ML20235Q851

Rev 1 to 32-1167603-01, Pressurizer Shell Temp Due to Radiant Heat

ML20235Q851
Person / Time
Site:	Rancho Seco
Issue date:	09/14/1987
From:	Schaefer R, White L BABCOCK & WILCOX CO.
To:
Shared Package
ML20235Q699	List: ML20235Q697 ML20235Q730 ML20235Q798 ML20235Q851
References
32-1167603-01, 32-1167603-1, TAC-64153, NUDOCS 8710070720
Download: ML20235Q851 (40)

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SUMMARY

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32-1167603-01  !

DOCUMENT IDENTIFIER  !

PZR SHELL TEMP DUE TO RADIANT HEAT )

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TITLE.b SM- DMA/lY, f RTLE M CM DM f VM COST CENTER O RFF PAGE(S) REVIEWER INDEPENDENCE PURPOSE AND

SUMMARY

OF RESULTS:

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Purpose:

Revision 00 I i

On November 21, 1986 while heating up the pressurizer at Rancho Seco Nuclear Station, the water level in the pressurizer dropped below the level of the upper heater bundle. Due to the lack of detailed site information, it was I conservatively assumed that a portion of the heater elements in the middle I bundle were also exposed to an air / steam envi-rui .  !

The purpose of revision 0 of this document was to determine maximum shell '

temperatures near the outboard region of the heater bundle. Temperatures near the heater bunile closure opening were determined in Ref. (1). The  !

localized shell temperatures due to the possible contact of heater element l end and shell were calculated in Ref. [2]. I Revision 01 l

The purpose of revision 1 is to determine the fatigue impact of the heater uncovery event on the pressurizer shell using the shell therral results of revision 00.

Summary of Results:

I

{

The raximum shell temperatures and temperatures in the region of the RDT probe are summarized in Appendix A. A shell tempenture of 700F was conservatively calculated to be the maximum.

The fatigue usage factor associated with this event was very conservatively calculated to be 0.063. 'Ihe total revised cumulative fatigue usage factor 4 for the pressurizer shell near the outboard end of the upper heater bundle j is 0.14 which is much less than 1.0, the allcwable fatigue usage factor. l 1

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i Babcock'& Wilcox B&W Doc. No. 32-1167603-01 I Record of Revisions

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1 Complete revision to- 9/87 incorproate.the shell fatique analysis. ,

(Microfiche of computer runs from Rev. O must be'used with Rev. 1 of this. document)

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Babcock _._& Wilcox B&W Doc, No. 32-1167603-01

,. TABLE OF CONTENTS SECTION DESCRIPTION PAGE Calculation Data / Transmittal Sheet 1 Record of Revisions 2 Table of Contents 3 l 1.0 Introduction 4 1

2.0 Summary of Results 4 3.0 Assumptions 5 4.0 References 6 5.0 Discussion of Analysis 7 6.0 Geometry 7 7.0 Description of Finite Element Model 8 8.0 Thermal Transient 12 9.0 Thermal Boundary Conditions 15 10.0 Results 17 11.0 Microfiche 26 Appendix A 28 Appendix B 31 Total pages = 40 Inserted pages 17A & 17B Prepared By [ b, Date YC// 2 7

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ReviLwed By Ihd Date ///4/87 Page E

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, Babcock & Wilcox B&W Doc. No. 32-1167603-01 1.0

Introduction:

On November 21, 1986 while heating up the pressurizer at Rancho Seco Nuclear Station, the water level in the pressurizer dropped below the level of the upper heater bundle (HB). To provide a reasonable and timely determination of the acceptability of the pressurizer equipment, it was conservatively assumed that 50 percent of the heater elements in the middle bundle were also exposed to an air / steam environment. This assumption was later ,

confirmed to be grossly conservative and as a result, the 1 calculated maximum temperature was reduced by a ratio method (See Appendix A).

The purpose of revision 0 of this document was to determine shell (diametrically opposite the HB opening) temperatures near the outer diameter of the heater bundle. [ Note: Temperatures near the heater bundle closure opening were determined in Ref. (1) and the localized shell temperatures due to the possible contact of heater element end and shell were calculated in Ref. (2)]. l 1

Appendix B was added in revision 1 of this document. The I appendix contains a fatigue analysis of the pressurizer shell due to the shell thermal gradients calculated in revisjon 00 for the event. I i

i 2.0 Summary of Results:

I The maximum shell temperature as well as the temperature in the j region of the RDT probe are surmarized in Appendix A. The j maximum shell temperature was conservatively calculated to be a maximum of 700F. l i

i The primary plus secondary stress intensity range is 52,374 psi  ;

which is less than the allowable stress of 62,400 psi. )i i

I Prepared By [A -- Date 'J/N l Reviewed By NC Date j I4d7 Page

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1

- Babcock & Wilcox B&W Doc. No. 32-1167603-01 The fatigue usage factor associated with this event was conservatively calculated to be 0.063, The total fatigue usage factor for the pressurizer 6" thick shell area near the outer diameter of the upper heater bundle is conservatively calculated to be 0.14 which is much less than the allowable fatigue usage ,

factor of 1.0.

3.0 Assumptions

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1. The heat flux distribution is symmetrical about the axis of i the heater bundle.

I

2. The bulk fluid temperature in the buttom of the pressurizer i is assumed to ramp from 80 0 to 2200 over 1 HR of heater on time. It is assumed that the lower bundle on times i

corresponds to the on times of the middle and upper bundle. j i

3. This model does not include the 3/16" cladding material.

Refs. [1] and [2] show that it is conservative to leave the cladding out. The cladding serves as a buffer material between the direct heat source and the base metal. Thus, the base metal temperatures will be higher without the cladding material present. 4

4. This evaluation assumed that 1.5 heater bundles where 1

exposed to the air environment. Appendix A of this j document shows that this is a conservative assumption. {

I

5. The total heater bundle heat flux is assumed to be concentrated on the outside diameter of the heater bundle.

This assumed distribution concentrates the heat to localized area maximizing a local " hot spot" effect on the shell.

Prepared By / [- Date {' d~

Reviewed By [#M Date /#/ Page -

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. Babcock & Wilcox B&W Doc. No. 32-1167603-01 4.0

References:

1. B&W Document No. 32-1167974-01 " Local Heating of PZR Shell Inside Corner," NSS-11.

2. B&W Document No. 32-1167984-00, " Pressurizer Contact Temperature with Heater Element," NSS-ll.

3. 'ANSYS' Computer Code, Engineering Analysis Systems, User's Manual (Rev 4) Volumes I and II, Swanson Analysis Systems, Inc. B&W Document No. NPGD-TM-596 Dated March 1982 (R4ANSYS Rev. E).

/ B&W Document No. 51-1167607-00, " Heater Element Activation Time Intervals," NSS-11.

5. B&W Document No. 51-1155656-00, " Standard Correlations for Natural Convection."

6. 3dW Document No. 32-1167978-00, "Smud Pressurizer Heater Radiant Energy Distribution," NSS-ll.

7. B&W Drawing No. 02-135489-E4 " Heater Belt Details",

NSS-11.

8. B&W Drawing No. 02-135484-E10 " Vessel Sub-Ass'y",

NSS-11.

e. B&W Drawing No. 02-135483-E7 " Pressurizer List Of Materials", NSS-11.

10. ASME Boiler and Pressurizer Vessel Code,Section III, 1980 Edition (For material properties only).

11. B&W Document No. NPGD-TM-500, Dated 2/1981, "NPGMAT", NPGD Material Properties, Program Users Manual. Rev 1.0A.

12. " Pressurizer Shell Analysis", Design Report No. 7,

" Pressurizer Stress Report", NPD Microfilm Roll No. 80-47, B&W Contract NSS-11.

l 13. B&W Document No. NPGD-TM-562, Rev. 2, March, 1985, B&W Computer Code P91232, Revision 1.0A.

14. ASME Boiler and Pressure Vessel Code, Section III, 1974 Edition with Addenda through Summer 1975.

Prepared By /Y - Date Reviewed By d Date ((Af/4'7 Page -

, Babcock & Wilcox B&W Doc. No. 32-1167603-01 5.0 Discussion of Analysis:

Revision 00 A three-dimensional thermal analysis was performed using the finite element method as implemented by the "ANSYS" computer code of Ref. [3]. The results of the analysis is in the-form of nodal temperatures. These nodal temperatures represent the pressurizer shell temperatures for the given thermal boundary cc,nditions.

Revision 01 The shell thermal gradient stresses and fatigue usage factors will be calculated based on the shell temperatures calculated in revisinn 00 of this calculation. A simplified but conservative method will be used to determine the stresses. Appendix B contains the calculations.

6.0 Geometry

The geometry information for the pressurizer shell is taken from references [7] to [9]. The information required for this analysis is summarized below.

Shell ID = 84 inches to base metal Shell thickness = 6.1875 inches minimum The axes of the heater bundles are 21 inches apart vertically and are rotated 40 degrees with respect to each other.

The RTD probe is located 24 inches above the axis of the upper heater bundle and 44 degrees circumferential1y around the shell.

Shell material is SA 516 GR 70 The material properties used in this analysis are taken from references [10] and [11].

Prepared By /' / - Date Reviewed By [#M Date M#7 Page

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, Babcock & Wilcox _. B&W Doc. No. 32-1167603-01 7.0 Description of T.s. nite Element Model:

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The finite element model cf the pressurizer shell is shown in i

Figures 2 to 4. Due to symmetry only a 900 segment of shell was modeled. The modeled ..eight of the pressurizer is 102". This is I tall enough to include 15" of water level, the upper and middle bundle elevations, the RDT probe elevation, and an additional 42" to provide a reservier for the heat to dissipate during the times when the heaters are off. The shell is represented by Isoparametric Thermal Solid Elements (STIF 70).. Detailed descriptions of this element may be obtained from Ref. [3]

(ANSYS).

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8.0 Thermal Transient:

l The thermal conditions during the Rancho Seco transient are taken I from Ref. [4]. A time history of the transient is summarized in Figure 5. The transient used in this analysis is a conservatively modified version of that shown in Figure 5. The analyzed transient combines some of the " heater on times" while )

eliminating the "off time" that separated them. The evaluated time history (along with analysis results) is contained in Table

1. A summary of the analyzed transient is given in Figure 6.

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. Babcock & Wilcox B&W Doc. No. 32-1167603-01 9.0 Thermal Boundary Conditions:

1 The thermal boundary conditions used in this analysis consist of convective heat transfer in the water filled region of the shell and a heat flux (Q) on the remainder of the shell inside diameter. The shell OD, top of-model, and bottom of model are assumed to be insulated. In addition, for times when the heaters  !

are off the shell ID above the water level is also assumed to be insulated. The convective heat transfer for the water region is assumed constant at its previous value.

l The convective heat transfer coefficients are based on the equations of Ref. [5], Page 5. For Laminar region on a vertical flat plate the film coefficient is:

h = (Delta T/L) 0.25 K1 K2 = BTU /HR-Ft 2_op Where: Delta T = Temperature difference between shell and fluid L = Plate height, 2 ft. assumed K1 = 0.55 K2 = From Ref. [5] Fig. NC1 The bulk fluid temperature is assumed to ramp from 80 0 F to 220 0 F over 1 HR of heater on time. The assumed delta T's at these temperatures are 10F and 300F respectively. The film coefficients are:

h80F = (1/2 FT)0.25 (0. 55) (4 6*) = 21.3 BTU /HR-Ft 2_op

= 0.1477 BTU /HR-IN _op 2

h220F = (30/2)0,25(0.55)(86*) = 93 BTU /HR-Ft 2_op 2

= 0.6464 BTU /HR-IN _op

• K2 from Ref. [5] Figure NCl Prepared By / 4u Date /3/'I Reviewed By [/M Date f[//[#7 Page /

. Babcock & Wilcox B&W Doc. No. 32 1167603-01 The heat flux values used in this analysis are discussed below.

The total heat output of the exposed heaters during the abnormal transient is discussed in Section 7.0 and summarized in Table 1 and Figure 6.

The pressurizer heater radiant energy distribution for the shell and upper head was determined in Ref. [6]. From Ref. [6] the percentage of total heat distributed at any point on the shell is given. The percentages of heat flux on the nodes of the finite element are given in Ref. [6] and in microfiche run MBXH.

The actual heat fluxes input to the finite element model are determined by multiplying the percentage Flux / Node (1/IN2 ) from Ref. [6], the total heat flux (BTU /HR) from Table 1, and the projected surface area (1N 2) of the node. The projected area of internal nodes is (6" X 5.998") = 35.988 1N 2. (NOTE: 6" is height, 5.998" is width along inside circumference.)

The projected area for the nodes along the edge of the model is 0.5 (35.988) = 17.994 1N2 For listings of actual input values refer to microfiche runs.

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Babcock & Wilcox B&U Doc. No. 32-1167603-01 10.0 Results: Revision 00 The results of this evaluation are in the form of nodal temperatures. The maximum nodal temperature and nodal temperature representing the RDT probe are' tabulated in Table 1 (along with total heat flux input) . A summary of the maximum temperatures and probe area temperatures are given in Figure 1.

i The maximum shell temperature calculated is 700F maximum and I occurs at node 2419 at time 3.7326 hours0.0848 days <br />2.035 hours <br />0.0121 weeks <br />0.00279 months <br /> (See Appendix A for a calculation of a less conservative maximum temperature) . This value is very conservative. Some of the conservatism in this analysis are;

1. The heat flux values used are very conservative. Appendix A shows that the resulting temperatures from more realistic but still very conservative heat flux value could reduce this maximum temperature by more than 250F.

2. The transient times used in this analysis were a conservative representation of the actual abnormal event.

Heater 'on' times were combined and the 'off' times between them were eliminated. A total of 29.75 minutes of 'off' time (soak time) was removed.

3. The F. E. model boundaries were assumed to be totally insulated. (i.e., no heat loss from metal to outside environment or back into the gaseous medium of the pressurizer). In addition the heat was confined to the material of 102 inch high, 6 inch thick cylinder with only 12 inches of water level. The heat removing capacity of the actual pressurizer is much greater than this.

4. Due to the model element sizes, it was necessary to leave the cladding out of the analysis. Ref [1] which contains the cladding shows that the temperature drop from the cladding ID to the base metal ID is approximately 50F for boundary conditions similar to those used in this analysis.

Prepared By / Date >[/  ?

Reviewed By ed Date fM#[8 Page /

. Babcock & Wilcox B&W Doc. No. 32-1167603-01

5. The total heater bundle heat flux is assumed to be concentrated on the outside diameter of the heater bundle.

This assumed distribution concentrates the heat to localized area maximizing a local " hot spot" effect on the shell.

Revision 01 The primary plus secondary stress intensity range is 52,374 psi which is less than the allowable stress of 62,400 psi.

The fatigue usage factor associated with this event was very conservatively calculated to be 0.063 (See Appendix B) . The 1 usage factor from the pressurizer stress report associated with the pressurizer shell at the hot spot location is 0.075.

Therefore, the revised cumulative fatigue usage factor for the pressurizer shell near the outboard end of the upper heater bundle is 0.14 which is much less than 1.0, the allowable fatigue usage factor.

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AEVIEWED BY 4FS tI 0 1E 2Je /n ..cE ~o zr

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• - Babcock &'Wilcox B&W Doc. No. 32-1167603-01

11.0 MICROFICHE LISTING MJVK Transient (Load steps 1 thru 4)

MDLT Transient (Load steps'S thru 8)

L MBHE Transient (Load steps 9 thru 11)

MAKD Transient (Load steps 12 thru 20)

MAWH Transient (Load steps 21 thru 24)

MAZW Transient (Load steps 25 thru 28)

MGTK 60 minutes of heat flow (1.5 bundles)

MBEE 60 minutes of heat flow (1.25 bundles)

MJAS Restart of MGTK, No flow for 60 minutes MHRY Transient Time 0.80 hrs. - P + S Stress MHSA Transient Time 1.07 hrs. - P + S Stress MBIO Transient Time 3.73 hrs. - P + S Stress Prepared By 6 Date 9/3 37 Reviewed By d4<J Date f #[87 Page S b

.c

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' Babcock & Wilcox B&W Doc. No. 32-1167603-01 l NOTE: The microfiche from revision 00 are applicable to revision 01 of this document also.

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Prepared By (( Date 9 / 3, 5/ 7 Reviewed By dA) Date f//#[87 Page ~ 7

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. 4-;. l; si Babcock-& Wilcox

, B&W Doc. No- 32-1167603-01 V'

4 L

APPENDIX A-

, Maximum Shell Temperature Discussion l '.

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Prepared By / ' Date /JI?T i Reviewed By [M Date [ 87 Page O5

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I e Babcock & Wilcox

, B&W Doc. No. 32-1167603-01 Maximum Shell Temperature Discussion The results described in Section 9 are based on heat flux values assuming one and a half heater bundles located at the upper bundle location. A more realistic but still conservative heat flux value was calculated after most of this analysis was completed. The later value considered the actual location of the middle bundle with respect to the upper bundle and still conservatively considered 25 percent of the elements to be

. radiating heat on the shell. This later assumption of the percent participation by the middle bundle was confirmed with Rancho Seco personnel to still be conservative as a result of the inspection performed on the middle bundle (i.e., one heater element deformed and four others discolored, thus, only a small portion of the middle bundle was ever exposed).

In order to determine the effect of the change of heat flux values (1.5 heater bundles exposed verses 1.25 heater bundles) on the shell temperatures, a test case was run. The test case involved running the finite element thermal model to represent one hour of continuous heat input for both heat flux cases. The j results of the test case are contained in microfiche runs:

MGTK -

1.5 heater bundles at the upper heater bundle location (Same as used in transient evaluation).

MBEE - More realistic but still very conservative case of 1 heater bundle at upper location and 0.25 heater bundles in the middle location i

The maximum temperatures during the test run and the ratio of the 1.25 bundle case verses the 1.5 bundle case are tabulated in the following table:

Prepared By -

Date U// 2 M ~

Reviewed By [#M Date f/Af/87 Page E

hi.* --

,- Babcock & Wilcox B&W Doc. No. 32-1167603-01 I

I Time Run MBEE Run MGTK Ratio 'I 0.385 hrs 477* 668 I 0.68-0.776 hrs 657* 940 0.675 1 1.000 hrs 751 1079 0.675

(* interpolated values for time point)

Based on these values, it is concluded that the 9480 (calculated for the transient) of Section 9.0 is very conservative.

The total heater element on time before the maximum temperature was observed was approximately 1.5 hours5.787037e-5 days <br />0.00139 hours <br />8.267196e-6 weeks <br />1.9025e-6 months <br />. If the test run time was increased to 1.5 hrs the percentage difference would remain approximately the same. Therefore, the maximum temperature observed (948F) can be reduced by the ratio 0.68. Thus the corresponding maximum temperature would be:

Tmax = 0.68(948-70) + 70 = 667F Therefore, the maximum shell temperature was less than 700F.  ;

This location was near the outside diameter of the heater bundle.

Prepared By // Date ~'/' 7'

/

Reviewed By 8M Date f/A#Il Page S b

~

, Eabcock & Wilcox B&W Doc. No. 32-1167603-01 i

APPENDIX B Pressurizer Shell Faticue Analysis Prepared By / > -

Date /

Reviewed By 8d Date /A /8 7 Page 8/ '

, Babcock & Wilcox B&W Doc. No. 32-1167603-01 B.1 Introduction A simplified but conservative method will be used to determine the shell thermal gradient stresses and associated.

fatigue usage factor. The method will assess possible localized thermal " hot spot" stresses.

B.2 Assumptions

1. The through wall thermal gradient corresponding to the maximum temperature will be analyzed assuming that the gradient is uniform around the entire circumference of the pressurizer shell. This assumption is conservative since the actual shell temperature decreases in all directions away from the localized " hot spot".

2. To account for localized thermal peak stresses at the

" hot spot" location, the inside surface thermal stress will be calculated based on two dimensional rigid constraint equations considering an instantaneous temperature change of the surface. The condensed version of the equation is:

S = 1.429 (E) (alpha) (Delta T) where; E = Modulus of Elasticity alpha = coefficient of thermal expansion delta T = instantaneous temperature change The thermal gradient across the thickness will be used as the basis. Also, the conservative temperature of (Tmax = 948F) will be used in the calculations.

Prepared By /

Date

{

Reviewed By d44.) Date Af[87 Page [E t

- _ - - _ _ l

e

, Babcock & Wilcox B&W Doc. No. 32-1167603-01 B.3 Calculations The ASME Code,Section III linear gradient stress PL+P3+

Q will be determined using B&W Computer Code P91232, Reference 13. The three largest differential 'through wall thermal gradient' times were input into the program. These times were used since the maximum stress range occurs between these time points and the zero stress state. The nodal temperatures for time points 0.8, 1.0667 and 3.7326 hours0.0848 days <br />2.035 hours <br />0.0121 weeks <br />0.00279 months <br /> are taken from reference microfiche MUVK, MDLT and MAKD.

Time (Hours)

NODE 0.8 1.0667 3.7326 2419 251.6 660.0 948.4 2442 249.1 535.2 845.7 2465 243.3 450.6 779.5 2488 228.5 353~4 709.5 2511 222.2 325.1 690.6 These time points were choosen because;

1) Times 0.8 and 1.0667 hrs. represent the maximum range of temperature change during any of the heater activation intervals (See figure 1).

2) Time 3.7326 hrs. represents the point at which the maximum temperature was calculated (See figure 1) .

The combination of these times with the zero stress state represent the maximum stress ranges for the shell.

Figure 7 is a plot of the shell wall thermal gradients for the time points analyzed. Additional temperature points were interpolated to assemble the required input data points for computer program P91232.

~'

Prepared By / Date -

Reviewed By [/4) Date 87 Page

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Babcock &'Wilcox B&W Doc. No.- 32-1167603-01 FIGIRE 7 - SHELL WALL THERMAL GRADIEMS 950-

-s 999 N6 TIME : 3.7326 859 Ns 899 -

759 %_

799 L. - _ _ _

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W 699 s N

9

!050 Ng\

450 A A TIME : 1.9667 g

359 wa

~N_ i 399 0 RIME : 9.8 259".

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2M b $ b b b b 6.b SHELL THICXMESS (IN.)

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Prepared By e K" Date '/ '

Reviewed By [#/J Date f #[87 page [ N i

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Babcock & Wilcox B&W Doc. No. 32-1167603-01 The primary plus secondary . stress intensity results of the runs are:

Time 0.80 hrs. S= -4,665 psi Reference Microfiche MHRY Time 1.07 hrs. S = -42,874 psi Reference Microfiche MHSA Time 3.73 hrs. S = -30,664 psi Reference Microfiche.MBIO An additional stress intensity is -tabulated from the Pressurizer Stress Report, Ref. 12, to account fcr stresses due to normal Heatup and Cooldown transients. The addition of this stress will determine the new maximum total primary j' plus secondary stress intensity range for this area of the pressurizer. The stresses from Oegment number 6, page B-9-7 of Ref. 12 are tabulated as typical of the shell area. The stress associated with Segment number 6 is 9.5 ksi. Thus,  !

the total primary plus secondary stress intensity range is 42,874 + 9,500 = 52,374 psi.

I The allowable stress will be calculated per the ASME Code, j Section III, based on the average of the' allowable stress at the highest and lowest base metal temperatures during the transient. The highest temperature will be conservatively taken as 700F and the lowest as 70F. For the pressurizer shell material (SA 516 GR 70) per Reference 9.

Sm@ 700F = 18.3 ksi Sm @ 70F = 23.3 ksi The average Sm= (18.3 + 23.3)/2 = 20.8 ksi Thus, 3Sm = 62.4 ksi Therefore, the primary plus secondary stress intensity range 52,374 psi is less than the allowable stress of 62,400 psi.

1

! j Prepared By i/I Date 9//!/f"

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Reviewed By [M Date 9/AI/c#7 Page J ,

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F v.

, Babcock & Wilcox B&W Doc. No. 32-1167603-01 The effect of a rapid rise in pressurizer water level during ,

the ' event also requires consideration. To maximize this

, , -effect, the initial temperatures for the shell will be.taken at the end of the heater actuation interval in which the maximum shell- temperature is experienced. For this hypothesized water-slap condition, the hot cladding' surface elements will instantaneously be subjected to a bulk fluid water temperature of 200F. This will grossly simulate the effect of a rising pressurizer water level that is totally covering the hot shell inside surface which has been conservatively calculated to be 700F in Appendix A.

Reference (1) contained a detailed ANSYS evaluation of this effect on the heater bundle shell opening area. The shell opening area is more sensitive to the Water-Slap condition due to the thicker shell and having two heat transfer surfaces near the corner. That evaluation revealed that the Water-Slap primary plus secondary stress intensity range did not increase as a result of these stresses and, therefore, it is obvious that the primary plus secondary stresses for this Water-Slap condition need not be calculated at this location. However, a simplified but very conservative method will be used to generate the required Water-Slap peak stresses for use in the fatigue analysis.

PEAK STRESS CALCULATIONS A conservative peak stress value will be calculated based on the maximum shell surface temperature differential experienced during each heater activation interval within the entire heater uncovery event transient. From the nodal temperature data given previously and from figure 1, it is seen that the maximum differential surface temperature change during any heater activation period occurs between l Prepared By // - Date Y 7/N

/ <

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Reviewed By #d Date f M/O Page U l I

i u .,a 9

Babcock & Wilcox B&W Doc. No. 32-1167603-01 time points 0.8 and 1.07 hours8.101852e-5 days <br />0.00194 hours <br />1.157407e-5 weeks <br />2.6635e-6 months <br /> and equals 251.6 - 660.0F =- )

408.4F. The peak stress (assuming two dimensional rigid constraint) is:

Sp = 1.429 (E) (alpha) (Delta T) I Where; E = 27.8 E6 psi (at T average = 456F)

Alpha = 6.78 E-6 in/in-F (at T average = 456F)

Delta T = -408.4 Sp = 1.429 (27. 8 E6) (6.78 E-6) (-408.4)

Sp = -110 ksi The maximum temperature change possible during the '

hypothesized Water-Slap condition is 700F -

200F = 500F.

Therefore, the maximum peak stress equals:

Sp = 1.429 (27.8 E6) (6.78 E-6) (500.0)

Sp = 134.7 ksi This value is very conservative since the calculation assumes the initial temperature through the entire shell thickness is 700F at the initiation of the Water-Slap condition. However, since the fatigue effect is not significant in this area of the shell, these stresses will be used in lieu of a detailed thermal calculation.

1 Prepared By [M _ Date 2

Reviewed By [/C Date f f/

87 Page 3 7

.s . .*

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. Babcock & Wilcox _ B&W Doc. No. 32-1167603-01 FATIGUE EVALUATION The range of peak stress is 134.7 -

(-110.0) = 244.7 ksi.

The alternating stress intensity is:

Salt = 1/2 (244.7)(Ecurve/Eused) ksi Where; Ecurve = 30 E6 psi (fig. I-9.1, Ref. 14)

Eused = 27.8 E6 psi Salt = 0.5 (244.7) (30 E6 / 27.8 E6) ksi Salt = 132.0 ksi The number of fatigue cycles allowed is 300 per Figure I-9.1 of Ref. 14. The allowable number of fatigue cycles required

, will be determined by conservatively assuming that the maximum. range of stress calculated, exists during each heater activation cycle. Per Figure 5, the pressurizer heaters were activated 19 times during the event. The cumulative fatigue usage factor for this event on the pressurizer shell is:

U = 19/300 = 0.063 I

The maximum cumulative fatigue usage factor in the current .

stress report, reference 12, for any area of the shell near the upper heater bundle is 0.075. For conservatism, this value will be used for the area of the shell being analyzed in this calculation.

Therefore, the total cumulative fatigue usage factor for pressurizer shell near the outboard end of the upper heater bundles is:

UT = 0.075 + 0.063 = 0.14 < 1.0 = Allowable )

I 1

Prepared By /Yd5 Date Yd/W Reviewed By efe<> Date // /8'7 Page ; ,