ML20137M894
| ML20137M894 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 03/17/1997 |
| From: | Gresham J, Spencer D WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20137M882 | List: |
| References | |
| WCAP-14846, NUDOCS 9704080197 | |
| Download: ML20137M894 (205) | |
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AP600 DOCUMENT COVER SHEET IDS: 1 S TDC: Form 58202G(5/94)[mA3499wnon:1b] AP600 CENTRAL FILE USE ONLY: ! 0058.FRM RFSe: RFS ITEM #: AP600 DOCUMENT NO. REVISION NO. ASSIGNED TO ; PCS-GSR-020 0 Page 1 of 202 ALTERNATE DOCUMENT NUMBER: WCAP 14846 WORK BREAKDOWN #: f DESIGN AGENT ORGANIZATION: i PROJECT: AP600 , TITLE: Scaling Analysis for AP600 Containment Pressure During Design basis Accidents ! ATTACHMENTS: DCP #/REV. INCORPORATED IN THIS DOCUMENT REVISION: , 4 I 1 CALCULATION / ANALYSIS
REFERENCE:
I ELECTRONIC FILENAME ELECTRONIC FILE FORMAT ELECTRONIC FILE DESCRIPTION . l 3499w.non .wpf Word Perfect 5.2 for Windows
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l (C) WESTINGHOUSE ELECTRIC CORPORATION 1997 i O WESTINGHOUSE This document containsPROPRIETARY CLASS ir tormation proprietary 2 to Westinghouse Electric Corporation: it is subrnitted in confidence and is to be used solely for the purpose for which it is fumished and retumed upon request. Ttus document and such informaton is not to be reproduced, transmitted, disclosed or used otherwise in whole or in part without pnor written authorization of Westinghouse Electric Corporaten. Energy Systems Business Unit, subtect to the legends contained hereof. O WESTINGHOUSE PROPRIETARY This document is the property CLASS of and contains 2C informaton owned by Westinghouse Electric Corporation and/or its subcontractors and Proprietary supplers. it is transtrutted to you in confidence and trust, and you agree to treat this document in stnct accordance with the terms and conditions of the agreement under which it was prov6ded to you.
@ WESTINGHOUSE CLAGS 3 (NON PROPRIETARY)
COMPLETE 1 IF WORK PERFORMED UNDER DESIGN CERTIFICATION """ OR COMPLETE 2 IF WORK PERFORMED UNDER FOAKE. 10 DOE DESIGN CERTIFICATION PROGRAM - GOVERNMENT LIMITED RIGHTS STATEMENT [See page 2) Copyright statement A license is reserved to the U.S. Govemment under contract DE-AC03-90SF18495. O DOE SubtectCONTRACT DELIVERABLES to specified excentons, (DELIVERED declosure of this data is restrictedDATA)l unti September 30,1995 or Design Certification under DOE conl 90SF18495. whichever is later. i EPRI CONFIDENTIAL: NOTICE: 10203@4 s O CATEGORY: A 0 B C DD E F 2 O ARC FOAKE PROGRAM - ARC LIMITED RIGHTS STATEMENT [See page 2) Copyright statement A license is reserved to the U.S. Govemment under contract DE-FCO2-NE34267 and subcontract ARC-93-3-SC-001. O ARC
$dbiectCONTRACT DELIVERABLES to spectlied exceptons. desclosure of (CONTRACT DATA) this data _is restricted under ARC-Subcontract ARC-93-3-SC-001.
ORIGINATOR SIGNAT ATE D. R. Spencer f pg mu 3)h?f97 AP600 RESPONSIBLE MANAGER SIG TUI '* APPRO AL DATE J. A. GreSham .3 f7k7 ment is compiete. ali required reviews are compiete, eiectronic tse is attached and oocument is Approvatgtne responsione manager signrhes tnet l
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AP600 DOCUMENT COVER SHEET Page 2 I Form 58202G(5/94) LIMITED RIGHTS STATEMENTS i DOE GOVERNMENT UMITED RIGHTS STATEMENT j (A) These data are submitted with limited rights under govemment contract No. DE-ACO3-90SF18495. These data may be ioproduced and used by the govemment with the express hmitation that they will not, without wntten permission of the contractor, be und for purnoses of manufacturer nor disclosed outside the govemment; except that the govemment may disclose these data outside the govemment for the following purposes,it any, provided that the government makes such disdosura subject to prohibrton against further use and disclosure: (1) This " Proprietary Data' may be disclosed for evaluation purposes under the restrictions above. (11) The ' Proprietary Data' rnay be disclosed to the Electne Power Research Insttute (EPRI), electric utility representatives and their direr.t consultants, excluding direct commercial compettors, and the DOE Natonal Laboratories under the prohibitions and restrictions above. (B) This notice shall be marked on any reproduction of these data, in whole or in part. I ARC UMITED RIGHTS STATEMENT: This propriatary data, fumished under Subcontract Number ARC 93-3-SC-001 with ARC may be duplicated and used by the govemment and ARC. subject to tne limitations of Article H-17.F. of that subcontract, with the express limitatons that the propnetary data may not be disclosed outside the govemment or ARC, or ARC's Class 1 & 3 members or EPRI or be used for purposes of manufacture wrthout pnor permission of , the Subcontractor, except that further disclosure or use may be made solely for the following purposes; j This proprietary data may be disclosed to other than commercial cornpetitors of Subcontractor for evaluation purposes of this subcontract under the restnction that the propnetary data be retained in confidence and not be further disclosed, and subject to the terms of a non-desclosure agreement between the Subcontractor and that organization, excluding DOE and its contractors. DEFINITIONS CONTRACTIDEUVERED DATA - Consists of documents (e.g. specifications, drawings, reports) which are generated under the DOE or ARC contracts which contain no background proprietary data. EPRI CONFIDENTIALITY / OBLIGATIONNOTICES NOTICE 1: The data in this document is subject to no con' Antiality obligations. NOTICE 2: The data in this document is proprietary and confidential to Westinghouse Electne Corporation and/or its Contractors. It is forwarded to recipient under an obligaton of Confedence and Trust for hmited purposes only. Any use, disclosure to unauthorized persons, or copying of this document or parts thereof is prohibited except as agreed to in advance by the Electnc Power Research Institute (EPRI) and Westinghouse I Electnc Corporabon. Recipient of this data has a duty to inquire of EPRI and/or Westnghouse as to the uses of the information contained herein that are permitted. NOTICE 3: The data in this document is proprietary and confidential to Westinghouse Electric Corporabon and/or its Contractors. It is forwarded to recipient under an obligation of Confidence and Trust for use only in evaluation tasks specifically authorized by the Electne Power Research insttute (EPRI). Any use, disclosure to unauthonzed persons, or copying this document or parts thereof is prohibited except as agreed to in vivance by EPRI and Westinghouse Electric Corporaton. Recipient of this data has a duty to inquire of EPRI and/or Westinghouse as to the uses of the information contained herein that are permitted. This document and any copies or excerpts thereof that may have been generated are to be retumed to Westinghouse, directly of through EPRI, when requested to do so. NOTICE 4: The data in this document is propriatary and confidental to Westinghouse Electne Corporaton and/or its Contractors. It is being l revealed in confidence and trust only to Employees of EPRI and to certain contractors of EPRI for hmited evaluation tasks authorized by EPRf. l Any use, disclosure to unauthorized persons, or copying of this document or parts thereof is prohibited. This Document and any copies or l cxcerpts ther?of that may have been generated are to be retumed to Westinghouse, directly or through EPRI, when requested to do so. i NOTICE 5: The data in this document is propnetary and confidential to Westinghouse Electnc Corporation and/or its Contractors. Access to thcs data is given in Cs 6tence and Trust only at Westinghouse facilities for limsted evaluation tasks assigned by EPRI. Any use, disclosure to unauthonzed persons, - ,opying of this document or parts thereof is prohibited. Neither this document nor any excerpts therefrom are to be removed from Westingh.. " facilibes. EPRI CONFIDENTIALITY / OBLIGATION CATEGORIES CATEGORY *A* -(See Delivered Data) Consists of CONTRACTOR Foreground Data that is contained in an issued reported. CATEGORY "B'-(See Dehvered Data) Consists of CONTRACTOR Foreground Data that is not contained in an issued report, except for cor iputer programs. 1 CATEGORY *C* - Consists of CONTRACTOR Background Data except for computer programs. CATEGORY *D* - Consists of computer programs developed in the course of performing the Work. CATEGORY *E' - Consists of computer programs developed prior to the Effective Date or after the Effectve Data but outside the scope s,. the Work. CATEGORY *F* - Consists of administrative plans and administrative reports. cosa_= t.m
WESTINGHOUSE NON-PROPRIETARY CIASS 3 WCAP-14846 Scaling Analysis for AP600 Containment Pressure During Design Basis Accidents , D. R. spencer March 1997 l l 1 l Westinghouse Electric Corporation Energy Systems Business Unit P.O. Box 355 Pittsburgh, Pennsylvania 15230-0355 C 1997 Westinghouse Electric Corporation All Rights Reserved
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1 TABLE OF CONTENTS' : h 3 LIST. OF ACRONYMS AND ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi .
'i ,
EX'dCUTIVE
SUMMARY
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' xii 1 PXEFACE . . . . . . ' . . . . . . . . . . . . . . . . . .' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxviii . l 1
1~ INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 i 2 DOMINANT PHENOMENA 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 1 i 3 . DESIGN, BOUNDARY, AND INITIAL CONDITION INPUT DATA . . . . . . . . . . 3-1 i a I y 4 CONSTITUTIVE EQUATIONS FOR HEAT, MASS, AND RADIATION , j
. TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 4-1 l 4.1 RADIATION HSAT TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 ,
1 1 4.2 . CONVECTION HEAT TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 ! 4.2.1- Turbulent Free Convection Heat Transfer . . . . . . . . . . . . . . . . . . . 4-2 ] 4.2.2 . Laminar Free Convection Heat Transfer . . . . . . . . . . . . . . . . . . . . 4-2 ! i 4.2.3 Turbulent Forced Convection Heat Transfer . . . . . . . . . . . . . . . . . 4-4 : I 4.2.4 Turbulent Opposed Mixed Convection . . . . . . . . . . . . . . . . . . . . . 4-4 4.3 CONDENSATION AND EVAPORATION MASS TRANSFER , . . . .. . . . . 4-4 l 43.1 '. Dimensionless Relationships for Data Evaluation . . . . . . . . . . . . . 4-6 -l 43.2 Gas Mixture Property Correlations . . . . . . . . . . . . . . . . . . . . . . . . 4-7 l 4.4 CONDENSATION AND EVAPORATION ENERGY TRANSFER . . . . . . 4-11 .I i 4.5 LIQUID FILM CONDUCTANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11 ! 4.6 ~ HEAT SINK CONDUCTANCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 ) 4.7 CONSTANT PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 5 GENERAL RELATIONSHIPS FOR SCALING EQUATIONS . . . . . . . . . . . . . . . . 5-1 5.1 ASSUMPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 5.2 GAS MIXTURE RELATIONSHIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 I 5.2.1 Ma ss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 5.2.2 : Molecular Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 5.23 Gas Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 5.2.4 En thalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3 5.2.5 Specific Hea t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4 5.2.6 Gas Compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5 53 EQUATION OF STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 5-6 5.4 RATE OF CHANGE OF INTERNAL ENERGY . . . . . . . . . . . . . . . . . . . . . 5-7 16L CONTAINMENT GAS ANALYSIS AND EQUATIONS FOR SCALING . . . . . . . 6-1 I i
- 6.1 MASS CONSERVATION EQUATIONS INSIDE CONTAINMENT . . . . . . 6-1 'i
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iv TABLE OF CONTENTS (cont.) 6.1.1 Containment Gas Conservation of Mass . . . . . . . . . . . . . . . . . . . . 6-1 i 6.1.2 Containment Liquid Conservation of Mass . . . . . . . . . . . . . . . . . . 6-3 6.13 Inner Film Liquid Conservation of Mass . . . . . . . . . . . . . . . . . . . . 6-6 6.2 ENERGY CONSERVATION EQUATION INSIDE CONTAINMENT . . . . 64 63 PRESSURE EQUATION INSIDE CONTAINMENT . . . . . . . . . . . . . . . . . . 6-9 63.1 Rate of Pressure Change Equation . . . . . . . . . . . . . . . . . . . . . . . . . 6-9 63.2 Normalized, Dimensionless RPC Equation .................. 6-10 6.4 INITIAL AND BOUNDARY CONDITIONS FOR CONTAINMENT ' MASS, ENERGY, AND PRESSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-13 6.5 MOMENTUM EQUATIONS INSIDE CONTAINMENT . . . . . . . . . . . . . 6-15 6.5.1 Froude Number Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-17 6.5.2 Froude Numbers in AP600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-19 6.53 Froude Numbers in the Large-Scale Tests (LSTs) . . . . . . . . . . . . . 6-23 7 HEAT SINK ANALYSIS AND EQUATIONS FOR SCALING . . . . . . . . . . . . . . . 7-1 7.1 DROP ANALYSIS AND SCALING EQUATIONS . . . . . . . . . . . . . . . . . . . 7-3 7.1.1 Drop Cond uctance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7 7.1.2 Drop Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7 7.13 Drop Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8 7.1.4 Drop Effect on Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-10 7.2 BREAK POOL ANALYSIS AND SCALING EQUATIONS . . . . . ..... 7-10 72.1 Pool Cond uctance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-11 7.2.2 Pool Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-12 7.23 Pool Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-13 7.2.4 Pool Effect on Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14 73 IRWST ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14 7.4 LIQUID FILM ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-15 7.5 INTERNAL SOLID HEAT SINKS ANALYSIS AND SCALING EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-17 d 7.5.1 Heat Sink Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-19 7.5.2 Heat Sink Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-19 7.5.3 Heat Sink Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-20 7.5.4 Heat Sink Effect on Pressure ............................ 7-20 7.5.5 Steel Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-21 7.5.6 Concrete Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-21 7.5.7 Steel-Jacketed Concrete Thermal Model . . . . . . . . . . . . . . . . . . . . 7-22 7.6 SHELL ANALYSIS AND SCALING EQUATIONS . . . . . . . . . . . . . . . . . 7-23 7.6.1 Shell Cond uctance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26 7.62 Shell Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-27 7.63 Shell Energy Transfer ................................. 7-28 mA34W.non\34h+wpt:n431297 March 1997 U
v s 1 TABLE OF CONTENTS (cont.) 7.6.4 ' Shell Effect on Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-29 j 7.6.5 Shell Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-30 ; 7.6.6 Weir and Water Coverage Timing . . . . . . . . . . . . . . . . . . . . . . . . 7-32 7.7 BAFFLE ANALYSIS AND SCALING EQUATIONS . . . . . . . . . . . . . . . . 7-35 ; 7.7.1 Ba ffle Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-35 1 7.7.2 Baffle Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-36 : 7.7.3 Baffle Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . . . 7-36 ; 7.7.4 Baffle Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-37 ; 7.8 SHIELD BUILDING ANALYSIS AND SCALING EQUATIONS . . . . . . . 7-38 l 7.9 CHIMNEY ANALYSIS AND SCALING EQUATIONS . . . . . . . . . . . . . . 7-38 7.9.1 Chimney Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-39 i 7.9.2 Chimney Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-39 7.9.3 Chimney Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-40 l 7.9.4 Chimney Thermal Me del . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-40 8 EVALUATION OF CON fAINMENT AND HEAT SINK PI GROUPS . . . . . . . . . 8-1 8.1 HEAT SINK SURFACE AREAS DURING 'lRANSIENTS . . . . . . . . . . . . . 8-1 ,
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8.2 CONDUCTANCE PI GROUP VALUES . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 ! I 83 MASS TRANSFER FI GROUP VALUES . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3 l l 8.4 ENERGY TRANSFER PI GROUP VALUES . . . . . . . . . . . . . . . . . . . . . . . . 8-3 1 i 8.5 PRESSURE PI GROUP VALUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-6 ] 4 9 PCS AIR FLOW PATH SCALING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1 9.1 PCS AIR FLOW PATH MASS TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . 9-1 1 9.2 PCS AIR FLOW PATH ENERGY TRANSFER . . . . . . . . . . . . . . . . . . . . . . 9-2 9.3 PCS AIR FLOW PATH MOMENTUM 'UATION . . . . . . . . . . . . . . . . . 9-2 9.3.1 Dimensionless PCS Momentum Equations .................. 9-S 9.3.2 Normalized PCS Momentum Equations . . . . . . . . . . . . . . . . . . . . 9-7 l 9.4 VALUES FOR PCS AIK FLOW PATH MOMENTUM PI GROUPS . . . . . . 9-9 i i 10 EVALUATION OF SCALED TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1 10.1 SEPARATE EFFECTS TESTS (SETS) AND CONSTITUTP/E RELATIONSHIP SCALING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-S 10.1.1 Condensation Mass Transfer ............................ 10-6 10.1.2 Evaporation Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-6 10.1.3 Convection Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 10-7 j 10.1.4 PCS Air Flow Path Flow Resistance . . . . . . . . . . . , . . . . . . . . . . . 10-10 i 10.1.S Wind Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 12 j 10.1.6 Wetting Stability . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-12 1 10.1.7 Liquid Film Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 10-13 l m:\M99w.non\34ha wpf:1t> 031297 March 1997 '
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vi TABLE OF CONTENTS (cont.) 10.2 INTEGRAL EFFECTS TESTS AND AP600 SCALING . . . . . . . . . . . . . . . 10-14 10.2.1 Governing Scaling Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-17 10.2.2 Steady-State Validation of the LST . . . . . . . . . . . . . . . . . . . . . . . . 10-20 11 DIFFERENCES AND DISTORTIONS BETWEEN THE TESTS AND AP600 . . . . 11-1 12 CONC LUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1 13 NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1 14 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-1 m:\M99w.non\3499w-a wptit431297 March 1997 L ._
vii ! i l 1 LIST OF TABLES 1 Table E-1 Phenomena Identification and Ranking Table - Summary of High and Medium Ranked Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Table E-2 Heat and Mass Transfer Correlations for AP600 . . . . . . . . . . . . . . . . . . . . . xxi ; Table E-3 Heat Sink Energy Equation Scaling for AP600 . . . . . . . . . . . . . . . . . . . . . . xxii l i Table E-4 Containment and Net Heat Sink Mass Scaling Pi Group Values . . . . . . . . xxiii l
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Table E-5 Containment and Net Heat Sink Energy Scaling Pi Group Values . . . . . . xxiv I Table E-6 Containment and Net Heat Sink Pressure Scaling Pi Group Values . . . . . . xxv Table E-7 PCS Air Flow Path Momentum Scaling Groups . . . . . . . . . . . . . . . . . . . . xxvi Table E-8 Comparison of AP600 Operating Range to Tests for Liquid Film i S tabili ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi Table E-9 Energy PI Group Comparison for AP600 and the LST . . . . . . . . . . . . . xxxiv Table E-10 LST Features That Differ from AP600 . . . . . . . . . . . . . . . . . . . . . . . .... xxxv i l Table F-1 Containment Processes Used to Initially Define Test Program . . . . . . . . . . . x1 Table 1-1 Parameters Selected for Scaling AP600 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 Table 21 Phenomena identification and Ranking Table - Summary of High and ] Medium Ranked Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 . Table 6-1 Types of Heat Sinks Considered in the AP600 Containment Pressure Scaling Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2 Table 6-2 Liquid Flow Rates Contributing to Containment Pressurization . . . . . . . . 6-5 Table 6-3 Reference Values for Containment Gas Scaling . . . . . . . . . . . . . . . . . . . . 6-16 Tabh. 6-4 Geometric Parameters and Critical Froude Numbers for AP600 and LST LOCA and MSLB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 6-22
'1 Table 7-1 Method Used to Model the Energy Absorbed by Heat Sinks . . . . . . . . . . 7-1 l l
l Table 7-2 Pool Evaporation Rate for a Saturated Liquid Break Source . . . . . . . . . . . 7-13 l l Table 7-3 Baak Pool Surface Area During DECLG Transient . . . . . . . . . . . . . . . . . . 7-13 i Table 7-4 Calc. lated Time Sequence of Weir Flow Events for AP600 . . . . . . . . . . . 7-33 i Table 8-1 Heat Sit i Areas During DECLG and MSLB Transients . . . . . . . . . . . . . . 8-1 j rn:\3499w.non\349Yw-a.wpf-1b-031297 March 1997
vm l LIST OF TABLES (cont.) Table 8-2 Heat Sink Energy Transfer Conductances Scaled to Shell Conductance . . 8-2 Table 8-3 Containment and Heat Sink Mass Scaling Pi Group Values . . . . . . . . . . . 8-4 i Table 8-4 Containment and Heat Sink Energy Scaling Pi Group Values . . . . . . . . . . 8-5 l Table 8-5 Containment ana Heat Sink Pressure Scaling Pi Group Values . . . . . . . . . 8-7 ; l Table 9-1 PCS Air Flow Path Momentum Scaling Groups . . . . . . . . . . . . . . . . . . . 9-9 Table 10-1 Containment and Heat Sink /Shell Mass Pi Group Values . . . . . . . . . . . 10-2 Table 10-2 Containment and Net Heat Sink Mass Pi Group Values . . . . . . . . . . . . . 10-2 Table 10-3 Containment and Heat Sink /Shell Energy Pi Group Values . . . . . . . . . . . 10-3 Table 10-4 Containment and Net Heat Sink Energy Pi Group Values . . . . . . . . . . 10-3 Table 10-5 Containment and Heat Sink /Shell Pressure Pi Group Values . . . . . . . . . 10-4 1 Table 10-6 Containment and Net Heat Sink Pressure Pi Group Values . . . . . . . . . . 10-4 j Table 10-7 Comparison of AP600 Operating Range to Tests for Liquid Film Stabili ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-13 i Table 10-8 Energy Rate of Change Equation Comparison to Steady State LST . . . . . 10-19 Table 10-9 Parameters for LST Transient 221.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 10-20 l Table 10-10 Energy Pi Group Comparison for AP600 and the LST . . . . . . . . . . . . . . 10-21 Table 11-1 LST Features That Differ from AP600 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-2 1 m:\34Ww.non\34Ww-a.wpf.It431297 March 1997 l
l ix li LIST OF FIGURES l Figure E-1 Metais and Eckert Plot Showing the Downcomer, Riser, and Chunney Heat Transfer Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx j i Figure E-2 Free Convection Condensation Data from the LST Compared to the l Correlation and the AP600 Operating Range . . . . . . . . . . . . . . . . . . . . . xxviii j Figure E Forced Convection Evaporation Data from the STC Flat Plate Test ! Compared 'o the Correlation and the AP600 Range of Operation . . . . . . . x>dx l Figure E-4 Chun and Seban Liquid Film Nusselt Number Correlation Comparison to Condensation and Evaporation Test Data . . . . . . . . . . . . . . . . . . . . . . . . xxx Figure P-1 PCS Test and Analysis Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . xliv i Figure P-2 PCS Scaling Role in PCS DBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xlv , Figure P-3 Relationship Between AP600 PCS PIRT, Testing, Scaling, Analysis, and ; Evaluation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xlvi j Figure 3-1 PCS Water Flow Rate after Overpressure Signal . . . . . . . . . . . . . . . . . . . . 3-3 Figure 3-2 Transient Mass Release Rate in AP600 During a DECLG LOCA . . . . . . . . 3-4 j l Figure 3-3 Transient Energy Release Rate in AP600 During a DECLG LOCA . , . . . . 3-5 l Figure 3-4 Transient Containment Pressure, Average Pressure, and Time Phases i for a DECLG LOCA in AP600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 Figure 3-5 Transient Mass Release Rate in AP600 during an MSLB . . . . . . . . . . . . . . 3-7 1 1 Figure 3-6 Transient Energy Release Rate in AP600 during an MSLB . . . . . . . . . . . . 3-8 Figure 3-7 Transient Pressure, Average Pressure, and Time Phase for an MSLB Transient in AP600 ......................................... 3-9 Figure 3-8 Break Pool Water Level and Surface Area in AP600 for a DECLG LOCA . 3-10 Figure 4-1 Metais and Eckert Plot Showing the Downcomer, Riser, and Chimney Heat Transfer Regimes for the AP600 PCS . . . . . . . . . . . . . . . . . . . . . . . . 4-3 Figure 4-2 Temperature and Concentration Dependence of the Thermal Conductivity of an Air-Steam Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Figure 4-3 Temperature and Concentration Dependence of the Dynamic Viscosity of an Air-Steam Gas Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9 Figure 4-4 Temperature and Concentration Dependence of the Prandtl and Schmidt Numbers for an Air-Steam Mixture . . . . . . . . . . . . . . . . . . . . . . 4-10 an. \34Ww.non\3499w-a.wpt:lt@l297 March 19W b
x LIST OF FIGURES (cont.) Figure 6-1 AP600 Containment Pressure During Blowdown . . . . . . . . . . . . . . . . . . 6-14 Figure 6-2 Froude Numbers Inside Containment for the AP600 DECLG . . . . . . . . . 6-20 Figure 6-3 Main Steamline Break Jet and Volumetric Froude Numbers . . . . . . . . . . 6-21 Figure 6-4 Steam Mixing Data Above and Below the Operating Deck from the LST . 6-26 Figure 7-1 Exponential Approximation to the Cool-Down of Saturated Drops Injected into Containment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-6 Figure 7-2 One-Dimensional Energy Balance and Temperatures for Energy Transfer Resistance to Solid Heat Sinks . . . . . . . . . . . . . . . . . . . . . . . . . 7-18 Figure 7-3 One-Dimensional Energy Balance and Temperatures for Energy , Transfer Conductance through the Containment Shell . . . . . . . . . . . . . . 7-24 Figure 7-4 Weir Ou tflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......... 7-34 Figure 9-1 Passive Cooling System Air Flow Path Momentum Parameters . . . . . . . 9-4 Figure 9-2 Buoyancy Calculation for the AP600 PCS Air Flow Path Comparing Distributed and Thermal Center Approaches . . . . . . . . . . . . . . . . . . . . . . 9-8 j Figure 10-1 Free Convection Condensation Data from the Large-Scale Test Compared to the Correlation and the AP600 Operating Range . . . . . . . . . 10-8 Figure 10-2 Forced Convection Evaporation Data from the STC Flat Plate Test Compared to the Correlation and the AP600 Range of Operation . . . . . . . 10-9 i Figure 10-3 Chun and Seban Liquid Film Nusselt Number Correlation Comparison to Condensation and Evaporation Test Data . . . . . . . . . . . . . . . . . . . . . 10-15 Figure 10-4 Heat Sink and Shell Inner Surface Energy Partitioning in AP600 from
.1YGOTHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-16 j m:\34Wwmon\34Ww.a wpt:1b-031297 March 1997
g xi LIST OF ACRONYMS AND ABBREVIATIONS DBA Design Basis Accident - DECLG Double-Ended Cold Leg Guillotine ECCS Emergency Core Cooling System
'IET Integral Effects Test IRWST In-Containment Refueling Water Storage Tank ISTIR . Integrated Structure for Technical Issue Resolution l LOCA Loss-of-Coolant Accident l LST Large-Scale Test !
MSLB Main Steamline Break ; PCS Passive Containment Cooling' Accident l PIRT Phenomena Identification Ranking Table l PWR Pressurized Water Reactor ! RPC Rate of Pressure Change t SET Separate Effects Test -i SSAR Standard Safety Analysis Report ! STC Westirghouse Science and Technology Center l l l l l i l l l l l l l 1 l l m.\3499wmon\3499w-a.wpf;1b-031297 March 1997 l
Xil EXECUTIVE
SUMMARY
Introduction This document presents the scaling evaluations performed to support the passive containment cooling system design basis accident (PCS DBA) es aluation model that is used to predict pressure in the AP600 containment during a DBA. The document supports design certification of the Westinghouse AP600. This document is one of the primary reports that 2 support the PCS DBA evaluation model. The other primary reports are the SSAR , the PIRT 2 report2, the EGOTHIC code description and validation report , and the EGOTHIC application report'. Test data reports, test analysis reports, and phenomenological model reports are incorporated into the primary reports by reference. Scaling is performed for the different time phases of the limiting large-break loss-of-coolant accident (LOCA) and the limiting main steamline break (MSLB). The double-ended cold leg guillotine (DECLG) pipe break and the MSLB initiated from 30 percent power, and the LOCA l and MSLB with the limiting pressure responses are evaluated. Containment pressure, energy, mass, internal momentum, and external momentum are scaled. The integrated structure for technical issue resolution (ISTIR), presented in NUREG/CR-5809,5 and the scaling example by Wulff* was used for guidance in the i I preparation of this document. Previous iterations on the scaling analysis were performed and documented'#'. Comments received from NRC and ACRS reviews are addressed and incorporated. The scaling analysis satisfies the AP600 needs for containment pressure scaling which are:
- Develop dimensionless, normalized equations for the AP600 containment pressure with pi groups that represent the important effects identified in the phenomena identification ranking table (PIRT) for mass, energy, and momentum transport among components.
. Calculate the relative magnitude of the dimensionless pi groups for AP600. . Use the quantitative evaluation to confirm the ranking of phenomena identified in the PIRT.
- Determine the range of dimensionless groups and the relevant separate effects tests (SETS) needed to validate models for the dominant phenomena in AP600.
. Confinn the use of the SETS and integral effects tests (IETs) to validate phenomenological models and the EGOTHIC computer code for use on AP600. m:\34Ww.ron\3499w+wpfM1297 March 1997
I xiii . Identify test distortions that limit the applicability of the tests to AP600. The PIRT The phenomena ranked high and medium in the PIRT are identified in Table E-1. All high and medium ranked phenomena are addressed by the scaling analysis, or references are provided showing where the phenomena are evaluated. In addition, many low ranked phenomena are also evaluated in the scaling analysis, thereby confirming their low ranking. ! Table E-1 is a simplification of the more detailed presentation in the PIRT. Only phenomena ranked high and medium during any time phase are listed. I I i I I m:\34Ww. rum \3499wwwptit>431297 March 1997 J
xiv Table E-1 Phenomena Identification and Ranking Table - Summary of High and Medium > Ranked Phenomena Phenomenon
- Effect on Containment Pi Groups Where Addressed Break Source Mass and The mass and energy source for x.p p % Scaling Analysis 1 Energy (IA) and Liquid containment pressurization np .pa,,6 Flashing (IE) and np ,-u Evaporation (SB) x,,,t, Gas Compliance (2C) Stores mass and energy in atmosphere, ng Scaling Analysis increasing pressure Initial Conditions Inside Temperature, humidity, pressure affect None Initial Conditions (4A, 4B, 4C) noncondensibles and energy storage Ref. 4, Section 5 Containment Solid Heat Store energy (and remove mass from npu Scaling Analysis Sinks (3), Pool (5), Drops, atmosphere) reducing pressure nyon and Shell (7) x p ,,n J Internal Heat Sink Limits conduction heat transfer into parameter Scaling Analysis Conduction (3D, heat sinks, shell, or pool, and through SE,7F) and Heat shell. Stratification in the break pool Capacity (3E,5A, can affect the effective heat capacity of 7G, IE) the pool.
Heat Transfer Water and noncondensible layers on parameter Scaling Analysis Through Horizontal upward facing horizontal surfaces limit Liquid Films (3C) heat and mass transfer to horizontal heat sinks ! Condensation Mass The single first order transport process x ,,y p Scaling Analysis Transfer (3F,5B,7C) that removes mass and energy from the npy,y containment gas Break Source Direction, elevation, density, and parameter Mixing and Direction and momentum can dominate circulation Stratification, Elevation (IB), and affect condensation rate. Existence Ref 4, Section 9 , Momentum (IC), of droplets in source during blowdown Density (ID), and affects the effective source density. Droplets (IE) Mixing and Intercompartment Flow (Circulation) , Stratification (2A) and stratification can affect the i
~ ~ ~ - - - ~ ~ ~ ~ - - -
distribution of steam near heat sinks parameters Intercompartment for condensation heat removal. Rising Flow (2B) _____ liquid level blocks lower circulation Break Pool fl w paths. Flooding Ixvel (5F) Source Fog (2D) Affects circulation and stratification via parameter buoyancy m:\34Ww.non\3499w-a wpt.lt431297 March 1997
nv Table E-1 Phenomena Identification and Ranking Table - Summary of High and Medium Ranked Phenomena (cont.) Phenomenon
- Effect on Containment Pi Groups Where Addressed Evaporation Mass i The first order transport process that n,,,,, Scaling Analysis Transfer (7N) removes mass and energy from the evaporating extemal shell PCS Natural Convective air flow provides heat and parameter Scaling Analysis Circulation (9A, mass transfer from containment shell.
13A) Liquid Film Flow Affects the upper limit for water parameter Film Stability Rate (8A), Water coverage on the extemal shell Ref. 4, Section 7 Temperature (8B), Film Stability (8C) Liquid Film Energy Inside: Transport (3A, 7E,7M) Carries 14% of condensation energy to Scaling Analysis the IRWST and break pool. Outside: Absorbs 8% of energy rejected by the extemal shell surface. Convection Heat Transfer A second order transport process that npy Scaling Analysis (3G, 7A, 7H,10A,10B, removes energy from the containment n,p,, 14A) gas, and from the extemal shell. Radiation Heat Transfer A second order transport process that n py Scaling Analysis (3H, 7B, 71) removes energy from the containment gas and from the extemal shell. Baffle Conduction (10D) Conduction through the baffle into None PIRT Sections and Baffle Leakage paths downcomer volume and leakage paths 4.4.10D and (10G) can influence the external natural 4.4.10G circulation flow rates
- Indicators in parentheses refer to phenomena in the " Phenomena Identification and Ranking According to Effect on Containment Pressure" table2, Scaling Equations j l
Basic Approach The goveming equations for the containment gas mass, energy, and pressure are derived by applying a simple control volume formulation, thermodynamic relationships, and an i equation of state. The governing equations treat containment as a single, well-mixed control volume that is coupled to multiple heat sinks. The above-deck region is well-mixed during and after blowdown due to the entrainment into the plume of more than 10 times its volumetric flow rate. The effect on heat sink utilization of deviations from a uniform vertical air / steam concentration distribution are showm in the l
- m. \3499w.non \ 3499w-a.wpf.l b-031297 March 1997 l
xvi mixing and stratification report to be minor. The mixing and stratification report also examines a range of break source momenta and directions, and shows that in all cases circulation between compartments maintains all but the dead-ended compartments at or above the well-mixed steam concentration, and the above-deck region within 2 or 3 percent of the well-mixed concentration of approximately 60 percent steam. Although containment is not perfectly mixed, the deviations from well-mixed are small enough that the conclusions of the scaling analysis are valid. For the LOCA, the heat sinks in dead-ended compartments are not included, since they are not effective heat sinks and it is conservative to ignore their heat capacity. In addition, upward facing large surfaces that may develop thick liquid films or may be blanketed with noncondensables are not included. None of the below-deck heat sinks are included for the MSLB. Conservation of Mass - Containment The mass conservation equation for the containment atmosphere, which consists of a constant > mass of air and a varying mass of steam, can be stated as the rate of change of mass in a control volume is equal to the sum of mass flows into the control volume minus the sum of flows out of the control volume: m - m,,+ m,,,, dm - dm, + dm,, dm., = 0 so dm - dm,,,,= rig-{s,y g) 7 The mass rate of change equation is made dimensionless and normalized by the reference break steam flow rate, rig,w resulting in the following dimensionless equation and pi groups: , l dm* . .. m
-n o rn,m + { x,3m,% m*- t* ._t (2) n ,, dt , , rh,m, I where V, p,m, p,V,rh,m, p, rh,m, , rn'"J" '
7 " J (3) ' JM.o bgMavE o gM4 O gMa Ib gMa E gMm l Conservation of Enerev - Containment ! The conservation of energy equation for the containment atmosphere is as follows (note that the liquid intemal energy and enthalpy of water at 120*F are used as a basis for changes in those properties): m:\3499w.non\3499w-a.wpt:1b 031297 March 1997 l l
Xvii d[m(u -u"")) p dt = th,,(h, g -h,7,) + _p, rh, (4)
-{[rh,,3(h,3-h,y) + rig (h,y -h,7,) + h, Aj (T-T,y)]
J The energy equation is rnade dimensionless and normalized by the break steam enthalpy - flow rate, thg ,6,, (hp ,6- h,,r ) = ru g ,uahp ,u, resulting in the following equation and pi groups: x,, d(mu) = x,, rh,*a Ah,*, - { (x,,,3rh,* 3, Ah,*,3 + x,,,yrh,* 3, Ah,,*3 + x,,3 ,3 3hi
- A *ATr*3) (5) dt 3 where:
x , , = x ,., x,, = 8**" 8*""
=1 x,,.
g.bris
,, = x ,., O f4 shk.o 3.M4 3.M.o (6) g ,g Ah,,3, g ,g Ah,,3, g e.qj ,
hg, A;,(T-T,y,) s.fgj mJ gghk.o e.ifj mj g g g 3.M.o 3.brk.o 3.brk.o Pressure Rate of Chanze - Containment Combining the conservation of mass and energy equations and applying an equation of state for real gasses, PV = ZmRT, the rate of pressure change (RPC) equation is derived: e , (1 +Z 7) y dP h8 *" -h'" + y (1 + Z T) P,, . , y (1 + z T) p (y - 1) T= .
**** s (y -1) p,, s '
(y - 1) 75
. (7)
) "
-E 'h a h,,3 -h,, + III *, -hgA,(T-T,y)
The compressibility function ZT = (T/Z)(dZ/dT), where Z is the (combined air and steam) gas compressibility and T is absolute temperature. The rate of pressure change equation is made dimensionless, then normalized by dividing each term by the reference break gas work term, yo(1+ZT)/(y-1), rh,3,u (P,./p,.): Z T
- V
- dP ' . .. y
- Z T* P,*, . .
7 zT mf. P, K.r .
- K .g.bek.suh p g.brk E ght
- I .g.brk.
p work . ghk +E pf. work y_ . dt . 7,, p ,, y, (g) f .. . . 3 I .enthj p M s
- E wwkJ p . .
- K .g.jh,*3 p A j' AT,*3i J INghk
. m,,o,g y, pson m:\M99w.non\M99w-a wpt 1b-031297 March 1997
xvill where P, p,,, (h,m-h,,),(y - 1), p,,,
, , V, p ,,,,,
rhg g , g"Ti P,,, p, "*"""'" P,,, y,(1 +Z T), p~ P* (y -1) K,4*s .mt "I K ,s.. art "E ms Apuna " K una in p" (h,,,3 -h,,,), (9) P r, p. Y.(; q 7). pin. (y -1) E,. ta " K m ; p p " h,3,A ,P T;), j E,43" Yo(; q 1 o ghk.o surto Conservation of Momentum - PCS Air Flow Path The conservation of mass, energy, and momentum equations were developed for the PCS air flow path to calculate the buoyant air flow rate that is needed to determine heat and mass transfer from the shell, and heat transfer rates between the riser and baffle, baffle and downcomer, and chimney and chimney concrete. The momentum equation was developed in vector form, following the example of Wulff*. The resulting momentum equation is: IEdt= G - R IKEI (10) where: Iis the geometry dependent inertia vector, in is the mass flow rate vector, G is the buoyancy defined by integrating the density times the dot product of the gravity and displacement vectors around a closed path, E is the impedance vector and R, is the sum of the form and friction resistance for each segment, EE is the vector of kinetic energies: The vectors are made dimensionless and the dimensionless momentum equation is normalized by the reference buoyancy, G,: d ' n ,,,,,,I = n,,,,%G * - n,,,,r ElP I, = [ I, R, = V I* sh*/t G R*rh*' where t= n,,,,= n,,% - =1 n ,,,,,, = m:\M99w.non\M99w-a.wpf:1b-031297 March 1997 L
xix The total buoyancy can be subdivided into components corresponding to the downcomer, riser, and chimney. Defining these as pi groups, n ,% = n,y, + n ,3 + n,e = 1.0, where: o n ,,, = o* n ,,,, = _ i n ,,,,, - o* W G, G, G, Constitutive Relationships Constitutive relationships are needed to calculate heat and mass transfer to the condensing film inside containment, heat transfer through the condensed and evaporating films, evaporation and heat transfer from the extemal film, and heat transfer from the baffle to the riser and downcomer. Operating points for the Grashof and Reynolds numbers were calculated for the PCS air flow path downcomer, riser, and chimney and plotted on a Metais and Eckert" plot to determine the turbulent heat transfer mode. Tne results are shown in Figure E-1. The riser and downcomer operate in forced convection and the chimney operates in opposed mixed convection. The inside of containment operates in forced convection during the large LOCA blowdown and the MSLB, and operates in free convection after the LOCA blowdown. However, free convection is assumed for the inside of containment for all analyses. This significantly underpredicts both heat and mass transfer during the MSLB and the LOCA blowdown, but is realistic for the LOCA after blowdown. The McAdams correlation is used for free convection, the Colbum correlation for forced convection, and a combination of free and forced is used for mixed convection. Heat transfer to the small diameter liquid drops is calculated using a correlation for laminar heat transfer to small spheres from Kreith". Mass transfer is calculated by the heat and mass transfer analogy. The heat and mass transfer correlations are summarized in Table E-2. m \3499w.non\3499w-a wptib-031297 Mardi 1997
I XX , l I I i P i
-)
+ - a, e J i
.i , i 2
1.0 E + 0 6 . ....... ................ . ..... ......... .. .... .... ... .~..
- : :: p w w . y er........
n..We...........De..............................n n eo m er................. ; 1 d
... Turbulent Flow ... ......
...................e- i i
r 1.0e+0s. . . . . . .Wa.t
.... . .S. .w. .. . . . . . . ... . . . . . . . . . ./. .. . . . . . . . . . .
i.
......................... ........................... l
. ...........................e.
......................je................. ................. ............g... !
............ . ...... g ............ .............. ...................... ......
If 1.0E+04! ....5555.5555
. 5 5 . .. . . ...... 5.?...itism..:i.ggi 355533..5. 5555 .:5.53 5333.555.5555555.Ghim r ..................................... ..............................................
J. . ....... ................................................. i Turbulent Flow :
- 3. ....................... ........................ .
n ............
- 1. ...
roe <
.................... ............................ Turbulent Flow ..... ...
............... .................................................................... -2
- 1.0E+02 . . . m. .....-....-.........-i.....................m.
1.0E+03 1.0E+05 1.0E+07 1.0E+09 1.0E+11 : 1.0E+04 1.0E+06 1.0E+08 1.0E+10 1.0E+12 lI Ra D/L I a I l I n t Figure E4 Metais and Eckert Plot Showing the Downcomer, Riser, and Chimney Heat j Transfer Regimes m:\3499w.non\3499w.a.wpf lt431297 March 1997 j 1
- g. w --. -c ,
xxi 4 Table E-2 Heat and Mass Transfer Correlations for AP600 Phenomena Constitutive Relationship Free Convection Heat Transfer Nu,, = 0.13( Ap /p )Pr '8 Nu = h(v2/g)/k (13) l Forced Convection l Heat Transfer Nu,, = 0.023 Re "8Pr ) Nu = hd/k (14) i 1
\
Opposed Mixed Convection Heat Nu, = (Nu/,,, + Nu,',,,)i') (15) l Transfer I Drop Heat Transfer u=2 Nu = hd/k (16) Free Convection - Mass Transfer 8 "" Sh = 0.13( Ap /p)Sc '8 8 Sh = (17) D,P Forced Convection - Mass Transfer I 8} Sh = 0.023Re0 8 Sc 8 ') Sh = 8 (18) D,P i Drop Mass Transfer ' k,RT(v 2fg)itap,, Sh = 2 _Sc "'3 Sh = (19) l r Pr D,P l Heat Sink Enercy Coupline to Containment Gas ! The containment gas equations are coupled by mass and energy transfer to the heat sinks and containment shell. The types of heat sinks considered for AP600 scaling are listed in Table E-3. m:\3499w.non\349Yw-a wpf;1tM)32697 D d 1997 i
xxil i Table E-3 Heat Sink Energy Equation Scaling for AP600 Heat Sink Abbreviation Equation Solution Method Drops d Exponential Approximation Break Pool p Evap from a spreading layer Intemal film if Steady state corduction Steel st Lumped parameter Concrete cc Integral equation Jacketed Concrete jc Bounded by steel or concrete - Shell: sh Integral equation Subcooled ss Integral equation Evaporating es Integral equation Dry ds Integral equation Baffle bf Lumped parameter Chimney Concrete ch Integral equation The energy equation for each heat sink was solved using the simplified technique listed in Table E-3. The internal steel and external baffle are thin enough to be modeled using a simple lumped parameter model, while the shell and concrete were modeled using integral approximations for thermally thick structures presented by Wulffo2 The drop and pool required special treatment due to a singularity in the mass transfer equation when P,,, = P,a. Simple methods were used to overcome the singularity and calculate the mass transfer rate. Scaling Results and Pi Group Evaluation The simultaneous solution of the mass, energy, and momentum equations produces the values needed to solve for the mass, energy, pressure, and momentum pi groups. The equations were solved for the four LOCA time phases and the MSLB. The conclusions of those calculations follow. Mass Scaline Results Conclusions of the mass flow rate scaling are:
- Relative to the break gas mass flow rate pi value of 1.0, the steel, concrete, jacketed concrete, dry shell, and evaporating shell have condensation and/or evaporation mass transfer rate pi values of order 1.0 during some time phases.
The pool, drops, subcooled shell, baffle, and chimney condensation and/or evaporation mass transfer rate pi groups are always of order 0.1 or less. . During blowdown the break source flow rate is so high that even with significant energy absorption, the heat sink :ondensation mass transfer rate pi groups are all order 0.1 or less. Since the containment gas mass rate of change responds to the sum of all the heat sink mass fluxes, it is relevant to combine all the internal heet sink mass transfer pi groups into a single value corresponding to mass transfer to a net heat sink. The result is presented in Table E-4]. The scaled mass rate of change, dm*/dt' is also presented. m:\3499w.non\3499w-a wpf:uM31297 March 1997
xxiii Table E-4 Containment and Net Heat Sink Mass Scaling Pi Group Values LOCA Pi Group MSLB Blowdown Refill Peak Press Long Term j 31 980 908 3309 392 l t. Contain- (sec) ment n, 1.31 1.27 1.30. 1.22 1.27 nm 1.00 0.00* 1.00*.. ~ 1.00 l1.00 , l x, 1.75 0.00 2.00 0.00 0.00 i Net Heat n.3 -0.01 -2.60 -1.37 - -1.26 -1.01 - Sink I
- x. . - - -0.02 -0.57 -
l dm*/dt* 0.76 -2.05 -0.30 -0.68 -0.01
- Refill was scaled with the same 200 lbm/sec flow rate used to normalize peak pressure.
The net heat sink shows the net blowdown mass is slightly negative (as shown by the detailed pi groups, this is due to the flashing and rapid evaporation of hot break liquid to steam). After blowdown, the condensation rate is greater than the source, indicating that dm*/dt* is negative, so the net mass of vapor in containment is decreasing. From the equation of state, since pressure is proportional to mass, it can be expected that pressure is also decreasing. Although this is contrary to predictions of the evaluation model that the pressure increases during the peak pressure time phase, the difference is due to more conservative mass transfer rate assumptions in the evaluation model. Enerev Scaline Results Conclusions of the detailed energy scaling pi groups are: Sensible heat transfer related phenomena (q subscripted pi groups) are always small. Phenomena associated with the energy carried away by liquid films (f subscripted pi groups) are much less important than phenomena associated with energy transferred into the heat sink by condensation (fg subscripted pi groups). Phenomena associated with the outside shell surface energy transfer are important during long-term but not during blowdown, refill, and peak pressure. Phenomena , associated with the inside of the dry shell during refill, and the inside of the evaporating shell during the peak pressure phase are very important, indicating the large shell energy storage capacity. Heat sink mass transfer related phenomena (fg subscripted pi groups) are important after blowdown and before the long-term phase of a large LOCA. e Phenomena associated with the baffle and chimney are second order effects. m:\3499w.non\3499w-a.wpt:IM31297 March 1997 l
xxiv The detailed energy scaling results for all the internal heat sinks are combined into a few net heat sink pi groups and presented in Table E-5. The scaled rate of change of internal energy l du'/dt* is determined according to the scaled energy equation and included in the table. l Table E-5 Containment and Net Heat Sink Energy Scaling Pi Group Values I LOCA Blowdown Refill Peak Press Long Term Contain- n,., 0.55 0.58 0.56 0.63' O.58 n,w 1.00- 0.00* 1.00* 1.00 1.00 n,j w 0.00 0.00 0.00 0.00 0.00 Net Heat x,,, 0.00 -0.14 -0.06 -0.03 -0.07 Sink n,,, -0.02 -2.49 -1.30 -1.14 -0.99 n,,, 0.00 -0.10 -0.09 -0.14 0.01 n,,,, 0.00 0.00 0.00 -0.06 - n,y,, - -0.01 -0.08 - n,jg, - -
-0.02 -0.81 -
d(mu)*/dt* 1.78 -4.71 -0.80 -0.49 -0.12
- Refill was scaled with the same energy normahzation used for peak pressure.
The net heat sink energy pi values show the heat sinks are not effective, relative to the source, during ble.vdc,wn. During subsequent time phases of the LOCA, more energy is removed from the gas than added. The sensible heat transfer (q subscript) and liquid film energy transfer (f subscript) are small compared to the mass transfer (fg subscript) both inside and outside (outside has x subscript). External heat transfer is insignificant until the long-term phase. Pressure Scaline Results The detailed pressure scaling pi values provide the basis for the following conclusions: All heat sink phenomena, except those associated with the drops and pool, reduce pressure during the time phases considered. a Drop-related phenomena produce a small pressure increase during blowdown, and thereafter are either a small pressure sink or a negligible pressure source. The pool is always a small pressure source. i l During the blowdown phase, phenomena associated with the internal solid heat sinks : and shell reduce the RPC by 10 percent of the source work, while flashing and l evaporation from the pool and drops increases the RPC by 9 percent. l l l 4 m:\3499w.non\34Ww.a.wpt 1t431297 March 1997
xxv + The work due to mass removal is the most significant pressure-related phenomena. Heat transfer-related phenomena (radiation plus convection) are typically much less important than flow work-related pher.omena.
- Enthalpy-related phenomena for both the source and heat sinks are not important.
- Phenomena associated with mass transfer dommates the RPC after blowdown.
The detailed breakdown of heat sinks is useful for clarifying the effect of the several distinct types and locations of heat sinks. However, the RPC equation shows the same pressure response would result from considering a net source and a net sink. The pi groups resulting from this composite heat sink approach are defined by adding the values for all heat sinks. The results are presented in Table E-6. Table E-6 Containment and Net Heat Sink Pressure Scaling Pi Group Values LOCA Blowdown Refill Peak Press Long Term Contain- n p., 0.76 0.76 ' O.77 ' O.76 0.76 n, p. 1.00. - 0.00* 1.00* - 1.00 '1.00
- n. m p 0.03 0.00 0.03 0.02 0.03 np f,, 0.00 0.00 0.00 0.00 0.00 Net Heat n,p -0.01 -0.43 -0.20 -0.12 -0.20 1 Sinks I npm 0.00 0.00 0.00 0.00 0.00 l np .% -0.01 -2.60 -1.37 -1.261 .-l.01 dP*/dt* 1.33 -3_99 -0.70 -0.47 -0.24
- Refill was scaled with the same pressure normali:.ation used for peak pressure.
Pressure scaling with a net heat sink shows the minor effect of the heat sinks during the LOCA blowdown and the major effect thereafter. As noted for the mass and energy scaling, the pi values indicate that containment is depressurtzing after blowdown, contrary to the evaluation model predictions, due primarily to mass transfer correlation conservatism in the evaluation model. Sensible heat transfer is an intermediate order (0.1 < x,,y., < 1.0) phenomena for pressure, whereas it was order less than 0.1 for energy. PCS Momentum Scaline Results The PCS momentum scaling pi groups are presented in Table E-7. The Ra D/L values are the horizontal axis for the values shown on the Metais and Eckert plot, Figure E-1. PCS operation is not considered for scaling the MSLB, due to the relatively short duration of the transient. m:\3499w.non\3499w-a.wyttb.031297 March 1997
xxvi Table E-7 PCS Air Flow Path Momentum Scaling Groups Group Blowdown Refill Peak Press Long Term to 70 58 15 7.0 K.,2,, 0.13 0.13 0.13 0.11 x,,,w 1.00 1.00 1.00 1.00 x,,,,,,, 1.00 1.00 0.97 0.86 x,,,e, 0.00 -0.05 -0.03 -0.16 x,,,,, 0.48 0.52 0.46 0.58 x,,a 0.52 0.53 0.58 0.58 Ra,D/L)o, - 247,000 7.6x10' 2.2x108 Reu, 16,100 18,500 74,000 151,000 Ra D/L),, 7,600 19,800 333 000 270,000 Reu 16,600 19,000 77,000 163,000 Ro,D/L),a 3.3x10" 3.2x10" 1.3x10" 4.5x10" Re a,,n 27,400 31,400 128,000 282,000 The following conclusions are drawn from the momentum scaling: . The pi groups show the inertial effect is relatively small, and the effect of the downcomer on the net buoyancy is relatively small. . The air flow Reynolds number is high (16,100) even during blowdown due to the assumed initial condition of 120 F shell temperature and 115 F riser air. During normal operation containment temperature is expected to be higher than the outside teniperature. . The free / mixed / forced convection regime of the flow in the downcomer, riser, and chimney are determined from the Reynolds and Rayleigh (rad /L) numbers on the Metais and Eckert plot in Figure E-1. I SETS and Constitutive Relationship Scaling j The energy and pressure pi values show the gas compliance, break source, condensation, and evaporation are the dominant order 1.0 terms. Internal sensible heat transfer is intermediate order, and external sensible heat transfer, liquid displacement, energy to the external subcooled film, energy carried by the condensed liquid, and enthalpy (of break and condensate) are order 0.1 or less terms. The conclusion is drawn that condensation and evaporation mass transfer are the dominant transport processes for containment pressurization. m:\34Ww.non\3499w-a.wpt:1b431297 March 1997
xxvii This section presents summaries of constitutive relationships and scahng of phenomenological data from SETS. The summaries show the selected correlations represent the test data and the range of AP600 operation is adequately covered by the test data. Condensation mass transfer was identified as a high importance phenomenon in the PIRT and was shown to be of order 1.0 in the scaling analysis. The dimensionless relationship for free convection condensation mass transfer, represented by the Sherwood number is presented in Figure E-2. Figure E-2 shows the range of parameters covered by the LST envelopes the operating range of AP600 and shows the test data agree well with the free convection mass transfer correlation. The data and correlation are discussed in more detail in the heat and mass transfer report". Evaporation mass transfer was identified in the PIRT as a high importance phenomenon, and was verified by scaling to be of order 1.0. The forced convection evaporation mass transfer, as represented by the Sherwood number correlation, is presented in Figure E-3. The range of Sherwood and Reynolds numbers for AP600 operation are shown in Figure E-3 to be within the range covered by the LST and Gilliland and Sherwood test data. The figure also shows the data agree well with the forced convection mass transfer correlation. Note that although the Gilliland and Sherwood data range is shown on the figure, the actual data were not local, so are not included on the plot. The data and correlation are discussed in more detail in Reference 13. Free convection heat transfer to surfaces inside containment was ranked medium in the PIRT. Scaling shows heat transfer to be of intermediate order, it accounts for approximately 10 percent as much energy and 10 to 20 percent as much dP/dt as condensation mass ; transfer. As second order energy transfer phenomena, heat transfer inside containment is modeled using the conventional correlations for radiation and free convection. Although the SETS and IETs included these phenomena, they were always present with condensation mass transfer, which dominated the energy transfer, and prevented measuring the second order phenomena. Although no direct measurement of heat transfer in the presence of mass transfer is available, by the heat and mass transfer analogy it can be claimed that heat transfer is as well modeled as the mass transfer presented in Figure E-2 and Figure E-3. That is, replace Sh Sc' with Nu Pr8 in Figure E-2 and Figure E-3 to estimate the agreement and uncertainty for heat transfer. The PIRT ranked forced convection heat transfer from the shell to the riser as medium importance, and the scaling analysis showed it to be a second order phenomenon. Forced convection heat transfer from the shell to the riser in AP600 is modeled using the Colburn forced convection heat transfer correlation: Nu = 0.023 Reo "Pr 'd where Nu = hD" (20) k where the length parameter is the annulus hydraulic diameter, D3 . Incropera and DeWitt", Table 8.4, suggests the use of Colburn, Dittus-Boelter, and Seider-Tate correlations for internal channel flows. m:\M99w.non\M99w-a.wpf:1b432697 March 1997
xxviii i l I l 1 l I a,b i h i t f i _ i i i l Figure E-2 Free Convection Condensation Data from the LST Compared to the Correlation and the AP600 Operating Range m:\3499w.non\3499w-a.wptib-031297 March 1997 L__. . . _ , . _ _ . _ . .
i xxxx l i
.i i
4 i
.I a,b j i
I I i i f i t t i I f i i t i Figure E-3 ' Forced Convection Evaporation Data from the STC Flat Plate Test Compared f to the Correlation and the AP600 Range of Operation ! m:\x99w.nonsu99w.a.wpelba31297 - unrch 1997 4 {
~, xxx i l l I I l I 1 1 )
~ -
\
Chun and Seban Turbulent Correlation ,, Chunand SebanWaW Nu = 0.0038 (Re^0.4) (Pr%.65)
. Larninar Correlation -
Nu = 0.822 (Re%.22) Pr = 5.1
~ ~
3 Pr = 5.7 p 4 93 M M M [ Pr =1.77
- I
$ z .
g E - Wisconsin Data - (Allothers are Chun 5 A 1 and Seban) ; AP600 Range (from second weir) ' O.1 . . . ...... . . . . . . . . . . . . . . . . . . . . . . ... 0.1 10 100 1000 10000 100000 Liquid Film Reynolds Number. Re i Figure E-4 Chun and Seban Liquid Film Nusselt Number Correlation Comparison to Condensation and Evaporation Test Data m:\3499w.non\3499w a.wpf;1b431297 March 1997
xxxi
*- The Dittus-Boelter correlation differs from Colburn by a Prandtl number exponent of 0.4 instead of 1/3. For the flow in the PCS riser (approximately 90 percent air and 10 percent steam by mass), Dittus-Boelter gives results that are 2 percent less than Colburn. . The Seider-Tate correlation adds a multiplier of (p/p,)* to the Colburn correlation.
For the PCS with air and bulk-to-surface temperature differences less than 100 F, Seider-Tate also gives results 2 percent less than Colbum. All of these correlations are recommended for Re > 10,000, L/D > 10, and .7 < Pr < 160. The corresponding AP600 parameters are 20,000 < Re < 163,000, Pr = 0.72, and L/D - 60 which satisfy the criteria for use of the Colburn correlation. The PCS flow resistance is one of the donunant terms in the PCS momentum equation. The flow resistance in the PCS air flow path was measured in the 1/6 scale air flow test". Although AP600 operates in natural circulation and the test was fan forced, the buoyant pressure, G, and the forced pressure drop, AP are interchangeable in the pi groups. Consequently, a fan forced test produces a flow resistance that is equally valid for a buoyancy driven system. I P : l An important aspect of the AP600 design is its sensitivitv +o evtamal wind. The external conditions might be postulated to affect the performarce of the PCS air flow path, due to high wind speeds and turbulence induced by upwind simctures or terrain. A series of tests were conducted in wind tunnels to characterize the effect on the AP600 PCS air flow of environmental wind speeds up to the AP600 design limit of 214 mph. Since the AP600 design is wind-positive, the particular concern was the effect of upwind terrain and obstructions that could subject the PCS air flow path to pressure fluctuations that might induce reversed flow in the riser. Such fluctuations have been evaluated relative to the assumed zero environmental effect. The effect of wind tunnel model scale was evaluated to insure the appropriate flow regime was simulated in the tests. The test evaluation (Ref. 4, Section 6) showed the wind-positive characteristic of AP600 more than offset the effect of . fluctuations. 1 The recirculation of the chimney outflow (warmer and more humid than the environment) to the downcomer inlets was evaluated (Ref. 4, Section 6) and determined to have an insignificant effect. Liquid film stability is an important parameter in the external evaporation calculation. This was identified in the PIRT and is included in the important phenomena listed in Table E-1. ' The film stability is discussed in detail in Reference 4, Section 7. Heated and unheated water distribution measurements were made on tests to support the modeling of water coverage on the external shell of AP600. The dimensionless groups appropriate for scaling water l I m:\3499w.non\M99w-a.wpf-It>031297 March 1997 I I
XXXii coverage are defined in the literature and those that are most significant for AP600 are the film Reynolds number, Marangoni number, and Bond number, defined respectively as: Re = $ Ma = do f 6b'
,, B = E80 QD p dT 2k2p o The range of these groups for AP600 and two of the supporting tests are presented in Table E-8. The comparisons show the range of AP600 operation is adequately covered by the test data.
Table E-8 Comparison of AP600 Operating Range to Tests for Liquid Film Stability AP600 Large Scale Test Water Distribution Test Film Reynolds Number: Upper Sidewall Bottom of PCS surface Marangoni Number: Upper Sidewall Bottom of PCS surface Bond Number: Upper Sidewall Bottom of PCS surface Heat transfer throuch the drainine liauid film on the inside and outside surfaces of the shell and heat sinks was ranked low importance in the PIRT. The Chun and Seban correlation was selected to model the film heat transfer. The validity of the Chun and Seban correlation for evaporating turbulent and wavy laminar films on vertical surfaces was demonstrated in the original paper. Data from tests at the University of Wisconsin27are added to extend the validity of the Chun and Seban correlation to condensing wavy laminar flow and to surfaces that are inclined, as in the dome region of the AP600. The Wisconsin and Chun and Seban data are compared to the Chun and Seban laminar and turbulent correlations in Figure E-4. The correlation predicts nearly best- estimate values over the full Reynolds number range of data. The range of film Reynolds numbers on the outside of AP600 is also shown in the figure and falls well within the range of the test data. Reynolds numbers on the inside of containment are less than outside due to film removal at the crane rail and stiffener ring, and the fact that the inside film flow rate starts at zero at the top of the dome and increases as the film flows down. The AP600 Prandtl number range is approximately 1.5 < Pr < 3.0, whereas the range of the Chun and Seban data Prandtl numbers is 1.77 < Pr < 5.9, which adequately covers the AP600 range with only a small extrapolation. Comparison of the correlation to the test data show that the Chun and Seban correlation is a reasonable, best-estimate representation of the data. m:\MWw.non\3499w-a.wpf 1b-032697 March 1997
xxxiii LST Scaling and Equation Validation A scaled comparison between the larce-scale (intecral test) and the AP600 plant is performed. The comparison shows the scaled LST captures highly ranked phenomena associated with the AP600 containment and therefore, the data obtained from the test is adequate for code validation. The scaling equations are compared to the LST and validated for both steady-state and transient predictions. The results for 21 steady-state LST cases show the average steady-state mass and energy transfer rates are predicted with a mean deviation of less than 0.01 and a standard deviation of 0.13. Such agreement is considered to adequately verify that the mass and energy equations accurately predict the transfer rates, thereby validating the mass and energy scaling equations. Since the RPC equation is the result of combining the mass and energy rate equations, with the equation of state, it is also true that the RPC equation is valid at steady-state. A comparison was made between the transient RPC eauation and the startup of LST 221.1. At startup there is no heat or mass transfer to the internal heat sinks or shell since there is initially no temperature or steam partial pressure differences to drive transport processes. The initial pressurization is adiabatic compression which is described by the RPC equation without heat sinks or a break liquid source. The calculated value was dP/dt = 0.38 psi /sec, whereas the measured transient pressure shows dP/dt = 0.29. The difference is likely due to the fact that the " adiabatic" assumption is not quite valid, and consequently, the source is not quite so effective. The agreement is considered to be sufficiently close to provide validation of the transient capability of the RPC equation. When combined with the steady-state comparisons, this transient comparison shows the RPC equation is valid. The scaled comparisons between the LST and AP600 focus on the phenomena associated with the containment features that are unique to AP600, that is, the PCS. Phenomena associated with the PCS become significant during the peak pressure phase of a DECLG LOCA, become dominant as peak containment pressure is approached, and remain dominant during the long-term phase of the transient. This is supposed by energy partitioning calculations that show heat sink energy removal rates for AP600. The external shell energy removal becomes important during the refill time phase (t-1000 sec) and is dominant by about 200 sec (i.e., during the peak pressure phase). Phenomena associated with the blowdown and refill phases of a DECLG LOCA are not unique to AP600. Those phenomena exist in current pressurized water reactors (PWRs). Therefore, these scaling comparisons focus on test validation to represent the peak pressure and long-term time phases, the time when the AP600 PCS performance validation requires unique test results. The detailed breakdown of individual pi groups shows that during all the phases of a DECLG LOCA, phenomena associated with the drops, pools, chimney, and baffle are not important and can therefore be neglected since the pi group numerical values are of order less than 0.1. The only pi groups of any significance are those ai sociated with the solid internal heat sinks and the shell. However, these heat sinks becc me saturated prior to the time when the peak pressure occurs. Therefore, only the pi groups identified as containment or shell are calculated for the AP600 plant and LST. mAMWW.non\MWw-a.wpt:1b 031297 March 1997
xxxiv l i The pi groups were calculated with the transport equations developed for scaling for both the IST and AP600. The calculation corresponded to conditions in AP600 expeded at 4000 to 5000 sec. into the transient. The results of the energy scaling comparison between the LST and the AP600 plant are summarized in Table E-9. The transient pi group x,, = 0, since d(mu)*/dt* = 0; the contamment atmosphere is in a quasi steady-state condition. : Th. dominant shell energy phenomena are condensation on the inside of the shell, x,,w, and evaporation on the exterior of the shell, x,,%,. Table E-9 shows the dominant phenomena (condensation and evaporation) compare favorably. The shell energy phenomena for subcooled and dry shell compare well as predicted, but as actually operated, the comparisons to test date are not as close. Although the subcooled and dry pi values, n,,, and n,,,, do not compare quite as well as condensation and evaporation, the former are second order phenomena in both the plant and test, so do not invalidate the use of the test data. Table E-9 Energy PI Group Comparison for AP600 and the LST Predicted at 41 psia Pi Group AP600 LST LST Measured x, , 1.24 1.24 1.22 x,a 1.00 1.00 1.00 nu 0.00 0.00 0.00 x,, 0.02 0.02 0.03 x,3,, 0.91 0.93 0.90 x,.,, 0.08 0.06 0.08 x, ,,, 0.13 0.18 0.09 x,,, ,, 0.13 0.15 0.09 x,g,,, 0.67 0.62 0.74 The scaline comparisons r>ermit the conclusion that the scaled LST represents the dominant internal and external energy transport processes with sufficient accuracy for use to validate phenomenological models and the AP600 evaluation model during quasi-steady (long-term) operation. Differences and Distortions between the LST and AP600 Prior to using data from the LST to represent some phenomena of AP600,it is necessary to identify the differences between the LST and AP600. Differences can be geometric or thermal-hydraulic parameters that are not prototypic. The differences are then evaluated as to whether they constitute distortions that must be considered when the LST data is applied to AP600. A difference becomes a distortion if it noticeably alters the phenomena in the test facility. Features of the LST that differ from AP600, the concern for each difference, and whether the difference constitutes a distortion are listed in Table E-10. m:\3499w.non\3499w-a.wpf:1b-031297 March 1997 i I
\
xxxv Table E-10 LST Features That Differ from AP600 Difference Concern Distortion Break Source Supe: Sat Condensation correlation and pressurization are not No prototypic because more thermal energy was input. Diffuser used for break 'Ihe actual break is a pipe break with a high velocity No l source jet. ; l No Downcomer Lack of downcomer may influence heat and mass No l transfer Riser Scaled 1/4 The riser heat and evaporation mass transfer are biased Yes : because the 3-inch riser width is 1/4 scale rather then l 1/8 scale, as is the remainder of the test. Fan Forced Riser Air The fan provides a forced air flow instead of the Yes Flow natural circulation air flow. , No Circulation Below The above/below-deck noncondensible distribution Yes ! Deck makes the test results inapplicable. j l External Water Flow too The extemal water flow rate removes too much energy No ; High by its subcooled heat capacity. I Extemal Water Coverage The water coverage was controlled artificially, rather No was too high than according to stability. The excess flow rate made the water more stable than it should have been. Extemal water flow was Cold water was not applied to a hot surface. No established before break Intemal heat sinks not The intemal concrete, steel, and pools are not Yes prototypic represented. Extemal water flow Oscillations in the extemal water flow rate affected the Yes , oscillation cooling and water coverage I Crane rails not the same Intemal liquid film is different No Extemal water not Extemal water coverage and stability are different No applied by weirs 1 Condensate drained out There was no break pool to interact with the No atmosphere in the test In conclusion, there are several distortions associated with the LST representation of AP600. Those distortions are recognized and taken into account. The distortions do not prevent the use of the LST results to validate the high-ranked phenomena of condensation mass transfer and liquid film stability and coverage. The temperatur.. and concentration mesurements from the LST provide data to understand and bourd stratification in the AP600 evaluation modsl. Heat transfer measurements from tests with no external water provided data to validah dry heat transfer to the riser. In addition, the steady-state and transient LST are used to validate predictions of the scaling equations and the evaluation model, and selected segments of the LST are scaled to represent portions of the dP/dt behavior of AP600. m:\3499w.non\3499w-a.wpt:1tK)31297 March 1997 j
xxxyl Executive Summary References
*1. "AP600 Standard Safety Analysis Report," Section 6.2, June 26,1992, Westinghouse Electric Corporation.
- 2. M. J. Loftus, D. R. Spencer, J. Woodcock, " Accident Specification and Phenomena Evaluation for AP600 Passive Containment Cooling System," WCAP-14811, Westinghouse Electric Corporation.
*3. D. L. Paulsen, et. al., "WGOTHIC Code Description and Validation," WCAP-14382, May 1995, Westinghouse Electric Corporation.
*4. D. L. Paulsen, et. al., "EGOTHIC Application to AP600," WCAP-14407, September 1996, Westinghouse Electric Corporation.
- 5. NUREG/CR-5809 EGG-2659, "An Integrated Structure and Scaling Methodology for Severe Accident Technical Issue Resolution," INEL, EG&G Idaho, Inc.
; ~ 6. W. Wulff, " Scaling of Thermohydraulic Systems," BNL-62325, May 1995, Brookhaven National Laboratory.
- 7. Letter, N. J. Liparulo (Westinghouse) to R. W. Borchardt (US NRC), "AP600 Passive Containment Cooling System Preliminary Scaling Report," NTD-NRC-94-4246, July 28,1994.
(Superceded by WCAP-14845).
- 8. D. R. Spencer, Scaling Analysis for AP600 Passive Containme,,dooling System," WCAP-14190, October 1994, Westinghouse Electric Corporation. (Superseded by WCAP-14845).
- 9. Ietter, B. A. McIntyre (Westinghouse) to T. R. Quay (USNRC), NSD-NRC-96-4762, July 1, 1996, D. R. Spencer, " Scaling Analysis for AP600 Containment Pressure During Design Basis Accidents," (Superseded by WCAP-14845).
- 10. B. Metais and E. R. G. Eckert, Journal of Heat Transfer, 86:295 (1964).
I 1. F. Kreith, Principles of Heat Transfer,1965, International Textbook Company.
- 12. W. Wulff. " Integral Methods for Simulating Transient Conduction in Nuclear Reactor Components," Nuclear Engineering and Design 151 (1994) 113-129.
- 13. R. P. Ofstun, " Experimental Basis for the AP600 Containment Vessel Heat and Mass Transfer Correlations," WCAP-14326, March 31,1995, Westinghouse Electric Corporation.
- 14. F. P, Incropera and D. P. DeWitt, fundamentals ofHeat and Mass Transfer, Second Edition, John Wiley & Sons.
- 15. W. A. Stewart and A. T. Pieczynski, " Tests of Air Flow Path for Cooling the AP600 Reactor Containment," WCAP - 13328,1992, Westinghouse Electric Company.
- 16. K. R. Chun and R. A. Seban, " Heat Transfer to Evaporating Liquid Films," Journal of Heat Transfer, November 1971, m:\3499w.non\3499w a.wpf:1M31297 March 1997 l
xxxvii
- 17. WCAP-13307, " Condensation in the Presence of a Noncondensible Gas - Experimental [
Investiga; ion," Westinghouse Electric Corporation. j
- One or more sections of report will be revised as a result of outstanding NRC open items.
I i r i
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4 l i l l I l l i i 1 I I j i i i m:\3499w.non\3499w4.wpf;1b431297 March 1997 ' 7 Y T'-mc1 V J= 4 g e +4- e ,M-e -g---m. e - -w. ---W c m
xxxviii l PREFACE ) This document presents the scaling evaluations performed to support the passive containment cooling system design basis accident (PCS DBA) evaluation model. This document is one of the primary reports (Tables 1 and 2 of Reference ) that support the PCS DBA evaluation model. The other primary reports are the SSAR2 , the PIRT report', the j EGOTHIC code description and validation report', and the evaluation model application ' report5 . Test data reports, test analysis reports, and phenomenological model reports are incorporated into the primary reports by reference. Although the focus of this report is to develop the scaling laws for AP600 PCS performance and to scale the tests, this preface describes how the scaling analysis fits into the overall program.
Background
The evaluation model for the PCS DBA has been developed using elements of scaling (top-down modeling of the integrated components), testing, and analysis (bottom-up phenomenological models and evaluations). The results have been used to identify bounding models and input values for use in the DBA evaluation model. The results of the evaluation model provide conservative predictions of design basis transient pressure and temperature response for the containment. The PCS DBA methodology has followed an approach that can be organized into four elements as shown in Figure F-1. The elements include tasks which together provide a structured, traceable, and practical method for
- Specifying the scenario
. Identifying and ranking phenomena important to the transient
- Evaluating data and scale effects
- Documenting and validating the computer code
- Assessing margins and uncertainties
. Developing and applying the evaluation model The process is represented as a once-through flow diagram for simplicity. The actual process followed includes iterations between the various tasks. For example, to better represent the observations of the large-scale test (LST) dome temperature distribution due to the subcooling of the liquid film applied to the LST, the initial WGOTHIC code version used in 1992 was augmented by the addition of a model for convective heat transport for the liquid film.
Review by representatives of industry, academia, and regulatory agencies were ince ps, ued into the process. The end result is documentation that describes the PCS DBA evaluati. a model and its bases in an auditable, traceable manner. Following is a brief description of the four major process elements. Element 1 Determine AP600 PCS Modelling Requirements l The PCS DBA methodology development process began with a review of the AP600 design and DBA scenarios and an identification of phenomena important for AP600 containment pressurization. This review identified several separate effects tests (SETS) to investigate specific phenomena such as the liquid flow over the outside of the containment shell, and m:\3499w.non\3499w Awpf:1b-031297 M:rch 1997
i xxxix l 4
. condensation and evaporation mass transfer. In addition, integral effects tests (IETs) at two ;
different scales were also identified to examine the integrated heat and' mass transfer l behavior of the PCS. The need for such tests was recognized and testing was initiated in the late 1980's.'- Table P-1 was used to identify tM containment phenomena unique to AP600 and the tests required to validate models of those phenomena. From this review, the . : Westinghouse-GOTHIC (E GOTHIC) comprier code was selected as the best available tool ! to evaluate containment pressure, j
- A phenomena identification and ranking table (PII T) is developed to identify the key j thermal-hydraulic phenomena which govem the tr msients of interest. To allow definition of the relevant phenomena, plant design parameters and design basis scenarios are first defined.-
The PIRT8 then ranks phenomena according to their relative importance to the particular j transient phase of interest. The PIRT process included input and review by representatives of academia, cross-functional Westinghouse technical reviews, and regulatory authorities. The bases for high, medium, and low rankings are documented with the PIRT. From the i PIRT, evaluation model requirements and approaches to address phenomena can be defined. j A key result of the PIRT is that the dominant phenomenon for t;ansferring energy from the
; containment is mass transfer - condensation on the inside and evaporation on the outside. !
Phenomena ranked high or medium during any accident phase are investigated, and j methods to bound uncertainties are developed (see Element 3 below). Phenomena with a j low ranking do not significantly influence the containment pressure response; thus, models 1 which capture the gross behavior are sufficient, and where justifiable, a low ranked l phenomenon may be neglected entirely. Evaluation model features are defined from the l PIRT. Section 2 summarizes the PIRT high and medium ranked phenomena and the approach that is used to address each. The EGOTHIC computer code was selected, upgraded, and frozen to allow explicit modeling of many of the phenomena identified in the initial review. As the scaling analysis and testing programs progressed, code upgrades to better model experimental results were completed according to guidelines consistent with life-cycle management identified in NQA 2a Part 2.7. Extensive hand calculations and spreadsheets were used to verify correct programming of the upgrades as documented within the Westinghouse QAprogram. Documentation of the code used in the evaluation model has been issued"# . J i i l
- at\3499wsorA3499w-b.wpf lb 031297 March 1997 - l
. l i aL - . . - _ . .
l x1 I Table P-1 Containment Processes Used to Initially Define Test Program ; AP600 Uniqueness with Respect to Containment AP600-Specific Containment Westinghouse Validation - Validation Process Plants? Does it Exist? Needed? Tests Identified Evaporative film Yes No Yes PCS tests,1/8 scale cooling tests, heated plate tests Liquid film Yes No Yes Film flow experiments distribution on to investigate the water containment distribution: heated plate tests
- large-scale film flow coverage tests 1/8 scale tests Condensation, No Yes, not Yes CVTR, University of with AP600-specific Wisconsin, literature noncondensibles Effect of hydrogen No Yes, not Yes 1/8 scale test on containment AP600-specific heat transfer Air cooling of Yes No Yes A large-scale test to steel shell, natural simulate air passage convection hydraulic characteristics Internal circulation No Yes, not Yes 1/8 scale test -
patterns in AP600-specific stratification; containment, International tests at Stratification large scale (HDR, , NUPEC) for circulation Effects of Yes No Yes Wind tunnel tests with buildings and building effects and site wind velocity on effects. air flow over steel Literature for effluent shell recirculation WM e m:\3499w.non\3499w4wpt1b-031297 March 1997 w
r XII 1 Element 2 Assess Phenomena Models and Code Capabilities with Tests t l Scaling has been used to support the PCS DBA evaluation model as summarized in Figure P-2. The PCS test program includes SETS5 ', as well as an IST' , that provided data ; for simultaneous external evaporation and internal condensation in an integral setting. A ; scaling evaluation identifies the effects of facility scales and differences and distortions between the AP600 and tests, and provides insight into the AP600 PCS system performance. Scaling results also have been used to confirm PIRT rankings. Scaling also identified the appropriate non-dimensional parameters for phenomena and AP600 ranges. The LST was , not designed to simulate a particular AP600 transient response from beginning to end. Rather, the LST varied boundary conditions over significant portions of the AP600 range to gain insight into the physics, confirm the selection of mass transfer correlations that were , based on smaller scale tests, and to ex:.adne the performance of the WGOTHIC computer t code in modeling AP600 phenomena. ; Where the IST does not well represent the AP600, other data and scaling considerations were
- used together with bottom-up phenomena modelling to develop a bounding approach.
Phenomena evaluations have been used to assess phenomena importance, develop correlations, and identify bounding approaches. Such phenomena evaluations include heat and mass transfer correlation development', water coverage on the external containment shell (Ref 5, Section 7), and mixing and stratification effects on mass transfer inside containment (Ref 5, Section 9), as well as specific phenomena evaluations used to assess PIRT phenomena such as forced convection and radiation heat transfer in the annulus. Results of phenomena reports have been factored into the PIRT. The results from the following tests were used to assess and validate the phenomena important in the AP600 containment:
- Heated Flat Plate Test performed at Westinghouse Science and Technology Center (STC)
- Wind Tunnel Tests performed at Boundary Layer Wind Tunnel Laboratory of the University of Western Ontario e Condensation Tests performed at University of Wisconsin
- Air Flow Path Tests performed at Westinghouse STC
- Water Film Formation Tests
- Water Distribution Tests performed at Westinghouse Waltz Mill
- Small-Scale Integral PCS Tests performed at Westinghouse STC
- Large-Scale Integral PCS Tests (LST) performed at Westinghouse STC
'fhe first six test series represent the SETS and the last two test series represent the IETs. An overview summary of these tests and a cross-reference between phenomena and test reports may be found in Reference 3. A listing of test reports issued for AP600 Design Certification has been issued". m:\M99w.non\M99w-b.wpf It>431297 March 1997
xlii In addition to the Westinghouse-sponsored tests, the evaluation of AP600 containment phenomena was supplemented with test data available in the open literature. These included the Hugot heated, parallel, vertical, isothermal plate tests; the Eckert and Diaguila heated vertical tube tests; the Siegel and Norris heated, parallel, vertical flat plate tests; and the Gilliland and Sherwood Evaporation tests. These tests, as described in Reference 9, provided additional data to validate models for convective heat and mass transfer in AP600. The PCS test data and other data from the literature were used to provide input to code validation *. The lumped parameter codes oversimplify the flow field by assuming a homogeneous mixture exists within each node. Since lumped parameter cannot resolve gradients within a node, effects such as stratification have been addressed extemal to the code to quantify the effects on AP600 containment pressure response. The use of the relatively large lumped parameter nodes in the AP600 evaluation model also overexpands an entering jet, leading to two competing effects on containment pressure calculation - overprediction of velodty and underprediction of steam concentration above the operating deck. The competing effects have been bounded (Reference 3, pages 8-9) by utilizing only free convection on the inside of containment, which effectively eliminates the non-conservative velocity. This leaves only the underpredicted above-deck steam concentration which is itself conservative with respect to PCS heat removal. Comparisons with LST data were also performed with calculations using the distributed parameter EGOTHIC formulation. The more detailed distributed parameter model (Reference 4, Appendix A) better represents phenomena, more closely matches the LST data, and helped confirm that phenomena occurring in the IST had been identified. Element 3 Assess Uncertainties and Develop Bounding Modeling Approaches The results of scaling, testing, and code validation were used to establish a bounding analysis approach for each of the PIRT phenomena. Results of code validation and assessment of model uncertainties were used to develop a method of applying the EGOTHIC lumped parameter formulation to create a bounding DBA evaluation model using fixed noding. Sensitivity calculations were performed to gain insight into the influence of important parameters on the predicted pressure 1sponse. A key aspect of the evaluation model is that phenomena that are not part of the code c iculation or are not well-represented within the code are evaluated separately and bounded by applying conservative boundary conditions or introducing biases into the evaluation model, as summarized in Section 2. Element 4 Perform DBA Calculations and Compare to Success Criteria The evaluation model was developed as described above to produce conservative, bounding , pressure transients for each postulated accident. The acceptance criteria are that the peak pressure must remain below the design pressure of 45 psig, and the pressure at 24 hours must be less than 1/2 of the design pressure. Road maps (Ref. 5, Tables 2-3 and 2-4) that address each phenomenon identified in the PIRT show:
- Relevant model in the code
- Test basis
- Report references
- Summary report conclusions
- Applicability of LST m:\34Ww.non\34WwAwpt:1b-031297 March 1997
xliii i
- Validation basis summary '
How validation results are used
- How uncertainty is bounded l This report documents the scaling evaluation performed for the AP600 DBA response, and !
fits within the AP600 PCS DBA licensing documentation as depicted in Figure P-3. The ; primary purpose of this report, as discussed in Element 2 above,is to develop scaling j relations, apply the results to determine appropriate non-dimensional groups for assessing j the effects of scale, and to assess the applicable test databases for application to AP600. I l r i i i b t ). 4 4 4 A 4 m:\3499wawn\3499w4.wyt lb431297 March 1997 t L
., , , ,,., .-,n . , , . -
' xliv l
PCS DBA oroaram element Princiole Outout
- i
-Scenario identification h Develop AP600 PCS - PIRT j modelling requirements - Evaluation model requirements i j -Code documentation baselined l
V I
-Scaling evaluation ;
~ Test definition and documentation i
@ Assess phenomena - Phenomena reports l models and code capabilities with tests -Code documentation (updated) .
-Code validation report and user guidance (including noding)
V
- Uncertainty and range assessment Assess uncertainties and -Sensitivity studies g a
[y,esgpo - Fixed AP600 containment noding d ng els l
- Appropriate EM method forinput l to bound each phemomenon U
@ Perform AP600 DBA -Confirmation that acceptance calculations and compare enteria are met a;
to success criteria I Figure F PCS Test and Analysis Process Overview m:\349Pw.stm\3499w-b.wpf:1b4131297 March 1997
xlv , insight into AP600 identification of nondimensional l PCS system parameters and AP600 ranges performance forimportant processes ; I f i r Identification of effects of facility Confirmation of PIRT rankings - scales (diferences and ' distortions relative to AP600) I f I f Determine applicability of LST Specifications for to represent specifc AP600 j phenomena models phenomena ; I 1 l Application of tests and phenomena models to a bounding PCS DBA ) Evaluation Model I j Figure P-2 PCS Scaling Role in PCS DBA m:\3499w.rmn\3499wewpf-1b431297 March 1997 l
}
xlvi PIRT 1 n L Test Reports Scaling Report Phenomenological WGOTHIC Reports Reports ; I l l l V l Evaluation Model u mma 1 1 i Figure P-3 Relationship Between AP600 PCS PIRT, Testing, Scaling, Analysis, and-Evaluation Model. m:\3499w.non\3499w44.wptit431297 March 1997
1 1-1 1 INTRODUCTION This report was prepared to support design certification of the Westinghouse AP600. This report presents the scaling analysis for pressurization of the AP600 containment. The scaling analysis was performed to identify the phenomena necessary to be modeled for accurate predictions of pressure within the AP600 containment during a design basis accident (DBA) and to permit a scaled comparison of the supporting separate effects (SETS) and integral ; effects tests (IETs) to the AP600 performance. The scaling analysis presented in this document generally follows the scaling methodology ; for severe accidents presented in NUREG/CR-5809". The passive containment cooling i system (PCS) air flow path momentum scaling is based on the example presented by W. Wulff" for scaling interconnected regions. I Containment pressure is the variable of primary interest for evaluating whether the PCS maintains containment pressure below the design limit during DBAs. The pressure rate of j change (RPC) equation is developed by combining rate of change equations for containment gas mass and energy with the gas equation of state. The containment gas volume is coupled by energy transfer equations to internal heat sinks and the external PCS. The equations are made dimensionless, and normalized to produce the pi groups required to scale containment pressure. The variables selected for AP600 scaling and the reference normalizing parameters are presented in Table 1-1. The pi groups are one of the analytical tools used to scale SET and IET phenomena to AP600. Table 11 Parameters Selected for Scaling AP600 Scaled Parameter Location Normalizing Parameter Mass Flow Rate Inside Containment Break mass flow rate, m pg, i Energy Transfer Rate Inside and Outside Containment Break enthalpy flow rate, ! I rit,36,Ahgug, Conductance Inside and Outside Containment Coated shell conductance, h,,, Pressure Inside Containment Break flow work rate,
%(1+ZT)/(pl),m,.3,u,P,1,/p,,,
Momentum inside Containment Buoyancy, ApgH l Momentum PCS Air Flow Path Buoyancy, G, I The dimensionless groups needed to scale jet and plume momentum for their effects on stratification in the containment volumes are presented and relationships between AP600 and introduction March 1997 m:\N99w.non\3499w-b.wptit> 031297
1-2 , i the LST are discussed. The evaluation of stratification in compartments, and circulation . between compartments, on AP600 are documented in Reference 5, Section 9. The momentum equation for the air flow through the PCS air flow path (downcomer, riser, and chimney) are developed, made dimensionless, and normalized to produce the pi groups required to scale momentum in the PCS air flow path. The pi group values for the AP600 phenomena are evaluated, thereby providing a numerical e basis for the importance of the dominant phenomena (transport processes and components) and validation of the PIRT rankings. f Scaled data from the SETS and IETs are compared to the scaling and phenomenological equations. The scaled tests are compared to AP600 to justify the use of the tests for , evaluation model validation. The rate of change equations for the containment gas mass, energy, and pressure are derived based on simple assumptions, using thermodynamic relationships, equation of state, and control volume conservation equations. The rate of change equations represent a single gas volume that is coupled to multiple heat sinks. The containment volume is assumed well-mixed, except for the dead-ended compartments. The above-deck region is nearly well- , mixed during and after blowdown due to the entrainment into the plume of more than 10 times its volumetric flow rate. The effect on heat sink utilization of deviations from a uniform vertical air / steam concentration distribution are shown in the mixing and stratification report to be minor. The mixing and stratification report examines a range of break source momenta and directions and shows that in all cases circulation between compartments maintains all but the dead-ended compartments at, or above the well-mixed steam concentration, and the above-deck region within 2 or 3 percent of the well-mixed concentration of approximately 60 percent steam. Although containment is not perfectly mixed, the deviations from well-mixed are small enough that the conclusions of the scaling analysis are valid. The Westinghouse containment scaling analysis has evolved through a series of issued documents, presentations, and reviews. Extensive input has been received from the USNRC and the ACRS Thermal Hydraulics Subcommittee.
- Westinghouse issued Passive Containment Cooling System Preliminary Scaling Report", July 1994.
. Westinghouse presentation to USNRC, AP600 Passive Containment Cooling System (PCS) Scaling - Iteration 1 Report Review Kickoff Meeting, July 26,1994.
Introduction March 1997 m:\M99w.non\M99wAwpf It41297
1-3
- Westinghouse issued Scaling Analysis for AP600 Passive Containment Cooling System", October 1994.
- Westinghouse presentation to ACRS Thermal Hydraulics Subcommittee, March 29,1995.
NRC presentation of (LASL) review comments on Containment Scaling, June 20-22,1995.
- NRC issued requests for additional information that are answered in this document.
- Westinghouse issued Scaling Analysis for AP600 Containment Pressure during Design Basis Accidents", June 1996.
NRC requested clarification of information contained in the June 1996 scaling report. l l l Introduction March 1997 m:\3499w.non\3499w-b.wyf-lb-031297
2-1 1 2 DOMINANT PHENOMENA The transport processes and components that affect containment pressure were identified and ranked according to importance in the PIRT. The phenomena ranked high and medium are the ones that receive more detailed treatment and validation, and should be addressed in the l evaluation model. The phenomena ranked high or medium importance are listed in l Table 2-1. The phenomena are organized according to whether they are represented by pi l groups in the scaling analysis or whether the phenomena appear as parameters in pi groups. i Those that appear as parameters are indented in the first column of the table, and identified ; as parameters in the column headed "PI Group." The high- and medium-ranked phenomena l evaluated in this scaling analysis are identified in the column headed "Where Addressed." ; Many low importance phenomena are also addressed in this scaling analysis. High ranked phenomena not evaluated in this scaling analysis are briefly discussed and referenced to source documents at the end of this section. The following high ranked phenomena are addressed by separate, detailed evaluations in , which AP600 parameters were ranged to derive bounding inputs for the evaluation model. ) l Mixing and Stratification - Mixing in AP600 can be characterized by stratification within compartments and circulation between compartments. The scaling of jets and plumes, and the relationship of large-scale test (LST) stratification data to AP600 operation is presented in Section 6.5 of this document. The application of those data to AP600 is presented in Reference 5, Section 9. The circulation rates of air and 1 steam between interconnected gas volumes (compartments) is addressed in Reference 5, Section 9. Intercompartment Flow - The mass flow rate of air and steam between interconnected gas volumes (usually referred to as circulation) affects heat sink utilization and is also addressed in the mixing and stratification report. Source Fog - Source droplets (fog) occur during blowdown and increase the steam source density, thereby reducing its buoyancy. However, during blowdown, mixing inside containment is momentum- and pressure-dominated, not buoyancy-dominated. After blowdown, drops do not occur in the break source, so the post-blowdown source buoyancy is not affected. The effect of blowdown-generated drops on post-blowdown circulation is addressed in the mixing and stratification report. However, the effect of droplets as heat sinks is addressed in this scaling document. l Dominant Phenomena March 1997 m:\N99w.ncm\M99w-b.wptib431297
i 2-2 Table 2-1 Phenomena Identification and Ranking Table - Summary of High and Medium Ranked Phenomena Pher.omenon
- Effect on Containment Pi Groups Where Addressed Break Source Mass and The only mass and energy source for x.g, p % Scaling Analysis Energy (1 A) and Liquid containment pressurization x.p,v p g Flashing (1E) and xpy.u Evaporation (SB) x,,,u., i Gas Compliance (2C) Stores mass and energy in atmosphere, x p., Scaling Analysis !
increasing pressure Initial Conditions Inside Temperature, humidity, pressure affect None Initial Conditions (4A, 4B, 4C) noncondensables and energy storage Ref. 5, Section 5 Containment Solid Heat Store energy (and remove mass from uy p ap ,,y Scaling Analysis Sinks (3), Pool (5), Drops atmosphere) reducing pressure (1), and Shell (7) Internal Heat Sink Limits conduction heat transfer into heat parameter Scaling Analysis Conduction (3D, sinks, shell, or pool, and through shell. SE,7F) and Heat Stratification in the break pool can affect the Capacity (3E, 5A, effective heat capacity of the pool. 7G, IE) Heat Transfer Water and noncondensible layers on parameter Scaling Analysis Arough Horizontal upward facing horizontal surfaces limit heat Liquid Films (3C) and mass transfer to horizontal heat sinks Condensation Mass ne single first-order transport process that up ,,y Scaling Analysis Transfer (3F,5B, 7C) removes mass and energy from the containment gas Break Source Direction, elevation, density, and parameter Mixing and Direction and momentum can dominate circulation and Stratification, Elevation (IB), affect condensation rate. Existence of Ref. 5, Section 9 Momentum (IC), droplets in source during blowdown affects Density (1D), and the effective source density. Droplets (IE) Mixing and Intercompartment Flow (Circulation) and Stratification (2A) stratification can affect the distribution of
~~~~~ ~~~
steam near heat sinks for condensation heat parameters Intercompartment removal. Rising liquid level blocks lower Flow (2B) circulation flow paths. Break Pool Flooding Level (SF) Source Fog (2D) Affects circulation and stratification via parameter buoyancy i l Dominant Phenomena March 1997 i m:\34Ww.non\3499w-b.wpf:lt>431297 I l
2-3 Table 2-1 Phenomena Identification and Ranking Table - Summary of High and Medium Ranked Phenomena (cont.) Phenomenon
- Effect on Containment Pi Groups Where Addressed Evaporation Mass The first-order transport process that x,3,,, Scaling Analysis Transfer (7N) removes mass and energy from the evaporating external shell PCS Natural Convective air flow provides convective parameter Scaling Analysis Circulation (9A, heat and mass transfer from containment 13A) shen.
Liquid Film Flow Affects the upper limit for water coverage parameter Film Stability, Rate (8A), Water on the extemal shell Ref. 5, Section 7 Temperature (8B), Film Stability (SC) Liquid Film Energy inside: Transport (3A,7E, 7M) Carries 14 percent of condensation energy to n,,w Scaling Analysis the IRWST and break pool. Outside: Absorbs 8 percent of energy rejected by the n,4,,, extemal shell surface. Convection Heat Transfer A second order transport process that x py Scaling Ar.alysis (3G, 7A, 7H,10A,10B, removes energy from the containment gas, x,y 14A) and from the extemal shell. Radiation Heat Transfer A second order transport process that x,y Scaling Analysis (3H, 7B, 71) removes energy from the containment gas nm and from the extemal shell. Baffle Conduction (10D) Conduction through the baffle into None PIRT Sections I and Baffle Leakage paths downcomer volume and leakage paths can 4.4.10D and j (10G) influence the extemal natural circulation 4.4.10G 1 flow rates Indicators in parentheses refer to phenomena in the " Phenomena Identification and Ranking According to Effect on Containment Pressure" table'. - Liquid Film Stability - Liquid film stability affects the amount of surface area that can be covered by the PCS cooling water. In AP600, the time constant for heat transmission through the shell is relatively long, so the external surface temperature rises slowly relative to application of cooling water. Once the PCS water supply valve is opened, the water distribution weirs begin to fill and spill, leading to a development time for flow rate, and coverage (spreading of the liquid film) develops as flow develops. Documentation of liquid film stability phenomena as they affect containment pressure performance, and a water coverage model that couples coverage to shell heat flux, is provided in the liquid film stability report (Ref. 5, Section 7). The Dominant Phenomena March 1997 m:\M99w.non\3499w-b.wpf:ltW1297 I I
_ ~ . . _ . . ,
- 2-4 -i
( I model shows that by the time of the peak pressure, approximately 40 lbm/sec is ; evaporated of the 60 lbm/sec applied. .i
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p 3-1 3 . DESIGN, BOUNDARY, AND INITIAL CONDITION INPUT
, DATA I I
The system to be analyzed is the AP600 containment, subjected to overpressure DBAs. ! I
- Sections 1,2, and 3 of the PIRT describe the plant geometry, the accident sequences, and the phenomena in more detail. The double-ended cold leg guillotine loss-of-coolent accident (DECLG LOCA), and the main steamline break (MSLB) from 30 percent power are the DBAs that produce the highest containment pressure and are the subject of this analysis. The design and boundary conditions for the plant and these accidents follow.
Earameter Value Ccmment Water Capacities: PCS Water Flow Rate Figure 3-1_
"'C Cold Leg Pipe ID Main Steamline ID IRWST Liquid Volume
. Double-End Cold Leg Guillotine Transient Mass Flow Rate Figure 3-2 Typical DECLG transient Transient Energy Flow Rate Figure 3-3 Typical DECLG transient Transient Pressure and Temp Figure 3-4 Typical DECLG transient Main Steamline Break: . Transient Mass Flow Rate Figure 3-5 Typical MSLB transient i Transient Energy Flow Rate Figure 3-6 Typical MSLB transient I Transient Pressure and Temp Figure 3-7 Typical MSLB transient Break Pool Water Level and Surface Area Figure 3-8 Typical DECLG transient Containment Vessel Shell Thickness 1.625 in. Externally Cooled Surface Area 52,662 ft.2 Vesscl Internal Free Volume 1,740,944 ft.2 Steel Heat Sink Surface Area 142,700 ft.2 Volume 4739 ft.' Concrete Heat Sink Surface Area 22,600 ft.2 4 Input Data March 1997 m:\3499w.non\3499w-b.wpf 1t4131297
3-2
-Jacketed Concrete Surface Area 46,500 ft.2 Baffle Thickness -
0.12 in. - Chimney Height - a,b Riser Height Downcomer Height Vessel Coating Material Properties Section 4.7 The large-scale integral test (IST) provided both SET and IET data that are used to validate phenomenological models used in the AP600 evaluation model, and ta scale transient behavior in AP600. The design and test results for the LST are presented in the test data reports *2', and the test as-built drawings". Design characteristics of the LST are summarized as follows: LST Vessel Coating
. LST Coating Thickness a,b Shell Thickness Shell Thermal Conductivity" External Wetted Surface area Vessel Intemal Free Volume _
Initial conditions for the inside and outside of containment follow. These were determined to be limiting in the sense of producing the highest containtnent pressure during transients. Environment, shield building, baffle, chimney, and PCS cooling water temperature 115'F Environment pressure 14.7 psia Environment humidity 25 % Containment air, shell, and heat sink temperature 120 F Containment pressure 15.7 psia Containment humidity 0% Input Data March 1997 m:\3499w.non\3499w-b wpt.1b431297 l l l
3-3 r
-t
.I i
.r 1
.k, I
+
L 60 % , 50- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - t A t a. J i 2 g g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l h 20- - - - - - - - - - - - - - - - - - - - - - - - - ' - - - - - - - - - - - - - - - - 10- - --- - - - - - - - - - - - - - - - - - - 1 J l l 1
.0 . . . ...... . . . . . . . . . . . . . . . . . . . . . ...... . . . . . . . . l 1 10 100 1000 10000 100000 :
Time (seconds) I 1 1 M Figure 3-1 PCS Water Flow Rate after Overpressure Signal Input Data , Mmh 1997 i
. m:\3499w.non\3499w b.wpf:1b 031297 . l l
l l l l
]
1 i
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j t 100000: :10000000 l Uquid
- 10000: 1000000 g
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/?
Gas h 4 3 m ; Gas Flow f 1000 100000 j :
- Ig !
t 100; E1 0000 - l 10 .......................................1000 10000 100000 1 10 100 1000 > Time after Break (seconds) 1 Figure 3-2 Transient Mass Release Rate in AP600 During a DECLG LOCA i Input Data Much 1997 m:\M99w.rm\M99w-b.wpf;1 bel 297 l l
3-5 i l e i b P 100: =100000 > 4 . . , M 10 Gas Rate E10000 3 4 : : m ; 3 m 5 5 k 6 : e .
.6 M Gas hw 1-i =1000 3'
m-
@ Rate :
3: o 5 - - E j sa
* "d *
- 2100
, 0.1: 8 i E W i p
/
3 , g W8 0.01::.
- 10 c
0.001 ......... .............u.... ......1 1 10 100 1000 10000 100000 Time after Break (seconds) ! l 1 1 i l I l I Figure 3-3. Transient Energy Release in AP600 During a DECLG LOCA j
'l Input Data W rch I M !
m:\M99w.non\M99wAwphlb431297 - ! i
)
_ ~ - _ . l 3-6 a 60 , 300 l 4% 50-g- l -260 g
._ m be 40- -240 2 2
c E B 3
-220 g '
m \ - E O. 30- V -200 S
' c
$ -180 g j 20- .g .
E -160 5C : f' O O O -140 0 10- Peak Bowdown Refill Precoure Long Term -120 0 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,, 1 00 1 10 100 1000 10000 100000 Time after Break (oeconds) i l Figure 3-4 Transient Containment Pressure, Temperature, and Tune Phases for a DECLG LOCA in AP600 l i Input Data u 39,7 m:\3499w.non\3499w-h.wpf.lb431897 I 1 1 j
h 3-7 P 4 t f f 1 10000. . .... .......................................................... . . t 000000 F , 4
!2 o . . . . . . . . . . . . . ' .............................y/.......
........... m y
.........p E a i 1000.- ~.~...~............-.....-#... . . . . . . . . - . . . . . ~ . ~ . . . ~ . . . .-100000 (/>
w . .. .. . . . . . . . . . . . X m . ................. ........... m
. ...........................,.s.+ % .......... .....................
g
. ........................,6........ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.................4....................... . . . . . . . . . . . . . . . . . . . . . .
Cf) . ................/................................. . . . . . . . . . . . . . . . . M m ./ ~ C
- ........../.......................................................
./ ,
- 1 100 . . . . . . . . . . . . . . . . . . . .....i. 10000 !
1' 10 100 1000 Time after Break (seconds) J I I I I 1 i i l 1 1 l. 1 1 l 1 i l Figure 3-5 Transient Mass Release Rate in AP600 during an MSLB l i Input Data . March 1997 m:\M99w.swm\M99w-b.wpf:11431297 l l b
)
8 1 i I 1 1 00. . .. .. . . . .. . . . . . . . . . . . . .. .... . . . . . .. . .. . . .. . . . . . . . . . ... ... . . . . .. ... . 1 0000 i m { 2
~
2 e 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1000 .
m . ................................................................. . w a-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E m
. . . . . . . . . . . . . . .n....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
g u) g ........> m w . ... _
.........=..............,...,
. .......................,gn...................... .......................................
y .- 6
. .............s,...................................... . . . . . . . . . . . . .
.s
.c.
i 0.1 . . . . . . . . ...o... . . > > . . . 10 - 1 10 100 1000 Time after Break (seconds) l 1 i, I i l l I I Figure 3-6 Transient Energy Release Rate in AP600 during an MSLB Input Data Wrch 1977 m:\3499w.non\3499w.b.wpf.lb C31297 I
)
3-9 l r I i 100 400 f 350
> Temperature
?, -
Cc3 i
-3003m :
~
-250s . i
_i liE ! il -200g ' 5 3 !
-150 >
0 . . . . .- . 100 ! 0 100 200 300 400 500 600 700 ,i Time after Break (seconds) l a i j l
-1 1
Figure 3-7 Transient Pressure, Average Pressure, and Time Phase for an MSLB ; Transient in AP600 , I Input Da'at . . March 2997 ' m:\M9ht.non\M99w4,wyf;1b431297 .,
.\
I-
^
3-10 i r e f 4 h 40 4000 , 3& - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-3500 Cold Leg CL 102'- 8.5" L 30- - - - - - - - - - - - - - - - - - - - - - - - -
-3000 .
A
- i
^
V 'f
-2500 5 s 2& To- p Bf Xchve- Fuei 95'-
i--~~-
- 2
} j.......>
.320" -~~7--~~~-----~~~~ ~ ~ - - - ~ ~
-2000l i 15 ---
i
--- - - - - - ~ ~ - - - - - - - - - - - - - - - - - - - - ~ ~ f .
i Rottnm of Arwe Fuel 83' -1500 D.
} !
10---i----~~~--~~----~~~~---~~-~~~~~--------1000 5"'" -[....-~.Bonan oWesselbrMead--...~.-._..~.._____ 500 4 :l l 0 . , , . . . . . . 0 l 0 5 10 15 20 25 30 35 40 45 50 i, WaterVolume (ft3) ' (Thousands) . 1 t 1 4 1 I i i e
~ Figure 3-8. Break Pool Water Level and Surface Area in AP600 for a DECLG LOCA Input Data m m ,97 i
_ nu\3499w. rum \$499w-b.wpf;1b431297 l 1 I l
4-1 4 CONSTITUTIVE EQUATIONS FOR HEAT, MASS, AND RADIATION TRANSFER The constitutive relationships for radiation, convection, condensation, and evaporation heat , transfer, and for condensation and evaporation mass transfer are presented and formulated j in terms of a conductance and a temperature difference. The formulation in terms of ' conductance and temperature difference facilitates coupling the inside of containment through the shell to the outside, and permits direct comparisons of energy transport coefficients for mass with radiation and convection. Summary comparisons of the correlations selected for convective heat and mass transfer to data, other correlations, and the AP600 range of operation is presented in Section 10. 4.1 RADIATION HEAT TRANSFER i Radiation heat transfer can be written in terms of a conductance and a temperature difference: q," - o e (T' -T,',) or 4," - h,(T -T,,) (1) where the conductance is h, = ccf(T,T,n) and f(T,T,s) = (T + T,n)(T2+ T2,n). The character e is the surface emissivity for surface-to surface radiation, and the product of the emissivity and ] beam length for radiation from the containment gas to the surface. j 4.2 CONVECTION HEAT TRANSFER The inside of containment is expected to operate in turbulent forced or mixed convection during both the LOCA and MSLB blowdown, and in turbulent free convection after blowdown. However, since insufficient data are available to validate forced or mixed convection models for the inside of containment, the inside of containment is modeled using turbulent free convection throughout the transient. This modeling approach underestimated energy transfer to the shell and heat sinks during blow-down, but is accurate after blowdown j as shown by the condensation mass transfer correlation to data in Section 10.1.1. ! Turbulent free convection heat transfer is expected for Grashof number (based on height) 4
> 10'. This is the case over all but 2 feet or less of height of heat sinks and the shell, after the first few seconds of the transient. The turbulent free convection correlation underestimates ;
heat and mass transfer at Grashof numbers less than 10', so its use is conservative for smaller structures or early time values. The turbulent free convection correlation is shown in Section 10 in a dimensionless form compared to the LST condensation data. The correlation compares well with the data, especially considering that the LST is 1/8 geometric scale and ! therefore has more of its total height within the 2 to 3 foot height limit for turbulent free ; convection. ! Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997 m:\3499w.non\3499w.c.wpf1b4131397
i l 4-2 1 The PCS air flow outside of containment operates over a range of free, mixed, and forced I convection heat transfer. The downcomer, riser, and chimney operating points were i 2 calculated as described in Section 9.0 and are shown on an Eckert and Metais plot in Figure 4-1. The progression of calculated operating points for the downcomer, riser, and chimney is from blowdown at the lower left point, to refill, peak pressure, and to long term operation at the upper nght point. The results from an alternate calculation 22 for a dry riser are also shown. That calculation concluded heat transfer in the riser is turbulent forced convection for shell surface temperatures more than 2'F above the environment air temperature. Figure 4-1 shows the downcomer and riser operate in forced convection, and chimney operation progresses from free to mixed to forced convection. The information presented in the figure supports the selection of the turbulent convection regimes specified for the downcomer, riser, and chimney. Convection heat transfer can be written in terms of a conductance and a temperature difference: 4" - h,(T -T,,) (2) where the conductance, he , is given by one of the following constitutive correlations. 4.2.1 Turbulent Free Convection Heat Transfer The McAdams correlation was selected' for scaling turbulent f;ee convection heat transfer for all surfaces inside containment, horizontal as well as vertical, except for drops: h = h"" - 0.13b(Gr t Pr) = 0.13
.0P. Pr /3 (3)
L 2 (v f g)i/3 p, The term (Ap/p) is the difference between the bulk density and surface density, divided by the bulk density. Note that in this form the Grashof number with its length dependence no longer appears and the heat transfer coefficient is dependent only on local properties. 4.2.2 Laminar Free Convection Heat Transfer Laminar free convection heat transfer is considered for the drops that result from the break liquid during blowdown, because their diameter is so small (~ 104 ft.) that Gr, << 1. For this case, Kreith22 presents the correlation for small spheres: k h, - h, = 2 7 (4) Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997 m:\M99w.non\M99w<wpf n41397
4-3 F 1 .0E+06 3 . . :.....
- . .. -. ... . . . . . . . . .. . i
. .. ....... i yh.........................................
..Cownoomer Forced Corwecbon . D...... ...... . . .......................... .........
n.g...................
... Turbulent Flow ... nrwwDs...... ~
...............~....................... ........... ............................... ;
m O a 1.0En.r .. .....
..............+..................................................
.............. ...... m.........
+ ..........
...........................A......................
. 9
..................... 4 ................... ..............................q...
............ . ......+ g ............ .............. ...................... ...... ,
cf 1.0E+045:: it!!!!!!!!:*i!!!= ..:33.r.i!!!!!!.!!.!!!!!!: .:3353:55 gri.!!!!!!!!! G himsay35533
......................................................ng.......
1 M. Turbulent Flow 1.0E+03........................
........................ ......................... Free Convect.on Turbulent Flow 1.0E+02 . m u- .om- . i u- iu- ou- . ou.
1.0E+03 1.0E+05 .".0"E+07 1 .1".0". E+09 . .o u - 1.0E+11 ; 1.0E+04 1.0E+06 1.0E+08 1.0E+10 1.0E+12 Ra D/L I l Figure 41 Metais and Eckert Plot Showing the Downcomer, Riser, and Chimney Heat Transfer Regimes for the AP600 PCS Constitutive Equations for Heat, Mass, and Radiation Transfer Much 1997 mM499w.non\3499w.c.wpf:1b431397 -
4-4 4.2.3 Turbulent Forced Convection Heat Transfer - The Colbum correlation was selected' for turbulent forced convection in a channel: h, - h, = 0.023 Re,"Pr W (5) where the hydraulic diameter is two times the riser width. On the inside of containment, turbulent forced convection is expected during blowdown, and produces heat and mass transfer rates significantly greater than free convection. However, forced convection is conservatively neglected during blowdown; free convection is assumed. This conservatism results in under-predicted heat sink energy absorption during blowdown, and a small overprediction of containment pressure. The assumption does not change the conclusions of the scaling analysis. 4.2.4 Turbulent Opposed Mixed Convection Opposed free and forced (mixed) convection exists in the chimney where the PCS natural circulation induces a bulk upward flow that is opposed by the negatively buoyant free convection on the cooler chimney concrete. The correlation for opposed turbulent mixed convection recommended by Churchill 22 is used: N, - ( N,', + N,8,)w (6) Using the correlations for free and forced turbulent convection, Equations (3) and (5), the mixed convection heat transfer coefficient correlation is: h , = _k (0.13D*)2 Ap* Pr, + (0.023)SRe,jPr, g 2 (7) D < (v /g) p, 2 4.3 CONDENSATION AND EVAPORATION MASS TRANSFER The mass transfer rate expressions are evaluated and simplified assuming both air and steam are ideal gasses. In AP600 compressibility is limited to approximately 0.97 < Z < 1.0, where the minimum value corresponds to 40 psia of saturated steam. The assumption that Z = 1.0 introduces an error of less than 3 percent and is a significant simplification over the neces-sary steam table look-up required to quantify Z. Although compressibility is neglected in 1 this application of the equation of state, compressibility has been considered where it is more j 4 Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997
' m:\3499w.non\3499w c.wpf;1t>431397 I
_ _ _ . . . ~ 1 4-5 ;
, significant: the evaluation of the enthalpy rate of change with pressure in the energy and l pressure change equations. ;
Kreith defines the mass flux from the bulk gas to the condensing surface as:
-l rh" = k,M,, AP,, (8)'
where AP,, = (P. 3a- P,,,,,n). The mass transfer coefficient, k, is determined from the heat ! and rr iss transfer analogy. The heat and mass transfer analogy can be expressed as Sh/Nu = (Sc/Pr)'d, and when rearranged in terms of the mass transfer coefficient: , h*PD' rSc"" i k=8
-.- (9) ;
RTPg t k Pr, ; i where the log-mean air pressure is defined P i , = (P.,3a- P,i,,g)/In(P,i,3,iu / P,3,,,). Combining these two equations gives the expression for condensation or evaporation mass flux: un , gu , h,M,,P D, AP,, rsc RTPmi,k g Pr, ; With the steam density defined p,,, = M,,,P/RT the mass flux is: . h' ** D, AP,, <scMn [ rh" = k P%, Pr, l Condensation and evaporation mass transfer are calculated from Equation (11) and the appropriate heat transfer correlation from Section 4.2. Three distinct mass transfer correla-tions result from the turbulent free, turbulent forced, and laminar free convection heat transfer correlations. For turbulent free convection mass transfer: p'" D' AP " un I m'"
= 0.13 2
r#E_Sc
- (12) i (v 7 g)ies p ,, p , ,
For turbulent forced convection mass transfer: . Constitutive Fquations for Heat, Mass, and Radiation Transfer March 1997 I m:\3499w.non\3499w c.wpf;1b 031397 - i
4-6 i m,",, = 0.023 " Ref'Sc'd (13) h im. alt i For laminar free convection mass transfer to the drops: l p '"D, AP" un p D' dP,,, AT 'Sc"" l Q = 2.0 'Sc- for small AT -2.0 (14) i d- P , Pr, **d dT P, Pr, The conductances, h, and h , are defined by the energy transfer relationships: _ (15) i rh,"g(h,-h,) - h,(T -T,,,) m ",yh,, = h,(T,,,-T,,) 4.3.1 Dimensionless Relationships for Data Evaluation Equations (8) and (12) for free convection can be cor: tined and rearranged in dimensionless form using the Shenvood number definition: 2 k,,ET,(v /g)'d Pu, ,
'Ap"#ge ln (16)
Sh' = D,, P, p,
- i 2 '
The term (v /g)'/8 has the units of length, so by defining the Sherwood number length accordingly, the simple relationship for the Sherwood number presented in Equation (16) results. Note that multiplying both sides of the equation by L, and dividing both sides by the term (v2 /g)'d produces the more familiar form: 1
- f M /3 8" ' '"""
- 0.13 $ 2 Sc " or Sh' = 0.13Gr'"Sc'd (17)
D,, P, (v /g)t" p 2 t Similarly for forced convection, Equations (8) and (13) can be combined and rearranged as: Constitutwe Equations for Heat, Mass, and Radiation Transfer March 1997 m:\3499w.non\3499wopf;1b4131397
4-7 k RT* D*P'""""
"" 2
- 0.023 Rej'Sc or Sh = 0.023Rej'Sc /3 i
(18) D vaPe 4.3.2 Gas Mixture Property Correlations A correlation for the air-steam diffusion coefficient is available to use in the mass transfer correlation2g
/ 4 81 14.2 psi T II9)
D' = 0.892 ft /hr 2 l P 460 R The temperature in the diffusion coefficient is the absolute boundary layer temperature: the arithmetic mean of the bulk and surface temperatures. The correlation is believed to produce air / steam diffusion values that are approximately 10 percent too high. However, the correlation has been used consistently in the scaling analysis, in the mass transfer correlation validation, and in ,11 GOTHIC. The validation shows the nominal mass transfer rate predictions are slightly less than the measurements, and the bias factors included in the evaluation model for condensation and evaporation further reduce the predicted mass transfer rates, accounting for the net uncertainty. The boundary layer steam mole fraction is assumed to be the arithmetic mean of the bulk and surface values. The dynamic viscosity, thermal conductivity, Prandtl, and Schmidt numbers in the heat and mass transfer correlations are evaluated at the boundary layer steam mole fraction and the boundary layer temperature. These parameters have been evaluated over a range of temperatures and air / steam compositions and are presented in Figure 4-2, Figure 4-3, and Figure 4-4. The mixture properties presented in Figun' 4-2, Figure 4-3, and Figure 4-4 were calculated using the semimmpirical formula of Wilke23, as presented in Bird, Stewart and Lightfoot26, pp 24-26. The properties of steam and air were taken from Kreith, Table A-3. Calculations for mass transfer inside containment use bulk (or system) values of P ,i,a and P,m, and assume the steam pressure at the liquid (film or pool) surface is the steam saturation pressure at the surface temperature. The air partial pressure at the surface is the total pressure minus the steam partial pressure, P, = P - P,,,,,,,. Calevi " , for mass transfer outside containment assume the riser or clumney gas is si his assumption overestimates the bulk gas xeam partial pressure, siru:e it is al .ss than or equal to saturation. The difference is generally small because the bulk saturation press is much less than the surface saturation pressure. The bulk air partial Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997 m:W99w.non\M99w c.wpf;1b-031397
4-8
. j 1
1 4 1 W . P 0.02 l t Q,Qj g ...........................u.................................................................... ,
- - - - - - - - - - - ~ ~ - - - - - - - ~ ~ - - - - - - - - - - - -
@ 0.018- --
=:
4. g 0.017-
---~~~ - - - - - - -NF----------------
e 0.016- --- ----- ----~~- '0E-~~--
.[, 0.015-N 80 F l
- - - ~ ~ ~ - - - - - - - - - - - - - - - - - --------- ------
e 50 F ;
+
0.014- - ~~--------~~-~~ - +2&F---- ~ ~ ~ ~ ~ - - - -- ! i 6
- - - - - ~ ~ - - - - - - - - - - - - - - - - - - - - - - - - ~ ~ ~ -- --
g 0.013
- - - - ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ - - - - - ~ ~ - - - - ~ ~ ~ ~ ~ - - - - - - -
h0.012-O.011 - - - - - - - - - - - - - - - - - - - - - - - ~ ~ - - - - - - - - - - - - - - - - - 0.01 . . . . . . . . . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole Fraction of Steam i l I l Figure 4-2. - Temperature and Concentration Dependence of the Thermal Conductivity of an Air-Steam Mixture 1 Constitutive Equations for Heat, Mass, and Radiation Transfer , March 1997 nue99w.non\He9w<.w;ttt411397 ; 1
)
i
1 4-9 :, F k i 4 4 i e 1.v P 1.5- - - - ~ ~ ~ - - ~ ~ - - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - - ~ ~ ~ - ~ ~ ~ - - - 240 F r 1.4- --- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 210 F , 180 F 1 3- -- --- - - - - - - - - - ~ ~ - ~ ~ - ~ ~ ~ ~ - - ~ ~ ~ ~ ~ ~
- 150 F 120 F .
hg"?j,g . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .... .......................... ... ...... ....... ! h1.1- - - - - - ~ ~ ~ ~ ~ ~ ~ - - -- --- -- - - ~ ~ - - - - - - - - - -
- j. . _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ . __ _ . . . _ . .._ _____
k N ' O.9- ~ ~ ~ - - - ~ ~ ~ ~ ~ ~ - - - - - - ~ ~ ~ - - - - - - - - - - - - - - - 0.8 - - - - - ~ ~ ~ ~ ~ ~ - - ~ ~ ~ ~ ~ ~ ~ - - - - - ~ ~ ~ - - - - - - ~ ~ - 0.7 . . . . . . . . . O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole Fraction of Steam Y
+
Figure 4-3 Temperature and Concentration Dependence of the Dynamic Viscosity of an Air-Steam Gas Mixture < r Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997
.m:\M99w.non\3499w<.wptib4131397
a
- o r 1
4-10 , i
.)
i
~t i
'I.
A
?
I. r
.i 1 ,
120 l 0.9 -- M # # ----~~ - ~~ -- ~~ - --- - - ~ ~ ~ ~ ~ ~ - - 240 F l nen c :
- g. . . . . . . . . . ~ . . . . . . . . . . . . . . . ................................... n........r t M- 120 F
. . . . . . . . . .. Pandtl.Nunbat .. .. .. . ...... .... ... ... ....... ... .. . . ... . . . ..... .. . ... ... . ...... .
.Q 07 I
l Z ! 0.6- - - - - - - - - - - - - - - - ~ ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ', 0.5-120.F...........
- --=sssus :;;c~ ~ ~
Schmidt Number 240 F b 0.4- - - - ~ ~ ~ ~ ~ ~ ~ - - - - - ~ ~ - ~ ~ ~ ~ ~ ~ ~ - ~ ~ - ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ ~ jo3 . c 0.2- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - - - - - ~ ~ ~ ~ ~ ~ - - - - - - - Qj- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t i C . . . . . . . . . ~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 j Mole Fraction of Steam 1 l t 1 1
- Figust 4 4 - Temperature and Concentration Dependence of the Prandtl and Schmidt l Numbers for an Air-Steam Mixture Constitutive Equatkes for Heat, Mass, and Radiat.on Transfer Mah 1997 m:\M99w.sen\M99w-c.wpf It>.031397 l
1 i i i
1 4-11 pressure is calculated P,a = P,, - P,,ma where P, is 14.7 psia. The partial pressure of the ; evaporating surface is assumed to be the saturation pressure at the liquid surface temperature, and the surface air partial pressure is calculated P ,a = P,, - P,,,,, where P., is 14.7 psia. 4.4 CONDENSATION AND EVAPORATION ENERGY TRANSFER The energy transferred by condensation and evaporation mass transfer is the product of the mass transfer rate and the enthalpy transported. For condensation, the condensed mass leaves the gas control volume with gas enthalpy, h,, and the condensate retains the liquid l enthalpy, h,. The difference, h,- h, is greater than h,, since the gas temperature is generally ; higher than the liquid temperature. For evaporation, the evaporated mass leaves the liquid surface at the liquid surface temperature, so the enthalpy change is h,,. Using the subscripts m for condensation mass transfer and mx for evaporation, the corresponding heat transfer rates in terms of conductances are: l 4" = h,(T,g -T) and q", - h,(T,g -T) (20) Thus the conductances are defined in terms of a temperature difference and an energy flux determined from the relationship 4" = rn"(h, - h,), where In" is determined from the relationships in Section 4.3. l 4.5 LIQUID FILM CONDUCTANCE l l Although the film flow rates vary considerably both inside and outside containment, a j detailed evaluation27showed the films quickly achieve a thickness of approximately 0.005 j inches, and.do not increase much thereafter due to the cube root dependence of thickness on i flow rate. Therefore, the conductance through both the inner film (if), and the extemal film (xf) can be adequately modeled for the scaling analysis using a constant mean film thickness l of 0.005 inches, and a thermal conductivity value for water of 0.38 BTU /hr-ft.-F. The conductance is determined from: h,= h,,= k/S (21) Since the resulting conductance value is 912 B/hr-ft.2-F, approximately 10 times greater than the limiting conductance from the gas to the surface, the error introduced by this approxima-tion is not significant. i l i Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997 m:W99w.nonW99w-c.mpf-1b.031397 ,
, - - - - , . , . n . . . . ~ 1 -. e a .-. a., x.-a...- 1- x- .s- +
l 4-12 4.6 HEAT SINK CONDUCTANCES The conductances for the heat sink energy equations presented in Section 7 are determined from the constitutive correlations presented in Sections 4.1 to 4.5. The correlations for the individual and combined conductances are presented in Section 7.2. 4.7 CONSTANT PROPERTIES i The water, steel, and concrete density, thermal conductivity, and specific heat are approxi-mated as constants. The liquid film thickness is approximated as a constant as discussed in Section 7.4. The heat sink thicknes; is a constant that is defined by the' total volume divided by the total surface area. The values of these and other constants are defined below. Water density p, = p,, = 60 lbm/ft.8 ' Water thermal conductivity k, = k,, = 0.38 BTU /hr-ft.-F Water specific heat c.,, = c,,,, = 1.0 BTU /lbm-F
- Steel density p,s= p,s , = 488 lbm/ft.8 Steel thermal conductivity k,, = k,,, = 26 BTU /hr-ft.-F ,
~ Steel specific heat cy ,, = c ,,,, = 0.11 BTU /lbm-F : Concrete density p, = pu, = 140 lbm/ft.8 Concrete thermal conductivity k, = k,= m 0.83 BTU /hr-ft.-F , Concrete specific heat c., = c.,, = 0.19 BTU /lbm-F
- Water film thickness 5= S, = 0.005 in. ;
Steel shell thickness 8,3 = 5,3, = 1.625 in. Steel heat sink thickness 6,, = 6,,,, = 0.40 in. 4 Radiation constant o= o, = 0.1714x10 BTU /hr-ft.2 R' Emissivity c= c, = 0.9 , Containment volume V, = V= 1.74x10' ft.8 l Figure 4-4 shows the Schmidt number is nearly constant at approximately 0.51 over all air-steam concentrations, so Schmidt Number Se = Sc, =0.51 i I i I i
- Constitutive Equations for Heat, Mass, and Radiation Transfer March 1997 j m:\3499w.non\3499w.c.wpf:lt@l397 l
5-1 i i 5 GENERAL RELATIONSHIPS FOR SCALING EQUATIONS . Assumptions and relationships are developed that are used in subsequent sections to develop the rate of change equations for the gas control volume mass, energy, momentum, and j pressure. 5.1 ASSUMPTIONS ; The following assumptions, combined with classical thermodynamic relationships, were used to develop the scaling equations:
*. The mass of the gas mixture is the sum of the individual air and steam masses: m = ;
m i, + m,..
. The gas species are in thermal and mechanical equilibrium - each volume has one -
temperature and total pressure. ) i
. The intemal energy of the mixture, U, is the sum of the individual air and steam intemal energies, that is, there is no reaction between the two: U = mu = m ,,u,i, + ,
m, u,.. The energy reference datum for air and water, where the internal energies are zero, is 32'F. The thermodynamic properties of air and steam in the containment gas mixture are defined by the partial pressure and temperature of each gas. The Dalton rule for additive partial pressures: the total pressure is the sum of the air and steam partial pressures, P = P oi , + P,.. Air can be approximated as an ideal gas due to high reduced temperature and low reduced pressure (T, > 2 and P, < 0.11). Thus P.,,V = Z,i,m ,,R.,,T where the compress-ibility factor Z,i, = 1. (Later in this analysis the containment is assumed to be well-mixed, resulting in a maximum air partial pressure of 20.6 psi at the containment design pressure. At 20.6 psi, the air pressure ratio is 0.038). l I Steam is a real gas with equation of state P, V = Z, m,,R, T where the compress-ibility factor Z,. = Z, (P,,,T). Steam properties are from steam tables. There is no liquid-vapor phase change within the gas control volume. Phase change occurs after the gas passes out of the gas control volume. Exterisive properties are defined in terms of the gas mixture P, T, m ,, and m,.. Intensive properties are defined in terms of P, T, and the steam mass concentration, C. l ] i i l General Relationships for Scaling Equations - March 1997 I mA3499w.non\3499w<.wpf;1b431397 ' l l
I 1 l 5-2 , I i 5.2 GAS MLYTURE RELATIONSHIPS The gas mixture relationships required to develop the conservation equations, and to evaluate the resulting pi groups are first defined. The gas is a mixture of air and steam with a relative concentration that may range from pure air to predominantly steam with little air - present. 5.2.1 Mass On a mass basis the mass of mixture is the sum of the masses of the individual gasses: m = m,, + m,, (22) ,
- On a molar basis for a non-reacting mixture, the number of moles of gas mixture is the sum of the moles of individual gasses:
n = n,, + n,, (23) ; 5.2.2 Molecular Weight Because the number of moles is defined n = m/M, the mixture molecular weight can be defined from (23): ; m , m,, m"' so M= '" '" (24) M M, M,, m,,/ M,, + m,,/M,, 5.2.3 Gas Constant The mixture gas constant can be determined from (24) and the definition of the gas constant R = R/M E (m,,/M,, + m,,/M,,) m,R,, + m,,R,, R= so R. (25) , (m, + m,,) m
)
r I General Relationships for Scaling Equations March 1997 m:\3499w.nop\3499w<.wyf:1bO31397
]
x -
.f .
~
..5-3 'l
?
y Defining the steam concentration C = m,./m, the air concentration is (1 C), so Equation (25) j can be written: , j
, ;3 ' R' = . (1 -C)R, + C R. .
(26) L j L l 2 5.2.4 ; Enthalpy; The mixture enthalpy can be derived from the definition of enthalpy, H = mh = mu + PV, i
. the intemal energy of the mixture, mu = m u + m,u, and the Dalton rule, P = P. + - ,
j i P,.: -j u l m h = m ,u , + mo, u
. + P,V + P,,V j m h, + m**h ' "
(27): : so- h= or h = (1 -C)h, + Ch,, j m a The gas mixture total enthalpy, H = mh = m,)t, + m, h,. is a function of the four indepen- l dent variables P, T, m., m,..- The derivative of H can be written: i l r Bh Bh d(mh) = m g dT + m g dP + h am* dm, + h, am, dm,,
, (28) ,
Bh ! so d(mh) = me,dT + mgdP + h,dm,g + h,dm. Examination of the steam tables shows that along the saturation line from 38 to 42 psia', Ah = l 1.9 B/lbm, while c,AT = 3.0 B/lbm and (Bh/BP)AP = -1.1 B/lbm. Although containment I pressurization does not follow the saturation line exactly, it does follow with, at most, a
- modest superheat. Consequently, the rate of change of enthalpy due to pressure is ,
approximately -1/2 of the total, while that due to temperature is 3/2 of the total. Clearly, the l
- e pressure derivative of enthalpy may be substantial, and thus may contribute to pressurization. The presence of air inside containment will soraewhat reduce the magnitude
, of the enthalpy rate of change with pressure. From thermodynamic relationships, the partial derivative of enthalpy with respect to pressure can be written" in terms'of a temperature derivative: Bh- &v - (29) W = .v - TW-
.With the equation of state v = ZRT/P, and considering Z and v to be functions of the l x - independent variables P, T, and C, the pressure derivative of enthalpy is:
q General Relationships for Scaling Equations ,
,,,_ March 1997 l m:\3499w.non\3499w<.wpf-1tHB1397 - j s, <
iN , ;: g i' '1 r , gg,
5-4' ; I Bh
-=v-T
'RT aZ+ ZR' so Bh - -T_v BZ W) i i
~5P P BT P BP Z BT_
r i r With this expression and the abbreviation Zr = (T/Z)(BZ/BT), d(mh) can also be written: i T (31) d(mh) = me,dT - VZ dP + h,,dm, + h,,dm,, 5.2.5 Specific Heat The mixture constant pressure specific heat can be derived by taking the partial derivative of : mh with respect to temperature, and noting that the masses are not functions of temperature: a a Bh i 7(mh) = g(m,,h, + m,,h,,) so mg = m, g Bh " + m,, Bh g m*cPh +m 82 cPAM and c, = or C p= (l -C)Cpj, + C C,,, A similar approach can be applied to the intemal energy to derive the mixture constant volume specific heat: m* c". + m* *c " or (33) c, - c, = (1 -C) C,, + C cy ,, m From the definition of the constant pressure and constant volume specific heats, and the definition of enthalpy: ; I"*
-c'= b
" ) " f )
e so c-c= 04) P BT W= BT -W P ' BT Substituting the equation of state, IN = ZRT: i c-c= P ' B(ZRT) = ZR_BT+ RTBZ so cP - c =
' ZR(1 +_T BZ)
_ (35) BT BT ST Z BT i General Relationships for Scaling Equations March 1997 l m:\3499w.non\3499w-c.wpf:1b-031397 l
)
l l
5-5 With the substitution ZT = (T/Z)aZ/BT 7 (36) c, - c, = Z R(1 + Z ) With the specific heat ratio y = c,/c ,y the ratio c /ZR p can be expressed: P, , Y T - (37) ZR (y -1){} +3 ) 5.2.6. Gas Compressibility
;The gas mixture compressibility, Z, can be derived from the Dalton rule and the equation of state:
T (33) P = P,, + P,, and P =' so Zn = (Zn), + (Zn),, Deleting ET/V from each term and divide by n: Z= * * + "'" '* (39) n With nE = mR, Equation (39) can be written: ZmR = Z,,m,, R, + Z,, m,, R,, or ZR = (1 -C)Z,,R,, + CZ,,R,, (40) The derivative of ZR is: (41) d(ZR) = -Z,R,,dC + (1 -C)(Z,dR, + R,dZ,) + Z,,R,,dC+C(Z,,dR,, + R,,dZ,,) i I General Relationships for Scaling Equations Mmh 1997 m:\3499wam\3499ww:.wpf.1M31397
.t-
54 The vahies of Z,i,, R , and R,. are constants, so Equation (41) can be simplified to: d(ZR) = dC(Z,,R,,-Z,,R,) + CR,,dZ,, (42) Whereas the concentration, C, can range from 0 to 1, Z,. is limited to the range 0.97 to 1.0. Therefore, the derivative dZ,. can be neglected and dZR expressed: d(ZR) = dC(Z,,R,,-Z,R,) (43) The property 27, where Z 7
= (T/Z)3Z /BT, can be expressed in terms of .ZT , and7 2,. with Equation (39):
- n. n T BZ T n ** '" T n,, BZ, (44)
~Yn YW ~ Y BT BT since n, n.,,, n,,, and Z, are not functions of temperature. With the substitution Z,.n,o/Zn = P, /P:
T n,, BZ,, Z,, n., T BZ,, 7 Zn BT Z n Z,, BT P"Z"=Zr P ' (45) T For steam at 40 psi and 280*F the magnitude of Z ,. is 0.13. Consequently, the temperature derivative of the compressibility factor may be significant. - 5.3 EQUATION OF STATE Starting with the equation of state, T = PV/ZmR, and differentiating: dT = T 'd(PV) _ d(ZR) , dm' (46) PV ZR m j Substituting Equation (43) for d(ZR): General Relationships for Scaling Equations March 1997 mA3499w.non\3499w <*pf1b 031397
l 5-7 dT = T d(PV) _ (Z,L R,, -Z,,,R,)dC _ dm (47) PV ZR m, l Or,in terms of the individual air and steam masses:
< 8 i
_ Z ,R ,1,d m ,, Z,, R,, dm,,, (48) j dT = T d(PV) - PV ZRm ZRm , i 5.4 RATE OF CHANGE OF INTERNAL ENERGY j The total derivative of the gas mixture internal energy can be expressed in terms of enthalpy and pressure: F (49) d(mu) = d(mh-PV) = d(mh) - d(PV) l Substituting Equation (31) for d(mh): T (50) d(mu) = me,dT - VZ dP + h,,dm,, + h,,dm,, - d(PV) i Now substitute Equation (47) for dT: ; d(PV) (Z,.R ** -Z .'"R ",)dC - dm - VZ dP T
+ h .'"dm '" + h* *dm* * - d(PV) d(mu) = mePT - l PV ZR m (51) <
Substitute PV/ZR for mT and combine coefficients on d(PV): ! l r ,
- c cPV (Z ,Rstm -Zan. R e a )gg , dm d(mu) = (-.1-1)d(PV) - P
_ ygTgp + h' ;'dm'" . + h dm < ZR ZR ZR m, '152) ** , i l General Relationships for Scaling Equations March 1997 , mA3499w.non\3499w<.wpf:1b431397 l t I
?
5 '
)
Substitute Equation (37) for c,/ZR and combine dP terms: j T d(mu) = (1+F)VdP + II*T IPdV y(1+Z )py Z,,R,,-Z,y dC (Y -1) (Y -1) (Y -1) ZR -(53) ! T y(1+Z )py dm (Y-1) m + h A" + h "dm " i Or in terms of air and steam mass, instead of total mass and concentration: [ 4 d(mu) = II*2 I VdP + II*7 I PdV III* IP V" (Y -1) (Y -1) (Y -1) ZRm'"dm"". (54) ! T
)PV "dm,, + h,,dm, + h,,dm,,
i With the relationships PV/ZmR = P,,V/Z,m J., = P,,V/Z,,m,,R,,: , r i IVdP + II
- 7 III* I d(mu) = II* I PdV P,Vdm* *
(Y -1) (Y -1) (Y -1) (55)
) P,,Vdm,, + h,,dm,, + h,,dm,,
(_) i i I l i 1 l General Relationships for Scaling Equations March 1997 m;\3499w.non\3499w<.wpf:1b 031397
1 6-1 6 CONTAINM'ENT GAS ANALYSIS AND EQUATIONS FOR f SCALING The parameter of primary interest for this scaling analysis is the containment gas pressure during transients. The pressure <.ulution requires consideration of mass, momentum, and energy transport, as well as an equation of state and constitutive relationships. , Consequently, the time constant and pi groups for mass, momentum, energy, and pressure scaling are developed and quantified. The assumptions and mathematical techniques used to ; quantify the scaling relationships are presented. ; i A containment gas pressure relationship is desired that couples the gas volume to the break source and heat sinks. Because the film retains a significant fraction of the energy transferred , by condensation, the liquid film must also be considered when the contamment gas is coupled to the heat sinks. The control volume equations that are used to model mass, energy, and pressure require a sign convention to distinguish between influxes and effluxes. The approach followed , consistently in this analysis is to assume a flux direction and assign it a positive sign if it ; flows into the control volume or a negative sign if it flows out of the control volume. In most equdions the direction of fluxes of mass, energy, and momentum are assumed and the - assignment of a sign imparts a greater level of information to the equation. When this . I appmach is followed consistently throughout the analysis, an incorrectly assumed flux direction does not cause an error in the solution. ; 6.1 MASS CONSERVATION EQUATIONS INSIDE CONTAINMENT ; Conservation of mass applied to a control volume can be stated as "the rate of change of mass in a control volume is equal to the sum of the mass fluxes in and out of the control volume." The equations for conservation of mass are developed and then made ; dimensionless and normalized. The time constant and pi groups are defined and quantified. ; Both the mass of gas (air and steam) and the me.ss of liquid water must be considered to develop the equations necessary to solve for the rates of change that are of interest for AP600 containment pressure scaling. 6.1.1 Containment Gas Conservation of Mass l l The conservation equations inside containment are written for a gas control volume with multiple convective flows from adjacent volumes (i subscripted), multiple heat sinks ; (j subscripted), and a single steam break source, although flow from a sink can be considered l 1 l Containment Gas Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w<.wptit431397
]
i
- 6-2 i
the same as a source. Conservation of mass can be applied to each gas species (air and steam) with the result:
- b IIlmr; and = g,, + { m,g - [ rh,g (56)
The index j represents condensation or evaporation steam mass transfer terms corresponding to the heat sinks listed in Table 6-1. Positive flows are into the control volume and negative flows are out. The air and gas mass equations can be added to produce the equation for conservatbn of the containment gas mixture mass:
" ~
d 'k d "3 *J Table 6-1 Types of Ileat Sinks Considered in the AP600 Containment Pressure Scaling Analysis Index - J Description Abbreviation 3 1 Wops d 2 Break Pool p 3 Steel heat sinks st 4 Concrete heat sinks cc 5 Steel-jacketed concrete je 6 Subcooled shell ss 7 Evaporating shell es 8 Dry shell ds 9 Baffle bf 10 Chimney ch j l l For the AP600 scaling analysis the assumption is made that containment is well-mixed, so j there are no intercompartment convection terms (the i subscripted terms vanish). The basis ! for this assumption was discussed briefly in Section 1.0. The resulting equation is: dm " dm dm "
=0 so = '
= g,, - [ rh,g (58)
Contamment Gas Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w c.wptit> 031397 L- . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ . . _ _ - . . _ _ _ _ _ _ . _ _ _ . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
6-3 All variables are made dimensionless by dividing by the initial value of the variable for the time phase under consideration. The DECLG transient has four time phases that are shown in Figure 3-4 and discussed in more detail in the PIRT S In general, the initial value of each variable differs for each time phase. Steam and air mass and flow rate dimensionless variables are defined: Containment gas mass m = mo m' Containment gas volume V = VoV* Containment gas density p = pop' Time t = T t' Break steam flow rate m g3,i = s 3,k,o#ghru g Break steam density pork = Pork.oP*ghrk Heat sink j steam flow rate rh,,m,3 = m,,mpm',,,,, The conservation of gas mixture mass equation, Equation (57), is made dimensionless by substituting these relationships and normalized by the reference break source term, mp,k,o as follows: mo dm* mg ,g , m,,,3 , E* ghrk.o T dt m rk.o j mg brk o dm* " m.t mhrk ghrk m,) sim,l g. Where T= *'" K = K " " m mbrk m.l ghrk o O ghrk.o ghrk.o 6.1.2 Containment Iiquid Conservation of Mass Conservation of mass can also be applied to the liquid that forms part of the gas control volume boundary. The changing volume of liquid does work on the containment gas by compressing the control volume boundary. The gas control volume excludes the volume upstream of the break, so the liquid released from the break displaces gas in the control volume. Thus, the liquid stored in the piping, heat exchangers, pressurizer, reactor, pumps, accumulators, and core makeup tanks (CMTs) displaces containment volume,if released from the break as liquid. During a LOCA transient, after the passive reactor cooling system depressurizes the primary system to contamment pressure, the in-containment refueling water storage tank (IRWST) drains by gravity into the reactor vessel, then out the break. Since the IRWST is open to containment, its liquid flow into the reactor is an outflow, whereas the break flow is an inflow. Containment Gas Analysis and Equations for Scaling Much 1997 m:\3490wmon\3499w-c.wpf:lt@l397
6-4 The total liquid mass that displaces gas volume includes the masses of the IRWST, break pool, drops, and liquid films. These are the liquid masses that displace gas in the containment volume, and cause the containment pressure to change. The rate of change of liquid mass is the sum of the flows of break liquid to the pool, break liquid to drops, condensation on heat sinks, minus the flow out of the IRWST: 1 dm I
~ ~ "
dt IMP f.brk,d snN i Where rty is the net liquid flow rate that displaces containment volume. The evaporation i' rates from the pool and drops appear as negative flow rates in the summation over the heat sinks. The break pool, break drops, IRWST, and heat sink liquid mass flow rate terms can be quantified for each time phase of a DECLG with the following assumptions. The total break flow rate for each time phase is determined from the break liquid flow rate curve in Figure 3-2. The blowdown value is the time average over blowdown, while the other break flow rates are read from Figure 3-2 for the beginning of each ; time phase. The drop flow rate, as discussed in Section 7.1, is 1/2 the break gas flow rate during blowdown and zero thereafter. The break flow to the pool is the total break liquid flow minus the drop flow.
. During blowdown the condensation rate on all heat sinks is a small fraction of the ;
break steam flow rate (see pi values in Section 7.10), and the break steam flow rate is l less than the break liquid flow rate. Thus the condensation rates are neglected. l The IRWST flow is zero during blowdown, refill, and the early portion of the peak pressure phase, since the RCS pressure is too high to allow the IRWST to gravity : drain. By the beginning of the long-term phase, the IRWST is the only source to the break, so thm = rtys + rh,u, and riy = 0. ) l
=
After blowdown, the pi groups are evaluated at inflection points on the containment I pressure curve, so dm, /dt = m,a - I rigy = 0. Thus, the break gas flow rate is approximately equal to the sum of the heat sink mass flow rates. Thus, rh,a = I m,,q. Containment Gas Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w<wpf IMl31397
l 6-5 f From these considerations, the rate of change of the liquid mass is presented for each time phase in Table 6-2. During an MSLB the total mass of gas released to contairunent, when condensed to liquid, has a volume of approximately 4000 ft.8 Expressed as a fraction of total containment gas volume, AV/V = 0.0023. Consequently, work due to gas volume change during an MSLB is similarly small and is neglected. The MSLB average flow rate for the first 600 sec of the transient is 367 lbm/sec, from Figure 3-5. Table 6-2 Liquid Flow Rates Contributing to Containment Pressurization Break Break Break Break Time Gas Liquid Pool Drops IRWST Condensed rit, Phase Ibm /sec lbm/see Ibm /sec lbm/see Ibm /sec lbm/sec lbm/sec ng Blowdown 4444 7777 5555 2222 0 neglected 7777 1.75 Refill 200' 0 0 0 0 0 0 0 Peak Pres 200 200 200 0 0 200 400 2.0 Long Term 45 200 200 0 245 45 0 0
- 1. A value of 200 lbm/see was assumed to provide a denominator for scaling during refill.
The net liquid mass flow rate, riy is made dimensionless with the substitution m, = rg, riy*, and scaled to the mass flow rate of break gas: m' . m m,* so ng - m'" (61) g,brke g.brk.a g.brLo l The mass pi values presented in Table 6-2 for blowdown and peak pressure are relatively large numbers, so it is reasonable to consider evaluating pi values for each of the j heat sinks and each of the mass ficw raie terms comprising the net liquid flow rate. However, when the energy and pressure equations are scaled (Section 8.0), the work term associated with the liquid rate of change is shown to be very small, so it is not useful to further subdivide an I already small term. Hence, only the net liquid mass flow rate term will be used to represent the liquid rate of change. l Containment Gas Analysis and Equations for Scaling March 1997 m:\3499w.nce\34%w<.wptit4131397
l 6-6 l 1 613 Inner Film Liquid Conservation of Mass A mass conservation equation can be written for the inner liquid film that forms on ; structure j. The rate of change of film mass is the condensation rate minus the film drain ! rate: dm (62) d4 , m**J_ g " "d dt I This equation is examined further in Section 7.4. 6.2 ENERGY CONSERVATION EQUATION INSIDE CONTAINMENT , Conservation of energy for a control volume can be stated as "the rate of change of internal - energy in a control volume is equal to the sum of the enthalpy fluxes and heat transfer in i and out of the control volume, and the work done on the control volume." Conservation of energy for the control volume encompassing only the containment gas relates the rate of
- change of gas intemal energy to the enthalpy of the break source, the sum of the air and -
steam convective flows from other volumes, the sum of the condensed steam enthalpy flows to each heat sink, the sum of the heat transferred by radiation and convection to each heat
~
sink, and the compression work done on the gas by a change in the volume of the control volume. These terms are presented, respectively, in the containment gas energy equation, where the sign on each term represents the assumed direction of flow: d(mu) ~ ^ dV
~ *d*
~
dt #^ **d **d **d '** "4 **J dt where hga is the total break steam enthalpy, hg a = h + v 2/2 + gz. Elevation is negligible, as ! is v 2/2 for all but the break source during blowdown. (Post-blowdown, v < 200 ft./sec, so 2 v /2 < 0.8 BTU /lbm.) ; Since the total containment volume is constant, the sum of the rates of change of the gas and liquid volumes must be equal, or dV/dt = -dV,/dt. With an approximately constant liquid ensity, dV,/dt = dm,/p,dt = rh,/p,, so the term PdV/dt can be expressed as -(P/p,)rn,. Thus: d(mu) dt
~
@^ @* ""> '"d **d **
~
**4 **4 *W*[p' .
i Containment Gas Analysis and Equations for Scaling March 1997 I mAM99w.non\M99ws:.wptib.031397
6-7 An energy equatix is desired that relates the rate of change of energy stored in the gas atmosphere to the heat input to each heat sink. The heat input to the heat sink is used in Section 7 to model the individual heat sink thermal performance. However, the energy out of the gas differs from the energy into the solid by the amount of energy retained by the film. The liquid film lies outside both the gas and solid heat sink control volumes. With the substitution h,% = h,w - h a+ h , yEquation (64) becomes: (65) d(mu) p
~ ~
dt #^ **J *"d * **d ** ** 4 ** 4 ' This energy equation now includes a term for the gas-to-liquid enthalpy difference that is equal to the energy transferred into the solid heat sink, and a term for the energy carried away by the liquid film that is defined by m,m,ha. When the condensation or evaporation is on a pool or drop, the liquid film is indistinguishable from the other liquid, so the terms are combined. This equation is still not optimal for scaling, since the enthalpy and internal energy are both measured relative to the triple point of water. This bias can be eliminated as follows: The gas mass is the sum of the air, and steam masses: m = m,, + m,,, and the gas specific intemal energy is: mu = m.,u,, + m, u . With this definition, a muumum energy reference datum, uom, can be defined that corresponds to the system with the specific intemal energies of water and air at the same temperature and pressure. That is, mu, = m ,u,y,,
+ m,,,u, . Note that although u u,, and u, are constants, um , is not constant since the air and steam masses change with time. The time derivatives of the gas internal energies i can be written:
d(mu) d[m(u-u )] d(mu ) d[m(u-u )]
+ ,
+u.' " " ." dm,, + u* *** dm,, (66) dt ,
dt dt dt dt dt With these derivative expressions and the definition of enthalpy, u = h - P/p, the gas energy equation can be written: d[m(u - u )] ' dt @^ @* **"" *"> *"d~ "" * **J **> ** (67) P**"" dm. P """ dm* * + p m, Is.w(h,w-h ig) + m, (h y -h,,,) + g ) + . **+ ' _P.,,, P P, I Containment Gas Analysis and Equations for Scaling March 1997 mA34%.non\3499w-c.wpf-1t>431397
6-8 , 1 In this form the energy equation represents the change in intemal energy relative to a minimum energy reference condition. For AP600 scaling, a single volume is considered, so the i subscripted terms and the term dm,/dt vanish. The heat transfer into the heat sink can be expressed in terms of conductance as q, = h,A,(T - g T ), where T,3 is the liquid fihn free surface temperature on heat sink j. The minimum energy state will be selected as the intemal energy of water at the initial temperature, T,. The internal energy and enthalpy of liquid are equal, and P, is zero for liquid, so the energy equation is: d[m(u-u . )] p
~
dt #' *' '#- ' (68)
- E Is..a(h,g -h )ya+ m,g(h,3 -h,,,) + h, A,(T -Tg) }
8 This equation shows the rate of change of internal energy is equal to the break steam enthalpy flowing in, plus the work done on the gas, minus the enthalpy that drains out of the films, minus the heat transfer into the heat sinks, minus the energy sto. red in the films. The term 4 = h A,(T - T m 3
) also appea ., in the heat sink energy equations, where it is further separated into terms representing convection heat transfer and radiation heat transfer as described in Section 7. Equations (65), (67), and (68) are used for all subsequent containment gas energy scaling.
Many of the mass and flow rate variables required to make the energy equation dimensionless were defined under mass scaling. Additional variables are defined: Containment gas mass m = m om* Containment gas volume V =Vy Containment gas density p = pop
- Break steam density p p ,g = pp,up*p,6 Time t = t t*
Break steam flow rate mp,6 = mp,um*p,6 Gas mtemal energy diff u-u. = Au,u' Contamment gas nuxture u - u,,, Break steam enthalpy diff h p ,5- h,,, = Ahp,uh*g,i reak B steam h,- liquid h, at T. Pressure P = P,P* Heat sink j: Steam flow rate m,m, = m mpm*,3 Gas-film enthalpy diff h,,,- hy = Ah,,ph *,,3 h, of steam j - h, of inner film j Film enthalpy diff ha- h,,, = Ahyph*n h, of inner film j - liquid h, at T, j Heat trans coef hp = h,wh*g radiation + convection (h,3 + hq) ! Heat transfer area A, = Ag ,A*, Gas -liquid surf temp diff T-Tg = (T - Tg),AT*g Contamment Gas Analysis and Equations for Scaling March 1997 m:\M99w.non\3499w-c.wpf;1Nm397
l 6-9 Substitutions are made to the conservation of containment gas energy equation to make it dimensionless, and the equation is normalized as follows: m,Au. d(mu)* ,_ sprk., Ah,y, , , P,s,, , , Nghrk, Ah,3,,,t dt* s g,uAh p ,g p,,mp,uAhp ,,,t
, stm4o stmam g . + "' **" " i*
sghrk,o Ah sbrka "'ih"*"d sghrk.o dd" s
- I ddd* h * + h"4A 9 3
- AT d *d I ghr's a mghrk.o&ghrka j K'
d
" X
# 6
~
'# 8d *d "4 "d "4 dd 'I ' '
where: Au P Ki "E m. g ' E. Ark " 1 K.;. work
* "m.: P o[shrka ghrka i (70)
Ah,g, Ah,3, h,,, Ag(T-T,,3) K ..rga " Kma 3 E ua " Ema g E qa " g g ghrk.a g.bi k.o <, brke shrke 6.3 PRESSURE EQUATION INSIDE CONTAINMENT Press are scaling requires the steam partial pressure, and when heat sink transport is considered, the air partial pressure is also required. With the well-mixed assumption discussed in Section 1.0, there is only one bulk value of P,,,, and one value of P,i, at any time. The air density is always constant at the initial value, so the air pressure is proportional to the absolute temperature. The steam pressure is the total pressure minus the air pressure: T P,, - d* P,i,, P,, - P - P,, (71) Labs 6.3.1 Rate of Pressure Change (RPC) Equation An RPC equation can be written by combining the equation for the rate of change of internal energy, Equation (55) with conservation of energy, Equation (64): l r 7 T (1 +Z ) V h8 ** - *h * + y (1 + Z +) m'7 P,, (1 n z T) p ; dt dP - m ** (Y -1) 8 (y -1) p, (y -1) p, i _ {7g sim.i h,,, -h,, + y(1 + Z T) P- h,, '
'" A,(T -T,)
l l Containment Gas Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w cwpf:lt> 031397 l
6-10 6.3.2 Normalized, Dimensionless RPC Equation Dimensionless variables used to make the RPC equation dimensionless are: Containment steam mass m,,, = m,,,,m*,. Time t = t t' Net liquid flow rate rit, = m,,m*, Heat sink j steam flow rate s, 3 = s, gs',% Heat sink surface area A3 = AA* Containment to liquid surf temp diff (T-Tus)
= (T-Tg3),AT*,;
Combined rad + cony heat trans coef h, = h,,h,' Cond/evap energy transfer coefficient hm = hm,hm
- Effective energy transfer coefficient h, = h,,h,*
Gas volume V = V,V' Break steam flow rate riig,u = mora,s*p,6 Break-bulk steam enthalpy difference (h,3,u - A,m) = %3,u-h,,m),& 3,6 Condensate enthalpy difference (h,% - h,,m) = (h,%-h,,m),Ah',% Bulk steam density p, = p.,p *,im Compressibility function (1+Z ) T = (1+ZT ),Zr. Specific heat ratio y = yf Specific heat difference (71) = (P 1),f. Total pressure P = P,P' Steam partial pressure P,,, = P,,,,,P*,,, The RPC is made dimensionless by substituting the expressions for the dimensioned variables defined above, and is normalized by dividing each term in the RPC by the T reference break gas work term, yo(1+Z )/(y-1), so ,u, (P,,m/p,,m). The following sections present the normalization, dimensionless substitutions, and pi groups that result for each term of the RPC. 6.3.2.1 Pressure Term (y -1), p, (1+Z T
)yg , (y - O, p ,,,, W ), P y y. P,d{
y,(1+Z'),mp ,u P,,,,, (y - 1) dt y,(1 +Z '),spg P,,,, (y -1),y
- t dt" Z T* V
- dP '
" " PM gg.
7+ Containment Gas Analysis and Equations for Scaling March 1997 m:W%.non\34%<.wpf:1b431397
6-11 where: g 1 P.im, P, i P, p ,, _ V, pg , , Yo Pghrk.o stme Yo .tm.o Po D ghrk.o 6.3.2.2 Break Source Gas Term The first term on the right side of the RPC represents the break source steam enthalpy and work. The dimensionless substitutions and normalization give: (75) 7 (7 ~1). y y,(1 g ra,m ,PP,, .im.* 8 * **#^ h "b (1 (y
+ Z ) P,,
-1) p ,,
g rh,3,,,rhl3,, _ (y 1 , p ,,,, ,
, (y -1), p,,,,, y,y *(1 + Z r) gr. p _p ._
rhp,,,, T S'"" "* ** y,(1 +Z ), P,,,, T y,(1 +Z ), P,, (y -1),y
- p ,,p ,*,_
" 8,.shru is&l3,um ;,,, + x y. ,,,,,,,,,Y* g TP** mg 7., P.,im where:
x p.g,,, (hg ,-h,,),(y -1), p,,
= and x,,g,3,, - 1 (76) y,( ,), , , , ,
6.3.2.3 Net Liquid Work Term The break source liquid displaces gas from the containment volume, and hence, does work on the containment gas. The normalized, dimensionless term is: (y -1), p,, rh,y (1 + Z7 ) p = y,(1 +Z '),rhp,g P,,,,, (y -1) p, 7 rh,,rn,' (y -1), p,, y,(1 + Z ),y
- Z *T P,P
- g rhp,,, y,(1 +Z T), P,,, (y -1),7
- p ,,
, , _ , r? rh, e-7 Containment Gas Analysis and Equations for Scaling Much 1997 m\3499w.non\3499w<wpf:lt@l397
6-12 where: m,, p ,,,, P, , p ,, P, (73)
, f,p,work m.f psame ghrk.o b i,o p,tme O f4 l
6.3.2.4 Condensation / Evaporation Phase Change Terms The second line of the RPC, Equation (72), represents the energy transfer associated with the heat sinks, and, because it is unwieldy, will be separated into phase change mass transfer , and convection / radiation heat transfer terms. The mass transfer (the steam that flows ] between the containment gas and the heat sinks) includes terms corresponding to enthalpy and gas flow work:
} ** (79) <
rh *4
' (h*J-h
* ' ") +(yTII -1)
- p, The enthalpy and work terms are normalized by the break enthalpy flow rate, and made dimensionless as follows:
(80)
/ T (Y - 1). ) '"
T P,*" rh '"4(h*
' *d-h '") + TII *
=
y,(1 +Z ),rn, P,m (y -1) P,q rh, rh,*,4 (y -1), p,,, , (y -1), p,, y,y *(1 +ZT ),ZT
- P,,P,('
**4 "' '""d rh,,, rh * , y,P +Z 7), P,,
, y,(1 +Z T), P,, (y -1),y
- p ,, p ,'
, th,*,3 7 zr . P,;
,g p,enthJ th,* 3 g.tm, J.g
. p,workj .
g,Frk ghrk Tm. b a.tm where: K ,w " Km =4 y,(17),[pD.(y -1)? N
,tm, 44.im). E , orka " Ep m a The enthalpy to or from the heat sink, h,tma and the value of risw needed to calculate x m,,%
can only be determined after calculating the heat sink temperature. This evaluation is performed in Section 7 for each heat sink. 6.3.2.5 Convection and Radiation Heat Transfer Terms The energy transferred between the gas and the heat sinks includes a convection heat transfer term and a radiation heat transfer term, h, = (h, + Ig). The heat transfer is normalized and made dimensionless as follows: Containment Gas Analysis and Equations for Scaling March 1997 mM499wJwn\3499w<wpf.It@l397
6-13 (y -1), p, , (y -1),p,,h,hy A gA,*(T-T g),ATg Y,(1 +Z '),thg PO y,(1+2T),dig ,,P (82)
=n g h
- A
- ATg 3
where: (y -1)" xg = p ** h, A p(T -T), (83) { Y,(1 +Z '),rh g P,. ; 6.4 INITIAL AND BOUNDARY CONDITIONS FOR CONTAINMENT MASS, ; ENERGY, AND PRESSURE It is desired to scale the RPC for four LOCA time phases: blowdown, refill, peak pressure, and long-term depressurization, and for the MSLB blowdor.n. The dimensionless variables have different values for each time phase. Initial values are used as the reference values for each variable for each time phase except blowdown. For blowdown, the time average pressure values are used to define all dimensionless, thermodynamic properties for two ! reasons: 4 The only non-zero pi groups at zero time are the transient and break source groups; all heat sink groups are zero. The transient and break source groups provide little useful information. ; l The time constant for the steel heat sinks is on the order of 80 sec, so the heat input to i the heat sinks during the 27 sec blowdown cannot be neglected. The use of the time average pressure allows the energy input to the heat sinks to be easily calculated. The calculation of containment pi values begins with the following assumptions: The initial containment pressure is 15.7 psia, composition is pure air, and temperature is 120*F. The air density remains constant throughout the transient. The initial temperature of all structures and the IRWST is 120 F. An estimate of the containment pressures at the beginning of each time phase was obtained from the.W_ GOTHIC code as a reasonable estimate. The specific pressure history does not significantly affect the results or conclusions of the scaling analysis. The containment pressure during the blowdown phase of a DECLG is shown in Figure 6-1. The time averaged pressure is 44 psia. Containment Gas Analysis and Equations for Scaling March 1997 m:\M99w.non\3499w<.wptib-031397
F 14 4 4 e f f 55 . . . . . .
- I I l 1 I I i
~
1 I i i i I i so - - i-- t l- --+ - - 4 - --
- i i i i i
~
l 1- 1 I I I 45 _~~ ~~~~ -[ Piyr - I- - i i
; ~~ ~ { --- - - I -
i i
~~- - }--~ ~ -
i
- l
- 1 1 1 I I .
...........L............l....... . . .... l .. ......1............l..............l.........
S. 40 . 1 I i i l I 4 1 E, . I .I I I I l I I I I I I E 35 I I I 2 - 1 I W ~
' l 1 1 1 I I
$ 30 I
_............)I..............I............y..........i..............l......... i I g g ..)............ ;
- I I I l i I t 1 I I I I i 25 _
1- - r -- - i- T ' ""' ~ l" "T""~~~~~ 1 I I I I I ,
+
. I I i l i 1
- r -- - -
20 - -
-r--- -r-~- -+---+-~--t-- - -
l I i l i I : 1 I I I I I 15 ' 0 4 8 12 16 20 24 28 Time (sec) h S I i i 1 Figure 61 AP600 Containment Pressure During Blowdown ) i Contavunent Gas Analysis and Equations for Scaling March 1997 m:\3499wJum\3499ww:.wpf.1b-031397 l
6-15 Reference pressures for the refill, peak pressure, and long-term depressurization phases of a DECLG are from Figure 3-4. Reference pressure for the MSLB is from Figure 3-7. ,
- The basis for the mass flow rates is discussed in Section 6.1.2.
- The containment temperature is the saturation temperature at the steam partial pressure. The presence of drops in the DECLG will maintain a state near saturation.
Even the MSLB is expected to operate near saturation, as shown by the superheated LST.
- The blowdown break source flow is assumed to enter containment at the saturation temperature corresponding to the total pressure. Saturation is also assumed for subsequent time phases to produce an upper bound on the drop and pool evaporation (Sections 7.1 and 7.2).
Given these assumptions, the reference values used to scale the containment gas are calculated and presented in Table 6-3. The containrnent gas pi groups for mass, energy, and pressure are presented in Section 8. 6.5 MOMENTUM EQUATIONS INSIDE CONTAINMENT l Mixing within and between the AP600 containment compartments is characterized by j stratification within compartments and by circulation between compartments. This section presents the relevant, dimensionless parameters and their context for scaling LST stratification results to AP600. The application of stratification results to AP600 is documented in Reference 5, Section 9. Circulation between compartments is analyzed and l applied to AP600 in Reference 5, Section 9. ] l The scaling of momentum from forced and buoyant jets in large stratified volumes, such as 1 the compartments and above-deck volumes m AP600, has been addressed by Peterson29 , a si, Baines and Tumers2presented scaled relationships for density gradients in a stratified volume as a function of dimensionless plume characteristics. These references provide analytical bases for evaluating the effect of jets and plumes on enclosed volumes, and present equations for scaling the effects. Those references provide the analytical basis for scaling momentum in i AP600 as it affects stratification and heat sink utilization during DBA. l Containment Gas Analysis and Equations for Scaling Much 1997 m:\3499w.non\3499w.exputet397
1 6-16 l Table 6-3 Reference Values for Containment Gas Scaling i DECLG LOCA MSLB Peak Long Parameter Blowdown Refill Pressure Term Blowdown Containment gas temperature, 'F 240 252 244 268 252 Total Pressure, psia, P. 44 50 46 60 50 Saturation Temp, *F 273 281 276 293 281 Bulk air pressure, psia, P., 18.9 19.3 19.0 19.7 19.3 Bulk steam pressure, psia, P.,,, 25.0 30.7 26.9 40.3 30.7 Bulk stm density, Ibm /ft.8, p,. 0.0587 0.0705 0.0627 0.0901 0.0705 Bulk air density, Ibm /ft.8, p., 0.0732 0.0732 0.0732 0.0732 0.0732 Total density, Ibm /ft.8, p, 0.1319 0.1437 0.1358 0.1632 0.1437 Liquid density, Ibm /ft.8, p,, 60.0 60.0 60.0 60.0 60.0 1 Break steam density, Ibm /ft.8, ppu, 0.1007 0.1132 0.1049 0.1337 0.1132 ' Specific heat ratio, % 1.34 1.33 1.33 1.33 1.33 Enthalpy diff, B/lbm, Ahgg, 1084 1086 1084 1090 1086 Excess enthalpy, B/lbm, hpg,-h,,,, 11.0 9.4 10.4 7.7 9.4 Internal energy diff, B/lbm, Au, 453.5 500.3 470.1 562.5 500.3 Break work, B/lbm 328.4 350.6 344.4 371.1 350.6 Compressibility Function, (1+27), 1.065 1.080 1.074 1.103 1.080 Break stm flow, Ibm /sec,rhpg, 4,444 200 200 45 367 l Break pool flow, Ibm /sec,rttu,,k.,, 5,555 0 200 200 0 Break drop flow, Ibm /sec, In,3,u, 2,222 0 0 0 0 1RWST lig flow, Ibm /sec, mm , 0 0 0 245 0 Definitions Stratification exists when ho::izontal layers overlie one another. A stably stratified gas volume has a vertical density distribution due to concentration and/or temperature in which the density decreases with elevation. The density gradient may change with time and must be considered, along with the vertical distribution of heat sinks in the volume, to calculate the heat and mass transfer rate histories. A stratified volume requires analytical methods with finer resolution than a single lumped volume. " Stably stratified" is not related to whether the gradient is weak or strong, only that it is stable over time. Containment Gas Analysis and Equations for Scaling March 1997 mA3499w.non\3499w c.wpf-1tHm307
6-17 An unstable containment atmosphere has no long-term, persistent temperature or ; concentration gradients, and requires such a high Froude number break source to disrupt stability that the resulting containment is well-mixed. In terms of the peak containment pressure, well-mixed is not necessarily good or bad, but produces well-defined boundary conditions for calculating heat and mass transfer rates between the atmosphere and the heat sinks. . A well-mixed gas volume can be represented as a single lumped volume. ;
" Weakly stratified" is used as a qualitative measure of the vertical density gradient observed .
in the LST data for the LOCA configurations. " Weakly stratified" implies little vertical I variation in the air / steam concentration, while "strongly stratified" implies nearly pure air at ! the deck elevation and nearly pure steam at the dome, which was never observed in the LST. ! If the jet entrainment is high enough, the resulting fluid circulation can nearly eliminate vertical concentn. tion gradients, resulting in a weakly stratified atmosphere. I 6.5.1 Froude Number Relationships i l The internal mixing and stratification phenomena relative to the steam jet can be represented by the jet Froude number, or the Richardson number which is 1/Froude. The Froude number can be considered as a ratio of kinetic energy to potential energy, or pU2/ApgH. The Froude number is sometimes defined as the ratio Re2 /Gr. In AP600, interest is focused on the extent that the jet kinetic energy enhances mixing inside containment. During a design basis transient, the jet potential energy varies by a factor of 2 to 3, while the kinetic energy varies by many orders of magnitude. The Froude number is a more direct measure of the kinetic energy than its inverse, the Richardson number, and thus, the Froude number is used for scaling the AP600 intemal phenomena. ! The internal containment phenomena that are of interest for AP600 scaling are:
. The jet type, whether predominantly forced or buoyant, is important because it !
determines the rate at which the jet entrains and otherwise interacts with the I containment volume.
. If the jet kinetic energy is high enough it msy eliminate vertical gradients in the upper containment volume and to also induce mixing between the above-deck and below-deck regions as observed in some of the LST. !
It is desired to use Froude number formulations that represent these phenomena in both l AP600 and the LST to permit scaled inferences regarding mixing and stratification within a volume or compartment. Containment Gas Analysis and Equations for Scaling March 1997 m\M99w.non\M99w<.wpf:1t>031397
6-18 6.5.1.1 Forced / Buoyant Jet Peterson recommended the following equation to determine the elevation where a forced jet
' transitions to a buoyant jet:
/ 3-1/4 f 3-1/4 f S PaU,2 z_ _
{g4) (P. - Po)g d, p, d, A jet Froude number can be defined, based on the jet source velocity, density, and diameter, and the ambient containment density:
* (85)
FrW = - g(p,-po)d, Rewriting Equation (84) in terms of the jet Froude number gives: f 31- f M/4 Fr#b= '"," or "'"'
= Fr /4 W
i $ (86) P. d d, p,> According to Equation (86), jet transition is not a function of the containment height or volume; the transition elevation only depends upon the jet source characteristics. Equation (86) is equally valid for predicting forced-to-buoyant jet transitions in AP600 and the LST. 6.5.1.2 Containment Stability Peterson also presented equations for jets in large stratified fluid volumes. Peterson defined ! a stably stratified fluid as one in which the horizontal gradients of temperature, density, and : concentration are negligible everywhere except at the boundaries of jets and wall boundary layers. Vertical gradients of temperature, density, and concentration remain, although their - magnitude may be very small. His equation for a stably stratified vol~ume is: M/3 f M/3 f(p,- p,)g do H d, gg7) 3 >1 P.U,2 do 4/2 aH > Taylor's jet entrainment parameter, a, can be assumed to be a constalit with a value of 0.05 for this analysis. 1 A volumetric Froude number can be defined that is the square of the jet Reynolds number, l divided by the containment Grashof number:
'** (88)
Fr" = g(p, -p,) H ' Containment Gas Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w<.wpf-1M31397
6-19 Rewriting Equation (87) for stable stratification in terms of the volumetric Froude number gives: e " do (89) Fr" < 1+ 4[2aH j l As a measure of stability, or lack thereof, the volumetric Froude number can also be used to , l correlate vertical density gradients. It is shown in Table 6-4 that stability corresponds to a l volumetric Froude number on the order of unity. Volumetric Froude values orders of : magnitude greater than unity imply Reynolds number (or kinetic energy) dominated phenomena, while Froude numbers much less than unity imply that the Reynolds number is not an important parameter for mixing inside containment. Equation (89) is equally valid for AP600 and the LST with jets that are forced over most of the containment height. 6.5.2 Froude Numbers in AP600 l l The transient jet and volumetric Froude numbers for the AP600 DECLG and MSLB transients were calculated and presented in Figure 6-2 and Figure 6-3. The calculation assumes the typical transient pressure, mass, and enthalpy inputs from Section 3. Values of the geometric parameters used to evaluate the jet and volumetric Froude numbers ; for AP600 and the LST are presented in Table 6-4. The values of the Froude numbers at the ! stability limit and for the jet transition elevation are summarized in Table 6-4 and compared to the AP600 transient Froude numbers in Figure 6-2 and Figure 6-3. The stability criterion shows the containment atmosphere is stably stratified during most of the transient (after i approximately 3 sec during a DECLG and 50 sec for the MSLB). It is considered unlikely that a more rigorously applicable stability criteria would permit the conclusion that the atmosphere is unstable during the majority of the transient time. Therefore it is necessary to address the consequences of stratified gas volumes in the AP600 evaluation model. The consequences of stratification within regions or compartments are addressed in Reference 5 Section 9. Equation (89) was derived from Peterson's equations for entrainment into a forced jet, so for Equation (89) to be applicable,it is necessary that the jet be predominantly forced, or Zm-H. Peterson also examined a stability criterion for buoyant jets, and concluded that buoyant jets almost never break up stably stratified fluid volumes. Thus, the criteria for instability are a predominantly forced jet, and violation of Equation (89).
' ontainment Gas Analysis and Equations for Scaling C March 1997 m:\34%.non\3499w<wpf:1Nm397
r 6-20. i i l l i
)
E II 3113 5 5 3 5 5 5 5 5 5 5 5 5 4 3 5 5 5 5 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 5 5 3 3 E 3 5 5 5 5 4 5 5 I 3 5 5 3 4 5 31B
- g. ::::::::- **- ---- : ::::::::::::::':::::::::::::::::::::::: :
.. .. A.
.. . ........TlnsEfNor.-..................*.-.-*.----..---.-.-.-*
.A . ................................... ..... ............
. .....4
.b .. .. b. M... M.. ................................ .....
1onnmi um umummnmmummmunnmununm1000 : m
- y. ......:.::.. .:.::::.*::*
6 .. . . . . . . . . . . . . u v a. _.......M.................................. w U.g IIllunliffittil finfilillittlltif f tIII!nlif filllllinlf ttillntn E ~~T i
.L,,,'L,,
m .8 z 0.01onnnnuum munnununnnnggggggig m_ ui0 E
..... ..... ................ ....... .neigbrusagant... ... ..
s z b 0.001mn nunmununun 2' t..: * .:*:::::::::: unmunn i e
.. .. . . . . ..........................hm
......nei r i u1 $
e
..mt.a.A.n.e . ... . .......... ........gnuxwant. ......
. . . . . . . . . . . . . . . . . . . . . .. 1 E 0.0001o: '::: mn I
nunnmu nunnnnnunununu E
""J i 3
c . . . .NNf@'.En
. . .:0.1 ,
s 1 E.05:o't:- n U:nnmunn unununmnnnnunt
- muunnu0.01 **:::: - :
1E.06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.001 1 10 100 1000 10000 100000 Time after Break (seconds) i a 1 { l 1 Figure 6 2 Froude Numbers Inside Containment for the AP600 DECLG Containment Gas Analysis and Equations for Scaling Mmh 1997 1 m:\MN.non\MNw:.wpf.lb-031397 j 1 l J
c . . . . _ .
?
L 6-21 1 L f s t r 10...... -
. . . . . . . . . ..................................................1M
............................r,,................................... .
. . ..... ......... ..........g......................................
,a%
s.#*................................
,. . . ....N..................* . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
- u. .
v Stably Stratified *...........
.g > r=:
u u.
............................... ..........s ..................10000 1 -
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... ........ ........ u.
3
.........s..s..............
,8 Z . .v....
15IFr....................._.............. .......... ........s.......... .
--. . .f)sta W- - ----. - -- -
- -- !g -- -- E.3 z .
- u. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. : .
. \
0.1 . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 1 l
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7-e. . . . . . . . . . . . . . . . .
3 3 . .......................................................... .......
......hh MQ QW- -
More than 90% of jet height buoyant 0.01 . . . ...... . . . . . , . . 100 1 10 100 1000 1 Time after Break (seconds) l l l l
]
i i Figure 6 Main Steamline Break Jet and Volumetric Froude Numbers i Containment Gas Analysis and Equations for Scaling Mmh 1997 m:\3499w.non\M99w c.wpf.1b 031397
6-22 Table 6-4 Geometric Parameters and Critical Froude Numbers for AP600 and LST LOCA and MSLB AP600 LST LST/AP600 LOCA.-
~
Height, H (ft.) 13.2 1/8.26 Source Diameter, d, (ft.) _ 1.66 1/6.09 Fr, at Stability Limit 2.% 3.57 1.21 Frg at zm =0.1H 1.46 0.62 0.42 Frp at z,,,, = H 1.46x10' O.62x10' O.42 4 MSLD:
~ ~
Height, H, (ft.) 9.01 1/8.30 Source Diameter, d, (ft.) _ 0.256 1/9.61 Fr, at Stability Limit 1.52 1.44 0.95 Frg at ztrans = 0.1H 138 227 1.64 Frg at ztrans = H 138x10' 227x10' 1.64 Stable / unstable regions are distinguished by the AP600 values of Fry presented in Table 6-4 calculated from Equation (89). Figure 6-2 and Figure 6-3 show the AP600 transients are expected to operate predominantly in the stably stratified regime. i For entrainment calculations it is important to know whether the jet is buoyant or forced, since buoyant and forced jets entrain the surrounding fluid at different rates. A forced jet , transitions to a buoyant plume after traveling some distance and dissipating some of its ) I kinetic energy. Thus, the first criterion to examine is whether the jet remains forced over the full height of containment, that is, what is the jet Froude number for Zm = H? The values were calculated for AP600 with Equation (86) and are presented in Table 6-4. Comparison to the transient Froude numbers in Figure 6-2 and Figure 6-3 show this criteria is never satisfied. So the jet always transitions to a plume before reaching the top of containment. , The buoyant height of the jet is H - Zm where H is the containment height above the ! source, and Z.,_ is the height of the forced jet calculated from Equation (86). ; The second criterion to consider is, since the jets cannot always be modeled as forced, can the j jets be modeled as always buoyant? The strict answer is no since Equation 86 always gives
)
a finite value of Z,, .. However, if the jet is predominantly buoyant, say over 90 percent of the containment height, then it is reasonable to model the jet as buoyant over its full height. The value for Z.,,, then is 10 percent of the height, and the corresponding jet Froude numbers are presented in Table 6-4. When compared to the AP600 jet Froude numbers, Figure 6-2 shows the DECLG jet height is 90 percent buoyant for the entire post-blowdown Containment Gas Analysis and Equations for Scaling March 1997 m:\3499w non\3499w-c.wpf-1b.031397
6-23 time. Figure 6-3 shows the MSLB jet height does not become 90 percent buoyant until the end of the transient. Thus, prior to the end of the MSLB, the jet transition height must be calculated as a function of the jet Froude number and modeled as mixed (that is, part forced and the remainder buoyant) to accurately calculate entrainment. 6.5.2.1 Loss of Coolant Accident (LOCA) l ne volumetric and jet Froude numbers were calculated for the AP600 DECLG, with the i assumption of a well-mixed containment. The results are presented in Figure 6-2. The fact that the jet and volumetric Froude numbers differ by a factor of 1000 simply results from the fact that (H/do)' = 1000, approximately. The jet Froude numbers show that the jet is mixed forced and buoyant over the first 27 sec. of the transient, and is buoyant over 90 percent or more of its height after 27 sec. The volumetric Froude numbers indicate that the containment is stably stratified after 4 sec. into the DECLG. The jet flow rate can cause the density gradients to increase or decrease, even while the containment atmosphere remains stably stratified. After approximately 1000 seconds, the time when extemal cooling becomes important, the volumetric Froude number is less than 1x10t This is four orders of magnitude less than the stability limit. Consequently, it is expected that mixing between elevations above and below the jet source and above and below the operating deck, is limited to that induced by the large-scale circulation due to'the rising buoyant jet. Furthermore, the very small magnitude of the volumetric Froude numbers (after 1000 sec.) indicates that the jet Reynolds number is not a factor in containment mixing during a LOCA. 6.5.2.2 Main Steamline Break (MSLB) The volumetric and jet Froude numbers were calculated for an MSLB, with the assumption of a well-mixed containment. He results are presented in Figure 6-3. The jet Froude number indicates that the jet is mixed throughout the entire transient. The volumetric Froude number indicates that the containment volume is unstable over the first 40 seconds of the 700-second transient, and stable thereafter. It can be anticipated that this instability has the potential to induce a well-mixed state inside containment, both above and below the jet source elevation, and if the Froade number is high enough the vigorous mixmg may even penetrate into the below-deck c'<evation. Comparison to the LST will indicate the effectiveness of mixing. 6.5.3 Froude Numbers in the Large-Scale Tests (LSTs) The LSTs were conducted in several different intemal configurations. The LST configuration with the steam source exiting from a diffuser located under the simulated steam generator approximates the geometric configuration of a LOCA, and the LST configuration with the steam source elevated 6 feet above the deck and exiting from a 3-inch ID pipe approximates Containment Gas Analysis and Equations for Scahng Mmh 1997 m:\3499w.non\3499w<.wpf.It>031397
6-24 the geometric configuration of an MSLB. The mixing and stratification report, Ref. 5, Section 9, contains more description and discussion of these tests. Also the test data reports" and test drawings" describe the tests and hardware configurations. 6.5.3.1 LOCA Configuration Twenty-five LSTs were conducted in the LOCA configuration, that is, with the diffuser located under the steam generator model. The jet Froude numbers ranged from 0.0016 to j 0.231 and the volumetric Froude numbers ranged from 5x104 to 6x104 . The IST Froude ; number ranges are compared to the AP600 DECLG Froude numbers in Figure 6-2. The figure shows that the LST data span the range of AP600 post-wetting operation. The jet Froude numbers indicate that over 92 percent of the LST jet height is buoyant, consistent with the post-blowdown buoyant height of 90 percent or more in AP600. The volumetric Froude numbers indicate that the LST containment atmosphere, like the post-blowdown AP600, is stably stratified with negligible momentum. It is concluded that both the LST and AP600 LOCA jets are predominantly buoyant plumes, and the internal jet-induced mixing phenomena in the post-blowdown AP600 lies within the range of the LST. As a further measure of mixing in the LST, steam concentrations just above the deck but below the jet source elevation (Elevation E) and below the deck in a dead-ended compartment near the bottom of the vessel (Elevation F) are presented in Figure 6-4. The plotted values are the ratio of the measured local steam partial pressure to the partial pressure of steam assuming perfect mixing. A value of 1.0 indicates perfect mixing. The values show the above-deck ratios generally range from 0.6 to 1.0 and the dead-ended compartment values range from 0.1 to 0.4. The data show no significant trend with the Froude number, as expected at these very low values of volumetric Froude number. These data support the fact that the jet Reynolds number is not a significant factor in containment mixing during the post-wetting phase of the DECLG. 6.5.3.2 MSLB Configuration - Four LSTs were conducted in the MSLB configuration, two with the steam jet directed horizontally and two with the jet directed upward. The jet Froude numbers ranged from 7,900 to 22,003 and the volumetric Froude numbers ranged from 0.286 to 0.695. The jet transitions from forced to buoyant in the LST at 25 to 35 percent of the containment height, compared to 40 to 71 percent in AP600. The greater forced height in AP600 will cause better mixing. The comparison of LST to AP600 volumetric Froude numbers in Figure 6-3 shows the LSTs lie at the minimum AP600 values and hence, confirm the least mixing to be ' expected in AP600. The mixing data measured in the LST and presented in Figure 6-4 show Containment Gas Analysis and Equations for Scaling March 1997 mA34%.nori\34%-c.wpf:1b 031397
6-25 that even at low volumetric Froude numbers mixing is nearly ideal, even in the bottom of the dead-ended compartment (MSLB-F in Figure 6-4). Rese results are valid for both horizontally and vertically directed jet sources. It is expected that the high jet momentum during an MSLB will produce very effective mixing throughout the above-deck region of AP600, and some penecation through openings into the below-deck compartments. l l J l 1 1 Containment Gas Analysis and Equations for Scaling March 1997 m:\3499wawn\ 3499w-c.wpf. l b-031397
i I 6 26 4 ta yL e t.s , te , e r I
\.
1C_-..,........,..,..,.,..,...,.,..,..,.,..,.,..,.,....,...,...,..,.,,,,,,,,,,,..,......,......,,,,,,,,,,,,,.,.,..,,..,..,...,.,.,,.,,.,,.,,,,.,.,,.,.,
.2s y .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i 1.,
.... .. .. .. ..... .. .. .......t........................W.
.....................................e...................................................................-..
9
. ..... ...............m...................
..........................................[.............................................................
.g .. . . . . . . . . . . . . . . . . . . .
e " a E e a a 0.1. ..........3...s........................................................................................... a .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , m .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t. 0.01 . . . . . - . . . . . . . . . . . . . . - . . . ...... . . . . . . . . . . . . ..... 1 E-06 1E-05 0.0001 0.001 0.01 0.1 1 Volumetric Froude Number LOCA, F + LOCA, E o MSLB, F
- MSLB, E i
,P t
t Figure 6 4 Steam Mixing Data Above and Below the Operating Deck from the LST o. Containment Gas Ana2ysis and Equations for Scaling March 1997 , mAM99w.non\3499w<.wpf;tt431397 I
7-1 7 HEAT SINK ANALYSIS AND EQUATIONS FOR SCALING Energy equations are required for each heat sink to track the temperature-time history that determines the heat and mass transfer rates between the atmosphere and the heat sink. As the heat sink temperature changes, the boundary layer and surface properties that appear in the transport equations also change. Consequently, for each heat sink, several properties must be determined. The boundary condition for the heat sink energy interaction with the containment gas is the containment gas temperature and pressure history from }YGOTHIC. This boundary condition is used to define the initial condition for each of the time phases shown in Figure 3-1. The containment gas energy interaction with the heat sinks is modeled using integral equations and other techniques to simplify the otherwise complicated time integration for each heat sink. The modeling method for each heat sink type is summarized in Table 7-1. Table 7-1 Method Used to Model the Energy Absorbed by lieat Sinks lleat Sink Method Drops, d Exponential Approximation Break Pool, p Evap from a spreading layer Intemal Film, if Steady-state conduction Intemal Steel, st Lumped parameter Intemal Concrete, cc Integral equation Jacketed Concrete, jc Bounded Shell, sh Integral equation Baffle, bf Lumped parameter Chimney Concrete, ch Integral equation The state of the heat sinks are determined by tracking the heat sink heat and mass transfer interactions with the bulk gas from the beginning of the transient. The bulk gas properties are modeled as simple functions (either constant or linearly changing with time) during a time phase. The heat sinks are modeled using solutions that provide the heat sink surface temperature, which is needed to calculate the heat and mass fluxes, and the heat sink bulk, or average temperature that is needed to track the energy stored in the heat sink. ) Heat sinks reduce containment pressure by absorbing energy that reduces the mass and energy stored in the gas atmosphere. Heat sinks are both solid and liquid. Solid heat sinks are Heat Sink Analysis and Equations for Scaling Mmh 1997 m:\N99w.rmn\M99w< wpf Ib401397
l 7-2 l composed of steel and/or concrete and indude walls, floors, ceilings, exposed structural steel, i equipment, and the containment shell. Liquid heat sinks indude drops, pools, and films. ; Solid heat sinks indude steel, concrete, and steel-jacketed concrete. These are treated as ! distinct heat sinks because each has different thermal conduction characteristics. Heat l transfer to steel heat sinks is limited by the heat and mass transfer coefficient, whereas heat f transfer to concrete is limited by internal conduction resistance. I Solid heat sinks are affected by condensation, radiation, and convection heat transfer. ; Evaporation from solid heat sinks requires a continuous liquid source which is not present inside containment. Consequently, internalI.olid heat sinks only reject heat by radiation and l convection. l ~ The shell is a solid heat sink with a surface that is subdivided into three regions, each with a distinctly different external energy transfer resistance. The three regions are subcooled, evaporating, and dry, corresponding to the dominant processes on the outside of the shell. In the subcooled region, the external liquid film is the heat sink. Evaporation, radiation, and t convection from the subcooled film are neglected. In the evaporating region all of the energy [ is transferred to the riser by evaporation and convection, and to the baffle by radiation. In , this scaling analysis, the evaporating film is assumed to have no sensible heat capacity, consistent with the dassic Nusselt film solution. In the dry region, there is no external liquid film; heat is rejected by convection heat transfer to the riser gas and by radiation to the baffle. Liquid heat sinks include drops, the break pool, the IRWST, and films. Liquid heat sinks can interact with the containment gas both by evaporation and condensation, as well as by radiation and convection heat transfer. A general form of the energy conservation equation for liquid and solid heat sinks is: f dT i m e, - rn,c,(T,-T) - rn,c,(T,-T) + 4, - q, (90) where the convective flow terms may be present for liquid heat sinks, but are absent for solid ! heat sinks. Equation (90) is modified as necessary for each of the heat sinks. Each of the 4 terms in Equation (90) may indude the three parallel energy transfer components: mass transfer, convection heat transfer, and radiation heat transfer. Using the subscripts c, r, and m to denote convection heat transfer, radiation heat transfer, and condensation / evaporation mass transfer, and adding an x for the outside of the containment shell or the outside of the baffle: , q" = 4" + q" + q" and q" = 4" + q" + q" (91) Heat Sink Analysis and Equations for Scaling Much 1997 ; m:\M99w.non\3499w(wpf.It> 031397 l
7-3 Each of these energy transfer terms can be written as the product of a conductance and a temperature difference,4" = HAT. In addition, the mass flux is written in terms of mass conductance, temperature difference, and enthalpy change, rn" = h,AT/(h,-h,). The subscript e is used to denote an equivalent heat transfer coefficient, h,, when conductances are combined in series and/or parallel. In general only three of the terms in Equation (90) are of interest for scaling AP600. The three terms include the two heat flux terms (in most cases there is only one of these two) that are normalized by the break enthalpy flow rate and define the n,3 groups in Equation (69), and the transient term that is normalized by the heat flux to define the heat sink time constant. The heat sink time constant provides valuable information on the time period when the heat sink is effective. 7.1 DROP ANALYSIS AND SCALING EQUATIONS Drops, or fog particles, are created when the blowdown break source steam disperses a fraction of the break liquid along with the gas. After blowdown, the gas velocities in the break are too low to entrain a significant quantity of drops from the break liquid. The MSLB break flow does not include liquid until near the end of the blowdown when the drops have little or no effect on pressurization. Consequently, drops are created only during the blowdown phase of the DECLG. Well-accepted phenomenological models are not available to predict the mass of drops created during blowdown, so an upper-limit entrainment rate equal to 1/2 the gas mass flow rate is assumed for the full blowdown period. It is assumed that the entire mass of drops are created with a diameter of 0.001 inch, which provides a sufficiently large surface area to strongly, thermally couple the drops to the containment atmosphere. In addition, at 0.001 in diameter, drops are strongly coupled by shear to the moving gas, even at low velocities, and persist for an extended period of time. (Since both couplings are strong, a smaller drop diameter has no effect, but a significantly larger diameter will reduce the coupling and further decrease the effect of drops). Ultimately, coalescence or other processes cause the drops to be removed from the atmosphere. The drops are assumed to enter containment at the saturation temperature based on the total gas pressure. The scaling calculations presented later show that even with assumptions that maximize the effect of drops, the effect of drops is small during blowdown and refill, and negligible thereafter. The assumption that the drops remain at a constant diameter throughout the transient can be checked against the maximum evaporation fraction that results from reducing the drop temperature to the minimum system temperature of 120 F, f = cvAT/h,, =1(273-120)/1000 = 15 percent. Since the volume is proportional to d5, the diameter change, Ad, will be approximately 1/3 of AVol, or only 5 percent. licat Sink Analysis and Equations for Scaling March 1997 m:\34%.non\34%<wpf.lb.031397
7-4 The assumption that the drop surface area remains constant throughout the transient maximizes the surface area and consequently, the effect of the drops on containment pressure. However, it is clear the drops will agglomerate and fall out, thereby reducing the available surface area during the transient. The assumption of constant area can be justified by showing that even when maximized, the drops have a negligible effect on containment pressure. Examination of the magnitude of the post-refill pressure pi groups in Table 8-5 shows the effect of drops on containment pressure is less than 1 percent of the source pressurization, and consequently can be neglected with no significant effect on pressure. The drops affect the containment atmosphere in three ways. First, a fraction of the drop flashes to steam when the drops enter containment. Second, the drops remain strongly coupled to the temperature of the atmosphere, so as the atmospheric temperature changes throughout the transient, the drop temperature closely follows the atmospheric temperature changes. The strong temperature coupling maintains the containment gas at or very near saturation. Third, the small diameter drops are strongly coupled to the moving convective gas flows, which effectively increases the gas density and affects circulation and potentially, heat sink utilization. The first and second of these effects are evaluated in this scaling analysis and the third is evaluated in Ref. 5, Section 9. The following calculations show how strongly the drops are coupled to the atmosphere, by showing the effective time constant for the flashing drop is very small. Drop Surface Area Calculation The major parameter involved in drop-atmospheric interactions is the large surface area of the drops. That area is calculated as follows: The drop specific length, L' = V,,op/Aa,,, = D/6 = 0.001 in /(6x12 in/ft.) = 139x10~5 ft. = At 50 percent of the gas mass the drop mass is rig,Jt/2 = 4444 lbm/sec'27 sec / 2 = 60,000 lbm.
- The drop total volume is m/p = 60,000 lbm / 60 lbm/ft' = 1000 ft'.
The total drop surface area is the number of drops times the area of a single drop, 3 A, = nA,,,p, and n = V,/V,,,p, so A, = Aa,,, V,/V,,,, = V,/U = 1000 ft /139x10-5 ft. = 7.2x10' ft 2. The drop characteristic length is L = V,/A, = 1.74x10'/7.2x10 7= 0.0242 ft. Heat Smk Analysis and Equations for Scaling Much 1997 m:\34Ww.non\3499w capf:1141397
7-5 Time Constant Calculation The " flashing and following" evaporation processes occur on two different time scales. Flashing occurs almost instantaneously as saturated drops are introduced to a containment atmosphere at a lower steam partial pressure, while following occurs on a time scale equal to the duration of the time phase. Drops are assumed to enter containment saturated at the containment total pressure. Since P .,a = P it must be the case that P,y,n = 0 so the log-mean air pressure in the denominator of the mass transfer rate equation approaches 0 and the mass transfer rate is unbounded. More realistically, the initial evaporation rate from the surface is very high, but bounded, due ; to the presence of dissolved gasses that are released along with the vapor. Furthermore, the liquid surface temperature must change continuously and remain bounded: the high initial mass transfer rate occurs over a very small time period so the product of mass transfer rate and Atime is finite, as is the internal energy change of the drop or surface layer. The initial high evaporation rate quickly cools the liquid and produces a value of P,,,,a less than Po . Then the air partial pressure is greater than zero, so the mass transfer rate equation is valid. The small drop can be modeled as a lumped mass, and the mass and energy equations for the initial drop flashing can be approximated by neglecting the sensible heat transfer terms, so: dmd dT
= rha,i,,, aM m,c, dt3
~
d***h '5 From this, a finite difference equation relating the evaporation rate to the drop temperature change can be written:
'8 AT,- d"" -
(93) dyC and integrated (or summed) to generate a time-temperature history. This was done for a i drop during blowdown and the results are shown in Figure 7-1. The singularity in the mass flux equation was avoided by starting with an initial temperature 0.05*F cooler than the { saturation temperature. A 0.05'F difference requires a negligible mass of evaporation and i avoids the zero air partial pressure singularity. The calculated drop temperature is compared I to an exponential temperature change and shows the calculated curve is steeper than the exponential initially, as expected since the slope is unbounded as t approaches zero. Later in the transient the exponential approximation decays faster than the calculated curve. Although a time constant cannot be defined based on dT/dt at t = 0, the time constant for the exponential curve shown in Figure 7-1 was determined by forcing the exponential to coincide with the calculated curve at 68 percent (one exponential time constant) of the Heat Sink Analysis and Equations for Scaling March 1997 mM499w.non\3499w<wpf 1t@l397
.s
. i l 1 7-6. e e T t F 280 !
- - - - - ~ ~ - - - - - - - - - - - - - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - - - ~ ~ ~ ~
275- , r 1 J
- - - - ~ ~ ~ - - - - ~ ~ ~ ~ ~ ~ ~ - - - - - - - - - - ~ ~ ~ ~ ~ ~ ~ ~ - - - - - ~ ~ - - - - ~ ~ - -
270 ,
. ..........n.......................................~....n................n.......m.............
G. g Exponential With 6e-5 Second Time Constant ; g ....................................................................................................
- 5 255- ---- - - - - - - - - ~ ~ - - - ~ ~ - - - - - - - - - - - - - - - - - - - - - - - - - - -
g P j 250- - - - - - - - - - - - - - - - - - - l--
.245- - - - ~ ~ ~ ~ ~ ~ ~ - ~ ~ - - "o-"~~~---------------------------- .
o ! gg ....................................................................................... O. ; i gg ...-...................................................................................................... 6 230 .- . . . . . . 0 SE-05 0.00010.00015 0.0002 0.00025 0.0003 0.00035 0.0004 Time (seconds) , i i t 1 4 Figure 7-1 Exponential Approximation to the Cool-Down of Saturated Drops : Injected into Containment j t Heat Sink Analysis and Equations for Scaling Much 1997 m:\Mh.non\M99w-c.wpf:1b-031397 ; 1 I L h
7-7 i temperature change. The resulting time constant is 6x10-5 sec. and can be used to , appr eximate the behavior of drops. The time constant for drops beyond blowdown changes l less man a factor of 2, so the drops remain in thermal equilibrium with the atmosphere as , long as they persist. ; i Since flashing is effectively instantaneous, relative to the other tirne constants for the system, f c the flashing will occur independent of other phenomena. The fraction of the drop that flashes can be estimated by relating the energy released by flashing to the sensible l temperature change of the drop: m c*(T - T) rit,,,3,,3h,, = 6,9 U,, - D or f= = N Calculations for the conditions during blowdown give f = 0.035, so 3.5 percent of the drop r flashes to steam upon entering containment. The rate at which drops enter containment is 2222 lbm/sec during blowdown and zero thereafter, so the value for m,;i,3 = 0.035 l (2222 lbm/sec) = 77.7 lbm/sec during blowdown and zero thereafter. 7.1.1 Drop Conductance
]
l The individual conductance terms for mass evaporation, heat convection, and radiation from l the drop to the containment atmosphere are: 2 2(h,-h,)p,,D, AP,, rSc Mn 2k ! h" = h' h' - ocf(T d,T) (T,-T)d Pg -Pr, d i (95) 2(h8 -h,)p,,D' rScvn dP,,, AT I h" - - (for AT = 0) and h,,-h" +h' + h' i d Pr dT P-air ( / The first definition of h, is used to calculate the drop flashing mass transfer rate in Section 7.1, and the second, containing dP,,,/dt is used to calculate the evaporation rate as the drops follow the containment temperature throughout the transient. The individual conductances are scaled by dividing each term by the shell conductance, that includes the shell and coating, h,u = (5,u/k,u+ 25,,,,/k )'so that: l l 8 , - h,,,/h,u c x,a - ha,/h,u gg - h,3,/h,u x,a - ha ,/h,, (96) l l 7.1.2 Drop Mass Transfer i l The mass rate of change equation includes terms for the drop source flow rate, the flashing rate, and the evaporation rate due to the atmospheric rate of temperature change. Because Heat Sink Analysis and Equations for Scaling Man h 1997 at\349N.non\3499w<.wpf:1b-031397-
7-8 the drops are assumed to persist for some time, the equation does not include a convective outflow mass term. The drop mass conservation equation is:
- m,3 - rh,,,,,, - m ,,,,,, M The drop flashing and evaporation rate terms at.%ct pressurization, so they are the terms of interest for scaling. The flashing and evaporation rates are normalized by the break source steam mass flow rate and made dimensionless with the constant mau = rhaw and the variable rho,,, = rho,,,jh',,,,.
dJiash " d.Aash.o dJiash . d,evap dwap.o evap . E m. flash 4 dJlash " " th,y, m,3,,,, rh,,,g,, mgbrk o m,evapA d.evap (98) rhu,rk, 2 p,,,D, dP. AT / Sc"'8 A where n -f and n ,,,,, - gbrk,o air ( j g,brk.o The two drop mass pi groups are added to get the single mass pi group defined for transfer to a heat sink in Equation (59). The values of the flashing and evaporating mass flow rates were calculated and scaled in Section 7.1. 7.1.3 Drop Energy Transfer The drops are assumed to enter containment as saturated liquid at the containment total pressure. This introduces saturated drops with a temperature and steam partial pressure higher than the containment temperature and steam partial pressure. Consequently, the liquid drops evaporate to the containment gas and also transfer heat to the gas by convection and radiation. Drop removal is neglected. The energy equation for the drop is: dT m, c,,, = rit,3c,fT, -T,) - rh .,,3h,, - rh,,,,h,, - h,3A,(T -T,) (99) o Since the drop source is zero after blowdown, the flashing term is also zero after blowdown. The dimensionless variables needed to make the flashing, evaporating, and heat transfer terms in the drop energy equation dimensionless are: I i Heat Sink Analysis and Equations for Scaling March 1997 m:\3499w.mm\3499w(wpf;1t431397
l 7 _9 bh4 " N flashA4 b evapA
- N evapA4b evapA h,, = h,,,h*,,
11, 4 = hy4,h*q,, A4 = A,,, (T-T,) = (T-T,), AT,' The energy transfer rate from containment to the drops is scaled to the containment gas energy equation, using the break source enthalpy flow rate,prh ,uAh p ,u and the dimensionless variables defined above: flash 4 is " flash,d4 Ig o . . . . g g g g flashA fg " eJgl flashA fg ghrko gbrLo ghrLo ghrk.o evapA tg evap.d4 Ig,o g. g. h* (100) rhg,brk.o&ghrLa rn ghrLo Ah ghrLo PA fg eJgj evapA ig h,3A,(T -T,) _ h,3,hl, A,,(T -T,), AT,* , ghrk.o g,brk,o ghrko g,brk.o where the pi groups are defined: h,, h,,, e.fgA31 ash m. flash 4 Ah '#5'd'P mevap,d g shrke shrke (101) h,,,, A,(T -T,)o '2 k A T-T,), n
=
Ihghrk,Ah p ,u
=
,d
+ ocf(Td,T) mg, ,(uAh p ,u This heat transfer pi group is the same ratio of terms ac defined in Equation (70) for ,
containment heat sinks. The flashing and evaporating groups are added to get the single phase change pi group, nej ,y defined in Equation (70). The liquid pi group is zero because the liquid film is part of the drop mass. After a drop is created and flashes to near-equilibrium with the containment atmosphere,its temperature remains strongly coupled to the containment temperature and follows containment temperature changes at the same rate dT/dt. The energy equation for the drop can then be written in terms of the equivalent heat transfer coefficient (that includes mass, convection, and radiation 1 1eat transfer) as: m,cy + h,,, A,(T,-T) (102) Heat Sink Analysis and Equations for Scaling March 1997 m:\34N.non\3499w-cwpt:1b431397
7-10 7.1.4 Drop Effect on Pressure The pressure scaling for the drops uses the pi group definitions of Equations (81) for each of the flashing and evaporating mass transfer pi groups. The single heat transfer pressure pi group, ngo, is defined in Equation (83). The drop pressure pi groups are: (Y -1) p P" @,,,,, 4,,,), n,,,,,,,,,,,=n,,,,,,, A .,nia,un.4 = n ,,,,,,,, ,7 ( ), p o (Y -1) Kp , a .ps " " K +.g.a "
".s MM
.pe Yo(3y), .
p oP~ @.ime r 4 . ). .pa n = (y -1), p,,, h, A,,(T -T,),
"# rig,u Yo(1 +Z '), P,,
7.2 BREAK POOL ANALYSIS AND SCALING EQUATIONS The break liquid is assumed to enter containment as saturated liquid at the containment total pressure. This is likely the case during the DECLG blowdown, whereas post-blowdown the liquid may be somewhat subcooled, depending on emergency core cooling system (ECCS) injection rates and mixing. The naximum containment pressure would result if all of the stored and decay heat produced steam with the liquid remaining at its initial temperature of 120 F. However, this would give the trivial case of no pool vaporization and maximum ; condensation on the pool. On the other hand, assuming the break liquid exits the break as i saturated at containment total pressure will maximize the evaporation rate from the break liquid. The latter case of saturated break flow is assumed to permit calculations that show pool evaporation is never very large. I During blowdown the break liquid flow rate is approximately 1.75 times the gas flow rate. This liquid flow rate splits into two fractions,0.5 times the gas flow rate is atomized to drops (Section 7.1), and the remainder is liquid flow rate to the pool. However, the vigor of blowdown causes extensive liquid splashing that wets most of the surface area in the break steam generator and the stairwell. This surface area, along with that of the blobs and large drops produce a large surface for mass transfer. In lieu of a mechanistic calculation of these complicated phenomena, an upper bound on the evaporation rate can be estimated by assuming that as much liquid evaporates as possible. This upper bound is calculated the same way as the flashing fraction of drops in Section 7.1: rn m,,,ph,, = m,,cy,,,R,,,) 4,,,T,,,D and f= , Q% m.p For a total pressure of 44 psia, steam partial pressure of 25 psia,vc = 1 B/lbm-F, and h,, = 918.6 B/lbm, f = 0.036. That is,3.6 percent of the pool flow flashes to achieve thermal Heat Sink Analysis and Equations for Scaling March 1997 m:\3499w.non\3409w<.wpf 1b-031397
7-11 ( and mechanical equilibrium with the bulk containment gas. Since the break gas mass flow - [ i rate and pool flow rates are equal, tha pool flashing pi group (Section 7.2) has the value j 0.036. j . l The total blowdown liquid mass is used as the reference value. The total blowdown liquid l [ mass is approximately 210,000 lbm, so the bounding break pool mass (total minus drops) is l 150,000 lbm. He corresponding break pool volume is 2500 ft 5. { L . l j At the initial containment pressure of 15.7 psia the initial liquid temperature is 215 F. .The j I liquid is surrounded by the containment air at 120 F and bounded by concrete heat sinks ' initially at 120"F. Consequently, the liquid evaporates to the containment gas, transfers heat l to the gas by convection and radiation, and transfers heat by convection and conduction heat l
- transfer to the concrete walls. De energy transfer rate to the solid heat sinks will likely be {
- greater than to the atmosphere. However, an upper limit estimate is desired for the j
evaporation to the atmosphere. Consequently, to maximize the evaporation rate, the , maximum pool temperature should be used. Assuming the pool stratifies strongly, which to + some extent will be the case, the pool surface temperature is the same as that of the incoming , liquid through the time of the peak containment pressure. This provides the surface ] temperature and saturation pressure needed to calculate heat and mass transfer to the gas. l At some time, well beyond the time of the peak containment pressure, the containment saturation temperatt. ' may be reduced to a value less than the pool temperature. The large heat capacity of the pool causes it to remain hot after containment temperature begins to l l drop. When the break liquid is no longer hotter than the pool, a lumped-mass calculation of
- the pool temperature, assuming only heat interactions with the atmosphere, can give a conservatively high pool surface temperature for evaporation calculations. However, this is i beyond the time under consideration for this scaling analysis, so only the stratified approximation is considered.
- l 1
l 7.2.1 Pool Conductance 1 1 1- The individual conductance terms for mass evaporation, heat convection, and radiation from the pool to the containment atmosphere are: 0.13(h,-h,)p,D, AP, fgMn 0.13k 'Ap "" Pr l
- e (105)
(T-Tg)(v 2f g)in p (p , 2 (y fg)us p h, = or f(T,T,) h,-h, +h, +h, The individual conductance terms are normalized by dividing each term by the shell - ! conductance, hu = ku/Su so that: ) i Heet S$k Analysis and Equations for Scahng Wrch 1997 m:\S499w.sen\3499w<.wptib 031M7 - [ g j i
7-12 i l t, - h,,,A,3, x ,, , - h,,,,, A,,,, n ,,,,, - h,,,,, A,,,, n ,,,,, - h ,,,,, M ,,,, U M i I 7.2.2 Pool Mass Transfer j The break pool is created from the blowdown break liquid that is not diepersed along with the gas but pours into the bottom of the steam generator and reactor cavities. Liquid from drop fallout and condensation below the operating deck also drain into the break pool. Liquid that condenses and falls out above the operating deck drains into the IRWST. The l pool mass rate equation is: dm e" ~ mp,p (107) dt *'k P utp The term that is of interest for scaling is the pool evaporation rate term. That term is normalized by the break steam flow rate and made dimensionless with the variable bevap.p " IIIevap.pNevap.p! evap,p.o evar.p.o ap.p (108)
=x ntevap p mevap
' .p gigg )rk,o ytg ghrk.o The effect of the pool on containment pressure is maximized by assuming the liquid enters at the containtnent saturation temperature, similar to drops. The saturated break liquid is assumed to flow across the top of the pool and to cool as it spreads. The net evaporation rate is the integrated evaporation flux over the surface area. The pool surface temperature was assumed to be at a steady-state with the spreading layer evaporating to the atmosphere, but not mixing or conducting to the cooler layer below. This maximizes the evaporation rate, resulting in the maximum pressure effect. The resulting evaporation rates are presented in Table 7-2 for each time phase. .
The break pool surface area changes with time as the pool level rises. Since the analysis shows the evaporation rate is a small fraction of the flow into the pool, the pool liquid volume can be estimated as the integral of the flow rate over time. Using the flow rates and times of each phase from Table 7-3, the pool volume at the start of each time phase was calculated and the pool surface area was determined from the relationship between break pool volume and surface area shown in Figure 3-8. The results are summarized in Table 7-3. Since the break flow rate drops to essentially zero during the refill time phase, the break pool evaporation rate during refill is assumed to be zero. Heat Sink Analysis and Equations for Scaling March 1997 i m \3499w.non\3499w<.wpf;15 031397 l
7-13 l i l Table 7-2 Pool Evaporation Rate for a Saturated Liquid Break Source ' Boundary Conditions Calculated Pool Values 1 Evap Rate Time Phase P total psia T sat T bulk 'F Pool Area ft2 lbm/sec rh,,,,/ rig Dlowdown 44 273.1 240.2 420 7.1 0.03593 Refill 50 281.0 252.0 533 0 0 l Peak Pressure 46 275.8 244.2 1933 5.20 0.02602 l Long Term 60 292.7 267.7 1933 4.60 0.0657 2 l
- 1. Calculated by flashing to equilibrium, Equation (104).
- 2. Calculated from spreading layer model.
l Table 7-3 Break Pool Surface Area During DECLG Transient l ATime Break Flow Rate Pool Volume Surf Area Phase see Ibm /sec ft2 ft2 Blowdown 27 4,444 2500 420 Refill 60 0 2500 555 Peak Pressure 1,500 200 7200 1933 7.2.3 Pool Energy Transfer 1 The break liquid is assumed to leave the break saturated at the containment total pressure. The resulting temperature is always greater than the containment gas temperature, since the i containment temperature remains approximately at the saturation temperature corresponding ) to the steam paitial pressure. The energy equation for the pool is: dT mye,, ' AJ 'l d * *PC vj fdram -b evap.p fg.p
~
q.p p p} dt The pi groups for scaling pool energy were defined in containment Equation (70) for the heat l sinks, with the exception that the liquid film is part of the pool, so is not separately l evaluated. The equations are: Heat Sink Analysis and Equations for Scaling March 1997 mA3499w.non\3499w.c.wpf;1t>C31397 . l \ l
I 7-14 fg.ps eJg,p " asp g@* (110) h,,, A,,(T - T,). 0.13k 'Ap ws A,,(T -T,), x = = Pr + oc f(T,T )
'4P P rhg Ah g rhp ,,,Ahp ,g, ,v(27g)us p ,
7.2.4 Pool Effect on Pressure The pressure scaling for the break pool uses the pi group definitions of Equations (81) for the evaporating mass transfer pi groups and Equation (83) for the heat transfer pi group: (y -1) p Apenth.p " E ap A *A np p.worLp Tog r)o p "a* @.im.pO.an). (111) (y -1), p,, h,,, A,,(T -T,), x P4P - 7,[} #7T ), p,_ rhpg 7.3 IRWST ANALYSIS The IRWST collects the condensate from above-deck, and after the primary system depressurizes, provides a gravity flow of borated water into the reactor. The gas space above the water level is dead-ended and does not circulate because the gas above-deck is less dense than that in the IRWST gas volume. The above-deck gas is less dense because the initial temperature of the IRWST water is 120*F or less, and the saturation temperature of the warmer condensate liquid that drains into the tank is less than that of the atmosphere, otherwise it would not have condensed. While flowing across the floor to the tank the water may heat, but at most it can only heat until the saturation pressure of the water reaches the steam partial pressure of the atmosphere at the operating deck. Consequently,it cannot become a vapor source by heating from the atmosphere, either while above-deck or after draining into the tank. (The draining fluid is assumed to stratify and spread across the surface without mixing with the cooler, deeper water). Consequently, the water in the IRWST, and the gas in the space above the water level both remain stably stratified relative to the atmosphere in the above-deck volume above the tank. As a stably stratified, dead-ended volume, only the small volume of steam forced into the IRWST gas volume by containment pressurization will condense. With only 0.7 percent of the containment volume, the net effect of the small, stably stratified IRWST gas volume and its interactions with the IRWST water and the containment atmosphere is negligible. Thus, it is not necessary to perform scaling calculations for the IRWST as a heat sink that interacts with the atmosphere. However, other aspects of the IRWST, such as its supply of cooling water to the reactor vessel, are considered. l i l Heat Sink Analysis and Equations for Scaling March 1997 ! m:\3499wmon\3499w-c.wpf:1b-031397 l
7-15 7.4 LIQUID FILM ANALYSIS . For containment analysis, liquid films can be categorized as draining films or stagnant films. , Films that form on structures with slopes greater than 1* drain and remain thin. The film on l ~ the shell was determined to be less than approximately 0.005 inches thick and have a heat j 2 transfer coefficient of approximately 900 B/hr-ft _op27 Horizontal surfaces facing downward
- ' show similarly high heat transfer coefficients.
"Ihe following two calculations help put the liquid film heat capacity and time constant in perspective: l 1 ' Heat Capacity: The ratio of the heat capacity of a draining film less than 0.005 in. thick to the heat capacity of the average steel heat sink can be expressed as:
(p 6 c)m., 60 0.005 1 - 0.012 (112) , (p 6 c), 490 0.5 0.11 i Since the film heat capacity is only 1 percent of the heat sink heat capacity, the film absorbs so little heat that its mass can be neglected relative to the mass of the heat sink in terms of energy storage. Transient Response: The average heat flux to the shell at the time of peak containment 2 i pressure is approximately 5000 B/hr-ft -F. The heat flux to the inner shell surface and heat sinks during blowdown and prior to the peak pressure is even higher. Since the heat flux is l predominantly due to condensation, and hgis approximately 1000 B/lbm, the condensation 2 rate that produces the average heat flux is 5 lbm/hr-ft , or at 60 lbm/ft',0.083 ft/hr of liquid. ,. This corresponds to a film thickness buildup rate, neglecting drainage, of 0.00028 in/sec. At this rate the time constant for a typical 0.005 inch film thickness is 18 sec. Thus, the film will be approximately fully formed by the end of the 27 sec blowdown, and transient film effects will be negligible thereafter. j l If it is assumed that the liquid film forms to an average thickness of 0.005 in. in 18 sec. ]' during blowdown, without draining, the maximum values of x ,w andn.u can be estimated. A total heat sink surface area of 250,000 ft2 is used, rather than calculating the pi groups for each heat sink. As the calculation shows, the magnitude of the combined heat sink liquid mass pi group is small so further breakdown into individual heat sinks would not be informative. m,,, , py,, A,,6,, / At , 60 lbm/ft' 250,000 ft2 (0.005 /12)ft /18sec = 0.078 rng ,g th p,g 44441bm/sec 1 i Heat Sink Analysis and Equations for Scaling March 1997 j mA3499wam\3499ec.wpf;n432597 - i
, I
r _ _ 7-16 ! l Evaluation of the energy pi group requires the term Ahs,, which is the difference between the film internal energy and the reference water internal energy at 120 F. Since the difference is zero at the beginnmg of blowdown, the blowdown time-average provides a rational approach that is used elsewhere. The area-weighted average film temperature on the steel, shell, and concrete at the end of blowdown is 165'F. With T = 120 F: Ah,, cy(Ty -T,,) g",g ,g
*" = 0.078 1 BMm-F W120) O - 0.003219 (114)
*" Ahp ,u Ahpg 1084 B/lbm Consequently, the transient energy storage rate in the film is negligible during blowdown, and even less thereafter. During blowdown the film drainage is neglected, and after blowdown the transient film mass storage is neglected, so the draining mass flow rate is equal to the condensation mass flow rate. That is:
dd - rh,y -mg =0 so (115) rn,y - rhy The conductance of draining films is included in the conductance term that couples the gas to the heat sink, as described in Sections 7.5 to 7.9. All draining films are assumed to have a thickness of 0.005 inches. The conductance pi groups show the film conductance is high enough that this assumption is a reasonable simplification and is a small conservatism that maximizes containment pressure. Stagnant films are those that do not drain effectively and consequently build up sufficient thickness to lead to a significant heat transfer resistance to the surfaces on which they form. They also present large surface areas for evaporation / condensation mass transfer interactions. That is, they behave as a large shallow pool. However, having formed by condensation on cooler surfaces, the film is cooler than the atmosphere and behaves as a heat I sink until reheated by the atmosphere. The sensible heating can only progress to the point j that the film partial pressure is equal to that of the atmosphere. After condensing, the films can have little net effect on containment heat removal or addition. Consequently, horizontal liquid film energy transport is neglected and only their thermal conductance is considered. Liquid films can form to a sufficient depth on nearly horizontal surfaces that their conductance becomes significant in limiting heat transfer. However, rather than tracidng draining film flow rates, estimating the flow paths, and calculating film conductances, a more conservative approach of eliminating heat transfer surface area is used in the scaling analysis. That is, the upward facing horizontal surfaces are assumed to be adiabatic. For concrete floors this effectively eliminates the heat capacity of the floor. i 1 Heat Sink Analysis and Equations for Scaling March 1997 m \3499w.non\3499w<.wpf.lb-031397
7-17 The only steel structures of any size with upward facing horizontal surfaces are the crane rail, stiffener ring, and hatch covers. These are modeled by eliminating the upward facing surface area, while retaining the mass, since the downward facing surface area is still active. Summarizing for liquid films, the heat capacity of draining film is negligible relative to the heat capacity of the surface they form on, and the conductance is included in the heat transfer coefficient. The heat capacity of stagnant films constitutes a heat sink for the gas, so is conservatively neglected, and the conductance to the horizontal surface is assumed to be so poor that the horizontal surface heat capacity is neglected. 7.5 INTERNAL SOLID HEAT SINKS ANALYSIS AND SCALING EQUATIONS Internal solid heat sinks include steel, concrete, and steel-jacketed concrete. The conduction terms necessary to couple the containment atmosphere to the heat sink surface are defined using the one-dimensional energy balance from the containment atmosphere to a heat sink shown in Figure 7-2. The energy balance shown assumes the total energy flux out of the containment gas is reduced by the liquid enthalpy of the condensed film prior to entering the liquid film, rather than conducting some of the film energy partway through the film. Because the conductance of the film is more than 10 times that of the conductance from the I atmosphere to the film, and the energy carried away by the liquid is only 1/10 that of the l condensing gas energy, the error introduced by not conducting the liquid film energy partway through the liquid film is negligibly small. This assumption greatly simplifies the resulting mathematics. j The energy fluxes can be related to the series temperature drops by assuming thermal conduction through the liquid film, and condensation, convection, and radiation heat transfer l l to the liquid surface. For time greater than zero, the heat conducted into the solid and the solid surface temperature can be calculated by various analytical models. The analytical models depend on whether the solid is modeled as a lumped mass, a thick wall, or a semi- j infinite conductor, such as concrete. ; 1 The temperature drop relationships to the heat fluxes are developed from Figure 7-2 for the l containment to inner film surface, and inner film surface to solid heat sink surface: T-T3 - q,"(hg h, + h[ and T .u. -T,g = q" (h,)-i (116) l These two equations are added, so T - T,a remains on the left side of the equation, and only multipliers on q/ remain on the right side of the equation: (T -T,,) - q l (hg h, + hy' + (h,)4 (117) Hear Sink Analysis and Equations for Scaling March 1997 l m:W99w.non\3499w-c.wpf.lb-031397 I
l 7-18 l l 1 N .. Containment [ Inner Film Heat Sink k m .g '
.., m =N m m C
7 C if " ' ~
,, y h, q i,
/ '
I l hgh" coa
/
T T if,, T,,, i t l Figute 7-2 One-Dimensional Energy Balance and Temperatures for Energy Transfer Resistance to Solid Heat Sinks ! Heat Sink Analysis and Equations for Scahng March 1997 mA3499w.non\3499w C.wpf:1b-031397
7-19 The term in brackets defines the inverse conductance from the inside of containment to the solid heat sink surface. The effective heat sink conductance is defined h, = [(h + h, + h,)-3 + hi' ] and is combined with the energy equation to give: dT" (118) m,cm - h, A (T -T,g) 7.5.1 Heat Sink Conductance The individual heat sink conductances are defined from the constitutive equations in Section 4: 0.13(h,-h,)p,,D, AP,, rap w) 0.13 k f Ap Pr ** h* = _ Sc h=c (T-Ty,)(v jg)us p 2 p (y 2f g)ies p (119) h, - o e f(T,T,,) h,, - k, /S, h, - [(h, + h, + h,)-' + h,;' ]-2 The individual conductance tenns are normalized to the shell conductance, h,u , to produce the pi groups for scaling the heat sink conductances: (120) n e , - h,/h,, ny - h,,/h,u ny - h,/h,u ng - h,,/h,g n,, - h,,/h,, Expressions are needed to relate the heat transfer coefficients relative to (T-T,n) to heat transfer coefficients relative to (T-T,,). Combining Equations (116) and (117), the ratio of temperature differences is: T-Td' hd (121) l
- -f7 T-T,, h, + h, + h, + h, ,
1 As the liquid film gets thinner and vanishes, the ratio represented by fr approaches 1.0. Note ; that the heat transfer to heat sinks with liquid films, Equation (118), is written in terms of I (T-T,n), while the evaluation of the individual heat transfer coefficients, Equation (119), is in terms of (T-Tu,), the liquid film surface temperature. 7.5.2 Heat Sink Mass Transfer The mass condensation rate from containment to heat sink j is scaled to the containment mass equation according to Equation (59) where all the properties in the pi expression are ] l Heat Sink Analysis and Equations for Scaling March 1997 l m:\3499w.non\3N9w-c.wpf.lb431397
1
~
7 l evaluated at their initial conditions for each time phase, using the bulk and liquid film surface conditions (not heat sink surface). ; mg , 0.13Ap,,D, AP,, rgvn ]
*# eg,u sgu(v /g)"' Pg 2
p , j i i 7.5.3 Heat Sink Energy Transfer ) The energy transfer rate terms' defined in Equation (70) scale the energy transfer to the heat l sinks. The properties in the pi expressions are evaluated at their initial conditions for each l time phase, using the bulk and liquid film surface conditions (not heat sink surface). (h,3-hyy) (h yp - h,,,) ! 8.;sa " 8"J ' 'd ' " "J i A h***
. A h*** .
(123) I h,yAg (T-Tv ). - 0.13k fAp "" Aw - x"#
= Pr + o e f(T,T,) s (T-T,),
ah s%Ah g pu ,(2 v / g)U2 p , , pg pg Heat Sink Time Constant The time constant for a steel heat sink is the energy storage capacity of the heat sink divided ; by the energy transfer rate to the heat sink: ng c.,,(T,,,-T), pu,cy ,L' (124) hu, A,(T,,,-T), h,u l 4 where the specific length L' = Vu,/A, i' The specific frequency is not defined for concrete and steel-jacketed concrete since the concrete thickness is not a valid measure of the useful heat capacity on a time scale less than i a few days. { 7.5.4 Heat Sink Effect on Pressure The pressure scaling for the intemal solid heat sinks uses the pi groups defined in Equation (81) for enthalpy and work, and Equation (83) for the heat transfer energy pi group: Heat Sink Analysis and Equations for Scaling March 1997 m:\M99w.non\M99w-c.wptib 031397
., - . -_. . ... . . - . . ~ . - - - - . ~ - __ - .~ .- -.
k
.7-21 m
~
' (y -1) p
- pean " " m4 Om). A p-oN " Ema 7o(3 7 )o p"" ' ma (125)
. (y -1), p h,A g(T-T),
e44 7,[} +7T ), p_ gn ;
-7.5.5 Steel Thermal Model' !
P The average steel thickness, calculated from the steel volume / area is 0.5 inches. The Biot number for the average steel is Bi = 0.08, so it is clear that the steel can be modeled as a , lumped mass. With this assumption, the surface heat flux and total stored energy in the heat sink can be related to the heat sink surface temperature and average temperature. ; i Each time phase is modeled 'by a linear change in the containment gas temperature from the j beginning temperature to the end temperature. The heat transfer coefficient is assumed to be j constant over the time phase at the beginning value. The surface and average temperature . ; are tracked by integrating Equation (118) forward in time, subject to the boundary condition ! 1' that at the beginning of the first time phase, t = 0, Tu = Ti = 120 F, and Ti at the beginning of l each subsequent time phase is equal to the value of Tu at the end of the previous time step. : By differentiation it can be shown that the solution to the differential equation and boundary l condition is: ! T, - T, + C,( t -t) + [ T, - T, - C,(t, - t)]e "'"* C, = t. (126) 4 l i 7.5.6 Concrete Thermal Model j i The thermal boundary layer cannot penetrate the thickness of the concrete during the 24-hour -l h period of interest, so the concrete can be modeled as always thermally thick. Its surface ! temperature and surface heat flux can be calculated by coupling the time history of steam !
- and air partial pressures and temperature to the surface, using the integral equations 28,29, ,
and 30 from Wulff 88 for thermally thick structures.
'Ihe containment boundary condition was modeled as a step function over each time phase, 7
with initial conditions equal to the final surface and average temperature from the prior time
- phase. Wulff Equation (31) relates the Biot number, based on thermal penetration depth, to :
; the time. The resulting equation: !
i^ ! I i I t i
^ Heat Sink Analysis and Equations for Scaling Manh 1997 ;
m:ue99w.non\3499w c.wpf Ite1397 j 9 i
7-22 f j r m e 3 , Bi, + 2 l Bi, + 2 21n (127) t=' 2 ,
,2 ,
S u,(h, /k,)2 , is evaluated for values of Bis until the desired value of t results. The desired values of t . correspond to the initial time of each time phase: 0,27,85,1500 sec. The value of h, is the ; time-weighted average of the heat transfer coefficients for each phase included by t-f The surface temperature of the concrete is determined from Wulff Equation (29) with x = 0. That is: { Bi* (128) T'"d
= T* + (T -T,) Bi, +2
~
' The value of Bis is from Equa_ .a (127) corresponding to t at each time phase. T o is the ! initial temperature,120"F inside containment, and 115"F outside. T. is the peak containment [ gas temperature during the transient. This gives moderately high heat fluxes earlier in the ! LOCA, when containment temperatures are less than peak. ; r
'Ihe average temperature of the structure can be calculated from Wulff Equation (30).
Although (30) is the heat-absorbed. division by mc v and addition of T ogives the average j temperature: Bi,2 ApcSk v Bi, gg
.y. - T* + (T -T,) H - T + (T -T,)
3 Bi, +2 mcy 3 Bi, +2 ! i The use of time-weighted average temperature and heat transfer coefficients compensates for ; the small variations in temperature and heat transfer coefficient relative to the model that ! assumes both are constant after a step change at time zero. 7.5.7 Steel-Jacketed Concrete Thermal Model A large portion of the concrete is jacketed by 0.5-inch thick steel plate. huilly, the composite behaves like steel, and later as concrete. The composite is conservatively modeled : (conservative in terms of underestimating heat flux and total heat storage) by modeling the , two structures in parallel and taking the larger of the two as the instantaneous heat flux. ; This neglects the concrete heat capacity during the early part of the transient, when the steel absorbs fastest, and neglects the steel heat capacity later in the transient when the concrete l
~
abkorbs fastest. In the long term, the conductance of the jacket is 624 B/hr-ft 2-F, so its i Heat Sink Analysis and Equations for Scaling Much 1997 mA34hnon\3499w-c.wptit431397 j l l l
7-23 conductance is not significant in comparison to that of the gas conductance (50 to 2 100 B/hr-ft -F). 7.6 SHELL ANALYSIS AND SCALING EQUATIONS The conduction terms necessary to couple the containment atmosphere to the shell, and the shell to the riser arc defined from the one-dimensional energy balance shown in Figure 7-3. As was done for the heat sinks (Section 7.5) the total energy flux out of the contamment gas is first reduced by the liquid enthalpy of the condensed film. The shell has such a high heat capacity that its heat capacity cannot be neglected until several thousand seconds into the transient. The energy fluxes in and out of the shell can be related to the series temperature drops by assuming thermal conduction through the film, condensation and evaporation mass transfer, and convection and radiation heat transfer. The temperature drop relationships to the heat fluxes are presented in the following equations. The temperature drops through each of the conductances into the shell are shown in Figure 7-3 and are the same as for energy transfer into the heat sink developed in Section 7.5. That is: (T-T,,,) = g (h, + h, + h,)-' + (h,,) i' (130) where the inverse of the term in brackets is the conductance from the containment atmosphere to the shell inner surface, h, = [(h + h, + h,)' + hi' ] Energy transfer out of the shell through each of the conductances to the riser and baffle are also shown in Figure 7-3. The shell outer surface to extemal film outer surface temperature drop is: T,3-Tg,, - g,(h,,) (131) and the extemal film outer surface with convection heat transfer and evaporation to the riser bulk flow, and radiation to the baffle is:
/
-I ) 3-1 Tg ,-T,,= C, h, + h,,+ h, (I"' ys (132)
( da d n Heat Sink Analysis and Equations for Scaling March 1997 nu\3499w.ncm\3499w-c.wpf.1b 031397
I 7-24 , i s [ Inner A Baffle Containment i Film Shell External) Film Riser ,q"g , l 4"a+ 4"a -O-4"r>4", -4". g k"r ki ki b , l t 3 If "A [ h "w
, m"c,T :
4 i
~
T L Tau T., T,3, T,t, T,, T,, I, i l l l Figure 7-3 One-Dimensional Energy Balance and Temperatures for Energy Transfer i Conductance through the Containment Shell j
- Heat Sink Analysis and Equations for Scaling Wrch 1997 i mA349Nmn\3499w<.wpf.lb431397 - ]
l
)
7-25 These two equations are added, resulting in the equation: r 3. (133) (T -T,) - C (h,,) + hj h, + h,, (T -T,,) (T,,, - T,) r >- The term in brackets is the inverse conductance for the outside of the shell, where the conductance is ho. Equations (130) and (133) can be combined with the general energy equation for a heat sink, Equation (90), to give: dT'h m, - h, A (T -T,,) - h,, A U,,,4,,) UM Equation (134) was written for the evaporating portion of the shell, but is also valid for the subcooled and dry portions of the external shell, with substitutions for the subcooled region hm, = h o= h,, = 0, and for the dry portion h,, = hm, = 0. The areas of the subcooled and evaporating regions can vary with time, so a basis for calculation is required. The area of the subcooled region is determined from an energy balance on the subcooled liquid in which the heat conducted from the shell heats the liquid from its sor e temperature to the temperature of the evaporating film, T,,. The subcoole:1 film is assumed to have no evaporation, radiation, or convection from its surface. The bases for this assumption are The subcooled water exists at the top of the shell where the riser temperature is at its maximum. When compared to the average subcooled film temperature, T ,,,,, = (Ta+ T,,)/2, the difference (T,,,,,- T n) is a small positive value at peak pressure, and a small negative difference at long-term pressurization. The subcooled surface area is relatively small, only a few percent of the total, so errors have little effect on the evaporating region where most of the shell heat !s removed. The calculation proceeds by calculating the temperature of the evaporating film independently of the subcooled or dry regions. The film energy equation is then applied to estimate the area covered by the subcooled film: m ,cy (T,,,,-T,) g* , (135) h,,,, (T,,,,,- T,,,) Heat Sink Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w<.wptib.031397
4 7-26 L l 1 The liquid film wetted surface area is then estimated as discussed in Section 7.6.6, and the evaporating ' area is the difference between the wet area and the subcooled area, A,,, = A.,, - -) A,,. 'Ihe dry area is the difference between the total area and the wei area, A,,y = 52662 ft.2 - l Awe ! l 7.6.1 Shell Conductance i The individual conductance terms inside the shell are free convection heat and mass transfer, i radiation, and liquid film conduction. These are evaluated independently for the internal l portions of the shell that correspond to the subcooled, evaporating, and dry portions of the external shell. , y "' 0.13(h,-h,)p,,D, AP,, rg n , 0.13k 'Ap
.Pr
" * (136)
(T-T,)(v /g)"3 P, 2 p , (v2 /g)'/3 p , h, - oc f(T,T,,) h, = k,/S, h, = [(h, + h, + h,)*' + hj']~3 k The conductance pi groups are each of these values divided by the reference shell conductance for each of the three shell portions. The fifteen pi groups result: , h,,, h,,,,,, h,,,,, h,,, h,,,,, c,eac "g she c m.sc
~
h sh.o "**
~
hshe
~
h sh,o '"
~
h she 1 h,,,,, ~ h,,,,, ~ h,,,, ~ h,,,,, ~ h,,, (137) K '"" "" "" *"" us hsh.o hsh,o hsh.o h she hsh.o h,3,, h,,,,, ~ h,,,,, ' h,3,, ~ h,3,,
*' ~
Eues " h " d' hsh.o ' ' d' h sko d' hsh.o ' d' she hsh.o i The evaporating portion of the shell outside operates with forced convection heat and mass transfer, radiation, and liquid film conductance: 0.023h,,p,,D, AP, , ,,3 0.023k h"" = D '" Re*8Pr (T -T,,) D, P, D, - (138)
/
. h,, = c c f(T,g T,,) h,, = k,, /5,, h,, - h, + h,, T,,,- + h,, d T,,) ((T + h,7 "-T,,) S-1
-u > -
The conductance pi groups for the external surface of the evaporating portion of the shell are each of these values, divided by the reference shell conductance: Heat Sink Analysis and Equations for Scaling March 1997 mAM99w.non\3499w-c.wpf;1b 031397 l
P t 7-27 h,,,, h o,, h,,, h,,, h,,,,(139) , 8 m= ~ ~ hshe *'"""~ hshe 8 """ ~ h """ hsh,o 'd" sh .o hosh The dry portion of the shell outside operates with forced convection heat transfer and radiation: 0 -T,,) ha,, y .023kRej'Pr us hy,, - o e f(T,,,,T,,) h,,, - hy,, + h,,,, (Tda (140) ;
, (T,,, ,
The conductance pi groups for the external surface of the dry portion of the shell are each of-these values, divided by the reference shell conductance: ; K ues. = ha ,, / h,a xy ,,, = ha ,o / h,a ny ,,, = hy ,,/ h,y (141) The subcooled portion of the shell outside has only conduction to the film with the pi group defined: h am -2k,,/8, x, = h,%/ h,, (142) 7.6.2 Shell Mass Transfer The mass condensation rate from containment for each portion, j, of the shell (evaporating, , dry, and subcooled) is scaled according to Equation (59) where all the properties in the pi j expression are evaluated at their initial conditions for each time phase, using the bulk and liquid film surface conditions (not heat sink surface). rh,% = 0.13 A p,,D, AP,, rap l
'v3 xW = _ Sc (143) !
rnpo 2 thg g(v f g)us pm, p ! The mass evaporation rate from the shell to the riser for the evaporating portion of the shell is also scaled according to Equation (59) where all the properties in the pi expression are 1 evaluated at their initial conditions for each time phase, using the external film surface (not shell surface) and bulk riser gas properties. l Heat Sink Analysis and Equations for Scaling March 1997 mA3499w.non\3499w c.wpf.lb-031397 l
28 i i II2.im,xt, 0.023Ap,,D, AP, ,,, rn,3,,, rh,3,1,D, P, i The external surface of the subcooled and dry shell portions do not evaporate, so there is no evaporating / condensing mass transfer. 7.6.3 Shell Energy Transfer The energy transfer rate terms defined in Equation (70) scale the energy transfer to the inner . surface of the evaporating, subcooled, and dry shell portions. The properties in the pi expressions are evaluated at their initial conditions for each time phase, using the bulk and liquid film surface conditions (not heat sink surface). In general conditions differ on each of the three portions. 1 y (h,3-h,3) , (h,,, - h,,,) , eau , , =J *d4 "4 Ah*6
.s Ah**s (145) h,pAg (T-Tu ). 0.13 k 'Ap m/3 Ag (T-T,),
x*=* rn,3,Ah,3%
=
,(2 v / g)i/2 p Pr
+ o e f(T,T,3) rh,3%Ahp ,u l The energy transfer rate from the shell to the riser for the evaporating portion of the shell is also scaled according to Equation (70) where all the properties in the pi expression are l evaluated at their initial conditions for each time-phase, using the external film surface (not l shell surface) and bulk riser gas properties. }
I h,,,,,, h,,,, A,,,,(T,,,- T,,) , x,,, = x m,, x,,,,, = 0 x ,,,,, = ;
. sh e . she s*'b (146) '
0.023k A,,,,(T,,,-TJ
=
Rej3Pr if3 + ocf(T *
,,T,') (T,,-T,,)
. D, (T,,-T,), m pg Ahp ,
'Ihe energy transfer rate from the shell to the riser for the dry portion of the shell is scaled according to Equation (70) where all the properties in the pi expression are evaluated at their initial conditions for each time phase, using the shell surface temperature (since there is no extemal film) and bulk riser gas properties.
l l l l Heat Sink Analysis and Equations for Scaling March 1997 m:\3499w.non\3499w<.wpt1M31397
7-29 g , hp ,^4.,(T,,,,-TJ ts'" m* *uAhs *u . (147) 0.023k d" 6' '"""'" '" d'
, D, Rej'Pr"8 + ocf(T ,,T ') (T,,,-T )_ pu 6
g m p ,Ah The energy transfer rate from the shell to the subcooled liquid is scaled according to Equation (70) where all the properties in the pi expression are evaluated at their initial conditions for each time phase, using the shell surface temperature and average subcooled film temperature and properties. h,,,,Ao (T,,,- T,,,) , k,, A,(Tm - T,,,) (148)
%,uAh,,g 26, nggAhp,u Shell Time Constant The shell time constant is the energy storage capacity of the shell divided by the heat transfer rate to the shell. A time constant can be defined for each of the three evaporating, subcooled, and dry portions, and for the inside and external heat transfer rates. Thus, the six time constants:
, , P.u c ,L' ,P,u cy,L' ,
P,u C.,L'
" , d'
- h. , h. 4...
h.xo (149)
, , P.u C.,L'
,d"
,Pcc.,
A L' , , P.u c ,L' heria,o h eAsa,o h e, sex.o where the specific length L' = V,u/A, = 6,3 l The time constant for the external heat transfer to the subcooled shell is much smaller than the time constant for the inner surtace, indicating that heat transfer to the subcooled water is ; limited by the shell heat capacity and/or heat transfer to the inside. 7.6.4 Shell Effect on Pressure i The pressure scaling for the internal surfaces of the evaporating, subcooled, and dry portions of the shell uses the pi groups defined in Equations (81) and (83): Heat Sink Analysis and Equations for Scaling March 1997 gru\3499w.non\3499w-c.wpf:1b-031397
.~ _ . . . _ _ _ . _ _ _ .
, i 7-30
' (y - p~
K r.,aha " Kma 7.(3[1)1).p=="@,ima4 ). 8 . orka " E .i p m (150) : (y -1), p,, h, A (T g -T), y,(1+Z'),P,,,_ nig,,, ; The properties are based on initial enditions for each time phase and on the bulk and ligdd film free surface conditions, not on the shell surface temperature. i 7.6.5 Shell Thermal Model : J As time progresses, the thermal boundary layer advances through the thickness of the shell l and eventually reaches the (nearly) adiabatic outer surface of the shell (thermal penetration). l The time of thermal penetration is an important characteristic time for modeling energy ! transfer into the shell. Intemal processes are not coupled to the riser until the thermal j boundary layer reaches the outside of the shell. Using the correlation developed by Wulff", j the thermal boundary layer reaches the outside of the shell in 22 seconds. Thus, the steel l' shellis modeled as a thermally thick structure during blowdown and as a thermally thin structure thereafter. Because the energy transfer from the shell outer surface is very low l ,. until it wets sometime after 300 seconds, the shell can be modeled with an adiabatic outer surface to 300 sec. and with evaporation heat transfer thereafter. l The shell energy equation was formulated in terms of the shell inner and outer surface l._ temperatures. The integral relationships developed by Wulff 833' for thermally thick ; structures are used to track the shell surface and average temperatures for appropriately short values of time, and Wulff" for thermally thin structures with heat transfer from two j sides. Both the thermally thick and thin regimes are modeled assuming the environment j changes as a step function over the time phase of interest. j The shell is modeled considering three independent regions defined by the external film: the relatively small area covered by subcooled liquid, the area covered by evaporating liquid, and the dry area. The integral relationships are applied separately to each of the three regions. The thermally thick solution is first applied to determine the time when the thermal boundary layer penetrates to the shell outer surface. Wulff gives the time in terms of the Fourier number for a plane-parallel slab, which is the geometry characterizing nearly all the surfaces of interest in AP600. For curved structures, such as the shell, the approximation is l valid as long as the radius of curvature is much greater than the thickness. The thermal j penetration time is: I 2 2 Fo = _I .+ + In (151) 12 3Bi 3Bia ( 2 + Bi, Heat Sink Analysis and Equations for Scaling Mmh 1997 m:\M99w.non\M99ws:.wpf:1M31397
I l 7-31
+
i i where Fo = at/62 [ a is the structure thermal diffusivity l t is time l 6 is the structure thickness ! Bi = h6/k l h is the surface heat transfer coefficient. k is the structure thermal conductivity Condensation on the inner shell surface produces a penetration time of 18.4 sec. With this j time, Equation (127) is solved for the Biot number, then Equation (129) is solved for the { average structure temperature. The solution to the temperature in a thermally thin structure uses as input an initial average temperature, gas boundary temperatures, and the Biot number (which is the dimensionless ] heat transfer coefficient) for each surface. The output is the temperature of each surface and the average temperature after some time increment. Thus, it is possible to do a series of j calculations to sequentially calculate the average and surface temperatures at the end of each l time phase, given the initial conditions for the time phase. The equations used are Wulff j Equations (14) - (18), and for the plane-parallel slab can be written-l dT 7= a [B,(T,-T,) - B,(T 2-T,)] H= 2 B' + B, B* + 2 B2 (152) T, -T 2 B, T,-T,3 T, -T. 2 B, e1 _I T, -T,3 i
- + e1_I_ + +
T, -T 2+H 2+B 2 T,-T T-T, 2+B 2+B 2 T-T, This is a system of 4 equations with the four unknowns: T the average structure temperature T i the inside surface temperature T, the outside surface temperature B the combined Biot number The input values are: T, the inside gas temperature
. T, the outside gas temperature Bi the inside Biot number B2 the outside Biot number a the thermal diffusivity, and 6 the plate thickness.
I Heat Sink Analysis and Equations for Scaling March 1997 au\M99w.non\M99w.c.wpf;1b-031397
)
i
7-32 i By substitution, T,, T 2, and B can be eliminated and the rate of change of average t temperature can be expressed in terms of known quantities: [ B,(2 + B,) + B2 (2 + B,) - 2(B, + B,B, + B2 )T] (153) [ Since this equation is of the form dT/dt = Ci - C,T with boundary conditions T = T, at t = t o it has the solution: T - (T~-C, /C2 )e' '" + C, / C, (154) ; where: , e 8 , 2+B' i _a 2(B + B B + B ) i2 2 (155) C' = 52a BT i6 2 + 2+B B* + B,T* + 2and H C' 52 2+B After Equation (154) is solved for i Equations'(152) are solved for surface temperatures T3 and T, to get the initial conditions for the next time phase. - 7.6.6 Weir and Water Coverage Timing The containment shell is assumed to be dry at the initiation of an overpressure signal that ; starts the external water flow. The time from signal actuation includes valve opening, pipe 3 filling, and the center bucket filling and overflowing. The water flows and fills the first weir, i then the second weir, and then flows down the side wall. The growth of initial coverage is a combination of two processes: the increasing flow rate, and the advancing contact line. ; l The flow rate out of each weir increases with time because the outflow increases with the elevation of the water backed up behind the weir. The greater the volume of water stored in the weir, the longer it takes to approach a steady-state where the outflow equals the inflow. The weir outflow rates were calculated for the 440 gpm PCS water flow rate and the results are shown in Figure 7-4). The time for significant occurrences are presented in Table 7-4. The steady-state time is assumed to be when the outflow has reached 90 percent of 440 gpm. Observations of the LST wetting, both on hot and cold vessel surfaces show, after achieving l an initial constant water flow rate, the width of the wet stripe may grow for a few seconds and is essentially static within 10 sec. Since the time constants for flow rate are much greater than the few-second time constant for contact line motion, the times considering only flow l' coverage will be used for scaling. The resulting elapsed time of 245 see for steady-state coverage below the second weir is a nominal approximation to the more conservative 353 sec value quoted in Reference 5. Heat Sink Analysis and Equations for Scaling Much 1997 mA3499w.non\3499w<:.wpf-lb.031397
l 7-33 j Table 7-4 Calculated Time Sequence of Weir Flow Events for AP600 Event Elapsed Time, sec ; Initiate Flow 0 l l Bucket Spills 37 ) l First Weir Spills 110 ; First Weir Steady 145 Second Weir Spills 205 Second Weir Steady 245 Using the times presented in Table 7-4 from this model, heat input to the subcooled liquid is
)
assumed to start at 105 sec from an initially dry vessel, and evaporation to start at 245 sec from an initially dry vessel. Consequently, the subcooled liquid scaling and evaporating scaling begin at the beginning of the peak pressure phase (85 sec). The fact that the time ; phase boundary does not coincide exactly with the 105 and 245 see times is of little concern, ; since conditions at the beginmng of the peak pressure phase (85 sec) and long-term phase ) (1500 sec) bound conditions for times between. I ja The method used to calculated the evaporating, subcooled and dry areas is: Calculate the subcooled area as described in Section 7.6 and Equation (135). Subtract the subcooled area from the maximum wet area (49,062 2ft - A,) to get the maximum evaporating area. Use the maximum evaporating area to calculate the total evaporation. If the total evaporation is greater than 40 lbm/sec (Reference 5, Table 7-9, peak heat flux) then reduce the evaporating area until the evaperation rate is 40 lbm/sec. Heat Sink Analysis and Equations for Scaling March 1997 m:\3499w.rm\M99ws;.wpf.1M31397
1 i 7-34 1 i 0*9- ~~~~~
~ Bucket -~~~~~~~~~~~~---~~--~.'~~~~-~~------~~~~-/ <
/- -
o Outfkw 0.8- - - - - - - -
-- ~ ~~ ~~~~~~"-~~ ~y/ ---l/-~~~~~~~""---~~~~~~~~/--- 1 o :
o : o n 0.7 . . . . . . . . . . . . . . .
............................,J.........: .
I 1....... o I : o o I
- 0.6- - - ~ ~ ~ ~ - ~~~-~~~~~~-*-~~~4--~~~~~~~-~~~~~~~s---~~
~First Box and l lFirstWer j -
t a
,g 0.5- - - ~ ~ ~ -
~~~~~~~~,r< -~~ ~
E porn QAftw--~j--~~~~-li: l pppqw --~~~
~~~-~~~--i'-----P--------~~-----rl-----
0.4 ~-------
- u o
- I o
o
.....................g...n........$......................................g.............
second
/ ! sea
- wer
~~~~~~~~r-~~~~~~::--- - and DMD ~~ ~~Out06w---~~---
i 0.2- - - - - ~ ~ - -- i ,
- Outfkw a 8 .
- I 0.1 - - - - - - - - -
---/------*!-------------------------s---------- 1 O
0 50
,I 100 150 200
,/
250 i Time (seconds) Figure 7-4 Weir Outflow , Heat Sink Analysis and Equations for Scaling March 1997 m:\349Pw.non\3499w<.wptib431397
7-35 Subtract the evaporating area and the subcooled area from the total area to get the 2 dry area A 4,7 = 52,662 ft - A , - A,,,p. 7.7 BAFFLE ANALYSIS AND SCALING EQUATIONS The baffle receives heat by radiation from the shell and loses heat by radiation to the shield building and by convection to the riser and downcomer. The energy equation for the baffle is formulated accordingly, assummg radiation heat transfer from both wet and dry portions of the shell that are generally at different temperatures. Examination of when the shell becomes wetted, and the temperatures calculated for the wet and dry portions of the shell shows that through the beginnmg of the post-refill time phase, the outer shell temperatures for wet and dry portions are sufficiently close in temperature that wet or dry does not matter. Furthermore, once wetting is well along, the shell heat rejection to the baffle can be minimized by assuming 100 percent of the shell is wet (although for shell evaporative heat losses to the riser a lesser fraction is assumed wet). For the scaling analysis the baffle was forced by the dry shell during blowdown and refill, and by the wet shell from the begmning of the peak pressure period and beyond. The baffle is a thin steel member with such a small Biot number that it is well-represented as a lumped mass with identical bulk and surface temperatures. Both sides of the baffle are subject to forced convection and radiation. The downcomer side of the baffle is always dry. The riser side of the baffle may be wet or dry, depending upon the radiation heat transfer rate to the baffle and the convection heat transfer from the baffle to the riser and downcomer. The energy equation for the baffle is: dT" m ,,c, = h,,,,,.y W,,, 4,,) + h,,,,,,, A U,, 43 ,) - h,,,.,, A R,, 4,,) (156)
- h,3,., A (T g -T,) + ris,,,h,,
In terms of inside and outside equivalent conductances, the baffle equation is: mgc, dT" = h,Ag (T,-Tg ) - h,, Ag (T g -T&) (157) ; 7.7.1 Baffle Conductance i The individual baffle conductance terms are: i I I Heat Sink Analysis and Equations for Scaling March 1997 m:\3499w.non\3499wcwpf.It431397
) -i 7-36 l h,4, = hp**D* AP "0.023Ref8Sc 2 h,4y = ocf(T,gT,,,) h,3,# . oc f(T,T,,) l
- (T,-T,,,)d3 P g k k (158) hay 0 {
=y .023Ref'Pr - h,# = g0.023 Re"Pr,2'8 -
h h -
.(T -T,,)
h, = hy +hy + h,, h,, - h,, + h,, f l f [ The riser operates in forced convection and the downcomer in opposed mixed convection. ; The liquid film conductance on the baffle is neglected.- l [ The individual conductance terms are normalized to the shell conductance, hu , to produce j the pl groups for scaling the heat sink conductances: l 1 ' h,, y, , hoy, h,3,#, , h,% l
, u.h +' ,
"d* *"d' b du> "*'* hahe h* hshe (159) -
huy, h,3,, h,,,,,,, !
~ ~
E .ea " c h.h,
*' '""*' h.iu, h.ho 7.7.2 Baffle Mass Transfer ,
The riser side of the baffle may experience condensation leat transfer if the baffle is colder j than the riser gas saturation temperature. The mass transfer rate and pi group are: i i I p'"D AP t th* **' = p'"D AP " 0.023Re"Sc d
x **' = rn
'?O.023Re"Sc d
/3 (160) !
dh Pkn.mr sarked , Pimair ! j i 7.7.3 Baffle Energy Transfer ! Each term of the right-hand side of Equation (156) represents energy transfer processes that are of interest to scale. The terms are normalized by the break source enthalpy flow rate and are made dimensionless with the substitutions defined above: Heat Sink Analysis and Equations for Scaling March 1997 ! m:\3499w.non\3499w-c.wpf:1b-031397
, l
._. _ _ ~. ___ .
7-37 i h,, yA (T,,4,,) . h,,,,,, $, 4,,) , h ,3,,,, W ,,- T ,) , h,3,,,,AU,,4,) ; i
'**pa, Ah,3,3 m,3,,, Ah,3,, m,3,gAh,3,, s,3,,, Ah,3,,, .,
- w h,,
h,,g,hl,yA,AT y ,ATL y h,,,y,,h
- g_ A,AT,y,AT,y ,
- 24,Ah,34, s rng,gAh pa, m p,,, Ah,3,,, (161) i h,3,#,h,*3,,,, A, ATw # ,A T; # _ h u ,# ,hj,,#A,ATg#,ATy# rit,g,,slg,h,yhl, ;
th,3,, Ah,3,3 s,3,,, Ah,3,,, rh,3,, Ahp ,g ,
"K uw+,h
- 3yATL_g + x,y.gh;. GAT,*g-x,,,3,,,,hl3,#ATy#
l'
-K u Al-dc h*3,#AT*# +x,,,,,s,*,3,hl, where the pi groups are defined: -
K um+ " h, ,.g,A,ATg,, ~ huy,A,AT,g, ~ h,3,#,A,ATg#, l mg Ah g "d* sg Ah g "*'* rhp,g Ahp ,(162) chf-dc.o o bf-des ig,o Ku.bf-de " 5*' th,3,,, Ah,3,,,, "'*'Ah,3,g, 1
' Baffle Time Constant The baffle time constant is defined in Section 7.7.4.
7.7.4 Baffle Thermal Model For scaling, it is of interest to determine the rate of change of baffle temperature, assuming other parameters are constants. Under this assumption and assuming the baffle can be i modeled as a lumped mass, the baffle energy equation can be written as: dT 68 . a - bTW (163) dt i where: ! (164) h, ,,,T,3+hyy T, + h,3,,,,T,, + h,3, ,T,, + hy.g T, , h, .g + hg g + h ,3, ,,+ hg,.,, + hoy l Pwc6 vg pgy e S,,
- With boundary condition T = Toat t = t , othe solution to Equation (163) can be shown to be: {
l i Heat Sink Analysis and Equations for Scaling March 1997 m:\M99w.non\M99w c.wphib-031397
7-38 Tg = a/b -(a/b -T,)e'"W for 't 2 t, (165) The ratio a/b can be set equal to T, then the solution to the energy equation is: T = Y - (T -T,)e *'W (166) where t = 1/b. This is the thermal model that is used to calculate the baffle temperature at the end of each time phase, given the values for ot and T , and with all the parameters in Equation (164) evaluated at t, and T,. The baffle Biot number, h6/k,is on the order of 0.04 for high condensation mass transfer rates, and less without mass transfer. Therefore, using the criterion Bi < 0.1, the baffle can be modeled as a lumped mass with little loss of accuracy. 7.8 SHIELD BUILDING ANALYSIS AND SCALING EQUATIONS The shield building is a concrete heat sink with dry forced convection to the downcomer and radiation heat transfer from the baffle. Because it is so thick it behaves as a semi-infinite solid. He shield building can potentially affect the downcomer air flow rate by heating the downcomer air, thereby inducing buoyancy that counteracts the riser and chimney buoyancy. , The maximum effect results if all the radiation from the baffle is assumed to be deposited into the downcomer, rather than some being absorbed in the concrete. It is shown in Section .8.4 that the energy transfer to the downcomer is small, and in Section 9.4 that the counterflow buoyancy is small, so it is reasonable to simplify the analysis by neglecting the shield energy interaction and allow the baffle radiation to be deposited directly into the downcomer air. 7.9 CHIMNEY ANALYSIS AND SCALING EQUATIONS The chimney and upper part of the shield building are large concrete structures that can cool the PCS air flow before it exits from the chimney, and thereby reduce the natural circulation buoyancy force. Section 4.2 shows the chimney operates in opposed mixed convection heat and mass transfer. The concrete was modeled with the same equation used for the internal heat sinks, except that radiation from the top of the shell to the concrete is neglected. Neglecting radiation reduces the heating rate and overpredicts the heat removal from the air flow path, thereby minimizing the air flow rate. Heat Sink Analysis and Equations for Scaling March 1997 m:\M99w.non\M99w<.wptib-031397 yv
7-39 The effective heat sink conductance is defined h, = [(h + h, )-2 + h,-2 ]~ and is combined with the general energy equation for a heat sink to give: dT'h (167) mac, = h, A (T -Tg) The right-hand side of Equation (167) is normalized by the break enthalpy flow rate and made dimensionless with the substitutions above. h,3A,(T, -T,y) " h,,gh,*3Ag ATg AT; h,,,, M,,,
"A exw rit p,u hp,u risp,u hp,u ggg) h, A g ATg where x" = .
risp,u hp g I 7.9.1 Chimney Conductance j l The individual conductance terms are:
' vn k l h* (0.13d")' 3P + (0.023)'Re 2 Pr "
- ha = k,/ S d 2
l d, (v g) p 2 d (169) P S1/3
'E h" - (h -h,)p,,D, AP 8
(0.13d )' AP + 0.023'Re 2 h 2 d Sc. 2 h e- [(h + =h )~2
+h,-2 ]-2 (T -T,,,) d, Pu r (v 7 g) p >
I i i The individual conductance terms are normalized to the shell conductance, h,u , to produce the pi groups for scaling the heat sink conductances. Radiation to the concrete is neglected, resulting in more heat transfer from the gas to the chimney, and consequently,less buoyancy to drive the natural circulation air flow. The liquid film is assumed to be 0.005 inches thick. x *^^ . =e" . "h* x *-"*h - deu n '**h . "" (170) g *h hsh,o hsh,o hshe hosh 7.9.2 Chimney Mass Transfer j The opposed mixed convection condensation mass transfer to the chimney is calculated and scaled: , Heat Sink Analysis and Equations for Scaling Much 1997 m:\3499w.non\3499w<.wpf:1b 031397
7-40 i f M/3 In,,,,, , p,,D,A ,AP,, (0.13d,)' g 3 ,,, (173) 3 d ' rh p,u rng ,ud, P g 2 (v /g) p , where the parameters are evaluated at initial conditiens at the bulk and condensed film free surface. 7.9.3 Chimney Energy Transfer Energy transfer terms similar to those for the intemal heat sinks are defined and scaled.
' Those are the energy change from the gas to the condensed film, the energy of the film above '
the minimum energy (here h, at 115'F) and the heat transfer to the film: t (h g -h,) ~ (h,- h,,) , Eelgeh " meh #h ""h Ah 7 Q (172)
=
h, A,(T,-T,3) =_ k (0.13d,)' AP + (0.023)'Re u Pr tes ^6(Tg-T,3) x *# Ihpru Ah p ,g d, (v 7g) p 2 d Ing ,gAhp ,u where the parameters are evaluated at initial conditions at the bulk and condensed film free - surface, and h, = h e. , 7.9.4 Chimney Thermal Model The time history of the chimney and shield building concrete surface temperature is predicted using the same integral methods for thermally thick structures as used for the internal concrete in Section 7.5.6. l Heat Sink Analysis and Equations for Scaling March 1997 at\3499w.non\3499w c.wpf 1b 031397
8-1 8 EVALUATION OF CONTAINMENT AND HEAT SINK PI GROUPS 8.1 HEAT SINK SURFACE AREAS DURING TRANSIENTS Surface area is a very important parameter for calculating the heat and mass transfer to the heat sinks. The surface area of some heat sinks change over time: the break pool volume and surface area increase with time, and the wetted area of the external shell initially increases, then varies with time as the source flow rate changes and the containment pressure causes , the shell heat flux to change. The pool areas were discussed in Section 7.2.2 and the shell I surface areas were discussed in Section 7.6.6. All other areas are assumed constant over the time covered by the scaling analysis. The areas of all heat sinks used in the calculations are summarized in Table 8-1. l Table 8-1 Heat Sink Areas During DECLG and MSLB Transients (Units are ft2) DECLG LOCA MSLB Heat Sink Blowdown Refill Peak Press Long Term Blowdown 7 7.2x107 7 7 Drops 7.2x10 7.2x10 7.2x10 0 i Break Pool 420 555 1933 1933 0 1 Steel 142,700 142,700 142,700 142,700 73,800 l Concrete 22,600 22,600 22,600 22,600 22,600 46,500 46,500 46,500 46,500 12,600 I Jacketed Concrete Evaporating Shell 0 0 47,613 27,000 0 Dry Shell 52,662 52,662 3,600 24,077 52,662 l l Subcooled Shell 0 0 1449 1586 0 l 8.2 CONDUCTANCE PI GROUP VALUES I Table 8-2 presents the energy transfer conductance pi values for each heat sink and shell region during each time phase. The conductance pi values are defined in Section 7 as the ratio of the equivalent conductance (that combines for radiation, convection, mns transfer, and the liquid film) to the shell conductance, that is, n, = h,/h,s. Since the normalizing value is the same for all values in Table 8-2, the values can be compared both horizontally and vertically. Evaluation of Containment and Heat Sink Pi Groups Mardi 1997 m:\3499w.non\3499w-d wpf.It>631397
8-2 Table 8-2 Heat Sink Energy Transfer Conductances Ssaled to Shell Conductance IIcat Sink Blowdown Refill Peak Press Long Term MSLB Drops x,3 141 165 149 202 - Pool x,,, 184 0.02 1.38 0.98 - Steel n,, 0.31 0.40 0.42 0.45 0.37 Concre'a n,u 0.25 0.41 0.35 0.50 0.29 Jacketed n, 0.31 0.40 0.42 0.50 0.37 Dry Shell x,3, 0.33 0.39 0.37 0.54 0.37 n,,,,, 0.01 0.01 0.01 0.02 - Subcooled n,, - - 0.39 0.58 - x,, - - 3.88 3.88 - Evaporat- x,,,, - - 0.37 0.60 - ing Shell n,, - - 0.10 0.52 - Baffle n,3 0.03 0.03 0.05 -7.6 - x,3 0.01 0.01 0.01 0.02 - Chimney na 0.03 0.03 0.02 0.07 - All the conductance values have been normalized to the coated shell conductance, h,3 = 216.58 B/hr-ft 2-F. The coated shell conductance is the shell plus the inner and outer inorganic zine coatings. The coating conductance is 4840 B/hr-ft2 -F, so has little effect on the shell conductance. Table 8-2 shows the conductances for the drops are extremely high, so the drops quickly reach thermal equilibrium with the gas and subsequently follow changes in the gas temperature with no significant lag. The conductance to the pool during blowdown is very high because it is assumed to flash to thermal and mechanical equilibrium with the average containment, as was assumed for the drops. After refill the assumption of a saturated source causes the pool evaporation conductance to remain high. During refill the pool condensation conductance is low. The conductance of the outside surface of the subcooled shell is very high because heat is conducted directly from the shell to the subcooled liquid through the thin film thickness. l
\
l Evaluation of Containment and Heat Sink Pi Groups March 1997 ! m:\3499w.non\3499wdwptit>431397
8-3 I i Since the film is the heat sink, there is no additional evaporation, radiation, or convection conductance. The conductances for the solid heat sinks, shell inside and evaporating shell outside all are j high, in the range of 0.10 to 0.62, due to the high mass transfer conductance. The external ' conductance on the evaporating shell at the time of peak containment pressure is nearly equal to the internal conductance, and both are approximately 1/2 the shell conductance. The remaining conductances range from 0.01 to 0.05 and are low mamly because mass transfer is not involved. The chimney operates with low conductances, even when i condensate forms, due to the high noncondensible concentration. The dry shell external l conductance is 1 to 2 orders of magnitude less than the internal conductance. The baffle j inside and outside both operate dry and have low conductances. The anomalously high ) negative baffle conductance resulted from a reversal of the baffle-riser temperature difference J that was coincidentally small. The energy transfer is low, similar to the value during the preceding time phase. 8.3 MASS TRANSFER PI GROUP VALUES , The containment mass flux pi groups discussed in Section 6.1, and the heat sink mass flux pi groups defined in Section 7 are presented in Table 8-3. The values greater than 10 percent are shaded. Conclusions of the mass flow rate scaling are:
- The mass flow pi groups show the break liquid mass flow rate is high, and the steel, concrete, jacketed concrete, dry shell, and evaporating shell have high-scaled mass flow rates during some time phases.
The pool, drops, subcooled shell, baffle, and chimney always have small-scaled mass flow rates. During blowdown the break source flow rate is so high that even with significant energy absorption, none of the heat sinks have high-scaled mass flow rates. 8.4 ENERGY TRANSFER PI GROUP VALUES The containment energy flux pi groups discussed in Section 6.2, and the heat sink energy flux pi groups defined in Section 7 are presented in Table 8-4. Values greater than 10 percent are shaded. Evaluation of Containment and Heat Sink Pi Groups March 1997 mA3499w.non\3499w4wptit@l397 l i
8-4 Table 8-3 Containment and Heat Sink Mass Scaling Pi Group Values Pi Group Blowdown Refill Peak Press Long Term MSLB t,(sec) 39 985 913 5173 537 Contain- . K,a 131/ 1.27. ' 1.30 : 1.22. ; 1.27 ment nm 1.00: 4 0.00* 1.00* 1.00 '1.00 ! Kg 1.75' O.00 '2.00 0.00 0.00 Drops now 0.02 0.00 0.00 0.00 - no ,.ps 0.01 0.00 , 0.03 -0.04 - l Pool n,m 0.04 0.00 0.03 0.07 - Steel n ,,, -0.05 '
-1.41 . -0.69 -0.02 -0.44 1 Concrete no -0.01 -0.08 -0.02 -0.09 . -0.12 JacLeted n, -0.02 -0.46 ' -0.23 . -0.18 -0.08
- Sc Shell no - - -0.01 -0.06 -
Evap nm - -
-0.43 -0.90 -
Shell K. - - -0.02 -0.89 - Dry Shell n 3, -0.02 -0.61 -0.03 -0.08 -037 Baffle n ,w 0.00 0.00 0.00 0.00 - Chimney ne 0.00 0.00 0.00 0.05 -
- Refill was r,caled with the same 200 lbm/sec flow rate used to normalize peak pressure.
Pi groups are normalized to different energy flow rates in each time phase, so cannot be compared between different time phases - only comparisons within the same column are meaningful. The sensible heat transfer terms (q subscripted) are always small. The energy carried away by the liquid film (f subscripted) is generally 10 percent or less of the energy transferred into the heat sink by condensation (fg subscripted). The inside of the dry shell during refill, and the inside of the evaporating shell during the peak pressure phase have large values of scaled energy transfer, while the outside is small, indicating the significance of the shell heat capacity. Energy interactions with the baffle and chimney are always small. Evaluation of Containment and Heat Sink Pi Groups March 1W7 ut\MWw.non\M09ww1.wpf.It>C31397
8-5 Table 8-4 Containment and Heat Sink Energy Scaling Pi Group Values Pi Group Blowdown Refill Peak Press Long Term MSLB Contain- n,, 0.55 ~ 0.58 0.56 0.63 0.58 ment - n,a 1.00- 0.00' 1.00* 1.00 1.00 n,1,,,, 0.00 0.00 0.00 0.00 0.00 Drops n,y 0.00 0.00 0.00 0.00 - n,.,g 0.05 -0.04 0.00 0.00 - Pool n,, , 0.00 0.00 0.00 0.00 - n,x, 0.03 0.00 0.02 0.06 - Steel n,,, 0.00 -0.08 -0.03 0.00 -0.03 n 3, -0.05 -1.35 -0.64 - 0.02 -0.44 n,j , 0.00 -0.05 -0.05 0.00 -0.01 l Concrete n,,, 0.00 0.00 0.00 0.00 -0.01 j n,,, -0.01 -0.07 -0.02 -0.08 -0.12 n,.,, 0.00 -0.01 0.00 -0.01 0.00 Jacketed n,4 , 0.00 -0.03 -0.01 0.00 -0.01 Concrete n,33 -0.02 -0.44 . -0.21 -0.16 -0.07 n,.,, 0.00 -0.02 -0.02 -0.02 0.00 Subcoor- n,4, - - 0.00 0.00 - ed Shell n;r - -
-0.01 -0.06 -
n,j, - - 0.00 -0.01 - n, ,, - -
-0.01 -0.08 -
Evaporat- n,., - -
-0.02 -0.03 -
ing Shell n .,, - -
-0.41 -0.81 -
n,;, - -
-0.02 -0.09 -
- n. ,, - -
0.00 -0.03 - n.3 - -
-0.02 0.81 -
Dry Shell n,g, 0.00 -0.03 0.00 0.00 -0.02 n,.,g, -0.02 -059 -0.03 -0.07 -0.36 n u. 0.00 -0.02 0.00 -0.01 0.00 n,g., 0.00 0.00 0.00 -0.03 -
- Refill was scaled with the same pressure normalization used for peak pressure.
Evaluation of Containment and Heat Sink Pi Groups March 1997 mA3499w.non\3499w-d.wpf.It>.031397
8-6 Table 8-4 Containn.ent and Heat Sink Pressure Scaling Pi Group Values (cont.) Pi Group Blowdown Refill Peak Press Long Term MSLB Chimney x,, 0.00 0.00 0.00 0.00 - x,,,g 0.00 0.00 0.00 -0.05 - x,a 0.00 0.00 0.00 0.00 - Baffle x,g 0.00 0.00 0.00 -0.02 - x, ,, 0.00 0.00 0.00 -0.02 -
- Refill was scaled with the same pressure normalization used for peak pressure.
8.5 PRESSURE PI GROUP VALUES The containment pressure pi groups discussed in Section 6.3, and the heat sink pressure pi groups defined in Section 7 are presented in Table 8-5. Values greater than 10 percent are shaded. The negative signs in Table 8-5 indicate pressure decreases, while all others are pressure increases. The drops produce a small pressure increase during blowdown, and thereafter are either a pressure sink, or at worst, a negligible pressure source. The pool is always a small pressure source that increases to 7 percent at the time of peak containment pressure. The remaining heat sinks reduce pressure during the time phases considered. The pi groups in Table 8-5 show the work due to mass removal is the most significant pressure reduction process: heat transfer (radiation plus convection) are typically us than 20 percent of the flow work. The enthalpy pi groups for both the source and heat sinks are i always small. The pi groups clearly show the importance of mass transfer as the process that dominates the rate of pressure change after blowdown. Volumetric compliance, ny, is always a significant factor that mitigates the rate of pressure rise. Evaluation of Containment and Heat Sink Pi Groups March 1997 m:\M99w.non\M99w<Lwpf:lt431397
8-7 Table 8-5 Containment and Heat Sink Pressure Scaling Pi Group Values Pi Group Blowdown Refill Peak Press Long Term MSLB Contain- n p., ?0.76i , 0.76' O.77 .. 0.76 . -. 0.76 : ment . n,.p,i i 1.00 0.00* 1.00* 1.00 -1.00 ' np .p,im 0.03 0.00 0.03 0.02 0.03 n,,.,. i 0.00 0.00 0.00 0.00 0.00 Drops npg 0.00 0.00 0.00 0.00 - nu p 0.00 0.00 0.00 0.00 - np .m 0.05 -0.04 0.01 0.00 - Pool np .,, 0.00 0.00 0.00 0.00 - n, p 0.00 0.00 0.00 0.00 - np .a, 0.04 0.00 0.03 0.07 - Steel n, p 0.01 4.24 -0.09 -0.00 -0.0" ap ,,. 0.00 0.00 0.00 0.00 0.00 n p. u, -0.05 i-1.41 -0.69 : ' 0.02 .
~-0.44 '
Concrete n, p 0.00 -0.01 0.00 -0.01 -0.02 l f
- n. p 0.00 0.00 0.00 0.00 0.00 1 1
n .m p -0.01 -0.08 -0.02 -0.09 ' -0.12 l l Jacketed n,p 0.00 -0.08 -0.03 -0.01 -0.02 Concrete n.e p 0.00 0.00 0.00 0.00 0.00 Ep ... -0.02 -0.46 - -0.23 -0.18 ' -0.08 Evaporat- n,p
-0.07 -0.08 -
ing Shell npm - - 0.00 0.00 - E p% - - J-0.43 : -0.90 - - Subcool- n,p 0.00 0.01 - ed Shell Epm - - 0.00 0.00 - j 1 n p. s, - -
-0.01 -0.06 - l Dry npp, 0.00 -0.10 -0.01 -0.01 -0.07 i Shell i npm 0.00 0.00 0.00 0.00 0.00 l n r. u. -0.02 ' 0.61
-0.03 -0.08 -0.37 '
, Refill was scaled with the same pressure nonnalization used for peak pressure. Evaluation of Containment and Heat Sink Pi Groups Mah 1997 m:\34h.non\34h4.wpf;1tW31397
9-1 9 PCS AIR FLOW PATH SCALING Outside containment, the PCS air flow path, consisting of the downcomer, riser, and chimney, has one inlet to the downcomer, one outlet from the chnnney, a source of steam that evaporates from the shell, and a steam sink for condensation on the chimney concrete > and baffle. It is necessary to write the conservation equations separately for the downcomer, , riser, and chimney, so the changes from the inlet to outlet of each can be tracked and factored into the buoyancy calculation in Section 9.3. 9.1 PCS AIR FLOW PATH MASS TRANSFER i The three mass equations can be written: dm,, dm, dt
" ~
d' dt d'
~
d **' ~ ** (173) ; dm, ~ dt d ~ * * ~ ** *
- The condensation and evaporation rates and the time constants are the variables of interest for scaling. The pi groups were defined, respectively, for the shell evaporation, baffle ,
condensation, and chimney condensation in Sections 7.6,7.7, and 7.9. The necessary flow rate variables are defined: Time t = t t' Volume V = V, Inlet air flow rate rig = rig.orit*, Downcomer density po, = pac,,pa,' Riser density pn = p, p3 Chimney density pa = p,upa' The downcomer, riser, and chimney time constants are definea as the mass of gas in each region divided by the air mass flow rate through the entire flow path. The steam , evaporation and condensation flow rates are an order of magnitude smaller than the air flow I rate, so contribute little to the time constants: V, p V,p, _ V,p , m,, rity m,,, j l PCS Air Flow Path Scaling - March 1997 m:\3499w.non\3499w-d.wrLit@l397
9-2 1 i 9.2 PCS AIR FLOW PATH ENERGY TRANSFER i The energy transfer terms for the PCS air flow path include the mass transfer terms discussed in Section 9.1, with their respective enthalpies, plus convective heat transfer between the gas and surfaces. Although there is radiation from the shell to the baffle and baffle to the shield, the beam length and steam partial pressure are too small to allow the gas to absorb significant radiation. Hence gas absorption is neglected. The one potential exception is if fog appears in the riser. Although the conditions assumed for safety analyses preclude fog formation, due to ! the rather high saturation temperature of the gas, it is important to evaluate what happens if other ambient conditions are assumed. Such an evaluation is presented in the PIRT, where it ! was concluded that the heat released to the gas by condensation increases the buoyancy, resulting in a net improvement in heat removal from contamment. Because the steam partial pressure in the PCS air flow path remains low, less than approximately 2 psi, steam can be approximated as an ideal gas. This permits the energy equations to be written in terms of specific heats and temperature differences: d(mu) i dt
'" * ""d' '
'" P ** "
- b' d(mu)
' " * ' ' ' " -h,,,) + qd
" ~ * ~
dt * *d' ** '**'** (175)
"
- i,C
. r ,a (T o -T,) + m,,,c,,,(T,, -T,) - m,,3,c y,,,(T -T,,) + 4, d(mu) " ~ ~
dt '" ** '"* ** ***' '"' '** *** ** ""h
" ** Cr (T, - T,,) + (m,,,,, + m,,3,) c,,,(Tg - T,,) - m,,,,,, g,,, F T,,) + q, where the de, ri, and ch subscripts on temperature, enthalpy, (and later) molecular weight, and density imply the value at the outlet of that region. T is the bulk temperature of the region, or the average of the inlet and outlet temperatures.
The evaporation, condensation, and heat transfer are the energy transfer rates of interest for scaling. These terms were defined for the shell, baffle, and chimney in Sections 7.6,7.8, and 7.9, respectively. 9.3 PCS AIR FLOW PATH MOMENTUM EQUATION The wind-positive character of the PCS air flow path is neglected and the PCS air flow is modeled as entirely buoyancy-driven (Ref. 5, Section 6). The positive buoyancy is provided by air heating and the evaporation of low density steam into the riser and chimney. A small amount of negative buoyancy is provided by heating from the baffle and shield walls in the j l PCS Air Flow Path Scaling March 1997 m:\M99w.non\M99w d* pf:IMD1397 '
9-3 downcomer, and heat and mass transfer to the cool shield building and chimney at the outlet. Wind-induced recirculation was shown to have a negligible impact on containment pressure (Ref. 5, Section 6). The PCS air flow path consists of the downcomer, riser, and chunney, which are modeled as ; distinct, series-connected flow paths. The PCS air flow path, with elevations of important , features, are shown in Figure 9-1. It is assumed that the heat and mass are added to, or : removed from, each leg of the path at thermal centers that are located to muumize the PCS air flow rate. i Following the example of Wulff ", the system of momentum equations for a single loop can be written in vector form where the overline indicates vectors: I - G - R IKEJ (176) dt iis the geometry dependent inertia vector: i (177) I - ((L/ A), , (L/ A),, , (L/ A),) in is the mass flow rate vector: in - (m, , rh, , rig) (178) G is the buoyancy defined by integrating the density times the dot product of the gravity and displacement vectors around a closed path: G = [p g ds = [p gdz +fp gdz +fp gdz+ fp gdz (179) S dc rt ch env E is the impedance vector and Ri is the sum of the form and friction resistance for each segment determined from the 1/6 scale pressure drop test3 ': 1 K, + f,L, /dM R= I (180) 2 p,A[R, , R,, , R,) where R'. - (A,/ A,,)2 l l I PCS Air Flow Path Scaling March 1997 an \3499wann\3499wdwpf;1t41397
.i : , y.
l t t . F ja - a,b i~ 4-t b 1 i s 4 1 e Figure 9-1 Passive Cooling System' Air Flow Path Momentum Parameters PCS Air Flow Path Scaling I#
' m:\3499w.non\3499wwi.g.1W1397
a > 9-5 KE is the vector of kinetic energies: , 2 (181) IKET = {rn,2, , rh2,rh) where
% = rh , - 4 + rtw,,, - rN,3, = r4 and rh i, + rh,., - rh,a - rh,e = rN. ;
9.3.1 Dimensionless PCS Momentum Equations j i The matrix elements are made dimensionless by setting each equal to the product of a reference value and a dimensionless value: Inertia I, = I,I,' where I, = I Im Mass flow rate rh, = rh orn,* Buoyancy G=GG* i Density p, = popf where p, = p,i, th, . nbient air density Flow resistance R, = R R
- where R, = the total PCS loss The reference macs flow rate comes from the reference buoyancy term, which is used to j normalize the inertia and resistance terms. The reference buoyancy is the steady-state solution to the momentum equation, that is, the solution to the momentum equation without the inertial term. The buoyancy term is defined, in terms of' thermal center differences shown in Figure 9-1. The thermal center values, Hi , H2 , Hy and H4 are [
] ft. respectively for the downcomer, riser, chimney, and outlet. The thermal center approach assumes the density changes step-wise at the thermal center. The buoyancy is:
~ ~
a,b (182) i where the last three bracketed terms represent, respectively, the downcomer, riser, and chimney buoyancy contributions. The density used in Equation (182) is defined from the ideal gas law, which is sufficiently accurate for air and steam at atmospheric pressure. The
~ molecular weight is defined for the air-steam mixture and the temperature is defined by the ;
steady-state portions of the PCS air flow path energy equations (175). ! l PCS Air Flow Path Scaling wrch 1997 mW99w.non\3499w-d.wpEll>431397
^
} <p' t
. 94 . ,
1 1 1 l
-PM*
M, .- M, T, - Tj *,q, (183) ! p, = RT, c,, .; i FM, M".= rh, + rh ,-0.5 th , Td = rh c,,T,+riyc,,T,-0.5mo c,,T, + 4, p* = RT, rh, rh, ,- 0.5 rh , s,c ,y + rh,u yg c -0.5 m ,cy , .; M, M,,, _ (134) l l PM, . rh,+ rig,-rh,-0.5 rh, j p* M*" : 7-RT, rh., rh -m,- 0.5 th u l M.ur M (185) ;
- h T^ = T". +
rh ,c + (rh,,, - m,g - 0.5 mm)c,, The q Hrms represent the net heat transfer into the gas, rh is the same in all terms, and P is j
- one atmosphere. The evaporation was assumed to enter at the temperature of the i evaporating surface, T,,,,a and the condensation was assumed to leave at the average of the _
(riser or chimney) inlet and outlet temperatures. A simultaneous solution was used to ; calculate the temperatures& (T , T,, T,), flow rates (riy, rh,.a, rh g, rh,d, and buoyancy l
. (G ). The calculated results are conservative in terms of minimizing air flow, because the !
thermal center of the riser and downcomer were both selected high up [ ] elevation in l' Figure 9-1), rather than at the geometric center (approximately at [ ] ft. elevation).
~
The areas, lengths, and loss coefficients for the AP600 air flow path are shown in Figure 9-1. From these values the R and I vectors are: l a,b l i I (186) l (187) PCS Air Nw Path Scaling m e 39,7 avu\3499w. mon \3499ww1.wpf:3b431397 _ _ _ _ - _ _ _u______________1_______
9-7 , a,b t Figure 9-2 shows an example of a simplified PCS buoyancy calculation using density values calculated with the scaling equations for AP600, and assuming the density variations are ; linear. The net buoyancy is represented by the enclosed area. The buoyancy calculated
~
using the thermal center approach is shown for comparison. For this case both the distributed density and thermal center approaches give the same result. Note that for this assumed case, the net buoyancy is not affected by the amount of heat transferred from the :
. riser to the downcomer. (Moving point 2 along the horizontal axis does not change the area
- within triangle 12-3). However, moving point 2 does change the relative ratio of negative !
downcomer buoyancy to positive riser buoyancy. i 9.3.2 Normalized PCS Momentum Equations I The dimensionless and reference variables defined in' Section 9.3.1 are substituted into l
. Equation (176), and each term is ncrmalized by the reference buoyancy. The result is:
G* R*rh2 I*th*I dijF *7 KE' or =x " " * "
- G*-x"'"F KE
- GT dt-
__ . G * - G, 2p,G, x"'*i diiF dt* (188) V Im
- Rm 3 I where t -g x,,, -
x ,, y - 1 x ,,, = O O O The three components of the buoyancy equation (182) are defined as pi groups: a,b (189) l I i PCS Air Flow Path Scaling March 1997 ,
' m:\3499w.non\3499w.d.wpf.lb4n397 1
I 1 1 9-8 1 I l i b M , jg.. C)ymnq y Qutigtg........... ..........J........ p..........j......Emrconment ......... 1.......... O4~'--4.------*--. 160- - i
-----------------8-----.
s : : : : i l Chi:b !. h- -+ ~..-:- -- . ney Th6. 1-.- rmal! Center U . 140- - --I: -
- ~..-..+--~d---
l : : pjg...........)
.........4..........4....................,......................:...........,..........
[ e . : S 100-' - , - 3 . Riser. Top.--..j.......-+- Dm 7 amer.lnlet..._ 1 ..... ....._.._
$ e : : : .m i .
i . W 80- t - -j - - - - - - -- -
- w- - - r - - t- - -
! ! : Therm Critr i j 60- i.-
-- f _ __ ..__-_________
- g. .
- i. - --- . - _.. -- Y..____--- -- -..___:____
!._----- 3,t--
i.--- -- --i._------- i 40- -- a --
-- -----------:------- ---1---
.iNr-iserTh.ermal :- -- -- . ,
- . Cent 9r :
20- '-4--------*------>--------+----<- -*----
--- ."--- Thermal Center Chiculatiort : 2 - Do- w- n- co- m- er- -- ;
' Bott4n iiinear vairiation Chiculatiori i i O . . . . . . . . .
0.06 0.061 0.062 0.063 0.064 0.065 0.066 0.067 0.068 0.069 0.07 Air Density (Ibm /ft^3) i
)
,i Figure 9-2 Buoyancy Calculation for the AP600 PCS Air Flow Path Comparing Distributed and Thermal Center Approaches PCS Air Flow Path Scaling March 1997 m:\3499w.non\3499w d wptit>031397
1 9-9 9.4 VALUES FOR PCS AIR FLOW PATH MOMENTUM PI GROUPS The reference PCS air flow path buoyancy is calculated using heat fluxes calculated from the equations presented in Section 9.2, and the reference mass flow rate is determined from the buoyancy. The time constant and pi groups are then calculated for each time phase and are presented in Table 9-1. The ratio of the branch buoyancy to the total buoyancy, G/G, is presented to show the relative contribution of the downcomer, riser, and chimney to the total buoyancy. The PCS is not considered for the MSLB, due to relatively short duration of the transient. Table 9-1 PCS Air Flow Path Momentum Scaling Groups Blowdown Refill Peak Press Long Term I t,, 70 61 15 7.0 x,,, 0.13 0.13 0.13 0.11 x,,% 1.00 1.00 1.00 1.00 x,,,,,, 1.00 1.00 0.97 0.86 x ,,3, 0 00 -0.05 -0.03 -0.16 x,,,, 0.48 0.52 0.46 0.58 x ,,3 0.52 0.53 0.58 0.58 Ra,D/L)o, - 247,000 7.6x10' 2.2x10" Re,a, 16,100 18,500 74,000 151,000 Rao D/L),, 7,600 19,800 333,000 270,000 Rea ,, 16,600 19,000 77,000 163,000 Ra,D/L),, 3.3x10" 3.2x10" 1.3x10" 4.5x10" Reo ,, 27,400 31,400 128,000 282,000 The pi groups show the inennt effect is relatively small, and the effect of the downcomer on the net buoyancy is relatively small. The air flow Reynolds number is high even during blowdown due to the assumed initial condition of 120 F shell temperature and 115 F riser air. The free / mixed / forced convection regime of the flow in the downcomer, riser, and chimney is determin(-d from the Reynolds and Rayleigh (rad /L) numbers ss shown in Section 4.2. At the time of the peak containment pressure, the shell temperature and evaporation rate are higher than during other time phases, so the buoyancy-induced volumetric air flow rate is PG Air Flow Path scalmg March 1997 m:\M99w.ncm\3499w.d wpf;lt>031397
9-10 highest, The riser Reynolds number is proportional to the riser volumetric flow rate so is - highest at the time of the peak containment pressure. The PCS air flow path time constant is the ratio of the air flow path volume to the volumetric flow rate so is lowest at the time of peak containment pressure. I f l l l l i PCS Air Flow Path Scaling , Mmh 1997 m:\3499WJhon\$499W-d.Wpf.lM31397
10-1 1 I 10 EVALUATION OF SCALED TESTS This section evaluates the effects of scale for the separate effects tests (SET) and the integral , effects tests (IET) relative to AP600. The SET and some IET data are used to validate l constitutive models for some of the dominant transport processes and phenomena in AP600. l The IET are used to validate the dimensionless rate of pressure change equation, and pi groups for the LST and AP600 are compared. The rather detailed breakdown of heat sinks presented in Section 7 is useful for clarifying the effect of the several distinct heat sinks. However, the rate of change equations show the same transient response results from considering a net source and a net sink. The scaled rate of change equations for, respectively, mass, energy, and pressure are:
*' (190) n ,, ; = n ,, rh * , + n y rh,*g d(mu)* (191) x .., +n yaWFu9 g,. -x.h*%aW-%,7.*,ma2.*,-l + "..ue.*meu*4 z' y dP* . y
- Z T P,*,, , y zT- , ,
K ' pi P'**"'" * *** 5**" 5* "" U Ym, dt* Ym* P.*im Ym* ; T rh '*'"d Y
- Z
.p g Path 4 rh *ima +Ah.*tma n ,workj p . . P'.*'"+ n p44h q*4A*AT*4 j d l I rh ghrk
. g ghrk m pstm j
The pi groups for the composite heat sink approach are defined by adding the values for heat sinks within the summation terms. It is useful to approach the simplification in two steps: the first produces a set of combined internal heat sink pi values and a set of combined shell pi values, while the second combines the internal heat sinks and shell into a single set of pi values. The results are presented in the following six tables for mass, energy, and pressure. In addition to the composite pi groups, the rate of change terms for each of the scaled parameters, dm'/dt*, d(mu)*/dt*, and dP'/dt* are calculated from the above rate of change equations and included in the following tables. Evaluation of Scaled Tests March 1997 m:\3499w.non\3499w.d,wpf.It697
10-2 Table 10-1 Containment and Heat Sink /Shell Mass Pi Group Values LOCA Pi Group MSLB Blowdown Refill Peak Press Long Term j t, (sec) 31 980 913 5173 537 Contain- i x, 131: 1.27 130, 1.22 -- 1.27 ment x.3,, 1.00 0.00* 1.00* 1.00. 1.00 n,m 1.75 ' O.00 2.00 . 0.00 0.00 Internal no 0.01 ~- 1.99 -0.90 -022 - -0.64 Heat Sink Shell no -0.02 0.61 -0.47 . -1.04 '037 x,,, j - -
-0.02 ' 0.89 l
- Refill was scaled with the same 200 lbm/sec flow rate used to normalize peak pressure.
Table 10-2 Containment and Net Heat Sink Mass Pi Group Values LOCA Blowdown Refill Peak Press Long Term Contain- x, 1.31 1.27 1.30 122 1.27 ment x m3. 1.00 0.00* 1.00*. 1.00 1.00-x, 1.75 0.00 2.00 0.00 0.00 Net Heat x ,. -0.01 -2.60 -137 -1.26 -1.01 Sink x - -
-0.02 -0.57 -
dm*/dt* 0.76 -2.05 -030 -0.68 -0.01
- Refill was scaled with the same 200 lbm/sec flow rate used to normalize peak pressure.
l Evaluation of Scaled Tests March 1997 ! m:\3499w.non\3499w-d.wpf:lt>.031397
10-3 r Table 10-3 Containment and Heat Sink /Shell Energy Pi Group Values LOCA Pi Group MSLB Blowdown Refill Peak Press Long Term Contain- x.. 0.55 0.58 0.56 0.63- 0.58 ment ' x,a 1.001 0.00* 1.00* 1.00- - 1.00 x,; , 0.00 0.00 0.00 0.00 0.00 Internal x,43 0.00 -0.11 -0.04 0.00 -0.05 Heat Sink x .g3 0.00 . -1.90 . -0.85 -0.20 - -0.63 x .,3 0.00 -0.08 -0.07 -0.03 -0.01 x,,,, 0.00 -0.03 -0.02 -0.03 -0.02 Shell x,.g,, -0.02 -0.59 -0.45 0.94 -0.36 x,,,, 0.00 -0.02 -0.02 -0.11 0.00 x,,,,, 0.00 0.00 -0.00 -0.% - x,,,, - - -0.01 -0.08 - x,.g,,, - - -0.02 -0.81 -
- Refill was seded with the same energy normalization used for peak pressure.
Table 10-4 Containment and Net Heat Sink Energy Pi Group Values LOCA Blowdown Refill Peak Press Long Term . Contain- a ,,, - 0.55 , - 0.58 -0.56 0.63 0.58
-~
ment - - l x, . 1.00 0.00* 1.00* 1.00 .1.00 l l x,3..., 0.00 0.00 0.00 0.00 0.00 Net Heat x,,, 0.00 ' 0.14
-0.06 -0.03 -0.07 Sink x,.g, -0.02 -2.49 -1.30 -1.14 -0.99 x,3, 0.00 -0.10 -0.09 -0.14 -0.01 x .. 0.00 0.00 0.00 -0.06 -
x,,,, - -
-0.01 -0.08 -
x,.g,.. - -
-0.02 -0.81 -
d(mul'/dt* 1.78 -4.71 -0.80 -0.49 -0.12
- Refill was scaled with the n.ae energy normalization used for peak pressure.
Evaluation of Scaled Tests unch 1997 m:\3499w.non\M99w4wpf:1t 031397 e
10-4 Table 10-5 Containment and Heat Sink /Shell Pressure Pi Group Values LOCA Pi Group MSLB Blowdown Refill Peak Press Long Term Contain- n,, 0.76 0.76 0.77 0.76 0.76-ment x,,6. ,, 1.00j 0.00* 1.00* 1.00 1.00 n, o,i,,,s 0.03 0.00 0.03 0.02 0.03 n,t.# 0.00 0.00 0.00 0.00 0.00 Intemal n, 3 -0.01 .-033 -0.12 -0.02 : -0.13 Heat
P"
Sinh
* ~ '
n,. ,g.h. 0.01 -1.99 -0.90 -0.22 -0.64 1 Shel! n,.,,, 0.00 -0.10 - -0.08 -0.10 -0.07 n,,, u 0.00 0.00 0.00 0.00 0.00 n, _,,,3 -0.02 -0.61 -0.47 -1.04 '037 Refill was scaled with the same pressure normalization used for peak pressure. Table 10-6 Containment and Net Heat Sink Pressure Pi Group Values LOCA Blowdown Refill Peak Press Long Term Contain- n,, 0.76- 0.76 0.77 0.76 0.76 - ment x, g,i...,6 1.00 . 0.00* 1.00* 1.00 -1.00 n,.m 0.03 0.00 0.03 0.02 0.03 np t ,6 0.00 0.00 0.00 0.00 0.00 Net Heat n,, -0.01 -0.43 -0.20 -0.12 -0.20 . Sinks n,,,o 0.00 0.00 0.00 0.00 0.00 n,. ,w -0.01 -2.60 -137 -1.26 -1.01 dP'/dt* 133 -3.99 -0.70 -0.47 -0.24
- Refill was scaled with the same pressure normalization used for peak pressure.
Evaluation of Scaled Tests March 1997 m:\3499wJum\3499w d.wpf:1b-031397
)
l 10-5 The scaled rate of change values show mass, energy and pressure increase during blowdown, then drop rapidly during refill. Since refill has no source, each is expected to drop. However, the scaled rates of change for the peak pressure phase are also negative, indicating a decrease in mass, energy, and pressure at the beginning of the peak pressure time phase. This is contrary to the pressure history presented in Figure 3-4 that shows pressure increasing at the beginning of the peak pressure time phase. The explanation is that the model that generated the " typical" pressure transient in Figure 3-4 included several conservative assumptions, including: The shell heat and mass transfer correlations are biased approximately 25 percent low The internal solid heat sinks are modeled using Uchida, which produces approximately 1/2 the energy transfer as McAdams free convection A 50 percent reduction in the heat and mass transfer rate to the internal heat sinks and a 25 percent decrease in the shell heat and mass transfer rate is estimated to change dP'/dt* from -0.70 to +0.14, which is at least consistent with the expected sign of the pressure rate of change. The value of dP'/dt* for the long-term time phase is also inconsistent with Figure 3-4 at the start of the long-term time phase. The same reasons for the inconsistency apply, and in addition, the pressure assumed for the start of the long-term time phase was 60 psia (approximately the containment design limit), which is even higher than the model predicted in Figure 3-4. The higher pressure produces higher energy transfer rates, resulting in an even higher rate of pressure decrease. 10.1 SEPARATE EFFECTS TESTS (SETS) AND CONSTITUTIVE RELATIONSHIP SCALING Examination of the containment and net heat sink energy pi groups summarized in Table 10-4 shows the largest pi group values for the gas compliance (n,,,), break source (n 3,6), energy absorbed by the shell and heat sinks by condensation (n,,,,,), and energy removed from the shell by evaporation (n.jg ) are of order 1.0. The pi groups for displacement work (n.,,,,i), energy absorbed by the subcooled liquid (n,4,,), energy transferred to the inside surface by sensible heat transfer (n,4,), energy carried off the internal condensing surfaces by the liquid film (n,j,), and energy rejected from the shell by sensible heat transfer (n,4,,) are of order 0.1. Examination of the containment and net heat sink pressure pi groups summarized in Table 10-6 shows the gas compliance (n g ,), break work (ngg,6.a), and condensation work (ng%) are order 1.0 terms; internal sensible heat transfer (ngym) is intermediate order; and Evaluation of Scaled Tests March 1997 m:\3499w.ncm\3499w4 wpf:1 b-031397
i 10-6 l l t break enthalpy (n p y), break liquid displacement work (npu,J, and condensation enthalpy (ny ) are order 0.1 or less. Combining the results of the energy and pressure pi values shows the gas compliance, break source, condensation, and evaporation are the dominant order 1.0 terms. Internal sensible heat transfer is intermediate order, and external sensible heat transfer, liquid displacement, energy to the external subcooled film, energy carried by the condensed liquid, and enthalpy i I (of break and condensate) are order 0.1 or less terms. From this the very important conclusions are drawn that condensation and evaporation mass transfer are the dominant transport processes for containment pressurization. Consequently, the constitutive relationships for condensation and evaporation mass transfer are examined in detail' and the results of the dimensionless correlations for AP600 are summarized in subsections 10.1.1 and 10.1.2. Since sensible heat transfer is of intermediate importance, its modeling is discussed in subsection 10.1.3. The constitutive relationships used in the scaling analysis for convective heat and mass transfer are compared to the test data and to the range of operation of the important dimensionless groups. The comparisons show the selected correlations represent the test data and the range of AP600 operation is adequately covered by the test data. The scaling of additional phenomenological data to AP600 is discussed in the following subsections. 10.1.1 Condensation Mass Transfer Condensation mass transfer was identified as a high importance phenomena in the PIRT, and as discussed in Section 10. The dimensionless relationship for free convection condensation mass transfer, represent, 2 by the Sherwood number, was developed in subsection 4.3.1, Equation (16). The Sherwood number correlation is presented in Figure 10-1. Figure 10-1 shows the range of parameters covered by the LST envelopes the operating range of AP600 and shows the test data agree well with the free convection mass transfer correlation. The data and correlation are discussed in more detail in Reference 9. 10.1.2 Evaporation Mass Transfer Evaporation mass transfer was identified in the PIRT as a high importance phenomena, and was verified by the discussion in Section 10 as a dominant phenomenon. The mass transfer correlation for forced convection evaporation mass transfer was developed in Section 4.3.1 and presented in Equation (18). The forced convection evaporation mass transfer, as represented by the Shenvood number correlation, is presented in Figure 10-2. The range of Evaluation of Scaled Tests Mmh 1947 mA3499w.non\3499w-d wpf;1tW1397
1 10-7 I Sherwood and Reynolds numbers for AP600 operation is shown in Figure 10-2 to be within the range covered by the LST and Gilliland and Sherwood test data. The figure also shows ] the data aglee well with the forced convection mass transfer correlation. Note that although ' the Gilliland and Sherwood data range is shown on the figure, the actual data were not local, so are not included on the plot. The data and correlation are discussed in more detail in Reference 9. l 10.13 Convection Heat Trt.nsfer , Heat transfer to surfaces inside containment was ranked medium in the PIRT. The scaling ; discussion in Section 10 shows heat transfer to be of intermediate magnitude: it accounts for j approximately 10 percent as much energy and 10 to 20 percent as much dP/dt as condensation mass transfer. Heat transfer inside containment is the sum of radiation and free convection; the calculations show that radiation and free convection are approximately equal in magnitude. As a second order energy transfer phenomena, heat transfer inside j containment is modeled using the conventional correlations for radiation and free convection presented in Sections 4.1 and 4.2. Although the SETS and IETs included these phenomena,
- they were always present with condensation mass transfer, which dominated the energy ,
transfer and prevented measuring the second order phenomena. l It is significant that the condensation mass transfer correlation discussed in subsection 10.1.1 is derived from the heat and mass transfer analogy. Since mass transfer is well modeled by the free convection mass transfer correlation, by e teat and mass transfer analogy it can be ! argued that heat transfer is equally well modeled. The PIRT ranked heat transfer from the shell to the riser as medium importance, and the scaling analysis presented in Section 10 showed it to be a second order phenomenon. Heat transfer from the shell to the riser in AP600 is modeled using the Colburn forced convection , heat transfer correlation: l l hDh 2 where Nu = (193) ! Nu = 0.0?3RefPr k l where the length parameter is the annulus hydrauhc diameter, Dn. Incropera and DeWitt'5, Table 8.4, suggest the use of Colburn, Dittus-Boelter, and Seider-Tate correlations for internal j flows. l Evaluation of Scaled Tests March 1997 m:\3499w.non\3499w-d.wyf:ltRG1397
i
'10-8
'i e
a,b ! i i
-4
-i t
I L 7 t f t t i t i f a f k Figure 101 Free Convection Condensation Data from the Large-Scale Test i Compared to the Correlation and the AP600 Operating Range { Evaluation of Scaled Tests March 1997
' n. \3499w.non\3499w<l.wpf;1b 031397 i
l i
10-9 - ~ a,b' Figure 10 2 Forced Convection Evaporation Data from the STC Flat Plate Test Compared to the Conelation and the AP600 Range of Operation Evaluation of Scaled Tests March 1997 m:\3499w.non\3499w-d.wpf;1H31397 .
10-10 ) i l
- The Dittus-Boelter correlation differs from Colbum by a Prandtl number exponent of
. 0.4 instead of 1/3. For the predominantly air flows in the PCS Dittus-Boelter gives results that are 2 percent less than Colburn.
i
= The Seider-Tate correlation adds a multiplier of (p/p,)* to the Colburn correlation.
For the PCS with air and bulk-to-surface temperature differences less than 100*F, i t Seider-Tate also gives results 2 percent less than Colburn. All of these correlations are recommended for Re > 10,000, L/D > 10, and .7 < Pr < 160. .The l corresponding AP600 parameters are 16,100 < Re < 163,000, Pr = 0.72, and L/D = 60 which satisfy the criteria for use of the Colburn correlation. 10.1.4 PCS Air Flow Path Flow Resistance l The natural circulation air flow rate in the PCS air flow path determines the riser Reynolds i i number, an important parameter in the evaporation mass transfer correlation. The PCS flow resistance is one of the dominant terms in the PCS momentum equation presented in l Section 9. The form loss coefficient measurements from a geometrically scaled model of the ! AP600 PCS air flow path are presented and extrapolated to AP600. [ The flow resistance in the PCS air flow path was measured in the 1/6 scale air flow test. ; Although AP600 operates in natural circulation and the test was fan forced, the buoyant pressure, G, and the forced pressure drop, AP are interchangeable in the pi groups. Consequently, a fan forced test produces a flow resistance that is equally valid for a , buoyancy driven system. The overall pressure loss coefficient for the system is a combination of form losses and friction losses. It is known from the test that the form and friction losses are approximately equal. Thus it is expected that the resistance should be a weak function of the Reynolds number, with an exponent on the Reynolds number approximately 1/2 the Reynolds number exponent for pure friction at the same Reynolds number. This can be demonstrated as follows. : Since form losses are known to be independent of Reynolds num'ber at high .Reynolds numbers (K = Ci Re'), and since the frictional losses are known to have only a weak dependence on Reynolds number at high Reynolds numbers (fL/d = C2Re", where n = -0.20), . it is reasonable to expect the sum of the form and friction losses can also be approximated by j a function of the form 14 = C 3Re". An approximating function can be defined as the tangent to the approximated function at some Reynolds number,14 The values of C3 and m in the approximating function can be determined as follows with the assumption: i I 1 Evaluation of Scaled Tests Much 1997 ) mA3499w.non\3499w4wpf;1t@l397
10-11 i
, 1. The form, K, and friction losses, fL/d, are equal in magnitude at Re = Ro, so i C = C 2Re",
3 , and with the definition of the tangent: ; l
- 2. The magnitudes of the approximated function, (K+fL/d), and the approximating function, K,, are equal at Re = Ro, so K,,, = K + fL/d, and j
- 3. The slope of the approximating function dK,,,/dRe is equal to the slope of the approximated function d(K+fL/d)/dRe, at Re = Ro. ]
From assumption (1): C2 = C /Ro"; from assumption (1) and definition (2): C3= 2C i /Ro"; i and from definition (3): nC Ro"'2 2
= mC 3Ro""2 Substituting the first and second expressions into the third to eliminate C2 and C 3results in the equation m = n/2.
a The root mean square roughness of the inorganic zine coating on three Westinghouse Science
& Technology Center (STC) tests ranged from 150 to 250 micro inches, and the rougl ness of the commercial steel baffle is estimated to be no rougher than the shell. Consequent 4y, c/d 3= 0.00012 in the riser where most of the friction occurs. At this relative roughness and the riser Reynolds number at the time of peak containment pressure,163,000 from Table 9-1, the tangent to the e/d = 0.0001 curve on the Moody friction factor chart has a slope of -0.20, hence the value used in the calculations. Although the Blassius friction factor correlation, with its exponent of -0.25, is a reasonable approximation for turbulent Reynolds numbers less than 100,000, it is not quite correct for the higher Reynolds numbers of the PCS. Thus, the loss coefficient is expected to be of the form C Re*2 l The loss coefficient is defined by setting x,,, = 1 and expressing the loss coefficient as the ;
ratio of pressure drop to stagnation pressure: AP* (194) : I R' - C Re
- 2' =
rn,2/(2 p,A,2) _ i a,b l (195) Evaluation of Scaled Tests Mah 1997 m \3499w.non\M99wdwptit>031397
l 10-12 j 10.1.5 Wind Effects I An aspect of the AP600 design is its sensitivity to external wind. The extemal conditions j affect the performance of the PCS air flow path, due to high wmd speeds and turbulence induced by upwind structures or terrain. A series of tests were conducted in wind tunnels to characterize the effect on the AP600 PCS , air flow of environmental wind speeds up to the AP600 design Ihnit of 214 mph. The l particular concern was the effect of upwind terrain and obstructions that could subject the PCS air flow path to pressure fluctuations that induce reversed flow in the riser. -Such fluctuations have been evaluated relative to the assumed zero wind effect. The test evaluation (Ref. 5, Section 6) considered the effects of wind tunnel model scale and showe~d ! the wind-positive characteristic of AP600 more than offset the effect of fluctuations. The recirculation of the chimney outflow (warmer and more humid than the environment) to the downcomer inlets was evaluated (Ref. 5, Section 6) and determined to have an l insignificant effect. l 10.1.6 Wetting Stability , Liquid film stability is an important parameter in the extemal evaporation calculation. This was identified in the PIRT and is included in the important phenomena listed in Section 2. The film stability is discussed in detail in Reference 5 and the results are summarized in the following. Heated and unheated water distribution measurements were made on tests to support the modeling of water coverage on the external shell of AP600. The model and its application to AP600 is presented in Reference 5. The dimensionless groups appropriate for scaling water I coverage are defined in the literature and those that are most significant for AP600 are the I film Reynolds number, Marangoni number, and Bond number, defined respectively as: Re = $ Ma = b P g , Eg (1 % p dT 2 kap a l The range of these groups for AP600 and two of the tests are presented in Table 10-7. The i comparisons show the range of AP600 operation is adequately covered by the test data. l EvaluatiJScaled Tests March 1997 m:\34%.non\34h-d.wpf:1t41397
10-13 Table 10-7 Comparison of AP600 Operating Range to Tests for Liquid Film Stability s (February 24,1997) h AP600 Large-Scale Test Water Distribution Test Film Reynolds Number: - - a,b Upper Sidewall 2900 Bottom of PCS surface 600 Marangoni Number: Upper Sidewall 2600 Bottom of PCS surface 720 Bond Number: Upper Sidewall 0.009 Bottom of PCS surface 0.005 - - 10.1.7 Liquid Film Model Validation Heat transfer through the draining liquid film on the inside and outside surfaces of the shell and heat sinks was ranked low importance in the PIRT. The film conductance calculated with the scaling equations is 840 B/hr-ft 2-F. This makes the conductance approximately an order of magnitude greater than that of mass transfer, so film conductance scales low importance. 3 The Chun and Seban ' corrcLtion was selected to model the film heat transfer. The validity of the Chun and Seban correlation for evaporating turbulent and wavy laminar films on vertical surfaces was demonstrated in the original paper. Data from tests at the University of Wisconsin" are added to enend the validity of the Chun and Seban correlation to condensing wavy laminar flow and to surfaces which are inclined, as in the dome region of the AP600. Five of the Wisconsin Tests were conducted without a noncondensible gas present. Without a noncondensible gas, the gas-to-liquid heat transfer coefficient is so high that the gas-to-liquid temperature drop is negligible compared to the temperature drop across the liquid film. Consequently, the temperature of the liquid film surface may be assumed equal to the gas teraperature and the liquid film heat transfer coefficient is heat flux divided by the liquid film temperature drop. Since the heat flux, solid surface temperature, and gas temperature are measured, the liquid film heat transfer coefficient may be derived directly from the measurements. The Wisconsin tests thus provided a relatively direct measurement of the liquid film heat transfer coefficient for a range of surface inclinations from vertical to horizontal. i Evaluation of Scaled Tests Narch 897 m:\3499w.non\3499wdwpf:lt@l397
10-14 The Wisconsin and Chun and Seban data are compared to the Chun and Seban laminar and turbulent correlations in Figure 10-3. The correlation seems to predict nearly best-estimate values over the full Reynolds number range of data. The range of film Reynolds numbers on
- the outside of AP600 is also shown in the figure, and falls well within the range of the test data'. Reynolds numbers on the inside of containment are less than outside due to film removal at the crane rail and stiffener ring, and the fact that the inside film flow rate starts at zero at the top of the dome and increases as the film flows down. The AP600 liquid film Prandtl number range is approximately 1.5 < Pr < 3.0, whereas the range of the Chun and Seban data Prandtl numbers is 1.77 < Pr < 5.9, which adequately covers the AP600 range.
Comparison of the correlation to the test data show that the Chun and Seban correlation is a good representation of the data, so the Chun and Seban model is sufficiently accurate for this low importance phenomena. Uncertainties in the small fraction of the total conductance due to the liquid film does not significantly affect the containment pressure. 10.2 INTEGhL EFFECTS TESTS (IETs) AND AP600 SCALING S This section presents a scaled comparison between the LST (integral test) and the AP600 plant, and validates the scaling equations by comparison to the LST. The purpose of the comparison is to show the scaled LST captures the high ranked phenomena associated with the AP600 containment and therefore the data obtained from the test can be used for correlation and code validation. The scaled comparison between the LS~ /600 focuses on the phenomena associated with the containment features that are h- a to AP600, that is, the PCS. Phenomena associated with the PCS become significant u._ ring the refill phase of a DECLG LOCA, and remain dominant into the long-term phase of the transient. This is shown in Figure 10-4 which shows heat sink energy removal rates for AP600. Referring to the figure, the energy transfer from the gas to the shell becomes important during the refill time phase and is dominant by about 200 sec (i.e., dunng the peak pressure phase). Phenomena associated with the blowdown and refill phase of a DECLG LOCA are not unique to AP600. Those phenomena exist in current pressurized water reactors (PWRs). These scaling comparisons focus on test validation to represent the peak pressure and long-term time phases, the time when the AP600 PCS performance validation requires unique test results. Evaluanon of Scaled Tests Much 1997 m:\Mhnon\M99w-d.wpt:1W1397 .
10-15 s
.1 1
' ~
Chun and Seban Turbulent Correlation ' Chun and Seban WaW Nu = 0.0038 (Rem.4) (Pr*0.65)
. Larninar Correlaticni - ,
Nu = 0.822 (Re%.22) Pr = 5.1
- ~
3 Pr = 5.7 p 493 , X i M M xX Pr =1.77 1 h z T I . g 2 - l Wisconsin Data k (AR others are Chun 5 A and Seban) AP600 Range (from second weir, 0.1 . . . . . . . . . . . . . . . . . . r. . . . . . . . . . . . . .. 0.1 10 100 1000 10000 100000 Uquid Fdm Reynokh Number, Re j i 1 i I 1 l Figure 10 Chun and Seban Liquid Film Nusselt Number Correlation Comparison to Condensation and Evaporation Test Data. Evaluation of Scaled Tests March 1997 - m:\3499w.non\3499w d.wphit431397
l l l'O i 3E+05
^
b s$ 2.5E+05 5 - e g 2E+05 a E - 9
$1.5E+05 E -
5m 1E+05 b 5 1 j SE+04 /
,4 - -u , ,xx .
OE+00
. . . ,...r ' ' --
. . . . . , 'r---'>>i-1E+00 1E+01 1E+02 1E+03 1E+04 1E+0!
Time (seconds) Rem 4 Room 5 Room 6 Room 7 IRWST & Rmm 103 50 East SG West CMT Refueling Dead Ended Vertical Access
^ ""
l I Figure 10-4 Heat Sink and Shell Inner Surface Energy Partitioning in AP600 from , WGOTHIC i Evaluation of Scaled Tests March 1997 m:\3499w.non\3499wd wptib 031397
10-17 10.2.1 Governing Scaling Equations The general form of the goveming equations and their normalized form have been previously derived in Section 6.2 for the AP600 plant. The normalized form of the energy equation for the containment gas is: E ..' d
' 8 '* ' '# 84 *4 "4 *#'l " "'i 94 ' 4 For a defined initial condition, all the
- terms have unit values so:
A' d
**~ '# 5'8 '#4 94 Since the containment gas is in a quasi steady-state during the long-term portion of the DECLG LOCA transient, d(mu)*/dt* = 0. By normalization, n,3,6 = 1, so Equation (198) can be simplified to:
(199) 0-1-h,n,,,,,+x,,3 + n,j The mass rate of change equation can be similarly reduced, for steady state, to: 1 0 = 1 -[n I g (200) These mass and energy equations are valid for both AP600 and the LST. A comparison of test measurements to predictions of Equations (199) and (200) will validate the rate of change equations for mass and energy. Since the RPC equation is the result of combining the mass and energy rate equations, with the equation of state, validation of the mass and energy equations also validate the RPC equation. These comparisons are provided in the following two subsections. 10.2.1.1 Validation of Steady-State Mass and Energy Transfer Equations The constitutive equations for steady-state heat and mass transfer inside and outside the LST were coupled and solved using properties measured on the LST as boundary conditions. The containment total pressure, steam pressure, and bulk temperature defined the state inside the LST. The riser gas velocity, bulk riser gas temperature, wetted fraction, and the external water flow rate and temperature define the state outside the vessel. The heat and mass Evaluation of Scaled Tests March 1997 m:\3499w.non\3499w-d.wpt1M31397
10-18 transfer rates inside and outside were calculated for the subcooled, evaporating and dry regions. The measured values for thp ,u, and thg,uAh p,u were used to normalize the predicted values, respectively, for mass and for energy that define the pi values in Equations (199). The results are summarized in Table 10-8 for 21 LST cases. All tests are included that had measured steam concentrations and the steam source located under the steam generator model. The results show the average quasi steady-state mass and energy transfer rates are very close to zero, with a standard deviation of 0.13. Such agreement is considered good for such a simple model. These results verify that the mass and energy equations used in the scaling analysis accurately predict the transfer rates, thereby validating the equations. Verification of the transient pressure predictions are presented in subsection 10.2.1.2. 10.2.1.2 Transient Validation of dP/dt Equation A comparison is made between the RPC equation and the startup of LST 221.1 (for which dP/dt data are available at t=0). At startup there is no heat or mas 3 transfer to the intemal heat sinks or shell since there is initially no temperature or steam partial pressure differences to drive transport processes. The initial pressurization is adiabatic compression which is described by the RPC equation without heat sinks or a break liquid source: f T (1 + Z') y dP = rh ) = (201) (y -1) dt dd h#* -h " + Y(1 (y -1) ( p,, ) Since the initial state of the LST is isothermal, full of air at 75 F and 14.2 psia, ZT = 0 and P,./p, = R, T, the simplified RPC equation is:
= rh p, ,(y -1)(h p ,-h,,) + y R,,T (202)
The values for the parameters in Equation 201 are listed in Table 10-9. The values, when input to the dP/dt equation give dP/dt = 0.38 psi /sec, whereas the measured transient pressure shows dP/dt = 0.29. The difference is likely due to the fact that the hot steam jet, as it enters the LST, immediately encounters the diffuser and the simulated steam generator model, and in 2 to 3 sec encounters the dome. The " adiabatic" assumption is not strictly satisfied, and consequently, the source is not quite so effective. The agreement is considered to be sufficiently close to provide validation of the transient capability of the RPC equation. 1 When combined with the steady-state validation in subsection 10.2.1.1, this transient comparison shows the RPC equation is valid. Evaluation of Scaled Tests Mmh 1997 m:\3499w.non\3499w-d.wpf;1t41397
10-19 Table 10-8 Energy Rate of Change Equation Comparison to Steady-State LST Large- Pressure Temperature di,wA,wu 1-I(n,43+xou ; Scale Test psia 'F BTU /sec +x,43) 1-I x..; j 212.1A 23.77 334.3 427.2 -0.167 -0.197 j 212.1B 2936 317.8 667.8 -0.058 -0.076 212.1C 36.93 317.7 963.4 -0.036 -0.948 213.1A 23.5 334.3 398.2 -0.185 -0.213 213.1B 28.83 327.0 642.1 0.039 0.022 213.1C 40.29 319.6 980.6 0324 0.321 216.1A 32.44 326.5 706.7 -0.173 -0.206 216.1B 50.18 329.1 711.7 0.092 0.068 217.1A 4237 314.9 1320.7 0.142 0.141 217.1B 50.86 319.7 1303.9 0.?16 0.115 1 218.1A 42.44 314.0 1329.4 0.051 0.017 l l 218.1B 50.05 317.6 1250.3 -0.001 -0.001 l 219.1A 34.97 343.0 145.9 0.082 0.088 219.1B 41.89 343.8 148.1 0.086 0.102 1 219.1C 23.24 340.2 143.8 -0.001 0.016 j 221.1A 1936 339.6 185.7 -0.117 -0,132 j 221.1B 26.02 333.2 189.5 0.089 0.080 j 221.1C 6336 336.7 186.0 0.098 0.106 222.1 99.66 331.1 719.1 -0.158 -0.167 224.1 45.51 298.9 309.5 -0.118 -0.064 224.2 55.54 310.4 712.2 -0.1% -0.087 Average = -0.00001 -0.004 ; 1 Standard Deviation 0.128 0.133 Evaluation of Scaled Tests Much 1997 mA3499w.non\3499w-d.wpf:lt>431397
10-20 Table 10-9 Parameters for LST Transient 221.1 Parameter Value ni,a a,b V 7 h,.i , h,. R,. T _ _ 10.2.2 Steady-State Validation of the LST Pi groups for both the LST and AP600 were calculated using a solution to the equations developed for scaling AP600. The calculations correspond to conditions expected in AP600 at 4000 to 5000 sec. into the transient. Inspection of the detailed energy pi groups in Table 7-8 shows that during all the phases of a DECLG LOCA, phenomena associated with the drops, pools, chimney, and baffle are not important and can therefore be neglected since the pi group numerical values are of order less than 0.1. The only pi groups of any significance are those associated with the solid intemal heat sinks and the shell. However, the solid heat sinks become saturated prior to the time when the peak pressure occurs. Therefore, only the pi groups identified as containment or shell were calculated for the AP600 plant and the LST. The results of the energy scaling comparison between the LST and AP600 are summarized in Table 10-10. The transient pi group x,,, is not applicable since d(mu)'/dt* = 0, that is, the containment atmosphere is in a quasi steady-state condition. Since the pi groups are normalized on break energy, x,a = 1.0. The table shows the dominant phenomena are condensation on the inside of the shell, x,,,, and evaporation on the exterior of the shell, n,,,,,. The values for n,,,, and x,,,,, in Table 10-10 show the dominant phenomena (condensation and evaporation) compare favorably. The shell energy phenomena for the subcooled and dry shell, n , and n , are shown to be second order phenomena. Although the pi values for subcooled and dry energy do not compare quite as well as those for condensation and evaporation, the former are second order phenomena in both the plant l and test, so do not invalidate the use of the test data. I 1 Evaluation of Scaled Tests March 1997 l m:\349%non\3499w.d.wpf:ll>031397
10-21 Table 10-10 Energy Pi Group Comparison for AP600 and the LST Predicted at 41.0 psia Pi Group AP600 LST LST Measured x,., 1.24 1.24 1.22 x,35 1.00 1.00 1.00 x,j .,6 0.00 0.00 0.00 x,.,. 0.02 0.02 0.03 x,;,, 0.91 0.93 0.90 x,,,, 0.08 0.06 0.08 x,,,,, 0.13- 0.18 0.09 x, ,, 0.13 0.15 0.09 x,;, , 0.67 0.62 0.74
- Not measured in LST The scaling comparison permits the condusion that the scaled LST represents the dominant internal and external phenomena in AP600 with sufficient accuracy that the tests can be used to validate computer codes during quasi-steady (long-term) operation.
Evaluation of Scaled Tests March 1997 m:\34Ww.non\3499w-d wpf.It>-031397
11-1 t 11 DIFFERENCES AND DISTORTIONS BETWEEN THE TESTS I AND AP600 Certain features of the design and operation of the LST prevent the use of the IST to , represent specific duty cycle transients in AP600. However, the LST was not designed and operated as a conventional integral test to represent specific AP600 transients. Rather, the LST was designed and operated to characterize the internal velocity, temperature, and concentration fields, the shell temperature and heat flux distributions, and the air flow path l and baffle temperatures under the effects of- ,
- Break source mass flow rate, elevation, direction, and velocity
- Noncondensibles
- External air flow rate
- External water flow rate and fractional coverage i
The results of the LST were used to help resolve high and medium ranked phenomena in AP600:
. The measurements of the steady-state condensation mass transfer inside the shell are used to validate the phenomenological correlations for condensation mass transfer used in the scaling calculations and in the evaluation model. i l
- The external evaporating liquid film water coverage data are used to validate the l liquid film stability models used in the evaluation model.
- Stratified temperature and air / steam concentration distributions measured inside the LST are used to address stratification for the evaluation model.
Heat transfer measurements from tests with no external water provided data to , validate dry heat transfer to the riser. In addition, the steady-state and transient LST are used to validate predictions of the scaling equations and the computer code and selected segments of the LST are scaled to represent the dP/dt behavior of AP600. Although the LST provided data to support the resolution of the most important phenomena in AP600, the test did not provide a transient simulation of specific duty cycle transient. It is therefore helpful to discuss differences between the test and AP600 that have been identified as concerns, and to consider whether those differences constitute distortions that must be considered when the LST data is applied to AP600. Features of the LST that differ from AP600, with the concern for each, are listed in Table 11-1. Each feature is discussed in the ; following text. i l Differences and Distortions Between the Tests and AP600 Much 1997 m:\3499wam\3499w-d wpf.lb4m397 i
11-2 Table 11-1 LST Features That Differ from AP600 Feature Potential Concern Distortion Break Source Superheat Condensation correlation and pressurization are not No prototypic because more thermal energy was input. Diffuser used for break The actual break is a pipe break with a high velocity No source jet. No Downcomer Flow instability in the downcomer may lirait the PCS No air flow rate. Riser Scaled 1/4 he riser heat and evaporation mass transfer are biased Yes because the 3-inch riser width is 1/4 scale rather then 1/8 scale, as is the remainder of the test. Fan Forced Riser Air Flow The fan provides a forced air flow instead of the Yes natural circulation air flow. No Circulation Below The above/below-deck noncondensible distribution Yes Deck makes the test results inapplicable. Extemal Water Flow too The extemal water flow rate removes too much energy No High for some tests by its subcooled heat capacity. Extemal Water Coverage The water coverage was controlled artificially, rather No i was too high than according to stability. The excess flow rate made the water more stable than it should have been. External water flow was Cold water was not 1.pplied to a hot surface. No established before break Intemal heat sinks not ne intemal concrete, steel, and pools are not Yes prototypic represented. Extemal water flow Oscillations in the extemal water flow rate affected the Yes oscillation cooling and water coverage Crane rails not the same Intemal liquid film is different No Extemal water not applied Extemal water coverage and stability are different Yes by weirs Condensate drained out There was no break pool to interact with the No atmosphere in the test l l I 1 Differences and Distortions Between the Tests and AP600 March 1997 ) m:\3499w.non\34Ww4wpf.It431397 )
11-3 Break Source Superheat - The phenomenological correlations used to predict pressurization due to heat transfer and mass transfer to the AP600 shell are independent. Sensible heat transfer is calculated using conventional radiation and free convection heat transfer relationships in which the heat transfer rate is proportional to the temperature difference between the bulk gas and the liquid (film or pool) surface. Condensation mass transfer is calculated from the free convection heat transfer correlation, modified according to the heat and mass transfer analogy, in which the mass transfer rate is proportional to the steam partial pressure difference between the bulk gas and the liquid surface. To achieve a steady-state, the net condensation rate from the containment gas must equal the steam source mass flow rate, and the net sensible heat transfer from the containment gas must equal the break source energy addition by superheat. This phenomenological independence was used in the mass transfer correlation validation, using LST data, to derive mass transfer data for evaluating the internal condensation correlation. Consequently, although the LST was forced with a steam source with more superheat than expected for an AP600 LOCA, the independence of the heat and mass transfer permits the use of the LST mass transfer data to validate the AP600 mass transfer correlation. The scaling analysis shows the pressure scaling pi group for superheat is approximately 0.03 in AP600 and 0.10 in the LST. Although the ratio is approximately 1/3, since the scaling analysis shows superheat is small relative to the source work term and superheat is accommodated by the pressurization model, the difference is not a distortion. Diffuser used for break source - The diffuser located below the steam generator model produced a relatively low velocity steam source where the steam exited the steam generator compartment into the large above-deck volume. This approximated conditions for a LOCA where the high velocity break is expected to dissipate and entrain, and exit the steam generator compartment at a relatively low velocity. The steam source into the above-deck region is a buoyant plume rather than a forced jet in both AP600 and the LST conducted in this configuration. The buoyant plume-driven tests produced a state of free convection heat and mass transfer above-deck in the LST, as is expected in AP600 after blowdown. The diffuser does not constitute a distortion in applying the LST results to AP600 LOCA modeling. No Downcomer - The scaling analysis shows both the energy and momentum contributions from the downcomer are sufficiently small that the downcomer does not have a significant effect on the PCS performance, and consequently, cannot induce instability. Consequently the downcomer is adequately treated by including it as a flow path with thermal and hydraulic interactions with the baffle and shield building. Based on scaling results tlus difference was not a distortion. Differences and Distortions Between the Tests and AP600 March 1997 mW99w.non\3499wwd wpf:lt431397
11-4 \ 1 Riser Scaled 1/4 - The riser removed sufficient energy from the test to achieve the necessary intemal and wall heat flux conditions to validate the condensation mass transfer model and the liquid film stability and wetted coverage model. However, the maximum Reynolds numbers achieved in the LST riser was approximately 1/2 that in AP600. AP600 is adequately covered by data from other tests. It was more important to achieve internal conditions for prototypic condensation mass transfer than to achieve scaled external conditions. Since other data are required to supplement the LST data for riser heat and mass transfer modeling, the difference is a distortion. Because of this distortion, other data were used to supplement the LST data for riser heat and mass transfer modeling. Fan Forced Riser Air Flow - The lack of a downcomer,less height, and significantly different air flow loss coefficients prevent the use of the LST to simulate the natural circulation air flow in the AP600 PCS air flow path. This is a distortion. However, the natural circulation air flow in the PCS was never intended to be verified by the LST due to the inherent difficulty of simulating natural circulation phenomena with a 1/8 vertical scale model. Although a fan was generally used to increase the riser Reynolds number, tests without the fan provide data to validate natural circulation models. The AP600 natural circulation air flow rate is determined from an analysis that uses a conservative upper bound on the PCS form and friction loss coefficient. Natural circulation LST data are not used to represent AP600 natural circulation performance. No Circulation Below-Deck - The lack of an opening between the simulated steam generator compartment and the other below-deck compartment that was open to the above-deck region prevented the above/below-deck circulation that would otherwise have developed. It also caused excessive air concentration below-deck and a steam-rich atmosphere above-deck. This is a distortion that prevents the use of the LST as a direct simulation of circulation during AP600 transients. However, the range of above-deck air / steam concentrations and mass transfer rates achieved in the tests was more than sufficient to span the range of AP600 l operating parameters, so the condensation mass transfer data are not distorted. 1 Extemal Water Flow too Hinh - The scaled external cooling water flow rates in the LST I spanned the range of AP600 operation. Since the flow rates were not too high, the effect is that of a ranged parameter, and is neither a difference nor a distortion. The magnitude of the external cooling water flow rates did not compromise the use of the data to validate the condensation mass transfer correlation or the external film stability and coverage model. External water flow was established before break - LST 219.1 operated at a dry steady-state with a shell temperature of 240 F, then water was applied. Video tapes were taken of a test with cold water applied to a hot shell at 250 F to provide data for assessing the transient shell wetting influence. Tests that started wet cannot be used to validate AP600 performance during the initial wetting portion of the transient. This has no effect on the steady-state condensation mass transfer data validity. Differences and Distortions Between the Tests and AP600 March 1997 mA34%.non\34N d.wpf:1b-031397
11-5 Intemal heat sinks not prototypic - The heat sinks in the LST have significantly less scaled heat capacity than those in AP600, so the transient test heat sink behavior cannot generally represent that of AP600. The lack of internal circulation prevents access of steam to the available below-deck heat sinks, further increasing the performance discrepancy between the test and AP600 intemal heat sinks. This difference is a distortion. However, the steady-state condensation mass transfer and external film stability and coverage remain valid for application to AP600, and the stratification data are useful for understanding and bounding behavior in AP600. External water flow oscillations - The external water supply rate oscillated. The flow rate dropped when the boiler feed-water level initiated refill of the feedwater tank, temporarily reducing the external water flow rate. The cycling rate was proportional to the steam flow rate, and was typically on the order of a few minutes. The reduced flow portion of the cycle was only a fraction of the total cycle, with the majority of the cycle operating at the set flow rate. The flow cycling may have affected the vessel cooling and water coverage. The test data were used to validate the heat and mass transfer models used time and spatial-averaged temperatures, flow rates, and fluxes. The averaging time period was long enough j to include several cycles, so fluctuations are averaged out. Furthermore, the transport models include data from other tests that did not experience such fluctuations. The fluctuations are not believed to have affected vessel cooling in a way that could compromisa the use of the LST for pressure, temperature, or transport predictions. The external water flow rate is a relatively steady flow, intenupted by a periodic drop and recovery. Since the water coverage grows with time, the state of coverage was continually recovering from a flow reduction. Consequently, the wetted coverage never reached its mar.imum possible at steady flow, although it may have been very close. The data were j evaluated using both the maximum and minimum flow rates, so a conservative approach was used for the data evaluation. However, the flow oscillations are considered a distortion. Crane rails are not the same - The LST lacked an internal structure to simulate the stiffener I ring located part-way up the vessel side wall. The crane rail and stiffener ring strip the l liquid film flowing down the inside surface. The film redevelops below these structures. The thinner film has a higher conductance than would an unstripped film, but both ! conductances are so high they have little effect on AP600 performance. Since the scaling analysis showed the film conductance was less than second order, relative to the other conductances, incomplete simulation in the test has an insignificant effect on the results so is not a distortion. External water not applied by weirs - Both the weir slots on AP600 and the J-tubes used on the LST apply water to the surface as a free-falling stream that impacts the shell surface and spreads radially outward. The difference is not considered a distortion. Data from the Water
~
Differences and Distortions Between the Tests and AP600 March 1997 ) m:\309w.non\3499w-d wpf:ltw031397 I I
11-6 distribution tests, that include a prototypic weir design and application are included in the water coverage model database. These latter data insure that the effect of application is represented by the model. , I i Condensate drained out -The condensate was drained from the LST to prevent the vessel j from filling during long test times, in contrast to the break pool that floods up from the j reactor cavity and sump in AP600. Since the scaling analysis showed the pool has a less than second order effect on containment pressure, the difference is not a distortion. The pool is { included in the evaluation model. l I l, i l j
)
r i i l l i l l l ?- I Differences and Distortions Between the Tests ar.d AP600 I# m:\h.rmn\3499w d.wpf;1b.031397
l 12-1
]
12 CONCLUSIONS l i The scaling analysis satisfies the five stated needs for AP600 containment pressure scaling. The five needs and the conclusions are:
- 1. Quantatively evaluate the relative magnitude of transport processes and physical components as they affect energy, pressure, and momentum inside containment and in the PCS air flow path. ;
The pi groups for the detailed component and transport process scaling is presented in Table 8-5, Table 8-6, and Table 9-1. From these details the important components are identified as the break, atmosphere, steel heat sinks, concrete heat sinks, jacketed concrete heat sinks, evaporating shell, and dry shell. The dominant transport processes are condensation and evaporation mass transfer. In the PCS air flow path, the riser and chimney are important components, and the buoyancy and flow resistance dominate the air flow rate.
)
- 2. Use the quantitative evaluation to confirm the importance ranking of components and :
transport processes in the PIRT. The conclusions of item 1 are consistent with the rankings in the PIRT.
- 3. Identify the important dimensionless groups and their range needed to scale test results to AP600.
The scaled comparisons between the SETS and AP600 show that the important phenomena are well modeled by the selected correlations, and the data cover the range important for AP600 operation.
- 4. Validate the use of the SETS and IETs to validate phenomenological models and the ly. GOTHIC computer code for use on AP600.
Predictions cf the scaling equations were compared to steady-state and transient LSTs. The agreement is sufficiently close to provide validation of the RPC equation. The scaling comparison permits the conclusion that the scaled LST represents the dominant internal and external phenomena in AP600 with sufficient accuracy that the tests can be used to validate phenomenological models and the AP600 evaluation model during quasi-steady (long-term) operation. Conclusions Much 1997 m:\3499w.non\3499w4wpt:1b431397
l i 12-2 ;
- 5. Identify test distortions that' limit the applicability of the tests to AP600. I
- 1 There are several distortions between the design and operation of the LST and l AP600. Those distortions are recognized and various analytical and j experimental results are used to account for those distortions. The distortions l do not prevent the use of the LST results to validate the high-ranked j phenomena of condensation mass transfer and liquid film stability and !
coverage. In addition, the temperature and concentration measurements from j the LST provide data to understand and bound stratification in the AP600 ' evaluation model. l
?
f 5
/
r i l l 1 I 1 1 1 Conclusions % 3,97 m:\3499w.non\3499w d.wpf:1b431397
13-1 13 NOMENCLATURE Symbol Quantity Letters A Area C Steam concentration, and arbitrary constants or coefficients ce Constant pressure specific heat cv Constant volume specific heat d Hydraulic diameter, drop diameter ; do Hydraulic diameter of jet at source D,, Gas phase diffusion coefficient f Friction factor, or a fraction defined in text g Gravitational acceleration h Convective heat transfer coefficient h,. Gas phase enthalpy h, Liquid phase enthalpy h,, Liquid-to-gas enthalpy H Height, height of containment above steam source k Thermal conductivity k, Gas phase mass transfer coefficient L Length L' Specific length m Mass rh ' Mass flow rate rn" Mass flux M Molecular weight n number of drops, number of moles, P Pressure or partial pressure Ps Log mean pressure difference = (P2 -P 3 )/In(P2 /P ) 3 q Heat flow rate q" Heat flux Q Volumetric flow rate R Gas constant for specific species R Universal gas constant t time T Temperature u, Liquid phase internal energy u, Gas phase internal energy u,, Liquid-to-gas internal energy Ua Velocity of jet at source v Specific volume, or velocity as defined in text Nomenclature Mmh 1997 rnA3499wmn\3499w-dSpl1b031397 i
~ '
y. l l 13-2 V' Volume i
- z. . Elevation for jet transition from forced to buoyant l Z. _
Gas compressibility Z = P/pRT - ! T
. ZT - a normalized partial derivative of compressibility _Z = (T/Z)(BZ/BT)? !
t Subscripts l a Ambient containment ' air Air bf i Baffle l brk Break source .i buoy Buoyancy pl group '! c Convection heat transfer, or conductance pi group cc Concrete ch Chimney l cond. Condensation ' I ct Containment gas - : l cx External convection [ d hydraulic diameier, or droplet value !
'de Downcomer j ds Dry shell inside l dsx Dry shell outside l e Equivalent heat transfer coefficient, or energy pi group 4 enth Enthalpy pi group i es Evaporating shell inside i esx External evaporating shell j evap Evaporation l ex External equivalent heat transfer coefficient f Fluid (or liquid) property value, fluid pi group fg Fluid-to-gas phase change property value, phase change pi group g Gas property value hs Heat sink, composite of all internal heat sinks (excluding shell) i if Intemalliquid film )
in Inertial pi group in Inlet value j Jet value , m Mass transfer, mass transfer pi group m v. Momentum pi group mx External mass transfer - ns ~ Net sink - combination of all internal shell and heat sinks out Outlet value p Pressure pi group
' Nomenclature March 1997 i m:\3499wman\3499w d.wptib 031397 )
l
m...-. .. _ . _ . . _ . _ _ . _ . . _ _ . _ . . _ _ _ . . _ _ . . _ . _ 13 I pi . Pool j q' Sensible heat transfer pi group j r Radiation i res Resistance pi group ! rx Extemal radiation 'l ri Riser i IR. IRWST water ss Subcooled shell inside l ssx Subcooled shell extemal ; sd Shield building' ) sh Containment shell sat Saturated srf. Surface . st Steel i stm Steam ~ l v A volumetric parameter ) work Work pi group . i x A suffix that means extemal, or outside - xf External liquid film o Initial or boundary value for nondimensionalizing 0 Value at jet nozzle exit A reference value defined in text Superscripts Dimensionless value
+ - A ratio of LST to AP600 pi values Greek Letters a Taylor's jet entrainment constant, value is 0.05 y Gas constant cp/c v 6 Thickness, subscript on Biot number indicating variable thickness A Difference c . Product of emissivity and beam length in radiation heat transfer p- Density
.o' Radiation constant
- v. Kinematic viscosity t: Time constant, pi group associated with scaled rate of change term Nomenciature - Wrch 1997 m:\3499w.non\3499w-d.wpl1NB1397 I
_ . _ . . . _ _ _ . , ~ - ,,- , _ _ _ , _ _ _ . .
l 13-4 .(
)
Dimensionless Groups . -
' Bi Biot number = ' ht/k (gas h and solid conductivity)
B Bond number = p g 627, 2 2 Uo /g(p -po)do or p 2Uo 2do2 /g(p -po)H - 5 Fr Froude number = po j Ma - Marangoni number, = do/dT(q"62p cr)/ (2 k2p) , Gr Grashof number = g(p -po)H8/p 2v or g(p -po)do 8
/p,v2 or g(p2- !
p3)L8 /p2V* Nu Nusselt number = hL/k (gas h and gas conductivity) ; Pr Prandtl number = pe/k p l Re Reynolds number = Undo /v or 4r/p, or pvd/p j Sc Schmidt number = p/pD, , i Sh Sherwood number = k/TPmL/D,P x Dimensionless Scaling Group. Initial subscripts m, e, p, c are respectively : mass, energy, pressure, and conductance. i i f 4 i h I i l l 1 I l i Nomenciature . March 1997 m:\3499w.non\3499w<twpf.1W1397
-- - _ ~ . .
t i 14-1 [ i 14 - REFERENCES
*1. NSD-NRC-97-4968, AP600 Passive Containment Cooling System Design Basis Analysis Reports, January 31,1997.
2
- 2. "AP600 Standard Safety Analysis Report," June 26,1992, Westinghouse Electric .
Corporation. i
- 3. M. J. Loftus, D. R. Spencer, J. Woodcock, " Accident Specification and Phenomena Evaluation for AP600 Passive Containment Cooling System " WCAP-14811, Westinghouse Electric Corporation.
l
- 4. D. L. Paulsen, et al., "WGOTHIC Code Description and Validation," WCAP-14382, May 1995, Westinghouse Electric Corporation. j i
'5. D. L. Paulsen, et al., "WGOTHIC Application to AP600," WCAP-14407, September 1996, Westinghouse Electric Corporation.
- 6. NTD-NRC-95-4563, " GOTHIC Version 4.0 Documentation," September 21,1995, Westinghouse Electric Corporation.
- 7. NTD-NRC-95-4577, " Updated GOTHIC Documentation," October 12,1995,
! Westinghouse Electric Corporation.
- 8. NTD-NRC-95-4595, "AP600,WGOTHIC Comparison to GOTHIC," November 13,1995, Westinghouse Electric Corporation.
- 9. R. P. Ofstun, " Experimental Basis for the AP600 Containment Vessel Heat and Mass Transfer Correlations," WCAP-14326, March 31,1995, Westinghouse Electric Corporation.
- 10. F. E. Peters, " Final Data Report for PCS Large-Scale Tests, Phase 2 and Phase 3,"
WCAP-14135, July 1994, Westinghouse Electric Corporation.
- 11. NTD-NRC-94-4138, AP600 Design Certification Test Program Overview, Rev. 6, May 17, 1994.
- 12. NUREG/CR-5809 EGG-2659, "An Integrated Structure and Scaling Methodology for Severe Accident Technical Issue Resolution," INEL, EG&G Idaho, Inc.
s References Much 1997 m:W99w.nonW99w-d.wpf:ll>031397 1
.,. , . .l
14 ;
)
- 13. W. Wulff, " Scaling of Thermohydraulic Systems," BNL-62325, May 1995, Sookhaven National Laboratory. .l
- 14. I.etter, N. J. Lipando (Westinghouse) to R. W. Borchardt (US NRC), "AP600 Passive :
^ Containment Cooung System Preliminary Scaling Report," NTD-NRC-94-4246, July 28,1994. (Superseded by WCAP-14845). -}
- 15. D. R. Spencer, " Scaling Analysis for AP600 Passive Containment Cooling System," l WCAP-14190, October 1994, Westinghouse Electric Corporation. (Superseded by l 3- WCAP-14845). ,
o 16. Istter, B. A. McIntyre (Westinghouse) to T. R. Quay (US NRC), NSD-NRC-96-4762, ! July 1,1996, D. R. Spencer, " Scaling Analysis for AP600 Containment Pressure During Design Basis Accidents," (Superseded by WCAP-14845). ! l ' 17. F. E. Peters, "AP6001/8th Large-Scale Passive Containment Cooling System Heat ; 1 Transfer Test Baseline Data Report," December 1992, Westinghouse Electric Corporationi f
- 18. Letter, N. J. Liparulo (Westinghouse) to R. W. Borchardt (US NRC), " Facility As-Built' Drawings for AP600 PCS Large (1/8th) Scale Test Facility," ET-NRC-93-3983, !
October 6,1993, Westinghouse Electric Corporation. i l
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~
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- One or more sections of these reports will be revised as a result of outstanding NRC open j items.
t References March 1997 m:\M99w.non\M99w-d.wpf.lb431397
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