ML031430498

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Supplement to Generic Letter 96-06 Resolution
ML031430498
Person / Time
Site: Point Beach  NextEra Energy icon.png
Issue date: 03/27/2003
From: Cayia A
Nuclear Management Co
To:
Document Control Desk, Office of Nuclear Reactor Regulation
References
GL-96-006, NRC 2003-0025
Download: ML031430498 (121)
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{{#Wiki_filter:Committed to Nuclear Excellence Point Beach Nuclear Plant Operated by Nuclear Management Company, LLC NRC 2003-0025 GL 96-06 10 CFR 50.54(0 March 27, 2003 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, D.C. 20555 POINT BEACH NUCLEAR PLANT DOCKETS 50-266 AND 50-301 SUPPLEMENT TO GENERIC LETTER 96-06 RESOLUTION The NRC staff issued Generic Letter (GL) 96-06 on September 30,1996. Wisconsin Electric Power Company (WEPCO), then licensee for the Point Beach Nuclear Plant (PBNP), provided its assessment of the waterhammer and two-phase flow issues for PBNP in letters dated January 28, June 25, and December 18,1997, and related submittals dated September 9, September 30, and October 30,1996. Responses to NRC requests for additional information were provided on September 4, 1998, and October 12, 2000. With these submittals, the GL 96-06 two-phase flow issues were fully addressed. Actions to fully address the waterhammer issues were deferred pending completion of the EPRI project and its review and approval by the NRC. EPRI Report TR-1 13594 was issued in December 2000, and NRC accepted it on April 3, 2002. On July 30, 2002, Nuclear Management Company, LLC, (NMC) submitted updated information regarding actions to address the resolution of GL 96-06 waterhammer issues at PBNP. On August 14, 2002, the NRC requested additional information regarding the July 30, 2002, submittal. During a conference call held on August 20, 2002, the NRC staff, PBNP plant staff, and Fauske & Associates (FAI) discussed the additional information requested by the NRC to support their review of Reference 5. During the conference call, PBNP proposed to provide sample cases and additional basis for the rationale that the FAI analyses for PBNP bound the EPRI methodology. On September 10, 2002, NRC staff agreed to review the additional information as proposed by PBNP. NMC recently replaced all eight containment fan cooler (CFC) units at Point Beach Units 1 and 2. The two-phase flow issues discussed in GL 96-06 were factored into the CFC replacement project. System piping configuration was changed in the course of the system redesign. The analysis provided in the enclosure to this letter is based on the flow and system characteristics of the new CFC unit configurations. The enclosure to this letter provides the FAI Calculation Note generated to calculate the waterhammer loads for the PBNP Containment Fan Coolers using the EPRI TBR methodology and comparing those results against the results generated previously using TREMOLO. As indicated in the comparison results of the enclosure, FAI concluded that the TREMOLO produced forcing functions used in the PBNP piping stress analyses generally bound the 'kc -7W 6590 Nuclear Road

  • Two Rivers, Wisconsin 54241 Telephone 920.755 2321

NRC 2003-0025 Page 2 EPRI TBR forcing functions. NMC agrees with FAI's conclusions. The enclosure demonstrates that the PBNP analyses are conservative with respect to the EPRI methodology. This letter contains no new commitments and no revision to existing commitments. A. .1 i;aa Site *c-rnt LASm@

Enclosure:

Transmittal of Fauske & Associates, Inc., Report FAI/03-07, Revision 1: Comparison of Point Beach TREMOLO Calculated Waterhammer Loads with the EPRI TBR Methodology, dated March 10, 2003.

References:

1. NRC Generic Letter (GL) 96-06, Assurance of Equipment Operability and Containment Integrity During Design-Basis Accident Conditions, dated September 30,1996.
2. Letter from DF Johnson (WE) to Document Control Desk, FL 96-06 120-Day Response, dated January 28, 1997.
3. Letter from AJ Cayia (WE) to Document Control Desk, Revision to GL 96-06, 120-Day Response, dated June 25, 1997.
4. Letter from AJ Cayia (WE) to Document Control Desk, Information pertaining to Implementation of Modifications Associated with GL 96-06, dated December 18, 1997.
5. Letter from B Link (WE) to Document Control Desk, Detailed Operability Evaluation of the Service Water System With Respect to Post-Accident Boiling in Containment Fan Coolers, dated September 9,1996.
6. Letter from B Link (WE) to Document Control Desk, Evaluation of Steady-State Service Water System Hydraulic Characteristics During A Design Basis Accident, dated September 30, 1996.
7. Letter from B Link (WE) to Document Control Desk, Assurance of Equipment Operability and Containment Integrity During Design Basis Accident Conditions, dated October 30, 1996.
8. Letter from LL Gundrum (NRC) to M. Sellman (WE), Request for Additional Information Regarding Responses to GL 96-06, dated June 25,1998.
9. Letter from VA Kaminskas (WE) to Document Control Desk, Reply to Request for Additional Information to GL 96-06, dated September 4,1998.
10. Letter from D Cole (NMC) to Document Control Desk, Reply to Request for Additional Information to GL 96-06, dated October 12, 2000.
11. FAI/97-60 Revision 5, Point Beach Containment Fan Cooler Analysis in Response to Generic Letter 96-06, dated August 8, 2001.

NRC 2003-0025 Page 3

12. EPRI Report TR-1 13594, Resolution of Generic Letter 96-06 Waterhammer Issues, Volumes 1 and 2, dated December 2000.
13. NRC Acceptance of EPRI Report TR-1 13594, Resolution of Generic Letter 96-06 Waterhammer Issues, dated April 3, 2002.
14. Letter from D. Spaulding (NRC) to M. Reddemann (NMC), Resolution of Generic Letter 96-06 Waterhammer Issues, dated May 3, 2002.
15. Letter from A. J. Cayia (NMC) to Document Control Desk (NRC), Electric Power Research Institute Report TR-1 13594, Resolution of Generic Letter 96-06 Waterhammer Issues, dated July 30, 2002.

cc: (w/ enclosure) Project Manager, Point Beach Nuclear Plant, NRR, USNRC (w/o enclosure) Regional Administrator, Region l1l, USNRC NRC Resident Inspector - Point Beach Nuclear Plant PSCW

ENCLOSURE TO NRC 2003-0025 FAUSKE & ASSOCIATES, INC. TRANSMITTAL OF COMPARISON OF POINT BEACH TREMOLO CALCULATED WATERHAMMER LOADS WITH THE EPRI TBR METHODOLOGY POINT BEACH NUCLEAR PLANT, UNITS 1 AND 2

MAY-22-03 THU 01:36 PH FRONT OFFICE POINT BEACH FAX NO, 920 755 6857 P. 02 FAI/03-07 Pagc I of 31 Rev. I Date: 03106103 FAUSKE & ASSOCIATES, INIC. CALCULATION NOTE COVER SHEET SF,CT ION TO BE COIPNIETED 3BY AUTH O1(,S);: Cnlc-Notc Number- ') tlic C FA 1103.07 Revision Numbcr I om patison of Point Beach TREMOLO -Calculared Walerhinrmner Loads with the EPRI TRR Methodolocv Project Number or Shop Order WEP015A Project Point BeacLLR0~ s PI IRqnm~aio

Purpose:

The purpose of this celculation is to calculate the watcrhammer loads for the Point Bench Containment Fan Coolers (Cl-Cs) using the 3EPRI TB3R methodology (EPPJ Report #1 006456) and comparing these rcsults against the results generated previously using TREMOLO. Revision I of this report was issued to address owners acceptance comments. These comments had no bcarinL: on the final conclusions. Hlowevr, the format of result tables changed slightly. Results Stimmary: Scc SecLion 5.0 for cornparison rcsults of TREMOLO versus the EPRI TBR, methodology. It is concluded that the TRltMOLO produced forcing functions generally bound the EPRI-TBR forcing funcions. Rcferences of Resulting rcports, Lcttcrs, or Memoranda (Optional) Author(s): Niann: (Print or Type) Completion Date Signature 3 / /03 R.W.Y Reevcs SE'CTION TO 13E COMPMLEDT ) BY V'ERTFIERSy: V'urifier(s): Completion Name (Print or Type) Signature Date Indepcndent Review or Mcthod of Verificutien: DeLkign Revicu Alternate Calculations X _., Tesling _ Oter (specify) SE1C-lON TO DE COMILETFIB) ItY MAN Responsible Manager: Nanic (Print oi Type) fL. JI lag-mnr lev -I - Sirnature Approval Date W> 12 d 900 7

HAY-22-03 THU 01:36 PH FRONT OFFICE POINT BEACH FAX NO. 920 755 6857 P. 03 FAI/03.07 Page 2 of 31 Rev. 1 Date: 03/06103 CALC NOTE NUMBER FAJ/03-07 -PAGE 2 CALCU LATlION NOTE METHODOLOGY CHECKLIST CIIECKLIST 1TO E3E COMPLETED BY AUTHOR(S) (CHECK APPROPRIATE RESPONSE) 1, Is the subjccr and/or the purpose of the design analysis clearly slaied? ".YES NO......... .... YES.. NO 5

2.

Are the rcquircd inputs and their sources provided?......................................... YES 0 NO El NIA O

3.

Are the issumptions ekarly identified nnd justifiedl....................................... YES 0 NO 5 N/A 5

4.

Aic the inethods and units cl:arly identified?.................. ............................ YES Z NO El N/A M

5.

Havc the limits of applicability been identified-?......... Y...................................... YES Z NO U NA E (Is the analysis fora 3 or 4 loop plant or for a single application.)

6.

Are the results of literature searches, if conducted, or othcr background dira provided?............ Y....... YES n NO 5 N/A 0

7.

Are all the pages sequentially numbcred and identified by the calculation note number?.......................................... YES 0 NO D

8.

Is the project or shop order clearly identified?................... ............................ YES 0 NO n

9. Ilas the required computer calculation information been provided?...................... YES 0 NO 5 N/A U 10 Wec e the computer codes used under configuration control?...............

........... YES 0 NOD N/A E II. Was the computer code(s) used applicable for modeling the physical andor comrputational problems identifcd?................... ............................ YES Z NO 5 N/A a (t.c., Is the correct computer code being used for the intended purpose.)

12.

Are the results and Conclusions cle3rly stated?................................................... YES 0 NO D 13 Are Open Itcms properly identified..................................................... YES D NO D NIA Z

14.

WUrc approved lDcsign Control practices followed without exception?.............. YES f2 NO M N/A (Approved Design Control practices refers to guidance documents within Nuclcar Services that state how the work is to be performed, such as how to performn a LOCA analysis.)

15.

Have all related contract reqi:irements been met?............................................... YES 0 NO E N/A U NOTE: If NO to any of the above, Page Number containing justification

FAI/03-07 Page 3 of 31 Rev. I Date: 03/06/03 FAI/03-07 COMPARISON OF POINT BEACH TREMOLO-CALCULATED WATERHAMMER LOADS WITH THE EPRI TBR METHODOLOGY Rev. 1 Prepared for Nuclear Management Co. LLC Prepared by Fauske & Associates, Inc. 16W070 West 83 rd St. Burr Ridge, IL 60521 March 2003

FAI/03-07 Page 4 of 31 Rev. 1 Date: 03/06/03 TABLE OF CONTENTS 1.0 PURPOSE....................................... 7

2.0 INTRODUCTION

8

3.0 REFERENCES

9 4.0 DESIGN INPUTS...................................... 10 4.1 Assumptions....................................... 1 5.0 RESULTS....................................... 17 5.1 EPRI TBR Waterhammer Calculations....................................... 17 5.2 TREMOLO Peak Force/Impulse Calculations....................................... 23

6.0 CONCLUSION

S....................................... 31 APPENDIX A: APPENDIX B: APPENDIX C: APPENDIX D: APPENDIX E: APPENDIX F: APPENDIX G: APPENDIX H: APPENDIX I: Point Beach CFC IA EPRI TBR Waterhammer Calculations Using MathCad 2000.......................... A-I Point Beach CFC IC EPRI TBR Waterhammer Calculations Using MathCad 2000.......................... B-i Point Beach CFC 2B EPRI TBR Waterhammer Calculations Using MathCad 2000.......................... C-I Point Beach CFC 2D EPRI TBR Waterhammer Calculations Using MathCad 2000.......................... D-I Service Water Pump Curve Calculations Using Microsoft EXCEL 97.......................... E-1 EPRI TBR Max Force/Impulse Calculations for Point Beach CFC IA Using Microsoft EXCEL 97.......................... F-I EPRI TBR Max Force/Impulse Calculations for Point Beach CFC IC Using Microsoft EXCEL 97.......................... G-1 EPRI TBR Max Force/Impulse Calculations for Point Beach CFC 2B Using Microsoft EXCEL 97.......................... H-1 EPRI TBR Max Force/Impulse Calculations for Point Beach CFC 2D Using Microsoft EXCEL 97.......................... I-I

FAI/03-07 Page 5 of 31 Rev. 1 Date: 03/06/03 LIST OF FIGURES 4-1 Diagram of EPRI TBR CFC Configuration (Open System)...................................... 16 5-1 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC IA......................... 20 5-2 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC IC.......................... 20 5-3 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC 2B.......................... 21 5-4 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC 2D......................... 21 5-5 EPRI Pressure-Force Time History Schematic................................................ 22 5-6 Sample TREMOLO Pressure Profile for a Point Beach SW Pipe Element Following a LOOP + LOCA.29 5-7 Sample TREMOLO Force-Time History for a Point Beach SW Pipe Element Following a LOOP + LOCA.30

FAI/03-07 Page 6 of 31 Rev. 1 Date: 03/06/03 LIST OF TABLES 4-1 EPRI TBR Calculational Inputs Table for Point Beach CFC IA.............................. 12 4-2 EPRI TBR Calculational Inputs Table for Point Beach CFC IC.............................. 13 4-3 EPRI TBR Calculational Inputs Table for Point Beach CFC 2B.............................. 14 4-4 EPRI TBR Calculational Inputs Table for Point Beach CFC 2D.............................. 15 5-1 Results of EPRI TBR Waterhammer Calculations for Point Beach CFCs................ 19 5-2a Comparison of TREMOLO - EPRI TBR Maximum Forces for Point Beach CFC lA..................................................... 24 5-2b Comparison of TREMOLO - EPRI TBR Maximum Impulses for Point Beach CFC IA..................................................... 24 5-3a Comparison of TREMOLO - EPRI TBR Maximum Forces for Point Beach CFC iC..................................................... 25 5-3b Comparison of TREMOLO - EPRI TBR Maximum Impulses for Point Beach CFC IC...................................................... 25 5-4a Comparison of TREMOLO - EPRI TBR Maximum Forces for Point Beach CFC 2B..................................................... 26 5-4b Comparison of TREMOLO - EPRI TBR Maximum Impulses for Point Beach CFC 2B..................................................... 26 5-5a Comparison of TREMOLO - EPRI TBR Maximum Forces for Point Beach CFC 2D..................................................... 27 5-5b Comparison of TREMOLO - EPRI TBR Maximum Impulses for Point Beach CFC 2D...................................................... 27

FAI/03-07 Page 7 of 31 Rev. 1 Date: 03/06/03 1.0 PURPOSE The purpose of this calculation is to calculate the waterharnmer loads for the Point Beach Containment Fan Coolers (CFCs) using the EPRI Waterhammer Issues TBR (EPRI, 2002a) Methodology. These calculations will be performed on an elevated fan cooler and a lower fan cooler (in terms of elevation within containment) for Point Beach Units 1 and 2. The results of these calculations will then be compared against the results generated for the previously performed TREMOLO analyses (FAI, 2000 and 2001a & b). This comparison is being performed to satisfy NRC requirements for Generic Letter 96-06 as discussed in Section 2.0

FAI/03-07 Page 8 of 31 Rev. 1 Date: 03/06/03

2.0 INTRODUCTION

In response to the requirements of NRC Generic Letter 96-06 (NRC, 1996), the waterhammer loads associated with column separation and energy transfer to the service water system (including the containment fan coolers) were analyzed using the FAI computer code TREMOLO Revision 1.02 (FAI, 1997). The analyses were performed for all of the fan cooler piping arrangements in both units and were based on the design basis accident conditions of a loss of off-site power event (LOOP), as well as a loss of off-site power combined with a large break loss of coolant accident (LOCA) in the containment (LOOP + LOCA). These conditions were evaluated with the TREMOLO code and the resulting waterhammer loads associated with both condensation induced waterhamrnmer and column closure following separation were assessed for the entire length of the fan cooler piping. These time dependent loads were transmitted to Sargent & Lundy to be analyzed with respect to the piping response to determine the associated loads on the piping hangers. The net result of this integrated analysis was that all of the piping hangers remained within their design basis loadings for both of the service water transients investigated. In general, the LOOP + LOCA transient provided the greatest loads. Since the TREMOLO code has not been generically reviewed by the Nuclear Regulatory Commission (NRC), closure of the issues identified in NRC Generic Letter 96-06 (NRC, 1996) requires either a review of the computer code by the NRC or a comparison between the results generated for the Point Beach units and a generic methodology which has been approved by the NRC. Generic approval has been given to the EPRI methodology Generic Letter 96-06 Waterhammer Issues Resolution Technical Basis Report (EPRI, 2002a) for evaluating loads resulting from column closure events which is intended to bound condensation induced waterhammer events. This calculation compares the calculated loads using the EPRI TBR methodology with those produced using the TREMOLO code.

FAI/03-07 Page 9 of 31 Rev. 1 Date: 03/06/03

3.0 REFERENCES

EPRI, 2002a, "Generic Letter 96-06 Waterhammer Issues Resolution - Technical Basis Report - Non Proprietary," EPRI Report # 1003097, May 2002. EPRI, 2002b, "Generic Letter 96-06 Waterhammer Issues Resolution - User's Manual," EPRI Report # 1006456, April, 2002. Fauske & Associates, Inc. 1997, FAI Q.A. File 5.17 (includes TREMOLO Revision 1 Test Plan, Test Documentation, and User Documentation, March 1997 and TREMOLO Revision 1.02 Software Change Specification and Test Documentation, August 1997). Fauske & Associates, Inc., 2000, "Point Beach Containment Fan Cooler Analysis in Response to NRC Generic Letter 96-06," FAI/97-60, Rev. 2. Fauske & Associates, Inc., 2001a, "Point Beach Containment Fan Cooler Analysis in Response to NRC Generic Letter 96-06," FAI197-60, Rev. 3. Fauske & Associates, Inc. 2001b, "Point Beach Containment Fan Cooler Analysis in Response to NRC Generic Letter 96-06," FAI/97-60, Rev. 5. NRC, 1996, "Generic Letter 96-06: Assurance of Equipment Operability and Containment Integrity During Design Basis Accident Conditions," September 30, 1996. WEPCo, 1999, Point Beach FSAR: Section 9.6 (Service Water System), Rev. 6. 1999. WEPCo, 2003, E-mails from Chuck Richardson (WEPCo) to R. J. Hammersley (FAI) dated 1/27/03 and 1/28/03, "Unit 1 & 2 WATER model output."

FAI/03-07 Page 10 of 31 Rev. 1 Date: 03/06/03 4.0 DESIGN INPUTS The objective of this calculation is to compare the loads calculated by TREMOLO and EPRI TBR due to column closure waterhammer once steam bubbles have been generated due to energy addition and a pressure reduction. The TREMOLO loads for each of eight fan coolers at Point Beach have been previously calculated and the results are documented in (FAI, 2000,2001 a, 200 lb). Tables 4-1 through 4-4 illustrate the design inputs required for the EPRI TBR methodology and the actual values used for the analyses performed on Point Beach CFCs lA, IC, 2B and 2D. Figure 4-1 illustrates a graphic representation of the EPRI TBR CFC model used to perform the pressure pulse calculations. As shown in Figure 4-1, the EPRI TBR methodology does not model the 6" and 2 V2" piping that branch off the 8"piping on the supply and return side of the CFC. This is due to the fact that the EPRI methodology does not model parallel flow paths, which is what occurs immediately before and after flow enters and exits the CFCs. However, since TREMOLO demonstrated that the peak forces occur in the 8" piping and the void collapse occurs in this piping as well, the 6" and 2 l/2" piping does not need to be modeled. The forces in the 6" and 2 V21 piping could be calculated using transmission coefficients calculated in the EPRI TBR methodology. Based on such transmission coefficients, the pressure pulses produced by void collapse in the 8" piping are reduced as they are transmitted to 6" piping and even further reduced when the pressure is then transmitted into the 2 V2? piping. Therefore, due to these pressure reductions the 6" and 2 V2" piping do not need to be modeled directly. The approach for developing the comparison was completed as follows:

  • Select two fan cooler units per unit based on elevational differences within containment (high and low elevation).

Assemble the information for the EPRI TBR calculation based on the piping configuration documented in the various TREMOLO parameter files for the selected CFCs for analysis.

FAI/03-07 Page 11 of 31 Rev. 1 Date: 03/06/03

  • Calculate the peak pressure pulse using the EPRI TBR methodology. The MathCad 2000 spreadsheet used to calculate the peak pressure pulses for the four Point Beach CFCs was developed and tested by implementing the EPRI Open Loop Example Problem (EPRI, 2002b) and verifying that identical results were produced.
  • Apply the EPRI TBR calculated pressure pulse using the methodology described in Figure 5-5 to determine the loads (peak force/impulse) from the TBR evaluations for the selected CFCs.
  • Determine the maximum forces from the previous TREMOLO analyses [FAI, 2000, 2001a, 2001b] and calculate the impulses associated with those forces.
  • Compare the results generated from the TREMOLO analyses to the results generated from the EPRI TBR methodology.

4.1 Assumptions Several assumptions were made in the EPRI TBR calculations for the Point Beach CFCs. Listed below is a summary of the assumptions made in this analysis:

  • The SW design temperature is used to calculate the amount of non-condensable gases that comes out of solution in the EPRI Waterhammer Calculations. A conservatively high temperature of 950F was assumed. This is conservative since a higher water temperature results in smaller amounts of non-condensable gases, which leads to less "cushioning" during void collapse.
  • Figure 4-1 illustrates two "other system loads" in the EPRI CFC model. The upper branch (b to f) "other system loads" (Qabf) was assumed to be the second fan cooler that branches off the supply header. Its flow was assumed to be = 800 gpm. The lower branch (a to g) "other system load" (Qag) in the 24" line was assumed to be equal to the total flow out of a SW pump minus the two CFC flows.

FAI/03-07 Page 12 of 31 Rev. I Date: 03/06/03 Table 4-1: EPRI TBR Calculational Inputs for Point Beach CFC 1A TBR Parameter Value Description/Reference Tvod 224 F Average void temperature when pumps restart [FAI, 2001 a] Pvoid 18.3 psia Saturation pressure of T,0 jd (steam table) Tpipe 75 F Initial pipe temperature [FAI, 2001a] (not used in EPRI methodology) Patm 14.7 psia Atmospheric pressure (absolute) Ntube 240 Number of fan cooler tubes [FAI, 2001 a] IDtwbe 0.527" ID of fan cooler tubes [FAI, 200 la] Ltube 22 ft Length of fan cooler tubes [FAI, 200 la] ELi 33.2 ft Elevation of node I [FAI, 2001 a] EL2* 82.3 ft Elevation of node 2 [FAI, 2001 a] Lab 30.5 ft Length from node A to B [FAI, 2001 a] Lbc 87.5 ft Length from node B to C [FAI, 2001a] Lcd 61.4 ft Length from node C to D [FAI, 2001al Lde 78.5 ft Length from node D to E [FAI, 2001 a] Lef 4.1 ft Length from node E to F [FAI, 2001 a] Lfg 87.6 ft Length from node F to G [FAI, 2001 a] IDabf 13.124 in ID of piping along path a-b-+f [FAI, 2001a] IDb:d 7.981 in ID of piping along path b-+c--d [FAI, 200 la] IDag 22.624 in ID of piping along path a-+g [FAI, 2001 a] ODbcd 8.625 in OD of piping along path b-+c-+d FAI, 2001a] H, 240.8 ft Pump shutoff head [WEPCo, 2003] (See Appendix E) Ai 0.2547 sec/ft 2 1" order pump curve coefficient [WEPCo, 20031 (See Appendix E) A2 -0.5783 sec2/ft5 2nd order pump curve coefficient [WEPCo, 2003] (See Appendix E) Qabf 800 gpm Flow along path a-+b->f during steady state (assumed) Qbcd 917 gpm Flow along path b->c->d during steady state [FAI, 200 la] Qag 5100 gpm Flow along path a-*g during steady state [WEPCo, 1999] Vwtr-fcu 0.0 ft3 Volume of water present in FCU when pump restarts [FAI, 2001 a] Kvalve 158.41 Throttle valve loss coefficient [FAI, 2001a] pwtr 62 lb/ft3 Water density Tdes 95 F Design temp of Service Water System (assumed) Rgas 1717 ft2/sec2 - R Universal gas constant PSS_ 19 psig Initial steady state system pressure [FAI, 200 la] Note: *Since the Point Beach CFCs have check valves on the 8" supply piping to the CFC, the void elevation (EL2) illustrated in Figure 4-1 will not be the same on the supply and return side of the CFC piping. For these analyses, EL2 was calculated to be the elevation of the void front on the supply side of the CFC. This is appropriate since EL2 is only used to determine the water head the SW pump must overcome.

FAI/03-07 Page 13 of 31 Rev. 1 Date: 03/06103 Table 4-2: EPRI TBR Calculational Inputs for Point Beach CFC 1C TBR Parameter Value Description/Reference Tvoid 223.0 F Average void temperature when pumps restart [FAI, 200 lb] Pvoid 18.3 psia Saturation pressure of Tvod (steam table) Tpipe 75 F Initial pipe temperature [FAI, 2001b] (not used in EPRI methodology) Patm 14.7 psia Atmospheric pressure (absolute) Ntube 240 Number of fan cooler tubes [FAI, 2001b] IDtube 0.527" ID of fan cooler tubes [FAI, 200 1bj Ltube 22 ft Length of fan cooler tubes [FAI, 200 lb] EL, 33.2 ft Elevation of node 1 [FAI, 2001b] EL2* 37.4 ft Elevation of node 2 [FAI, 2001b] Lab 30.5 ft Length from node A to B [FAI, 2001b] Lbq 67.8 ft Length from node B to C [FAI, 2001b] Lcd 32.3ft Length from node C to D [FAI, 2001bl Lde 79.8 ft Length from node D to E [FAI, 200 lb] Lef 2.2 ft Length from node E to F [FAI, 200 lb] Lf_ 86.4 ft Length from node F to G [FAI, 2001b] IDabf 13.124 in ID of piping along path a->b--f [FAI, 2001b] IDbcd 7.981 in ID of piping along path b-*c->d [FAI, 200 1b] IDag 22.624 in ID of piping along path a->g [FAI, 2001b] ODbcd 8.625 in OD of piping along path b->c--d FAI, 200 lb] H, 240.8 ft Pump shutoff head [WEPCo, 2003] (See Appendix E) Al 0.2547 sec/ft2 1st order pump curve coefficient [WEPCo, 2003] (See Appendix E) A2 -0.5783 sec2/ft5 2nd order pump curve coefficient [WEPCo, 2003] (See Appendix E) Qabf 800 gpm Flow along path a-+b->f during steady state (assumed) Qbcd 851 gpm Flow along path b->c->d during steady state [FAI, 2001b] Qag 5200 gpm Flow along path a->g during steady state [WEPCo, 1999] Vwtrt'cu 0.0 ft Volume of water present in FCU when pump restarts [FAI, 200 lb] Kvalve 161.472 Throttle valve loss coefficient [FAI, 2001b] Pwtr 62 lb/ft3 Water density Tdes 95 F Design temp of Service Water System (assumed) Rgas 1717 ft2/sec 2. R Universal gas constant PSYS 19 psig Initial steady state system pressure [FAI, 2001b] Note: *Since the Point Beach CFCs have check valves on the 8" supply piping to the CPU, the void elevation (EL2) illustrated in Figure 4-1 will not be the same on the supply and return side of the CFC piping. For these analyses, EL2 was calculated to be the elevation of the void front on the supply side of the CFC. This is appropriate since EL2 is only used to determine the water head the SW pump must overcome.

FAI/03-07 Page 14 of 31 Rev. 1 Date: 03/06/03 Tahle 4-3! EPRI TBR Calculational Innuts for Point Beach CFC 2B TBR Parameter Value Description/Reference Tvoid 217.1 F Average void temperature when pumps restart [FAI, 2000] Pvoid 16.3 psia Saturation pressure of T,01d (steam table) T_ __e 75 F Initial pipe temperature [FAI, 20001 (not used in EPRI methodology) Patm 14.7 psia Atmospheric pressure (absolute) Ntube 240 Number of fan cooler tubes [FAI, 2000] IDtube 0.527" ID of fan cooler tubes [FAI, 2000] Ltube 22 ft Length of fan cooler tubes [FAI, 2000] EL, 33.2 ft Elevation of node 1 [FAI, 2000] EL2* 72.0 ft Elevation of node 2 [FAI, 20001 Lab 36.8 ft Length from node A to B [FAI, 2000] Lbc 139.4 ft Length from node B to C [FAI, 20001 Lcd 83.6 ft Length from node C to D [FAI, 2000] Lde 129.2 ft Length from node D to E [FAI, 2000] Lef 4.8 ft Length from node E to F [FAI, 20001 Lfg 118.6 ft Length from node F to G [FAI, 2000] IDabf 13.124 in ID of piping along path a-*b--f[FAI, 2000] IDbcd 7.981 in ID of piping along path b-*c->d [FAI, 2000] IDag 22.624 in ID of piping along path a-*g [FAI, 2000] ODbcd 8.625 in OD of piping along path b->c--d FAI, 2000] H, 240.8 ft Pump shutoff head [WEPCo, 2003] (See Appendix E) Al 0.2547 sec/ft 1st order pump curve coefficient [WEPCo, 20031 (See Appendix E) A2 -0.5783 sec2/ft5 2nd order pump curve coefficient [WEPCo, 20031 (See Appendix E) Qabf 800 gpm Flow along path a->b--f during steady state (assumed) Qbcd 886 gpm Flow along path b-*c--d during steady state [FAI, 2000] Qag 5200 gpm Flow along path a-*g during steady state [WEPCo, 19991 Vwtr-fcu 0.0 ft Volume of water present in FCU when pump restarts [FAI, 2000] Kvalve 165.447 Throttle valve loss coefficient [FAI, 2000] Pwtr 62 lb/ft3 Water density Tdes 95 F Design temp of Service Water System (assumed) Rgas 1717 ft2/sec 2. R Universal gas constant PSS 19 psig Initial steady state system pressure [FAI, 2000] Note: *Since the Point Beach CFCs have check valves on the 8" supply piping to the UCF, the void elevation (EL2) illustrated in Figure 4-1 will not be the same on the supply and return side of the CFC piping. For these analyses, EL2 was calculated to be the elevation of the void front on the supply side of the CFC. This is appropriate since EL2 is only used to determine the water head the SW pump must overcome.

FAI/03-07 Page 15 of 31 Rev. 1 Date: 03/06/03 Table 4-4: EPRI TBR Calculational Inputs for Point Beach CFC 2D TBR Parameter Value Descrintion/Reference Tvoid 204.4 F Average void temperature when pumps restart [FAI, 2000] Pvoid 12.7 psia Saturation pressure of T,0 id (steam table) Tipe 75 F Initial pipe temperature [FAI, 2000] (not used in EPRI methodology) Patm 14.7 psia Atmospheric pressure (absolute) Ntube 240 Number of fan cooler tubes [FAI, 2000] IDtube 0.527" ID of fan cooler tubes [FAI, 20001 Ltube 22 ft Length of fan cooler tubes [FAI, 2000] ELI 33.2 ft Elevation of node 1 [FAI, 2000] EL2* 30.3 ft Elevation of node 2 [FAI, 2000] Lab 36.8 ft Length from node A to B [FAI, 2000] Lbc 161.8ft Length from node B to C [FAI, 2000] Lcd 46.5 ft Length from node C to D [FAI, 2000] Lde 161.2 ft Length from node D to E [FAI, 2000] Lef 6.4 ft Length from node E to F [FAI, 20001 Lfg 86.8 ft Length from node F to G [FAI, 20001 IDabf 13.124 in ID of piping along path a-*b->f [FAI, 20001 IDbcd 7.981 in ID of piping along path b-+c--d [FAI, 20001 IDag 22.624 in ID of piping along path a-*g [FAI, 2000] ODbcd 8.625 in OD of piping along path b-*c--d FAI, 2000] H_ 240.8 ft Pump shutoff head [WEPCo, 2003] (See Appendix E) Al 0.2547 sec/ft2 1st order pump curve coefficient [WEPCo, 2003] (See Appendix E) A2 -0.5783 sec2/ft5 2n order pump curve coefficient [WEPCo, 2003] (See Appendix E) Qabf 800 gpm Flow along path a->b--f during steady state (assumed) Qbcd 949 gpm Flow along path b-*c-*d during steady state [FAI, 2000] Qag 5100 gpm Flow along path a-*g during steady state [WEPCo, 1999] Vwtr-fcu 0.0 ft3 Volume of water present in FCU when pump restarts [FAI, 2000] Kvalve 139.326 Throttle valve loss coefficient [FAI, 20001 pwtr 62 lb/ft3 Water density Tdes 95 F Design temp of Service Water System (assumed) Rgas 1717 ft2/sec2 - R Universal gas constant PM 19 psig Initial steady state system pressure [FAI, 2000] Note: *Since the Point Beach CFCs have check valves on the 8" supply piping to the CFC, the void elevation (EL2) illustrated in Figure 4-1 will not be the same on the supply and return side of the CFC piping. For these analyses, EL2 was calculated to be the elevation of the void front on the supply side of the CFC. This is appropriate since EL2 is only used to determine the water head the SW pump must overcome.

FAI/03-07 Page 16 of 31 Rev. 1 Date: 03/06/03 Figure 4-1 Diagram of EPRI TBR CFC Configuration (Open System). VOIDED l 12" 4VOIDED EL2 f a 2-4'

FAI/03-07 Page 17 of 31 Rev. 1 Date: 03/06/03 5.0 RESULTS 5.1 EPRI TBR Waterhammer Calculations During a postulated LOCA (or MSLB) with a concurrent LOOP (Loss of Offsite Power), the service water pumps that supply cooling water to the CFCs and the fans that supply air to the CFCs will temporarily lose power. The cooling water will lose pressure and stop faster than the fans stop. During the fan coastdown, the high temperature steam in the containment atmosphere will pass over the CFC tubing with no forced cooling water flowing through the tubing. Boiling may occur in the CFC tubing causing steam bubbles to form in the CFCs and pass into the attached piping creating steam voids. Prior to pump restart, the presence of steam and subcooled water presents the potential for waterhamrnmer. As the service water pumps restart, the accumulated steam will condense and the pumped water can produce a waterhamrnmer when the void collapses. The hydrodynamic loads introduced to the service water piping by such a waterhammer event could challenge the integrity and function of the CFCs and the Service Water (SW) System, as well as containment integrity, should the waterharnmer loads fail the Service Water piping supports. Section 7.0 of the EPRI TBR Waterhammer Users Manual (EPRI, 2002b) provides a prescribed methodology to calculate the pressure pulse due to a SW system column closure waterharnmer event. The analysis is performed in the following manner:

  • Calculate the initial closing velocity
  • Calculate the lengths of the accelerating water column
  • Calculate the mass of gas in the voided region
  • Calculate a "cushioned" velocity based on initial velocity, pipe size, void and column length
  • Calculate sonic velocity
  • Calculate the waterharnmer pressure pulse rise time
  • Calculate the pulse duration
  • Calculate the transmission coefficients

FAI/03-07 Page 18 of 31 Rev. 1 Date: 03/06/03

  • Calculate the pulse pressure with no clipping
  • Calculate the pressure considering clipping
  • Calculate the pressure pulse shape.

Using this methodology and the design information specified in Tables 4-1 through 4-4, the calculations for the Point Beach CFCs using the EPRI TBR methodology were performed and the calculation for each of the four Point Beach CFCs (lHX15A, IHX15C, 2HX15B, and 2HX15D) is attached as Appendices A through D. Table 5-1 summarizes the results and Figures 5-1 through 5-4 illustrate the EPRI TBR calculated pressure pulses for each of the four Point Beach CFCs. The pressure pulse calculated (see Figures 5-1 through 5-4) for each of the four Point Beach CFCs were then used to calculate the force history and impulse loading on the SW piping upstream and downstream for each of the four CFCs analyzed. The void collapse location was determined from the corresponding TREMOLO results [FAI, 2000, 2001a, and 2001b]. Figure 5-5 illustrates the manner in which the forces/impulse will be calculated when applying the EPRI-calculated pressure pulse to the Point Beach SW piping. Since the void collapse occurs in the return line, the force and impulse calculations focused on the piping between the CFC outlet header which is upstream of the void collapse and the MOV throttling valve that is downstream of the void collapse. As shown in Figure 5-5, the EPRI-calculated pressure pulse (b) can be applied to a pipe network (a) to calculate the force on the two elements PI and P2 (c). The force on PI is simply equal to the pressure times the pipe area. Since the pipe diameter is the same at points PI and P2, the force magnitude on P2 is the same as PI, except it is in the opposite direction and delayed by the transient pressure pulse's transient time between the two points. The transient time equals the length of the pipe between P1 and P2 (L2) divided by the sonic velocity. Due to the delay in the pressure pulse reaching P2, the pipe section experiences an unbalanced force until the pressure pulse reaches P2. Therefore, due to this time delay and the forces being in the opposite direction, the resulting force (d) on the pipe section between P1 and P2 is used to determine the peak forces and impulses.

FAI/03-07 Page 19 of 31 Rev. 1 Date: 03/06/03 Table 5-1 Results of EPRI TBR Waterhammer Calculations for Point Beach CFCs Unit 1 Unit 2 CFC 1A CFC 1C CFC 2B CFC 2D Rise time (ms) 48 39 39 28 Duration (ms) 79.7 78.8 118.2 119.1 AP (psi) 191 202 223 286 APno clippin __174 222 203 260 Refill velocity (Vnitial) ft/S 7.9 8.8 8.5 10.9 Cushion velocity (VcuMhi.n) ft/s 6.1 7.1 7.1 9.1 Total duration (ms)* 127 118 157 147

FAI/03-07 Page 20 of 31 Rev. 1 Date: 03/06/03 Figure 5-1 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC IA. Pre e Pulse ,210 276,25O co c pressure PSI U,9-150 time ms time (ns) ,127.492, trace I Figure 5-2 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC IC. Pressure Pulse ,24 1 la an pressure e psi c-0 50 100 ISO time ms time (Ms) ,1 18.206, trace I

FAI/03-07 Page 21 of 31 Rev. I Date: 03/06/03 Figure 5-3 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC 2B. Pressure Pulse ,241 903.300 co2 a pressure Vi Psi C. ,19, 100 100 0 50 100 150 ,0, time ms time (Ms) 200 . 57.424, trace 1 Figure 5-4 EPRI TBR Waterhammer Pressure Pulse for Point Beach CFC 2D. Pressure Pulse ,304 lo in pressure 15 2 ps 2 0 50 100 150 ,147 461, ,0, time Ms time (ms) trace I

FAI/03-07 Page 22 of 31 Rev. 1 Date: 03/06/03 Figure 5-5 EPRI Pressure-Force Time History Schematic. Pi L1 L2 (a) Rise Time Dwell Time Fl P iTm (b) Time F T \\ 5> g Time I I I I~~~ Ii I X I I I III I (d ) \\ Time RR032001 CDR 2-28-2003

FAI/03-07 Page 23 of 31 Rev. 1 Date: 03/06/03 The resulting force (d) begins to rise once the pressure pulse reaches PI and continues to rise until the pressure pulse reaches P2. When the pressure pulse reaches P2, the resulting force levels out until the pressure pulse at Pi reaches its peak at which time the resultant force turns around and goes to zero when the pressure pulse at P2 reaches its peak. The force in the pipe remains balanced until the pressure pulse begins to exit PI. The resulting force then goes in the negative direction until the pressure pulse begins to exit P2. At this time the forces balance until the pressure pulse completely exits Pi. The resultant force then goes to zero as the pressure pulse completely clears P2. The maximum forces and impulses are tabulated in Tables 5-2b through 5-Sb for the four Point Beach CFCs. The maximum force and impulses were calculated assuming a single pressure pulse calculated for each CFC (shown in Appendices A through D) is propagated through the SW piping. The point of collapse for the calculation was assumed to be at the same location of final void collapse calculated by TREMOLO for each CFC. The peak forces and impulse calculation for each of the fan CFCs analyzed are attached as Appendices F through I. As shown in these Appendices and Figure 5-5, the peak force is limited by the length of piping between two sequential elements (i.e., elbow). Once the pressure pulse reaches one elbow it begins to exert a force on the section of piping between the two elements. However, when the pressure pulse is transmitted to the next elbow, which is length of pipe divided by the sonic velocity of the pulse, the force on the second element counteracts the first force, thus limiting the peak force on the piping due to the relatively short length of piping between the various elements within the system (typically less then 20 ft). The pipe section peak forces and corresponding impulses (calculated as the rise time of the pressure pulse x the peak resultant force) are summarized in Tables 5-2b through 5-Sb for each of the four CFCs analyzed. 5.2 TREMOLO Peak Force/Impulse Calculations The TREMOLO peak forces were taken from the previously performed TREMOLO analyses [FAI, 2000, 2001a and 2001b] on the Point Beach CFCs. The corresponding impulse for these forces was not directly calculated in the TREMOLO analyses referenced above, rather they were determined separately by conservatively estimating the area under the peak force pulses.

MAY-22-03 THU 01:36 PM FRONT OFFICE POINT BEACH FAX NO. 920 755 6857 P. 05 FAI/03.07 N.- 24, or i ,Rev. 1. Datc: 03/06/03 Table 5-2a ComT1parison of TREMOLO - EPRI TBR Mkaximuin Forces for Point Beach CFC 1A. TlRENIOLO-Calculated EPRI-Calculated Nfaximrnum Forcc (llr) Maximum Force (BMr) 1858 907 1840 605 1796 592 1702 559 1633 4S8 1201 326 997 302 Table 5-2b Comparison of TREMOLO - EPRI TBR Maximum Impulses for Point Beach CFC 1A.

MAY-22-03 THU 01:37 PM FRONT OFFICE POINT BEACH FAX NO. 920 755 6857 P. 06 FA[IJ0 (07 Pagc '25r i-I Rev. 1. Dale 03/06/03 Table 5-3a Compairison of 'TENIOIO -EPRI 'rBR MIaximum Forces ror Point Beach CFC IC. TREINIOLO-Calculatcd -EPRI-Calculated Maximum Force (lb[) I Maximnum Force (lbr) 3119 1200 2917 732 2545 732 2422 732 1950 706 1599 580 1303 535 Table 5-31b Comparison of TRE!MOLO - EPRI TBR Maximum Impulses ror Point Beach CFC 1C. TREMOLO-Cailcilated EPRI-Calculated Impulses (lbr - s) Impulses (Ir-s) 102.5 46.8 68.9 28.6 63.3 28.6 62.5 28.6 58.5 27.5 35.5 22.6 32.1 [ 20.9

MAY-22-03 THU 01:37 PM FRONT OFFICE POINT BEACH FAX NO. 920 755 6857 P. 07 FAE/03*07 Pa:c 26 (if 31 Rev. 1, Daic: 03/06/03 Tablle 5-la Comparison of lTRFNIOLO - EPRI TB3R MIaximurm Forces for Point Beach CFC 2B. TRENMOLO-calculated EPRI-Calculaled Manimum Forces (lbt) Maximum Forces (lb) 2619 2408 1664 1299 1248 1144 1039 943 898 870 889 678 822 6i3 T.aible 5-4b Comparison of TREMOLO EPRI TD3R Maximum Impulses for Point Beach CFC 213. U ThREMOLO-Calculated FERI-Calculated Impulscs Ibr-S) Implulses (I-S) 104.3 93.9 75.0 50.6 65.3 44.6 63.9 36.8 49.9 33.9 40.6 26.4 37.5 23.9

MAY-22-03 THU 01:37 PM FRONT OFFICE POINT BEACH FAX NO. 920 755 6857 P. 08 FAI/O3-07 P3"c 27 of 31 Rev. 1. Date: o03l6/03 T'Ible 5-Sa Comparison of TREMOLO - EPRI TBR Maximum Forces for Point Bench CFC 2D. Trit EMOLO-('alculated EPRI-Calculated Maximum Forces (Ibr) Maximum Forces (lbr) 3551 4779 3264 3596 2670 1541 1521 1075 1516 1075 1474 836 1330 818 Tabln S-Sb Comparison or TE6MOLO - EPRI TBR NMaximum Trnpulses for Point Beach CFC 2D. 4 .i I J-A ! rE MOLO-Calculated EPRI-Calculated Impulses (Ibt) Imn ulses _lbr s) 283.5 133.8 254.8 100.7 166.9 43.2 90.2 30.1 SS.5 30.1 73.4 23.4 63 22.9

FAI/03-07 Page 28 of 31 Rev. 1 Date: 03/06/03 The peak forces and impulses tabulated in Tables 5-2a through 5-5a for the four Point Beach CFCs analyzed were identified and tabulated independently. As stated earlier in Section 2.0, TREMOLO is a transient code that models the fluid hydrodynamics within the SW piping system as well as performs pressure and force calculations in the piping network following a waterhammer event. TREMOLO also considers distributed voids in several pipe segments which upon collapse will transmit a pressure pulse. A sample illustration of these multiple pressure pulses is illustrated in Figure 5-6. As shown in Figure 5-6, the pressure response through this particular piping event is very dynamic. This is due to the fact that once TREMOLO calculates void collapse within a node, a pressure pulse is calculated and is transmitted throughout the system. In addition, TREMOLO models the pressure wave transmission and reflections. The net result is numerous pressure waves traveling through the SW-system as the voids collapse throughout the piping system. Since the void collapse occurs in the CFC return line, the TREMOLO force and impulse calculations focused on the piping between the CFC outlet header which is upstream of the void collapse and the MOV throttling valve which is downstream of the void collapse. The pressure pulses traveling throughout the system exert forces on the piping as shown in Figure 5-7. Figure 5-7 illustrates the force history for a typical pipe segment during the time interval when the pumps would restart and voids would begin to collapse. As shown in this figure, TREMOLO predicts that a pipe segment will undergo numerous force pulses throughout this time window. However, since TREMOLO calculates the multiple force pulses as a function of time and the EPRI TBR methodology yields a single pulse through the SW piping, the values listed in Tables 5-2a through 5-5a only consider the single maximum force pulse calculated by TREMOLO over a pipe element and its corresponding impulse. As shown in Figure 5-7, the SW piping forces are very dynamic and the piping forces are "pushing and pulling" the piping and pipe restraints for each period of time (i.e., tens of seconds) such that the TREMOLO analyses performed on the Point Beach CFCs provided a dynamic force-time history analysis.

FAI/03-07 Page 29 of 31 Rev. I Date: 03/06/03 Figure 5-6 Sample TREMOLO Pressure Profile for a Point Beach SW Piping Element Following a LOOP + LOCA. C-CS 0 co -j o S 0 C01S 0 ILl I I I I i 0 9I 001 0 0 ISd (WflaNd

FAI/03-07 Page 30 of 31 Rev. I Date: 03/06/03 Figure 5-7 Sample TREMOLO Force Time History for a Point Beach SW Piping Element Following a LOOP + LOCA. 0 0 -J 0 0 -j %n X 0 z 3 0L 'C C, 0 000U M co 17- _ill,enu

' I-I JGI (Et)X1Vd I-E0 1 X

FAI/03-07 Page 31 of 31 Rev. 1 Date: 03/06/03

6.0 CONCLUSION

S The results of the comparison of the EPRI TBR methodology versus the TREMOLO code for calculating the peak forces and impulse loading on the SW piping due to waterhammer events following a LOOP + LOCA event are summarized in Tables 5-2 through 5-5. The impulses were included in this comparison because they provide a measure of the dynamic character of the forcing function when comparing the overall loads that pipe supports/restraints must overcome when pressure induced loads are calculated to occur within the piping. The impulse measures the integrated force over a period of time that the pipe supports must overcome. As shown in these tables, the peak forces and impulse loading calculated by TREMOLO are generally larger than those calculated using the EPRI TBR methodology. It should be noted, although it was not quantified in this comparison, that the TREMOLO force calculations include the effects of multiple pressure wave reflections and void collapses which would significantly add to the total impulse loadings on the SW piping. The dynamic TREMOLO forcing function histories were used in the piping and piping supports stress calculations. The simplified EPRI-calculated methodology only assumes a single pressure pulse propagated through the SW piping. Based on the comparison of the pipe section forcing functions provided in this assessment, it is concluded that the TREMOLO produced forcing functions generally bound the EPRI-TBR forcing functions for the Point Beach containment fan cooler cooling water supply and return piping.

FAI/03-07 Page A-1 of A-16 Rev. 1 Date: 03/06/03 APPENDIX A Point Beach CFC 1A EPRI TBR Waterhammer Calculations Using MathCad 2000

POINT BEACH CFC 1 A Figure 1 Open Loop Configuration Pressure & Temperature Note, pressures listed as "psi" are absolute (psia) or differential (psid) unless otherwise stated Patm:= 14.7-psi Td

= 224.0 F Tpipeimtial := 75*F Pipe Geometry EL := 33.2-ft EL,:= 82.3-ft Lb:= 30.5-ft Lbc:= 87.5-ft Lcd := 61.4-ft L
= 78.5-ft Lef 4.1-ft Lfg 87.6-ft Lg_,n:= 400 ft IDabf:

13.124-in IDbcd 7.981-in Wag:= 22.624-in ODbcd := 8.625-in Pressure above reservoir and above heat sink (absolute) Temperature in the void when the pumps restart (i.e. surface temperature of piping) [Ref. FAI/97-60 Rev. 3] (Assumed average T in void at 25 sec) Temperature of the fluid and piping when the transient starts [Ref. FAI/97-60 Rev. 3] Elevation of node "1" [Ref. FAI/97-60 Rev. 3] Elevation of node "2" [Ref. FAI/97-60 Rev. 3] Length from node "a' to node Vb" [Ref. FAI/97-60 Rev. 3] Length from node "b" to node Mcw [Ref. FAI/97-60 Rev. 3] Length from node "c to node 'd" [Ref. FAI/97-60 Rev. 3] Length from node "d" to node 'e" [Ref. FAI/97-60 Rev. 3] Length from node "e" to node 'f" [Ref. FAI/97-60 Rev. 3] Length from node "f" to node "g" [Ref. FAI/97-60 Rev. 3] Length from node "g" to the ultimate heat sink [Ref. N/A -not used] I.D. of piping along path from 'a" to "b" to "f" [Ref. FAI/97-60 Rev. 3] I.D. of piping along path from "b" to "c" to "d" [Ref. FAI/97-60 Rev. 3] I.D. of piping along remaining path from "a" to `"g [Ref. FAI/97-60 Rev. 3] O.D. of piping along path from "b" to "c" to "d" [Ref. FAI/97-60 Rev. 3] Page 2

Flows Qbf 800 g Flow along path from "a" to "b" to "f" during steady state condition without min voiding [Ref. FAI/97-60 Rev. 3]. Assume other CFC 800 gpm. Qbcd 917-gal Flow along path from 'b" to "c' to "do during steady state condition without min voiding [Ref. FAI/97-60 Rev. 3] Qag := 5100.-- Flow along path from "a" to "g during steady state condition without voiding min [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03]. Per FSAR nominal flow is 6800 gpm. FCU Characteristics Nmbe 240 Number of tubes in cooler [Ref. FAI/97-60 Rev. 3] IDube := 0.527-in Internal diameter of tubes [Ref. FAI/97-60 Rev. 3] Ltube = 22-ft Length of tubes [Ref. FAI/97-60 Rev. 3] Pump Characteristics H:= 240.8-ft Al:= 0.2547-- ft2 A2:= -0.5783s-ftl5 Pump shutoff head [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03] 1st order pump curve coefficient [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03] 2nd order pump curve coefficient [Ref. Chuck Richardson Emails dated 1/27/03 & 1128/03] Hpump(Qp):= A2-Qp2 + Al-Qp + Hs Pump curve equation Other Inputs KVI, := 158.41 VWtr fu := 0.0-ft 3 Vwt2pChase := 6ft3 pwt, := 62.- ft3 Tdes := 95-F ft2 Rgas:= 1717-2 sec *R Valve frictional flow coefficient for throttled globe valve [Ref. FAI/97-60 Rev. 3] Volume of water that is left in the FCU when the pump restarts [Ref. FAI/97-60 Rev. 3] Volume of water that flows into the cooler after voiding has started and before the pumps restart. This volume of water is exposed to two phase flow conditions. [Ref. N/A -not used] Water density Design temp of the system Gas constant Page 3

FAI/03-07 Page A-4 of A-i 6 FAI/03-07 Page A-4 of A-1 6 Rev. 1 Date: 03/06/03 ~ Pump Flow Rate Equation Qt~tnorma 0

= Qag + Qbcd + Qabf Qtot,,j = 6 817 x 103 gal min H.O
= Hpump(Qtotnormali)

H.orm 1=1 1 ft The total system flow rate is solved at any pump operating point using: -Al -,A2 A2-(Hs - Hd) 2-A2 Qpump(Hd):= Qpump(Hno,,,) =6.817x 103 gal min 300 0 200 100 4000 GPM Pump Curve 00 Operating Point PUMP CURVE & OPERATING POINT Figure 2 SW Pump Curve Page 4

FAI/03-07 Page A-5 of A-i 6 Rev. 1 Date: 03/06103 7.4.1 Initial Velocity & FLOW COEFFICIENT PREDICTION The water at the front of the void (point "d") is assumed to not move or simplification of this problem. More detailed hydraulic modeling may be performed to determine the reverse or forward flow at point "d". In many cases this flow is less than 10% of the incoming flow. After combining parallel paths the system is then simplified to: Figure 3 Simplified Open Loop Model In terms of the initial flow diagram (Figure 1), the flow area for each path is calculated: 2 Aabf := -.Dabf 4 Aabf 0.93 9 If~t It 2 Abed := - IDbcd 4 Abcd =0.347 ft Ag 4 Dag Aag = 2.792 ft2 The velocity for each path is calculated: Qabf Aabbf Abf Vabf = 1.9-S Qbcd Abcd Vbcd = 5.9 ft ag Qag Aag Vag = 4.1-Calculate equivalent velocity for all other loads: Veq - Qabf + Qg Abbf + Aag ft V-q= 3.523-S Page 5

FAI/03-07 Page A-6 of A-1 6 Rev. 1 Date: 03/06/03 The flow coefficient for each path is calculated. The flow resistance from point "a" to point "b" and from point "f" to point "g" are assumed to have a negligible effect on the flow split to the different paths. In an actual plant system, the engineer may choose to use values from a previously qualified system hydraulic model to determine a more accurate initial velocity. 2=K 2 g-bf V2 2-g-H*Hor, Kabf = VabC 2-g Hnorm Kbcd= v Vbed2 2Vg H... -a g Y,( = 1.989x i03 Kbcd = 207 Kag = 432 An equivalent flow coefficient for the "other loads' path (Figure 1) is calculated from: el A~bf Y-other :=1 AWb A~g I I Kothr = 37 Aother := Abf IDother := IDabf An equivalent flow coefficient from all other loads is calculated from: 2-g Iio.r Kothr = V.q Kothr = 576.797 Aether := Aabf + Aag Moh 0 t:= ( othn= t IDather = 2.18 ft The flow coefficient for the path to the void is calculated by subtracting the flow coefficient downstream of the void along this path. To simplify this sample problem only the valve resistance downstream of the void is considered: Kvoid Kbcd - K-1v KYoid = 49 The pressure in the void is assumed to correspond to the saturation pressure for the void temperature. Pvoid := 18.6.psi Absolute pressure based on saturation pressure of Tvoid shown above. Comes from TREMOLO output. [Ref. FAI/97-60, Rev. 3] Page 6

FAI/03-07 Page A-7 of A-16 Rev. 1 Date: 03/06/03 The pump total developed head (TDH) is written by using Bernoulli's equation Hatm + EL1 + TDH = Hv,,d + EL. + Hf where the following terms are defined in terms of feet H20 Hatm = atmospheric pressure head EL, = elevation of node "1" TDH = total developed head from pump EL2 = elevation of node "2" Hf = frictional losses from point "1 " to "2" The frictional losses are written using Darcy's formula with an appropriate units conversion factor: Hf = 0.00259-Kloss, ( where ID4 Koss = loss coefficient 0 = flow rate in gpm ID = pipe diameter in inches Two equations for the total developed head (TDH) by the pump are written with a corresponding flow balance and initial guesses for the simultaneous solution of these equations: Qvoid :=.1 Qothe, := *5 TDH:= 300 Given TDH = 0.00259*Koth,, frictional losses along "other" path equal the total

tIDjhe, 4

developed head QVoid2 Patm Pv 'id TDH = 0.00259 Koid- + (EL EL, - + -- I X Bemoulli's along ( IDbd 4 P PWg PWrg) the 'void" path in ) (gal \\ Qwher + Qo.d = Qpump(TDH-ft). ) pump curve min The solution to the simultaneous equations is solved and defined as 'Results". Results := Find(TDH,Q 0t. Qvoid) TDH := Results.-ft TDH = 105.207 ft Qoth,:= Results,- g.l th = 5.741 x 103 gal nin min Qvoid := Results-ga Qvoid = 1.231 X 10 gal min nun The initial velocity is then: The total resistance for this path is: Vmn ot

=n-ital

= 7.9-Kvold = 49 Abcd S Check: is the velocity within the RBM bounds? Vm.Ua < 20 ft/sec

===> yes, velocity is within bounds of RBM runs Page 7

7.4.2 VOID & WATER COLUMN LENGTHS The volume of piping that is voided is calculated: Vpipeyvotded := Lcd' -IDbcd Vpipe-voided = 21 ft 4 The void of the fan cooler unit is calculated: Vfr.

= Nmbe--Ltbe-n IDtube Vf=

8 ft 4 The equivalent void length is then: Lao.= Vpipeivoided + Vfau Lao = 84 ft Abcd The initial water column length is assumed to be the distance from point Nau to point "cu. The discussion that follows explains why point "a" was chosen. Ignoring the FCU, the flow area changes from the closure point to node "a' are the same as the area changes from the closure point to node mg" on the return side. The transmission coefficients calculated for the return side demonstrate that less than 10% of the pressure pulse propagates to the header. Because of the similar flow area changes, less than 10% of any pressure would propagate into the supply header upstream of point 'a'. In general, this indicates that the header acts like a large pressurized reservoir during the void closure process and water in the supply header does not add to the inertia of the decelerating water column. Note: if desired, a plant could select a length all the way back to the pumps. However, this is considered excessively conservative. The length if the accelerating water column is then: Lwo := Lab + Lc Lwo = 118ft Check: are the lengths within the bounds of the RBM runs? Lao < 100 ft Lwo < 400 ft

===>> yes lengths are within bounds of RBM runs Page 8

FAI/03-07 Page A-9 of A-16 Rev. 1 Date: 03/06103 7.4.3 GAS RELEASE AND MASS OF AIR CONCENTRATED IN VOID The mass of air concentrated in the void during the void phase of the transient is calculated by assuming that the water that has experienced boiling and subsequent condensation releases its air as described in Section 5 of the User's Manual. For this problem, the tube volume only will be credited, assuming a draining of the FCU in which the headers do not remain full. This mass of water will release 50% of its non-condensable gas. Vf,, = 7.998 ft3 or Vf,, = 226 liter from 7.4.2 This represents the mass of water in the tubes which will lose 50% of its non-condensable gas. The concentration of gas is obtained from Figure 5-3. Tdes = 95 F TS-32F = 35 deg C 1.8F CONar := 18.5 mg liter From Figure 5-3 ma := 0-.5CONir-Vfcij rror = 2095 mg Check: is the mass of air within bounds of UM? for void closure in 8" piping there should be at least 900 mg of air per Table 5.2

===> yes, mass if air is within RBM run bounds. Page 9

7.4.4 Cushioned VELOCITY The graphs presented in Appendix A for the velocity ratios are solutions to the simultaneous differential equations that capture the acceleration of the advancing column and pressurization of the void. In order to determine the cushioned velocity the following terms that are needed are repeated: V,.,tl = 7.897-S Kvo.d = 49 Lao = 84.422 ft Lwo = 8ft ma, = 2.095 x 103 mg Tvmod = 224 F Check: is the temperature within the bounds of the RBM? Tvoid > 200 F===> yes, the temperature is within the RBM run bounds 7.4.4.1 Air Cushioning If only credit for air cushioning is considered then Figure A-1 0 from Appendix A is selected. This figure corresponds to 10" piping while the sample problem has 8" piping. 10" piping bounds the 8" piping since the inertia modeled in the 10" piping runs is greater than that in the 8" piping runs and the velocity has reached a steady state until the final void closure occurs. This is apparent by comparison of the 4" and 1 QN RBM run results for the same gas mass; the velocity is reduced more in the smaller pipe case. If the pipe size at a given plant is not shown then the Velocity Ratio chart for the next larger size pipe will always be bounding Figure A-10 corresponds to an initial velocity of 10 fps. The initial velocity calculated in this sample problem is less. The higher velocity chart is selected because the higher momentum associated with the higher velocity bounds the lower velocity. If the initial velocity at a plant Is not shown then the Velocity Ratio chart for the next larger velocity will always be bounding. For a K of 49 as calculated in the sample problem, from Figure A-1 0 the ratio of the second to initial velocity is: l- =82%I only air cushion credited Therefore, the final closure velocity will be reduced by 18% just considering air in this sample problem. Pressure "clipping" is not included here and is calculated later. Page 1 0

7.4.4.2 Air and Steam Cushioning The velocity that results by considering steam cushioning is found using Figure A-37 from Appendix A. Note that the condensing surface temperature was verified being within the bounds of the RBM run limitations so steam condensation cushioning may be credited. The steam and air cushioning result in a ratio of cushioned to initial velocity of: 7VCUStO= 77%' [Vruial l air and steam cushioning The cushioned velocity is then: Vcushion := 0. 7 7.Vmltial vcusmon = 6.1-S 7.4.5 SONIC VELOCITY The sonic velocity is calculated from Equation 5-1 and 5-2 in the main body of the User's Manual. Pvoid= 18.6psi where B=bulk modulus of water E=Young's modulus for steel OD=outside diameter of pipe t=wall thickness B := 319000psi E:= 28-10 psi C B .Pwtr C BODd 1 IL + B.OD~b d-o -d E ( b d C = 4274-S Page 11

7.4.6 PEAK PRESSURE PULSE WITH NO "CLIPPING" The peak waterhammer pressure is calculated using the Joukowski equation with a coefficient of 1/2 for a water on water closure: APno-cilppin := IPwtrfC Vcushuon APnqclipping = 174 psi 7.4.7 RISE TIME The rise time is calculated by using equation 5-4 from the UM. ms := 0.001s TR := 0.5sec{ V; 1 0 fl TR = 48rms sec Page 12

FAI/03-07 Page A-i 3 of A-1 6 Rev. 1 Date: 03/06/03 7.4.8 TRANSMISSION COEFFICIENTS The pressure pulse may be affected by rarefaction waves as it is developing and the peak may be "clipped". In addition, the pressure may be attenuated as it propagates through the system as a result of area changes. In order to calculate each of these effects, the transmission coefficients at junctions is required. The transmission coefficients are calculated consistent with section 5.3 of the UM. At points "f" and " the transmission coefficients are calculated using Equation 5-8 from the UM; for simplification here the sonic velocity is assumed to be constant up and downstream of the junction: 2 *Aincident T= Arnadent + E Aj J T _2-Abcd _f = 0.312 => this fraction of the incident pulse Abcd + Aabf + Aabf continues past point "f" and the remainder of the incident pulse returns towards the initiation point. 2.Abf Irg = 0.288 => this fraction pulse that is incident upon Abf + Ay + Ag point "g" continues past point "g" and the remainder of the incident pulse returns towards the initiation point. Ttotal = f'Tg 'tto = 0.09 When the pressure pulse travels past point "g" only 10% of the pulse will continue on. 69% of the incident pulse was reflected as a negative pulse at point "f and then 71% of the pulse that was incident upon point "g' was reflected back as a negative pulse. The net reflection effect is: IP~rf = Pmc'(-69%) + K31%M.Pn (-71%) = P,.c(-69% - 31%.71 %) = 91% This reflection travels back to the initiation point. The pulse at the initiation point is 9% of its original value when this reflection arrives. For simplicity, the compounding effect of the "f" node transmission coefficient on the reflected wave from node g"' is ignored. The transmission coefficient evaluation needs to consider the control valve. The transmission coefficient at the control valve is calculated by assuming the valve acts like an orifice as the pressure pulse propagates through it. Equation 5-14 provides a simple relationship for an orifice flow coefficient in terms of its diameter ratio (a). This equation is used to back calculate an equivalent 0 ratio for the control valve knowing its coefficient and assuming Co=0.6. 0.5 Initial guess for the iteration below D 2 Too 1-I -KVV p0.35 0.6-* Page 13

For this f3 ratio and for the approximate waterhammer pressure already solved, the control valve will have a slight effect on the pressure pulse propagation by inspection of Figure 5-15. The reflection from this interaction will add approximately 10% to the incident pulse. In general what this means is that 10% of the pulse magnitude is reflected in a positive sense back towards the initiation point. To account for this effect, the peak pressure pulse is conservatively increased by 10%. 7.4.9 DURATION The pressure pulse is reduced to approximately 10% of its peak value as a result of the reflections from the area changes at points Of" and "g". As a result, the time that it takes the pressure pulse to travel to point `g" and back may be used to calculate the pressure pulse duration. (Lde + Lef + Lfg)-2 TDeg: C Deg = 79.7 ms Time for pulse to travel to and from point "g". Note that reflections from "a" and Wb" are not credited. The total duration is conservatively increased by adding the rise time. TD:= TDeg + TR TD = 127 ms 7.4.10 PRESSURE CLIPPING The peak pressure is checked for "clipping" using Table 5-3. Le:= Lde + Ler + Lfg Le = 170.2 ft TR-2 = 102 ft 2 t wot = 0-09 This corresponds to the conditions in row two of the table referenced and no pressure clipping is expected. AP l.lPno clipping 1.1 is from the control valve AP = 191 psi Page 14

7.4.11 PRESSURE PULSE SHAPE The pulse shape is then characterized by four points. lPsys := 9psil this is the steady state system pressure [Ref. FAI/97-60 Rev. 3] Using an index, i=0,1,2,3

O.. 3 time, :

Oms TD - TR TD E v-tL pressure, := Psys AP + PSYS 'P + Psys Psys This provides the following values, which are plotted below.

0. 04 1210) time = 008s pressure = 210 psi 0.08 2109 0.127i

( 19)/ Pressure Pulse 150 tume (ms) trace I Calculate the area underneath the curve to get the pressure impulse: integral := TR-AP + AP-(TDeg - TR) integral = 1.05 x 105 kg M s impulse -integralVAbcd impulse = 762.175 Ibf -s Page 15

7.4.12 FLOW AREA ATTENUATION To simplify the analysis of the SW structures, the approach suggested here is to take the initiating pressure pulse and propagate the pulse through the system. For this example problem, the duration of the pulse is assumed to remain unchanged as it travels. In reality, the duration of the pulse is shortened as it approaches negative reflection sites. Maintaining the duration conservatively increases the impulse. As the pressure pulse propagates through the system it will be atenuated/amplified by flow area changes. For this example, only the downstream propagation is considered. The pulse will be attenuated by the increase in area at "1" and 'g". The transmission coefficients were previously calculated. incident pulse transmitted pulse transmission pulse AP= 191 psi APf := -AP APf 6 psi APf = 60psi AP.- T-APf APg = 17 psi Downstream of point "g" only the following pulse magnitude will remain: APg = 17 psi Page 16

FAI/03-07 Page B-1 of B-16 Rev. 1 Date: 03/06/03 APPENDIX B Point Beach CFC 1C EPRI TBR Waterhammer Calculations Using MathCad 2000

POINT BEACH CFC 1 C EL 1 OTHER SYSTEM LOADS a OTHR SYTE i24' Figure 1 Open Loop Configuration Pressure & Temperature Note, pressures listed as Opsi" are absolute (psia) or differential (psid) unless otherwise stated P,,m := 14.7-psi Tv01 d 223-F Tppe-tiar.-_ 75-F Pine Geometry EL,:= 33.2-ft EL,:= 37.4-ft Lab:= 30.5-ft Lb :=67.8-ft L~d :=32.3-ft Ld :=79.8-ft Lrf.- 2.2ft Lfg:= 86.4-ft Lg_ ik:= 400-ft LDabf := 13.124-in IDbOd:= 7.981-in Dag := 22.624-in ODbud:= 8.625-in Pressure above reservoir and above heat sink (absolute) Temperature in the void when the pumps restart (i.e. surface temperature of piping) [Ref. FAI/97-60 Rev. 5] (Assumed average T in void at 25 sec) Temperature of the fluid and piping when the transient starts [Ref. FA1197-60 Rev. 5] Elevation of node m1" [Ref. FAl/97-60 Rev. 5] Elevation of node "2" [Ref. FAI/97-60 Rev. 5] Length from node "a' to node "b" [Ref. FAI/97-60 Rev. 5] Length from node "bV to node 'c' [Ref. FAI/97-60 Rev. 5] Length from node "c' to node Vd" [Ref. FAI/97-60 Rev. 5] Length from node "d" to node "e- [Ref. FAII97-60 Rev. 5] Length from node "e" to node "f" [Ref. FAI/97-60 Rev. 5] Length from node "f" to node "g" [Ref. FAI/97-60 Rev. 5] Length from node "g" to the ultimate heat sink [Ref. N/A -not used] I.D. of piping along path from "a' to Vbu to I " [Ref. FAI/97-60 Rev. 5] 1.D. of piping along path from "b" to "c" to "d" [Ref. FAI/97-60 Rev. 5] I.D. of piping along remaining path from ua" to "g" [Ref. FA1197-60 Rev. 5] O.D. of piping along path from "b" to "c" to *d" [Ref. FAI/97-60 Rev. 5] Page 2

Flows Q~bf := 800 gal Flow along path from "a' to "b" to "f" during steady state condition without min voiding [Ref. FAI/97-60 Rev. 5] Qbcd := 857-gal Flow along path from "b" to "c" to 'd" during steady state condition without min voiding [Ref. FAI197-60 Rev. 5] Q =g 5200- gal Flow along path from 'a" to "g during steady state condition without voiding min [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03] FCU Characteristics Nmbe:= 240 Number of tubes in cooler [Ref. FAI/97-60 Rev. 5] IDtube := 0.527-in Internal diameter of tubes [Ref. FAI/97-60 Rev. 5] Lbe =22-ft Length of tubes [Ref. FAI/97-60 Rev. 5] Pump Characteristics A:= 240.8-ft Pump shutoff head [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28103] Al 0.2547-- 1st order pump curve coefficient [Ref. Chuck Richardson Emails dated fi 1/27/03 & 1/28/03] 2 A2 -0.5783-- 2nd order pump curve coefficient [Ref. Chuck Richardson Emails dated ft5 1/27/03 & 1/28/03] Hpump(Qp)= A2.QP2 + Al -Qp + H1, Pump curve equation Other Inputs K,1, := 161.472 V fcu:= 0.0-ft3 Vwtt p, e 6-ft3 lb pw:= 62-ft3 Tdes := 95-F ft2 Rgas:= 1717--X sec-R Valve frictional flow coefficient for throttled globe valve [Ref. FAI/97-60 Rev. 5] Volume of water that is left in the FCU when the pump restarts [Ref. FAI/97-60 Rev. 5] Volume of water that flows into the cooler after voiding has started and before the pumps restart. This volume of water is exposed to two phase flow conditions. [Ref. N/A -not used] Water density Design temp of the system Gas constant Page 3

FAIIO3-07, Page 8-4 of 8-16 FAI/03-07, Page B-4 of B-16 Rev. 1 Date: 03106/03 Pump Flow Rate Equation Qtotn.:, := Qg + Qbcd + Qbf Qtotn, 0mj = 6.857 x I0 gal rmm Hn Orm := Hpump(Qt~totrml) I-lnorm IIoft The total system flow rate is solved at any pump operating point using: -Al - Al2 - 4.A2.(H -Hd) Qpump(Hd) := 2.A2 Qpump(HO0,a,) = 6.857 x 10 gal mnu 300 0200 I 4000 GPM Pump Curve 00 Operating Point PUMP CURVE & OPERATING POINT Figure 2 SW Pump Curve Page 4

7.4.1 Initial Velocity & FLOW COEFFICIENT PREDICTION The water at the front of the void (point "d") is assumed to not move or simplification of this problem. More detailed hydraulic modeling may be performed to determine the reverse or forward flow at point "d". In many cases this flow is less than 10% of the incoming flow. After combining parallel paths the system is then simplified to: Figure 3 Simplified Open Loop Model In terms of the initial flow diagram (Figure 1), the flow area for each path is calculated: Aaf:=--IDabf( 4 Aabf = 0.939ft2 Abcd := 1 -]Dtcd2 4 Abcd = 0.347 ft2 ag := S 4 Dag Aag = 2.792 f The velocity for each path is calculated: Qabf Vabf =- Aabf Vabf = 1.9-tS Qbcd Vbcd: = Abcd Vbcd = 5.5-S Vag :=Ag Aag Vag = 4.2-S Calculate equivalent velocity for all other loads: Veq - Qabf + Q9 Aabf + Aag ft Veq= 3.583-S Page 5

FAI/03-07, Page B-6 of B-16 Rev. 1 Date: 03/06/03 The flow coefficient for each path is calculated. The flow resistance from point 'a" to point "b" and from point f" to point "g" are assumed to have a negligible effect on the flow split to the different paths. In an actual plant system, the engineer may choose to use values from a previously qualified system hydraulic model to determine a more accurate initial velocity. V2 hf=2K-- => 2-g K= 2ghf 2-g HO0 0 n VabW 2-g 2 no. Kbcd d Vbcd2 Kag:= o Vag Ka1b, = 1.961 x 10 Kbcd = 234 Kag = 410 An equivalent flow coefficient for the 'other loads" path (Figure 1) is calculated from: -Kothcr := I AaXf Aag. Kothe. = 35 Aether := AW IDother := IDabf An equivalent flow coefficient from all other loads is calculated from: Kofter := VNeq Kother =549.974 Aother := Aabt + Aag 4Aother.t.5 Iother := IDother = 2.18 ft The flow coefficient for the path to the void is calculated by subtracting the flow coefficient downstream of the void along this path. To simplify this sample problem only the valve resistance downstream of the void is considered: Kvoid := Kbcd - K-,, Kvoid = 72 The pressure in the void is assumed to correspond to the saturation pressure for the void temperature. PvCid := 18.3.psi Absolute pressure based on saturation pressure of Tvoid shown above. Comes from TREMOLO output. [Ref. FAI/97-60, Rev. 5] Page 6

The pump total developed head (TDH) is written by using Bernoulli's equation: H1,m + EL, + TDH = Hvod + EL2 + Hf where the following terms are defined in terms of feet H20 Hatm = atmospheric pressure head EL1 = elevation of node "1" TDH = total developed head from pump EL, = elevation of node "2" Hf = frictional losses from point "1' to 12' The frictional losses are written using Darcy's formula with an appropriate units conversion factor: Hf = 0.00259*K 1os Q-where ID4 K]K0s = loss coefficient 0 = flow rate in gpm ID = pipe diameter in inches Two equations for the total developed head (TDH) by the pump are written with a corresponding flow balance and initial guesses for the simultaneous solution of these equations: Qvold =1 Qother =.5 TDH := 300 Given TDH = 0.00259-Koth, o frictional losses along "other" path equal the total (IDother 4 developed head Qv1oid ( trn Pvloid TDH = 0.00259 -KVOd +EL, -EL, + - f I Bernoulli's along IDocd Pwtr g Pwtg) the "void" path Qother + Qvoid = Qpump(TDH-ft)-. C nun pump curve The solution to the simultaneous equations is solved and defined as "Results". Results := Find(TDH,QotherQvoid) TDH := Resultsw-ft Qothe = RResultsIl Qvoid = Results,. gal The initial velocity is then: TDH = 99.906 ft Qother = 5.729x 10 gal mnu Qvoid = 1.376x lO3 gal min The total resistance for this path is: Vmnit.3 :=Q1-Viiti. = 8.8-Kvoid = 72 Abcd S Check: is the velocity within the RBM bounds? V~nital < 20 ft/sec

===> yes, velocity is within bounds of RBM runs Page 7

FAI/03-07, Page B-8 of B-16 Rev. 1 Date: 03/06/03 7.4.2 VOID & WATER COLUMN LENGTHS The volume of piping that is voided is calculated: Vpipe voided := Lcd*- IDbcd Vpipe voided = I ft 4 The void of the fan cooler unit is calculated: Vf.

= Ntbe Ltbe 4 IDtube Vf

= 8 ft 4 The equivalent void length is then: 1.o - Vpipe voided + Vfcu Lao 55ft Acd The initial water column length is assumed to be the distance from point "a" to point "c". The discussion that follows explains why point "an was chosen. Ignoring the FCU, the flow area changes from the closure point to node "a' are the same as the area changes from the closure point to node "g" on the return side. The transmission coefficients calculated for the return side demonstrate that less than 10% of the pressure pulse propagates to the header. Because of the similar flow area changes, less than 10% of any pressure would propagate into the supply header upstream of point "a". In general, this indicates that the header acts like a large pressurized reservoir during the void closure process and water in the supply header does not add to the inertia of the decelerating water column. Note: if desired, a plant could select a length all the way back to the pumps. However, this is considered excessively conservative. The length if the accelerating water column is then: Lwo:= Lab + Lb Lwo = 983 ft Check: are the lengths within the bounds of the RBM runs? Lao < 100 ft Lwo < 400 ft

===>> yes lengths are within bounds of RBM runs Page 8

7.4.3 GAS RELEASE AND MASS OF AIR CONCENTRATED IN VOID The mass of air concentrated in the void during the void phase of the transient is calculated by assuming that the water that has experienced boiling and subsequent condensation releases its air as described in Section 5 of the User's Manual. For this problem, the tube volume only will be credited, assuming a draining of the FCU in which the headers do not remain full. This mass of water will release 50% of its non-condensable gas. VrcU = 7.998 ft3 or Vf,,, = 226 liter from 7.4.2 This represents the mass of water in the tubes which will lose 50% of its non-condensable gas. The concentration of gas is obtained from Figure 5-3. Tdes = 95 F Tdes - 32F = 35 deg C 1.8F CONar := 18.5 g From Figure 5-3 liter matrO:= 0.5-CONr-Vf Mair = 2095 mg Check: is the mass of air within bounds of UM? for void closure in 8" piping there should be at least 900 mg of air per Table 5.2

===> yes, mass if air is within RBM run bounds. Page 9

FAI/03-07, Page B-10 of B-16 Rev. 1 Date: 03/06/03 7.4.4 Cushioned VELOCITY The graphs presented in Appendix A for the velocity ratios are solutions to the simultaneous differential equations that capture the acceleration of the advancing column and pressurization of the void. In order to determine the cushioned velocity the following terms that are needed are repeated: V,,tl, = 8.826-S Kvo.d = 72 Lao = 55.322 ft Lwo = 98.3 ft mnar =2.095 X 103 mg Tvod = 223 F Check: is the temperature within the bounds of the RBM? Tvoid > 200 F===> yes, the temperature is within the RBM run bounds 7.4.4.1 Air Cushioning If only credit for air cushioning is considered then Figure A-1 0 from Appendix A is selected. This figure corresponds to 10" piping while the sample problem has 8" piping. 10" piping bounds the 8" piping since the inertia modeled in the 10" piping runs is greater than that in the 8" piping runs and the velocity has reached a steady state until the final void closure occurs. This is apparent by comparison of the 4" and 10" RBM run results for the same gas mass; the velocity is reduced more in the smaller pipe case. If the pipe size at a given plant is not shown then the Velocity Ratio chart for the next larger size pipe will always be bounding. Figure A-10 corresponds to an initial velocity of 10 fps. The initial velocity calculated in this sample problem is less. The higher velocity chart is selected because the higher momentum associated with the higher velocity bounds the lower velocity. If the initial velocity at a plant is not shown then the Velocity Ratio chart for the next larger velocity will always be bounding. For a K of 72 as calculated in the sample problem, from Figure A-1 0 the ratio of the second to initial velocity is: lVcon = 83% only air cushion credited [VrutlS I Therefore, the final closure velocity will be reduced by 17% just considering air in this sample problem. Pressure "clipping" is not included here and is calculated later. Page 10

7.4.4.2 Air and Steam Cushioning The velocity that results by considering steam cushioning is found using Figure A-37 from Appendix A. Note that the condensing surface temperature was verified being within the bounds of the RBM run limitations so steam condensation cushioning may be credited. The steam and air cushioning result in a ratio of cushioned to initial velocity of: vcusuon% lVmitual l air and steam cushioning The cushioned velocity is then: jvcusluon := 0-80 VinmthaI V.,Iusn = 7.1-S 7.4.5 SONIC VELOCITY The sonic velocity is calculated from Equation 5-1 and 5-2 in the main body of the User's Manual. Pvond = 18.3 psi where B=bulk modulus of water E=Young's modulus for steel OD=outside diameter of pipe t=wall thickness B := 319000psi E := 28-10 6psi C B C:= + Pwt] .- ~ B ODbcd i E ( °Dbcd - IDbcd) 2 C = 4274-f S Page 1 1

FAI/03-07, Page B-12 of B-16 Rev. 1 Date: 03/06/03 7.4.6 PEAK PRESSURE PULSE WITH NO "CLIPPING" The peak waterhammer pressure is calculated using the Joukowski equation with a coefficient of 1/2 for a water on water closure: APno_cippn := 2 Pwtr CVcushion APo._cijppjng = 202 psi 7.4.7 RISE TIME The rise time is calculated by using equation 5-4 from the UM. ms := O.OOls TR= 0.5secf Vcon TR = 39 ms sec) Page 12

FAI/03-07, Page B-13 of B-16 Rev. 1 Date: 03/06/03 7.4.8 TRANSMISSION COEFFICIENTS The pressure pulse may be affected by rarefaction waves as it is developing and the peak may be "clipped". In addition, the pressure may be attenuated as it propagates through the system as a result of area changes. In order to calculate each of these effects, the transmission coefficients at junctions is required. The transmission coefficients are calculated consistent with section 5.3 of the UM. At points "f" and "9g the transmission coefficients are calculated using Equation 5-8 from the UM; for simplification here the sonic velocity is assumed to be constant up and downstream of the junction: 2 'Aincident Auicident + E A3 f = _ 2Abcd _f = 0.312 => this fraction of the incident pulse Abcd + Aabf + Aabf continues past point "f' and the remainder of the incident pulse returns towards the initiation point. T = Tg = 0.288 => this fraction pulse that is incident upon AW + Aag + Ag point g"9 continues past point g"9 and the remainder of the incident pulse returns towards the initiation point. Ttotal = Tf-Tg -total = 0.09 When the pressure pulse travels past point g" only 10% of the pulse will continue on. 69% of the incident pulse was reflected as a negative pulse at point 'fV and then 71% of the pulse that was incident upon point "g" was reflected back as a negative pulse. The net reflection effect is: 1Pref = P{c ( 6 9%) + (31%Pc) -(-71%) = PMC(&69% - 31%-71 %) = 91 % This reflection travels back to the initiation point. The pulse at the initiation point is 9% of its original value when this reflection arrives. For simplicity, the compounding effect of the "f" node transmission coefficient on the reflected wave from node Og" is ignored. The transmission coefficient evaluation needs to consider the control valve. The transmission coefficient at the control valve is calculated by assuming the valve acts like an orifice as the pressure pulse propagates through it. Equation 5-14 provides a simple relationship for an orifice flow coefficient in terms of its diameter ratio (P). This equation is used to back calculate an equivalent D ratio for the control valve knowing its coefficient and assuming Co=0.6. 0-:= 0.5 Initial guess for the iteration below P:=roo{ 0

1) -K.vi 3

=0349 Page 13

FAI/03-07, Page B-1 4 of B-1 6 Rev 1 Date: 03/06/03 For this,B ratio and for the approximate waterhammer pressure already solved, the control valve will have a slight effect on the pressure pulse propagation by inspection of Figure 5-15. The reflection from this interaction will add approximately 10% to the incident pulse. In general what this means is that 10% of the pulse magnitude is reflected in a positive sense back towards the initiation point. To account for this effect, the peak pressure pulse is conservatively increased by 10%. 7.4.9 DURATION The pressure pulse is reduced to approximately 10% of its peak value as a result of the reflections from the area changes at points 'fI and "gm. As a result, the time that it takes the pressure pulse to travel to point 'gf and back may be used to calculate the pressure pulse duration. TD-(Lde + Lef + Lfg)-2 Beg = C TDe = 78.8ms Time for pulse to travel to and from point "g". Note that reflections from "a' and "b" are not credited. The total duration is conservatively increased by adding the rise time. TD := TDeg + TR TD = 118ms 7.4.10 PRESSURE CLIPPING The peak pressure is checked for 'clipping" using Table 5-3. Le:= Ld + Lef +Lfg Le = 168.4ft TR~- = 84ft 2 ttotal = 0.09 This corresponds to the conditions in row two of the table referenced and no pressure clipping is expected. IAP:= 1-1-"no-dippjng I 1.1 is from the control valve AP = 222 psi Page 14

7.4.11 PRESSURE PULSE SHAPE The pulse shape is then characterized by four points. IPsys := l9psi this is the steady state system pressure [Ref. FAI/97-60 Rev. 5] Using an index, i=0,1,2,3 i := 0.. 3 time, := EOrs TD -IR iD pressure,:= Psys AP + Psys AP + Psys Psys This provides the following values, which are plotted below. 0.039 12411 time = 0.079 s pressure = 241 psi "0.118 192I1 Pressure Pulse 300 0.c e) 200 100 0 50 time (ms) trace I 150 Calculate the area underneath the curve to get the pressure impulse: integral := TR-AP + AP-(TDcg - TR) integral = 1.207 x 05 kg ms impulse := integralAbcd impulse = 875.596 Ibf *s Page 15

7.4.12 FLOW AREA ATTENUATION To simplify the analysis of the SW structures, the approach suggested here is to take the initiating pressure pulse and propagate the pulse through the system. For this example problem, the duration of the pulse is assumed to remain unchanged as it travels. In reality, the duration of the pulse is shortened as it approaches negative reflection sites. Maintaining the duration conservatively increases the impulse. As the pressure pulse propagates through the system it will be atenuated/amplified by flow area changes. For this example, only the downstream propagation is considered. The pulse will be attenuated by the increase in area at "ft and "g". The transmission coefficients were previously calculated. incident pulse transmitted pulse transmission pulse AP =222 psi APf := Tf-AP APf = 69 psi APf= 69 psi APg := rgsApf AP = 20psi Downstream of point "g" only the following pulse magnitude will remain: APg = 20 psi Page 16

FAI/03-07 Page C-1 of C-16 Rev. 1 Date: 03/06/03 APPENDIX C Point Beach CFC 2B EPRI TBR Waterhammer Calculations Using MathCad 2000

POINT BEACH CFC 2B VOIDED t 86 VOIDED -di EL2 a Figure 1 Open Loop Configuration Pressure & Temperature Note, pressures listed as "psi" are absolute (psia) or differential (psid) unless otherwise stated Patm := 143-psi Td := 217.1-F Tpipeuitia := 75*F Pipe Geometry EL, := 33.2-ft EL,:= 72.0-ft La :36.8-ft Lb, :=139.4-ft Ld :=83.6-ft L& :=129.2-ft Lef 4.8.ft Lfg :=118.6-ft Lgs-k := 4004ft IDabf := 13.124-in EDbcd:= 7.981*in ag:= 22.624-in ODbcd:= 8.625-in Pressure above reservoir and above heat sink (absolute) Temperature in the void when the pumps restart (i.e. surface temperature of piping) [Ref. FAI/97-60 Rev. 2] (Assumed average T in void at 26 sec) Temperature of the fluid and piping when the transient starts [Ref. FAI/97-60 Rev. 2] Elevation of node "1- [Ref. FAI/97-60 Rev. 2] Elevation of node "2" [Ref. FAI/97-60 Rev. 2] Length from node 'a" to node "b" [Ref. FAI/97-60 Rev. 2] Length from node "b" to node 'c' [Ref. FAI/97-60 Rev. 2] Length from node "c" to node "d" [Ref. FAI/97-60 Rev. 2] Length from node "d" to node "e" [Ref. FAI/97-60 Rev. 2] Length from node "e" to node I"f [Ref. FA1197-60 Rev. 2] Length from node 'f" to node "g" [Ref. FAI/97-60 Rev. 2] Length from node "g" to the ultimate heat sink [Ref. N/A -not used] I.D. of piping along path from "a" to "b" to "f" [Ref. FA1197-60 Rev. 2] I.D. of piping along path from "b" to "c" to 'd' [Ref. FAI/97-60 Rev. 2] I.D. of piping along remaining path from "a" to "g" [Ref. FA1197-60 Rev. 2] O.D. of piping along path from "b" to "c" to "d" [Ref. FAI/97-60 Rev. 2] Page 2

FAI/03-07, Page C-3 of C-16 Rev. 2, Date: 03/06/03 Flows Q.bf := 800 gal min Qbcd := 886-gal min Qg:= 5200- gal mini Flow along path from 'a" to "b" to "f" during steady state condition without voiding [Ref. FAI/97-60 Rev. 2] Flow along path from "b" to "c" to "d" during steady state condition without voiding [Ref. FAI/97-60 Rev. 2] Flow along path from 'a' to "g during steady state condition without voiding [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28103] FCU Characteristics Nbe := 240 Number of tubes in cooler [Ref. FAI/97-60 Rev. 2] IDtube := 0527-in Internal diameter of tubes [Ref. FAI/97-60 Rev. 2] Lube.- 22-ft Length of tubes [Ref. FAI/97-60 Rev. 2] Pump Characteristics 1s := 240.8-ft Pump shutoff head [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03] Al := 0.2547-- 1st order pump curve coefficient [Ref. Chuck Richardson Emails dated ft2 1/27/03 & 1/28/03] 2 A2 := -0.5783-- 2nd order pump curve coefficient [Ref. Chuck Richardson Emails dated ft5 1/27/03 & 1/28/03] Hpump(Qp) := A2-Qp2 + Al.Qp + Hs Pump curve equation Other Inputs KVIV := 165.447 Vwtr fcxa := 0.0 ft3 Vwtr_2pjhe := 6.ft lb p,,.:= 62-b ft3 Tde 95.F Rga:= 1717.- sec R Valve frictional flow coefficient for throttled globe valve [Ref. FAI/97-60 Rev. 2] Volume of water that is left in the FCU when the pump restarts [Ref. FAI/97-60 Rev. 2] Volume of water that flows into the cooler after voiding has started and before the pumps restart. This volume of water is exposed to two phase flow conditions. [Ref. N/A -not used] Water density Design temp of the system Gas constant Page 3

FAI/03-07, Page C-4 of C-16 Rev. 2, Date: 03/06/03 Pump Flow Rate Equation Qttnormal= Qg + Qbcd + Qbf H.Orr:= Hpump(Qt~tnot l) Qtotno,,a =6.886 x 103 gal Hnor, = 109 ft min The total system flow rate is solved at any pump operating point using: -Al-_A,2 A2.(H 3 - Hd) Qpump(Hd):= 2-A2 Qpump(H',o:n) =6.886x 103 gal mTin 300I t100 _ 100 0 2000 4000 6000 8000 Io-10 GPM Pump Curve 00 Operating Point PUMP CURVE & OPERATING POINT Figure 2 SW Pump Curve Page 4

7.4.1 Initial Velocity & FLOW COEFFICIENT PREDICTION The water at the front of the void (point sd") is assumed to not move or simplification of this problem. More detailed hydraulic modeling may be performed to determine the reverse or forward flow at point "d". In many cases this flow is less than 10% of the incoming flow. After combining parallel paths the system is then simplified to: Figure 3 Simplified Open Loop Model In terms of the initial flow diagram (Figure 1), the flow area for each path is calculated: Abf = iDab Aabf = 0.939ft Abcd := -IDbcd 4 Alcd =0.347 ft2 Ag := IDag2 4 Aag = 2.792fC-The velocity for each path is calculated: Qabf Vabf := -Aabf ft Vabf = 1.9-S Qbcd Vcd := Abcd Vbcd = 5.7ftS V

Qag Vago-Aag ft Vag = 4.2-S Calculate equivalent velocity for all other loads:

_ Qabf + Qag AaW + Aag V-q = 3.583-S Page 5

The flow coefficient for each path is calculated. The flow resistance from point 'a" to point "b" and from point f" to point "g" are assumed to have a negligible effect on the flow split to the different paths. In an actual plant system, the engineer may choose to use values from a previously qualified system hydraulic model to determine a more accurate initial velocity. V2 hf = K- => 2-g K2.g hf K-v V2 2-g-H.Orm Kabf := VVaabf Kbcd := 2-nrm Vbcd Kg = 2 oa V.9 Kab, = 1.941 x 163 Kbcd = 216 Kag = 406 An equivalent flow coefficient for the "other loads" path (Figure 1) is calculated from: Koter Aabf Ag Kother = 35 Aother = Aabf IDother := IDabf An equivalent flow coefficient from all other loads is calculated from: Kother := a2 Veq Aether :A + Aag Kother = 544.321 4 -Aothier0.5 Ilother := IDother = 2.18 ft The flow coefficient for the path to the void is calculated by subtracting the flow coefficient downstream of the void along this path. To simplify this sample problem only the valve resistance downstream of the void is considered: K.oid := Kbcd - K 1lv 'Kvoid = 51 The pressure in the void is assumed to correspond to the saturation pressure for the void temperature. Pvod := 16.3-psi Absolute pressure based on saturation pressure of Tvoid shown above. Comes from TREMOLO output. [Ref. FA1197-60, Rev. 2] Page 6

The pump total developed head (TDH) is written by using Bernoulli's equation: Hatm + ELI + TDH = H,,d + EL + Hf where the following terms are defined in terms of feet H20 Hatm = atmospheric pressure head EL, = elevation of node "1" TDH = total developed head from pump EL, = elevation of node "2" Hf = frictional losses from point "1" to "2" The frictional losses are written using Darcy's formula with an appropriate units conversion factor: Hf = 0.00259-Ki 0 Q-where ID4 Koss = loss coefficient 0 = flow rate in gpm ID = pipe diameter in inches Two equations for the total developed head (TDH) by the pump are written with a corresponding flow balance and initial guesses for the simultaneous solution of these equations: Qvoid :=.1

th,

=.5 TDH := 300 Given TDH = 0 00259-Kothc, frictional losses along 'other' path equal the total developed head _________ (Patm Pvoid TDH=0 00259 Kvold-4 + , - EL, -EL-+ ftv - 4 in ) wtr-g Pwt gJ Bernoulli's along the "void" path ( gal I up uv Qother + Qvomd = Qpump(TDH-ft)--) pump curve The solution to the simultaneous equations is solved and defined as "Results". Results := Find(TDHQother9Qvoid) TDH := Resultsn-ft Qother := Results,- gal min Qoid := Results.) gal mm TDH = 100.189 ft Qother=5.767x 103 gal min Qvoid = 1.331 x le3 gal min The total resistance for this path is: The initial velocity is then: ViQioI := - VmItial = 8.5k KVaid = 51 Abcd S Check: is the velocity within the RBM bounds? Vinial, < 20 ft/sec

===> yes, velocity is within bounds of RBM runs Page 7

7.4.2 VOID & WATER COLUMN LENGTHS The volume of piping that is voided is calculated: Vpipe voided = Lcd' 4I]Dbcd volded = 29 ft 4 The void of the fan cooler unit is calculated: Vf =Ntbe-Ltben IDittbe' =' 8 ft3 4 The equivalent void length is then: Lao := Vp-pevoided + Vf. Lao = 107 ft Abcd The initial water column length is assumed to be the distance from point 'a' to point Vc". The discussion that follows explains why point "a' was chosen. Ignoring the FCU, the flow area changes from the closure point to node "a' are the same as the area changes from the closure point to node "g" on the return side. The transmission coefficients calculated for the return side demonstrate that less than 10% of the pressure pulse propagates to the header. Because of the similar flow area changes, less than 10% of any pressure would propagate into the supply header upstream of point Ha". In general, this indicates that the header acts like a large pressurized reservoir during the void closure process and water in the supply header does not add to the inertia of the decelerating water column. Note: if desired, a plant could select a length all the way back to the pumps. However, this is considered excessively conservative. The length if the accelerating water column is then: Lwo:= Lab + Lbr Lwo = 176.2ft Check: are the lengths within the bounds of the RBM runs? Lao < 100 ft Lwo < 400 ft

===>> yes lengths are within bounds of RBM runs Page 8

7.4.3 GAS RELEASE AND MASS OF AIR CONCENTRATED IN VOID The mass of air concentrated in the void during the void phase of the transient is calculated by assuming that the water that has experienced boiling and subsequent condensation releases its air as described in Section 5 of the User's Manual. For this problem, the tube volume only will be credited, assuming a draining of the FCU in which the headers do not remain full. This mass of water will release 50% of its non-condensable gas. Vf,, = 7.998 ft3 or Vf,, = 226 liter from 7.4.2 This represents the mass of water in the tubes which will lose 50% of its non-condensable gas. The concentration of gas is obtained from Figure 5-3. T&s = 95 F T&S - 32F =35 degOC 1.8F CON,,r := 18.5 mg From Figure 5-3 liter ma,, := 0.5-CONair-Vfu, mair = 2095 mg Check: is the mass of air within bounds of UM? for void closure in 8" piping there should be at least 900 mg of air per Table 5.2

===> yes, mass if air is within RBM run bounds. Page 9

FAI/03-07, Page C-10 of C-16 Rev. 2, Date: 03/06/03 7.4.4 Cushioned VELOCITY The graphs presented in Appendix A for the velocity ratios are solutions to the simultaneous differential equations that capture the acceleration of the advancing column and pressurization of the void. In order to determine the cushioned velocity the following terms that are needed are repeated: VD.t,., = 8.538-S Kvoid = 51 Lao = 106.622 ft Lwo = 176.2ft moir = 2.095 x 103 mg Tv01d = 217.1F Check: is the temperature within the bounds of the RBM? Tvoid > 200 F===> yes, the temperature is within the RBM run bounds 7.4.4.1 Air Cushioning If only credit for air cushioning is considered then Figure A-13 from Appendix A is selected. This figure corresponds to 10" piping while the sample problem has 8" piping. 10" piping bounds the 8" piping since the inertia modeled in the 10" piping runs is greater than that in the 8" piping runs and the velocity has reached a steady state until the final void closure occurs. This is apparent by comparison of the 4" and 10" RBM run results for the same gas mass; the velocity is reduced more in the smaller pipe case. If the pipe size at a given plant is not shown then the Velocity Ratio chart for the next larger size pipe will always be bounding. Figure A-13 corresponds to an initial velocity of 10 fps. The initial velocity calculated in this sample problem is less. The higher velocity chart is selected because the higher momentum associated with the higher velocity bounds the lower velocity. If the initial velocity at a plant is not shown then the Velocity Ratio chart for the next larger velocity will always be bounding. For a K of 51 as calculated in the sample problem, from Figure A-1 0 the ratio of the second to initial velocity is: 8 88%I only air cushion credited Therefore, the final closure velocity will be reduced by 12% just considering air in this sample problem. Pressure "clipping' is not included here and is calculated later. Page 10

7.4.4.2 Air and Steam Cushioning The velocity that results by considering steam cushioning is found using Figure A-40 from Appendix A. Note that the condensing surface temperature was verified being within the bounds of the RBM run limitations so steam condensation cushioning may be credited. The steam and air cushioning result in a ratio of cushioned to initial velocity of: c 83% air and steam cushioning The cushioned velocity is then: Vcushlon:= 0.8 3 -Vmitmal VCUShO. = 7 s 7.4.5 SONIC VELOCITY The sonic velocity is calculated from Equation 5-1 and 5-2 in the main body of the User's Manual. Pvoid = 16.3 psi where B=bulk modulus of water E=Young's modulus for steel OD=outside diameter of pipe t=wall thickness B := 319000psi E:= 28-106psi C I B C := l + DB ODbcd j l E (O°DI,,d - Dbd) Eo C = 4274-f S Page 1 1

FAI/03-07, Page C-12 of C-16 Rev. 2, Date 03/06/03 7.4.6 PEAK PRESSURE PULSE WITH NO "CLIPPING" The peak waterhammer pressure is calculated using the Joukowski equation with a coefficient of 1/2 for a water on water closure: APnoichppng := - Pwtr CVcus on APno clhpping = 203 psi 7.4.7 RISE TIME The rise time is calculated by using equation 5-4 from the UM. ms := 0.OOls TR:= 0.5sec{ in TR = 39ms sec Page 12

7.4.8 TRANSMISSION COEFFICIENTS The pressure pulse may be affected by rarefaction waves as it is developing and the peak may be "clipped". In addition, the pressure may be attenuated as it propagates through the system as a result of area changes. In order to calculate each of these effects, the transmission coefficients at junctions is required. The transmission coefficients are calculated consistent with section 5.3 of the UM. At points Tf" and `g' the transmission coefficients are calculated using Equation 5-8 from the UM; for simplification here the sonic velocity is assumed to be constant up and downstream of the junction: 2-Aincident Aincident + IA, J Tf 2 -Abcd Tf= 0.312 => this fraction of the incident pulse Abcd + AWbf + AWbf continues past point 'f" and the remainder of the incident pulse returns towards the initiation point.

=_-______

=0.288 => this fraction pulse that is incident upon Aar + Aag + Aag point "g" continues past point "g" and the remainder of the incident pulse returns towards the initiation point. T total := f`g Ttoca! 0.09 When the pressure pulse travels past point "g only 10% of the pulse will continue on. 69% of the incident pulse was reflected as a negative pulse at point f" and then 71% of the pulse that was incident upon point "Wg was reflected back as a negative pulse. the net reflection effect is: IPrf = P,*(&69%) + (31% Pmc (-71%) = PJc-69% -47%.71%) = 91% This reflection travels back to the initiation point. The pulse at the initiation point is 9% of its original value when this reflection arrives. For simplicity, the compounding effect of the "1 node transmission coefficient on the reflected wave from node "g" is ignored. The transmission coefficient evaluation needs to consider the control valve. The transmission coefficient at the control valve is calculated by assuming the valve acts like an orifice as the pressure pulse propagates through it. Equation 5-14 provides a simple relationship for an orifice flow coefficient in terms of its diameter ratio (f). This equation is used to back calculate an equivalent P ratio for the control valve knowing its coefficient and assuming Co=0.6. 0.5 Initial guess for the iteration below f3:=rootr I - 1) -i KVIV f]jj 0.347 0.6132 Page 13

For this 0 ratio and for the approximate waterhammer pressure already solved, the control valve will have a slight effect on the pressure pulse propagation by inspection of Figure 5-15. The reflection from this interaction will add approximately 10% to the incident pulse. In general what this means is that 10% of the pulse magnitude is reflected in a positive sense back towards the initiation point. To account for this effect, the peak pressure pulse is conservatively increased by 10%. 7.4.9 DURATION The pressure pulse is reduced to approximately 10% of its peak value as a result of the reflections from the area changes at points "f" and "'g". As a result, the time that it takes the pressure pulse to travel to point "g9 and back may be used to calculate the pressure pulse duration. peg:= (Lde + Lef + Lfg).2 TDeg = 118.2 ms Time for pulse to travel to and from point "g". Note that reflections from 'a" and Vb" are not credited. The total duration is conservatively increased by adding the rise time. TD := Teg + TR TD = 157 ms 7.4.10 PRESSURE CLIPPING The peak pressure is checked for 'clipping" using Table 5-3. Le:= Lde + Lef + Lfg Le = 252.6ft TR-C = 84ft 2 Ttotao = 0 09 This corresponds to the conditions in row two of the table referenced and no pressure clipping is expected. AP- =l.l'APnocdippngi 1.1 is from the control valve AP = 223 psi Page 14

7.4.11 PRESSURE PULSE SHAPE The pulse shape is then characterized by four points. Psys := l9psi this is the steady state system pressure [Ref. FAI/97-60 Rev. 2] Using an index, i=0,1,2,3 i = O..3 time, := pressure, := Psys AP + Psys AP + Psys Psys This provides the following values, which are plotted below. ( 0 ~( 19 " I 0.039 I 2l492 time = 0.I39 s pressure = 242 psi 0.118 1242 Pressure Pulse 200 0I c. 0 50 100 150 200 time (Ms) trace I Calculate the area underneath the curve to get the pressure impulse: integral:= TR-AP + AP- (TDg - TR) integral = 1.817 x 105 kg ms impulse := integral.Abcd impulse= 1.318x 103lbf-s Page 15

7.4.12 FLOW AREA ATTENUATION To simplify the analysis of the SW structures, the approach suggested here is to take the initiating pressure pulse and propagate the pulse through the system. For this example problem, the duration of the pulse is assumed to remain unchanged as it travels. In reality, the duration of the pulse is shortened as it approaches negative reflection sites. Maintaining the duration conservatively increases the impulse. As the pressure pulse propagates through the system it will be atenuated/amplified by flow area changes. For this example, only the downstream propagation is considered. The pulse will be attenuated by the increase in area at "f" and "g". The transmission coefficients were previously calculated. incident pulse transmitted pulse transmission pulse AP =223 psi APf := Trf-AP APf = 70psi APf 70 psi APg:= Tg-lPf APg = 20 psi Downstream of point g" only the following pulse magnitude will remain: AP, = 20psi Page 16

FAI/03-07 Page D-1 of D-1 6 Rev. 1 Date: 03/06/03 APPENDIX D Point Beach CFC 2D EPRI TBR Waterhammer Calculations Using MathCad 2000

POINT BEACH CFC 2D EL 1 I U I Figure 1 Open Loop Configuration Pressure & Temperature Note, pressures listed as "psi" are absolute (psia) or differential (psid) unless otherwise stated Pawnt:= 14.7-psi Tvod := 204.4-F Tpipeinitial := 75-F Pipe Geometry EEL, := 33.2-ft EL,:= 30.3*ft Lob := 36.8-ft Lbc:= 161.8-ft Lad := 46.5 -ft Lde:= 161.2-ft Lef := 6.4 ft I' := 86.8-ft Lgsuok:= 400-ft IDabf := 13.124-in lDbsd 7.981-in MDag:= 22.624 in ODbd 8.625-in Pressure above reservoir and above heat sink (absolute) Temperature in the void when the pumps restart (i.e. surface temperature of piping) [Ref. FAI/97-60 Rev. 2] (Assumed average T in void at 26 sec) Temperature of the fluid and piping when the transient starts [Ref. FAI/97-60 Rev. 2] Elevation of node "1" [Ref. FAI/97-60 Rev. 2] Elevation of node "2" [Ref. FAI/97-60 Rev. 2] Length from node "a" to node 'b" [Ref. FAI/97-60 Rev. 2] Length from node "b" to node "c" [Ref. FAI/97-60 Rev. 2] Length from node "c" to node "d" [Ref. FAI/97-60 Rev. 2] Length from node "d" to node "e" [Ref. FAI/97-60 Rev. 2] Length from node "e" to node "f" [Ref. FAI/97-60 Rev. 2] Length from node "f" to node "g" [Ref. FAI/97-60 Rev. 2] Length from node "g" to the ultimate heat sink [Ref. N/A -not used] I.D. of piping along path from "a" to 'b" to "fT [Ref. FA1197-60 Rev. 2] I.D. of piping along path from "b" to "c" to "d" [Ref. FAI/97-60 Rev. 2] I.D. of piping along remaining path from "a" to "g" [Ref. FAI/97-60 Rev. 2] O.D. of piping along path from Nb" to "c' to 'd" [Ref. FAI/97-60 Rev. 2] Page 2

FAI/03-07, Page D-3 of D-16 Rev. 1, Date: 03/06/03 Flows Qabf : 800 gal Flow along path from "a" to "b" to Tf" during steady state condition without min voiding [Ref. FAI/97-60 Rev. 21 Qbd := 941-g Flow along path from "b" to "c' to 'd" during steady state condition without min voiding [Ref. FAI/97-60 Rev. 2] Qag:= 5100 g Flow along path from "a" to "g during steady state condition without voiding min [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03] FCU Characteristics Nw,, := 240 Number of tubes in cooler [Ref. FAI/97-60 Rev. 2] IDtube := 0.527-in Internal diameter of tubes [Ref. FAI/97-60 Rev. 2] Ltbe. := 22-ft Length of tubes [Ref. FAI/97-60 Rev. 2] Pump Characteristics q := 240.8-ft Pump shutoff head [Ref. Chuck Richardson Emails dated 1/27/03 & 1/28/03] Al := 0.2547-- 1st order pump curve coefficient [Ref. Chuck Richardson Emails dated ft2 1/27/03 & 1/28/03] A2 := -0.5783.- 2nd order pump curve coefficient [Ref. Chuck Richardson Emails dated ft5 1/27/03 & 1/28/03] Hpump(Qp) := A2-Qp + Al-Qp + I-l Pump curve equation Other Inputs KVI := 139.326 Vw~tf. := O.Oft3 Vwut 2phase := 6-ft pwt := 62-b ft3 TdeS = 95-F ft2 Rga := 1717-sec -R Valve frictional flow coefficient for throttled globe valve [Ref. FAI/97-60 Rev. 2] Volume of water that is left in the FCU when the pump restarts [Ref. FAI/97-60 Rev. 2] Volume of water that flows into the cooler after voiding has started and before the pumps restart. This volume of water is exposed to two phase flow conditions. [Ref. N/A -not used] Water density Design temp of the system Gas constant Page 3

FAI/03-07, Page D-4 of D-16 Rev. 1, Date 03/06/03 Pump Flow Rate Equation Qt~tnorma 0 Qg + Qbcd + Qabf HnOrm:= Hpump(Qtotnonnal) Qtotnola= 6.841 x I03 gaHlorm 0 = IIoft min The total system flow rate is solved at any pump operating point using: -Al -IA1 A2.(HI - Hd) Qpump(Hd):= 2-A2 Qpump(H.,0,,n) = 6.841 x 103 gal min 200 x 100 _ 0 2000 40 GPM 8000 1-l Pump Curve 00 Operating Point PUMP CURVE & OPERATING POINT Figure 2 SW Pump Curve Page 4

FAI/03-07, Page D-5 of D-16 Rev. 1, Date: 03/06/03 7.4.1 Initial Velocity & FLOW COEFFICIENT PREDICTION The water at the front of the void (point 'd") is assumed to not move or simplification of this problem. More detailed hydraulic modeling may be performed to determine the reverse or forward flow at point 'd". In many cases this flow is less than 10% of the incoming flow. After combining parallel paths the system is then simplified to: EL VOID - Kvoid V I MAC Figure 3 Simplified Open Loop Model In terms of the initial flow diagram (Figure 1), the flow area for each path is calculated: Aa 4 =TDabf2 4 Aabf = 0.939 ft Abcd := 4 -IDbcd Abed = 0.347 ft A2ag = 2.792ftr The velocity for each path is calculated: Qabf Vabf := -Aabf Vabf = 1.9-S Qbed Vbed := Abcd Vbed = 6-S aag V-g :=- Aag Vag = 4.1-Calculate equivalent velocity for all other loads: Vq Qabf + Qag Aabf + Aag Veq = 3.523-S Page 5

The flow coefficient for each path is calculated. The flow resistance from point "a" to point "b" and from point "f" to point "g" are assumed to have a negligible effect on the flow split to the different paths. In an actual plant system, the engineer may choose to use values from a previously qualified system hydraulic model to determine a more accurate initial velocity. hf = K- => 2-g K=gLh V2 Vabf Kbcd =2gH VW 2 Va 2 Kabt 1.972 x i0' Kb-d = 195 Kag = 429 An equivalent flow coefficient for the "other loads' path (Figure 1) is calculated from: K := Aabf 1 he b f A 2 " Kother = 36 Acther := Aabf IMother := Mab An equivalent flow coefficient from all other loads is calculated from: Kother =- q2 VK 5 9 K.,he, = 571.989 Aother := Aabf + Ag M~other := (. o h r IDother = 2.18 ft The flow coefficient for the path to the void is calculated by subtracting the flow coefficient downstream of the void along this path. To simplify this sample problem only the valve resistance downstream of the void is considered: K-,.id := Kb~d - YA KVOid = 56 The pressure in the void is assumed to correspond to the saturation pressure for the void temperature. Pold:= 12.7-psi Absolute pressure based on saturation pressure of Tvoid shown above. Comes from TREMOLO output. [Ref. FAI97-60, Rev. 2] Page 6

FAI/03-07, Page D-7 of D-16 Rev. 1, Date: 03/06/03 The pump total developed head (TDH) is written by using Bernoulli's equation: Hatm + EL, + TDH = H,,id + EL, + Hf where the following terms are defined in terms of feet H20 171tr = atmospheric pressure head EL, = elevation of node "1 " TDH = total developed head from pump EL2 = elevation of node "2" Hf = frictional losses from point "1" to '2' The frictional losses are written using Darcy's formula with an appropriate units conversion factor: Hf = 0.00259.K, 0 Q-where ID KIOSS = loss coefficient = flow rate in gpm ID = pipe diameter in inches Two equations for the total developed head (TDH) by the pump are written with a corresponding flow balance and initial guesses for the simultaneous solution of these equations: Qold :=.1 Qother = *5 TDH := 300 Given TDH = 0.00259-K,,,erQ frictional losses along "other" path equal the total IDother 4 developed head Qvoid2 Patm Pvoid ' TDH = 0.00259-Kv0,d, + -EL - EL, - + ft Bernoulli's along (IDbcd' ( Pwtr g Pww g) the "void" path in Qother + Qvoid = Qpump(TDH-ft) m pump curve The solution to the simultaneous equations is solved and defined as "Results". Results := Find(TDHQtherPQvoid) TDH := Resultsn-ft TDH = 95.792 ft Qothr:= Results, Qoth0 = 5.501 x 103 gal min min Qvod := Results~. gal Qvoid = 1.706 x 103 gal min min The initial velocity is then: The total resistance for this path is: Qvoid ft Vmnitial =- Vmodl = 10.9f Kvold = 56 Abcd S Check: is the velocity within the RBM bounds? V~nitial < 20 ft/sec

===> yes, velocity is within bounds of RBM runs Page 7

7.4.2 VOID & WATER COLUMN LENGTHS The volume of piping that is voided is calculated: 71 2 3 Vpjpe voided = Lcd - IDbcd Vpipe voided = 16ft 4 The void of the fan cooler unit is calculated. Vf. := N ueLtube IThube 2 Vf u= 8 ft3 4 The equivalent void length is then: Lao Vpipevoded + Vf:= Lao = 70ft Abed The initial water column length is assumed to be the distance from point "a" to point "cm. The discussion that follows explains why point 'a" was chosen. Ignoring the FCU, the flow area changes from the closure point to node "a" are the same as the area changes from the closure point to node "g" on the return side. The transmission coefficients calculated for the return side demonstrate that less than 10% of the pressure pulse propagates to the header. Because of the similar flow area changes, less than 10% of any pressure would propagate into the supply header upstream of point "a". In general, this indicates that the header acts like a large pressurized reservoir during the void closure process and water in the supply header does not add to the inertia of the decelerating water column. Note: if desired, a plant could select a length all the way back to the pumps. However, this is considered excessively conservative. The length if the accelerating water column is then: Lwo := Lab + Lb, Lwo = 198.6ft Check: are the lengths within the bounds of the RBM runs? Lao < 100 ft Lwo < 400 ft

===>> yes lengths are within bounds of RBM runs Page 8

7.4.3 GAS RELEASE AND MASS OF AIR CONCENTRATED IN VOID The mass of air concentrated in the void during the void phase of the transient is calculated by assuming that the water that has experienced boiling and subsequent condensation releases its air as described in Section 5 of the User's Manual. For this problem, the tube volume only will be credited, assuming a draining of the FCU in which the headers do not remain full. This mass of water will release 50% of its non-condensable gas. VfN = 7.998 ft3 or VfN = 226 liter from 7.4.2 This represents the mass of water in the tubes which will lose 50% of its non-condensable gas. The concentration of gas is obtained from Figure 5-3. Tds =95 F Tds -32F T 3 = 35 deg C 1.8F CONr:= 18.5 mg From Figure 5-3 liter majr := 0-5-CONarVfcu Mair = 2095 mg Check: is the mass of air within bounds of UM? for void closure in 8" piping there should be at least 900 mg of air per Table 5.2

===> yes, mass if air is within RBM run bounds. Page 9

FAI/03-07, Page D-10 of D-16 Rev. 1, Date: 03/06/03 7.4.4 Cushioned VELOCITY The graphs presented in Appendix A for the velocity ratios are solutions to the simultaneous differential equations that capture the acceleration of the advancing column and pressurization of the void. In order to determine the cushioned velocity the following terms that are needed are repeated: V~t,, = 10.941 - S Kvold = 56 Lao = 69.522 ft Lwo = 198.6ft mar =2.095 x 03 mg Tv0 id = 20.4F Check: is the temperature within the bounds of the RBM? Tvoid > 200 F===> yes, the temperature is within the RBM run bounds 7.4.4.1 Air Cushioning If only credit for air cushioning is considered then Figure A-1 3 from Appendix A is selected. This figure corresponds to 10" piping while the sample problem has 8" piping. 10" piping bounds the 8' piping since the inertia modeled in the lO" piping runs is greaterthan that in the 8" piping runs and the velocity has reached a steady state until the final void closure occurs. This is apparent by comparison of the 4" and 10" RBM run results for the same gas mass; the velocity is reduced more in the smaller pipe case. If the pipe size at a given plant is not shown then the Velocity Ratio chart for the next larger size pipe will always be bounding Figure A-1 3 corresponds to an initial velocity of 10 fps. The initial velocity calculated in this sample problem is less. The higher velocity chart is selected because the higher momentum associated with the higher velocity bounds the lower velocity. If the initial velocity at a plant is not shown then the Velocity Ratio chart for the next larger velocity will always be bounding. For a K of 56 as calculated in the sample problem, from Figure A-13 the ratio of the second to initial velocity is: i 8 87% only air cushion credited virutia Therefore, the final closure velocity will be reduced by 13% just considering air in this sample problem. Pressure "clipping' is not included here and is calculated later. Page 10

7.4.4.2 Air and Steam Cushioning The velocity that results by considering steam cushioning is found using Figure A-40 from Appendix A. Note that the condensing surface temperature was verified being within the bounds of the RBM run limitations so steam condensation cushioning may be credited. The steam and air cushioning result in a ratio of cushioned to initial velocity of: l = 83%i lVnmnal l air and steam cushioning The cushioned velocity is then: Vcushion = 0.83.VurutiaI ft V =suo - 9.1 - S 7.4.5 SONIC VELOCITY The sonic velocity is calculated from Equation 5-1 and 5-2 in the main body of the User's Manual. Pvoid = 12.7 psi where B=bulk modulus of water E=Young's modulus for steel OD=outside diameter of pipe t=wall thickness B := 319000psi E := 28-106psi B C := Pwtr -B-ODbcd l E (Dcd - IDbcd) 2 C = 4274 f-s Page 1 1

FAI/03-07, Page D-12 of D-16 Rev. 1, Date: 03/06/03 7.4.6 PEAK PRESSURE PULSE WITH NO "CLIPPING" The peak waterhammer pressure is calculated using the Joukowski equation with a coefficient of 1/2 for a water on water closure: APno clipping:= I PwtrCVVcuson APno-clipping = 260 psi 7.4.7 RISE TIME The rise time is calculated by using equation 5-4 from the UM. ms := 0.OOls TR := O.5sec-VIhj° l TR 28ms scc Page 12

7.4.8 TRANSMISSION COEFFICIENTS The pressure pulse may be affected by rarefaction waves as it is developing and the peak may be "clipped". In addition, the pressure may be attenuated as it propagates through the system as a result of area changes. In order to calculate each of these effects, the transmission coefficients at junctions is required. The transmission coefficients are calculated consistent with section 5.3 of the UM. At points *u and '"g the transmission coefficients are calculated using Equation 5-8 from the UM; for simplification here the sonic velocity is assumed to be constant up and downstream of the junction: 2 *A1ncidfft Aincident + z A3 Tf 2-=d Tf = 0.312 => this fraction of the incident pulse Abcd + Aabf + Aabf continues past point "f" and the remainder of the incident pulse returns towards the initiation point. 2.Aabf Tg = 0.288 => this fraction pulse that is incident upon Abf + Aag + Aag point "g" continues past point `g" and the remainder of the incident pulse returns towards the initiation point. Ttotal :=Tf-^Tg ttotal = 0.09 When the pressure pulse travels past point "'g only 10% of the pulse will continue on. 69% of the incident pulse was reflected as a negative pulse at point '" and then 71% of the pulse that was incident upon point 'g' was reflected back as a negative pulse. the net reflection effect is: IPrf =Pc.(-69%) + (31%-P,,,).(-71%) =PC(-69% -47%-71%) =91%1 This reflection travels back to the initiation point. The pulse at the initiation point is 9% of its original value when this reflection arrives. For simplicity, the compounding effect of the "f1 node transmission coefficient on the reflected wave from node "g" is ignored. The transmission coefficient evaluation needs to consider the control valve. The transmission coefficient at the control valve is calculated by assuming the valve acts like an orifice as the pressure pulse propagates through it. Equation 5-14 provides a simple relationship for an orifice flow coefficient in terms of its diameter ratio (D). This equation is used to back calculate an equivalent 0 ratio for the control valve knowing its coefficient and assuming Co=0.6. 0.5 Initial guess for the iteration below ro .I -1 ]KI, =0.361 0.6.02 Page 13

For this f3 ratio and for the approximate waterhammer pressure already solved, the control valve will have a slight effect on the pressure pulse propagation by inspection of Figure 5-15. The reflection from this interaction will add approximately 10% to the incident pulse. In general what this means is that 10% of the pulse magnitude is reflected in a positive sense back towards the initiation point. To account for this effect, the peak pressure pulse is conservatively increased by 10%. 7.4.9 DURATION The pressure pulse is reduced to approximately 10% of its peak value as a result of the reflections from the area changes at points "f" and "g". As a result, the time that it takes the pressure pulse to travel to point "g' and back may be used to calculate the pressure pulse duration. TD (Ld' + Ler + Lrg)-2 TDg = 119.1 ms Time for pulse to travel to and from point mg". Note that reflections from "a" and "b" are not credited. The total duration is conservatively increased by adding the rise time. TD.= TDeg + TR TD = 147 ms 7.4.10 PRESSURE CLIPPING The peak pressure is checked for 'clipping' using Table 5-3. Le:= Lde + Lef + Lfg Le = 254.4 ft TR-C =61ft 2 ttotal = 0-09 This corresponds to the conditions in row two of the table referenced and no pressure clipping is expected. lAP :=- 1-*I'Apno-clippingi 1.1 is from the control valve AP = 286 psi Page 14

FAI/03-07, Page 0-15 of D-16 Rev. 1, Date: 03/06/03 7.4.11 PRESSURE PULSE SHAPE The pulse shape is then characterized by four points. lPsys := 19psi this is the steady state system pressure [Ref. FAI/97-60 Rev. 2] Using an index, i=0,1,2,3 o

O.. 3 time, :

Omsl TD - TR TD ._c pressure, := Psys AP + Psys AP + Psys Psys This provides the following values, which are plotted below. 0.0e28j 3051 time = 0.119 s pressure = 305 psi 0.147 19) Pressure Pulse o 50 time (Ms) trace I Calculate the area underneath the curve to get the pressure impulse: integral := TR-AP + AP-(TDg - TR) integral = 2.345 x 105 kg ms impulse := integralAbcd impulse= 1.701 x 103 Ibf s Page 15

7.4.12 FLOW AREA ATTENUATION To simplify the analysis of the SW structures, the approach suggested here is to take the initiating pressure pulse and propagate the pulse through the system. For this example problem, the duration of the pulse is assumed to remain unchanged as it travels. In reality, the duration of the pulse is shortened as it approaches negative reflection sites. Maintaining the duration conservatively increases the impulse. As the pressure pulse propagates through the system it will be atenuated/amplified by flow area changes. For this example, only the downstream propagation is considered. The pulse will be attenuated by the increase in area at "fif and "g". The transmission coefficients were previously calculated. incident pulse transmitted pulse transmission pulse AP =286 psi APf := tf-AP APf = 89 psi APf 89 pSi Pg: t = 26 psi Downstream of point "g only the following pulse magnitude will remain: = 26psi Page 16

FAI/O3-07 Page El of E2 Rev. 1 Date: 03/06/03 APPENDIX E SERVICE WATER PUMP CURVE CALCULATIONS USING MICROSOFT EXCEL 97

FAI/03-07 Page E2 of E2 Rev. 1 Date: 03/06/03 Below is the pump-head curve for the Unit 1 & 2 Service Water Pump Curves for the Point Beach Waterhammer EPRI TBR Analysis. This curve was generated from the Unit 1 & 2 WATER data sent to FAI from Chuck Richardson (WEPCo) on January 27,2002 (Unit 1) and January 28, 2002 (Unit 2). Therefore, from the data below using the EXCEL, the pump curve coefficients can be calculated using a polynomonial (A2k0 2 + A,1 Q + H) curve-fit features within EXCEL. As shown below, the coefficients are A2 = -0.5783 and Al = 0.2547. Flow (gpm) 1814.05 2824.87 3823.52 4500 4739.93 5795.15 6735.92 7532.61 ) Head (ft) 237.95 214.81 196.22 182.09 177.08 155.69 125.45 71.99 Flow (cu ftWs) 4.042 6.294 8.519 10.027 10.561 12.913 15.009 16.784 Point Beach SW Pump Curve 250 200 ~- 150 ii _' 10 !-Pump curve data 0 Poly. (Pump curve data) 0.100 5.000_0.000 15.000 20.00 50 0.000 5.000 10.000 15.000 20.000 Flow (cu ft/ sec)

FAI/03-07 Page F-1 of F-5 Rev. 1 Date: 03/06/03 APPENDIX F EPRI TBR MAX FORCEJIMIPULSE CALCULATIONS FOR POINT BEACH CFC IA USING MICROSOFT EXCEL 97

FAI/03-07 Page F-2 of F-5 Rev. 1 Date: 03/06/03 POINT BEACH CFC1A INPUTS: Wave Speed (C) = Rise Time = Duration = Peak Pressure = Area (8" line) Area (6" line) Area (2.5" line) Trans. Coeff. (elbows) = Trans. Coeff. (8" x 6") Trans. Coeff. (6" x 2 5") = 4274 0.048 0.127 191 50 28.89 4.79 1 0.7759 0.9234 ft/s sec sec psia sq in sq in sq in Rate = 3979.166667 psVsec Direction - Downstream Towards Throttle Valve Flow Element Pipe Area (sq In) Length (fl) 35 50 3.16 36 50 18 37 50 3 38 50 7 39 50 12 40 50 22.5 41 50 2 42 50 2 43 50 13 P1 -time 0 0 0 0 0 0 0 0 0 P2 -time 0.00074 0.00495 0.00565 0 00729 0 01010 0.01536 0.01583 0.01630 0.01934 P3 -time 0.04874 0.05295 0.05365 0 05529 0.05810 0 06336 0.06383 0.06430 0.06734 P4 - time P5 -time 007974 0.12774 0 08395 0.13195 0.08465 0.13265 0 08629 0.13429 0 08910 0.13710 0.09436 0.14236 0.09483 0.14283 0.09530 0.14330 0.09834 0.14634 Direction - Upstream Towards Fan Cooler Flow Element PIpe Area (sq In) Length (ft) 34(*) 50 14 83 33 50 6.5 32 50 4 31 50 6.4167 30 28.89 4.1 29 28.89 1.5 28 28.89 7.667 27 28.89 2.25 26 28.89 2.25 P1 -time 0 0 0 0 0 0 0 0 0 P2 -time 0 00347 0.00499 0.00593 0.00743 0.00839 0.00874 0.01053 0 01106 0.01158 P3 -time 0 05147 0.05299 0.05393 0.05543 0.05639 0.05674 0 05853 0.05906 0.05958 P4-time PS -time 0 08247 0.13047 0.08399 0.13199 0.08493 0.13293 0.08643 0.13443 0.08739 0.13539 0.08774 0.13574 0.08953 0.13753 0 09006 0.13806 0 09058 0.13858 DIrectIon - Downstream Towards Throttle Valve Flow Element Delta-Time (s) Force (Ibf) Impulse (Ibf-s) 35 0.00074 147.100686 7.060832943 36(') 0.00421 592.495592 28.43978842 37(-) 0.00070 98.7492653 4.739964736 38 0 00164 325.855951 15.64108563

FAI/03-07 Page F-3 of F-5 Rev. 1 Date: 03/06/03 39 40(#) 41 42(') 43 0.00281 0 00526 0.00047 0 00047 0.00304 558 610201 907.069922 93.1017002 65.8328436 605.161051 26.81328966 43.53935626 4.46888161 3.159976491 29.04773046 Direction - Upstream Towards Fan Cooler Flow Elem Delta-T (s) Force (It 34(') 0 00347 488.1505 33 0.00152 302.5805 32 0.00094 186 203 31(l) 0.00150 231.7502 30 0.00096 85.5598C 29 0.00035 31.3023E 28(l) 0 00179 147.7483 27(l) 0.00053 43.35905 26(l) 0.00053 43.35905 Ibf) 535 26 34 205 052 677 196 573 573 Impulse (Ibf-s) 23.43122568 14.52386523 8.937763219 11.12400986 4.106870648 1.502513652 7.091923028 2 081234748 2.081234748 Notes: (*) - denotes the flow element as a 45-degree elbow (#) - denotes the flow element as a 30-degree elbow (I) - denotes the flow element as a reducing tee

FAI/03-07 Page F-4 of F-5 Rev. 1 Date: 03/06/03 POINT BEACH CFCtA INPUTS: Wave Speed (C) = Rise Time = Duration = Peak Pressure - Area (8-line) Area (6-line) Area (2 5-line) Trans. Coeff. (elbows) = Trans. Coeff (8-x ") - Trans. Coeft. (8-x 2 5") - 4274 0048 0127 191 28 89 4 79 t =2-C7/(C7+C7+CS) =2-C8/(C8+C8+C9) ft/s sec sec psla sq in sq In sq In Rate. =C6/C4 psVsec Direction - Downstream Towards Thrc Flow Element 35 36 37 38 Pipe Area (sq In) 50 50 50 50 50 50 50 50 50 Length (ft) Pt -time 316 18 3 7 12 225 2 2 13 0 0 0 0 0 0 0 0 0 P2 -time -C I 7/C3 =(C17+C18)IC3 =(Cl7.C18+C19)IC3 =(Cl7+C1l8+C1l9.C20)1C3 = (C 17+C 1 8+C1I9+C20+C2l1)/C3 .(Cl7+CI8O+Clg+C20+C21 +C22)/C3 =(C17+CI8+C19+C20+C21+C22+C23)/C3 =(C17+C1 8+C19+C20+C21+C22+C23+C24)/C3 .(Cl7+C1 8'Cl9+C20+C21 +C22+C23+C24+C25)/C3 P3 -time P4 - time EE17+C4

  • E17+(C5-C4)

=Et8+C4 =Et8+(C5-C4) -E19+C4 .El9+(C5-C4)

  • E20+C4
  • E20+(C5-C4)
  • E21+C4

=E21+(C5-C4) =E22+C4 =E22+(C5-C4) .E23+C4 =E23+(C5-C4) =E24+C4 =E24+(CS-C4) =E25+C4 =E25+(C5-C4) Ps -time

  • E17+C5

=E18+C5 .E19+CS

  • E20+C5

=E21+C5 =E22+C5 =E23+C5 =E24+CS =E25+C5 40 41 42 43 Direction - Upstream Towards Fan Co Flow Element 34(") 33 32 31 30 29 28 27 26 Pipe Area (sq In) 50 50 50 50 =C8 =C8 =C8 =C8 =C8 Length (It) 1483 65 4 6 4167 4.1 1i5 7 667 225 225 0 0 0 0 0 0 0 0 0 P1 -time P2 -time =C30IC3 =(C30+C31 )/C3 .(C30+C31.C32)/C3 =(C30+C31 +C32+C33)/C3 .(C30+C31 +C32+C33+C34)/C3 =(C30+C31 +C32+C33+C34+C35)/C3 =(C30+C31.C32+C33+C34+C35+C36)/C3 =(C30+C31+C32+C33+C34+C35+C36+C37YC3 =(C30+C31 +C32+C33+C34+C35+C36tC37.C38)/C3 P3 -time P4 -time =E30+C4 =E30+(C5-C4) =E31+C4 =E31+(C5-C4) =E32+C4 =E32+(C5-C4) =E33+C4 =E33+(C5-C4)

  • E34+C4

=E34+(C5-C4) =E35+C4 =E35+(C5-C4) =E36+C4 =E36+(C5-C4) =E37+C4 =E37+(C5-C4) =E38+C4 =E38+(C5-C4) PS -time =E30+C5 =E31+C5 =E32+C5 =E33+C5 =E34+C5 =E35+C5 =E36+C5 =E37+C5 =E38+C5 Direction - Downstream Towards Thrc Flow Element 35 Delta-Time (s) =Et 7 =E18-E17 =E19-E18 Force (Ibj) Impulse (Ibf-s)

  • B43 F6-B17

=C43-C4 =B44-F68Bi8-COS(45'PI(Y180) =C44-C4 =B45-F6-Bt9gCOS(45'PI(Y1 80) =C45-C4 =846-F6-B20 =C46-C4 37(.) 38

  • E20-E19

FAI/03-07 Page F-5 of F-5 Rev. 1 Date: 03/06/03 39 40(#) 41 42( ) 43 =E21-E20 =E22-E21 =E23-E22 =E24-E23 =E25-E24 =B47'F6B21 =B48'F6'B22'C0S(3O'P1(yl BO) =B49'F6B23 =B5O0F6824'C0S(45'P1(Yl 80) =851PF6'B25 Direction - Upstream Towards Fan Co Flow Elem 34(*) 33 32 31(f) 30 29 I 28(l) 27(l) 26(l) Defta-T (a) =E30 =E31-E30 cE32-E31 -E33-E32 .E34-E33 .E35-E34 =E36-E35 =E37-E38 =E38.E37 Force OMb) =B55-F66B30COS(45-Pt(/1 80) -856P8B'3I .557'F6832 =F6858B33'C1 I =B59'F6'34'C1 I =B6O0F68B35'C1 .-BG1FBeB368C1lC12 -E162'FSB37rc1 VI2 =B63'F6B38'C1 PC12 .-C47'C4 =C48'C4 -C49'C4 -050'C4 .-C51 C4 Impulse (Ibf-s) =C55'C4 =CSG'C4 =C57tC4 =C58'C4 =C59'C4 ..06OC4 =C6I1C4 =C62'C4 .-C63'C4 Notes: () - denotes the flow element as a 45-de (8) - denotes the flow element as a 30-df (I) - denotes the flow element as a reduc

FAI/03-07 Page G-1 of G-5 Rev. 1 Date: 03/06/03 APPENDIX G EPRI TBR MAX FORCE/IMPULSE CALCULATIONS FOR POINT BEACH CFC 1C USING MICROSFOT EXCEL 97

FAI/03-07 Page G-2 of G-5 Rev. 1 Date: 03/06/03 POINT BEACH CFC1C INPUTS: Wave Speed (C) = Rise Time = Duration = Peak Pressure = Area (8" line) Area (6" line) Area (2.5" line) Trans. Coeff. (elbows) = Trans. Coeff. (8" x 6") = Trans. Coeff. (6" x 2.5") = 4274 0.039 0.118 222 50 28.89 4.79 1 0.7759 0.9234 fWs sec sec psia sq in sq in sq in Rate = 5692.307692 psi/sec Direction - Downstream Towards Throttle Valve Flow Element Pipe Area (sq in) Length (ft) 42 50 0.65 43 50 8.035 44 50 5.3 45 50 11 46 50 11 47 50 22 48 50 11 49 50 15 50 50 4 51 50 3 P1 -time 0 0 0 0 0 0 0 0 0 0 P2 -time 0.00015 0.00203 0.00327 0.00585 0.00842 0.01357 0.01614 0.01965 0 02059 0.02129 P3 -time 0.03915 0.04103 0.04227 0.04485 0.04742 0.05257 0.05514 0.05865 0.05959 0.06029 P4 - time 0.07915 0.08103 0.08227 0.08485 0.08742 0.09257 0.09514 0.09865 0.09959 0.10029 P5 -time 0.11815 0.12003 0.12127 0.12385 0.12642 0.13157 0.13414 0.13765 0.13859 0.13929 Direction - Upstream Towards Fan Cooler Flow Element 41 40 39 38 37 36 35 34 33 32 31 30 Pipe Area (sq 50 50 50 50 28.89 28.89 28.89 28.89 28.89 28.89 28.89 28.89 in) Length (ft) 8.711 1.654 1.689 0.583 1.612 3.73 0.583 1.579 5.521 4.625 2.25 2.25 P1 -time 0 0 0 0 0 0 0 0 0 0 0 0 P2 -time 0.00204 0.00243 0.00282 0.00296 0.00333 0.00421 0.00434 0.00471 0.00600 0.00709 0.00761 0.00814 P3 -time 0.04104 0.04143 0.04182 0.04196 0.04233 0.04321 0.04334 0.04371 0.04500 0.04609 0.04661 0.04714 P4 -time 0.08104 0.08143 0.08182 0.08196 0.08233 0.08321 0.08334 0.08371 0.08500 0.08609 0.08661 0.08714 P5 -time 0.12004 0.12043 0.12082 0.12096 0.12133 0.12221 0.12234 0.12271 0.12400 0.12509 0.12561 0.12614 Direction - Downstream Towards Throttle Valve Flow Element Delta-Time (s) Force (bf) Impulse (Ibf-s) 42 0.00015 43.2849789 1.688114179 43 0.00188 535.068932 20.86768835 44 0.00124 352.939059 13.7646233 45 0.00257 732.515028 28.5680861 46(A) 0.00257 732.515028 28.5680861 47(@) 0.00515 1200.08237 46.80321226 48 0.00257 732.515028 28.5680861 49(*) 0.00351 706.317742 27.54639192 50(*) 0.00094 188.351398 7.345704512 51 0.00070 199.776826 7.79129621

FAI/03-07 Page G-3 of G-5 Rev. 1 Date. 03/06/03 Direction - Upstream Towards Fan Cooler Flow Elem Delta-T (s) Force (Ibf) 41 0.00204 580.08531 40 0.00039 110.143623 39(!) 0.00040 112.474353 38(&) 0.00014 38.8232965 37 0.00038 62.0249509 36($) 0.00087 143.519272 35(-) 0.00014 15.8618905 34(*) 0.00037 42.9604205 33 0.00129 212.431609 32(!) 0.00108 164.332897 31 (!) 0.00053 79.9457336 30(!) 0.00053 79.9457336 Impulse (Ibf-s) 22.62332709 4.29560131 4.386499766 1.514108563 2.418973084 5.597251614 0.618613731 1.675456399 8.284832752 6.408982977 3.117883611 3.117883611 Notes: All other flow elements are assumed to be 90-degree elbows (*) - denotes the flow element as a 45-degree elbow (#) - denotes the flow element as a 30-degree elbow (@) - denotes the flow element as a 55-degree elbow (I) - denotes the flow element as a reducing tee (A) - denotes the flow element as flow orifice ($) - denotes the flow element as a flow control valve (&) - denotes the flow element as a 8" x 6" reducer

FAI/03-07 Page G-4 of G-5 Rev. I Date: 03/06/03 POINT BEACH CFCIC INPUTS: Wave Speed (C) = Rise Time - Duration D Peak Pressure = Area (8-line) Area (6 line) Area (2 5' line) Trans Coeff (elbows) = Trans Coeff (8 x 6) = Trans. Coeff (65 x 2 5 ) = 4274 0 039 0 118 222 50 28 89 4 79 1 =2 C7/(C7+C7+C8) -2 C8/(C8+C8+C9) ft/s sec sec psla sq In sq in sq In Rate = =C6/C4 psVsec Direction - Downstream Towards Flow Element 42 43 44 45 48 47 48 49 so 51 Pipe Area (sq In) 50 50 50 50 50 50 50 50 50 50 Length (ft) P1 time 065 8 035 53 11 11 22 11 15 4 3 0 0 a 0 0 0 0 0 0 0 P2-time =C17/C3 =(C17+C18)/C3 =(C17+C18+Clg)C3 =(C17+C1l8+Clg+C20)/C3 =(CI 7+CI 8+C19+C20+C2 1)1C3 =(CI7+Cl8+C19+C20.C21+C22)/C3 =(C17+C18+CIlg+C20+C21 +C22.C23)/C3 =(C17+CI8+Clg+C204C21.C22+C23+C24)/C3 =(Cl7+CI 8+CIlg+C20+C21+C22+C23+C24.C25)/C3 =(C17+C18+C19+C20+C21+C22+C23+C24+C25+C26)/C3 P3 -time =E17+C4 =E18+C4 =Et9+C4 =E20+C4 =E21+C4 =E22+C4 =E23+C4 =E24+C4 =E25+C4 .E26+C4 P4 - time =El7t(C5-C4) =E18+(CS-C4) =EI 9+(CS-C4) =E20+(CS-C4) =E21+(C5-C4) =E22+(C5-C4) =E23+(CS-C4) =E24+(CS-C4) =E25+(C5-C4) =E26+(C5-C4) PS5-time =E17+C5 =EIB.C5 =1:19+CS =E20+CS =E21+C5 =E22+C5 =E23+C5 =E24+C5 =E25+C5 =E26+CS Direction - Upstream Towards Fs Flow Element 41 40 39 38 37 36 35 34 33 32 31 30 Pipe Area (sq In) 50 50 50 50 -C8 =C8 =C8 =-8 =C8 28 89 28 89 28 89 Length (ft) P1 -time 8711 1 654 1 689 0 583 1 612 373 O 583 1 579 5521 4 625 2 25 225 0 0 0 0 0 0 0 0 0 0 0 0 P2 -time =C31/C3 =(C31 +C32)C3 =(C31 +C32+C33)/C3 =(C31 +C32+C33+C34YC3 =(C31 +C32+C33+C34+C35/C3 =(C31 +C32+C33+C34+C35+C36/C3 =(C31 +C32+C33+C34+C35+C38+C37YC3 =(C31 +C324C33+C34+C35+C36+C37+C38yC3

  • (C31 +C32+C33+C34+C35+C38+C37+C38+C39/C3

=(C31 +C32+C33+C34+C35+C38+C37+C38+C39+C40)/C3 =(C31+C32+C33+C34+C35+C38+C37+C38+C39+C40+C41)/C3 =(C31 +C32+C33+C34+C35+C36+C37+C38+C39+C40+C41 +C42)C3 P3 -time =E31+C4 =E32+C4 =E33+C4 =E34+C4 =E35+C4 =E36+C4 =E37+C4 =E38+C4 =E39+C4 =E40+C4 =E41+C4 =E42+C4 P4 -time =E31+(C5-C4) =E32+(C5-C4) =E33+(C5-C4) =E34+(C5-C4) cE35+(C5-C4) =E36+(C5-C4) =E37+(C5-C4) =E38+(C5-C4) =E39+(C5-C4) =E40+(C5-C4) =E41+(C5-C4) =E42+(C5-C4) P5 -time =E31+C5 =E32+C5 =E33+C5 =E34+C5 .E35+C5 =E36+CS =E37+C5 =E38+C5 =E39+C5 =E40+C5 =E41+C5 =E42+C5 Direction - Downstream Towards Flow Element Delta-Time (s) Force (Ibf) =B46 F6'B17 Impulse (Ibf-s) =C468C4 42 =E1 7

FAI/03-07 Page G-5 of G-5 Rev. 1 Date: 03/06/03 43 44 45 46(A) 47(0) 48 49(*) 50(-) 51 =EI8-E17 -E19-ElS .-E20.E19 =E21.E20 =E22-E21 =E23-E22 =E24-E23 =E25-E24 =E26-E25 =B4rF6'B18 =B48'F6'B19 =549'F6B20 =B50'F6821 =B5 PF6'B22'COS(35'Pl(Yl 80) =852'F6823 =B53'F6'B24'COS(45'PI(yl 80) =B54'F6'25'COS(45'PI(Y 80) =BS55F6'26 .C47'C4 =C48'C4 .-C49'C4 =CSO'C4 =C51PC4 -CS2'C4 =C53'C4 =C54'C4 =C5SSC4 DIrection. Upstream Towards Fs Flow Elem Detta-T (a) 41 =E31 40 =E32-E31 39(l) =E33-E32 38(&) =E34-E33 37 =E35-E34 36(S)

  • E36-E35 35( )
  • E37-E36 34()
  • E38-E37 33

=E39-E38 32(l) =E40-E39 31(t) =E41-E40 30(1) =E42-E41 Force (IbI) =BS9¶F6B31 =BB0F6'B32 =B61*FBB33 =B62'F6834 =B63'F8835 -864'F8B36 =B65'F6'B37'COS(45'PlI/180) =066'F6838'COS(45'Pt(Y1 80) =B6rF6B839 =B68PF6640`C12 -B69'F6041*C12 =B70`F6'B42'C12 Impulse (lbf-s) =CS9'C4 =COO'C4 =C61PC4 -C82'C4 =C63'C4 -C64'C4 -C65'C4 -C68tC4 -C67'C4 =C68'C4 .C69'C4 =C70tC4 Notes: All other flow elements ar (') - denotes the flow element as a (t) - denotes the flow element as a (0) - denotes the flow element as i (I)

  • denotes the flow element as a (A). denotes the flow element as fli (S) - denotes the flow element as a

(&) - denotes the flow element as a

FAI/03-07 Page H-1 of H-5 Rev. 1 Date: 03/06/03 APPENDIX H EPRI TBR MAX FORCE/IMPULSE CALCULATIONS FOR POINT BEACH CFC 2B USING MICROSFOT EXCEL 97

FAI/03-07 Page H-2 of H-5 Rev. 1 Date: 03/06/03 POINT BEACH CFC2B INPUTS: Wave Speed (C) = Rise Time = Duration = Peak Pressure = Area (8" line) Area (6-line) Area (2.5" line) Trans. Coeff. (elbows) = Trans. Coeff. (8" x 6") = Trans. Coeff. (6" x 2.5") = 4274 0.039 0.157 223 50 28 89 4.79 1 0.7759 0.9234 fWs sec sec psia sq in sq in sq in Rate= 5717.948718 psi/sec Direction - Downstream Towards Throttle Valve Flow Element 41 42 43 44 45 46 47 48 49 50 51 52 53 Pipe Area (sq in) 50 50 50 50 50 50 50 50 50 50 50 50 50 Length (ft) 10.33 13 6 6.2 36 7 5 17.1 7 24 2 1 14.1 P1 -time 0 0 0 0 0 0 0 0 0 0 0 0 0 P2 -time 0.00242 0.00546 0.00686 0.00831 0.01674 0.01837 0.01954 0.02354 0.02518 0.03080 0.03127 0.03150 0.03480 P3 -time 0.04142 0.04446 0 04586 0.04731 0.05574 0.05737 0.05854 0.06254 0.06418 0.06980 0.07027 0.07050 0.07380 P4 - time 0.12042 0.12346 0.12486 0.12631 0.13474 0.13637 0.13754 0.14154 0.14318 0.14880 0.14927 0.14950 0.15280 PS -time 0.15942 0.16246 0.16386 0.16531 0.17374 0.17537 0.17654 0.18054 0.18218 0.18780 0.18827 0.18850 0.19180 Direction - Upstream Towards Fan Cooler Flow Element Pipe Area (sq in) 40 50 39 50 38 28.89 37 28.89 36 28.89 35 28.89 Length (ft) 1.16 13.063 2.167 6.5 2.25 2.25 P1 -time 0 0 0 0 0 0 P2 -time 0.00027 0.00333 0.00383 0.00536 0.00588 0.00641 P3 -time 0.03927 0.04233 0.04283 0.04436 0.04488 0.04541 P4 -time 0.11827 0.12133 0.12183 0.12336 0.12388 0.12441 P5 -time 0.15727 0.16033 0.16083 0.16236 0.16288 0.16341 Direction - Downstream Towards Throttle Valve Flow Element Delta-Time (s) Force (Ibf) Impulse (Ibf-s) 41 0.00215 613.401845 23.92267197 42 0.00304 869.599127 33.91436593 43 0.00140 401.353443 15.65278428 44(#) 0.00145 359.168353 14.00756578 45 0.00842 2408.12066 93.91670566 46 0.00164 468.245684 18.26158166 47 0.00117 334.461203 13.0439869 48 0.00400 1143.85731 44.61043519 49 0.00164 468.245684 18.26158166 50( @) 0.00562 1298.80702 50.65347396 51 0.00047 133.784481 5.217594759 52(*) 0.00023 47.2999569 1.844698318

FAI/03-07 Page H-3 of H-5 Rev. 1 Date: 03/06/03 53 0.00330 943.180591 36.78404305 Direction - Upstream Towards Fan Cooler Flow Elem Delta-T (s) Force (Ibf) 40 0.00027 77.594999 39(!) 0.00306 677.95278 38 0.00051 83.7552793 37(!) 0.00152 194.915965 36(!) 0.00053 62.3057254 35(!) 0.00053 62.3057254 Impulse (Ibf-s) 3.02620496 26.44015841 3.266455894 7.601722646 2.429923292 2.429923292 Notes: All other flow elements are assumed to be 90-degree elbows (*) - denotes the flow element as a 45-degree elbow (#) - denotes the flow element as a 30-degree elbow (@) - denotes the flow element as a 36-degree elbow (I) - denotes the flow element as a reducing tee

FAI/03-07 Page H-4 of H-5 Rev 1 Date 03/06/03 POINT BEACH CFC2B It Wave Speed (C) = Rise Time - Duration = Peak Pressure = Area (8' line) Area (6 line) Area (2 5-tine) Trans Coeff. (elbows) = Trans. Coeff. (8-x 6) = Trans Coeff. (6 x 2 5) 4274 0 039 0157 223 50 28 89 4.79 1 =2 C7/(C7+C7+C8)

2-C8/(C8+C8+C9) ft/s sec sec psia sq tn sq In sq In Rate

=C6/C4 psi/sec Direction - Downstream Flow Element 41 42 43 44 45 46 47 48 49 50 51 52 53 Pipe Area (sq In) 50 50 50 50 50 50 50 50 50 50 50 50 50 Length (it) P1 -time 10 33 13 6 6 2 36 7 5 17.1 7 24 2 141 0 0 0 0 0 0 0 0 0 0 0 0 0 P2 -time =C17/C3 =(C17+C18)/C3 =(C17+C1 8+C1 9)/C3 =(C17+C1 8+C1 9+C20YC3 =(C17+C18+C19+C20+C21)/C3 =(C17+C1 8+C1 9+C20+C21+C22)/C3 =(C17+C1 8+C19+C20+C21+C22+C23)/C3 =(C17+C1 8+CI 9+C20+C21+C22+C23+C24)/C3 =(C17+CI 8+C19+C20+C21+C22+C23+C24+C25)/C3 =(C17+C1 8+Cl 9+C20+C21 +C22+C23+C24+C25+C26)/C3 =(C17+C1 8+C19+C20+C21 +C22+C23+C24+C25+C26+C27)/C3 -(Cl 7+C18+C1 9+C20+C21 +C22+C23+C24+C25+C26+C27+C28)/C3 .(C17+C1 8+C1 9+C20+C21+C22+C23+C24+C25+C26+C27+C28+C29)/C3 P3 -time =E1 7+C4 =E 18+C4 -E 9+C4 =E20+C4 =E21 +C4 =E22+C4 =E23+C4 =E24+C4 =E25+C4 =E26+C4 =E27+C4 =E28+C4

  • E29+C4 P4 - time P5 -time

=E17+(C5-C4) =E17+C5 -El8+(C5-C4) =E18+C5 =E19+(C5-C4) =E19+C5 =E20+(C5-C4) =E20+C5 =E21 +(C5-C4) =E21 +C5 =E22+(C5-C4) E22+C5

  • E23+(C5-C4)

-E23+C5 eE24+(C5-C4) =E24+C5 -E25+(C5-C4) =E25+C5 =E26+(C5-C4) =E26+C5 =E27+(C5-C4) =E27+C5 =E28+(C5-C4) =E28+C5 =E29+(C5-C4) =E29+C5 Direction - Upstream To Flow Element 40 39 38 37 36 35 Pipe Area (sq In) 50 50 28 89 28 89 =C8 =C8 Length (ft) Pt -t1me 1.16 13 063 2167 65 225 225 0 0 0 0 0 0 P2 -t1me =C34/C3 =(C34+C35)/C3 =(C34+C35+C36)/C3 =(C34+C35+C36+C37)/G3 =(C34+C35+C36+C37+C38)/C3 =(C34+C35+C36+C37+C38+C39)/C3 P3 -time =E34+C4 =E35+C4 =E36+C4 =E37+C4 =E38+C4 =E39+C4 P4-time P5 -time =E34+(C5-C4) =E34+C5 =E35+(C5-C4) =E35+C5 =E36+(C5-C4) =E36+C5 =E37+(C5-C4) =E37+C5 =E38+(C5-C4) =E38+C5 =E39+(C5-C4) =E39+C5 DirectIon - Downstream Flow Element Delta-TIme (s) 41 =E17-E34 42 -E18-E17 43 =E19-E18 44(#) =E20-E19 45 -E21-E20 46 =E22-E21 47 =E23-E22 48 =E24-E23 49 =E25-E24 50(@) =E26-E25 Force (Ibt) Impulse (Ibf-s) =B44-F6-B17 .C44C4 =B45-F6'B18 =C45'C4 =B46'F6'B19 =C46'C4 =B47'F6'B20'COS(30'Pf(/180) =C47-C4 =B48'F6'B21 =C48-C4 =B49-F6-B22 =C49-C4 =B50-F68B23 =C50-C4 =B51 'F6'B24 =C51'C4 =852'F6'825 =C52'C4 =B53'F6'B26'COS(36'Pi()180) =C53-C4

FAI/03.07 Page H-5 of H-5 Rev 1 Date 03106103 51 52(-) 53 =E27-E26 =E28-E27 =E29-E28 =B54'F6-B27 =C54tC4 =B55-F68B28'COS(45-P1(/180) =C55-C4 =856-F6-B29 =C56'C4 Direction - Upstream To Flow Elem Delta-T (s) 40 -E34 39(t) -E35-E34 38 =E36-E35 37(1) =E37-E36 36(I) =E38-E37 35(1) =E39-E38 Force (Ibf) =860-F6-B34 =B61-F6-B35-C11 -862-F6-B36 =F6-B63-B37-C11 =B64-F6-B38-C11 C12 =B65-F6-B39-11 -C12 Impulse (lbf-s)

  • C60-C4

=C61-C4 =C62-C4 -C63-C4 =C64-C4 =C65-C4 Notes: All other flow ele (') - denotes the flow elerT (0) - denotes the flow elen (0) - denotes the flow ele (1) - denotes the flow elerr

FAI/03-07 Page I-1 of 1-5 Rev. 1 Date: 03/06/03 APPENDIX I EPRI TBR MAX FORCE/IMPULSE CALCULATIONS FOR POINT BEACH CFC 2D USING MICROSOFT EXCEL 97

FAI/03-07 Page 1-2 of 1-5 Rev 1 Date: 03/06/03 POINT BEACH CFC2D INPUTS: Wave Speed (C) = Rise Time = Duration = Peak Pressure = Area (8" line) Area (6" line) Area (2.5" line) Trans. Coeff. (elbows) = Trans. Coeff. (8-x 6") = Trans. Coeff. (6' x 2.5") = 4274 0028 0.147 286 50 28 89 4.79 1 0.7759 0.9234 ft/s sec sec psia sq in sq in sq in Rate = 10214.3 psi/sec Direction - Downstream Towards Throttle Valve Flow Element Pipe Area (sq in) Length (ft) 48 50 6 85 49 50 9 50 50 7 51 50 6 52 50 8 53 50 4.3 54 50 7 55 50 40 56 50 9 57 50 6.9 58 50 4 59 50 37.2 60 50 3 61 50 2.9 62 50 12.9 P1 -time 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 P2 -time 0.00160 0.00371 0.00535 0.00675 0.00862 0.00963 0.01127 0.02062 0.02273 0.02434 0.02528 0.03398 0.03469 0.03536 0.03838 P3 -time 0.02960 0.03171 0.03335 0.03475 0.03662 0.03763 0.03927 0.04862 0.05073 0.05234 0.05328 0.0619B 0.06269 0.06336 0.06638 P4 - time P5 -time 0.12060 0.14860 0.12271 0.15071 0.12435 0 15235 0.12575 0.15375 0.12762 0.15562 0.12863 0.15663 0.13027 0.15827 0.13962 0.16762 0.14173 0.16973 0.14334 0.17134 0.14428 0.17228 0.15298 0.18098 0.15369 0.18169 0.15436 0.18236 0.15738 0.18538 Direction - Upstream Towards Fan Cooler Flow Element Pipe Area (sq in) Length (ft) 47 50 2.75 46 50 3.667 45 28.89 6.438 44 28.89 3.667 43 28.89 3.667 42 28.89 5.625 41 28.89 2.25 40 28.89 2.25 P1 -time 0 0 0 0 0 0 0 0 P2 -time 0.00064 0.00150 0.00301 0.00387 0.00472 0.00604 0.00657 0.00709 P3 -time 0.02864 0.02950 0.03101 0.03187 0.03272 0.03404 0.03457 0.03509 P4 -time 0.11964 0.12050 0.12201 0.12287 0.12372 0.12504 0.12557 0.12609 P5 -time 0.14764 0.14850 0.15001 0.15087 0.15172 0.15304 0.15357 0.15409 Direction - Downstream Towards Throttle Valve Flow Element 48 49 50 51 52(*) 53(*) 54 55 56 57(-) 58 59(#) Delta-Time (s) 0.00160 0.00211 0.00164 0.00140 0.00187 0.00101 0.00164 0.00936 0.00211 0.00161 0.00094 0.00870 Force (Ibf) 818.5289792 1075.439535 836.4529715 716.9596898 675.956078 363.3263919 836.4529715 4779.731265 1075.439535 583.0121173 477.9731265 3596.201955 Impulse (Ibf-s) 22.91881142 30.11230697 23.4206832 20.07487131 18.92677018 10.17313897 23.4206832 133.8324754 30.11230697 16.32433928 13.38324754 100.6936547

FAI/03-07 Page 1-3 of 1-5 Rev. 1 Date: 03/06103 60 61(-) 62 0.00070 0 00068 0.00302 stream Towards Fan Cooler Flow Elem Delta-T (s) 47 0.00064 46 0.00086 45(!) 0.00151 44($) 0.00086 43 0.00086 42(1) 0.00132 41(!) 0.00053 40(!) 0.00053 358 4798449 245 0340783 1541.463333 Force (Ibf) 328 6065245 438 1818638 344.8679016 196.4322142 196 4322142 278 250345 111.300138 111.300138 10 03743566 6 860954192 43.16097333 Impulse (Ibf-s) 9.200982686 12.26909219 9.656301244 5.500101998 5.500101998 7.791009659 3.116403864 3.116403864 Notes: (*) - denotes the flow element as a 45-degree elbow (#) - denotes the flow element as a 36-degree elbow (!) - denotes the flow element as a reducing tee (S) - denotes the flow element as a flow control valve

FAI/03-07 Page 1.4 of l-5 Rev. 1 Date 03106/03 POINT BEACH CFC2D INPUTS Wave Speed (C) - Rise Time = Duration = Peak Pressure - Area (IS ine) Area (65 line) Area (2 5 line) Trans Coetf (elbows). Trans Coelt (8" x B-) - Trans Coeff. (6-x 2 5) = Direction - Downstream Towai 4274 0 028 0147 286 50 28 89 4 79 1 =20C7/(C7+C7+C8)

2'C8/(C8+C8+C9) its sec sec psia sq In sq In sq In Rate

=C6tC4 psVsec Flow Element 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Pipe Area (sq In) 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 Length (lt) P1 -time 6 85 9 7 6 8 43 7 40 9 6 9 4 37 2 3 29 129 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 P2 -time =C17/C3 =(C17+C18)/C3 =(C17+C18+C19g)C3

  • (C17+C18+C19+C20)tC3

=(C1 7+C18+C1 9+C20+C21 )/C3 =(C17+C18+C19+C20+C21+C22)/C3 -(C1 7+C18+C19+C20+C21+C22+C23)tC3 =(C1 7+C18+C19+C20+C21 +C22+C23+C24/C3 =(C17+C1 8+Cl9+C20+C21+C22+C23+C24+C25)tC3

  • (C17+C1 8+C19+C20+C21+C22+C23+C24+C25+C26)tC3

=(C1 7+C18+C19+C20+C21 +C22+C23+C24+C25+C26+C27YC3

  • (C17+C1 8+C19+C20+C21+C22+C23+C24+C25+C26+C27+C28)/C3

=(C17+C18+C19+C20+C21+C22+C23+C24+C25+C26+C27+C28+C29)/c3 =(C17+C1 8+C1 9+C20+C21 +C22+C23+C24+C25+C26+C27+C28+C29+C30)/C3 =(C17+C18+C19+C20+C21+C22+C23+C24+C25+C26+C27+C28+C29+C30+C31)/C3 P3 -time =E17+C4 =E18+C4 =E19+C4 .E20+C4 =E21+C4 =E22+C4 =E23+C4

  • E24+C4
  • E25+C4

=E26+C4 =E27+C4 =E28+C4 =E29+C4

  • E30+C4

=E31+C4 P4 -time =El7+(C5-C4) =E18+(C5.C4) =EI 9+(CS-C4) =E20+(C5-C4) =E21 +(C5-C4) =E22+(C5-C4) =E23+(C5-C4) .E24+(C5-C4) =E25+(C5-C4) =E26+(C5-C4) =E27+(CS-C4) =E28+(C5-C4) =E29+(C5-C4) =E30+(C5-C4) =E31+(C5-C4) P5 -time =E17+C5 =E18+C5

  • E19+C5

=E20+C5 =E21+C5 =E22+C5 =E23+C5 .E24+C5 =E25+C5 =E26+C5 =E27+C5 =E28+C5 =E29+CS -E30+C5 =E31+C5 Direction - Upstream Towards Flow Element 47 46 45 44 43 42 41 40 Pipe Area (sq In) 50 2.75 50 3 667 288 9 6 438 28 89 3 667 =C8 3 667 =C8 5 625 =C8 2 25 -C8 2 25 Length (ft) Pt -time 0 0 0 0 0 0 0 0 P2 -time

  • C36/C3
  • (C36+C37)/C3

=(C36+C37+C38)/C3

  • (C36+C37+C38+C39)/C3

=(C36+C37+C38+C39+C40)tC3 =(C36+C37+C38+C39+C40+C41)/C3 =(C36+C37+C38+C39+C40+C41 +C42)1C3 =(C36+C37+C38+C39+C40+C41 +C42+C43yc3 P3 -time .E36+C4 =E37+C4 =E38+C4 .E39+C4 .E40+C4

  • E41+C4
  • E42+C4

=E43+C4 P4 -time .E36.(C5-C4) .E37.(C5-C4) =E38+(C5-C4) =E39.(C5-C4) =E40.(C5-C4) =E41+(C5-C4) =E42+(C5-C4) .E43.(C5-C4) P5 -time =E36+C5 =E37+C5 =E38+C5 =E39+C5 =E40+C5 =E41+C5 =E42+CS .E43+C5 Direction - Downstream Towai Flow Element Delta-TIme (s) 48 =E17 49

  • E18-E17 50

=E19-E18 51 =E20-E19 52(-) =E21-E20 53(-)

  • E22-E21 54
  • E23-E22 55
  • E24-E23 56

=E25-E24 57(-)

  • E26-E25 58

=E27-E26 Force (Ibf) Impulse (Ibl-s) =B47-F6-B17 C47-C4

  • B48-F6-B18

.C48-C4 =B49-F6-B19 C49-C4 =B50-F6-B20 =C500C4

  • B51 F6-B21*COS(45-PI(/180) =C51*C4

=B52-F6"B220COS(45"P1(I180) =C52-C4

  • B53-F6-B23

=C53-C4 .B54-F6-B24 =C54-C4

  • 855-F6-B25
  • C55-C4

=B56-F6-B26-COS(45-PIO/180) *C56-C4 =B57-F6-B27 =C570C4

FAI/03-07 Page 1-5 of 1-5 Rev I Date: 03/06/03 59(#) 60 61(-) 62 =E28-E27 .E29-E28 =E30-E29 =E31-E30 =B58'F6-B28'COS(36-Pl(y18o) =C58-C4

  • B59-F68B29
  • C59sC4

=B60¶F6-B30-COS(45SP(yI18O) =C60-C4 =B61-F6-B31 =C61 C4 Direction - Upstream Towards Flow Elem Delta-T (a) 47 =E36 46 =E37-E36 45(l)

  • E38-E37 44(S)

=E39-E38 43 =E40-E39 42(1)

  • E41-E40 41(1)

=E42-E41 40(l) =E43-E42 Notes: () - denotes the flow element as (t) - denotes the flow element a: (t) - denotes the flow element as ($) - denotes the flow element at Force (Ibt)

  • B65-F6-B36

=B66-F6-B37 =B67-F6-B38C1 1 =F6-B68-B39C1 1 =B69-F6-B40C1 1

  • 870-F6-B41tCt 1CI2

=B71-F6-B42-C11-C12 =B72-F6-B43'C11*C12 Impulse (Ibf-s) =C65 C4

  • C66-C4

=C67-C4 =C68-C4 =C69-C4 =C70-C4 =C71-C4 =C72 C4}}

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