ML20090M834
ML20090M834 | |
Person / Time | |
---|---|
Site: | Byron, Braidwood |
Issue date: | 09/30/1989 |
From: | Strauch P WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
To: | |
Shared Package | |
ML20034D376 | List: |
References | |
WCAP-12388, NUDOCS 9203250334 | |
Download: ML20090M834 (46) | |
Text
- . . . .-. - _ _. - . - _ . - . - . . _ _ _ - - _ . - _
WESTINGHOUSE CLASS 3 WCAP-12388 4
a EVALUATION OF THERMAL STRATIFICATION l FOR THE BYRON AND BRAIDWOOD UNITS 1 AND 2 RESIDUAL HEAT REMOVAL LINES P. L. Strauch
. September 1989 Reviewed by: A N/
D.'H. Roarty V Approved by:M/Or- S #
/ 5. 5,~Palustmy, Manager Structural Materials Engineering Work performed under shop veder BFLP-961 and filed under CAE-961/TDE-12.
WESTINGHOUSE ELECTRIC CORPORATION Nuclear and Advanced Technology Division
- P.O. Box 2728 Pittsburgh, Pennsylvania 15230-2728 nn.winne 9203250334 920316 gDR ADUCK 0500o454 PDR
TABLE OF CONTENTS Section Title Page
1.0 BACKGROUND
AND TRANSIENT ANALYSIS 1-1 g 1.1 . Description of the Genkai Phenomenon 1-1 1.2 Comparison of Genkai and the Byron and Braidaood Units b3 1.3. Development of Postulated Transient 1-4 2.0 STRESS ANALYSES 2-1 p 2.1 Piping System _ Structural Analysis 2I
'2.2 Local Stress Due to Non-linear Thermal Gradient 2-3 2.3 Stress Results 2-4 3.0 ASME SECTION 111 FAllGUE USAGE FACTOR EVALUATION 3-1 3.1' Code and Criteria 3-1 3.2 Previous Design Methods 31 3.3 Analysis for Thermal Stratification 3-1 3.4 Fatigue Usago Results 3-2 4.0 FAT!GUE CRACK GROWTH EVALUATION 4-1 4.1_ Method Description 4-1 42 Fatigue Crack Growth Results 42 -
5.0 --
SUMMARY
AND CONCLUSIONS S-1 REFERENCES 5-2 APPEND 1X A: THERMAL STRATlflCATION AfiM.YSIS A-1 n n.=in. io gg
. _ _- _ _ _ _ _ _ _ - - _ - - _--- l
SECTIDN
1.0 BACKGROUND
AND TRANSIENT ANALYSIS With the oiscovery of a crack in the Genkai Unit 1 Residual Heat Removal (RHR) suction linc in June of 1989, attention has been focused on the possibility of stratification occurring in the RHR suction lines. This incident led to the issuance of NRC Bulletin 88-08, Supplement 3: "Thermsl Stresses in Piping Connected to Reactor Coolant Systems." rn April 11, 1989. This report addresses tnis issue for the Byron and Braidwood Units 1 and 2 RHR suction lines.
The assessment begins with a detailed description of the Genkai phenomenon, and a ecmparison of the Genkai, and Byron and Braidwood RHR suction line configurations. This comparison is very important, because it will support conclusions on the likelihood of such a transient occurring at the Byrcn ano Braidwood Units.
A review is then provided of the overall approach used to assure that the structural integrity of the Byron and Braidwood RHR suction liner. will not be compromised within conservatively determined inspection intervals, should 5tratification occur, Detailed thermal, stress, fatigue, and fatigue crack growth analyses have been performed to assess the effects of potential stratification.
1.1 Description of the Genkai Phenomenon _
Around 9 a.m. on June 6,1988, there was an increase in the water flow into the drain sump in the reactor containment vessel of Kyushu Electric Power Company's Genkai Nuclear Poner Plant Unit 1 (PWR, 599 MWe), then operating at rated output, and a pool of water was seen on the floor. Manual operation for shutdown of the reactor was therefore started at 1:15 p.m. on the same day, and the reactor was brought to complete shutdown by 5:20 p.m.
'he fluid which leaked was the primary coolant, containing radioactivity. The water flow to the drain sumo, which normally is approximately one liter per en,w an in 11
hour, rose to about fifty liters per hour as of 11 a.m. on June 6. Although I
the amount of leakege was below Kyushu Electric's safety regulation level, the power company shut down the reactor as a precaution to investigate the source
- of the leakage. The amourt of coolant that leaked out ultimately reached about 1,100 liters, but there was no outside radioactivity. The leakage occurred in the RHR and Si lines attached to loop A. The plant started I initial commercial c,peration in October 1975.
Results of the inspection conducted by Kyushu Electric Power Company showed that the point of leakage was in the unisolable section of the branch line from the main primary coolant piping as shown schematically in figure 1-1. It .
was confirmed that the coolant leaked from a pinhole with a diameter of about one millimeter, near the welded section (elbow to straight horizontal pipe) of I the stainless pipe _(55 316TP), which has an outer diameter of P.6 inches and thickness of 0.81 inches.
I The cause of cracking was determined to be high cycle thermal fatigue l resulting from valve leakage. The section of the pipe was replaced and the plant was returned to power.
The cyclic leading which caused the cracking is believed to have occurred in ,
the following way:
i The isolation valve developed a packing leak, which allowed hot water from the main loop to flow down the vertical leg, and through the valve. The actual leakage' flow was small, and stratified at the top of the horizontal pipe - '
since it was hotter than the bulk water in the horizontal section of the pipe between'the elbow and isolation valve. The hot water reached the valve,-
werming it, and when the valve reached about 385'F the leakage flow stopped.
Once the stratified flow was cut off. the valvo temperature again cooled down and-the leak recurred. As'the stratified hot water reached tho valve again
. the cycle repeated. This led to a severe fatigue cycling which initiated and propagated the crack. This scenario was simulated in laboratory tests.
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i 1.2 Conca,rison of Genkai and the Byron and Braidaoed Units Although there are similarities between the Gonkai and the Byron and Braidaced RHR suction lines, there are differences which support the conclusion that a Genkai-type transient is unlikely to occur at B>ron and Braidaood. (A comparison is provided in table 1 1).
The study of the Genkai cracking incident showed that without leakage the hot water from the main loop was unable to reach the bottoin of the vertical pipe because turbulence was limited to about five feet from the main loop junction, for Byron and Braidwcod, the hot water is expected to reach the i
bottom of the vertical pipe, because the pipe is larger in diarneter (12 ss. 8 L
inches) and the vertical distance is much shorter (4 vs. 9 feet). The isolation valves in the Byron and Braidwood RHR lir.es are about a foot and 9 feet away from the vertical leg for loop l'and loop 3, respectively, as >
compared to 2-3 feet at Genkai. The schematic layouts for RHR lines at Byron and Braidwood are shown in figures 1-2 through 1-9.
, When a pipe (such as the RHR suction line) is connected to a larger diameter pipe (in this case the hot leg) with high veiocity turbulent flow, the
, turbuler.ce will penetrate into the smaller pipe. The distance of penetration depends on the flow velocity (Reynolds number) in the larger pipe, the-relative pipe inside diameters and the relative angle between the pipes. A number of experiments have been performed at Westinghouse and Nitsubishi Heavy Industries to obtain this information, and the results are summarized in figure 1-10.
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( ),a,c.e Even though strat4fication and cycling are unlikely at Byron and Braidwood, an assessment was carried out to quantify and evaluate the effects of postulated stratification on pipe integrity. . i 1.3 Development of Postulated Transient -
The development of a stratification transient for RHR suction lines began with the temperature profile epplicable to the Genkai plant, as obtained experimentally by Mitsubishi Heavy Industries. The transient at Genkai was due to intermittent valve leakage, which provided a path for hot water to be drawn into the RHR line from the main loop. At the bottom of the vertical ,
pipe, a stratified flow was established, with hot water filling the top 10 percent of the horizontal piping.
To establish a stratified flow transient for the Byron and Braidwood Units, a simplified, yet conservative, representation of the Genkai temperature profile was assumed to exist in the horizontal portion of each line. The saine-portion ,
of the pipe as at Genkai was assumed to be filled with leakage flow at Byron and Braidwood. The water from the loop connection to the horizontal piping was assumed to be at hot leg temperature due to loco flow turbulence, since '
this distance is about six pipe diameters. The water was assumed to stratify in the horizontal piping. The water in the bottom of the pipe was stagnant, and was assumed to cool by a conduction-limited mechanism. The stratified flow at the top of the pipe does not cool as quickly because of its flow, as shown in figure 1-11. This creates a rather large temperature difference between the top and bottom of the pipa, which is maximized at about four feet -
i from the start of stratificatier. As the flow continues, it gradually loses heat to the stagnant bulk fluid, and the top to bottom of pipe temperature -
difference-diminishes. The development of this temperature profile is provided in detail _in Appendix A.
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TABLE 1-1 COMPARISON Of GENKAl AND BYRON AND BRAIDWOOD
. f i
BYRON AND BRAIDWOOD*
Line Size 8 inch 12 inch 12 inch i Vertical Drop from RCS 9 feet 4 feet 4 feet ;
Distance to isolatior. '/alve 2-3 feet 4 feet 9 feet .
from Vertical Drop Total length of P.ipe. RCS to 14-15 feet 8 feet 13 feet ,
first Isolation Valve 4
- All pipe lengths are approximate since this is a compilation of eight lines for the Byron and Braidwood Units; however, the lengths are correct to about one foot.
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SECTION 2.0 STRESS ANA!.YSES
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}a.C,0 Section 2.1 Addresses the structural effect of stratification Section 0.2 Addresses the local stress effects of stratification
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2.1 Piping System Structural Analysis 2.1.1 Introduction
. The therttal stratification computer enalysis of the piping system to determine loads in the ;:iping is referred to as the piping system structural analysis.
These loads are used as input to the fatigue evaluation. The thermal streti-fication condition consists of both axial and top-to-bottom variations in the 3-pipe metal temperature, as described in section 1.0. The codel consists of straight pipe and elbow elements for the ANSYS computer code (ref. 4),- [
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2.1.2 Discussion The piping layouts are very similar for all locp 1, and for all loop 3 RhR .
lines at the Byron and Braidwood Units (see figures 1-2 through 1-9). The loop 3 layout has about five additional feet of horizontal piping and an ,
additional elbow near the isolation valve, which the loop 1 layout does not have. Per the discussion of turbulent penetration in section 1.2, stratification is more likely to occur in the loop 3 configuration thcn in the loop I configuration. Also, the longer length of horizontal piping will result in larger structural stresses due to potential stratification, i
The piping layout for the RHR suction line analyzed (Byron Unit 1, Loop 3) is shown in figure 2-1. (
)*'C The analyses for this line will siso be conservatively applicable to the other Byron and Braidwood RHR iine:. The piping analysis model consists of straight pipe and elbows. These elements provide the capability to lead the piping with a top-to-bottom temperature gradient. Spring-damper elements were used at rigid support locations.
Two tht.rmal expansion loadings were applied to the ANSYS structur.1 model in .
ordar to determine the effects of cyclic valve leakago on pipe loading.
The first case assumea no valve leakage, therefore no top-to-bottom tempera-ture gradient. The axial temperature gradient along the line was determined by heat transfer analysis (Appendix A) and is shown in figura 1-11 (bottom curee). The line was assumed to be at the RCS tempeiature between the hot leg conn 2ction and the horizontal piping due to loop turbulence.
The-second analysis case assumed [
]"*C'" The axial temperature distribution of this leaktge was also determinea by hest transfer analysis (Appendix A) and is shown in figure 1-11 (top curve). The axial temperature distribution of the remaining stagnant ater was assumed to be the same as the ,
cistribution of the no-leakne case (figure 1-11, bottom curve). Therefore, a tcp-to bottom te'rpurature gradient was input for this case as a step change at ,
the-leakage flow / stagnant water interface (figure 2-5).
2-2
For the ANSYS code an (-
ja c.e 2.2 Local Stress Oue to Non-Linear Thermal Gradient E
2.2.1 Explanation of Local Stress-f:lgure 2-3 shows the local axial stross components in a bedm with t charply 2- ' nonlinear metal temperature geadient. Lucal axial strestes develop due to the restraint of-axial expansion or contraction. This restraint is providad by the material in the adjacent beam cross section, for a linear top-to-bottom temperature gradient,-the local axial stress would not exist. (
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ja.c.e 2,2.2 Superposition of Local and Structural Stresses for the! purpose of:this discussion, the stress resulting frcm the structural analysis (section 2.1) wili be referred to as " structural stress." {.
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3a,c,e Local ar.d structural stresses may be superimposed to obtain the total strecs. This is true because i linear' elastic analyses are perforced and'the~two stresses'are indenendent of one another.-
- Fisure 2-4Lpresents the results of 4 test csse that was cerformed to-J
. . . l
'demonstratefthe validity of superposition. As chewn in - the figur e, the super- '
- position' of local- ar.d structural stress is valid. (- Ja.c.e d
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3a.t.e 2.2.3 Finite Element Model of Pipe for Local Stress The pipe finite element model is shown in figure 2-5, along with thermal boundary conditions. The entire cross section was used for modell'g and analysis. (
)a.c,e 2.3 Stre.s Results The temperature and stress results for the WECAN finite element model are presented in the plots in figures 2-6, 2-7 and 2-8. ( .
Ja,c.e The high teccerature region 7s ve.y localized at the top of the pipe, as expected, and the pipe wall temperature quickly dro;3 to the stagnant water temperature of about 270*F, for the majority of the circumference. The axial stresses from this stratified flow are shown in figure 2-7, and it can be seen that the highest stress is near the hot cold water interface, and is a positive 17.3
-ksi. Compressive stresses are found at both the top and bottom of the pipe.
The stress intensity (figure, 2-5) was highest at the top of the pipe, at a value of 24.2 ksi.
These stresses were combined with the structural stresses discussed in secticn 2.1 to obtain the tttal stresses from the postulated stratification event.
This combined stress is ther used in the fatigue and fatigue crack growth ,
analyses of sections 3 and 4.
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SECTION 3.0 ASME SECTION III FATIGUE USAGE FACTOR EVALUATION 3.1 Code and Criteria Fatigue usage f actors for the RHR suction line were evaluated based on the requirements of the ASME B & PV Code, Section 111, Subsec; ion NB-3600 (ref. 7), for piping components. The fatigue evaluaticn required for level A and B service limits in NB-3653 is summarized in table 3-1. ASME 111 fatigue usage factors were calculated assuming that the maximum moment stress range and the maximum stratification AT can coincide at any location in the horizontal piping.
3.2 Previous Desian Nethods Previous evaluations of RHR suction line piping fatigue used the NB-3653 techniques but with thermal transients defined by Westinghouse design specifications, assuming the fluid flows to sweep the RHR line piping with an axisymmetric temperature loading on the pipe inside wall, cnd that no stratified flow cue to valve leakage occurred.
3.3 Analysis for Thermal Stratification Using the thermal transient to account for thermal stratification as described in section 1.0. the stresses in the piping components were established (section 2) and new fatigue usage factors were calculated.
Stresses in the pipe well due to thermal stratification loading were obtained from the WECAN 2-0 analysis of a 12 inch, schedule 140 pipe. [
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Two stress ranges were considered in the fatigue analysis. (
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pressure, moment, stratification were calculated for the transient. [
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- 1) Calculating the Snand Spranges K,, and Salt for the I stratified /no load and stratified /unstratified load stress ranges,
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- 2) For each value of Salt, use the design fatiguo curve to determine the maximum number of cycles which would be allowablo if this type j l of cycle were the only one acting. These values, N3 , N 2 ...N n '
were determined from Code figures I-9.2.1 and I-9.2.2, for '
l austenitic stainless stoels. l For the stratified /no load case, calculate the contribution to the l
3)- l
- ' usage factor based on 200 design cycles. !
- 4) For the stratified /unstratified load case, calculate the time l required for crack initiation (usage factor = 1.0) based on the I I
L assumed cy:lic period. 4 l -:
l L 3.4 Fatigue Usage Results ,
[ . A stress analysis was completed for the stratified flow condition, including i local thermal stresses and structural piping stresses resulting from the .
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postulated stratification. Deadweight stresses were constant, so they were not included since they would not contribute to the alternating stress. The 4
_ transients analyzed alternated f rom rtratified flow to an unstratified stagnant condition, and from stratified flow to no load cor.dition. For stratified flow, the two curves of fig;re -111 were used, while the unstrati-fied stagnant condition only the bottom curve was used for the bulk temperature. The criteria used are shown in table 3-1. The fatigue results are shown in table 3-2 for the critical locations.
. i
- For stresses cycling between the stratified and no load cases, the contribu-
. tion to the cumulative usage. factor is negligible (0.02), since only 200 4
cycles will-occur over the design life of the plant. For the stratified /
unstratified case, a usage factor of 1.0 would be obtained within the plant design life assuming continuous cycling at the governing location, and a short '
cyclic period (e.g. five minutes). This assumes that the full range of thereal and moment stresses occurs over the five minute period, which is conservative since the heat transfer over five minutes will not render the pipe completely unstratified, Because ASME fatigue usage factor requirements could potentially be. exceeded, fatigue crack growth analysis (section 4) will be used to determine-inservice inspection frequency, in 3ddition to1the usage fsetor determination, a check was made for ASME Section 111:equationfl2._ The maximum equation 12 stress for the stratified /no
- load and stratified /unstratified ranges is 30.5 ksi, which is well within the 4
equation 112' limit:of 3 S,-(or 50 ks1)' .
t s 4 nn.eu. u -
33
TABLE 3-1 CODE /CRiiERIA ASME B&PV Code, Sec. !!!
o KB3500 NB3200 o Level A/B Service Limits Primary Plus Secondary Stress Intensity 5 3Sm (Eq. 10) -
Simplified Elastic-Plastic Analysis (when Eq. 10 > 3 5,) -
' Expansion Stress, S, 5 35m (Eq. 12) - Global Analysis Primary Plus Secondary Excluding Thermal Bending < 35m (Eq. 13)-
Elastic-Plastic Penalty Factor 1.0 $ K ,3 3.333 Feak Stress (Eq.11)/ Cumulative Usage Factor (Ucy,)
Salt " Kep 3 /2 (Eq. 14)-
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Design fatigue Curve ,
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'TABir 3-2 FATIGUE RESULTS - BYRON UN'T 1, LOOP 3 RHR 1
Stratified /No Load Case (200 design cycles): l i
COMPONENT ALTERNATING STRESS (ksi; INCREMENTAL USAGE FACI 0ii i
l
. Long Radius Elbow 35.4 .001 1
. . Valve Kold 46,7 .005 l Elbow Weld 41.2 .002 I
. Tee. 65.5 .C20 Stratified /Unstratified Case:
COMPONENT- ALTERNATING STRESS (ksi) ALLOWABLE CYCLES Long Radius Elben 22.5 2 x 10 6 Valve Weld -31.8 3 x 10 5 Elbow Weld' 29.2 6 x 10 5 lee. 20.2 .5 x 10 6 t
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+
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SECTION 4.0 FAi!GUE CRACK GROWTH CVALVATION a
Per the previous section, it was shown that should valve leakage and sPatification occur in the RHR piping, without a mechanism to induco continuous cycling during power operatica, 200 cycles would occur over the life of the unit, 6nd t. racks would not initiate. However, should a mechanism 5 -
o is; to induce cycling, crack initiation could occur. This section deals with the time recuired for crack propagation, and consequently, the ,
determination of inservice inspection frequency.
i 4.1 Method Description
! The ALKE Section XI method is based on stress analysis results and hiatorial -
! crack growth laws. The stress intensity factor (K;) required for the l #atigue crack growth calculations is obtained from the K; expression given
- is reference 2 for an aspect ratio (2a/1) of 1
- 6. The fatigue crack growth l, law for stainless steel in a pressurized water environment was obtained from ,
referenN 3. The crack growth per cycle da/dN is
[ ds/dY=(C)(f)(S)(E)4K.30 3 ,
m whore: -C a 2.42 x 10 -20
.F = frequency factor (F = 1.0 for temperatures below o00*f) .
5= minimum K to maximum K ratio correction (S
- 1.0 for R = 0; S =
1 + 1.8R for 0 < R < 0.8; and S = -43.35 + 57,97R for R >
E 0.8)
E= environmental factor. E=2.0(conservativerecommendation
~
fromASMESectionXItaskgroupforPWRenvironment) i AK = range of stress intensity factor, psi 5 t- ,
The Strecs intensity _ range input to the fatigue crac's growth 6nalysis is a
. .- function _of the assumed cyclic period. for shor_t cyclic periods, the stress
& intensity range is smaller, but the number of cycles is higher than for long i
- nn.mme a 43 (
.1L i L
._. . _ - _ _ . ._ _ ._ _ ._ _._._ _. _ _ ._.~._ _ _ _ - . _ .. _ __.___ _ _ _____.
cyclic periods. The reason for this is that the piping requires tine to cool !
since it is well insulated. Stresses were obtained from transient thermal and !
stress analyses of a 2-D WECAN finite element model.
- 4.2 Fatigue Crack Growth Results, '
For the fatigue crack growth calculation, a number of cases were analyzed corresponding to various assumed cyclic periods. Table 4.1 summarizes the assumed periods, stress r6nges, and periods of time required for the initially assumed flaws to propagate to 60 percent af the wall depth. Based on these calculations, the minimum time required for the flaw size to reach 60 percent '
of the wall thickness is about four years.
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k TABLE 4.1 FAllGUE CRACK GROWTH RESViTS
SUMMARY
AT GOVERNING LOCATION (1)
STRESS RANGE (ksi)
PERIOD MAXIMUM MINIMUM DROPAGATION (Minutes) INSIDE OUTSIDE INSIDE OUTSIDE TIME (?)(Years) 10 28.1 29.5 20.3 21.2 95 40 28.1 29.5 11.5 11.7 4.1 i
60 28.1 29.5 9.4 9.5 4.6 I
NOTES:
(1) Initial flaw size (a/t) of 15% conservatively selected.
, (2) Assuming.oropagation to 60% of wall depth. i I t 6
6
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SCCTION 5 SUYRARY AND CONCLUSIONS l
~
A detailed evsluation of the residual heat removal lines for the Byron and Braidwood Units 1 and 2 has been completed in response to conceras raised by a pipe crack incident which occurred at Genkai Unit 1 in Japan. Although geometrical differences exist between the Byron and Braidwood Units and the Genkai D W which would make such a cracking incident very unlikely at the f ormer c.itt., the stratification transient was postulated for completeness. '
Af ter a detailed structural and finite element stress analysis was completed for the system, an ASME section 111 fatigue analysis showed that crack initiation is possible should continuous cycling occur during power operation.
Fatigue crack growth analysis was then perfcrmed to determine the time required for a 60 percent through wall crack to occur based on the postulated transient stratification loading, using a range of assumed cyclic periods from ,
10 to 60 minutes. Results of this analysis indicate that a minimum of four years of oparation is required for an initial flaw of 15 percent wall ,.
thickress to grow to 60 percent wall thickness. Therefore, inservice inspection frequency should be every other refueling outage, or about three i years of operation.
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REFERENCES
- 1. United States Nuclear Regulatory Commission Bulletin 88-08, Supplement 3 -
" Thermal Stresses in Piping Connected to Reactor Coolant Systems, 4/11/89.
- 2. McGowan, J. J. and Raymund, M. " Stress Intensity Factor Solutions for
. Internal Longitudinal Semi-Elliptical Surface Flaws in a Cylinder Under Arbitrary Loadings," Fracture Nechanics, ASTM STP 677, 1979, pp. 355-380.
i
- 3. James, L. A and Jones, D. P., " Predictive Capabilities in Environmentally Assisting Cracking," Special Publications, PVP-Vol. 99, ASME, Nov. 1985.
- 4. Program ANSYS, revision 4.28 Swanson Analysis Systems, Inc., flouston, Pennsylvania.
, 5. Program WECAN, version date 9/3/02A, cycle 22, 4/11/89, Westinghouse l Proprietary.
I
- 6. Program FCG, cycle 3, 8/2/89. Westinghouse Proprietary.
, 7. ASME Boiler snd Pressure Vessel Code, Section 111, Division 1,1977 l Edition, through Summer,1979 Addendum (1989 Edition, Appendix 1 used for j high cycle fatigue curve),
i D
l 3935s % 3184 10 5-2 L
_ _ . . _ _ . - . _ . _ _ _ . . _ . _ _ _ _ _ _ ._ . _ ~ ._ __.__-__. .._ _ ... _ . _ _ . _ _ _ . _ . _ ._.-..._....- _ . _ -... _ _.
i APPENDIX A
, THERMAL STRATlflCATION ANALYSl$
i
- It is of interest to estimate maximum temperature differt,nces between e
stratified layers of fluid in horizontal piping layouts for the purpose of i
- studying the propensity of a given configuration for developing high stresses 4
at the inner radii of the pipes.
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