ML18054B011

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Reactor Pressure Vessel Temp Limits Determination.
ML18054B011
Person / Time
Site: Palisades Entergy icon.png
Issue date: 09/14/1989
From:
CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
To:
Shared Package
ML18054B007 List:
References
EA-A-PAL-89-098, EA-A-PAL-89-098-01, EA-A-PAL-89-98, EA-A-PAL-89-98-1, NUDOCS 8909280100
Download: ML18054B011 (120)
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Text

  • ATTACHMENT IV Consumers Power Company Palisades Plant Docket 50-255 PALISADES REACTOR PRESSURE VESSEL TEMPERATURE LIMITS DETERMINATION September 22, 1989 119 Pages TSP0889-0101-MD01-NL04

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EA-A-PAL-89-098-01 PALISADES REACTOR PRESSURE VESSEL TEMPERATURE LIMITS DETERMINATION September S, 1989 RP0588-0237B-PT04-0P03

I E:A-A~PAL-89-098-01 PALISADES REACTOR PRESSURE VESSEL TEMPERATURE LIMITS DETERMINATION Table of Contents Page No I . OBJECT! VE * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

  • 1 CI.

SUMMARY

/CONCLUSION ******************************************** 1 Ill. DESCRIPTION ................................................... 1 IV. ASSUMPTIONS AND DATA *********************************** *...... 5 V. P/T LIMIT EQUATIONS - DEVELOPMENT ***************************** 7 VI. LIMIT TABLES AND FIGURES *********************************** ."... 25 REFERENCES ********************************************************** 55

  • ADDENDUMS A. Appendix G Limit Curve Calculations forl .8 X io 19 Fluence B. Appendix G Limit Curve Calculations for 3.35 x iol9 Fluence
c. Appendix G Limit Curve Calculations for 3.82 c 1019. Fluence RPOS88-0237B-PT04-0P03

EA-A-PAL-89-098-01 PALISADES REACTOR PRESSURE VESSEL TEMPERATURE LIMITS DETERMINATION I. oaJECTIVE Provide the pressure-temperature limit curves (Tech Spec Figure 3-1, 3-2 and 3-3) for maximum reactor vessel fluence of 1.8 X 10 19 neutrons/square centimeter and for estmated end-of-life fluence.

II.

SUMMARY

/CONCLUSIONS The analysis provides the requested pressure-temperature limit curves appropriate for Technical Specifications and for operating p.rocedures.

The Technical Specification curves do not include reactor vessel metal temperature measurement uncertainty of 5° F (nor the 30 psi for pressure uncertainty). This engineering analysis documents the development of the limit curves for peak reactor vessel fluences projected to occur in August 1993, January 2007 and April 2011.

Ill. DESCRIPTION To operate safely, the RPV must be kept in a ductile condition. There-fore, pressure-temperature limits are defined which ensure the RPV will not be stressed under conditions which promote brittle failure. The basic parameter used in determining these limits is the stress intensity factor, Kr, which is a function of the stress state, material properties and flaw configuration. The minimum Kr that can cause failure is defined as the critical. stress intensity factor or reference stress intensity I

KrR* (Reference 1)

KrR is a measure of the material's ability to arrest a crack of specified length and depth. The crack used in this analysis is specified in the ASHE Boiler and Preaaur* Veaa*l Code (hereafter referred to as the Code),

Section III, Article G-2000, as the Maximum Postulated Defect (MPD). The MPD ia said to be a sharp surface defect normal to the direction of

~P0588-0237B-PT04-0P03

2 EA-A-PAL-89-098-01 maximum stress. It has a depth one-fourth the section thickness and a length of one and one-half times the section thickness.

The basic approach to determining new pressure temperature limits, therefore, is to evaluate Kra for the material and determine the operat-ing stresses. Given the MPD as the limiting flaw, these (K1a and P) are evaluated at the one-quarter and three-quarter wall thicknesses.

Three sets of pressure-temperature limits will be evaluated. These are:

a) First the temperature/pressure limits will be established for 1.8 X 1019 n/cma fluence. These will not contain pressure or temperature measurement error. Based on 1.8 X 1019 n/cm 2 limiting fluence assuming 75% capacity factor between EOC 8 and the future, the following is the time when this fluence will be reached~ (EOCS (3/1990), fluence = 1.411 x 10 19 n/cm 2 )

  • 1.8 x 10 19 - 1.411 0.389 X io

x 10 19 = 0.389 x n /0.152 X 10 '-' n 10 1 9 n/cm 2

= 2.559 EFPY cm 2 cm2 - EFPY 2.559 EFPY: 0.75 = 3.412 years 3/1990 + 5/3 years = 8/1993 years

b. Assuming ~% capacity factor, no uncertainty in fluence accumulation until year 2007 and the highest fluence accumulation of 0.152 X io 19 n/cm 2 EFPY ( Reference 11) for circumferential weld results i~ the following fluence in year 2007.

2007 - 1990 = 17 years 0.75 X 17 = 12.75 EFPY RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 12.75 EFPY X 0.152 X 10 19 n/cm 2-EFPY = 1.94 x iol9 n/cm2 1.411 x io 19 + 1.94 x io 19 = 3.35 x io 19 n/cm2

c. Assuming 75% capacity factor, no uncertainty in fluence accumulation until year 2011 and the highest fluence rate of 0.152 X 10 19 n/cm 2-EFPY results in the following fluence in year 2011.

2011 - 1990 = 21 years 0.75 X 21 years= 15.75 EFPY 15.75 EFPY X 0.152 X 10 19 n/cm 2-EFPY = 2.394 x iol9 n/cm2 1.41 X 10 19 n/cm 2 + 2.40 X io 19 n/cm 2 = 3.81 X iol9 n/cm2 A. DETERMINING Kra Kra depends on a materials reference nil ductility temperature (RTNoT) as stated in the Code. This dependency is given ~y the expression:

(Reference 1)

KIR = 26.78 + 1.233 exp [0.0145 (T-RTNDT + 160)) (1)

Therefore, knowing RTNDT and the operating temperature (T), Kra can be determined.

I Since RTNDT increases with increased neutron exposure, the shift (~RTNor>

associated with projected fluence must be determined. This also deter-mines the length of time the new limits are valid. The projected maximum inner wall tluence used here.

1) 1.8 X 1Ql9 n/cm2 for 8/1993 no calculational uncertainty in fluence RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

2) 3.35 X 10 19 n/cm 2 for 1/2007 with no calculational uncertainty in fluence
3) 3.82 X 10 19 n/cm 2 for 4/2011 with no calculational uncertainty in fluence Reg Guide 1.99 provides methodology for determining ~RTNDT* For this analysis, the Revision 2 to Reg Guide 1.99 will be employed (Reference 2).

B. DETERMINING OPERATING STRESSES During operation, the RPV is subjected to pressure-induc~d membrane hoop stresses and stresses resulting from thermal gradients. The hoop stress am is calculated using the method taken from Reference 5 and the thermal stress is covered in Appendix G-2000.

Thermal stresses depend on thermal gradients through the RPV wall.

Battelle Columbus Laboratory (BCL) has determined the Palisades RPV thermal gradients for various heatup and cooldown rates as shown in Table I (Reference 4).

C. Determining Operating P/T Limits In Section IV of this analysis, equations are derived which calculate allowable pressures for selected temperatures. These temperatures are selected ~.!:.th specific temperature change rates for both heatup and cooldown conditions. The result is tabulated P/T data from which the most limiting values are chosen.

In addition to operating P/T limits, limits are calculated for the in-service leak and hydrostatic tests. At all times that the reactor is critical (except for low power physics tests),the temperature must be higher than that required for inservice hydrostatic testing

  • and in addition, the pressure-temperature relationship shall provide RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 at least 40°F margin over that required for heatup and cooldown o per at i on s

  • IV. ASSUMPTIONS AND DATA
1. The temperature limitations of Appendix G, 10 CFR 50 with respect to flange material, critical oper:-ation and noncr:-i.tical oper:-ation will be super-posed on the P/T limits contained in this document.
2. The refer:-ence temper:-ature of the flange material is defined as 60°F (Refer:-ence 5).
3. The P/T limits established in this document are based on a projected.

fluence of 1.8 x 10 19 and 2.35 X 10 19, 3.82 X 19 19 n/cm 2** This tr:-anslates to appr:-oximately 2.56 EFPY, 12.75 EFPY and 15.85 EFPY r:-espectively between EOCS (3/1990)

4. The weld material is considered to be limiting. All the gir:-th and the longitudinal welds plus base metal need to be consider:-ed, and their:- chemistries have been established (see Reference 6) as follows:

Girth Weld Longitudinal Weld Base Metal

0. 21% Cu 0.19% Cu 0.25% Cu 0.98% Ni 1.10% Ni 0.54% Ni
5. The weld mater:-ial initial refer:-ence temperatur:-e is -56°F and -S°F for base metal ac<<irding to Refer:-ence 7.
6.
  • Temperature measurement err-or is +/-5°F. (when utilized)
7. Pressure measurement adjustment is 84 psi due to:
  • RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 28 psi pressure drop from beltline to RPV outlet 26 psi head in the pressurizer and 30 psi measurement system error (when utilized)

8. The hydrostatic test pressure is l.lp = 2310 psi for determination of the minimum criticality temperature.
9. MISCELLANEOUS TERMS AND DATA ART =Adjusted Reference Temperature (°F)

CF =Chemistry Factor From RC 1.99, Revision 2 f = Fluence = 1.8 x 1019 n/crn2, 3.35 x 1019 n/cm 2 , 3.82 x 10 19 n/cm 2 Krm = Membrane Hoop Stress Intensity Factor KSI ~in KIR = Reference Stress Intensity Factor KSI ~in KrT = Thermal Stress Intensity Factor KSI ~in Mm = Membrane Stress-to-Stress Intensity Factor Mt = Thermal Stress-to-Stress Intensity Factor p = Operating Pressure = 2,100 psig RTNDT = Reference Temperature (°F)

~RTNDl - Reference Temperature Shift (°F) t = RPV Wall Thickness at Beltline = 8 .5 Inches T = RPV Metal Temperature Actual (°F)

Tm = Heas~.red RPV Metal Temperature (°F) ll.TMAX = Through - Wall Thermal Gradient

~Tx = Thermal Gradient at Location X in Wall or = Standard Deviation on Initial RTNDT = l7°F a~ = Standard Deviation on ~TNDT {Weld) = 28°F

  • RP0588-0237B-PT04-0P03

7 EA-A-PAL-89-098-01 am = Membrane Hoop Stress x = Radial Location in Wall

@ x l/4t = 2.125 Inches

@ x 3/4t = 6.375 Inches ri = RPV Inside Radius r0 = RPV Outside Radius ay = Material Yield Strength X = Thickness of the Vessel in Inches V. P/T LIMIT EQUATIONS - DEVELOPMENT (Based on RG 1.99, Revision 2.)

The weld chemistries have been determined to include:

Girth Weld Longitudinal Weld Base Metal

  • 0.21% Cu 0.98% Ni 0.19% Cu 1.10% Ni 0.25% Cu 0.54% Ni According to the Reg Guide 1.99, Revision 2 (Reference 2), adjusted reference temperatures are determined as follows:
1. Apply the material chemistry to Table I of (Reference 2) and obtain the chemistry factor for the girth weld (CF= 225.8) for the longitudinal weld (CF= 229) and for base metal (CF= 167.6).
2. Divide the assumed fluence 1.8 x io 19 by 10 19 and obtain f = 1.8. and x 10 1 ~ 10 ~

1 J.35 by to obtain f = 3.35 or 3.82 x io 19 by io 19 to obtain 3.82.

3. Evaluate the term~:

Initial RTNDT = -56°F (from Reference 7) for welds and -5°F for base metal

  • Margin =2 RP0588-0237B-PT04-0P03

~aI2 + aA2 (from Reference 3)

EA-A-PAL-89-098-01 a1 = 17°F aA = 28 for welds (0.28 - 0.10 log f) 6RTNDT surface = [CF]f f attenuated = f surface e -x 0.24 Where X = thickness of attenuated media in inches ARTNDT attenuated = (CF) f attenuated (0.28 - 0.10 log f attenuated)

4. Calculate the ART's.

The general equation for adjusted reference temperature (ART) is:

ART = Initial RTNDT + ARTNDT + Margin Initial RTNDT = - 56° for welds Inital RTNDT =-5°F for base metal Margin = 6S.S°F for welds - 66°F for welds Margin = 34°F for base metal

  • RPOS88-0237B-PT04-0P03

1

{

EA-A-PAL-89-098-01 6RTNDT Calculations for 1.8 X 1019 n/cm 2 Fluence Circumferential Weld 6RTNDT = 225.8 X (1.8 [0.28 - 0.10 log 1.8])

6RTNDT Surface = 262.16°F f at 1/4 t = 1.8 e -1/4 x 8.5 x 0.24 f = 1.080892 6RTNDT 1/4 t = 225.8 X (1.080892 (0.28 - 0.10 log 1.0809))

6RTNDT 1/4 t = 230.71 °F ART= 230.71°F + 66°F - 56°F = 240.71°F f at 3/4 t = l.8e - 3/4 8.5 X 0.24 f = 0.3897 6RTNDT 3/4 t = 225.8 X (0.3897 (0.28 - 0.10 Log 0.3897))

  • 6RTNDT 3/4 t =

ART= 166.87°F +

166.87 °F 66°F - 56°F = 176.87°F Base Metal 6RTNDT = 167.6 X (1.8 (0.28 - 0.10 Log 1.8))

6RTNDT = l194.64°FI Surf ace 6RTNDT At 1/4 t = 167.6 X (1.080892 (0.28 - 0.10 log 1.080892))

6RTNDT At 1/4*-t = 171. 24 "F A.RT 1/4 t :::i -5° F + 34°F + 171 .z "F = 200.24"F 6RTNoT at 3/4 t = 167.6 x (0.3897 (0.28 - 0.10 log 0.3897))

6RTNDT at 3/4 f = 123.86°F ART 3/4 t = - 5°F + 34°F + 123.86°F = 152.86"F RP0588-0237B-PT04-0P03

) l)

EA-A-PAL-89-098-01 Axial Weld 30°: 2.559 EFPPY X 0.070 x 10 19 n/cm 2-EFPY + 1.006 X 1019 ~/cm2

= 1.185 x 10 19 n/cm2 0°: 2.559 EFPY X 0.065 X 1019 n + 1.014 X 1019 n = 1.180 X 10l9n/cm2 EFPY cm 2 cm2 6RTNDT = 229 X 1.185 (0.28 - 0.10 log 1.185) 6RTNDT = 239.86°F Surface fat 1/4 t = 1.185 X 1019.e - 1/4 X 8.5 X 0.24 fat 1/4 t = 0.7115872 X 1019 n/cm 2 6RTNDT at 1/4 t = 229 (0.7115872 (0.28 - 0.10 log 0.7))

6RTNDT at 1/4 t = 207.l5°F ART= -56°F + 66°F + 207.15°F = 217.l5°F f at 3/4 t = 1.185 X 1019 x e - 3/4 X 8.5 X 0.24 f at 3/4 = 0.2565947 X 1019 n/cm 2 6RTNDT at 3/4 = 229 (0.2565947 (0.28 - 0.10 log 0.26))

6RTNDT at 3/4 = 144.38°F ART = 144.38°F + 66°F - 56°F = i)4.38°F Therefore the limiting ART's for 1.8 X 1019 n/cm2 fluence are ART limiting 1/4 t welds (circumferential)= -56° + 66°F + 240.71°F

= 240. ll°F ART limiting 3/4 t welds (circumferential) = -56°F + 66°F + 166.87°F

= 176.87°F

  • RP0588-0237B-PT04-0P03

/I EA-A-PAL-89-098-01 19 2 Fluence = 3.82 X 10 n/cm in year 2011 (no uncertainty).

Evaluation of ARTNDT ARTNDT = (CF} f (0.28 - 0.10 log f)

Surface Fluence for Axial Weld 0° is:

15.85 EFPY X 0 310 X ~o 19 nicm 2-EFPY + 1.006 x 1019 n/cm2

= 2.10515 X 10 1 n/cm ARTNDT = 229°F X (2.10515 X (0.28 - 0.10 X log 2.10515>>

Surface ARTNDT = 275.36°F Surf ace t.RTNDT 1/4 t Where t is the thickness of the weld Fluence = 2.10515 X 1019 e - 1/4 x 8.5 x 0.24 = 1.264 X 10 19 n/cm2 t.RTNDT = 229°F X (l.264 (0.28 - 0.1 log 1.264))

1/4 t ARTNDT = 243.93°F 1/ 4 t ART= - 56°F + 66°F + 243.93°F = 25J..93°F Fluence = 2.10515 X 1019 e - 3/4 X 8.5 X 0. 24 = 4.558 X 1018 n/cm2 3/4 t t.RTNDT = 229°F X (.4558 (0.28 - 0.1 log 4.5585))

3/4 t t.RTNDT = 178.92°F 3/4 t ART = 56°F + 66°F + 118.92°F = 188.92°F Surface Fluence for Axial weld 30° is:

15.85 EFPY X 0.065 X 10 19 n/cm 2 -EFPY + 1.014 x 10 19 n/cm2 = 2.1682 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

.t.RTNDT for Axial Weld 30°

~RTNDT = 229 X (2.1682 (0.28 - .10 log 2.168181))

Surface LRTNDT = 277.11 °F Surf ace Fluence = 2.162 X 1019 e -1/9 X 8.5 X 0.24 = 1.3 02 X 10 19 1/4 t LRTNDT = 229 X (1.302 (0.28 - 0.1 log 1.30198))

1/4 t

~RTNDT = 245.82°F 1/4 t ART= - 56°F + 66°F + 245.82°F = 255.82°F Fluence = 2.1681813 X 1019 e -3/4 X 8.5 X 0.24 3/4 t Fluence = 4.69488 X 1018 n/cm2 3/4 t LRTNDT = 229 X (0.4695 (0.28 - 0.1 log 0.4694))

3/4 t

~RTN.DT = 180. 76° F 3/4 t ART= - 56°F + 66°F + 180.76°F = 190.76°F

~RTNDT for Circumferential Weld LRTNDT Surface= 225.8 X ( 3.81857 (0.28 - 01 log 3.81857))

llRTNDT Surface = 303.945°F Fluence = 3.81857 x 1019 e -8.5 X 0.24 1/4 t I 4 Fluence = 2.29303 X*l019 n/cm 2 1/4 t .

llRTNDT = 225.8 X ( 2.29303 (0.28 - 0.1 log 2.2930))

1/4 t

~RTNDT = 276.471°F RP0588-0237B-PT04-0P03

/J EA-A-PAL-89-098-01 1/4 t ART= - 56°F + 66°F + 276.47°F = 286.47 Fluence = 3.81857 x 1019 e - 8.5 X 3/4 X 0.24 3/4 t Fluence = 8.26856 X 1018 3/4 t 6RTNDT = 225.8 X (0.826856 (0.28 - 0.10 log 0.826))

3/4 t 6RTNDT = 213.76°F 3/4 t ART= - 56°F + 66°F + 213.76 = 223.76°F 6RTNDT for Base Metal Weld is:

6RTNDT = 167.6 X ( 3.81857 (0.28 - 0.10 log 3.81859))

Surf ace 6RTNDT = 225.60°F Surface 6RTNDT = 167.6 X (2.29303 (0.28 - 0.1 log 2.2932))

1/4 t 6RTNDT = 205.2!°F 1/4 t ART= -5°F*+ 205.21°F + 34°F = 234.21°F 6RTNDT = 167.6 X ( 0.826856 (0.28 - 0.1 log 0.8268))

3/4 t 6RTNDT = 158.66°F 3/4 t ART= - 5°~ + 34°F + 158.66°F = 187.66°F Therefore the limiting ARTs for 3.82 X 1019 n/cm2 fluence are:

ART Limiting = -56°F + 276.47°F + 66°F = 286.47 °F '

1/4 t Welds (Circumferential)

ART Limiting = -56°F + 213.76°F + 66°F = 223.76°F 3/4 Welds (circumferential)

RP0588-0237B-PT04-0P03

If EA-A-PAL-89-098-01 19 2 Fluence = 3.35 X 10 n/cm in Year 2007 (No Uncertainty) 2007 - 1990 = 17 years 0.75 X 17 years= 12.75 EFPY 12.75 EFPY x 0.152 x io 19 n/cm 2 = 1.938 x iol9 (1.411 + 1. 938) X 10 19 = 3. 349 X 10 19 n/cm 2 for circumferential and base metal At this time the longitudional weld will have:

19 30° 1.006 X io + 12.75 EFPY X 0.070 X 10 19 n/cm 2-EFPY = 1.895 X 1019 n/cm2 19 0° 1.014 X 10 + 12.75 EFPY X 0.065 X 10 19 n/cm2-EFPY = 1.893 X 1019 n/cm2 Fluences Attenuated:

At 1/4 t Circumferential & Base:

  • 3.35 X io 19 e Axial Limiting Weld:

- 0

  • 24 X l/ 4 X *8
  • 5 = 2.01105 X 10 19 n/cm 2 1.898 X 10 19 e - 0
  • 24 X l/ 4 X 8
  • 5 = 1.14004 X 10 1 ~ n/cm 2 At 3/4 t Circumferential & Base:

3.349 X io 1 9 e - 0

  • 24 X 3 14 X 8
  • 5 = 0.725177 X 10 19 cm2 Axial Weld 1.8985 X 10 19 e - .Q. 24 X 3/ 4 X 8
  • 5 = 0.411092 X 10 19 n/cm 2 I

. t.RT NOT

C1rcum

. f erent1a . l:

At Surf ace 2 29 x (3. 349 (0.28-0.10 Log 3.395)) = 301

  • 5 oF ART = -56°F + 66°F + 30l.5°F = 3ll.5°F
  • RP0588-0237B-PT04-0P03

/J EA-A-PAL-89-098-01 f).RTNDT Ci rcwnferent ial 1/ 4 t f).RTNDT 1/4 t = 229 X (2.01105 (0.28 - 0.10 log 2.01105)) = 272~6a~

1/4 t ART = 272.6°F + 10°F = 282.6°F f).RTNoT 3/4 t = 229 x 0.725177 (0.28 - 0.10 log 0.725177))

f).RTNDT 3/4 t = 208.4 °F ART = 10°F + 208.9°F = 218.4°F

~RTNDT AXIAL WELD: .

~RTNo Surface:

~RTNo = 225.8 x 1.8985 (0.28 - 0.1 log 1.8985) = 265.40F Surf ace f).RTNDT 1/4 t = 225.8 X 1.14004 (0.28 - 0.1 X log 1.14004) = 234.06aF ART = 10 °F + 234.06°F = 244.06°F 6RTNDT 3/4 t = 225.8 X 0.4110921 (0. 28 - O.l log 0.411092) = 170.10°F ART = 170.40°F + 10°F = 180.10°F These ARTs are used to calculate the reference stress intensity factors (Kra) to be used in determining allowable pressure from Reference 1:

KrR: = 26.78 ..! 1.233 exp [0.0145 (T-RTNDT + 160)), where:

KrR = Reference Stress Intensity Factor T = RPV (Beltline) Inlet Temperature

  • RP0588-0237B-PT04-0P03

It EA-A-PAL-89-098-01 For Technical Specification Pressure Temperature limits are calculated without measurement errors. Therefore, the Kra for 1993 corresponding.*to 1.8 X io 19 n/cm 2 fluence is going to be calculated without the measurement's uncertainties. The t.RTNDT for operational curves for 2007 and 2011 years must be modified to account in addition to the thermal gradients in the vessel wall for the temperature measurement error. The adjustment is as follows:

T =Tm - S*+/- ATx Where: Tm = Measured Temperature 6Tx = Thermal Gradient at Location X Therefore equation (1) for2007 or 2011 becomes:

KIR = 26.78 + 1.233 exp [0.0145 (Tm+ 155 +/- ATX - ARTNnT>l (2)

For. calculating of Technical Specification limits:

KrR = 26.78 + 1.233 exp (0.0145 (T + 160 +/- ATX - t.RTNoT)]

The thermal gradients are subtracted for heatup calculations and added for cooldown. BCL determined t~e thermal gradients for selected heatup/cooldown rates in Reference 4. These are presented in Table 1.

Using the ART values for RTNDT' we can calculate KrR for different heatup and coOldown rates at the 1/ 4 wall and 3/4 wall locations for

weld materi;als. The calculations will consider the limiting welds to reflect the highest ARl' values *
  • H.J:>O 588-02 37 B-PT04-0P03

I?

EA-A-PAL-89-098-01 TABLE 1 A. LIMITING WELDS Kra - 1.8 x 10 19 n/cm2 FLUENCE No Measurement uncertainty:

(Circumferential)

Heatup@ l/4T Kra = 26.78 + 1.233 exp [0.0145 (T~ ~T1/4)] (3)

(Circumferential)

H_eatup @ 3/4T Kra = 26. 78 + 1.233 exp [0.0145 (Tm -16.9 - t.T3/4)) (4)

(Circumferential)

Cooldown@ l/4T Kra = 26.78 + 1.233 exp [0.0145 {Tm - 81 + t.T1/4)] (5)

LIMITING WELDS Kra - 1.8 x 1019 n/cm FLUENCE 5°F Measurement Uncertainity: (Calculated only for LTOP curve pre para ti on.

(Circumferential)

Heatup@ l/4T Kia= 26.78 + 1.233 exp [0.0145 {Tm t.T1/4))

(Circumferential)

Heatup@ 3/4T Kra = 26.78 + 1.233 exp (0.0145 {Tm - 21.9 - t.T3/4)]

(Circumferential)

I Gooldown@ l/4T Kia= 26.78 + 1.233 exp (0.0145 (Tm - 86 + t.T1/4)]

(5)

The limiting welds Kra is for fluences of 3.35 X io 19 n/cm 2 and 3.82 X io 19 n/cm 2 will be addressed in summary of the governing equations *

  • Equations 3 through 8 give stress intensities at selected tempera-tures and heatup/cooldown rates. It is required to relate these RP0588-0237B-PT04-0P03

Jg EA-A-PAL-89-098-01 values to allowable pressures so the pressure-temperature limits may be determined.

The RPV is subjected to :both pressure-induced Membrane Hoop Stress and Thermal Stress due to Through-Wall Thermal Gradients. The stress intensity factors for Membrane Hoop Stress and Thermal Stress are derived from the following fundamental requirement:

Kia > 2 Kim + Kit (9)

Where Kim = Membrane Stress Intensity Factor Kit = Thermal Stress Intensity Factor KIM can be converted to Membrane Hoop Stress (am> with Equation 10.

From Reference 1, Kim = Mm Om (10)

Where om = Membrane Hoop Stress Mm = Stress-to-Stress Intensity Factor Also, according to Reference 1, Kit can be expressed in terms of a maximum Through-Wall Temperature Gradient.

= Mt '1Tmax ( 11 )

I Where Mt = Stress-to-Stress Intensity Factor

~Tmax = Through-Wall Temperature Gradient

  • RPOS88-0237B-PT04-0P03

EA-A-PAL-89-098-01 Now Equation 9 can be rewritten as:

KIR > 2 Hm om + Ht ~Tmax (12)

The Hm and Ht terms in Equation 12 are obtained from Figures G-2214-1 and G-2214-2, respectively, in Reference 1. Determining Mt is straightforward:

Mt = 0.34 To find Hm, we must first evaluate the ratio omloy*

From Reference 3, the Membrane Hoop Stress due to pressure may be estimated as:

Pr Om = t (13)

Where: P = Operating Pressure (PSIG) r = Average Vessel Radius t = Vessel Thickness (Inches)

Using the values given in Section II:

Om = 22.3 ksi Given that the yield stress for SA-302-B at 550°F is 44 ksi:

a m = 0.506, Hm = 2.8 oy An accurate expression relating Membrane Hoop Stress due to pressure can be taken from Timoshinko (Reference 9) or Harvey (Reference 10 as RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 (13)

By com~ining Equation 12 with the above expression with X=r, we have:

r a (1 + ;r-0

) +Ht 6Tmax (14)

RPOS88-0237B-PT04-0P03

21 EA-A-PAL-89-098-01 Conservatively ATmaxHt is assumed to be 0 at an isothermal condition.

Therefore the hypothetical case of an isothermal heatup 0 F/hr is applied to heatup curves at 1/4 t for conservatism.

(1 + +>

r p

p s lOl (86.125 + 2.125) 2 ((94.625) 2 ~(86.125) 2 ) KIR 2 x 2.8 (86.125) 2 ((86.125 + 2.125) 2 + (94.625) 2 )

Ps 17.206 Kra Adjusting for the pressure drops due to the location of measurement equipment.

P s 17.206 Kra -.28 - 26 P ~ 17.206 Kra - 54 At 3/4 t heatup:

The tensile stress in the membrane and the thermal stress are additive because thermal stress is tensile at 3./4 t.

Therefore the formula becomes:

P S KIR - Mt ATmax 2nm P ~ KIR - Ht ATmax x 10 3 ( ( 86.125 + 6.375)2 X [94.625) 2 -(86.125)2 2 mot L ((86.125 + 6.375)2 + (94.625)2) X ,(86.125)2 RP0588-0237B-PT04-0P03

2L EA-A-PAL-89-098-01 P ~ 18.073 K1a - 6.145 ~Tmax to account for 54 psi of pressure drop for the head and core ~p.

P ~ 18.073 K1a - 6.145 ~Tmax - 54 For the case of cooldown, the pressure calculations need only be performed at 1/4 t thickness location since the membrane. and thermal stresses are tensile and additive. The 3/4 thickness location would always be stressed to a lesser or equal degree and therefore need not "

be considered.

For cooldown at 1/4 t:

P ~ 17.206 K1R - Ht ~Tmax X 17.206 P ~ 17.206 K1R - 5.85 ~Tmax Corrected for the pressure drops in pressurizer head and core ~p.

P ~ 17.206 K1R - 5.85 ~Tmax - 54 B. IN-SERVICE LEAK AND HYDROSTATIC TESTING - CRITICALITY TEMPERATURE Since the hydro is performed with the core not critical, heatup rates I

are low and thermal gradients through the wall are negligible.

Therefore, the isothermal heatup condition will govern the test pressure limits. For purposes of scaling up the curves, however, limits for rates greater than 0°F/h will be calculated *

  • RPOS88-0237B-PT04-0P03

2J EA-A-PAL-89-098-01

  • Only heatup rates, not cooldown, need to be considered* for the hydro and, according to Reference l, the equations for KiR during the hydro are:

Kia= 26.78 + 1.233 exp [0.0145 (T - RTNDT + 160))

(15)

Therefore, using Equations 10 and 14:

Substituting the appropriate values:

Since we have assumed the 0°F/h heatup rate to be limiting and since PttYDRO = 2,310 psi, we have:

PHYDRO ~ 1 22.94 Kia - 54 for 1/4 t Resulting in:

Kia = 103.05 KSI ~in and p HYDRO = 24.097 K1a - 54 for 3/4 t Resulting in:

Kia = 98.10 KSl Jin Substituting this value.into the heatup equations for l/4t and 3/4t we get:

@ l/4t Tcrit = 365.5°F At 3/4t Tcrit = 296.7°F RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 With measurement uncertainty for l/4t and 3/4t At l/4t Tcrit = 371.6°F At 3/4t Tcrit = 302.9°F TABLE I Thermal Gradients Temperature Heat up t.T Cool down t.T Change Rate °F/h t.T 1/4 t.T 3/4 max t.T 1/4 t.T 3/4 ~

0 o.o o.o o.o o.o o.o o.o 20 6.3 13 .3 14 .2 4.4 9.5 10.l 40 12.4 26.3 28.0 9.0 19.2 20.5 60 18.2 38.6 41.1 13.9 29.8 31. 8 80 24.3 51.4 54.7 18.5 39.6 42.2 100 30.0 63.2 67.3 23.6 50.6 54.0

  • RPOS88-0237B-PT04-0P03

EA-A-PAL-89-098-01 VI. LIMIT TABLES AND FIGURES The following tables contain the results of pressure temperature limit calculations. In all cases, the l/4t location was found to be limiting for cooldown. For heatup, either the l/4t of 3/4t location can be limiting, depending upon heatup rate and the temperature of interest.

For heatup, the table reflects bounding values.

The Interactive Graphics Utilities (ICU) computer program on the IBM 9570 computer generated the following figures. The temperatures corresponding to a pressure limit of 3000 psia were calculated. The additional data points were calculated to prevent ICU from improperly extrap?lating from the last two data points when the next data point is beyond the graph boundary.

The SRP requires that the pressure-temperature curves provide at least 40°F margin over that required for heatup and cooldown for core operations. Palisades Tech 9pec Section 1.1 requires the PCS temperature to be greater than 525 °F before the reactor is in hot shutdown, hot standby or power operation condition. At 525°F, the limiting pressure is greater than the safety valve setpoint of 2500 psia. Therefore, the 40°F shift was not included in the pressure-temperature limit curves *

. I

  • RPOS88-0237B-PT04-0P03

J..6 EA-A-PAL-89-098-01

SUMMARY

OF THE GOVERNING EQUATIONS For Heatups and Cooldown For 1.8 X 1019 n/cm 2 Fluence No Measurement Uncertainty Heatup 1/4 t Circumferential KIR = 26.78 + 1.233 e (0.0145 (T-81-~T 1/4)]

P = 17.206 KrR - 54 Heatup 3/4 t Circumferential KrR = 26.78 + 1.233 e (0.0145 [T - 16.9 - ~T 3/4)]

P = 18.073 KrR - 6.145 ~Tmax - 54 Cooldown 1/4 t Circumferential KrR = 26.78 + l.233e (0.0145 [T-81 + ~T 1/4] )

P = 17.206 KrR - 5.85 ~Tmax - 54

  • RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

SUMMARY

OF GOVERNING EQUATIONS For Hydro-test for 1.8 X 10 1 9 n/cm2 fluence, no measurement uncertainty Kra ~ 1.5 Mm om+ Ht 6Tmax For 1/4 t Circumferential

[0.0145(T ~T 1/4)]

Kra = 26.78 + l.233e P ~ 17.206 x (2/1.5) Kra - 54 P ~22.94 Kra - 54 For 3/4 t Circumferential [(0.0145 (T - 16.9 ~T 3/4)]

Kra = 26.78 + l.233e P ~ 18.073 x (2/1.5) Kra - (6.145 X 2/1.5) ~Tmax -54

  • P ~ 24.097 Kra - 8.193 6Tmax - 54 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

SUMMARY

OF THE GOVERNING EQUATIONS For 1.8 X 1019 n/cm 2 Fluence With Measurement Uncertainty Heatup 1/4 t Circumferential KrR = 26.78 + 1.233 e [0.0145 (T-86-~T 1/4)]

P = 17.206 .KIR - 84 Heatup 3/4 t Circumferential KrR = 26.78 + 1.233 e (0.0145 [T - 21.9 - ~T 3/4)]

P = 18.073 KrR - 6.145 ~Tmax - 84 Cooldown 1/4 t Circumferential KrR = 26.78 + l.233e (X 0.0145 [T - 86 + ~T 1/4] )

P = 17.206 KrR - 5.85 ~Tmax - 84 Hydro l/4t Circumferential K'rR = 26.78 + l.233e (0.0145 .CT-86))

P = 22.94 KrR - 84 Hydro 3/4t Less limiting than l/4t

    • RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

SUMMARY

OF GOVERNING EQUATIONS For 3.82 X 1Ql9 n/cm 2 fluence No Measurement. Uncert.aint.y Heat.up 1/4 t.

Circumf erent.ial KIR = 26.78 + l.233e [0.0145(Tl - 125.5 - 6T)l/4]

P ~ 17.206 KIR - 54 Heat.up 3/4 t.

Circumf erent.ial KIR = 26.78 + l.233e [0.0145 (T - 63.0 - 6T 3/4}]

P ~ 18.073 KIR - 6.145 6Tmax -54 Cooldown 1/4 t.

Ci rcumf e'rent.ial KIR = _ + _ e [0.0145 (T - 1.25.5 - 6T 3/4)]

26 78 1 233 P ~ 17.206 Kra - 54

  • RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

SUMMARY

OF GOVERNING EQUATIONS For 3.82 X 1Ql9 n/cm2 Fluence For Hydro-test KIR ~ 1.5 Hm om+ Ht 6Tmax For 1/4 t KIR = 26.78 + l.233e (0.0145(T - 12T.T - 6T 1/4))

P ~ 22.94 KIR - 54 For 3/4 t KrR = 26.78 + l.233e (0.0145 (T - 63.0 - 6T 3/4))

P ~ 24.097 KrR - 8.193 6Tmax - 54 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 HEATUP - CIRCUMFERENTIAL WELD (3/4 t)

K1a = 26.78 + 1.233 e (0.0145(T - 16.9 - 6T 3/4)]

p = 18.073 K1R - 6.145 6Tmax - 54 f = 1.8 X io 19 n/cm2 Heat up Allowable Pressure at Noted Tem:eeratures Rate °F/h 50°F 100°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F 0 466.0 504.3 583.5 747.0 1084.5 1781.3 3220.l 6190.7 12324.4 20 372.4 404.0 469.3 604.1 882.4 1457.0 2643.4 5093.1 10150.9 40 282.5 308.7 362.8 474.4 704.9 1180.8 2163.4 4192.2 8381.1 60 198.0 219.9 265.2 358.5 551.4 949.5 1771.6 3469.0 6973.6 80 111.0 129.2 166.7 244.3 404.5 735.2 1418.0 2827.9 5738 .8 100 30.8 46.2 77 .8 143.2 278.2 556.9 1132. 3 2320.5 4773. 7 RPOS88-0237B-PT04-0P03

EA-A-PAL-89-098-01 HEATUP - CIRCUMFERENTIAL WELD (1/4 t)

Kia= 26.78 + l.233e [0.0145(T 6T 1/4)]

P = 17.206 K1R - 54 f = 1.8 X 10 19 n/cm 2 Heat up Allowable Pressure at Noted Temperatures Rate °F/h 50°F 100°F 400°F . 450°F 0 420.3 434.7 464.5 525.9 652.7 914.6 1455.4 2571.8 4877 .1 20 419.1 432.3 459.4 515.5 631.3 870.3 1363.8 2382.8 4486.8 40 418.l 430.1 455.0 506.3 612.3 831.1 1282.8 2215.6 4141.4 60 417.2 428.2 451.1 498.3 595.7 796.8 1212.2 2069.7 3840.2 80 416.3 426.4 447.3 490.5 579.7 763.8 1144.0 1928.9 3549.5 100 415.5 424.9 444.1 483.9 566.0 735.5 1085.5 1808.2 3300.2 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 HEATUP - LIMITING WELD Circumferential (1/4 t & 3/4 t)

  • f = 1.8 X 10 19 n/cm 2 Heat up Allowable Pressure at Noted Tem~eratures Rate °F/h 50°F 100°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F 0 420.3 434. 7 464.5 525.9 652.7 914.6 1455.4 2571.8 4877 .1 20 372.4 404.0 459.4 515.5 631.3 870.3 1363.8 2382.8 4486.8 40 282.5 308.7 362.8 474.4 612.3 831.1 1282.8 2215.6 4141.4 60 198.0 219.9 26.5. 2 358.5 551.4 796.8 1212.2 2069.7 3840.2 80 111.0 129.2 166.7 244.3 404.5 735.2 1144.0 1928.9 3549.5 100 30.8 46.2 77.8 143.2 278.2 556.9 1085.5 1808.2 3300.2 RPOS88-0237B-PT04-0P03

EA-A-PAL-89-098-01 COOLDOWN - CIRCUMFERENTIAL WELD (1/4 t)

Kia= 26.78 + l.233e [0.0145(T - 81 + 6T 1/4)]

P = 17.206 KrR - 5.85 ~Tmax - 54 f = 1.8 X 10 19 n/cm 2 Heat up Allowable Pressure at Noted Temperatures Rate °F/h 50°F 100°F 400°F 450°F 0 420.3 434.7 464.5 525.9 652.7 914.6 1455.4 2571.8 4877 .1 20 362.1 377.5 409.2 474.7 609.9 889.0 1465.4 2655.4 5112 .5 40 302.3 318.7 352.6 422.6 567.1 865.5 1481.6 2753.7 5380.3 60 237.3 254.9 29.1.3 366.5 521.6 842.0 1503.5 2869.3 5689.2 80 177 .6 196.4 235.4 315.7 481.6 824.0 1531.1 2991.1 6005.6 100 109.9 130.2 172 .1 258.6 437.2 806.0 1567.3 3139.4 6385.2 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 HYDRO TEST (3/4 t)

Kra = 26

  • 78 + l. 233 e [O.Ol45(T - 16.9 - AT 3/4)]

P = 24.097 - 8.193 ATmax - 54 f = 1.8 X io 19 n/cm 2 Heat up Allowable Pressure at Noted Tem~eratures Rate °F/h 50°F l00°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F 0 639.3 690.5 796.0 1013.9 1463.9 2393.0 4311.3 8272.2 16450.2 20 514.6 556.7 643.8 823.5 1194.5 1960.7 3542.5 6808.7 13552. 3 ,i 40 394.7 429.6 501.7 650.5 957.9 1592.4 2902.5 5607.5 11192.6 60 282.0 311.2 371.5 496.1 753.2 1284.0 2380.l 4643.3 9316.l 80 165.9 190.2 240.3 343.7 557.3 998.2 1908.7 3788.4 7669.7 100 59.l 79.6 121.8 209.0 388.9 760.5 1527.8 3111.9 6382.8 RP0588-0237B-PT04-0P03

  • EA-A-PAL-89-098-01 HYDRO TEST (1/4 t)

K1R = 26.78 ~ l.233e [0.0145(T 6T 1/4)]

p :;; 22.94 - 54 f = 1.8 X 10 19 n/cm2 Heat up Allowable Pressure at Noted Temperatures Rate °F/h 50°F 100°F 150°F 200°F

250°F

300°F 350°F 400°F 450°F 0 578.4 597.6 637.3 719.2 888.3 1237.4 1958.4 3446.9 6520.4 20 576.8 594.3 630.5 705.3 859.6 1178.3 1836.3 3194.9 6000.0 40 575.4 591.5 624.6 693.0 834.3 1126.0 1728.3 2971.9 5539.6 60 574.2 588.9 619.4 682.3 812.2 1080.4 1634.1 2777 .4 5137.9 80 573.0 586.5. 614.4 672.0 790.9 1036.4 1543.2 2589.7 4750.4 100 572.0 585.4 610.l . 663 .1 772.6 998.6 1465.2 2428.7 4418.1 RP0588-0237B-PT04-0P03

  • EA-A-PAL-89-098-01 HYDROSTATIC TEST LIMITING WELD Circumferential (1/4 t & 3/4 t) f = 1.8 X 10 19 n/cm 2 Heat up Allowable Pressure at Noted Tem2eratures 50°F 100°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F Rate °F/h 0 578.4 597.6 637.3 719.2 888.3 1237.4 1958.4 3446.9 6520.4 514.6 556.7 630.5 705.3 859.6 1178.3 1836.3 319L1. 9 6000.0 20 40 394.7 429.6 501. 7 650.5 834.3 1126.0 1728. 3 2971.9 5539.6 282.0 311.2 371.5 496.1 753.2 1080.4 1634.1 2777 .4 5137.9 60 165.9 190.2 240.3 343.7 557.3 998.2 1543.2 2589.7 4750.4 80 59.1 79.6 121.8 209.0 388.4 760.5 1465.2 2428.7 4418.1 100 RP0588-0237B-PT04-0P03

PALISADES PRESSURE AND TEMPERATURE LIMITS FOR HEATUP 19 2 r = 1.8 X io n/cm (No r1easure111ent llncertaintv Inclu<'led)

PRESS PSIG 3000 r--:--, .-*-., ... 1 I ..' I ., -*

  • II I

~  ! ' I

' ' .. **- - 'J. ..

_i 2750 ---- -- .

'1*

~l I

.- . - I ..

2500 ~---*-1

... - *-* **i --* - - .. :. .L . . . .i I.

~:

2250 L----~

.j: ' .,

. *- - --r - --- -- - . I

- .. .., . . - ... - )

-1:  : 0 '

2000 k--***. ;. *- ~

--- --* .. ~* .... *- ... ... --- I I

/.0

  • 1 .. .' -

l

-1:

I I

I

60 40 1750 -tt------. -. . - - I *I-* ..  ; . .. .. ~ .

'11  :* 80

r  :* 100

~. l 1500 *------- .;_ .. - . *'-** *-* -;* *..... **1 - **t* . . - !, *** - . * -- . ~- .

-1*:

-l:

1250 f:----; --* --*- --:- - *---- .. L. - - -t -

-1:

1000 ~- -- .i - -

1:

150L--. . t- - . . l.. .

... -- 1 i i . *---*r I i I 0

I t 1 1 t

  • f .. t 1 **1 I. , ,_,.,_

nn rr* ,. ,...., In-*' ,,,.! .... . I 1* I I r I I r .... l.... I....1.. ~J 50 75 100 125 150 175 200 225 250 275 - 300 325 350 375 400 425 450 TEMPERATURE DEGREES F HEATRAT 0 20 40 BO BO ----- 100

PRESSURE ATURE LIMITS FOR OWN PRESS PSIG I'

  • = l

.H X 10 l <J n I cm 2 (No Measurement Uncertainty Included) 3000 . I 2750

. In /

'~,

2500 0rr ~

2250 t~

2000

/L1 ~~

1750 (l

1500

~

40 20 60 80 1250 .

i~~

1000

. f

~~

. 100 750

_;t--:: ~

' - 80

c. \

500

--~ ~~ ll 250 .

I

- *- 20 0 - .' ' ' .' . **** ' ... ' . .. ' ' ..

0 I I I I *

  • I I I 0 0 ' I
  • I
  • I I 0 I

' ' ' ' ' 0 ' I 'I I 0 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 <450 TEMPERATURE DEGREES F COOLRAT 0 20 40 60 BO --100

<J

~

PAL PRESSURE PERATURE LIMITS FOR 19 2 PRESS PSIG f = 1.8 X 10 n/cm aooo 2750

..  !//; !/;'

2500 0

!///, I/

2260

. 20 /;V//;'

2000 . //h I/

1750 40 J/

~

!//;}'

1500 6( J~ If' 1250 BO

  1. ~ ~

~~/

100 v

1000

~

' ~-

v--- / I v

~

v 750

~ ..... / " *-

. 500 ' _;__--

~

~

.... ~

~

~.

~

~ ... L-"""""'

250 ~

~ ...

0

. .

  • I * ' **** I I
  • I

.,...,.., **** **** ... ..' ' ' J I I I

' ' . ' I * * * .. ' . I I I I 50 75 100 125 150 175 200 225 250 275 aoo 325 350 375 400 425 450 TEMPERATURE DEGREES F RATEFOH 0 20 "40 BO BO --100

EA-A-PAL-89-098-01

SUMMARY

OF THE GOVERNING EQUATIONS For Heatups and Cooldown With 3.35 X io 19 n/cm 2 Fluence With Measurement Uncertainty Heatup 1/4 t Circumferential KrR = 26.78 + 1.233 e [0.0145 (T-127.6-6T 1/4)]

P = 17.206 KrR - 84 Heatup 3/4 t Circumferential KrR = 26.78 + 1.233 e (0.0145 [T - 63.4 - 6T 3/4)]

P = 18.073 KJR - 6.145 6Tmax - 84 Cooldown 1/4 t circumferential KJR = 26.78 + l.233e (X 0.0145 [T - 127.6 + 6T 1/4] )

P = 17.206 KJR - 5.85 6Tmax - 84

  • RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

SUMMARY

OF THE GOVERNING EQUATIONS For 3.35 X 10 19 n/cm 2 Fluence with Measurement Uncertainty For Hydro-test KrR ~ 1.5 Hm om+ ~Tmax For 1/4 t KrR = 26.78 + 1.233 e (0.0145 {T - 127.6 - ~T 1/4)]

P = 22.94 KrR - 54 For 3/4 t KrR ~ 26.78 + 1.233 e {0.0145 [T - 63.4 - ~T 3/4)]

P ~ 24.097 KrR - 8.193 ~Tmax - 54

    • RP0588-02378-PT04-0P03

EA-A-PAL-89-098-01 HEATUP - LIMITING WELD (1/4 & 3/4 t) f = 3.35 X 10 19 n/cm 2 With Measurement Uncertainties Heat up Allowable Pressure at Noted Temperatures Rate °F/h 50°F 100°F 150°F 200°F 250°F

~~

300°f 350°F

~~

400°F 450°F 0 383.7 391.0 406.1 437.4 501.9 635.2 9J0.3 1478.4 2651.3 20 327.9 344.0 377 .2 432.l 491.0 612.6 lJ.ij *i. 7 1382.2 2452.7 40 240.5 253. 8. 281.4 338.2 455.7 592.7 822.5 1297. l 2277.0 60 157.9 169.1 192.l 239.7 338.0 540.9 786.6 1222.9 2123.7 80 72.6 81.8 101.0 140.5 222.l 390.6 738.6 11-51.2 1975.8 100 -6.2 1.6 17.7 51.0 119.8 261.8 555.0 1089.8 1849.0 RP0588-0237B-PT04-0P03

  • EA-A-PAL-89-098~

HEATUP - (1/4 t) CIRCUMFERENTIAL f = 3.35 X io 19 n/cm 2 KJR = 26

  • 78 + l. 233 e [0.0145(T - 127.6 - ~T 1/4))

P = 17.206 KIR - 84 With Measurement Uncertainties Heatup Allowable Pressure at Noted Temperatures Rate °F/h 50°F 100°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F 0 383.7 391.o 406.l 437.4 501.9 635.2 910.3 1478.4 2651.3 20 383.1 389.8 403.6 432.1 491.0 612.6 863.7 1382.2 2452.7 40 382.5 388.7 401.3 427.4 481.3 592.7 822.5 1297.1 2277.0 60 382.l 387.7 399.3 423.3 472.9 . 575 .2 786.6 1222.9 2123.7 80 381.6 386.8 397.4 419.4 464.8 558.4 751.~ 1151.2 1975.8 100 381.2 386.0 395.8 416.0 457.8 544.0 722.i 1089.8 1849.0 RP0588-0237B-PT04-0P03

  • EA-A-PAL-89-098~

COOLDOWN - (1/4 t) CIRCUMFERENTIAL f = 3.35 X 10 19 n/cm 2 KIR = 26.78 + 1.233 e (0.0145 [T - 127.6 + 6T 1/4])

P = 17.206 KIR - 5.85 6Tmax - 84 With Measurement Uncertainties Heat up Allowable Pressure at Noted Temperatures Rate °F/h 50°F l00°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F 0 383.7 391.0 406.1 437.4 501.9 635.2 910.3 1478.4 2651.3 20 325.0 332.8 349.0 382.3 451.1 593.l 886.4 14~1.9 2742.0 40 264.7 273.1 290.3 325.9 399.4 551.3 864.8 1512.0 2848.4 60 199.2 208.1 226.7 264.9 343.8 506.8 843.4 1538.3 2973.1 80 138.9 148.5 168.3 209.2 293.6 467.8 827.6 1570.4 3104.2 100 70.6 80.9 102.2 146.2 237.1 424.7 812.1 1612.0 3263.4 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098~

HEATUP - (3/4 t) CIRCUMFERENTIAL f = 3.35 X 10 19 n/cm 2 K1a = 26.78 + 1.233 e [0.0145 (T - 63.4 - ~T 3/4))

P = 18.073 Kia - 6.145 ~Tmax - 84 Heat up Allowable Pressure at Noted Temperatures Rate °F/h 50°F 100°F 150°F 200°F 250°F 3i00°F 350°F 400°F 450°F 0 481.3 437.9 478.2 561.5 733.5 1088.5 1821.6 3335.3 6460.6 20 327.9 344.0 377 .2 445.9 587. 7 881[).5 1485.0 2733.2 5310.4 40 240.5 253.8 281.4 338.2 455.7 698.2 1198 .8 2232.6 4367.0 60 157.9 169.7 192.1 239.7 338.0 540.9 959.7 1824.6 3610.4 80 72.6 81.8 101.0 140.5 222 .1 390.6 738.6 1456.9 2940.2 100 -6.2 1.6 17. 7 51.0 119.8 261.8 555.0 1160.4 2410.4 RP0588-0237B-PT04-0P03

ADES PRESSURE AND T PERATURE LIMITS FOR 1 'J 2 PRESS PSIG f ~ 3. 35 x 10 n/cm (mP.as11rement uncertaintv for P.T. included)

t=J. -. r: _, ~ -L~~ *1-.* ~ r-
  • _ ---r-~--*- :.. *.-~- -r .:.- r-~- _* *- _*_J_ ~- -* ~

2250 -__,--********-,--- . -*-l-- ---i---- **i---** -****i-- . *t . * *-* 1*** .... t **--1* *- *- ----

2000 , **--1-*---.*-***j-**---r--+-* . . * - - -*-*-*-t *** ......... t* **-*r --*1---- . -****.

1150 t-. *-*T-* *--1* -- *- *-** ***t---- ----** **-* --* --*-***j- ...... j. -.~ -----~-- -+--* L. . .,__,_, _. _

1500 r*--°+-**-r--**- ---t----- t** *--~

o_ 0 **.. - * - - - - -*-+- . I *-* -- --+-----~*-~'----+

1250 -~-**- *-!*--*-**+ ***--- *---** *-**** . 1 **--**-. **-****** *****-- **- *** ...1 _ .... _J ________ --***- *i . . .L * .6LL....£.6.

1000--

750 l . . . - - .- *-*- -

soo i-:- .- . ~- *-*-- ........ -- . . . . .. ***-** ... . - . . . .. ..--* .... L. .. .. __ _J 1

. . , __ -* .. .. .. . .* -*-* .- -* . 1... -.--.. -

0 lt=.,.1_=,.,=.. ,.t..

=. =.. ,_,=,=.,+.=rT=,_=,.+=,. . .,-.,

,.=,.=-.t_= . -,t-,-.,-,- ., . r-.,-.,-..,1. n*n 0-1 , .*. 1. 0*o I 0 ,. .,. ,.,

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 TEMPERATURE DEGREES F HEATRAT 0 20 40 80 --- BO - - 100

'J:;

PAL~ADES PRESSURE & TEM ATURE LIMITS FOR CO OWN 1 ') 7 PRESS PSIG f = 1. l'i x 10 n/cm** (mr>aS\JrPmPnt uncPrtainty for P.T. included) 3000 .

2750

~

2500 ~~

2250 VII!

2000

~~ ~

11-1750 1500 0 20 40 60 80 00 1250 v

II 1000 ~

750 500 . , ---

--- ::::::::=:::::

~ ~ ~

~

'/""

250 .

-~

- l..,----

0 I I

' ' ' ' ' ' ' ' I '

' '

  • u I I . . . .. . . .. 1 I I
  • I ' I

' ' ' ' I I 1 . .. I I I I I I I '

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 TEMPERATURE DEGREES F COOLRAT 0 20 40 60 80 . --100

EA-A-PAL-89-098-01

SUMMARY

OF THE GOVERNING EQUATIONS For 3.82 X 10 19 n/cm 2 Fluence With Measurement Uncertainty Heatup 1/4 t Circumferential K1a = 26.78 + 1.233 e [0.0145 (T - 130.5 - ~T 1/4)]

P ~ 17.206 KIR - 84 Heatup 3/4 t Circumferential K1a = 26.78 + 1.233 e (0.0145 [T - 68.0 - ~T 3/4)]

P = 18.073 KIR - 6.145 6Tmax - 84 Cooldown 1/4 t Circumferential KIR = 26.78 + l.233e (X 0.0145 [T - 130.5 + 6T 1/4] )

P ~ 17.206 K1a - 5.85 6Tmax - 84 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01

SUMMARY

OF THE GOVERNING EQUATIONS For 3.82 X 1019 n/cm 2 Fluence With Measurement Uncertainty For Hydro-test KIR ~ 1.5 Mm om+ Ht ATmax For 1/4 t K1a = 26.78 + 1.233 e [0.0145 (T - 130.5 - AT 1/4)]

P ~ 22.94 K1a - 84 For 3/4 t K1a = 26.78 + 1.233 e (0.0145 [T - 68.0 - AT 3/4)]

P ~ 24.097 K1a - 8.193 ATmax - 84 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 COOLDOWN - (1/4 t) CIRCUMFERENTIAL f = 3.82 X 10 19 n/cm2 With Measurement Errors K1R = 26.78 + 1*233 ~

[0.0145(T - 130.5 + AT 1/4))

P ~ 17.206 K1a - 5.85 ATmax - 84 Heat up Allowable Pressure at Noted Tem2eratures Rate °F/h 50°F 100°F 150°F 200°F 250°F 300°F 350°F 400°F 450°F 0 383.4 390.4 404.9 434.9 496.8 624.5 888.3 1433.0 2557.6 20 324.7 332.2 347..7 379.6 445.6 581.8 862.9 1443.5 2642.2 40 264.4 272.4 288.9 323.1 393.6 539.1 839.7 1460.3 2741.7 60 198.8 207.4 225.2 261.8 337.5 493.8 816.5 1482.8 2858.5 80 138.5 147.7 166.7 205.9 286.8 453.9 798.9 1511.1 2981.7 100 70.2 80.1 100.5 142.7 229.8 409.7 781.2 1548.1 3131.6 aro588-0237B-PT04-0P03

EA-A-PAL-89-098-01 HEATUP - LIMITING WELD (1/4 t & 3/4 t) 1 = 3.82 X 10 19 n/cm 2 With Measurement Errors Heat up Allowable Pressure at Noted Tem~eratures Rate °F/h 50°F 100°F 150°F 200°F 250°F _300°F 350°F 400°F 450°F 0 383.4 390.4 404.9 434.9 496.8 624.5 888.3 1433.0 2557.6 20 326.9 342.0 373.1 429.8 486.3 602.9 843.7 1340.8 2367.2 40 239.7 252.l 277.9 331.1 441.0 583.8 804.2 1259.2 2198.7 60 157.2 167.7 189.2 233.8 325.7 515.5 769.7 1188.0 2051.8 80 72.0 80.7 98.6 135.6 211.9 369.6 695.0 1119.3 1910.0 100 -6.7 0.6 15.7 46.9 111.2 244.1 518.3 1060.4 1788.3 RP0588-0237B-PT04-0P03 I'-\

EA-A-PAL-89-098-01 HEATUP - (3/4 t) CIRCUMFERENTIAL f = 3.82 X 10 19 n/cm 2 With Measurement Errors KIR = 26

  • 78 + l. 233 e [0.0145(T - 68.0 - 6T 3/4)]

P ~ 18.073 Kia - 6.145 6Tmax - 84 Heat up Allowable Pressure at Noted Temperatures Rate *F/h 50°F 100°F 400°F 45o*F 0 417.2 435.4 473.2 551.1 712.0 1044.1 . 1729.9 3145.9 6069.6 20 326.9 342.0 373.1 437.3 570.0 843.9 1409.4 2577 .o 4987.9 40 239.7 252.1 277.9 331.1 441.0 667.8 1136.2 2103.2 4099.9 60 157.2 167.7 189.2 233.8 325.7 515.5 907.3 1716.4 3386.9 80 72.0 80.7 98.6 135.6 211.9 369.6 695.0 1367.l 2754.6 100 -6.7 0.6 15.7 46.9 111.2 244.1 518.3 1084.7 2254.0 RP0588-0237B-PT04-0P03

EA-A-PAL-89-098-01 HEATUP - (1/4 t) CIRCUMFERENTIAL f ~ 3.82 I 10 19 n/cm2 With Measurement Errors KIR. 26.78 + 1.233 e [0.0145(T - 130.5 - ~T 1/4)]

P. ~ 17.206 KIR - 84 Heat up Allowable Pressure at Noted Temperatures Rate *r/h 50°F l00°F uo°F 200°F 250°F 300°F 350°F 400°r 450°F 0 383.4 390.4 404.9 434.9 496.8 !024.5 888.3 1433.0 2557 .6 20 382.8 389.2 402.5 429.8 486.3 602.9 843.7 1340.8 2367.2 40 382.3 388.2 400.3 425.3 477.0 583.8 804.2 1259.2 2198.7 60 381.8 387.2 398.4 421.4 468.9 567.l 769.7 1188.0 2051.8 80 381.4 386.4 396.6 417.6 461.1 551.0 736.4 1119.3 1910.0 100 381.l 385.6 395.0 414.4 454.4 537.l 707.9 1060.4 1788.3 RP0588-02378-PT04-0P03

t PAL.ADES PRESSURE AND T.ERATURE L.IMITS FOR TUP l 'J .

f = 3.fl2 x JO n (m1*as11n!mt>11I. uncertaintv for P.T. included)

PRESS PSIG aooo r--- j * .. . I . -** * *----t

-____ _J 2750r 1 . 1 . .. I 1

2500 #--J

~I I

I*

. 1. - I . .I I i I . .l I I i I. . i

-1. i- i i i  !  !

,_ I I

-~--*-J-+.

2000 r- -

225Dr-* *-I *I- - -*--- -

r- *-*-*-*- * -*-* - I I

1 l - -- t --1 **-

1*-*

i .. ---- -- - - *- -* i ... -.. -- --

. I

-*l--1-.---

~I l*-*1-** - ,--1-~--**

I '

1500r-i--*------L ... j- --1--

1250 I -+ 0

- - - 0 . wi- I - ,~-

ao --*- ;1'!0 ---- ----- -*- - - --- I.. --- --1-----

1ODO i 1- 1-.-- 1

-- I . -r - .---...-... I -1

.750.t- +*- ! - .. !  ! . .. . . ' . -l--4 500 --~*-- -* - *- . . --1 --- ..... -- . . . 1.

. .

  • f-** *--t 250~==r===+==--~--~--~*-~--~-~~.~-~- .  :...:. JJ '

50 75 100 . 12.5 150 175 200 225 250 275 300 325 350 375 400 425 450 TEMPERATURE DEGREES F*

HEATRAT 0 -- 20 ---- 40 60 --- 80 - - 100

PALISADES PRESSURE & TEMPERATURE LIMITS FOR COOLOOWN

(measurement uncertainty for P. T. included)

PRESS PSIG cm 2 3000

. Ji 2750 2500

,ra 2250 2000 u

i

~

,11/11 1750 20 1500

~

1250

~

40 60 BO 100

~

1000 750 (.....-'.

~~

500

~

--~ ~~

c::--:: ::~ ~

250 L---

--- t:::::::;: ~

0-I I I I I I 1 1 I I I I I I I I I I I I I I I I I I . . . .. I I

  • I I I I-. T I I I ' I I I I I I I I I I 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 TEMPERATURE DEGREES F r.nrn RAT 0 20 40 60 80 100

.r 7 EA-A-PAL-89-098-01

  • REFERENCES
1. ASHE Boiler and Pressure Vessel Code,Section III, 1977 S78, Appendix G-2000.
2. Requlatory Guide 1.99, Revision 2.
3. USNRC Standard Review Plan, Section 5.3.2, "Pressure Temperature Limits."
4. Battelle Columbus Laboratories Report, "Palisade& Nuclear Plant Reactor Pressure Vessel Surveillance Program: Capsule A-240," March 13, 1979.

S. Branch Technical Position HTEB No 5-2, "Fracture Toughness Requirements."

6. June 14, 1985 submittal from CP Co to the Director of Nuclear Reactor Regulation.
7. "Evaluation of Pressurized Thermal Shock Effects Due to Small Break LOCAs With Loss of Feedwater for the Combustion Engineering NSSS, 11 CEN-189, CE Power Systems, December 1981.
8. ASHE Boirer and Pressure Vessel Code,Section III, 1986, Appendix I.
9. "Strength of Materials, Part II, Advanced Theory And Problems",

3rd Edition, D VanNoatrand Company, Inc., Princeton, NJ.

10. "Theory and Design of PreHure Vessels", 1985, First Edition, VanNostrand Reinhold Company, In.s_., New York, NY.
11. "Analy~is of the Reactor Pressure Vessel Fast Fluence for the Palisades Nuclear Plant through end of Cycle 811 by Reactor Engineering Department, Palisades Nuclear Plant, Consumers Power Company *
    • RP0588-0237B-PT04-0P03 i

I I

~

EA-A-PAL-89-098-01 ADDENDUM A Appendix G Limit Curve Calculations for 1.8 X 10 19 Fluence Tech Spec Curves Data Heatup l/4t (1 degree increments)

Heatup 3/4t Cooldown l/4t Hydro 1 /4t Hydro 3/4t Operating Limit Curves Data Heatup l/4t (1 degree increments)

Heatup 3/4t Cooldown l/4t (1 degree increments)

    • RP0588-0237B-PT04-0P03
  • i ~~

...~-

  • -~~~~i9*

... *- . ~.

. -~**

. ~~

,,..'J*,_:if.'"~

~-~

&j"

'** . . ,. .* ~ . . .:;.

.=* . .., , . . T~ ~e& .

  • . ..., ...,j. .,&. ,. ........ ".... f .,...._

10 CLS c.. ,,..c..it 20 DIM T#(450>

30 DIM DT14#<6>

40 DIM P#<6,450J 50 f# ( 1) =1 #

60 FOR 1=2 i*o 450 70 f#(!)=f#(l-ll+l#

80 NEXT I 90 FOR [ =1 ro 6 100 READ DT14#(1) 110 NEXT I 120* F'R I NT 130 LPRINT

!40 FOR J=1 TO 450 150 F'RINT USING ###.tt:#.#";T#<J) ;,

11 160 LPRINT USING #####.#";T#<J>; 11 1 70 FOR I=_ 1 ro 6 180 KIR#=26. 78#+1. 2:s3#*EXF' C. 0145#* <T# (J >-81#-DT14# (I>>) V 190 P* < I , J > = \ 7. 206#*~~ I R#-54# ~

200 PRINT USING 11 #####.#";F'#<I,J>;

210 LPRINT USING 11 #####.#";F'#CI,J>;

220 NEXT I PRINT LF'RINT NEXT J OPEN 11 a: datal" FUR OUTPUT AS 1 270 BS=" II 280 FOR J=l 10 450

290 PRINT #1,USING 11 #####.## 11 ;T#(J);

300 FOR I=1 TO 6 310 IF !=6 THEN GOTO 340

.20 F'R I NT # 1 'us l NG II##### ..... II; P# ( I
  • J) ;

330 GOTO .350 340 PRINT #1,USING #####.##";P*<I,J> 11 350 NEXT 1 360 NEXT J

.370 CLOSE # 1 380 DATA 0.#,6.3#,12.4#,18.2#,24.3#,30.# \/

.390 END a

./,

. I

I' 1 * (l 4 i.:::.. 4 412.8 412 ...::. 411. 9 411.5 411. 1

2. (l 413.5 412.9 412.4 412.0 411.5 411. 1
3. <) 413.6 41.J.(> 412.5 412.(l 411.6 411. 2 4.0 413.7 41-3. 1 412.6 412.1 411. 7 411.3
5. (I 413.8 4L:.. '2 412.7 412.2 411.7 411.3 6.0 413.9 413.3 412.8 412.3 411. 8 411.4 7.0 414.0 413.4 412.8 412.3 411.9 411.5
8. 0 414. 1 413.5 412.9 412.4 412.(l 411.5 9.0 414.2 413.6 413.0 412.5 412.0 411.6 10.0 414.4 413.7 413.1 412.6 412. 1 411.7
11. (I 414.5 41::..a 413.2 412.7 412.2 411. 8
12. °<) 414.6 413.9 413 *.3 412.8 412.3 411.8
13. (l 414.7 414.0 413.4 412.9 412.3 411.9 14.o 414.8 414. 1 413.5 412.9 412.4" 412.<)

15.0 414.9 414.2 413.6 413.(1 412.5 412.1 16.0 415.0 414.3 "413.7 413.1 412.6 412.1 1 7. 0 415.2 '414. 4 413.8 413.2 412.7 412.2

.18. (l 415.:.::. 414.5 413.9 413.3 412.8 412.3 t*=t. 0 415.4 414.7 414.0 413.4 412.8 412.4 20,, 0 415.5 414.8 414.1 413.5 412.9 412.4

21. (J 415.7 414.9 414.2 413.6 41-:3. '.) 412.5
22. *) 415.8 415.0 414.3 413.7 413. 1 412.6 415.9 415. l 414.4 41."3.8 41-3. 2 412.7 24.0 416. 1 415.2 414.5 413.9 413.3 4i:2. 8 416.2 41!:3.4 414.6 ~14.0 41.3. 4 412.9 26.0 4 !.:>. :.:;: 415. ::; 414.8 414. 1 413.5 413.(l
27. (l 416.5 415.6 414.9 414.2 41-3.6 41.3. 1 28.(l 416.6 415.8 415.0 414.3 413.7 413.1 29.(l 416.8 415.9 415. l 414.4 413.8 413.2 408.(l 2838.1 2625.9 2438.(l 2274.2 2116.1 1980.5 409.0 2873.7 2658.3 2467.7 2301.5 2141.1 2003.S 410.0 2909.7 2691.2 2497.8 2329.1 2166.4 2026.8 411.0 2946.2 2724.5 2528.3 2357.2 2192.1 2050.S 412.0 2983.3 2758.4 2559.3 2385.7 2218.2 2074.5 413.0 3021.0 ~792.7 2590.8 2414.6 2244.6 2098.9

~*A ~ -n~o 1 ~o~~ L ~~~- - ~~n~ o ~~~1 ~ ~1~~ L

.*~

.i?""'~~

~)

.,. *1=s. 4* ~-

~~-~--**l~~.5 414".9- 41~1..

  • ;4*~- 41~.6 414.9 414-.2'

~5'!::'416.. . 415. 8 41~. 0 414.4 417-** -~ 4t b. 7 41 5

  • 9 41 ~. 1 414.5
41. 0 4{7~~- 416.e 416.o 415.2 414.6 42.0 43.0 419.(J 417.9 417.0 416.2 415.4 414.7 44.0 419.2 418.1 417.1 416.3 415.5 414.8 45.0 419.4 418.3 417.3 416.4 415.6 414.9 46.0 419.5 418.4 417.4 416.6 415.8 415.0
47. 0 H9. 7 ~18.6 4L7.6 416.7 415.9 415.2 48.0 419.9 418.8 417.8 416.9 416.0 415.3 49.U 420. l 419.U 41 7 .'t 417.0 416.2 415.4 50.0 42<) *.3 41 'T'. 1 418. 1 41 7.::: 416.:3 415.5
51. (l 420.5 *419. ,j 418.2 417 *.3 416.4 415.7
52. () 420.7 419.5 418.4 417.5 416.6 415.8 53.0 420. '~ 41'~. 7 418.6 417.6 416.7 415.9 54.0 421.1 419. 9 418.8 417.8 416.9 416.1 55.0 421. :3 420. l 418.9 418.(1 417.C> 416.2 56.0 421. 5 .42('. :J 419. 1 418.1 417.2 416.3 57.0 421.8 420.4 419.3 418.3 417.3 416.5 58.0 422. (> 420.6 419.5 418.5 417.~ 416.6 59.0 422.2 420.9 419.7 418.6 417.6 416.8 60.0 422.4 421. 1 419.8 418.8 417.8 416.9
61. 0 422.7 421.3 420. (I 419.0 417.9 417.1 62.0 422.9 421.5 420.2 419.1 418.1 417.2 63.0 421.7 420.4 419.3 418.3 417.4 o4.{> 423.4 421.9 420.6 419.5 418.4 417.5 65.0 423.6 422.1 420.8 419.7 418.6 417.7 66.0 423.8 422.4 421. 0 419.9 418.8 417.8 67.0 424. l 422.6 421. 2 420.1 419.0 418.0 68.0 424.3 422.8 421. 5 420.3 419.1 418.1 69.0 424.6 423.0 421.7 420.5 419.3 418.3 70.0 424.9 423. ~3 421. 9 420.7 419.5 418.5
71. (l 425.t 4:23.5 422.1 420.9 419.7 418.7 72.0 425.4 423.8 422.3 421. 1 419.9 418.8 73.0 425.7 424.0 422.6 421.3 420.1 419.0 74.0 425.9 424. :.:; 422.8 421. 5 420.3 419.2
75. (l 426.2 424.5 423.0 421. 7 420.4 419.4 76.0 426.5 424.8 423.3 421. 9 420.6 419.5 77.0 426.8 425.0 423.5 422.2 420.9 419.7 78.0 427.1 425.3 423.7 422.4 421.1 419.9 79.0 427.4 42~.6 424.0 422.6 421. 3 420. 1 80.0 fl27.7 425.9 424.2 422.8 421.5 420.3
81. 0 428.0 426.1 424.5 42::.. 1 421.7 420.5 82.0 428.3 426.4 424.8 4~3.3 421. 9 '420.7
33.0 428.6 426.7 425.0 423 .. 6 422. 1 420.9 84.0 428.9 4:27. (l 425.3 423.8 422.4 421. 1 85.0 429. :,!. 427.3 425.6 424.0 422.6 421. 3 86.0 429.6 427.6 4~.8 424.3 422.8 421.5 87.0 429.9 427.9 426. 1 424.6 423.0 421.8 88.0 430. ::. 428.2 426.4 424.8 423.3 422.0 8'7. 0 430. ,'.J 428.5 426.7 425. l 423.5 422.2
90. <) 430.9 428.8 427.0 425.3 423.8 422.4
91. 0 431. 3 429.2 427. :3 425.6 424.0 422.7 92.0 431.7 429.5 427.6 425.9 424.3 422.9 93.0 432. <) 42-1.8 427.9 426.2 424.5 423.1 94.0 4'.'!.2. 4 430.2 428.2 426.5 424.8 423.4
95. ') 432.8 428.5 426.7 425.0 423.6

~~-..-..-

-;.,~

/;'"- "':,

~42C1:2*,

-~~451.

. , .... .:1<*429.

. ~

    • "3i.9;. 429.9 437.3 -~ 4'32.2 430.2 428.2 107. (l 437.7 "l~.o 432. 6 ..* 430. 5 428.5 108.0 438.2 43S.-* 433.0 '430.9 428.8 427. 1 109.0 438.6 435.8 433.4 431.2 429.2 427.4 110.0 439.1 436.3 433.8 431.6 429.5 427. 7.

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  • RP0588-0237B-PT04-0P03

~o.o 100.0 150.0 200.0 2~0.0 300.0 350.0 400.0 4~0.(>

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100 NEXT I 110 FOR J=1 TO 9 120 PRINT USING ""#'ft"##"#.#"; T# <J >;

130 LPRINT USING "#~Ut:lt:tt.#";T#<J>;

140 NEXT J 150 PRINT 160 LPRINT 170 FOR I= 1 TO 6 180 FOR J=l TO 9 190 KIR#=26.78#+1.233#*EXP<.0145#*<T#(J)-127.6#-DT14#(1)))

200 P#<I,J>=17.206#*KIR#-84#

210 PRINT USING "###****";P#<I,J>;

220 LPRINT USING "###~Ut. #"; P# <I, J >;

230 NEXT J 240 PRINT 250 LPRINT

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@:&..n PALISADES NUCLEAR Pt.ANT EA* e..s..s,e 3.P 7.Z? - cfa- c'

,.. I ENGINEERING ANALYSIS WORK SHEET M* on Shfft / of J Title d*a* r::ac ~£:**.1:, .. 1:. ~ (. d=~..:a

~~-=***

1llUTIATION ANO REVIEW 1n1t1it~ 1n1t1*tor A*v1ew M*tlIOd Cl"ltcll (.I) recl"ln1c1lly A* .. **w~ At,.*twtr Atv DtS(r1pt1on By Oitt Appd By Alt Ci IC Ott A..w 01.1*1 Ten By O*t*

Appd 9y 0 Issue ~ /~~ Rt;C ~~ -

Or1g1nal vo/,,L.u Q(.l, (J I , / I I. OBJ!CTIVI: .

The objective of thi1 en1ineerin1 analy1ia i1 to calculate the hoop 1tre11 due to internal pre11ure, throuab th* wall thickn*** of th*

Pali1ade1 le.actor Ye11el

  • II. R!FEIEHCISI A. P'or111la1 For StreH anci Strain, Fifth !ditioa, by loark and Youns.

B. H-lA NSSS Ceneral Sy1t** De1criptioa llo. 2966-010, Ravi lion o.

PalisadH Plant Primary Coolant Sy1t...

c. PalisadH 'Nuclear Plant Adaini1trative Proc9dure, Sec ti ca 9.ll.

III. ANALYSIS IJIPUTI A. Ina id* lacliua.. of. Ve11el 1 86 inchea Out1ide ladiua of Ve1 ..11 94.5 inchea Clefereilc* c>-** -- -

IV. ASSUMPTIODI -

i A. T'1e inaid* radiua anci vall tbiclmeu u1M in thi1 analy1i1 for the re*crar v****l is con"9ct.

a. The mat*rial of tbe ve11el i i linur, i1otropic aDci homoaeneous.
v. ANALYSIS I A* CDIDAL
  • The circumferential 1tre11 produced by an internal 1*1* pre11ure only, i1 callecl a hoop 1tre11. See Fiaur* 1.

/DO

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  • =-sn J I

PA.LISA.DES NUCLEAR PL.ANT ANALYSIS CONTINUATION SHEET EA* c-.ss~ ~~ ?..2.? -r:/s Shett Rev I L of J I "

F E_p F Figure l For a thin-wall pre11ure ve11el, the hoop str*** i1 con1idered uniform throu&ft the wall of th* pre11ure ve11el and i1 1i~en by the follovins equation (Reference A, Pa1* l)t 0 .u 2t a i* the normal circUllferential 1tre11 p i1 the unit pre11ure ia pound1 per 1quare inch d i* the out1ide di ...ter of the ve11el t i1 the wall thickne11 of the ve***l However, for a thick wall ve11el the hoop 1tr*1* i1 not considered to be uniform tbrouahout the thickne11 of the wall. therefore, the wall 1tr***** throu&tt the ve11el1 tbickne11 aa1 be foUDd b7 the follovin1 fo~la (leferenc* A, Pa1* 1)1 ro 1 + ri 1 a

  • P [ 1 l ro ri a wheres p i1 the-,mit pre11ur* in pound* per square incb ri i1 the internal radiu1 of the v****l (fia*d) r 0 i1 the ouc1ide radiua varyin1 throuah th* wall thickn***

The vall thickne11 point* coaaidered in thia calculation will be at 1/4, 1/2 and 3/4 of the total wall thickn****

@=*..

I oI PALISADES NUCLEAR ?LANT EA* ess.e />-¥ 7 ..z. 7 . -::/.s -:

iUUL I ANALYSIS CONTINUATION SHEET Sheet ..z of J

    • Rev I B. RESULTS The results of th* calculation show that the hoop 1tre11 varie1 decreasingly a1 it is ob1erved fros th* insid* to the outside radius.

The masimum circumferential 1tres1 i1, therefore, on th* inside surface of the reactor ve11el.

C. CALCULATIOHI

..,__... __.:.,:.ri~~ 1 I 2 [ 31

  • I' 1617 I I a l/4t l/2t 3/4t Figure 2 Th* wall thickn11a i1 8.5 iacba1. Th* in1ide racliu1 of tba v111el Cri) i1 86 inch*** At 1/4 t, 1/2 t, and 3/4 t the out1ide radiu*

(r 0 ). ii 81.125, 90.25, and 92.375 incba1 r11pectivel1. Ulin1 the afor...ntioned formula and an internal pre11ure (p) of 1000 p1i1 th*

follovin1 hoop 1tr111e1 are obtained&

01/4

  • 10,364 p1i 01/2
  • 10,106 p1i OJ/4
  • 9,866 pli VI. CONCLUSIONS:

The f or1111la for calculatiaa ttw hoop 1tre11 in a thin-wall pressure YHHl i1:

Oc

  • 2!

2t This formula will re1ult in a hoop stre1* of 10,118 p1i at a pr111ure of 100~ p1is. HaveYer, the hoop str111 vari** a1 one 110ve1 away fro* th*

midpoint of tba ve11el wall. Th* thick-wall hoop 1tr111 formula listed in Section V, Part A of this calculation i1 a little 110r1 accurate in deteraiaiaa. tba 1tr111 throu1bout t!w thiclule11 of the v111el

  • l Io*'

Ca-l~c;/~ °"'.077

-~;

E .s-.s,e 117~ 7 - c/.s - a ..z_

*****======== I MA G E S ~ D =============

Copyriqht <c:> 1~84 C*~l,:sti-.:i. .l '.3,~~b1-.u*e Inc:.

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=:============~===~====~========:===

NOTICE

~----------------------------------------------=

Celestial Software Inc. assum*5 no responsi-

- bility for the validity, ~ccuracy, or =

applicability of th* results obt*ined from

= IMAGES-30. ~

Any que9tions or comm*nts concerning th* us*

of IMAGES-30 or the u5ers manu*l should b*

addressed to:

=

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SUMMARY

IN 1 SLOCKS Minimum Di~g~nal Stiffness *****

  • 13400*+-1.0 Eq No of Minimum Diaqonal ****..

Maxi1num *-01 aqonal *3ti f ~11ess *****

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