ML20064D932
| ML20064D932 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 09/30/1982 |
| From: | EBASCO SERVICES, INC. |
| To: | |
| Shared Package | |
| ML20064D909 | List: |
| References | |
| RTR-NUREG-0737, RTR-NUREG-737, TASK-2.D.1, TASK-TM NUDOCS 8301040791 | |
| Download: ML20064D932 (40) | |
Text
.. . . , . _
1 1
l LOUISIANA POWER & LIGHT WATERFORD STEAM ELECTRIC STATION UNIT NO. 3 4
ANALYSIS OF PRESSURIZER SAFETY VALVE DISCHARGE PIPING i
i NRC NUREG 0737 ITEM II D.1 l
Prepared by: EBASCO SERVICES INC. .
2- WORLD TRADE CENTER NEW YORK, N.Y. 10048 l
l l September, 1982 O
8301040791 821229 PDR ADOCK 05000382 A PDR
- . - . . _ . - . - ~_ .. _ _ _ _ _ . .- __ _ _ _ _ _ _ . _
1 r
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TABLE OF CONTENTS Pane i
- 1. INTRODUCTION 1 ,
'i
- 2. SYSTEM DESCRIPTION 2
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, 3. DESCRIPTION OF ANALYSIS 6 j
- 4. CONCLUSIONS 11 ,
- 5. APPENDIX l
1 6. REFERENCES 38 l
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1.0 INTRODUCTION
[} This report describes the study performed to evaluate the adequacy of the pressurizer relief piping and its supports / restraints for the Waterford Steam Electric Station Unit No. 3, as required by NUREG 0737 Item II D.1.
The pressurizer safety relief valve discharge piping was designed for a combination of PIPE SHOCK /RELAP3 hydrodynamic loads. Later, however, this piping and supports / restraints system had been evaluated for the fluid forces calculated (2) using RELAP4/MDD6 and CALPLOITII computer codes. Therefore, the approach taken in the evaluation is to redevelop the hydraulic loads on the piping utilizing an EPRI verified computer code and to compare these forces with those previously computed. The hydraulic analysis is therefore, performed using the RELAP5/ MOD 1(
thermal-hydraulic computer program and post-processed by the CALPLOTF III computer code to estimate the fluid forces. The planned approach is con-sistent with the suggestions contained in the EPRI PRR Safety and Relief Valve Test Program Guide for Application of Valve Test Program Results
(} to Plant Specific Evaluations ( .
The hydrodynamic loads on the pressurizer relief piping system are induced by the opening of one or both of the spring loaded, self ac-tuated safety relief valves (SRV). Actuation of these valves allows discharge of high pressure steam from the top of the pressurizer into the quench tank via the connecting discharge piping causing pressure and momentum transients throughout the system. These transients result in significant time varying unbalanced forces in each straight segment of the piping until steady flow is achieved.
The time histories of the discharge loading are determined throughout the system by employing the hydraulic model described in this report.
This hydraulle model is suitabic for execution with the RELAPS computer p rogram. Forces on each pipe segment are computed by a post processor code, CALPLOTF III, described in Appendix A to this report.
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O This post processor computer program has been written by Ebasco to develop forces from the output of RELAP5 for each of the piping segments. The necessity for writing the post processing code arose from the unavailability of a similar code which EPRI is developing for interfacing with REIAP5.
2.0 SYSTEM DESCRIPTION The pressurizer pressure relief piping system for the Waterford Steam Electric Station ~ (SES) Unit No. 3, consists of two spring loaded self actuated Dresser Safety Valves (Type: 31709 NA ), the intercon-necting discharge piping, and the quench tank.
The geometric configuration of the piping system is shown in Figure 2.1.
Also shown in the figure are the design pressure and temperature of the various piping segments, and the location and type of supports and restraints.
The two safety valves are each independently connected to the pressurizer nozzles. The valves discharge into eight in. lines. The two discharge lines merge into a common header which connects to a relief tank. The safety valves are set to discharge saturated steam at 2485 psig with
+ 37. margin (2574.25 psia) which is typical of experimental results re-ported in reference 5. The discharge orifice area is 4.34 in. .
The valve is assumed to open linearly in time. The opening time is 12 - 18 milliseconds according to EPRI results. However, for conservative estimate of forces,12 milliseconds opening time is considered in the analysis. Each valve has a ASME rated capacity of 504,874 lbs/hr and maximum actual capacity of 575,371 lbs/hr. , both at 37. accumulation.
In the event d an abnormal transient causing a sustained increase in pressurizer pressure at a rate exceeding the control capacity of the O
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O gresseriser serar. a hish eress re tri,1evet is reached hich tries the reactor and at the set pressure the safety valves open as needed to relieve the overpressure.
Table 2.1 provides a list of the transients which can result in opening of SRVs. The categories of transients listed are representative of a larger number of specific transients which are des::ribed in detail in reference 6.
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- TAB 12 2.1 WATERPORD SES UNIT 3 Calculated Pressuriser Safety Valve Inlet Pluid Conditions During Pressurization Transients Peak Pressure Pressurisation Pressoriser Ramp Rate Transient Pluid Pressure (PSIA) (PSI /SEC) Condition Loss of Condenser vacuum (IDCV) 2555 72 Steam IDCV with Pailure of a Pressurizer Level Measurement Channel Associated with the Pressurizer 14 vel Control System (PICS) 2557 104 Steam Feedwater System Pipe Breaks 2688 96 Steam Uncontrolled CEAW from a Suberitical i
or Iov Power Condition 2559 45 Steam Uncontrolled CEAW at Power 2534 33 Steam CEA Ejection 2574 93 Steam CVCS Melfunction (Increase in RCS Inventory) 2539 62 Steam Sequence of Events for Pressurization Transients Which Actuate Safety valves TIME, SECONDS Pressurizer Transient Uncontrolled CEAW From CVCS loss of IDCV Feedwater Suberitical or Uncontrolled Malfunctior Event During Condenser & System Pipe or Low Power CEAW at CEA (Increa se ir Transient Vacuun SF Breaks & Condition Power Ejection Inventory)
, Event Initiation 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Reactor Trip:
- 1. High Power - - - - -
0.5 -
- 2. High Pressurizer Pressure 8.2 8.1 15.4 69.5 - -
1641.5
- 3. DNBR - - - -
42.8 - -
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Opening of Safety valve 9.2 9.0 15.9 72.2 45.9 2.3 1643.9 Peak Pressure 10.6 11.0 20.8 73.7 46.6 3.1 1644.2 Safety Valve closing 13.0 12.8 25.4 95.7 50.0 5.0 1646.4 0
5
()
3.0 DESCRIPTION
OF ANALYSIS HYDRAULIC MODEL The pressurizer pressure relief piping system shown in Figure 2.1 is modelled using RELAP5/ MOD 1 pipe components consisting of a net-work of fluid control volumes connected by junctions for pipe segments, and single junction components for valves. The desig-nation of the control components is given in Figure 3.1. The safety valves are represented in the model by ' valve' components. The transient opening characteristics of the valve are modelled through use of the control system feature available in the code. The opening characteristics included the time at which valve opened and the valve flow area versus time. The valve effective flow area change is assumed to be linear. The piping network consisting of pipe lengths, bends, and area changes are accounted for, and appropriate dimensions, loss coefficients and piping roughness applied. To preserve adequately the pressure wave shapes in the bounded pipe segments in the model, and following the recommendation that significant differences in control volume length be avoided, the Waterford SES Unit 3 system is modelled with control volumes of between 0.5 and 1.0 feet in length.
The thermodynamic properties in each control volume and the flow con-ditions at each junction are computed as a function of time following valve actuation utilizing the RELAPS/ MODI computer program. This hydr-aulic information is post processed by CALPLOTF III program to generate forces on each segment of piping. The piping segments on which the hydrodynamic forces are computed are shown in Figure 3.2.
(}
6
The hydrodynamic force calculations have been performed for the 3 pressure relief piping network assuming simultaneous opening of the two safety relief valves. Opening time for SRV is chosen to be 12 msec.
STRUCTURAL MODEL A linear elastic structural model which utilizes the computer program PIPESTRESS 2010 (0) has been constructed for the piping system. The PIPESTRESS 2010 computer program performs a generalized response analysis of the system which is subjected to the simultaneous application of the transient hydraulic loadings in each of the piping segments. Generalized response analysis is of course known to produce conservative results in terms of both stresses in the piping system and support / restraints loads. A particular feature of this program is that it retains information in memory that enables it to perform Os V selected model superposition time history analysis of piping segments indicated to be near to or at overstressed conditions, without performing time history analysis of the entire system. Because PIPESTRESS 2010 automatically prints out stress and stress ratios at each point in the piping system, and is reasonably economical to run, it is ideal for determining whether there is potential for problems in the existing design.
If stresscs in the piping and reactions on supports / restraints as con-servatively predicted for the SRV actuation by the generalized response method, when combined with the previously calculated stresses and reaction loads from the appropriate loading combinations, are below or near the allowable values, then the existing system is demonstrated to be adequately designed for SRV operation.
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() In locations where reaction 1 cad or piping stresses exceed the allowables by a significant margin,a reduction in conservatism can be effected by utilizing the selective time history option.
If stresses or reaction loads are then computed to be in excess of allowable values, again when combined in the proper com-binations with dead weight, pressure, and seismic (OBE) loads, this is a positive indication that the system as presently con-figures may require modification.
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PRESBURIZER r18
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OUENCH TANK Figure 3.1 DIAGRAM OF TIE RELAPS/ MODI
' INPUT F0 DEL- Waterford SES Unit 3 (Numbers refer to RELAPS components)
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OUENCH TANK Figure 3.2 PRESSURIZER RELIEF SYSTEM - Waterford SES Unit 3 (Numbers refer to CALPIDTF III Piping. Segments) w-
4.0 CONCLUSION
S The hydraulic loads resulting from the simultaneous actuation of all the safety valves as computed from a previous analysis (2) had been employed in the design of the pressurizer relief piping and its supporting system. Hence comparing the hydraulic forcing functions from the new analysis to those which resulted in the system design can provide a quick indication of whether the design is adequate. Consistent with this approach of comparing results of the present analyses with the prior analyses, the transient force-time histories have been computed at the same location as chosen in Reference 2. The values both for minimum and maximum forces computed utilizing RELAP5/CALPLOTFIII and RELAP4 0)/
CALPLOTFII ( thermohydraulic and postprocessor computer codes and the results of a PIPESHOCK ( } analysis are given in Table 4.1. The valve opening time assumed was 15 milliseconds for RELAP4 calculations ( }.
Additionally, the typical transient force-time histories obtained from the results of RELAP5/ MOD 1 and RE1JP4/ MOD 6 thermohydraulic computer codes are shown in Figures 4.1 to 4.9. Each leg number desig-nation referred to in these figures corresponds to the same pipe seg-ment in the system. The forcing functions are evaluated at each change of direction in the piping. Area changes in the piping are accounted for in the force calculations. The direction of the forces is along the axis of the piping segments with positive force being defined opposite to the flow existing in the SRV line. The RELAP5 I
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force-time history was terminated at 0.3 seconds, since the major
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forces on the upstream and near downstream piping are observed to occur within this time interval ( ).
The typical transient hydraulic forces shown in Figures 4.1 to 4.9 represent:
- 1. Horizontal force acting on the first leg connected to pressurizer-Leg 1
- 2. Vertical force acting on the first upstream leg of the safety valve R-1503 A. - Leg 2
- 3. Horizontal force acting on the first pipe segment downstream of the safety valve R-1503 A. - Leg 3
- 4. Horizontal force acting on the second pipe segment downstream
, of the safety valve R-1503 A. - Leg 4
- 5. Horizontal force acting on the long straight segment past the second elbow in the same line - Leg 5 l 6. Horizontal force acting on the straight segment past the third l
elbow in the same line - Leg 6
- 7. Vertical force acting on the straight segment connecting common header through a reducer - Leg 7
- 8. Horizontal force acting on the straight segment past the first elbow in the common header - Leg 8
- 9. Horizontal force acting on the straight segment past the second elbow in the common header - Leg 9 The positive peak values of the forcing functions obtained from RELAP5 are in l
l general higher than those of RELAP4 results but are less than the values com-l puted by PIPESHOCK.(11) The only exception is pipe segment #7 where there is an area change. PIPESHOCK (11) code calculates the forces induced by the shock l
l wave travelling in the piping downstream of a fast opening relief valve. The l
l l 12
code has been written to handle only straight pipe lengths with bends. Area changes and tees cannot be handled by the code.
The primary reason for the differences in results between RELAP4 and RELAP5 is their relative capability to correctly predict the steep pressure waves.
RELAP4/ MOD 6 is a one-dimensional homogeneous equilibrium fluid-flow analysis program. It is designed to analyze the thermal-hydraulic response of light water reactors to LOCA conditions. In RELAP4, due to limitations in the number of possible piping volumes, longer volumes are required to model the system. The longer the volumes, the poorer the ability of a code like RELAP to faithfully reproduce the steep pressure waves which characterize relief valve transients. The alternative of specifying a choking option as a means of overcoming the piping volume limitation generates an averaging process which leads to an erroneous prediction of pressures.
O RELAP5/ MOD 1 is an entirely new computer program which calculates thermal-l hydraulic transients with a complete two-fluid, two-velocity, two-temperature description. In addition, the code permits the use of a large number of I
i control volumes. The maximum length of fluid piping volume used in the present model is 1.06 ft compared to 4.4 ft. used in RELAP4. EPRI has demonstrated that the predicted results of RELAPS compare favorably with test results .
The attempt to predict the forces for the EPRI valve test piping system using RELAP4/ MOD 6 has clearly demonstrated underprediction of the forces . The dif ferences in results are also attributable to the dif ferent valve opening times used in these two predictions. It is therefore, concluded that the results of RELAP5 are more realistic than RELAP4 predictions.
l 13
4 O Since the piping was initially designed for a combination of PIPESHOCK/RELAP3 results ( } , it could be anticipated that the piping system is adequate even for the loads calculated with RELAPS code since these loads are less than PIPESHOCK results. To indeed verify such adequacy a linear stress analysis of the piping system has been performed.
Several load combinations (see Table 4.2) must be considered when determining the adequacy of the present Waterford Unit 3 pressurizer relief piping system for SRV discharge loading. For the purpose of this analysis, the most severe load combination, the upset condition, has been chosen.
The results of stress analysis of the complete system using PIPESTRESS 2010 (8) code with the generalized response method option indicate that they exceed the allowable values. Therefore, the selective time history option is used in PIPE-STRESS code predictions. The results indicate that the stresses in Class 1 piping, upstream of safety valve, are within the code allouable ( }. The calculated dynamic hydraulic loads on piping supports / restraints based on the force-time histories generated using RELAP4 and RELAP5 codes are given in Table 4.3. The results of piping stress analysis for the upset conditions are listed for the piping support / restraint node points in Table 4.4. The ratio of combined stress to allowable stress for all the points is less than unity. The nonsafety related portion of piping, downstream of SRV also meets the applicable code stress criteria ( . Consequently, the design of the pressurizer relief piping is addquate as originally proposed and no changes to the system need be mde. Since the piping restraints were originally designed for a combination of forces calculated by RELAP3 and PIPESHOCK, it was expected that their design will be adequate for the newly calculated RELAPS results. Subsequently, the restraint design was reviewed and found acceptable. The loads on the pressurizer 14
1 O nozzle and SRV valve outlet flange have also increased with the revised forcing functions. These results have been forwarded to CE and Dresser in order to verify that these loads are within the allowable values.
The backpressure calculated for steady flow following the discharge of both the safety valves is given in Table 4.5.
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O V TABLE 4-1 FLUID FORCES FOR SRV ACTUATION PIPE SEGMENT NO. MAXIMUM FORCE MINIMUM FORCE RELAP4 PIPE SHOCK RELAP5 RELAP4 RELAP5 1 569 __ 1639 -132 -628 2 1512 1938 -189
_, -405 3 2303 8350 3546 -473 - 54 4 1732 8350 3822 -750 - 95 {
5 3598 8350 7509 301. l -302 6 2279 8350 6883 -668 360 '
p 7 979 3760 6445 -492 -1035 d 8 3099 12000 10376 -2265 -2308 a
10 6818 12000 7221 -7502 -3509 11 583 1627 - 191 -895 12 1948 2595 -446 -743 '
13 3798 8350 5929 -397 -140 14 1192 8350 3556 -201 -84 15 1239 8350 3842 -222 -105 16 3140 8350 6839 -943 -305 17 1947 8350 5956 -900 -917
= - - - . . _ . _ - . . . - . . - . - - -- - - - - - -- ----
O 25
TABLE 4.2 LOADING COMBINATIONS FOR ASME CODE CLASS 1 COMPONENTS OTHER THAN VALVES Condition Design Loading Combination (s)
Design PD Normal (b) PO+DW Upset PO+DW+0BE PO+DW+0BE+DU Emergency PO+DW Fault ed PO+DW+SSE+DF
- (a) Legend
PD = design pressure O
PO = operating pressure DW = dead weight OBE = operating basis earthquake SSE = safe shutdown earthquake DF = dynamic system loadings associated with a postulated pipe rupture (LOCA)
DU = other transient dynamic events associated with the upset plant condition (e.g., valve opening and/or c los ur e).
(b) As required by ASME Code Section III, Division I, other loads such as thermal transient, thermal gradient, and anchor point displacement portions of the OBE require consideration in addition to the primary stress producing loads listed.
O 26
TABLE 4 l
RELAP4/M006 RELAP5/ MODI NOS. POINT NO. IYPE NNAMC TOTAL LOADING DYNAMIC i
TOTAL LOADING WDRAULIC LOADS NORMAL & UPSET HYDRAULIC LOADS NORMAL & UPSET (1bs) (1bs) (1bs) (Ibs) 1 2102 S.H. -
-686 -686 2 2101 Y-SNUBBER
- 1336 +3143 + 1925 +3731 3 21 AXIAL SNUB- t 3821 t8169 t 5894 110241 BER 4 1800 Z-SNUBBER + 3522 +4456 + 6773 +7707 5 16 Y-SNUBBER t 1151 t1719 t 1830 +2398 6 15 Z-SNUBBER + 3692 +4222 1 8718 t9247 7 14 X-RESTRAINT + 3549 +4094 t 8999 19544 1
y 8 1300 S.H. -
-557 -557 9 6 Y-SNUBBER t 6896 t7366 t 8796 19266 10 555 S.H. -
-1768 -1768 11 4 X-SNUBBER + 7240 +7933 + 8368 t9060 12 4101 S.H. -
-1534 -
11534 13 41 AXIAL SNUB- t 3292 15451 + 4089 16249 BER 14 39 Y-SNUBBER t 237 t3924 t 5853 t6676 15 37 Z-SNUBBER 12832 13129 t 5734 16031 16 34 S.H. -
- 604 -
- 604 17 33 Y-SNUBBER +2154 t1670 t2960 t3445 18 32 Z-SNUBBER f4734 t5319 18056 t8641 19 31 X-RESTRAINT t5164 15974 t11656 t12466 20 '3001 S.H. --
- 447 -447 21 18 S.H. -
- 451 -451
- S.H. - Spring Hanger
..I
e TABLE 4.4.
STRESSES IN WATERFORD 3 PRESSURIZER RELIEF LINE RESULTING FROM UPSET CONDITIONS S.NO. DATAPOINT CLASSIFICATION OF COMBINED STRESS DUE TO ALLOWABLE RATIO PIPING PRESSURE + WEIGHT + OBE STRESS
+SRV TRANSIENT IAADS (Psi) (Psi) 1 2400 Safety Class 1 9222 23843 0.387 2 27 19933 23843 0.836 28 "
3 23498 23843 0.986 4 48 23035 23843 0.966 5 46 19671 23843 0.825 45 "
6 15402 23843 0.646 4400 "
7 6451 23643 0.396 8 2102 Non-sa fety B31.1 8998 22560 0.339 9 2101 7669 22560 0.340 10 21 6913 22560 0.307 11 1800 6731 22560 0.298 12 16 11110 22560 0.493 13 15 9860 22560 0.437 14 14 10387 22560 0.460 15 1300 10030 22560 0.445 16 6 8998 22560 0.399 17 555 10232 22560 0.454
" 0.355 18 4 8013 22560
" 22560 0.419 19 4101 9441 20 41 10891 22560 0.483
" 8821 22560 0.391 21 39
" 22560 0.368 22 37 8309
" 22560 0.335 23 34 7553
" 12034 22560 0.533 24 33
" 22560 0.429 25 32 9679
" 9854 22560 0.437 26 31
" 9447 22560 0.419 27 3001 28 " 6338 22560 0.281 18
" 22560.
29 38 10160 0.450 28
- r -w-- --. - -, ---,-~--n,- -
i TABLE 4.4 (Cont'd)
STRESSES IN WATERFORD 3 PRESSURIZER RELIEF LINE RF.SULTING FROM UPSET CONDITIONS S.NO. DATAPOINI CLASSIFICATION OF COMBINED STRESS DUE TO ALINABLE RATIO PIPING PRESSURE 4 WEIGHT + OBE STRESS
+SRV TRANSIENT LOADS (Psi) (Psi) 30 36 Non-safety B31.1 10889 22560 0.483 31 3400 "
10188 22560 0.452 32 3100 "
12714 22560 0.564 33 8 "
17244 22560 0.764 34 1 " '
13617 22560 0.604 i 35 5 "
10314 22560 0.457 36 7 "
10537 22560 0.467 37 12 "
9919 22560 0.450 1400 "
11091 22560 C.492 W
19 "
8902 22560 0.395 40 20 "
8763 22560 0.388 Piping has been analyzed and supported seismically.
1 0
29
O O O Attachment to LW3-1595-82*
l TABLE 4.5 WATERFORD SES UNIT 3 STEADY STATE BACKPRESSURE CALCULATIONS i
i SRV ACTUATION SRV DOWNSTREAM SRV FLOWRATE CAILULATED FLOWRATE PRESSURIZER PRESSURE (1bm/sec) Rated Flow rate ' Pressure (psia)
VALVE / PRESSURE (psia) i i
- 1) SIMULTANEOUS ACTUATION R 1503A/336.5 160.2 1.14 2574.25 0F BOTH SRV's R 1504B/342.3 160.2 1.14
- 2) ACTUATION OF ONLY R1503A/295.4 160.2 1.14 2574.25 ONE SRV-1503 A R1504B/118.5 0.0 0.0 i $
) 3) ACTUATION OF ONLY R1503A/120.2 0.0 0.0 2574.25 ONE SRV-1504B R1504B/305.3 160.2 1.14 1 Steady State values at the end of 0.3 see of EELAP5 run 2 SRV (Dresser 31709NA) Rated Flow Rate (ASME) is 504,874 lbm/Hr (Rev. 16) 1 w
l N D
2 m
O a
- 5. APPENDIX l . DESCRIPTION OF CALPLOTFilT.
O l
l O
31 l
I Mathematical Model The CALPLOIFIIIcomputer code has been written to convert the transient flow conditions calculated in a piping system by the RELAPSPOD 1 Computer code into transient forces on the piping system. Specifically, CALPLUTFIIIcalculates and plots the forces on straight lengths of pipe between changes in pipe direction (bends), or between a change in direction and a pipe break. The derivation of the equations used in the code are given below.
I-1 Straight Lengths of Pipes Between Directional Changes
, The force on a streight length of pipe between direction changes .
(Figure B.1) is calculated using the momentum equation:
( 4- Ypay =
V(pV=d)+h Y (pav) (1) cv ca k cv .
If t.he gravity terin is assumed negligible, the following equation results:
V (pdv)
] $= Y (pY = d) + h (2) es k cv )
Since the force on the straight pipe length only exists in one dimension, the above equation can be written in a scalar form:
F, = V (pV
- dA) + Vpdv (3) cs key )
' ~
Since the RELAPS }DD 1, Computer code ca1culates,the ,
pressures and the flowrates at different physical positions in the piping system, it is necessary to subdivide a piping length into two control volume types for application of the momentum equation. The first division creates the pressure control volumes. The divisions for the pressure control volu=cs are the positions in the pipe length where the pressures are calculated by the computer code, and serve as the boundaries across which the control volume surface forces are calculated. The second control volume divisions are due to flow conditions. The boundaries of the flow control volumes are located at the pipe length locations where flows are calculated by the computer code. The forces in the pipe length which are due to the rate of efflux of momentum across a control volume O and the change of momentum in a control volume are calculated using the flow boundaries as flow control volume divisions.
32
O The re it t force on the fi id cre the he d rF of the Pre control volumes 1, 2, and 3, shown in Figure B.1, are:
re F
37
=
-(Pg - P,) AA + h '.(4 )
F S2
Bb+ a (A,- Ag ) + R2 (5)
F =
(P B - + (0) 33 a) AB 3 The net surf ace force on the straight pipe length is obtained by summing equations B4, B5, and B5:
F + F; + F33 =
g+R2 +I (7) 37 3 3 Fg = R (8)
Therefore, the force on the straight pipe length due to surface forces is equal to the net normal and chear stres'ses on the pipe wall length.
The right side of equation B3 can now be evaluated for each of the fic.v l control volumes A and B:
l F =
P2 Y2 A +
I A
l 31 A Bt
-P 2 Y2 A A
8A B
F "
- AB J(10)
S2 g Be Since the RELAPS computer code calculates non thermal equ11brium conditions for two phase flow conditions and allows the two phases to possess different velocities, the parameters of equations (B9), (B10) are defined as:
- #gA gA"A ^A (11)
A 1A 1A ( A
(# 1B 1B B #gB gB"B b .(12)
- Y 2
- nY (1-"2) + #g2 2"2 (13)
O 33
O s<-mina eeustions 39 nd >1o. nd usine eeustion is, the net f1uid force on the pipe length can be obtained:
-3AA SA, K = -7 3
-R
gt h -
gt M N If the straight length of pipe considered is bounded by a directional change and an open end, a break, the forces obtained using equation ill must be modified to account for the force developed at the pipe exit plane. Consequently, using the momentum equation, the force on the straight pipe Icngth shown on Figure B.2, for unchoked break flow, can be written as:
2 -
-P 2 Y2 A 8M
" 2 A E -
A (15) unc 3 8t a
If choked break flow is determined to exist by the fluid transient i
computer code, then equation B15 must be modified to account fer the pressure unbslance that occurs at the pipe exit plane. A rederivation of the equation for the straight pipe length for this case results in the following relation:
-p 2 Y2 'IA A K =
-(P2 - P,) A2 A AA ch g 2 gg (36) or K
h
= K une
~
I 2~#) a A2 (17)
{
l where:
l 2 2
~P2V2 V
Py = P + PA A ~ -
AP g -
P - #2 2 2 PA+ AA 2g 2g -(19)
O 2 2 2
- ~
AA #
1A 1A ( + #gA SA A A (20) 34 n---- =
() Nomenclature A flow area B body force of a control volume F, surface force resultant on a control volume 3 gravitational constant K force of fluid on piping M control volume flowrate F pressure P, pressure outside pipe control volumes R normal and shear stresses in a control volume t time v volume of a control volume 7 velocity of fluid in a control volume O
Greek Letters p density in control volume a void fraction i
Subscripts acc acceleration f friction ch choked flow ce control surface cv control volume el elevation unc unchoked 1 liquid O e.,s 35
O O O Figure 5 1 m VOL.1 mIm VOL. 2 m
's, VOL. m I
,' W . l l
i
! 1 ! ! j i 1 2 1 l
4 4
(, l !
i t -
l- I I i , + FORCE
, - l m 1 ! 8 e
i ! ; - i I I e l j A !
E i l
l B ]
l 1
1
, . I 4 i
I I
! V
f ,
m i LEGEND:
- - - PRESSURE BOUNDARY
! ------ FLOW BOUNDARY l
4 1
l
- i
O ls 8 I;l1!
2 -
,,l !!
m- m, 2
L O -
V Y R
A m7 D Y N R 2 E U A C O D 5 R B O e r
u O
F A
A E
R N
U O
g m, + U B i S F
l .;-li Ij I.l.'
^ S W m- E O R L P F D
N E -
G -
E -
L - -
1 L
O V (
,2 _
_ 2 l(; '
g ,i 1t b.
2, lg r i O
w~
\ii>;1 ,! II il i1
6.0 REFERENCES
O
- 2. Waterford Steam Electric Station Unit 3 - Dynamic Relief Valve Discharge Analysis of Pressurizer Relief Piping System, Applied Physics-Calculation Number 004, 3-E-9, May,1982.
- 3. Ransome V H, Wagner R J et al., RELAP5 Mod 1 Code Manual, Vol 1 & 2, EGG Idaho Inc. NUREG/CR 1826, EGG 2070 Draf t, Revision 2, Sept., 1981.
tion of Valve Test Program Results to Plant Specific Evaluations, MPR Assoc. Draft Report, February 1982.
- 5. Safety and Relief Valve Test Report, EPRI Safety and Relief Valve Test Program, Interim Report, April,1982.
- 6. Safety val _ye and Power Operated Relief Valve Inlet Fluid Conditions for CE Plants, EPRI Safety and Felief Valve Test Program.
- 7. EFRI, Application of RELAP5/M0D1 For Calculation of Safety and Relief Valve Discharge Piping Hjdrodynamic Loads. Interim Report March,1982.
i 8. User's Manual for Pipe Stress Analysis, PIPESTRESS PROGRAM 2010,
() G. Cohen, J. Chester, Ebasco Services Inc. , New York, June,1979.
- 9. RELAP4bHD6 - A Computer Program for Transient Miermal-Hydraulic Analysis of Nuclear Reactors and Reactor Systems, User's Manual, EG6G Idaho, Inc. CDAP TR 003, January,1978.
i
- 10. "CALPLOTFIII - A Computer Code to Calculate and Plot Forces", W J Krotiuk, Ebasco Services Incorporated, Applied Physics Procedure Nc. 4, February, 1982.
l 11. "PIPESHOCK - A Computer Code to Predict Shock Wave Conditions
- Downstream of a Relief Valve" W J Krotiuk, Ebasco, Applied Physics
, Procedure No. 4, December,1980.
i 12. Analysis of Pressurizer PORV and SRV Discharge Piping, St. Lucie Nuclear Power Plant Unit No. 1, Ebasco Services, Inc. , New York
! 13. Memo from J. Damitz/M. Parmar to K. Sathyanarayana, September 16, 1982.
- 14. Memo from J. Damitz/M. Parmar to K. Sathyanarayana, September 21, 1982.
l
- 15. Waterford Steam E1cetric Station Unit 3-Pressure Relief Valve Discharge Pip,ing Analys_is, Applied Physics-Calcular lon Number 001, 3-E-9, November, 1976.
- 16. Dresser, Industrial Valve and Instrument Division, order Control Drawing No. 3NC-047, Sheet l of 9. Rev. No. 6
(
i 38