Cold Legs

                   -        Cold Leg Balance Lines a id CMTs Steam Generator U-Tubes
                   -        Hot Legs
                   -        PRHR Heat Exchanger
                   -        Pressurizer Upper Plenum The potential escape paths for non-condensible gases are as follows:

Break

                   -        ADS Stage 1-3 Valves (Off Pressurizer)
                   -        ADS Stage 4 Valves (Off Hot Legs)
                   -        Upper Head Cooling Nozzles To Upper Plenum To ADS Valves
                   -        Cold Legs To SG To Hot Legs To ADS Paths he AP600 plant design is such that the main energy removal path (s) prior to ADS actuation are the break and the Passive Residual Heat Removcl (PRHR) System. The existence of the PRHR system results in the steam generaters transitioning from a heat sink to a heat source relatively early (prior to the discharge of non-condensible gas from the accumulators) in the SBLOCA transient scenario. As a result, the potential collection of l         non-condensible gas in the steam generators, following completion of the accumulator liquid discharge period, has little effect on the AP600 SBLOCA scenario.

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(mv) W-Westinghouse 448.72 8-1 l

NBC RE99EST FOR ABBm8 MAL INFORMATitM n$ HE O Following actuation of the ADS system, the main energy removal paths become the break and ADS paths themselves with much less reliance being placed on the performance of the PRHR system. The opening of the ADS paths also provides a direct vent path for the non-condensible gas from the RCS in addition to the break itself. , The NOTRUMP simulations performed for the OSU, SPES and AP600 plant calculations remove the PRHR model following ADS Stage 3 actuation. A review of the test data and NOTRUMP simulations indicate that the injection of non-condensible gases, following completion of the accumulator liquid discharge period, does not typically occur until well after ADS stage 3 actuation. As such, these gases can not collect in the PRHR heat exchanger unti'. after this point in time. Since the test data indicates that the importance of the PRHR model is diminished following ADS Stage 3 actuation and non-condensible gas is not introduced into the RCS prior to this time, this collection process can be deemed unimportant to the SBLOCA transient progression. It should be noted that in the AP600 SSAR analyses the PRHR was typically removed later than in the test simulations, relative to ADS 3 actuation time, and has a small effect on non-limiting small break LOCA cases due to the relative unimportance of the PRHR system post ADS 3. Collection of non-condensible gas in the cold leg balance line/CMTs will only serve to enhance CMT draindown (should liquid still exist in the tank) since steam condensation would be reduced and liquid discharge increased. By not modeling the non-condensible gas collection process in this component, CMT injection (following non-condensible gas injection) would be under-predicted by the NOTRUMP code and ADS 4 actuation would be subsequently delayed. Following sufficient draindown of the CMT tanks, the ADS Stage 4 valves open thereby providing an additional O vent path by which non-condensible gases can be removed from the RCS. With all ADS valves open, the following escape paths exist for the injected nitrogen: out the break, through the head cooling jets into the hot legs and out ADS 1-4, and through the cold legs, steam generators and hot legs out ADS 1-4. In most cases the last path is the most significant. Therefore, collection of non-condensible gases in the pressurizer, hot legs and upper plenum can not be sustained due to the venting of the primary system. The opening of the ADS 4 valves provides the means for the final depressurization of the RCS which allows for the injection of water from the IRWST. References 440-721(b)-1 RAl-440.325 440-721(b)-2 RAl-440.499 440-721(b)-3 Cunningham, J. P., et. al., "AP600 SPES-2 Test Analysis Report," WCAP-14254, May 1995. 440-721(b)-4 Andreychek. T. S., et. al., "AP600 Low Pressure Integral Systems Tests at Oregon State University Test Analysis Report," WCAP-14292: Revision 1, September 1995. SSAR Revisiom NONE l l "D# W-Westinghouse h l l

i l' . l NBC REGOEST F6B ASBITl0NAL INFSBIAATitN g= =

IE Question 440.721(c) Provide a thorough explanation regarding NOTRUMP's misprediction of mass now out of the ADS stage 1,2, and 3 valves in the OSU experiments (and related pressurizer refill). Improve the justification as to why this deficiency is acceptable.

Response

An evaluation is first presented of the processes occurring in the pressurizer during the early stages of ADS 1-3 blowdown. The subsequent draining period is evaluated in the response to RAI.440.721(f). Review of test data: Just prior to ADS 1-3, the system has partially drained by mass loss through the break. The pressurizu is empty of water. De CMT has been draining, filling the downcomer, lower plenum, and part of the core with cooler water. Above this cool water is a warmer layer of saturated liquid and two phase mixture, consisting mostly of the original primary side inventory. Figure 440.721(c)-1 shows the pressurizer collapsed liquid level in the OSU 2 inch cold leg break, expressed as a fraction of the overall pressurizer height (this graph therefore also indicates liquid fraction in the pressurizer). He ADS 13 valves begin to open at [ l'* seconds. When the ADS 1-3 valves open, the pressurizer refills, then drains in three distinct phases. Rese are denoted phase I (partial refill /two phase ADS), Phase II(complete refill /nearly all liquid ADS), A4 (after ADS 4, pressurizer draining). Figure 440.721(c)-1 indicates the time periods during which these phases j occur. Phase 1: When the ADS 13 valves open, the system depressurizes. The warm two phase mixture and any liquid which is near saturation temperature flashes and generates steam. The mixture swells and enters the pressurizer. This mixture then flows out through the ADS valves. Figure 440.721(c)-2 shows the measured vapor and liquid flow out the ADS 1-3 Separator. As the warm layer moves into the pressurizer, it is replaced by colder liquid from the downcomer, and additional cold liquid from the CMT, Re vapor generation rate in the core is completely suppressed as cold liquid fills the core. Figure 440.721(c)-3 compares the measured vapor flow out ADS l 3 (ADS 13VR) with the vapor generation rate in the core calculated by an energy balance (RPVRXV). It can be seen that nearly all the measured ADS vapor flow is from the flashing two phase mixture. At about [ l'* seconds, the cold liquid has filled the vessel and can be seen entering the pressurizer surge line, as indicated by fluid temperature (Figure 440.721(c)-4), and by surge line void fraction (Figure 440.721(c)-5, from [ l'6 seconds). At this time, the measured mass Sow out ADS l 3 increases,

                                                                                                       ""'M W Westinghouse i

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- 1 NRC RE45EST FOR ABBITittlAL INFORMATitu A a i

and consists primarily of liquid. There is some question about the ability of the measurement system to measure low vapor now (to be discussed later), but the nearly all-liquid nature of the flow at this time can be confirmed by the fact that the pressurizer is almost completely full of water (Figure 440.721(c)-1). Phase II: As system depressurization proceeds, the depressurization rate decreases so the driving force for How through the core, surge line, and pressurizer and out the ADS l-3 valves also decreases. However, the lower pressure and core flow causes the initially subcooled liquid there to begin to boil (Figure 440.721(c)-3 at [ -] seconds). He vapor reaches the pressurizer surge line at about [ l'* seconds (Figure 440.721(c)-5, high void fraction in surge line), and causes the mixture in the pressurizer to swell again. A4: The mass in the pressurizer remains fairly constant until ADS 4 opens at about [ J'6 seconds. The pressurizer begins to drain, but at a lower rate than what would be expected if the pressurizer were allowed to drain freely. This draining phase will be discussed in additional detail in the response to RAI.440.721(f).

     ' Review of NOTRUMP predictions of pressurizer level:

A review of the NOTRUMP predictions of SPES and OSU in Reference 440.721(c)-1 indicates that the pressurizer refill prediction is generally poor (the level is underpredicted ) in the SPES predictions and better in the OSU predictions, when the delay in ADS l-3 actuation is accounted for. Figure 440.721(c)-6 compares the predicted and measured water levels for the OSU 2 inch cold leg break measured from the time that the ADS l 3 is actuated. Figure 440.721(c)-7 compares the ADS 1-3 flowrate on the same time-shift basis. De flow prediction is low early in the transient, but is then good (similar integral slopes) during the remainder of the transient (Figure 440.721(c)-7 A). Figure 440.721(c)-7A was obtained by offsetting the integrated ADS 1-3 Flow curves by their value at the start of Phase II. De prediction shows the same two phases of blowdown: an initial two phase period when the warm water layer swells and flashes, and a second period when colder water is pushed into the pressurizer as the core begins to generate significant vapor again. He predictions can be explained in terms of the mass and average subcooling in the system at the time that ADS 1-3 is actuated. He reason for the poorer prediction in the SPES test is explained by the modeling of the pressurizer. In both test facilities, the onset of ADS 13 was predicted to occur later than in the test. Because of this, the mass in the system was depleted to a lower level just prior to ADS l-3. In several of the tests, the temperature of the liquid entering the vessel from the DVI line was higher because of the lack of a thermal stratification model in the CMT. As a result, the degree of level swell 448.721(c} 2 3 Westinghouse

                                              - _ - _ _ ~ - _ _ _ - - - _ _ _ _ - - _ _ _ _ - _ _ _ _ _ _ _ _ _ . _ - _ _ _ _ _ - - - - - . - - _ _ _ _ _ - - - _ _ _ _

! l l i l ! NRC RE45E81 fet A38tileMAL INf0RIAAT10N l l

j. 'in the layer of warm water and two phase mixture which occupies part of the core, and the upper plenum, is smaller, and the vapor content of the mixture entering the pressurizer is higher. The calculated now through ADS 1-3 is therefore of higher quality, and the total predicted now is lower.

Conclusions:

The difference between the SPES and OSU predictions was discussed in the response to RAI.440.610. In that response, it was demonstrated that the large metal heat release from the pressurizer walls resulted in a significant void fraction distribution in the pressurizer, which could not be modelled by the single node used in NOTRUMP. Since this level of heat release in SPES will not occur in AP600, this discrepancy is not considered serious. An alternate explanation could be that the ADS 1-3 flow is underpredicted because the break flow is l overpredicted. In fact, in all of the tests with the exception of the DVI line breaks (discussed in the { response to RAI.440.721(d)) the break flow prediction is generally good. The misprediction is therefore 1 attributed to the delay in ADS 1-3 actuation and lower system inventory when ADS 1-3 opens, rather than , errors in the break flow model. Since the important quantity which must be predicted is the pressurizer j mass during the refill process (this will lead to a delay in the IRWST flow as described in the resgnse i to RAI.440.721(f)), and this is predicted well in the more correctly scaled OSU tests, the discrepancies in predicted ADS l-3 flow are considered to be acceptable.

The NOTRUMP calculations below confirm that the misprediction of ADS l-3 is due to boundary conditions in the pressurizer rather than errors in the break flow model: NOTRUMP Stand-alone Model Results:

In order to quantify the effects of boundary conditions on the predicted ADS 1-3 performance, a stand-l alone NOTRUMP model of the OSU ADS Stage 1-3 system was developed. Two separate models were developed for this effort. One model representing the detailed OSU ADS Stage 1-3 system from the Pressurizer to the IRWST Tank as described in Reference RAI.440.721(c) 1, and a sirnplified model representing the conditions on either side of the ADS Stage 1-3 valves via boundary conditions. He detailed model (Figure RAI.440.721(c)-8) is identical to that used in OSU simulations in Reference , RAI.440.721(c)-1 with the exception that the pressurizer conditions are provided as boundary conditions derived from Reference RAI.440.721(c)-2 test data. He simplified modelis a subset of the detailed model in that it removes the fluid nodes associated with the IRWST tank (Fluid Nodes 67 and 77) with the ! downstream conditions for the ADS Stage 1-3 valves now being provided directly via a boundary node representing either the IRWST or the ADS Stage 1-3 separator tank (Figure 440.721(c)-9). The conditions l utilized for the boundary nodes were derived from the available information from Reference 440.721(c)-2 l for the pressurizer, IRWST and ADS 13 Separator respectively. t 448.721(cl-3 T Westinghouse

l l I NRC REME8T Ftt ADDITitNAL INFSRMATitN

=- =u ;

                ..J The available information for the pressurizer, utilized for the stand-alone models, were pressure,           )

temperature, collapsed mixture level and void fraction respectively. In order to drive the NOTRUVP model, a pressure /enthalpy boundary condition must be provided and was derived from the available information. It should be noted that although collapsed mixture level and void fraction information are available from the OSU Test Analysis Report, the number of caps and locations does not provide an exact indication of the conditions at the top of the pressurizer near the ADS Stage 13 piping connection point. The available pressurizer level indication taps (one nca the top of the Pressurizer and one near the bottom) only provide an indication of the entire span as opposed te finer indications near the top of the pressurizer / ADS piping connection point. As such, it is expected that tr.e stand-alone NOTRUMP model will tend to over-predict the ADS Stage 1-3 flow behavior due to the void fraction indication for the entire span as opposed to the conditions at the ADS Stage 1-3 piping connection point. For the simplified model, the ADS Stage 1-3 downstream conditions were modeled two different ways. First, the ADS Stage 1-3 downstream pressure condition was modeled with a constant pressure which represents the IRWST conditions (neglecting the static head of water above the ADS Stage 1-3 sparger). Second, the ADS Stage 1-3 downstream pressure conditions were modeled from the known ADS Stage 1-3 separator conditions near which the ADS flow measureme ,ts are obtained. Figure 440.721(c)-10 presents the results of the NOTRUM' and-alone models. When these models are driven by the pressurizer conditions, they exhibit highet u than either the test data or the original NOTRUMP simulation results. De detailed model preu..ts the occurrence of a flow reversal in the calculated ADS 1-3 flow. His occurred as a result of not modeling the vacuum breaker which exists on the ADS l-3 piping downstream of the ADS 1-3 valves. Modeling of this feature,in this detailed stand-alone model, would have prevented the calculation of reverse ADS l-3 flow conditions. Note that the results of the simplified model, which utilizes the ADS 1-3 Separator as the boundary and inherently includes the vacuum breaker effects, does not exhibit the flow reversal period but indicates a continuation of flow through the ADS Stage 1-3 valves. , As discussed previously, the results obtained with the stand-alone models were not unexpected due to the uncertainty associated with the actual conditions which may exist at the Pressurizer ADS 1-3 piping connection point. He results indicate that the conditions in the pressurizer dominate the break flow response. Improved predictions of the conditions upstream of the ADS Stage 13 valves would yield a more accurate prediction of the calculated ADS 1-3 flows and result in an improved simulation response. l l 440.mic14 T Westinghouse

NRC BitGEST fet A88m0NAL INf9RMATION gw w I.

References:

440.721(c)-1 WCAP-14807 Revision 2, "NOTRUMP final Validation Report For AP600," June 1997. 440.721(c)-2 WCAP-14292, Revision 1 "AP600 Low-Pressure Integral Systems Test At Oregon State University, Test Analysis Report," September,1995. SSAR Revision: NONE l 1 l l l l l 1 1 1 W westinghouse

NRC REQUEST FOR ADDITIONAL. INFORMATION s OSU 2 INCH COLD LEG BREAK: PRESSURIZER LEVEL (NORMALIZED TO

PRZ HEIGHT) [i'#*' l i I i L l l Figure 440.721(c) 1 Collapsed liquid level in pressurizer (relative to pressurizer height). 440.721(c)4 IN I l 1

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1 NRC REQUEST FOR ADDITIONAL INFORMATION f

                                                                   -             V OSU 2 INCH COLD LEG BREAK LIQUID AND VAPOR FLOWS THROUGH ADS 1-3, MEASURED BY SEPARATORS AND FLOWMETERS.

( q l i 1 l l Figure 440.721(c)-2 Measured vapor and liquid flow out ADS 1-3 440.721(c)-7 T Westingh0088 l l r- e e

NRC REQUEST FOR ADDITIONAL INFORMATION e=; Ir , OSU 2 INCH COLD LEG BREAK CORE VAPOR GENERATION RATE CALCULATED BY ENERGY BALANCE. (, , 1 f I

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Figure 440.721(c).3 Measured ADS 13 vapor flow compared with calculated core steam generation rate 440.721(c)-8

NRC REQUEST FOR ADDITIONAL INFORMATION l Wlil CSU 2 INCH COLD LEG BREAK FLUID ENTHALPY (FROM TEMPERATURE) IN HOT LEG NEAR SURGE LINE. _ ( S,6, c.h l UB Figure 440.721(c)-4 Fluid temperature in the surge line (compared with Tsat) gg 440.721(c)-9 O

NRC REQUEST FOR A00mONAL INFORMATION i OSU 2 INCH COLD LEG BREAK ' VOID FRACTION INFERRED FROM dP MEASUREMENTS ACROSS < SURGE LINE (SL) AND HOT LEG (HL). / s , - L 6,-. i 4 , L i 1. i i 1 i ii Figure 440.721(c) 5 Void fraction inferred from dP measurements in surge line and hot leg 440.721(c)-10 IN

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1 i 1 NRC REQUEST FOR ADDITIONAL INFORMATION i

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      '                                                                                                        IP t                                                                                                                 L Figure 440.7219 (c)-7 Comparison of measured and predicted ADS l-3 flows after adjusting for ADS 13 actuation time.

440.721(c)-12 IN

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 %  Nat RitutsT FOR A381TitilAlINFORMATitN                                                                                                                                                                       b Question 4'40,721(d)

Provide an explanation for NOTRUMP's misprediction when compared to the OSU test results of DVI line breaks.

Response

   'lhe mi; predictions observed for the DVI line breaks are higher core and downcomer collapsed liquid levels, after ADS 1-3 opened, for OSU test SB12 (Double Ended DVI Line Break). For example, the levels are overpredicted beginning at [     ] " seconds (Figures 8.3.414 and 8.3.418 of Reference 440.721(d)-1). In addition, the mass discharged from ADS 1-3 is underpredicted (Figure 8.3.4 27 of Reference 440.721(d)-1), while the mass discharged from the broken DVI line is overpredicted (Figure                                                                              .

8.3.4-29 of Reference 440.721(d)-1). The time when the misprediction occurs is shortly after ADS 1 opens, and extends to about [ ]" seconds. After this time, the core collapsed level is in good agreement with the test data, while the downcomer level is slightly higher than the test data. During the review of the information related to this RAI, it was discove%1 t- at ;: correct values were utilized for the ADS 1-3 valve areas in the NOTRUMP simulation de tt2d i' xeference 440.72)(d)-1. The revised results, while improved, still exhibit similar ; +< to that observed in Reference 440.721(d)-1. The revised results will be provided in Revision 3 of the aforementioned reference. The test and the revised prediction are examined in more detail below: Review of Test Data: Test data can be utilized to compare what is happening in the tests relative to the NOTRUMP simulation. Figure 440.721(d)-1 shows the collapsed liquid across several spans in the downcomer. These spans are shown in Figure 440.721(d)-2. The collapsed liqaid level in span 1 drops to the top of span 2, then the level in span 2 begins to drop, while all lower spans remain liquid solid. This is indicrive of the draining of a single phase liquid layer. At about [ ]" seconds, spans 3 through 5 show signs of voiding. This is an indication that a two phase mixture has formed (if there were no voiding in the downcomer liquid, the collapsed liquid level in span 4 would remain at 45 inches until the liquid level in span 3 dropped to [ ]" inches). At [ ]" seconds, the ADS 2 valves open and additional voiding of the two phase mixture occurs. 'Ihere is also an indication of two phase level swell, in that the mixture level enters span 2 at about [ ]" seconds, which corresponds to the ADS-3 actuation time. Figures 440.721(d)-3 to 9 show the downcomer fluid temperature from the top to the bottom, compared to the saturation temperatures at the top and bottom of the downcomer. Two locations are shown; one below the intact DVI, and one below the broken DVI. It can be seen that there is a distinct two dimensional temperature pattern, with subcooled water penetrating the intact side of the downcomer, but not completely mixing with the fluid on the broken side. Figure 440.721(d)-3 also shows that the fluid in the top of the downcomer region is superheated; this is discussed later. W Westinghouse l

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Figures 440.721(d)-10 through 12 present additional information related to the ruptured DVI Cold Leg Balance Line (CLBL)/ cold leg which further supports the existence of two dimensional downcomer behavior. Figure 440.721(d)-10 indicates a two phase mixture level swell is observed in the downcomer at the cold leg connection elevation between [ ]"and [ ]" seconds. Subsequently, this level swell is observed to propagate into the ruptured DVI line CLBL (Figures 440.721(d)-11 and

12) which affects the core /downcomer level behavior; this is discussed later.

From these figures, it is concluded that ponions of the downcomer Duid remain two-phase, even while subcooled water is being injected via the intact DVI line. The two phase mixture prevents additional liquid from being stored in the downcomer, and swells to the broken DVI line CLBL, such that vapor now out the DVI side of the break is suppressed. NOTRUMP Predictions: The next series of figures examine the NOTRUMP prediction, and compare various quantities with test quantities. Figure 440.721(d)-13 shows the downcomer, lower plenum, and bottom of core Guid node temperatures. The downcomer Guid becomes subcooled when ADS Stage 2 opens at ~140 seconds. Since the NOTRUMP downcomer Guid node is cae-dimensional, it cannot simulate the two < dimensional temperatures, levels and flow patterns observed in the test. As a result, more mass is stored in the downcomer and core regions. Figure 440.721(d)-14 shows the pressurizer two-phase mixture level predicted by NOTRUMP. The mixture level reaches the top of the pressurizer following ADS Stage 3 actuation, so two- phase now is calculated out of the ADS 1-3 paths (Figure 440.721(d)-15). The predicted two-phase level remains at the top of the pressurizer until the act.vation of ADS Stage 4, at which time the NOTRUMP simulation and test data diverge. Details regarding the explanation of the pressurizer drain mispredictions are found in the response to RAI.440.721(f). It should be noted that the ADS 1-3 How measurement instrumentation is located downstream of the ADS 1-3 separator tank in the test facility. The flows are separated, measured, re-combined and subsequently discharged into the IRWST tank. The NOTRUMP simulation of the ADS flow paths do not model this level of detail. The NOTRUMP model simply consists of three separate flow paths, each simulating an ADS valve stage, which discharge directly into the IR'VST tank. As such, the measured and predicted ADS 1-3 How quantities are not identically comparable. The following discussion attempts to consider the effect of these differences. Figure 440.721(d)-16 shows the measured vapor and liquid flow via the ADS Stage 1-3 valves. The liquid flow measurement indicates a low, intermittent flow of liquid following ADS Stage 1 actuation. It is indicative of either a two-phase mixture level which did not reach the top of the pressurizer, but where there was entrainment above the mixture level, or a two-phase mixture level which reached the top of the pressurizer for intermittent time periods. Based on the collapsed pressurizer level instrument reading off span low (i.e. indicating an empty pressurizer), the initial liquid discharge measured,

     .                                                                                                        3 Westinghouse

. NRC Riq0!5T FOR ADDITIONAL INf0RMATl8N @ following ADS 1 opening, may not be indicative of conditions leaving the ADS valves (Figure 440.721(d)-17). Also, the measured liquid discharge, following ADS Stage 2 opening at [ ]" seconds, is likely the result of ADS vapor discharge displacing ADS separator liquid which is subsequently measured as ADS liquid discharge. Figure 440.721(d)-18 compares the separator liquid level and measured ADS liquid flow. There is a sudden drop in level at [ ]" seconds and corresponding increase in measured ADS liquid now. To determine the impact of these observed test facility phenomena on the NOTRUMP comparison, the measured liquid now prior to ADS-3 actuation was eliminated. A comparison plot of the integrated raw test data, adjusted test data, and the NOTRUMP predicted ADS 1-3 liquid discharge is presented in Figure 440.721(d)-19. As can be observed, the comparison between the NOTRUMP simulation and the test data are better matched following the adjustment. While some ent,ainment is expected to occur during this period, it is not expected to be of the magnitude measured in the test facility. Based on the amount of liquid entra'nment, the predicted vapor now into the pressurizer and ADS 1-3 is somewhat lower in the NOTRUMP simulation when compared to the test. Note that although a comparison between the

  , predicted and measured vapor flows supports this conclusion, the degree of difference may be misleading because the measured vapor now includes liquid which has Dashed after passing through           !

the ADS valves into the separator. Figure 440.721(d)-20 compares the total predicted vapor flow from the core with the predicted vapor l Gow into the pressurizer surge line. Evidently, a large portion of the vapor generated in the core is ; bypassing the pressurizer / ADS path. Figure 440.721(d)-21 compares the core flow with the total flow from the downhill side (i.e. SG cold side tubes) of both steam generators. This shows a significant portion of the generated vapor is Dowing through the hot legs, steam generators, through the cold legs to the ruptured DVI paths (either via the ruptured DVI CLBL or downcomer). Figure 440.721(d)-22 compares the steam generator outlet and broken DVI line (vessel side) vapor flows and confirms that a majority of the vapor is being discharged via this path. Since the SG outlet now is slightly higher, this figure also indicates that vapor is also being discharged through another location. Figure 440.721(d)-23 presents the NOTRUMP predicted vapor discharge from the DVI side of the DVIline break which represents the additional steam vent path. Figure 440.721(d)-12 indicates the test undergoes a liquid , in-surge into the ruptured DVI line CLBL thereby preventing vapor venting via this path. This is a l result of the two-dimensional behavior occurring in the test facility downcomer region, which can not l be predicted to occur with the NOTRUMP model. This lack of two dimensional capability results in l the diversion of core generated vapor away from the ADS Stage 1-3 flow paths. Confirmation that a similar vapor flow patterns exists in the test, with the exception of the previously mentioned DVI side vapor venting, can be obtained by comparing the measured and predicted Guid temperatures at the top of the downcomer, Figure 440.721(d)-3 and 24. In both cases, the vapor at the top of the downcomer is superheated. This can only occur if the vapor has first passed through the steam generator tubes. Figures 440.721(d)-25 and 26 compare the predicted break vapor and liquid flows with measured test data. Before [ ]" seconds, there is measured vapor flow, even though the DVI line is covered and

 . the Guid is subcooled. As previously noted, this is due to flashing of the Guid as it enters the separator W Westinghouse

9

==

W NRC RitutST FOR ADDITl8NAL INFORIAATiON _ Y-which is near atmospheric pressure (the figures show the NOTRUMP predicted flows as they enter the broken DVI line, prior to flashing). The measured vapor flow prior to [ ]" seconds is seen tc nearly account for the difference between the measured and predicted liquid flows prior to [ ]" seconds (Figure 440.721(d)-25). After about 200 seconds, predicted vapor flow is higher out the DVI line and somewhat lower out the ADS 1-3 line (comparc Figures 440.721(d)-15 and 16). The above discussions demonstrate that:

1. A two dimensional temperature / level pattern forms in the downcomer, allowing portions to remain saturated and Dash when ADS 1-3 open. Because of the Dashing and level swell occurring in the downcomer fluid in the test, less mass is stored in the downcomer.

2. Much of the vapor generated in the core exits through the broken DVI line for this break. No vapor venting is observed via the DVI + of the DVI line break as a result of the two dimensional downcomer behavior whe: the NOTRUMP model exhibits vapor venting via this path.

3. The one-dimensional downcomer model in NOTRUMP does not predict the two-dimensional temperature pattern. Instead, the downcomer fluid becomes subcooled. This additional mass then distributes into the core, leading to overprediction in the collapsed liquid level. In addition, less vapor is generated in the core and subsequently flows out ADS 1-3.

Conclusion:

For DVI line breaks, the same complex temperature and flow patterns as observed in the test can be l expected to occur in the AP600. This means that NOTRUMP overpredicts the vessel mass for some ! time period after ADS 1-3 opens. However, once the ADS 1-3 blowdown has been completed, the core mass is predicted well in both SPES and OSU, such that when intact IRWST injection is initiated, the correct amount of mass must be replenished by the IRWST. Therefore, the misprediction of core /downcomer mass during the ADS 1-3 blowdown period is not a serious deficiency. In addition. l application of the IRWST level penalty derived in response to RAI 440.721(g), will introduce additional conservatism into the vessel mass prediction. l t 1 440.721td) 4 W Westinghouse

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References:

1 440.721(d)-1 "NOTRUMP Final Validation Report for AP600", WCAP 14807, Revision 2, June 1997 440.721(d)-2 "AP600 Low-Pressure Integral Systems Test At OSU: Test Analysis Report," l WCAP-14292, September 1995. 440.721(d)-3 "AP600 Low Pressure Integral Systems Test As OSU: Final Data Report," WCAP, May 1995. SSAR Revisions: None I W wesuous. Ai

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q Question 440.721e (OITS - 5650) ' l t (e) . Explain the significance and justify the bases for any differences in the Nodalization between the ; two integral test facilities (OSU and SPES) and the AP600. I i l Response. ]

    .                                                                                                                       1 NOTRUMP nodalization differences among the test facility models and the AP600 SSAR plant model are a consequence of the geometries of the units, ne differences in geometry which lead to different fluid node / flow link nodalizations are discussed in detail below.                                          I The differences in PRHR heat exchanger nodalization among the SPES-2, Oregon State University (OSU) and AP600 SSAR NOTRUMP models are the result of atypicalities of the test facilities. He SPES-2 PRHR model (Reference 440.721(c)-1, Figure 7.2-2) employs four nodes to represent the full-height vertical length single tube within the IRWST, and the AP600 SSAR nodalization also uses four nodes in the vertical tube section of the PRHR heat exchanger. The horizontal length of the SPES-2 tube is very short relative to the AP600 design, so a single node in each of the SPES-2 heat exchanger horizontal sections is sufficient. The OSU facility, on the other hand, is 1/4 height scale relative to the AP600. As a result, as shown in Figure 8.2-2 of Reference 440.721(c)-1, the OSU PRHR modeling of two nodes in the vertical segment of the heat exchanger tubes is adequate to capture the liquid G     thermal / gravity effects in the PRHR. In contrast, because the horizontal PRHR tube segments are consistent with (on a scaled basis) the actual AP600 design, the simulation of the OSU PRHR is made consistent with the horizontal noding of the AP600 SSAR, namely four nodes in the inlet horizontal and one in the exit horizontal segment, to validate the AP600 SSAR horizontal noding as found in Reference 440.721(c)-2, Figure 4-1.

l Atypicalities of the SPES-2 facility are the reason for other differences in the SPES-2 NOTRUMP noding from that of the OSU and AP600 NOTRUMP models. Specifically, the additional piping segments used in SPES-2 to connect the hot legs and the reactor coolant pumps with the steam generator inlet and outlet plena are modeled with separate fluid nodes (nodes 110,17,120 and 27 in Figure 7.2-2). The equivalent nodes are unnecessary in the AP600 and OSU models. In addition, the SPES-2 downcomer is comprised of annular and tubular sections; it is modeled with three fluid nodes rather than one as used in the OSU and AP600 noding to capture the different geometric parameters. Also, to properly represent the SPES-2 piping from the accumulator to the DVI entrance pipe a fluid node is added which is not present in the OSU and AP600 modeling. The AP600 and OSU NOTRUMP nodalizations are very similar, as befits a facility designed to specifically represent the AP600 geometry. To preserve a one-foot core node length among the three models, the OSU core has four nodes rather than the 12 nodes used in the SPES and AP600 models. Otherwise, except for the PRHR and ADS piping nodal differences specified above, the OSU and AP600 NOTRUMP models are almost identical; the exception to this is the added nodes used in the

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v

     *i NBC RitBEST F05 A85meNAL INFSRtlATION g8E

.p , modeling of the AP600 DVI line relative to the OSU simulation. Nodes are added to the DVI line to model a revised AP600 piping layout near the entrance to the reactor vessel from that which was simulated in the OSU facility tests. De noding in NOTRUMP downstream of the ADS Stage 1/2/3 valves in the SPES and OSU simulations is specified according to the mass collection systems of the test facilities. Separate flow links are employed for the ADS Stage 1, Stage 2, and Stage 3 valves. He basis for the nodalization of the ADS Stage 1/2/3 valves and piping in the AP600 SSAR analysis is the VAPORE facility test simulations (Reference 440.721(c)-1, Section 5). VAPORE is a full-scale model of the AP600 sparger located under water in a simulated IRWST and of the piping connecting it to the ADS Stage 1/2/3 valve discharge. The VAPORE simulation uses separate nodes for the sparger body and sparger arms, a single Dow path for the Stage 1/2/3 valves, and it also includes six nodes to model the piping from the ADS valve exit to the sparger inlet. De AP600 SSAR nodalization uses the same separate nodes for the sparger body and arms and the same single, lumped How path for the ADS flow paths as VAPORE; five nodes are used to model the piping between the ADS valve exit and the sparger inlet because of the small differences in piping layout from the VAPORE configuration. He noding used upstream of the ADS Stage 1/2/3 valve location in the VAPORE simulation is specific to the test facility design. The SPES-2, OSU and AP600 NOTRUMP models each have a single node between the pressurizer and the ADS valve location. Another difference in the SPES-2 NOTRUMP modeling from the other two applications is the ambient heat loss modeling described in Reference 440.721(e)-1. We high surface / volume ratio of the SPES-2 facility components and piping made detailed modeling of the heat losses with added metal nodes and heat links important in simulating the SPES-2 tests with NOTRUMP. De OSU NOTRUMP simulations used the metal node and heat link modeling approach used in the AP600 SSAR NOTRUMP analyses.

References:

440.721(e)-1: WCAP-14807, Revision 2. "NOTRUMP Final Validation Repoit for AP600," Proprietary, June 1997. 440.721(e)-2: WCAP-14601, Revision 1, "AP600 Accident Analyses- Evaluation Models," Proprietary, June 1997. SSAR Revision: NONE 448.721e -2 3 Westinghause h

i une niestsiren asemem surenmanen a= =g 1 .. _ e Question 440.721(f) Provide more details on NOTRUMP's misprediction of pressurizer drainage in the OSU tests. ( Thoroughly explain the significance of this deficiency in the code, such as non-conservatively predicting IRWST flow, and how it will be treated in performing AP600 calculations.

  . Response:

The response to RAI 440.721(c) described the pressurizer refilling phase. Near the end of the depressurization, the pressurizer begins to drain. The draining does not become significant until ADS-4 opens, and even then the draining process is relatively slow, it will be shown in the response to RAI.440.721(g) that OSU is more correctly scaled for this period than SPES, so OSU will be examined in detail. Review of test results: Examination of the collapsed liquid level (Figures 8.3.x-3 in Reference 440.721(f)-1) shows that the drain rate for most of the smaller breaks (2 inch cold leg and 0.5 inch cold leg) ranges from about [ ]" ft/s. This drain rate is much slower than draining of the pressurizer limited only by the surge line resistance. It is concluded that the drain rate is being limited by vapor flow into the pressurizer. This is examined in further detail below. The measured vapor flow out ADS 1-3 is [ ]" during this time, but the analysis below indicates that this is due to the inability of the measurement system to measure low vapor mass flows which could still result in high volumetric flows. As shown in Figure 440.721(f)-1, the core begins to generate vapor at approximately [ ]" seconds (based on an energy balance calculation). The two major escape paths for this vapor are ADS 1-3 and the two ADS-4 lines. As a first approximation, the vapor generated in the core can be assumed to split up among these paths according to the flow area available. For OSU, the total flow area through the valves in ADS 1-3, ADS-4 on the hot leg connected to the pressurizer (hot leg 2), and on hot leg I are [ ]" square feet respectively. The vapor flows through each path are then: Win = [ ]" W . W=[ ]" W . W,=[ ]" W. The total flow into hot leg 2 is: W westinghouse

r 9 NRC RitWEST FOR ADDIT 10NAL INf0RMAT10N l l 1 Wm=[ ]" W,, Dividing the mass flows estimated above by vapor density and the Dow path areas yields vapor l volumetric flux. Figure 440.721(0-2 shows the vapor volumetric flux in the surge line and into hot leg 2 (the flow fractions used to obtain these plots were slightly different than those listed above; Wm=[ 3"W =, Wo2=[ c

                                          ]"W,,, and Wy =[      ]"W,,; however, these differences do not significantly affect the results). When ADS-4 opens, the surge line vapor flow drops from about

[ }" ft/s to [ ]" ft/s, initiating the drop in pressurizer level shown in Figure 440.721(0-3 at this time. However, after ADS-4 opens, the total vapor generation rate increases and the vapor density decreases due to decreasing pressure, so the surge line vapor velocity remains relatively high, slowing l the pressurizer drain rate. Figure 440.721(0-3 compares the pressurizer level with the estimated vapor flux. It can b.e seen that the level tracks well with the vapor flow. Figure 440.721(0-4 shows the volumetric flux through the ADS-4 valves. The estimated vapor velocities are relatively high, and could be sufficient to cause some liquid entrainment from the hot leg. The response to RAI.440.721(c), indicated that a second level swell occurred when the core fluid began to boil at about [ ]" seconds. The estimated vapor flux through the surge line into the pressurizer after the core begins to boil can be used in the Yeh correlation (Equation 2.3-1, Reference 440.721(0-1) to calculate the mixture void fraction qin the two phase mixture in the pressurizer. Dividing the collapsed level by (1-%) gives the mixture level as plotted in Figure 440.721(0-5. It ! can be seen that during phase II ([ ]" seconds), the mixture level is calculated to be above the top of the pressurizer, providing additional evidence that a second level swell occurred. Estimation of the drain rate limited by flooding To confirm that the drain rate is limited by flooding, the following calculations were performed: The pressurizer drain rate can be expressed as: M an,y g t.sz Evn"A sl

        &          Afu '*'

where: i l M,.paz = pressurizer liquid mass = Araz 4.enz Pi Araz = average pressurizer crossectional area 440.721W -2 3 Westinghouse l. l l

t , NRC RitBE81 FOR ABBITitMilNFORIAATitu

                                                                                                          ?TI 2mz         =     collapsed liquid level W ut        =     liquid flow rate out of the surge line           =       Ast Pijat jut = liquid volumetric flux in surge line (negative downwards)

Assume that the liquid flow rate in the surge line is controlled by the flooding limit. Assume a flooding limit of the form, utilizing Kutatladze scaling (see page 1.7-9 of Reference 440.721(f)-1): k,* E m(-k,* */') = C r,. . J. . J,_

                 ' o b pg' W      K 2

P, i k,* = ?.ll.L

                $   p, K Assume that m=0.7 and C=1.5 (see Equation 1.7-33 in Reference 440.721(f) 1). If j, is known, jic an be determined by:

CKt /2.j,g2 hu=- f p ,'

m

( P,, 7he vapor flow from the core can be assumed to split up according to the flow areas available,and the flow path resistances. For the OSU test facility, these ratios are: Win = [ ]" W,, W,=[ ]" W,, , W Westinghouse

i l l

4 e 4 NRC RitIEST FOR ABBm8MA11NFORMAT18N k where W, is the total flow through both ADS-4 lines (the ratios are slightly different from the previous values because the line resistances have been taken into account). Therefore, the vapor flux through , the surge line is:

                     -}*' W, 4,n= l.

9/n During the period from [ ]" seconds, the vapor generation rate in the core is about [ ]" Ib/s and the pressure is about [ ]" psia in test SB18. Using these values in the above equations and calculating the rate of change of liquid level results in a value of [ ]" ft/s, reasonably close to the observed value of [ }" ft/s. His confirms that the drain rate is controlled by flooding and by the fraction of vapor generated in the core which flows through ADS 1-

3. His process will be examined further in the response to RAI.440.721(g), to determine whether the drain rate in OSU is appropriate for AP600.

ne effect of a partially filled pressuriur can be seen in Figure 440.721(f)-6. His figure compares ! the measured downcomer pressure with the incremental pressure above atmospheric which would be obtained by conves.ing the pressuriar level to hydrostatic head. A significant portion of the pressure in the downcomer is the result of this hydrostatic head. Therefore, liquid held up in the pressuriur increases the downcomer pressure which in turn will delay and reduce the IRWST flow. NOTRUMP results: The OSU predictions all show th71 while the refill rate in OSU is predicted well in NOTRUMP, the overall drain rate is much faster. The predictions are characterized by a sudden drop in the water level shortly after the ADS-4 valves open. Since the evaluation of the NOTRUMP drift flux model in Section 1.7 of Reference 440.721(f)-1 indicated that it would underestimate the liquid downflow for a given vapor upflow, it is likely that the reason for the NOTRUMP misprediction is due to an underprediction of the vapor flow through the ADS 1-3 while ADS-4 is open. The NOTRUMP analysis described below was performed to confirm that this was the case. Notrumo Simulations In Support Of RAI.440.721M Several NOTRUMP simulations were performed, with the OSU model, to attempt to improve the pressuriur drain response observed following ADS Stage 4 actuation. De 2 inch cold leg break simulation (Test SB18) was utilind as the basis for this effort. Modifications performed to the base model, developed in Reference 440.721(f)-1, included the following: 448.721m -4 T Westinghouse

 .                                                                                                           \

l 1

    .                                                                                                        1 l

NRC RiggitT FSB ABBITittlAlINitRMATitu I l Inclusion of a multi. node pressurizer (3 nodes) to better model the pressurizer void fraction I distribution. Inclusion of multi-node CMT rr , del as developed in response to Reference 440.721(0-1, Appendix A, " Response to RAI 440.339". l The following cases were performed during this effort:

1. Baseline Case 20 Node CMT,3 Node Pressurizer Model Rerun Of Final Validation Repon (FVR) Case (Reference 440.721(0-1, Section 8.3.1).

2. Homogenous Hot Leg - Modified Case 1 For Homogenous Hot Legs'To Improve ADS 1-3 Performance.

3A. Homogenous Hot Leg - Modified Case 2 ADS Stage 1-3 Flow Links Downstream End Elevations Raised In IRWST Tank. 3B. Homogenous Hot Leg - Modified Case 2 To Change Downstream End Of ADS 1-3 Links To Discharge To A Constant Pressure Boundary Node. Case 1 Results: No significant changes in transient results were predicted by this simulation. This was expected since the OSU facility pressurizer is well scaled and the facility itself is operated at relatively low temperature and pressure. The observed differences are a result of the inclusion of the multi-node I CMT model, which were also observed in performing runs in suppen of RAI.440.339 (Included in I Reference 440.721(0-1). The use of the multi-node CMT model results in a delay in the onset of increased CMT injection temperature observed in the base Final Validation Repon (FVR) simulations. The multi-node CMT ; model results in higher sub-cooling at the core inlet which delays the onset of core re-saturation and I the subsequent pressure hang which was observed in the Base FVR results. Selected comparison l figures, between the Base FVR case SB18 simulation results and the Case 1 results, can be found in Figures 440.721(0-7 and 440.721(0-8 respectively. l l Case 2 Results: The next case considered was an attempt to alter the ADS flow distribution by homogenizing the hot legs (Fluid Nodes 10 and 20 of Figure 8.2 2 of Reference 440.721(0-1). By doing so, the liquid l content of the flow reaching the ADS-4 valves would be increased, thereby reducing the vapor flow through ADS-4 and forcing additional vapor flow through the ADS 1-3 valves. W Westinghouse i

P l ne m m m u.m.m ===nu g; y l _ e l As expected, the change to homogenous hot legs resulted in a change in the predicted pressurizer mixture level and IRWST injection now rates following ADS Stage 4 actuation. The predicted pressurizer mixture level (Figure 440.721(0-9) remains substantially higher than the base case (Case 1) until approximately 1750 seconds, while minimally affecting CMT drain behavior. This change results in an increase in the predicted downcomer pressure, Figure 440.721(0-10, and subsequently delays

 . IRWST injection flow (Figure 440.721(0-11). The predicted drop            -ssurizer level at approximately 1800 seconds was still too rapid, relative to the test data, and addi:  <

simulations were attempted to improve this behavior. Case 3A Results: The purpose of this run was to further alter the ADS 1-3 flow distribution by relocating the ADS Stage 1-3 downstream connection point in the Upper IRWST tank node (Fluid Node 67 of Figure 8.2 2 of Reference 440.721(0-1). This change would reduce the static pressure on the downstream end of the ADS Stage 1-3 How links which would increase the duration of the ADS Stage 1-3 flow. By increasing the duration o;* ADS Stage 1-3 flow, the pressurizer mixture level would remain at a higher level due to continued CCFL conditions in the pressurizer surge line. With the added static head in the pressurizer, the IRWST flow would be affected due to increased downcomer pressure. While the pressurizer mixture level indeed increased betwcen 1000 and 1500 seconds, the IRWST injection now rate actually increased slightly due to a decrease in the predicted system and downcomer pressures which occurred as a result of the altered ADS Stage 1-3 How. Figures 440.721(0-12 through RAI.440.721(0-15 provide selected comparisons between the Case 2 and Case 3A results. Case 3B Results: This case represents an alternate approach to that performed in Case 3A. Namely, as opposed to moving the ADS Stage 1-3 How link connection points within the IRWST Duid node, the ADS links l were connected directly to a boundary node at constant pressure. This provides for an altemate representation of the ADS Stage 1-3 valves connection point to the ADS Stage 1-3 separator in the OSU test facility. The predicted response for this case was very similar to Case 3A. However, Case 3B was able to execute for an extended period of time. Note that the predicted pressurizer level was observed to remain on span for the duration of the transient simulation and thus affect the downcomer pressure. However, since the system pressure is also affected by the altered boundary condition, the IRWST injection rate, compared to the unmodified Case 2 results, exhibits a slight increase in How as a result. 448.72MH -8 3 Westinghouse

e NRC RE45tST f0B AD9filellAL lititRIGATitN l Figures 440.721(0-16 through RAI.440.721(0-18 provide selected comparisons between the Case 2 and Case 3B results.

Conclusions:

The results obtained tend to support the argument that the slower draining of the pressurizer levelin the OSU test simulations is a result of a difference in the predicted ADS flow distribution from the test value. The cases provided, while not providing an exact duplication of the tests, indicate that an increase in pressurizer level will indeed inhibit or reduce the predicted IRWST injection flow. This information will be used to support the IRWST level penalty to be described in the response to RA1.440.721(g). References. 440.721(0-1 "NOTRUMP Final Validation Report for AP600", WCAP 14807, Revision 2,1997 440.721(0-2 "AP600 Low Pressure Integral Systems Test At OSU: Test Analysis Repon", WCAP-14292, September 1995 SSAR Revision: NONE l

   . T Westinghouse 1

9-NRC REQUEST FOR ADDITIONAL INFORMATION l l 1 CSU 2 INCH COLD LEG BREAK CORE VAPOR GENERATION RATE CALCULATED BY ENERGY BALANCE. b, b o C. l i n . J 4 W i 4

        ~
                                                                                                   ~

CORE COMPLETELY SUBCOOLED FROM 400 TO 700 SECONDS; VAPOR GENERATION SUPPRESSED. MEASURED ADS 14 VAPOR FLOW DUE TO FLASHING OF WARM LIQUID LAYER ABOVE SU8 COOLED LAYER. ADS 14 MEASUREMENT NOT PICKING UP LOWER VAPOR FLOW AFTER . 700 SECONDS. Figure 440.721(f) l Measured ADSt 3 vapor flow compared with calculated core steam generation rate 440.721(f) -8 W Westinghouse

i NRC REQUEST FOR ADDITIONAL INFORMATION ! ~ M 4 l l OSU 2 INCH COLD LEG BREAK ASSUME CORE GENERATED VAPOR FLOWS THROUGH ADS VALVES ACCORDING TO AREA RATIO. 4 b, b , C. 1 l 1 1 4

             ^                                                                             ~

VAPOR VELOCITIES APPEAR SUFFICIENT TO LIMIT LIQUID DRAINING IN SURGE LINE. Figure 440.721(f)-2 Estimated vapor flux through surge line and hot leg 3 Westinghouse 440.721(f) 9

NRC REQUEST FOR ADDITIONAL INFORMATION N . OSU 2 INCH COLD LEG BREAK PRESSURIZER COLLAPSED LEVEL AND CALCULATED SURGE LINE VAPOR FLOW.

b, b , C

CHANGES IN CALCULATED VAPOR FLOW THROUGH SURGE LINE TRACK WELL WITH PRESSURIZER WATER LEVEL Figure 440.721(f).3 Estimated vapor flux through surge 'ine compared with pressurizer water level 440.721(f) -10 .

__ . - . . . . - - . . . - . . .- . . - . _ =- . . - . - . .. .. e

NRC REQUEST FOR ADDITIONAL INFORMATION OSU 2 INCH COLD LEG BREAK CALCULATED VAPOR FLOW THROUGH ADS 4,

b, b , C,. VAPOR VELOCITY THROUGH ADS 4 APPEARS SUFFICIENT TO ENTRAIN LIQUID FROM STRATIFIED LAYER. Figure 440.721(f)4 Estimated vapor flux through ADS 4 valves 440.721(f)-11

NRC REQUE3T FOR AD0mONAL INFORMATION OSU 2 INCH COLD LEG BREAK' USING YEH YOID FRACTION CORRELATION AND CALCULATED ' VAPOR FLOW, CALCULATE PRESSURIZER MIXTURE VolO-FRACTION AND MIXTURE LEVEL 1

                                                                                                          ^ b, b , C                I l
                 ^

MIXTURE LEVEL AT TOP OF PRESSURIZER ColNCIDES WELL WITH SECOND OUTSURGE. WHEN MIXTURE LEVEL DROPS BELOW PRES $URIZER AT 1000 l SECONDS, LlQUID OUTSURGE STOPS. Figure 440.721(f)-5 Estimated mixture level in pressurizer 440.721(f) -12 T Westinghouse

               . . . . . .           . . . . -- . . .   . - - . . . _ _ . - . ......n.. ... . _ , .- . _ .,   ..      .n.   - -.. __~

NRC REQUEST FOR ADDITIONAL INFORMATION

==

OSU 2 INCH COLD LEG BREAK MEASURED DOWNCOMER PRESSURE AND CALCULATED PRESSURE ABOVE ATMOSPHERIC DUE TO WATER LEVEL IN PRESSURIZER.

                                                                                                                     ^ b, b , C A

LIQUID HOLD UP IN PRESSURIZERINCREASES DOWNCOMER PRESSURE AND REDUCES IRWST FLOW. Figure 440.721(f>6. Effect of pressurizer level on downcomer pressure 440.721(f)-13

Figure 440.721(0 7 Case 1, Pressurizer Mixture Level Comparison OSU Sb18. 2 inch Cold leg Break Pressurizer Wixture Level osu rva u...i

                              ---osuu.iii-=...u...i 20 h ,,       5                 i 'Im '!ONI.          l 5                I           ko.        I

i if ihJ

                          .$         k               l              N b-                       I
                            ' 10 a               :               bam                       &

5 5 l & A.

                                '        t i     6 u

a : 500 1000 IPLH P 15'00 2000 2500 Time (s) l Figure 440.721(0-8 Case 1,IRWST-2 Injection Flow Comparison l OSU Sb18, 2 Inch Cold Leg Break IRWST-2 Flow Osu FYR u...t i

                              ----osuu.m-w...u...

_ 3.5 . d 3 E I 1 1 i i, l l 225 ; U; i i

s i, in -

l

lll >, eh, 3 ;; jll 4W 1%

w

                               .5
                                       ;                              p        r                g "0
                               .5 W             Suo         1000        1500         2000         2500 Time       (s)
         /ttnp_mnt/home/gagnona/wp/ docs /AP600/RAls/440.721f. doc October 16.1997 4:37 pm

t Figure 440.721(0 9 Case 2, Pressurizer Mixture Level Comparison OSU F 918. 2 Inch Cold Leg Break Piessurizer Mixture LeveI osu W.iii-=... W.e. . sir.iiri.e u.i t.,

                         ---.osuW.iii-=...               W.e.i. w.......... *.i t.,

m :0 _

                     ~          '

gg b l 7[ #

                      " 14                                    '   - ~ ' " ' ~

I

                      .                         I                                     y j

o ,, i lli.- ', T

                     ' to
                               ]

8

                                               ,                "IIIIIlll
                     $,                        !                               l$ '4
                     $g                                                           ,

d , . W 500 1000 15'00 2000 2500 Time (s) Figure 440.721(010 Case 2, Downcomer Pressure Comparison OSU Sb18, 2 Inch Cold Leg Break e,....,. Downcomer Presaure

                                      <,.i.)

I CSU W.Iti-N.e. W. .l. Str.tifl.. n.t L.g

                        ---.OSU       W.ItI-N... W. .I.          w.m. gen....               n.t L.g 400 30                   I 7           _
                                                                                                         - 28 7 m 300                         *4                                                 '         '~

c. -

i 23 n p n. v t

24 *

                               .            I
                    ,200-      --

22 I

                    ;          :              i
                                                                                                         - 20 n 100                       '                                                               "

1 s 13 n s C. 0 ' 14 l 0 500 1000 1500 2000 2500 ' Ilme (3)

   /tmp_mnt/home/gagnona/wp/ docs /AP600/RAls/440.721f. doc October 16.1997 4:37 pm

\ P Figure 440.721(0-11 Case 2,IRWST 1 Injection Flow Comparison ; OSU Sb18, 2 Inch Cold Leg Break l lRWST-1 Flow osuv.iii-=...w...i. sir.iiri.. a.i t.,

                            - - - . o s u u. i i i-=. . . u. 4. i . w. ........ a.           t.,

n 2 3i.5 h'>^

l/fV V 5, $[

u. -

m .,3 . , , . , , ,, 9 SWO 1000 1500 2000 2500 Time (s) Figure 440.721(012 Case 3A, Pressurizer Mixture Level Comparison OSU Sb18. 2 Inch ~ Cold leg Break Pressurizer Mixture Level osu u.iis-n.a. v.4.i. crit, w... ut. s...

                             ---.osuv.iii-u...v..i.                     crit. w... wt. u... Aos                -s
                       ,to-        --

[,,,l

                                                              " U  N UEs           am.C 'S
                       -                                                  7 M
                                   }                                                       '

fe

e 14 k , 6

i lg

i 'i ' J 12 o 5\ k g

                          ' 10                                                                           i
                          =          :

g@i 58 ' 2 g n Sue 1000 1500 2000 Time (S) l l l

      /tmp mnt/home/gagnona/wp/ docs /AP600/RAls/440.721f. doc October 16.1997 4:37 pm

.g e

4 Figure 440.721(013 Case 3A, IRWST 1 Irdection Flow Comparison OSU Sb18, 2 Inch Cold Leg Break lRWST-1 Flow osu u.iii-=... u...i. crii. n... wt. s... 1

                                       ---osuv.iii-=...u...i.                          crai. w... wt.         u... Aos i-s
                                   ,    2 n

, N -

,. .t.5 . ,, I

o 1 1 C .s . 5 0 U 500 1000 1500 2000 Time (S) 1 Figure 440.721(014 Case 3A, Pressurizer Pressure Comparison OSU SB18 2 INCH COLD LEG BREAK (REWOVED PRHR Pressure (psio) PFN 172 u O PRES 5URIZER PRESSUR

                            ----PFN                              172            0            0 PRESSURIZER PRESSUR Pressure             (pelo)                                                                              -

PFN 172 0 0 PRES $URIZER PRESSUR

                            ----PFN                              172            0            0 PRESSURIZER PRESSUR m    400                                                                                              30 y                                                       m h                                                                                   '28..

300 [ 0 26 a"

                                                                                                                          '24*
                        .,200 [                                                ,q                                           2 2 ,,
                                                                                                                          ' 20 $

f'

n. O h

                                      ~ ' ' ' '                '

( ' t c. . iQ . 14 .i 's f y 500 1000 1500 2000 Time (S) 9

           /tmp mnt/homelgagnona/wp/ docs /AP600/RAls/440 72if doc October 16. 1997 4:37 pm

s t , P Figure 440.721(0-15 Case 3A, Downcomer Pressure Comparison OSU Sb18. 2 inch Cold Leg Break Downcomer Pressure er....r. <,.i.) . osu u.iii-=... u...i. crit. w... wt. s...

                                - - - o    s u u n i t i-N. .. u...l. Crii. w.m. ut. u.ve Aos 1-3 400                                                                             30 7                                            6                                     - 28 7 m J00                                                                                28 m
                         ~

a -

                                                                    'T p                                            =
                                                                                                                                        ,200 [                                                                               22 ,

m . -

                           =
                                                                                                            - 20 =
                                                                             -  nG 4%                     .

g

\g L i

                                                                                                             - ts y 0                                                                            14 0              500            1000               1500             2000
     ,                                                         Time         (s)

Figure 440.721(016 Case 3B, Pressurizer Mixture level Comparison OSU Sb18, 2 Inch Cold Leg Break Pressurizer Wixture Level osu v.iii-w... u... . crii. w... ut, s...

                                - - - o s u u. i i i -w. . . u. . . i . c , i i w ... u t , so.          w...

n 20 .

                                ,,                      'l7E r ** 't b                                              -        l i,                                                      .

l I j e

                            > I4 b'        i o                                                                  i
                                      ~                                                        \
                             ' 12                                                         l,   '.
                            ,         :I
                                      ~

ill% w to '%

                           =          -

NRh bJ A g o 500 1000 1500 2000 2500 Time (s) l l l

         /tmp mnt/home/gagnona/wp/ docs /AP60&RAlv440.721f. doc October 16.1997 4i37 pm

t

Figure 440.721(017 Case 3B,IRWST-1 Flow Rate Comparison OSU Sb18. 2 Inch Cold Leg Breck lRWST-1 Flow esu u.iii-=... ...i. crit, w... wt. s...

                                  ---osuw.so-=...u....                             crit,   w... wt. sa. =...

m 2.5 , a - s - E - 2 2 Q l 1 A d g' V%%

                         $'5
                         "                [
                                     ,                                                     i rd E

I F

                         '                ~

gg

                                   .s     -

O

                         =           a
                                                .                                 ,il.            .        .           ,

! W 500 1000 1500 2000 2500 Time (s) 1 l Figure 440.721(018 Case 3B, Downcorner Pressure Comparison ! OSU Sb18, 2 inch Cold Leg Break er....,. Downcomer Pressure (,.i.) l osu v.iii-=... u...i. crit. w. . wt. s... i

                                ---osuv.iii-=...w...i.                             crit. w... wt.       s.. w...

l 400 30 l n bE m \ a

l

                                                                                                                     -20 a                 '

m 300 20 m

s

      .                *                                   )                                                         -24

m

I

                         ,,200           ,

22 ' w w l . : -20

u m 100 ' il n l w n.

                                        -                                                s\                          . tg w I

0

                                                  ' '          '   '         '           '     '    %f~
                                                                                                    '"?      '
                                                                                                               *~ ' 14     cL.

0 500 1000 1500 2000 2500 Time (3) 1 4 l i Amp mnt/home/gagnona/wp/ docs /AP600/RAls/440.721f. doc October 16, 1997 4:37 pm l'

                                                   -        -        -             --              .-             .-           . - ~ _
 .                                                                                                                                     i NRC REQUEST FOR ADDITIONALINFORMATION                                                                                            I e

l Question 440.721(g): Related to (f) above, Westinghouse is proposing to apply a penalty in IRWST level. Provide a detailed explanation of how the penalty is determined via scaling from the OSU test data to the AP600. Justify why this is conservative.

Response

In the response to RAI 440.721(c), the pressurizer refilling phase was described, and in the response to RAI ( 440.721(f), the pressurizer draining process was described, ne filling process was shown to result from the level swell in the system due to the vapor flow through ADSl-3 and the resulting system depressurization. The draining , process was shown to be limited by vapor still flowing through ADSI 3 after the system had fully depressurized and ADS 4 had opened. It was shown in the response to RAI 440.721(f) that the residual mass left in the pressurizer contributed to a higher downcomer pressure late in the transient. This higher pressure effectively reduced thq net hydrostatic driving head I available for the IRWST, and caused a delay in the time at which IRWST water began to inject. In NOTRUMP, the l draining of the pressurizer occurred more quickly, resulting in an earlier and a higher predicted IRWST injection. l ne refill phase is important because this will determine how much mass must be drained from the pressurizer. The j draining phase is important because this will determine the time it takes to drain the pressurizer. Each phase is discussed below, first to establish whether the OSU test facility is correctly or conservatively scaled, and then to l establish an equivalent IRWST level reduction for use in the AP600 calculation to account for the observed NOTRUMP deficiencies. Refilling rihase: Just prior to ADSI-3, the system has partially drained by mass loss through the break. He pressurizer is empty of water, ne CMT has been draining, filling the downcomer, lower plenum, and part of the core with cooler water. Above this cool water is a warmer layer of saturated liquid and two phase mixture, consisting mostly of the original primary side inventory. Because the level swell is controlled primarily by vapor flow and void fraction, these variables need to be scaled correctly in the test facility. Since steam generation rate is important, OSU will exhibit fewer scaling distortions during this period than SPES because the energy contribution from heated structures has been substantially reduced. On the other hand, OSU is a reduced pressure and reduced height test facility, so other scaling issues will become important. Reference 440.721fg)-3 provides a detailed scaling analysis of the OSU and SPES test facilities. The OSU test facility ADS valves were sized to produce the appropriate response, taking into account the lower initial pressure of OSU It was concluded that the OSU test was more appropriate than the SPES-2 test for assessing the effects of pressurizer tefill because OSU was not distorted by excess heat release from metal structures. De test results show that any distortion in level swell results in a conservative estimate of the pressurizer refill relative to AP600. This is because in most of the OSU tests, the pressurizer nearly fills completely with water. If the test facility is accurately scaled, then this is an accurate depiction of the behavior of AP600. If the test facility is not accurately scaled. then from the point of view of pressurizer refill and subsequent draining, the OSU test is conservative, since it results in the highest possible refill of the pressurizer. W Westirighouse 440.721(g)-1

i-l g ( o NRC REQUEST FOR ADDITIONAL INFORMATION l- ! Drainine chase: Examination of the collapsed liquid levelin the pressurizer shows that the drain rate for most of the smaller breaks is much slower than draining of the pressurizer limited only by the surge line resistance. It was concluded that the drain rate is being limited by vapor flow into the pressurizer (see response to RAI 440.721(f)). Because the liquid l draining from the pressurizer, surge line, and hot leg is interacting closely with the vapor through interfacial drag, an l , increase in the pressure of the vapor occurs. Since the onset of IRWST draining is controlled by the downcomer

    .         pressure, this pressurization delays IRWST injection as previously noted. It is expected that the same process will occur in the AP600, so account must be taken of the effect of liquid holdup in the AP600 calculation. Because the ADS 4 valve is oversized in the SPES test relative to AP600,it was again concluded that the OSU tests were more appropriate for examining this effect.The effect of this liquid holdup in the OSU test will be scaled up to AP600 conditions using the following simple model.

Assume that the downcomer pressure at the location of the DVIline is approximately equal to the system pressure. Assume that the system pressure is controlled by the resistance which the ADS vent valves present to the vapor

          . generated in the core, and an " effective" height of liquid held up by the vapor in volumes above the DVI injection point. The system pressure P is then related to core vapor flow W, by:
                                                  'Wf- h g,144(P - P,) = K 1          -
                                                                + p,h'g                         __              44o.72u o - 1 2 p, q A >

where P,is the IRWST tank pressure (15.2 psia), and h' is an effective liquid height. To determine if this is a reasonable model for the system pressure late in the transient, the effective height was calculated from known test I conditions for several of the OSU tests. The various quantities needed to calculate h' are listed below: QUANTITY VALUE BASIS P Measured test data (psia) Instrument Clrr 111 is located at top of DC P. Measured test data Instrument CPT-701 is located at top of IRWST p, 0D45 lb/ft3 Vapor density at 18 psia (typical system pressure) pi 60 lb/ft8 Liquid density at 18 psia K [ ]" (all tests ex. DEDVI) Composite loss coefficient thru ADSl 3 ADS 4 [ }"(DEDVI) A [ ]" ft:(all tests ex. DEDVI) Total flow area thru ADSl 3, ADS 4 [ ]" ft We Calculated from test data (Ib/s) RPVRXV (eg., Fig. 5.3.2-55, ref 440.721(g) 2) 440.721(g)-2 W Westinghouse

l o I - NRC REQUEST FOR ADDITIONALINFORMATION i Using the above values results in the following formula for h': l l l i a .c ; 440,721(g)- 2 i De above equation will be used for all the tests except Sbl2 (DEDVI). For Sbl2, the second term value is [ Figures 440.721(g)-l to 6 show the calculated effective liquid height h' for OSU tests Sbl8, Sbl3, Sbl2, Sb09,

                                                                                                                                   }"       l Sbl0, and Sbl4 using Equation 440.721(g>2. Also shown on the plots is the time at which the IRWST begins to inject. Early in the transient, the system is still depressurizing and the steam generation rate is underestimated because flashing is ignored in Equation 440.721(g)-2 (for example, at 1000 seconds in Figure 440.721(g) 1). On the              l average for all the tests, however, the effective liquid height settles to approximately 5 feet after the system has            i depressurized and IRWST has begun.

The same, approach can be used to calculate the effective liquid height present in the NORUMP predictions of the above tests. In this case, Equation 440.721(g>2 is again used, but P and W, are NOTRUMP calculated values. Rese results are shown in Figures 440.721(gh7 to 12. h can be seen that the effective liquid height is correctly predicted at the time IRWST injection begins, and then is underpredicted (for example, after 1600 seconds in Figure-440.721(g)-7). De time at which the predicted effective level drops below the test value usually coincides with the 3 time at which the pressurizer is predicted to empty. As pointed out in the response to RAI 440.721(f), the result of , the lower effective liquid levelis a reduced downcomer pressure, which then causes the IRWST flow to be l overpredicted. With the exception of test Sbl2 (DVIline break) and Sbl4 (Inadvertent ADS), the effective level l drops to about 2 feet (for example, Figure 440.721(gb7 after 1600 seconds) so the extent to which the effective

liquid level is underpredicted during this time is about 3 feet. In the prediction of tests Sbl2 and Sbl4, the effective l

level drops to near zero late in the transient, well after continuous IRWST injection has been established. In Test Sbl2, the reason that the level is lower than in the other cases is partly because in the NOTRUMP prediction, much of the core steam is calculated to flow out of both sides of the broken DVI line (see response to RA!440.721(d)). Rese additional paths are not taken into account in Equation 440.721(g>2. With a lower resistance to vapor flow, the second term would be smaller and the effective liquid height would be larger. In addition to these effects, there is ! also a misprediction of the downstream pressure of ADSI.3 as indicated in the response to RAI 440.721(d). In the ! Sbl2 test, somewhat less vapor was vented out the broken DV1, so the effect of ignoring this vent path would be smaller (since ignoring this vent path leads to a larger difference between test and prediction, the approach is conservative). In the Sbl4 test, the're is significantly more steam generated in the NOBUMP prediction, because the core inlet subcooling is much lower (see Figure 8.3.7-42 in teference 440.721(g>2). In this case, Equation 440.721(g>2 adequately depicts the available vent paths, since there is no break path. l It is proposed to account for the underprediction of effective liquid level in NOTRUMP by reducing the level in the IRWST. The basis for correcting the calculation this way is given by the equations below, which describe the previous mom (nrum balance and the flow equation for the IRWST: l l l l T Westingh0use 440,721(g)-3

NRC REQUEST FOR ADDITIONAL INFORMATION g,144(P - P,) = 2p, A] sos Wl + p,h'g K '" 440.72u g>-

=-

2 W , + p,h,,g 3 2PiAta

                       '"                                       ^

2P Aa 2 i W,g = p,(h g - h') - 29,A]Aos Wl i where K ai and Aia are the IRWST injection line resistance and area, and Wi n is the IRWST flowrate. This ec i uation shows that the effective liquid height can be viewed as a reduction in the.lRWST water level. Increasing the effective level by 3 feet in the NOTRUMP predictions by some means such as modifying the flow models would bring the downcomer pressure up and the IRWST flow down the required amount to agree with the data. Ba sed on Equation 440.721(g) 3, an equivalent adjustment is to reduce the IRWST level by 3 ft. By inspection, for a'.4 cases, adding 3 feet to the predicted effective liquid height will result in a conservatively high downcomer pressure at the time ofIRWST injection. Figures 440.721(g)-13 to 16 compare the test equivalent height to the NOTRUMP ! prediction after adding 3 feet for selected tests (Sb9, Sbl0, Sbl2, Sbl4). In some cases, the adjusted effective liquid height falls below the test value late in the transient. However, this occurs well after the IRWST has begun to inject. , _ in the long term cooling phase of the LOCA event. For all cases, the added 3 feet results in a higher downcomer ! pressure at the time IRWST injection begins which will delay IRWST injection and reduce its flow for the important period of time when the IRWST flow is not yet sufficient to make up the mass lost from the system. Since NOTRUMP is not used for AP600 SSAR long term cooling csiculations, this non-conservatism late in the transient is considered to t.?. unimportant. t

          ' In order to establish the value of h' and the necessary correction at the AP600 scale, teke as the reference condition l

l the point at which the IRWST flow is just zero. From Equation 440.721(g)-3: i l

440.721(g)-4 W Westinghouse

I l NRC REQUEST FOR ADDITIONALINFORMATION l e

                                                   %2 l

(h,, - h ) = Kaos 1 (Qc 2 440.72ng>- 4 l AAos 2AA8 ghf, , where the core steam generation rate has been replaced by the core power Q, and the heat of vaporization hr,. De OSU facility scaling . and the values of some key parameters relative to AP600 are (Table 8.2-4. Reference 440.721(g)-3): QUANTITY OSU AP600 Power 1.0 96.0 Area 1.0 48.0 Height 1.0 4.0 Kes [ }" 3.13 IWRST ievel(ft) 8 32 Takir.g the ratio of Equation 440.721(g)-4. canceling property terms which are assumed similar, we get: (h,, - h')^'" _ Ks'$s" ' Aff ' 960 **" (hia - h') '" ~ Kll" g48Affl,q Q, '" , 440.721(g)- 5 f 3.13 I V 96

                               =             -
                                                    =7.6 (1.65)(48, For an average effective hquid height of [ ]" ft in OSU. therefore. the following effective liquid height applies in AP600:

(hj a - h')^'" = 7.6(hig - h') '" h " = 4 hja " - 7.6(hga - h') '" 440.721(g)- 6

                               = 7.6hmu - 3.6h f,3"
                               = 9.2ft De effective liquid level correction should therefore be adjusted by:

9.2 '

        &" =                 3 osu                                                               44o.72u9)- 7
                       <5>

j . where 6h osu is the incremental increase in effective liquid height needed to produce agreement with the OSU data. , The adjustment of 3 feet in the OSU tests therefore translates to a value of 5.5 feet in the AP600 calculations. A jnel oenalty of 6 feet is conservatively acclied to the AP600 SS AR small break LOCA NOTRUMP calculations. l j T Westinghouse 440.721(g)-s

r o

    -                                                                     NRC REQUEST FOR ADDITIONAL INFORMATION
           =

In one other imponant respect, reduction of the initial IRWST level to conect for the NOTRUMP deficiencies is conservative because the effect is permanerit, even after the pressuriter has drained. In the AP600 calculation, additional conservative assumptions with regard to the core power as required by 10CFR50.46, Appendix K, result in substandally less liquid above the core, which would cause the effective liquid level to be reduced relative to the OSU test conditions.

      ,   References.

440.721(gF1 "NOTRUMP Final Validation Report for AP600", WCAP 14807. Revision 2,1997 440.721(g>2 "AP600 Low-Pressure Integral Systems Test At OSU: Test Analysis Report", WCAP-14292, September 1995. 440.721(g)-3 "AP600 Scaling and PIRT Closure Report", WCAP-14727. Revision 1.Iuly 1997. . 4 i 440.721(g) W Westinghouse 1 1 _ - - -- ___-____ __-_ - - -._ _ -________ - - _ 1

 .     . __ .          .    . . - _ . _ _ . . . _ _ . _ _ . . . _ - _ .   . - _ _ _ . . ~ . . - . . . _ _ _ _ _ _ - _ _ _ - _ _ _   .._.-. . . _ _ _ _ . _ - . _    . _ _ _ . - .

NRC REQUEST FOR ADDITIONAL INFORMATION i

      -          -                                                                                                                                               -%c l

i 1 l l 1 1 i

Figure 440.721(g)-l Effective liquid level above the DVI injection point for Test Sbl8.

T M in M 440.721(g)-7

_ - - _ . . ._ _ ...__. . _ ._. ...._-..-._.-_.___.__.....____..._-m.. ._ ._..._-___. .. b* !

   .                                                                                      NRC REQUEST FOR ADDITIONAL INFORMATION N
                                                                                                                                         ,4C 4

mus Figure 440.721(g) 2 Effective liquid level above the DVI injection point for Test Sbl3.

                 -9
                                                                                                                                              }

440.721(g)-8 W-Westinghouse e

         .   - _                   . ..      -       ._        . -      .     .          . - . - . - . . . _ . . ~ _   _ -       _ _ - _ . _ - . .
     ~

NRC REQUEST FOR ADDITIONAL INFORMATION

1 a., f-i I l l

Figure 440.721(g)-3 Effective liquid level above the DVI injection point for Test Sbl2.

+ T Westinghouse 440.721(g)-9 f r ,

NRC REQUEST FOR ADDITIONAL INFORMATION j

b A P6 01 - . l AO I Figure 440.721(g)-4 Effective liquid level above the DVI injection point for Test Sb09. 440.721(g) W Westinghouse

l

1 I

I NRC REQUEST FOR ADDITIONALINFORMATION e l I 1 i 4 l s g e& i 1

                                                                                                             %i Figure 440.721(g)-5 Effective liquid level above the DVI injection point for Test Sbl0.

NUD" 440.721(g)-11

1

NRC REQUEST FOR ADDITIONALINFORMATION "f

as 4 Figure 440.721(g)-6 Effective liquid level above the DVI injection point for Test Sbl4. 440.721(g)-12 W Westinghouse

NRC REQUEST FOR ADDITIONAL INFORMATION i l OSU Sb18 2 Inch Cold Leg B r e.a k v!M00049 1 0 0 00WNCOME R' P R E S SUR E C' _ l v _ I 15 - E [ : l JtWs7' b10 I i o - ! m . V

                  $                          '             r kd  '
                                                                                  .6
                                                 ' 17    1

[' w g kW 1000 1200 1400 1600 1800 2000 ( l Iime (S) l l Figure 440.721(g)-7 Predicted (NOTRUMP) effective liquid level above the DVI injection point for Test Sbl8. 4 W Westinghouse 440.721(g)-13 L l

     '                                                                                                                           NRC REQUEST FOR ADDITIONAL INFORMATION OSU               Sb13                                                        2                      Inch      DVI       Line Break NOIRUMP Effeetive height-

_ 20

~_,

15

         .T        -

e . . jfW s?

         .3                       1
          ,    10
         .I         "_           V a           n .. .s n .  ,

5 h h&,NMd. . 5) ri %. ..d,,b rw rubMIdbMEhr i- i i iw AMi i n ' ima"s u 0~ 1400 1500 800 900 1000 1100 1200 1300 Time (s) Figure 440.721(gp8. Predicted (NOTRUMP) effective liquid level above the DV1 injection point for Test Sbl3. 440.721(g)-14 gp 1

NRC REQUEST FOR ADDITIONAL INFORMATION OSU Sb12 DEDVl Line Breok ' NOTRUMP Effeetive height

                         ,20        ,

C - t 15 Z _ v -

n 10 s tklJ Y 5 lV

                -           0 flh jjgg        h,, ,i d J f % i 0                   200  '

400 600 .800 1000 IlMS (S)

                  . Figure 440.721(g) 9 Predicted (NOTRUMP) effective liquid levtl above the DVI injection point for Test Sbt2.

440.721(g)-15

l

   >                                                                                                                                   l e                                                                       NRC REQUEST FOR ADDITIONALINFORMATION                       l pm                                                                  .

j m ov

OSU Sb09 2 lnch Balance Line Br.eak MTH00052 1 0 0 00WNCOWE)t PRESSURE l l _ 20 1 i - - 1

                 = 15
                 >           _                 /4Ns r o           .

0

               ~;: 1 0       -

n - ].

               . E       3 21 k1
                             .                        v   73 0

l 1000 1200 1400 1600 18'00 2000 i Iime (S) Figure 440.721(g)-10 Predicted (NOTRUMP) effective liquid level above the DVI injection point for Test Sb09. uo.721(g)-16 T westinghouse i

NRC REQUEST FOR ADDITIONAL INFORMATION r , I l OSU Sb10 Double Ended Bolonce Line Break l NOTRUMP Elfactive height IRus T*

             ..33 i                     As[

y,,#

10 , g. . i' illyl ill'

                =          -

I

                           ~
                           ~                                    \l[ j l  '

lIl 400 600 . 800 1000 1200 1400 1600 Time (s) Figure 440.721(g) l1 Predicted (NOTRUMP) effective liquid level above the DVI injection point for Test Sbl0. ( l ww poo uo.72ico).i7

t 0 NRC REQUEST FOR ADDmONALINFORMATION fy A P60(- OSU Sbl4 Inadvertent ADS A c t, u a t 'i o n NoiRUMP Effectiwe height 20 . it5 _

                                                                                                                                                          *                              -                                      IthlW
                                                                                                                                                          ;; I 0
                                                                                                                                                          -                                                                       V ljj
                                                                                                                                                    "                                     .                                       ll 5

5

                                                                                                                                                                                                                                        ] lhM '

C

0 , 400 600 800 1000 1200 1400 Time (S) i l Figure 440.721(g)-12 Predicted (NOTRUMP) effective liquid level above the DVI injection point for Test Sbl4. 440.721(g)-18 T westingmuse

              -             .         . ~ - . - . -        ..             . - - - = . .   . - .      _ . . . - -    - _ - _ . . .
   ~

' C NRC REQUEST FOR ADDITIONALINFORMATION

j l

4.,6 i l i l I l Figure 440.721(g).13 Comparison of test effective level with NOTRUMP level increased by 3 feet for test Sb09. T Westinghouse 440.721(g)-19

o NRC REQUEST FOR ADDITIONAL INFORMATION s 1 1

_ a [" i 3 I Figure 440.721(g) 14 Comparison of test effective tevel with NOTRUMP level increased by 3 feet for test Sbl0. 440.721(g)-20 W Westinghouse

   =n l

j 4 l NRC REQUEST FOR ADDITIONALINFORMATION i l y iii. i i

ev,o< -

I-l t l

                                                                                                                                                                .a,c'l 1

l l i l s l Figure 440.721(g)-15 Comparison of test effective level with NOTRUMP level increased by 3 feet for test Sbl2. l T westinghouse 440.721(g)-21 ?

                                                                                                                                                                                      . . . . _ _ _ . . . . . _ . . . _ . - - - - _ . . _ _ _ _ _ . - . - _ .   . . . . _ . . ~ . - _ . _ . . _ _ _

p. O e

  =                                                                                                                                                                                                                                     NRC REQUEST FOR ADDITIONAL INFORMATION f~'ily wtrol.
                                                                                                                                                                                                                                                                                                      . o.,c-          5 l

l l l l l l Figure 440.721(g)-16 Comparison of test efrective level with NOTRUMP level increased by 3 feet for test Sbl4. M0.721(g) 22 W Westinghouse l

    . .        . -      . _ _           . .       -~         . - . .         .-      _ - -                  -      ... -.-            -_. - -                  -

i

                              ~ .     .       _
                                                          . - we e         .      .,*er.amwe m.    .c=4.,       ..%.            .    - _ , , _ . . .

i i I f l NRC REQUEST FOR ADDITIONALINFORinATION l0 l 1 Question 440.721(h): Provide detailed justification for not including momentum Cux in the NOT. RUMP models. l l

Response

(The following discussion will be insened in Section 1.7.5 of reference 440.721(h)-1)

        ' As noted in Section 1.7 of Reference 440.721(h)-1, NOTRUMP does not include the second and third terms of equation 1.71. The momentum flux terms arise from the acceleration imposed on the flow by density and area changes along the pipe. This can more easily be seen by simplifying the momentum equation to consider steady, horizontal, homogeneous equilibrium flow (the importance of drift or slip effects will be discussed later). The           ,

pressure gradient in this case is given by: dP

           - = -       fvr ' W' * @2 1d f                   ss u +I W uf)                              440.721thi- 1 dz          2D CA>                       A dz(W where P is the pressure, fis the friction factor, D is the pipe diameter, W is the mixture mass Oow rate (subscripts f and g define the gas and liquid flows), A is the area, v,is the fluid specific volume (1/ density), @ is the two phase multiplier, and u is the mixture velocity. Assuming homogeneous (u,=u,) conditions (the importance of drift or slip                                    ,

efrects will be discussed later), the momentum equation becomes: I dP

-=-

fv f ' W' ' @f, W du 2 440.721(h)- 2 h 2D < A) A& Since u=Wy/A, where v is the mixture specific volume, the velocity derivative can be replaced to yield: j dP /v t 2 2 2

G'v dA

-=-

G $f ' - G dv - 440.721(h)- 3 dz 2D dz A dz Where G = W/A. The above equation separates the influence of changing specific volume, and changing flow area. In two phase flow, the mixture specific volume is given by: v = v, + xvy, u here x is the steam quality. Since the phasic specific volumes are functions of pressure only, the spatial derivative . can be split into: 440.721(h)- 4 dv 'dy, + xdv/dP dx . dx

-=

dz < dP b- + vf, dr = (xv* + (1 - h

                                                                                                +v,-

x)v})dP f dP > dz where v' means the derivative of specific volume with respect to pressure. Combining the above equations yields the following equation (similar to equation 2.44 of reference 440.721(h)-2): l

,gs         T Westinghouse'                                                                                            440.721[h)-1 l

6'- b[

   +                               4                       __      _ . _ . , _

i m... _ _ . . _ _ -~~ l l NRC REQUEST FOR ADDITIONALINFORMATION l e l l 3 dx v df G

           -  'fvi@          +v g dz 2

dP <2D A dzi 440.?21(h)- S l -= l dz 1 + G*(xv, + (1 - x)vy) This equation shows that the rr.omentum Oux terms innuence the pressure gradient locally (via the area and quality gradients in the numerator), and globally via the denominator. l ! The area change term is accounted for in the NOTRUMP momentum equation by adding an overallloss factor K to the frictional term which calculates the overall loss in pressure across the area change. Typically, area changes in the AP600 piping network are abrupt, and therefore introduce additional irrecoverable losses which must also be accounted for in the loss factor. Application of the momentum Oux term shown above evaluates only the l i recoverable pressure change, and would not be accurate if applied without the additional or offsetting irrecoverable losses. The quality gradient term is important where there is boiling due to heat transfer or Dashing due to a pressure gradient. If the quality gradient is dominated by boiling from a surface, the energy equation gives: Wd(hf+ xh g) = q, 440.721(h)- 6 dz where h denotes fluid enthalpy and q' is the local linear heat rate (Btu /fVs). Expanding the derivative (assuming pressure effects are small), the acceleration effect due to boiling becomes: dx = vg (q'/ A) 440.721(h)- 7 vh dz h3 G The momentum Oux term may be important during the natural circulation period, where mixture density differences drive the now. Estimates using typical values indicate this term is comparable to the friction term at low mass velocities in a boiling channel. In NOTRUMP, this component of the overall pressure drop is accounted for via the two phase multiolier correlation, which is derived from a data base which includes data in heated tubes (reference 440.721(h)-3, page 57). NOTRUMP does not account for the increase in the overall pressure gradient resulting from the denominator in equation 440.721(h)-5. This term is examined in more detail below. The increase in Guid quality can also be dominated by the pressure gradient. Across an orifice, for example, the Guid enthalpy can be assumed to be fs.irly constant, such that x=(h h,)/h,, where h is constant. Therefore: dx a 'h - hy ' dP vs dP 440.721(h)- 8 v =v 3 3 dz iP < hg dz = --(h.f

                                     ,             hg         + xh.3) dz 440.721(h)-2 W Westingtiouse

(.3

               . . . .         .--                  -- -       -. . -             . . ~                  - ..       ~    .. ._ ~ . . _ . _ _ _                       ~. .
  -                --..             , . - _ , . .                       .._          . _ . .      . . ~ . _ . _m..,              . . _ , _ , . _ . , _ . _ _ _

l f NRC REQUEST FOR ADDITIONAL INFORMATION i The quailty gradient term m this case appears m tne denomutator such that;

                                                      'fv              2       v dA~

G1 f @i* dP

          -=
                                                      <2D                      A dzs
                                                         .                                                            440.721(h)- 9 d:           1 + G'[x(v, - vf ,h, I hf ,) + (l - x)(v'                              f - vfy,h I hf,))

where as before the h' terms denote derivatives with respect to pressure. The value of the denominator is controlled by mass velocity. At high mass velocities, the denominator becomes less than one and the pressure gradient is increased. The denommator m fact is a measure of the degree to which the flow is approachmg cntical conditions. , l l Effect of unequal phase velocity l Equation 440.721(Ei)-5 and 9 assume that the liquid and vapor move at the same velocity. Most flows will develop some difYerence in phasic velocity. The effect of this relative velocity on the pressure gradient will be examined. Because the denominator is important at high mass velocities, and the slip ratio (u of the flow condition than the relative velocity (u -u,), the effect ofvelocities unequalwillphase be examined /u,) isusing a more appropriate mea the slip ratio. The mass velocity can be expressed as (reference 440.721(h) 2, equation 3.17): r 3 -1 G= xv# + (1 - x)v 440.721(h)- 10 yO

                 \us                 u/ )

l Let S=u/u, Then-l I r T -l y 3 -1 G= 1 ut xv' + (1 - x)v =- q uf) \ S f> cf 440.721(h)- 11 r 5 -l

G= -} ,

xv, + 5(1 - x)vy' _l N

                                                                            = 1-8'
                \ U)                                                           C, g

Now evaluate the inerna term in Equation 440.721(h)-l assuming constant area and flow to simplify the derivation, and use the equations above to get: 1dr 2 d-gW,uj + F uf) f =G xc, + (1 - x)Cf 440.721(h)- 12 The expression in square brackets can be rearranged to give: l O l Q . T Westinghouse 440.721(h)-3 i

                                                                                                      . - . -      - . . - . - . . . ~
                      -. - ..             . . ~             . . ~ -

NRC REQUEST FOR ADDITIONAL.INFORMATION ! Y 7 T i 44o.721(hl- la xc, + (1 - x)cf = xv, + (1 - x)vf + x(1 - x) - - 1, v, + (S - 1)vf . Assuming the quality and slip ratio are independent of pressure, the denominator in Equation 440.721(h)-5 is now:

                                                       'rg         3  *
                                                                                     -]          4 4 0. 7 21 (h) - 14 2

1+G yy, , (i _ x)y', , ,(i _ y) __i y, , (S _1)yf The effect of the additional terms in Equation 440.721(h) 14 relative to the denominator in Equation 440.721(hb5 will be examined below. Calculated mass velocities in AP600 - Figures I.7-7 to 1.713 of reference 440.721(h)-1 show the vapor and liquid volumetric flux calculated by NOTRUMP in various components of the AP600. Rese figures indicate that mass velocities are generally quite

low except in the ADS lines, it should be noted that the velocity shown for the ADS 4 line is higher than actually calculated in NOTRUMP, because the area used to calculate the velocity from the code output volumetric flow rate was about 20 percent smaller than was actually utilized in the NOTRUMP calculation. Nevertheless, fluid velocities are likely to be on the order of several hundreds of feet per second in these lines. Since the mass velocity is likely to be highest in the ADS lines when the valves are open and critical flow exists at the valves, the importance of the denominator in determining the overall pressure drop will be examined at these locations. For 440.721(h>$ and 14 will be evaluated; sample calculations simplicity, the compressibility terms in' Equations g value of h .

indicate the quality terms in Equation 440.721(h>9 are smaller because of the relatively large Table 440.721(hF1 lists fluid saturation properties at various pressures, from which the derivatives are obtained as shown. Table 440.72)(hF2 evaluates the denominator at several pressures and qualities for ADSI.3, and Table 440.721(h>3 does the same for ADS 4 at the lower pressure. For each quality, the mass velocity in the piping approaching the valve is estimated by multiplying the entical mass velocity for the given pressure and quality (using the HEM model) by the area ratio of the valve to the upstream piping. Rese calculations indicate the following: a) For ADSI 3, the pressure gradient leading up to the ADS valves could be underestimated by as much as 9 percent (the denominator ranges from .91 to .99). However, during the important period of low quality two phase flow, when the mixture level is at the top of the pressurizer, the error is substantially smaller. By itself, this differer.cc is not sufficient to explain the differences between predicted and measured mass flow rates which are observed in some of the OSU tests (see response to RAI 440.721(c)). For ADS 4, where two valves are assumed open, Table 3 indicates'that the pressure gradient could be b) significantly underpredicted during the initial period just after the valves open, when the pressure is high enough that critical conditions exist. This is because the total valve area is comparable to the upstream piping area. Figure 440.721(hbl shows the efrect on the denominator of assuming a slip ratio of 6. for the conditions shown in Table 440.721(h>3. It can be seen that phase slip increases the value of the denominator, and reduces the efrect of acceleration on the pressure gradient. His is consistent with the observation that the Moody critical flow model, which assumes a large slip ratio, predicts a higher critical mass velocity than HEM (ie, acceleration must be greater to produce large pressure gradients and choked conditions). Therefore, the conditions estimated in Tables 440.721(hk2 and 3 for homogeneous flow are the most severe to be expected. 440.721(h)-4 T W use l x

l 1

                                                                                                                     .                   1 o

NRC REQUEST FOR ADDITIONAL INFORMATION g NOTRUMP model for ADS piping and critical now Figure 440.721(h)-2 illustrates the noding used to model the ADS piping and valses in AP600. The piping from the hot leg or pressurizer to the valve is simulated with a Guid node. A portion of the oserall line resistance is allocated to the Dow link connected to the pressurizer or hot leg. De local static pressure and enthalpy in the ADS piping node. P and h , are used in the Henry Fauske and HEM critical now models to calculate the critical mass velocity (Section 2.17 of reference 440.721(h)-1). With this modeling, the frictional pressure drop in the piping leading to the ADS valve is accounted for. The HEM modelis applied over the short remaining distance to the valve, where l the effect of friction can be ignored. However, the NOTRUMP model contains two deficiencies: a) The model does not account for acceleration effects in calculating the pressure distribution up to the ADS valve (previous sections). l b) The model does not account for the effect of significant upstream kinetic energy on the critical now calculation. I As indicated in the previous section, lack of momentum flux terms in the momentum equation may result in an underprediction of the pressure drop to the ADS valves. In the next s,:ction, the efrect of ignoring the kinetic energy terms in the calculation of critical flow is examined. The HEM critical flow model assumes frictionless, adiabatic, steady flow and begins with the following simplified mass, energy and momentum conservation equations: l dW=0 1 f 25 l d h+u =0 (* < 2, . 1 440.721(h)- 15 dP + pudu = 0 d dP

                 .-+- =0 u

ep 2> where h is the fluid enthalpy. Because the flow is assumed frictionless and adiabatic, the flow is isentropic. Therefore either the momentum equation or the energy equation can be replaced by: ds = 0 In the HEM, the energy and entropy equations are used. The differentials are expanded to give: 2 2 9-h, + 2"L- = ha + "2 440.721(h)- 16 S = So g where the subscript t represenu the conditions at the throat, and the subscript 0 represents conditions at the location where the acceleration to the throat is assumed to begin. Usually this is taken as a location where the kinetic energy is negligible (u, is small). Given the stagnation enthalpy and entropy, the stagnation pressure and the conditions at the throat leading to the maximum mass velocity can be determined. In NOTRUMP, the Henry Fauske and HEM } models consist of a series of tables giving critical mass flux as a funct ion of stagnation enthalpy, and stagnation I oressure. I T Westinghouse 440.724h)-5 n

                                                                          .  . . .                  -    .~            . --            -    . . _ . . .

l l

                                                                                                                    -~        -    - -   -
                                                                 ~   . - ~

NRC REQUEST FOR ADDITIONAL.lNFORMATION in the modeling of the ADS, the effect of a significant kinetic energy component at the start of the process must be examined. To determine what the appropriate stagnation pressure should be, retain the second form of the momentum equation, and expand the differential to yield:

                     $                 3 l         e. dP                                                                                                44o.721(h)- 17
            - + -u'~ - uf = 0 4p               2 Assume that an average density can be defined such that:

, e. dP P, - Po 44 o . 721 t h) - 18 l -=

      'A P               P                                                                                                  .

Then:

                 -2                         -2 s                                                              44 o .121 t h) - 19 P, + pu' = Po + pu This indicates that the " reservoir" pressure should include the recoverable portion of the fluid dynamic pressure at the point where acceleration is to begin.

Because of the energies and pressures involved, a significant velocity must exist at point 0 before significant error i introduced. For example. at 50 psis the enthalpy of steam is 1174 Btu /lb. For a I percent increase in the total enthalpy, the fluid velocity must be about 770 ft/s. For a 1 percent increase in the total pressure, a fluid velo about 200 ft/s is needed. This would indicate that the efrect of including the dynamic pressure in the reservoir l conditions is more important than the efrect of including the kinetic energy. Ignoring these terms, as is done in NOTRUMP. would be expected to result in a prediction of critical flow which is too low. To confirm this. an attemate flow calculation was performed on the ADS 4 piping system to compare with the NOTRUMP prediction (as noted previously, the efrects of compressibility were determined to be most important this component). For steam flow in a piping system, the effects of compressibility can be taken into account by use of net expansion factors Y (reference 440.72)(h)-4). These factors are functions of the pressure difference through the pipe, and the loss coefficient in the pipe (Figure 440.721(h)-3). The flow rate through the pipe is l calculated by the following equation (Equation 1 11, reference 440.721(h) 4): 2 r Yut - P,)p,yt_ ,,,,,,,(,,, ,, {D4 = 0.525Yd ) K h both valves assuming compressible where d is the pipe diameter in inches. The calculated flow rate throuS conditions is compared with the incompressible result (Yal)in Figure 440.721(h)-4. To compare with the NOTRUMP AP600 predictions, vapoe flow is plotted against hot les pressure for the ADS 4 pipe in Figure 440.721(h)-5. The NOTRUMP values are seen to remain below the calculated value assuming compressible conditions. 440.721(h) 6 T mstense g', e w 6l

l l

 +       4                           - . . _ . .                   .                  . , _ . . _ . _ , . .              ,_                _ , , _

l NRC REQUEST FOR ADDITIONAL INFORMATION pm

Conclusion:

It is concluded that NOTRUMP has a compensating error in regions where the fluid acceleration is significant. On the one hand, lack of a momentum Oux term causes the pressure gradient upstream of the valve to be underestimated. On the other hand, neglecting the dynamic pressure terms in the critical flow model will tend to underestimate the critical flow rate. Both errors become significant only in the ADS 4 piping where both valves are open. The overall effect is to produce a low estimate of the vapor now through ADS 4. as indicated in Figure 440.721(h) 5. Since this will reduce the depressurization rate of the system and delay the onset of IRWST, the presence of these compensating errors in NOTRUMP is judged to be acceptable. i l l I ,( v i i (/

l l

l i t i T Westinghouse 440.721(h)-7 m t-

GI>

t gw I

_ _ - . . . - . . _ _ . . . . L._ . . . . _ . NRC REQUEST FOR ADDITIONALINFORMATION u= O n-Re ferences. 440.721(h)-1 "NOTRUMP Final Validation Report for AP600". WCAP 14807. Revision 2.1997 440.721(h)-2 Wallis. G. B. One Dimensional Two Phase flow. McGraw Hill.1969 440.721(h) 3 Collier. J. G., Thome J. R., Convective Boiling and Condensation. Third Ed.. Clarendon press,1994. 440.721(h)-4 Flow of Fluids through Valves. Fittings, and Pipe". Technical Paper No. 410. CRANE Co. 1973. O i t. l l 4 440.721(h)-8 3 Westinghouse O, Y'N), .,[+ f 5' ', l '

     .                                                 -.-.t---          -.        - . .        - - -    .. - ~. .-.~.                             - _ _ _ . . _ . - . _ . . .

NRC REQUEST FOR ADDITIONAL INFORMATION lO gg TABLE 440.721(h)-1. WATER SATURATION PROPERTIES AND DERIVATIVES l PRESS TSAT VF' VG VFG HF HG HFG VF' VG' l 40 267.25 0.017151 10.496 10.47885 236.15 1169.8 933 65 0 0 45 274.44 0.017214 9.3988 9.381586 243.52 1172 928.48 1.26E-05 -0.21944 ' 50 281.02 0.017274 8.514 8.496726 250.25 1174.1 923.85 1.2E-05 -0.17696 l 55 287.08 0.017329 7.785 7.767671 256.4 1175.9 919.5 1.1 E-05 0.1458 60 292.71 0.017383 7.1736 7.156217 262.2 1177.6 915.4 1.08E-05 -012228 , 90 320.28 0.017659 4.8953 4.877641 290.7 1185.3 894.6 0 0 l 95 324.13 0.0177 4.6514 4.6337 294.7 1186.2 891.5 8.2E-06 0.04878 100 327.82 0.01774 4.431 4.41326 298.5 1187.2 888.7 8E-06 0.04408 110 334.79 0.01782 4.0484 4.03058 305.8 1188.9 883.1 8E-06 0.03826 120 341.27 0.01789 3.7275 3.70961 312.6 1190.4 877.8 7E-06 -0.03209 420 449.4 0.01942 1.1057 1.08628 429.6 1204.7 775.1 0 0 460 458.5 0.01959 1.0092 0.98961 439.8 1204.8 765 4.25E-06 0.00241 500 467.01 0.01975 0.9276 0.90786 449.5 1204.7 755.2 4E-06 -0.00204 540 475.01 0.0199- 0.8577 0.8378 458.7 1204.4 745.7 3.75E 06 -0.00175 580 482.57 0.02006 0.7971 0.77704 467.5 1203.9 736.4 4E-06 -0.00152 ! - 600 486.2 0.02013 0.76975 0.74962 471.7 1203.7 732 3.5E 06 0.00137 620 489.74 0.02021 0.74408 0.72387 475.8 1203.4 727.6 4E-06 -0.00128 980 542.14 0.02152 0.4561 0 /3458 539.5 1193.7 654.2 0 0 1020 546.99 0.02166 0.4362 0.41454 545.6 1192.2 646.6 3.5E-06 -0.0005 1000 544.58 0.02159 0.44596 0.42437 542.6 1192.9 650.3 3.5E-06 -0.00049 1060 551.7 0.02181 0.4177 0.39589 551.6 1190.7 639.1 3.75E-06 0.00046 1100 556 28 0.02195 0.4006 0.37865 557.5 1189.1 631.6 3.5E-06 0.00043 O T Westinghous8 440.721(h) 9 O

                                                                                                                                                                                       '4 l

(

                                                                                                                                                                                                                  . ~ . . . .

_ . . . . _ - _ . . - . ~ . _ . . _ _ l NRC REQUEST FOR ADDITIONAL INFORMATION l O ! TABLE 440.721(h)- 2. ACCELERATION EFFECTS IN ADS 1-3 PIPING ! (note: see Table 440.721(h)-3 for nomenclature) 50 AVA.VE 0.324 APIPE= 0.6827 PRESS = VFG= 8.496726 VF= 0.017274 I VF's 1.2E-05 6 HFG= 923.85 SLIP = VG's -0.17696 1+G2V STERM 1+G2VS I X GCRIT GPIPE V i 0.94 0.0015 0.99 0.01 861 409 -0.00176 0.93 0.0133 0.98 0.1 283 134 -0.01769 0.91 0.0369 0.95 0.5 145 69 -0.08847 0.91 0.0133 0.91 0.9 110 52 -0.15926 0.91 0.0015 0.91 0.99 106 50 -0.17519 PRESS = 100-VFG= 4.41326 VF= 0.01774 VF's 8E-06 l HFG= 888.7 SLIPS 6 VG's -0.04408 i X GCRIT GPIPE V 1+G2V STERM 1+G2VS l 0.95 0.0004 0.99 0 01 1565 743 -0.00043 0.94 0.0033 0.96 0.1 539 256 -0.0044 0.91 0.0092 0.95 0.5 282 134 0.02204 103 0.03967 0.91 0.0033 0.92 0.9 216 0.91 0.0004 0.91 0.99 207 98 -0.04364 , PRESS = 600 VFG= 0.74962 VF= 0.02013 VF's 3.5E-06 HFG= 732 SLIP = 6 VG's -0.00137 X GCRIT GPIPE V 1+G2V STERM 1+G2VS

                                                                        -1E 05                                                              0.98      0.0000            1.00 0.01                 6284              2982 1263 -0.00013                                                                            0.95      0.0001            0.99 0.1                 2661 759 -0.00068                                                                           0.92      0.0003            0.95 l              0.5                  1599 595 -0.00123                                                                           0.91      0.0001            0.91 0.9                  1254 571 -0.00135                                                                           0.90      0.0000            0.91 0.99                    1204 PRESS =                        1000 VFG=           0.42437 VF=                   0.02159 VF's             3.5E-06 HFG=               650.3 SLIP =                          6 VG's            -0.00049 X      GCRIT                   GPIPE                                                        V                         1+G2V STERM 1+G2VS 0.01                    8633           4097 -1.4E-06                                                                           0.99 4.2E 06                  1.01 1983 4.6E-05                                                                             0.96 3.82E-05               0.99 0.1                   4177 1252 -0.00024                                                                            0.92 0.000106               0.95 0.5                   2639 997 -0.00044                                                                           0.91 3.82E-05               0.91 0.9                    2101 959 -0.00048                                                                           0.90 4.2E-06                 0.91 0.99                     2021 440.721(h)-10 3 W use O

jh:

i

 *       ..                         ...        _.              .       _             s.-==%              . . . . - . . . ~         . .      ,

l NRC REOUEST FOR ADDITIONAL INFORMATION A . C lb t l l ! TABLE 3. ACCELERATION EFFECTS IN ADS 4 PIPING

     .oRESS=                50 AVALVE=            0.527 APIPE=           0.559 VF's            1.2E-05                            VFG=       8.496726 VF=             0.017274 VG'-           0.17696                             HFG=           923.85 SLIP =                 6 A        GCRIT        GPIPE           V                1+G'V      STERM 1 +G'VS 0.01           861          812 -0.00176                       0.75   0.0015         0.96 0.1           283          267 -0.01769                       0.73   0.0133         0.93 0.5           145          136 -0.08647                       0.64   0.0369         0.79 0.9           110          104 -0.15926                       0.63   0.0133         0 66 0.99           106          100 0.17519                        0.63   0.0015         0.63 Nomenclature:

GCRIT = critical mass flux at ADS valve I GPIPE = mass flux upstream of the valve = CCRIT* AVALVE/APIPE V' = x v,' + (1 x) v/ 1+G2 y. = denominator in equation 440.721(h)-5 STERM = last term in equation 440.721(h)-13

V O 1+G'V'S = equation 440.721(h)-14 l

l 6,. l l l

      %,"    Westinghouse                                                                              440.721(h)-11 h

I4 l fed

                                                                      -      .           - .-     _    ~           --. .
                      . _ _ , _ . . .       . . - ~ ~ ~ _

NRC REQUEST FOR ADDITIONAL INFORMATION g e JFFECT OF SLIP RATIO ON DENOMINATOR 1.00 0.90 0 80

                                      . ,~~

0.70 ,

               ., 0.60 2

h 0.50 l 2 .- 5 0.40 - --- HOMOGENEOUS SLIP =6 0.30 0,20 0 10 1 l 0.00 - -- - 0 0.2 0.4 0.6 0.8 1 QUALITY l Figure 440.721(h)-l. Effect of Slip Ratio on Momentum Flux Equation Denominator

*+

440.721(hl-12 YN g l

~4:

l r

        - . . . . .                    - - . . - . - .          . .        _. , . . _ .    - - .          . . . . . _ . . . - . . -            ._..-. .   .-... . - ~

s t

            . . . + , ,        , . - -             s.m . ..            yo.        -_w.           Ne . ,     .w h    ,Mem --                 ___%%%.,        ,

i-4 i

, NRC REQUEST FOR ADDITIONAL INFORMATION ( A 4 J s Pe . h. Ge 1 i

J h . PRZ 1 4-2 . ? ? 4 4 Ge 1 l n P,h, HOT LEO i u Figure 440.721(h)-2 NOTRUMP noding for ADS valves. P

T Westinghouse 440.721(h)-13

      .                                                                                                                                                        f-k-

b. .:

[s

l

                                                                                              ----~~~'-~~-

NRC REQUEST FOR ADDITIONAL INFORMATION Not Expension Factor Y for Compressible Mow Through Pipe to e Larger Mow Aroe k = 1.3 lr ..rpn umaists t 3 for CO, 50. Hg. H $ NHs N0. CI CH,C3H and C H. . w 3 Io

                                                                                                 . Lim.iting . . . . ..e.t..e 0.si 3        g                                                                                6 - i.:

0.s0

                      \d 5-s ap DJ5 3 hbh s kh-        b                                                 1.2           .sts   .612 M      N        N                                        t.s           .uo    .ut a se sqh    s  m                                                       2..           . s.   .us 0.n
                                     \                                                               3              642  .us N \NN                                                        !             :S :E 1

0.13 W\N,Q4fN"s

bbN@r.Yg_,:

                                                                 . ,                               gg

= :=

                                                                                                                   ,,a7   ,ng n,so                                          Ns,ybe ** "\t\                                  n n
                                                                                                                  .ut
                                                                                                                   .sn
                                                                                                                          .ns
                                                                                                                          .ns f,. l                                       in               .no    .ns
     ,,3 3                                                                                                                      -

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 OJ 0.9 1.0 \ AP

Figure 440.721(h) 3 Effect of compressibility on the calculated flowrate through a piping system (Refennce 440.721(h) 4). l l l 440.721(h)-14

                                                               .                                                                  L, p+

     ._   _      .. _ -             .         . _ _ _ _ . - _ _                 .. . . ~ . . _ _ __                   _     _ _ _                _ _ _         _ _ _ . _ _ _ _ _ _
  ~-                    .    - - - - . ~ .                        -.        . . . . -               .    - - . . .                 _ . . _ .            _   __

1 l 1 i l

,       NRC REOUEST FOR ADDmONAL INFORMATION l

f% V l-i- i ADS 4 FLOW VS PRESSURE USING COMPRESSIBILITY FACTOR 80.000 - - - - - -- ---- l \ 70.000 -- .- - - - -

                                                                                                                              /                                                            .._

60.000 - - - - - - - - - . 50.000 - - - - . 7 ' s'

                                                                                                                   '-                   .   !- - - W4 COMP -

2 40.000 . W4114C , s- .,- .

                                                                                                                                                                                           . l y                                                                               ,s                           t l

2 d'* I (% 30.000 --

20.000 - - -- j,4 - - - -

                                         /
                                       /
                                   /

10.000 - - - - - - - - ty 0.000 - - - - - -- 15 20 25 30 35 40 45 50 HOT LEG PRESSURE (PSIA) i Figure 440.721(h)-4 Effect of Compressibility on ADS 4 Flow vs. Pressure I f 4 l b l G, T Westinghouse 440.721(h)-15 e r 1 .

,1%

tt

i

                                                                                                     .    ,.       e                                                                          l NRC REQUEST FOR ADDITIONAL INFORMATICN lig e                      ;

AP600 21NBREAK IN FN0DE 49 12 node core Moss flow Rote (Ibm /s) A WGFL 185 0 0 ADS 4A VAPOUR FLOW Wass Flow Rote (Ibm /s)

                                                                  ----Blending volve 80 80 -

s" s _ E j - 60 -- C, 6 0 O

                                                                                                                                                     .-         40 m o

o 40

                                                           =                                                                      ,

O

                                                                                                                  'A                                            20 -

w 20 ,- g3 - g m

                                                            =                                           ,

a , O O / ' 2

                                                                                             ' ' ' '            ' '           ' ' ' '                         0 0                                                                         40              50              r-0                  10                 20              30 Pressure                     (psia) i Figure 440.721(h)-5 NOTRUMP predicted vapor flow compared with Reference 440.721(h) 4 calculat on.

b3 440.721[h)-16 IN g : L , O

                                                                                                                                                                                  #C,$
                                                                                                                                                                                    -4 .g..

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l l l l . i NRC REQUEST FOR ADDITIONAL INFORMATION ' O 'V Question 440.72 l(s): Provide discussion on how NOTRUMP treats entrainment (waterspout) in branch lines.

Response

Section 1.8.2(b) of Reference 440.721(i)-l discusses the NOTRUMP phase separation model at a branch connected to the top of the main coolant pipe. The model assumes that water will be entrained into the branch with vapor if the water level is within 1 branch diameter of the top of the main pipe. The question results from the observation that the fluid velocity into the ADS 4 piping in which two ADS 4 valves are open is high (see response to RAI , 440.721(h)). This could cause significant entrainment (via a " waterspout" or other mechanisms) from a stratified water level in the hot leg, even when the water level is relatively low. l l The experiments performed by Shrock et al and discussed in reference 440.721(i)-1 provide data for the onset of

           , liquid entrainment from a liquid pool into a branch line as a function of the branch line fluid velocity and the distance of the pool from the branch. For the highest calculated vapor velocities (about 800 ft/s for AP600 shortly after the ADS 4 valves open), the modified Froude number is (assume system pressure is 40 psia):

f p, ' "' U,,3 ' p, ' "' 800 '0.1'"' l F,,3 = = -

                                                                                         =6                                                  ,

r ap> }D,g<Ap> 40.84*32.2 \60)

This value is within the range of data obtained in the entrainment experimentt, as can be seen in Figure 1.8 6 of (q U j reference 440.721(i) l. The distance of the water level below the branch is about 2 to 3 times the branch diameter at the onset ofliquid entrainnient, whereas NOTRUMP assumes that entrainment does not occur until the mixture level is equal to the branch diameter, in the NOTRUMP prediction, therefore, the hot leg must fill to a higher level before entrainment is calculated. As discussed in the response to RAI 440.721(f), one reason that the pressurizer is predicted to drain earlier is that more vapor is predicted to flow through ADS 4 rather thap ADSl 3. A sensitivity calculation in which the hot leg was made homogeneous (resulting in liquid entrainment mto the branch line at all hot leg thrid levels) did delay pressurizer draining by increasing the pressure drop through the ADS 4 lines. The overall impact was relatively small, however, since the pressurizer continued to drain early in the NOTRUMP calculation. I It is concluded that for very high ADS 4 fluid velocities, NOTRUMP will underpredict the amount ofliquid entrained into the ADS line. This contributes to the overprediction of pressurizer drain, because the resistance to vapor flow through the ADS 4 lines is reduced without entrained liquid. The addition of the IRWST level penalty (response to RAI 440.721(g)) will account for this deficiency as well as other code deficiencies which result in early pressurizer draining. In all other locations such as the CMT balance line, fluid velocities into the branch are much lower, and the NOTRUMP model is adequate, predicting that the entrainment is negligible until the water level is close to the branch line. References. 440.721(i)-l "NOTRUMP Final Validation Report for AP600", WCAP 14807 Revision 2,1997 l !.- l \ 3 Westirighouse 440.721(i)-1 , t

   -.                                  _          -                        .~           . ,_

NBC RES9EST FOR AB9m0NAL INF9ttlAT10N im Question 440.721j (OITS - 5655) (j) Justify and demonstrate why use of Henry-Fauske/ HEM rather than Moody is conservative for calculating break flow through the ADS stage 1,2, and 3 valves and why this is appropriate for an i appendix K type calculation. l

Response

De AP600 SSAR presents analysis of a spectrum of small break LOCA events in subsection 15.6.5.4B. In the subsection 15.6.5.4B NOTRUMP analyses, critical Dow through each of the ADS valves is calculated using the Henry-Fauske/ homogeneous equilibrium model, which is described in Reference 440.7210)-1. his modeling approach differs from the method used to compute critical flow through the break in the SSAR analysis, which complies with the 10CFR50 Appendix K (Reference 440.7210)-2) requirement that critical flow through the break be computed using the Moody model during two-phase flow. To assess the impact of applying the NOTRUMP Appendix K critical flow model (Moody model) to compute the flow through the ADS paths, the two-inch cold leg break in the CMT loop presented in

   /N   the SSAR was reanalyzed with the critical flow through all of the ADS valves computed using the
   'd   Appendix K-required critical flow model. In the absence of core uncovery and cladding heatup during the AP600 SSAR small break LOCA events, the minimum RCS mass inventory is used as an indication of the severity of the event: the lower the predicted minimum inventory, the smaller the margin to core uncovery and the more severe the event. Larger breaks in the spectrum, while more limiting in minimum mass inventory, exhibit their minimum values early in the transients, before or coincident with actuation of ADS Stage 1; their minimum inventory values are independent of the ADS critical flow model selection. De two-inch break selected is representative of the break sizes for which the ADS performance is the primary factor influencing the RCS minimum inventory.

Results of the two-inch cold leg break with the ADS flow paths calculated using the Appendix K- (. - required critical flow model are shown in the attached figures. Here is little change in the timing of the transient sequence of events, relative to that of the case in SSAR subsection 15.6.5.4B.3.3 part C. De largest changes are that the accumulators empty more rapidly (at 1510 seconds, versus 1579 l seconds) after initiation and IRWST injection is achieved sooner (at 3082 seconds rather than 3416 i seconds). The timing of these events is earlier in the current run due to the more effective ! depressurization provided by the ADS when the NOTRUMP Appendix K-required critical flow model is applied. Figure 440.7210)-1 indicates the lower pressure which occurs after ADS Stages 1,2, and 3 are activated at 1133 seconds and following, which results from the greater mass flow through these ADS flow paths predicted by the Appendix K critical flow model. Figures 440.7210)-2 and 3 show that t A

, l V)     W Wednghouse 448.m H I

l I Mj l

NBC RE45EST FOR ABBITitNAL INf0RIAATISM slightly lower downcomer and core mixture levels exist in this case than in the SSAR case during the time period prior to ADS Stage 4 actuation. The slightly lower mass inventory at this time is also visible in Figure 440.7210)-4, which compares the RCS mass inventory transient of the current case with the corresponding SSAR case. The RCS minimum inventory in this analysis of 127,400 lbs mass compares favorably with the 126,300 lbs mass minimum inventory in the corresponding SSAR two-inch cold leg break analysis. Figure 440.7210F5 presents the integrated total mass vented through the ADS Stage 4 valves in the analysis in which the NOTRUMP Appendix K-required critical flow model is applied.

  'Ihe conclusion of this sensitivity analysis is that the relevant AP600 parameter to evaluate the severity of a small break LOCA event, minimum RCS mass inventory, is more favorable when the Appendix K-required critical flow model is applied to the ADS flow paths. Therefore, for the AP600 small break LOCA events, it is conservative to calculate the flow through the ADS flow paths using the Henry-Fauske/ homogenous equilibrium critical flow model, as is done in the SSAR Chapter 15 small break LOCA analysis.

References:

440.7210Fl: WCAP-14807. Revision 2 "NOTRUMP Final Validation Report for AP600," Proprietary, January 1997. 440.7210p2: WCAP-10079-P-A, "NOTRUMP: A Nodal Transient Small Break and General Network Code " Proprietary, August 1985. SSAR Revision: None l

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_ __, _.. - . - ~ ~ - ~~- - NBC REGOEST FOR ABtm0NAL luftREATitu n==am 4 in O ' lll181 l AP600 55AR 2inCLBREAK. REvlSED ADS FLOWTO USE WOODYCASE EWlXFN 1 0 0 00WNCOMER WiXTURE L V/ 32

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G NBC RE40EST Fet A38m85AL INFORMATi4N L]j $ ___.. [.- AP600 SSAR 2inCLBREAN. REvlSED ADS FLOWTO USE WOODYCASE WTH00017 84 0 0 ADS 4 /NTSM.4i.r L O W i 120000 100000 r 80000 l 60000 N _ 40000 20000 l \ .

                                                    '   '      '   '           '        '     '  '           '       '   '   '                  i l                                             0 0                     1000                             2000                     3000                             4000 Time                (s)                                          .
                                                                                 . Figure 440.721(j)-5 l

O 448.721-7 l T Westinghoust l l l 9

} ENCLOSURE 4

j. WESTINGHOUSE LETTER DCP/NRC1410 l AUGUST 13,1998 l

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