ML20115H333

Rev 1 to User Guide for Preslok,Gate Valve Pressure Locking Analysis Program Using Commonwealth Edison Model

ML20115H333
Person / Time
Site:	Point Beach
Issue date:	02/07/1996
From:	WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
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ML20115H322	List: ML20115H320 ML20115H324 ML20115H326 ML20115H330 ML20115H333
References
PROC-960207, NUDOCS 9607230062
Download: ML20115H333 (44)

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Proprietary Class 2C APPENDIX A, Pag: 1 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE t.

USER'S GUIDE FOR PRESLOK, A GATE VALVE PRESSURE LOCKING ANALYSIS PROGRAM USING THE COMMONWEALTH EDISON MODEL REVISION 1 February 7,1996 While this information is presented in good faith and believed to be accurate, the Westin;nouse Owndr's Group does not guarantee satisfactory results from reliance upon such infornation.

Nothing contained herein is to be cons:ruec as a warranty, express or implied, regarding the performance, merchantability, ilmess or any other matter with re:pect to the product, nor as a recormnendation to use any product or process in ccallict with any patent. Tne Westinghouse Owner's Group reserves the right. without notice, to alter or improve the methods described herein.

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• Uto g Proprietary Class 2C APPENDIX A 9Page 2 l

Verification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FO! PRESLOK ,

GATE VALVE PRESSURE LOCKliG ANALYSIS PROGRAM -

l USING THE COMMONWEALTH EDISON MODEL RECORD OF REVISION PAGE Rev.0 Original Issue January 2.1996 i

Rev.1 Corrected various typographical errors that had no February 7,1996  !

effect on the content. Removed erroneous negative sign from the equation for Qb on page 16. Corrected the ,

! equation for K 3, and added a note after the equation  :

for K 3, on page 16. Subscript corrected from ybw to y3 , in the calculation of shear deflection due to seat ,

load, page 17. The section concerning the calculation of the equilibrium contact load and the load per seat  ;

was rewritten, page 18. Minor spelling and English  ;

corrections were made to the section discussing l l

"Determuung the Disk to Seat Friction Coef5cient." -

page 18. The calculation of the stem force component  ;

required to overcome the pressure locking seat load was  !

put into standard equation format, page 18. Clarified that the Static Unseating Force is a program input. -

, page 18. (Fvert) was removed from the subheading title ,

" Reverse Piston Effect," page 19. The figures on pages  :

14 and 19 were redrawn. An equation for the total force [

l required to overcome pressure locking force was added, page 19. The final parag:aph, which discussed  ;

acceptance criteria, was deleted, page 19. Table numbers were added to the case numbers given next to equations l which were taken from Roark, various pages. j w-l I

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Proprietary Class 2C APPENDIX A. Pzge 3

Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.

WOG-220 Calc. No.: V-EC-1606 Group: AEE

(

l USER'S GUIDE FOR PRESLOK GATE VALVE PRESSURE LOCKING ANALYSIS PROGRAM USING THE COMMONWEALTH EDISON MODEL TABLE OF CONTENTS SECTION PAGE NO.

TITLE PAGE I REVISION

SUMMARY

2 l

j TABLE OF CONTENTS 3 .<

INTRODUCTION 4 HARDWARE / SOFTWARE REQUIREMENTS 5 GETTING STARTED 6 RUNNING THE PRESLOK ANALYSIS 7 INPUT PREPARATION 9 l THEORY ,

1I EXAMPLE USING PRESLOK VERSION 1 20 EXAMPLE USING PRESLOK VERSION 2 26 REFERENCES 32 j

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'o8/10 z Proprietary Class 2C APPENDDC A, Pag: 4 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK LNTRODUCTION Pressure locking is a phenomenon which can cause the unseating thrust for a gate valve to increase dramatically from its typical static unseating thrust. This can possibly result in the valve failing to open due to the actuator having insufficient thrust capability. Pressure locking can also result in valve damage in cases where the actuator thrust capability exceeds the valve structural capacity. For these reasons, a proper understanding of the conditions which may cause pressure locking, as well as a methodology for predicting the increase in unseating thrust for a pressure locked valve, are necessary.

A method of analyzing gate valves :o predict the increase in unseating thmst for a pressure locked valve has been developed by Commonwealth Edison, and has been presented by Mr. Brian Bunte (Ref.1). The Westinghouse Owner's Group, in the Pressure Locking / Thermal Binding Task Team meeting on November 13 and 14, 1995, authorized the preparation of a MATHCAD program and accompanying user's manual to allow the uniform use of the Commonwealth Edison pressure locking analysis methodology. This manual is the result of that authorization.

This manual and the program file for performing the analysis are available from the

. Westinghouse Owner's Group and may be obtained by contacting L.1. Ezekoye at (412) 374-6643 or W. E. Moore at (412) 374-6351. Please indicate whether the program is to be supplied on 3.5 inch diskettes or 5.25 inch diskettes.

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M /// g Proprietary Class 2C APPENDIX A, Page 5 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK HARDWARE / SOFTWARE REQUIREMENTS The program has been written using the MATHCAD 5.0 for Windows program. This program is available from MathSoft. Inc.

101 Main Street Cambridge, MA 02142 1-800-628-4223 or 617-577-1017 Fax: 617-577-8829 The program is also widely available from software vencors.

The following hardware and software requirements for running the MATHCAD 5.0 for Windows program are extracted from the User's Guide which is supplied with the MATHCAD program:

8 a An 80386 or higher IBM or compatible computer. A math coprocessor is not required. but its presence will significantly improve performance.

m Microsoft@ Windows Version 3.1 or later or Windows NT e At least 4MB of RAM. All memory above 640K should be configured as extended memory.

u At least 14MB of free hard disk space for MATHCAD files.

s An additional IMB on the hard disk where MATHCAD is installed.

8 At least 8MB of virtual memory. See the Windows user manual for how to specify virtual memoty.

s A monitor and graphics card compatible with Windows.

m A mouse supported by Windows.

a Any printer supported by Windows.

The User's Guide supplied with the MATHCAD program should be followed t'or installation of the MATHCAD program onto your computer. The scope of this manual is to explain the usage of the PRESLOK analysis using the MATHCAD program.

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~7 0//0 8' Proprietary Class 2C APPENDIX A, Page 6 Verification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK 1

1 GETTING STARTED '

The PRESLOK files are supplied to you on either a 3.5 inch or a 5.25 inch diskette, per your request. It is recommended that the first step to use the files is to copy a

" working version" of the files to your hard disk so that the diskette can be retained as j a record copy. The files which are included are as follows:

preslokl.mcd MATHCAD program using the closing valve factor as an  !

input. -

L preslok2.med MATHCAD program using the coefficient of friction .

between disk and seat as an input.

plinputl.dat ASCH file ofinput data required by version 1 of the  !

PRESLOK program.  ;

.g plinput2.dat ASCII file of input data required by version 2 of the  !

PRESLOK program

~

The next step to use the program is to create a data file to transfer the input values for the variables to the PRESLOK analysis program. The PRESLOK program is  ;

expecting these variables to appear in text file in plain ASCH format with the name "plinputi.dat" for use with version 1 or "plinput2.dat" for use with version 2. The

. , i various numbers in the "plinputi.dat" or "plinput2.dat" file can be separated by spaces. -

commas, or carriage returns, and may appear as integers floating point numbers.w.is .. j E. format numbers such as 2.35E-2. An ASCII text file can be created using the Windows utility Notepad, or by numerous other methods. This file should be located -

in the same directory as the PRESLOK file, since when the PRESLOK file is loaded,  ;

that directory will become the MATHCAD default directory. The user is also referred to the chapter on " Data Files" in the MATHCAD User's Guide if funher explanation  ;

of the use of the ".dat" file is needed.

i Sample data files are included in the program diskette which can be use[ simply' by ,

changing the input values to the proper values for your analysis. Alternately, other * -

file names can be used for the input data by changing the input file name on the page  !

l 1 of the PRESLOK program to the file name desired. '

~

5

,.m I

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7 I /c ir Propri;tary Class 2C APPENDIX A. Pag 7 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V.EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK RUNNING THE PRESLOK ANALYSIS At this point it is assumed that the user has the MATHCAD 5.0 program loaded onto his computer, and that the PRESLOK Version 1 or PRESLOK Version 2 file and the "plinputl.dat" or "plinput2.dat" file are available to the computer in the same directory. To run the PRESLOK analysis, the user should perform the following steps:

1. Double click on the MATHCAD 5.0 icon to stan the MATHCAD program.

2. Go to the File pulldown menu and click on Open (or click on the Open File icon on the Tool Bar.)

3. In the Open dialogue box, select the directory containing the preslokl.med or preslok2.med file and select the desired version of the program. Then click on OK.

4. The PRESLOK program will pick up the input values from the plinputl.dat or plinput2.dat file and perform the analysis if the program is in the automatic mode (Automatic Mode has a check mark next to it in the Math pulldown menu.) If the MATHCAD program is not in the automatic mode. it can be ,

forced to perform the calculation by clicking on the Calculate Document function in the Math pulldown menu. Results may be inspected by using the scroll bar on the right hand side of the display to scroll through the display as l desired.

5. To change the inputs, open the Windows utility Notepad and open the plinputi.dat or plinput2.dat file. Make the desired changes to the file and then j save it. To have MATHCAD re. perform the analysis with the new input j values, open the Math pulldown menu and click on Calculate Document. This j altemate use of Notepad and the MATHCAD function Calculate Document i should be repeated until the analysis is correct.

6 The output may be printed using the Print command in the pulldown menu under File or using the print icon in the Tool Bar. The user is referred to the MATHCAD User's Guide if any changes are desired to the Page Setup or the Printer Setup.

Note that valve identifiers or other identifying titles may be added to the output j

l by using the MATHCAD text entry methods given in the MATHCAD User's

! Guide. If the user desires to add the identifier / title to each page, the use of a header is recornmended. The header can be defined through the l Headers / Footers command in the Edit pulldown menu or through the Header vec1606 wog 0207961339

7.Q ) c'f Pr prietary Class 2C APPENDIX A, Pega 8 Verification of Pressure Locking Analysis Program PRESLOK .

Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE  ;

USER'S GUIDE FOR PRESLOK RUNNING THE PRESLOK ANALYSIS (continued) i command in the Page Setup dialogue box. See the Documents and Windows section of the MATHCAD User's Guide for further information about Headers.

7. The program may be exited using the Exit command in the File pulldown menu.

k l

[

+

e Y

O r Sec.t Angle

~

l c

F H Hub Length .

Disk . . .

Thickness FIGURE 1 Disk Geometry I

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.. - -. - . . - . _ - - - . . . . - ~ - - . - . _

D //op Proprittary Class 2C APPENDIX A, Paga 9 l

Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE I USER'S GUIDE FOR PRESLOK INPUT PREPARATION 1

The following inputs are required for the use of the PRESLOK analysis using version l 1 of the program: ,

l l

u Pressure Conditions at the time of the pressure locking event. This includes l

the upstream, downstream, and bonnet pressure.

l l [

Bonnet Pressure: P bonnet Psi ,

I Upstream Pressure: P up psi l Downstream Pressure: P down psi  ;

t i

! u Valve Disk Geometry. This includes the hub radius, hub length, mean seat  :

radius, average disk thickness, and seat angle.

I Disk Thickness: t inches l

! Seat Radius: a inches Hub Radius: b inches  ;

Hub Length: Hublength inches L

Seat Angle: 0 degrees I

The disk thickness recommended for use in these calculations is the thickness I l

at the centerline of the disk vertically. See Figure 1. This will normally be a l value which is intermediate between the nummum and maximum thickness of f

the disk, and this is the thickness which has been used in the comparisons of test measurements which Commonwealth Edison is making with the analytical results. It is noted that the magnitude of the pressure locking force increases with the thickness of the disk, so that use of the maximum disk thickness l

would yield conservative results. The pressure locking forces predicted by using the maximum value of disk thickness are likely to be unreasonably high though.

The seat radius used in these calculations is the mean seat radius which

. corresponds to the radius at which one half of the seat area would be outside  ;

the mean seat radius and one half of the seat area would be inside the mean radius. Thus, given the inner and outer seat diameters, the mean seat radius is

! ODh + ID*

c=\ 8 -

voc1606 wog 0207961339

Pr:prietary Class 2C 74/ liv APPENDIX A, Pzge 10 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK When the hub cross-section is not reasonably circular (e.g. many Westinghouse gate valve designs), then an effective hub radius is used which corresponds to a circle of equal area to the hub cross-sectional area.

1. A*

b=h x The hub length is the distance from the inside face of the hub to the inside face of the hub at the hub radius, as shown on Figure 1. The seat angle is as shown on Figure 1.

m Valve Disk Material Properties. This includes the modulus of elasticity and the '

Poisson's ratio for the disk base material, at the temperature being considered.

Poisson's Ratio: v dimensionless Modulus of Elasticity: E psi a Valve Stem Diameter Stem Diameter: D,,,, inches This is the stem diameter in the region of the stem which is inside the packing.

s Static Unseating Thrust Static Pullout Force: Fpo pounds This is the static pullout force obtained from testing of the valve for which the calculation is being performed.

r a Closing Valve Factor Valve Factor: VF dimensionless _

It is suggested that this valve factor be the factor obtained from test measurements of closing the valve being considered in a DP test. if possible.

To use version 2 of the program instead of version 1, the closing valve factor VF is replaced by the co-efficient of friction to be considered between the disk and the seat.

and the input data file is named plinput2.dat. All other inputs remain the same as for version 1. The different input value is a

Coefficient of Friction between Disk and Seat Seat to Disk Coefficient of Friction: 9 dimensionless voc1606.wog 0207961339

~15/t o y Propri;tary Class 2C APPENDIX A, Page 11 Verification of Pressure Locking Analysis Program PRESLOK Project /S,0. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK THEORY ASSUMPTIONS

1. The valve disk is assumed to act as two ideal disks connected by a hub. That is, the disks are assumed to be round, of uniform thickness, and perpendicular to a cylindrical, concentric hub. A line perpendicular to the hub centerline and at the middle of the hub length is an axis of symmetry for the wedge. The equations in reference 2 for this idealized structure are assumed to conservatively model the actual load due to pressure forces. This assumption is considered conservative since inspection of the disk drawings show large fillets between the disk hub and seats which should make the valve disk stiffer than -

assumed in the reference 2 equations.  ;

2. The coefficient of Eiction between the valve seat and disk is assumed to be the same under pressure locking conditions as it is under DP conditions. This assumption is considered to be justified based on bench marking of the calculations against Comed and EPRI pressure locking test data for similar flex-wedge gate valves.

3. The upstream, downstream, and bonnet pressure values are considered to be known. ,

l DESIGN INPUTS The following design inputs are used in calculating the force required to unscar a pressure locked MOV:

a Pressure Conditions at the time of the pressure locking event. This includes the upstream, downstream, and bonnet pressure.

Bonnet Pressure: P bonnet psi Upstream Pressure: P up psi Downstream Pressure: P down psi a Valve Disk Geometry. This includes the huo radius, hub length, mean seat radius, and average disk thickness.

Disk Thickness: 1 inches Seat Radius; a inches vec1606.wog 0207961339

l 7L //oif I Proprietary Class 2C APPENDIX A, P:g212 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK Hub Radius: b inches Hub Length: Hublength inches Seat Angle: 0 degrees l The disk thickness reconunended for use in these calculations is the thickness at the centerline of the disk vertically. See Figure 1. This will normally be a value which is intermediate between the muumum and maximum thickness of the disk, and this is the thickness which has been used in the comparisons of test measurements which Commonwealth Edison is makmg with the analytical i results. It is noted that the magnitude of the pressure locking force increases with the thickness of the disk, so that use of the manmum disk thickness would yield conservative results. The pressure locking forces pred;cted by using the manmum value of disk thickness are likely to be unreasonably high though. i The seat radius used in these calculations is the mean seat radius which corresponds to the radius at which one half of the seat area would be outside the mean seat radius and one half of the seat area would be inside the mean radius. Thus, given the inner and outer seat diameters, the mean seat radius is OD* + IDh a=T 8

~

When the hub cross-section is not reasonably circular (e.g. many Westinghouse gate valve designs), then an effective hub radius is used which corresponds to a 4 circle of equal area to the hub cross-sectional area.

Hub Area y,S x The hub length is the distance from the inside face of the hub to the inside fa'ce -

of the hub at the hub radius, as shown on Figure 1. The seat angle is as shown- 4 on Figure 1.

m Valve Disk Material Properties. This includes the modulus of elasticity and the Poisson's ratio for the disk base material. '

Poisson's Ratio: v '

f nensionless Modulus of Elasticity: E psi voc1606 wog 0007961339

I APPENDIX Ac Page 13 7/at \

Proprietary Class 2C Verification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG 220 Calc. No.: V EC-1606 Group: AEE 1 1

l USER'S GUIDE FOR PRESLOK )

i e Valve Stem Diameter l D stem inches )

Stem Diameter:

This is the stem diameter in the region of the stem which is inside the packing.  !

l

' I u Static Unseating Thrust Static Pullout Force: F po pounds j l

This is the sta:ic pullout force obtained from testing of the valve for which the calculation is being perfonned.

j I

e Coef5cient of Friction between Disk and Seat Seat to Disk Coefficient of Friction: p dimensionless i

The analysis program is presented in two versions, one of which requires that the coefficient of friction to be used between the disk and the seat be input directly, and l the other which allows the input of the closing valve factor instead. For the version l j

which allows the input of the closing valve factor, the coefficient of friction is ,

)

calculated as follows:

l 1

cos 6 y , yy .

1 + VF sin B ,

l CALCULATIONS The metnodology for calculating the thrust required to open the MOVs under the pressure locking scenario is based on the Reference 2 (Roark's) engineering handbook.

The methodology determines the total force required to open the valve under a pressure locking scenario by solving for the four components to this force. h, four components of the force are the pressure locking component, the static unseating component, the piston effect component, and the " reverse piston effect" component. ,

These rnagnitudes of these components are determined using the following steps: l l

l I

i l

I I l \

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'7S/tssi Proprietary Class 2C APPENDIX A, Page 14 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK i Pressure Lockine Component of Force Recuired to Open the Valve i

The valve disk is modeled as two plates attached at the center by a hub which is  ;

concentric with the valve disk. A plane of symmetry is assumed between the valve i disks. This plane of symmetry is considered fixed in the analysis.

l

- Ptene 1 I

/[

/

mnetry v / _

\

Modeled As:

_/ Axis of f ,/ synne:ny n

f

/

/

I l

1 t

-f Based on this geometry, the following constants are calculated using the reference 2 ...

equations: .

Average DP Across Disk DP ,=Pw -

Disk Stiffness Constants -

5 D=

12 -(1 -v )

5 G=

2 -(1 +v)

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- - - - - 1

~7 9/n5 f Proprietry Class 2C APPENDIX A, Pag: 15 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE i

l USER'S GUIDE FOR PRESLOK l Geometry Factors b'*'1+2In a"'

C,* = 1 l 4 ( a; ( ( b ss.  ;

1 In a ' + 'b# -1 b l C3 b '*+

4a ,( a ; .

gb; rai  ;

I C, = 2 1 +v +(1-v) at bc ,

I C, = p 1+v in +

1-v 3_ pf as 2 bi 4 at i

Deflection Due To Pressure Force The pressure force is assumed to act uniformly upon the inner surface of the disk between the hub diameter and the outer disk diameter. The outer edge of the disk is '

assumed to be unimpeded and allowed to deflect away from the pressure force. In addition, the disk hub is allowed to stretch. The total displacement at the outer edge  ;

of the valve disk due to shear and bending and due to hub stretch are calculated using the reference 2 equations. .

Corresponding Equations Additional Geometry Factors (ro= b for Table 24. Case 2L) t3 l

. _ ._ 1 4. S -5 S -4 S 2+ b in #]  !

64 sa; sa; (as (as , ir jj o j 1-v 'r "' o f

r a

'2' '

a

L 11 1- 1 + (1 + v)ln n=4 4 (as (as (r,.,.o l

l l

I i

voc1606 wog 0207961339 l

l l

Proprietary Class 2C APPENDIX A, Pzg216 l

Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: %EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK Moment Factors (ro= b for Table 24. Case 2L) 2 M,, = -DP" a C, '2ab C' (a2-r)_t l7 o 2

DP 0*2-6 { -r) o 2

Bending Deflection due to Pressure 1 3 ys, = M,, C + Q, C, - DP* a' L,, ,

Shear Deflection due to Pressure (ro= b for Table 25, Case 2L)

K* = -0.3\ f2 rb> in -1+ 1 - 2 In ras r b l. )

f y" \ '

Note: Since ro = b, 1 - 2 in -1 r b 1.

~

K, DP, a 2 ..

M g .g -

Deflection from Hub Stretch due to Pressure Pg = x(a2 _ 3 2).ppm Py Hub 4 l ym = - ,

x b, -

2E ' ,

Total Deflection due to Pressure l

1g

• 1sq

• 14

• 1.am-s l An evenly distributed force is assumed to act between the valve seat and the outer edge of the valve disk. This force acts to deflect the outer diameter of the valve disk inward and to compress the disk hub. The pressure force is reacted to by an increase vec1606.wog 0207961602 l

Si//og i Proprietary Class 2C APPENDIX A, Paga 17 Vcrification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG-220 Calc. No.: V EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK in this contact force between the valve disk and seats. The valve body seats are l conservatively assumed to be fixed. Therefore, the deflection due to the known i pressure load must be balanced by the deflection due to the unknown seat load. The )

deflection due to the pressure force was previously calculated. Now, the reference 2 l equations are used to determine the contact force between the seat and disk which  ;

results in a deflection which is equal and opposite to the deflection due to the pressure i l

force. This is done by first calculating the amount deflection created by a unit load ^

of seat contact force (w = 1 lb/in). The equilibrium contact load is then determined by dividing the deflection caused by the unit contact load into the previously calculated deflection due to the pressure force. The equations are provided below.

Additional Geometry Factors (For Table 24, Case IL, r0 = a, ..L3 = L9 = 0 r r sz l 'f r 3 r r q . _o _o '2 1 .in . _o _1 '

4a O a s .

tros ka)

' f ro '2 r a' +

1-v -

1-4 . _oa 1 +2 v .in (r, -

4 (a;

o .

Bending Deflection due to Seat Load ( ro= a for Table 24, Case IL) 3 ' C, C, '

rC y ,. _ _a . --..'r o

-g -

o 3

.g 1

D . C, t. b i b .

Shear Deflection due to Seat Load (ro= a for Table 25 Case IL)

K*=-1.2 bin a i a

Is~ " K" t G l

Deflection from Hub Compression Due to Seat Load (w = 1, /. Compressive force = 2 n a) J

,_22a f

Huby'

" n b; c 2E ,

I l

. Total Deflection from Unit Seat Load (w = 1) i

1.

• yn

• ys.

• yw

!- vec1606 wog 0207961602

81lioz Proprietary Class 2C APPENDIX A, Pzg218 Verification of Pressure Locking Analysis Program PRFELOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK Therefore, the equilibrium contact load distribution, in pounds per inch, and the corTesponding load applied to each seat is calculated using the relationships below:

y wm ._=i Ja where y,is calculated for w = 1.

Note that the sign of the equilibrium contact load is positive. This is because the sign conventions of Reference 2 have been maintained for all of the calculations, resulting in both the pressure load analysis and the line load analysis giving negative deflections, even though the loads and defections for the line load case are phyically in the opposite direction from the loads and deflection for the pressure load case.

The load per seat is then given by r

y 8 F, = 2 x a i ry,>

Determinine The Disk To Seat Friction Coefficient Several methods can be used to detemtine an appropriate seat to disk friction coefficient. The coefficient of fdction between the seat and disk is perhaps best r determined based on the opening valve factor from a DP test. However, due to the difficulty sometimes encountered in obtaining a good, consistent value of the opening I valve factor from testing, the PRESLOK program is written to accept either a closing valve factor or a co-ef5cient of friction directly. The equation used to calculate the coefficient of friction from the closing valve factor is given in the Design Inputs section of this User's Manual. -

The stem force required to overcome the contact load between the seat and disk which .

~

opposes the pressure force is equal to the following, considering two disk faces:

Fg = 2 F - (p 3 case - sin 0)

Static Unseatine Force 4

The static unseating force represents the opening packing load and the pullout force due to wedging of the valve disk during closure. These loads are superimposed on the loads due to the pressure forces which occur during pressure locking. The value for ,

this force is based on static test data for the MOVs, and is one of the inputs to the program (Fpo).

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3 3 // 0 3 Proprietary Class 2C APPENDIX A0 Page 19 ,

Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC 1606 Group: AEE t

l l USER'S GUIDE FOR PRESLOK Piston Effect The piston effect due to valve internal pressure exceeding outside pressure is -

calculated using the standard industry equation. This force assists movement of the I valve stem in the open direction.

1 F, y - DL {Pw - P,)

Reverse Piston Effect The reverse piston effect is the term used in this calculation to refer to the pressure force acting downward against the valve disk. This force is equal to the differential pressure across the valve disk times the area of the valve disk times the sine of the seat angle times 2 (for two disk faces).

F, = : a sine 2

-(2 P w -P,-Pw)

Bonne Pressure Oostrean v Downstrean Dressure Pressure m

% Seat Angle t _J j Bonnet Pressure Total Force Recuired to Overcome Pressure Locking As mentioned previously, the total stem force (tension) required to overcome pressure j

locking is the sum of the four components discussed above. All of the terms are positive with the exception of the piston effect component.

Fu=F - F, - F,, y + F, vec1606 wog 0207961602

S+hN Proprietary Class 2C APPENDIX A, Paga 20 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK EXAMPLE OF AN ANALYSIS PERFORMED WITH PRESLOK., VERSION 1 The following is an image of the input file plinput1.dat used to run an example problem on version 1 of the PRESLOK analysis program:

1005 380 350 2 4.36 1.25 0.5 5 0.3 27.6E6 1.875 15409 0.52 The input fle corresponds to input values as shown:

i Bonnet Pressure: Pw = 1005 psi Upstream Pressure: Pop = 380 psi Downstream Pressure: Pdown = 350 psi Disk Thickness: t = 2.00 inches Seat Radius: a = 4.36 inches Hub Radius: b = 1.25 inches Hub Length: L = 0.50 inches Seat Angle: 0 = 5 degrees Poisson's Ratio: v = 0.3 (dimensionless)

Modulus of Elasticity: E = 27,600,000 psi i-Stem Diameter: D3te, = 1.875 inches Static Pullout Force: Fg = 15,409 pounds Vaive Factor: VF = 0.52 (dimensionless) s The next five pages contain the output of the PRESLOK program. Version 1, using the above input.

I l

voc1606 wog e207961339

W /Sh i l

Proprietary Class 2C APPENDIX A, Page 21 Verification of Pressure Lockirg Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V EC-1606 Group: AEE USER'S GUIDE TO PRESLOK  !

Program PRESLOK, Version 1 Revision 0 December 22,1995 1 This Mathcad Program is designed to calculate the estimated opening force under pressure locking scenarios for flex-wedge gate valves using a calculational methodology that accounts for wedge stiffness resisting pressure locking forces. This program was prepared by the Westinghouse Owner's Group based upon the l calculational methods developed by Commonwealth Edison.

While this information is presented in good faith and believed to be accurate, the l Westinghouse Owner's Group does not guarantee satisfactory results from reliance  !

upon such information. Nothing contained herein is to be construed as a warranty, j express or implied, regarding the performance, merchantability, fitness or any other l matter with respect to the product, nor as a recommendation to use any product or j process in conflict with any patent. The Westinghouse Owner's Group reserves the right, without notice, to alter or improve the methods described herein. )

This section of the program reads the thineen items of input data from the plinput1.dat i file.

i := 0.12 inputi := READ (plinputl)

P bonnet := input 0' Psi v := input 8 P up := inputi psi E := input9 psi P down := input7 psi D ste m := inputto'i" t := input3 in F po := input tt #

a := inputfn i VF := input i b := input5 'I" Hub length := input6 E O := inputydeg PRESLOK. Ver. ), Rev. 0 12 22195 Westinghouse Owner's Group 21819610:10:08 AM Page ) ofS

!? (o//36 Proprietary Class 2C APPENDIX A, Pag 2 22 Verification of Pressure Locki. g Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V EC-1606 Group: AEE 1 USER'S GUIDE TO PRESLOK Program PRESLOK, Version 1 INPUTS:

Bonnet Pressure P bonnet = 1005 psi Upstream Pressure P up = 380 psi Downstream Pressure P down = 350 psi Disk Thickness t = 2 in (taken at centerline of the hub vertically)

Seat Radius a = 4.36 in (corresponding to maan seat diameter)

Hub Radius (taken at plane of symmetry, b = 1.25 in perpendicular to the hub, radius of circle of equivalent area for non-circular hubs)

• Seat Angle 0 = 5 deg Poir son's Ratio (disk material at temperature) v=0.3 7

Modulus of Elasticity (disk material at temperature) E = 2.76 10 psi ~

1 Static Pullout Force F po = 15409 lbf (measured value from diagnostic test) l Close Valve Factor VF = 0.52 Stem Diameter D stem = 1.875 in .

o' .

Hub Length Hub length =0.5 in 1

(from inside face of disk to inside face of disk) 1 PRESLOK. Ver.1. Rev. 0 12l22195 Westinghouse Owner's Group 2/8/9610:10:12 AM Page 2 of5 1

l 97//og Proprietary Class 2C APPENDLT A, Page 23 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V-EC-1606 Group: AEE I

USER'S GUIDE TO PRESLOK Program PRESLOK, Version 1 i PRESSURE FORCE CALCULATIONS Coefficient of friction between disk and seat:

cos(0) = 0.496

= VF-1 e VF sin (0)

Average DP across disks:

P up+P down DPavg := P bonnet - DPavg =640 psi Disk Stiffness Constants

'(* ~

D = 2.02210 7

lbf in D :=

12-(1 - V )

7 G := G = 1.06210 psi 2-(1 + v)

Geornetry Factors:

C >- : = -- 1 - 2 In f

• C 2 = 0.1781 4 al ( \bj / .

2 b bi2 i b C -

l t1 In a <t -

-1 C 3 =0.0311 3 := 4 a at b/ a l

C 8 := 2 1

1 + v t (1 -al v) b)2' '

C 8 =0.6788 l 2-1tv 1-v C

b Ini a)*

4 1-ba C 9 = 0.2789 l 9 := a- 2 (b/

la 2 a la 2 a

L -

"I 'l" "' -

-l L 3=0 3"4a .(a a (a 1+v l 1-V l L -a 1 - a32.

.in t a - L 9=0 9 = a. 2 \a 4 (a/

PRESLOK. Ver.1, Rev. 0 12122/95 Westinghouse Owner's Group 21819610:10:24 AM Page3 of5 l

t

88/tcy '

Proprietary Class 2C APPENDIX A, Pag) 24 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE TO PRESLOK ,

Program PRESLOK, Version 1 Geometry Factors: (continued)

Ib I\ Ii I\ fa L

g g := 64 1

1 + 4-l -$b" -4'b .-

2+'b In! -

L i t =0.0069 (a (a) (a/ (a/ (b

1. Ib)2 l i 1-v

~L 17 l

• I- ba -'-'*

1 +(I + V)'l"'ai'jl L 17 =0.1526 4 4 (a/ (b),

Moment 8 2 2 M tb := -(a - b ) - L 17 M tb =-5265 lbf Qb DPavg= (a 2 - b2 ) Q =4466.5 b 2b m Deflection due to pressure and bending:

2 3 a a DPavg a# -4 ybq

• M rb' D C 2"Q b D C 3- L i; y bg =-3.9041 10 in D

Deflection due to pressure and shear stress:

r la K sa := -0.3 2 in l - - 1 + y\ 2' l i K sa =-0.4743 (b a/

l 2

K g DPavg a _

.y q:= y sq =-2.7177 10 , in l

. _l

. D 5flection due to hub stretch:

e

.;.y 2 2 P force := x (a - b ) DPavg P

force Hub lencth ~

! Y stretch -5 1 l nb 2 (2 E) Y stretch = 6.4731 10 in  ;

~

Total Deflection due to pressure forces: .

yq := y bq

• Y sq - Y stretch Y q =-7.2691 10'# in l PRESLOK. Ver.1. Rev. 0 12 22195 Westinghouse Owr.er's Group 21819610:10:37 AM Page 4 of5 l

4

9 ]//:{

Proprietary Class 2C APPENDIX A. Page 25 ,

l Vcrification cf Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE l

USER'S GUIDE TO PRESLOK

! Program PRESLOK, Version 1 l

l Deflection due to seat contact force and shear stress (per Ibf/in.):

l f\

a 1.2 l a\t In;a' sw OO '

I y 3 ,:= -

G (V)

Deflection due to seat contact force and bending (per Ibf/in.):

I g3\ 'IC d 'f a C 9\

~

(

l g\ 1C ~7 -

in ybw " ~b 9- .(b/

3 eL 3 Y bw =-6.012 10 (D) ,(C gj \ b / j Deflection due to hub compression:

I 2na Hub length \ -8 -

in

~ Y cmpr =-5.055 10 Ycmpt 2 2E j

\ in /

l Total deflection due to seat contact force (per Ibf/in.): ~

y w = y bw

• Y sw ~ Y cmpt Y w =-9.597 10 j

l (&*

Seat Contact Force for wNch deflection is equal to previously calculated deflection from pressure forces:

F s= 20750.5 lbf j F 3. = 2 n a-Yw

! UNSEATING FORCES

aacng is included in measured static pullout Force F piston

= "D- ste m P bonnet F piston = 2775 lbf I

2 -P up -P down) F vert = 6662.4 lbf f F vert := n a sin (0)-(2bonnet P F preslock := 2 Fs -(p cos(0) - sin (0)) F preslock = 16871 lbf l

F po = 15409 lbf F total := - F piston eF vert + F preslock - F po F total = 36167.4 lbf Westinghouse Owner's Group 2/8/96 10:10:49 AM Page5 of5 PRESLOK. Ver.1. Rev. 0 12122195

90ll%

Proprietary Class 2C APPENDIX A 0Page 26 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Cale. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOK EXAMPLE OF AN ANALYSIS PERFORMED WITH PRESLOK, VERSION 2

'~

The following is an image of the input file plinput2.dat used to run an example problem on version 2 of the PRESLOK analysis program:

1005 380 350 2 4.36 1.25 0.5 5 0.3 27.6E6 1.875 15409 0.496 The input file corresponds to input values as shown: ,

Bonnet Pressure: Pbonnet = 1005 psi Upstream Pressure: Pop = 380 psi Downstream Pressure: Pdown = 350 psi Disk Thickness: t = 2.00 inches Seat Radius: a = 4.36 inches Hub Radius: b = 1.25 inches  :

Hub Length: L = 0.50 inches Seat Angle: 0 = 5 degrees Poisson's Ratio: v = 0.3 (dimensionless)

Modulus of Elasticity: E = 27,600.000 psi --

y Stem Diameter: Dstem = 1,875 inches Static Pullout Force: Fpo = 15,409 pounds Seat to Disk Coefncient of Friction: p = 0.496 (dimensionless)

The next five pages contain the output of the PRESLOK program, Version 2. using-the above input.

I l

l l

l vec1606 wog 0207961339

Proprietary Clau .C APPENDDC Ac Page 27 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOCK Program PRESLOK, Version 2 Revision 0 December 22,1995 t

This Mathcad Program is designed to calculate the estimated opening force under pressure locking scenarios for flex-wedge gate valves using a calculational methodology that accounts for wedge stiffness resisting pressure locking forces. This program was prepared by the Westinghouse Owner's Group based upon the calculational methods developed by Commonwealth Edison.

While this information is presented in good faith and believed to be accurate, the Westinghouse Owner's Group does not guarantee satisfactory results from reliance upon such information. Nothing contained herein is to be construed as a warranty, express or implied, regarding the performance, merchantability, fitness or any other matter with respect to the product, nor as a recommendation to use any product or process in conflict with any patent. The Westinghouse Owner's Group reserves the .

right, without notice, to alter or improve' the methods described herein.

- This section of the program reads the thirteen items of input data from the plinput2.dat  ;

file.

i := 0.12 input;:= READ (plinput2)

P bonnet := input0 Psi v := inputg E := input9 psi P up : inPutypsi P down : input2 psi D stem := input 10'iD t := input3 in F po := input3 pIbf a := inpurgin p := input 12 b := input5 'i" Hub len# := input 6'IU 0 := inputydeg PRESLOK.Ver.2, Rev.012122193 Westinghouse Owner's Group 218196 10:19:37 AM Page 1 ofS

l l

M /tc5 l Proprietary Class 2C APPENDIX A, Page 28 i i Vcrification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG-220 Calc. No.: V EC 1606 Group: AEE I

USER'S GUIDE FOR PRESLOCK j Program PRESLOK, Version 2 )

INPUTS:

I Bonnet Pressure P bonnet = 1005 psi 1 1

1 Upstream Pressure P up = 380 psi Downstream Pressure P down =350 psi Disk Thickness t = 2 in (taken at centerline of the hub vertically)

Sdat Radius a = 4.36 in (corresponding to mean seat diameter) l Hub Radius (taken at plane of symmetry, b = 1.25 in l peroecdicular to the hub, radius of circle

! of equivalent area for non-circular hubs)

Seat Angle 0 = 5 deg l ... Poisson's Ratio (disk material at temperature) v=0.3 i

7 Modulus of Elasticity (disk material at temperature) E = 2.76 10 psi Static Pullout Force F po = 15409 lbf (measured value from diagncctic test) l l Coefficient of Friction between disk and seat: p = 0.496 .

Stem Diameter D stem = 1.875 in l

l Hub Length Hub length = 0.5 in

~

l (from inside face of disk to inside face of disk) l l

l

\

i l

l l

l l

PRESLOK Ver.2, Rev.012122195 Westinghouse Owner's Group 218196 10:19:41 AM Pcge2 ofS l

9 3/we Proprietary Clam 2C APPENDDC Ag Paga 29 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: WEC-1606 Group: AEE USER'S GUIDE FOR PRESLOCK Program PRESLOK, Versicn 2 PRESSURE FORCE CALCULATIONS Average DP across disks:

P DPavg = 640 psi DPavg := P bonnet - yp + P down 2

Disk Stiffness Constants 7

E-(t)3 D = 2.022 10 lbf in D:= ,-

12 1 - v')

7 E G = LO6210 psi G:=

2-(1 + v)

Geometry Factors: .

C , := 1-4 1 fI

\a/ (

1-2inf-

\b//

C >- = 0.1781 I\ fa b\

b b C - l - In '

t -1 C 3 =0.0311 3 := 4 a ,, \al' +1 (b al C -

1 + V t (1 - V C 8 =0.6788 8 := 2 (a

~

- In - l- C 9 =0.2789 C 9:=

.a [ v1 In +! -1 L 3=0

• g 3 , 4.a ai \aj (al a 1-v 1-v a' L In allt I L 9=0 9 := a-, 2 al 4 a Westinghouse Owner's Group 218/9610:19:32 AM Page3 ofS PRESLOK Ver.2. Rev.012!22195 i

Proprietary Class 2C *Aq Verification of Pressure Locking Analysis Program PRESLOK APPENDIX A, Page 30  !

Project /S.O. No.: WOG-220 l Calc. No.: V-EC 1606 Group: AEE USER'S GUIDE FOR PRESLOCK Program PRESLOK, Version 2 Geometry Factors: (continued)

I. 1,41-' -5.bl bi2 l 4

- 4 ' lby2 l b32' (3 L  !- 2+i 3 g := 64 \a)

- l In .

(a ra) (a) . \b/. L 3 3 = 0.0069

~

L i 1_y /bl# /bi2 -

lai '

I I- -' -  ;

17 4' 4 I

• C l

• V)'IA' -

(a/ (a) (b),, L 17 = 0.1526 Moment ga 2 2 2 t

M tb * -(a - b ) - L 17 '

M tb =-5265 Ibf Q b;" DPavg (a, - b2) g Q b =4466.5 lbf Deflection due to pressure and bending:

2 3 a DPavg a#

ybq = M rb'3 C 2 e Qb=a C 3-D D 11 bq =dWO -4 +

Deflection due to pressure and shear stress:

K sa := - 0.3-2in a\l - 1 + y\ 2. -

b/ al , K sa =-0.4743 K sa DPavg a 2 '

• 4*

y sq

• _

tG Y sq =-2.7177 10 , in Deflection due to hub stretch:

P 2 2 force := n-(a - b ) DPavg P

force Hub length Y stretch , , .

l n b- (2 E) -5 Y stretch = 6.4731 10 in

! Total Deflection due to pressure forces:

Yq :' Ybq

• Y sq Y stretch ~#

Yq =-7.2691 10 in PRESLOK. Ver. 2. Rev. 0 12122/95 Westinghouse Owner's Group 21819610:20:03 AM Page 4 ofS

W//c g Proprietary Class 2C APPENDIX A, Paga 31 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V-EC-1606 Group: AEE USER'S GUIDE FOR PRESLOCK Program PRESLOK, Version 2 l Deflection due to seat contact force and shear stress (per Ibf/in.):  !

f) a 1.2 ai. In ! -

'a ysw *~

G sw "E .

/g_fy i

\m/

Deflection due to seat contact force and bending (per Ibf/in.):

I 3\ ^ IC d 'lat 9\

\ -7 *

~

• L Y bw =-6.012 10

, b) 'C 3 ybw ~b 9 3 Ibf

\D) '(C 8/ -( b )

i in j Deflection due to hub compression:

I 2xa Hub lengthk -8 , ' m

). cmpt '

y cmpr =-5.055 10

(,2 2.E Ibf\

f i in /  !

Total deflection due to seat contact force (per Ibf/in.):

-7 -

y w = y bw ' Y sw

• Y cmpt Y w =-9.597 10 Seat Contact Force for which deflection is equal to previously calculated deflection from pressure forces: l F s:= 2 n a- F 3 = 20750.5 lbf Yw f UNSEABNG FORCES Fpacking is included in measured static pullout Force i

F piston := D P F piston = 2775 lbf ste m bonnet 2 -P F vert := n a sin (0)-(2 P bonnetup -P down) F vert = 6662.4 lbf cos(0) - sin (0)) F preslock = 16889.1 lbf )

F preslock := 2 F3-(

F po = 15409 Ibf F total := - F piston " F vert eF preslock + F po j

7 F total = 36185.5 lbf Westinghouse Owner's Group 218i9610:20:17 AM Page S ofS PRESLOK. Ver. 2. Rev. 0 12122195 l

Pr@prietary Class 2C 96 //or APPENDIX A, Page 32 Verification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE '

USER'S GUIDE FOR PRESLOK REFERENCES 1.

Bunte, Brian, " Comed Pressure Locking Methodology and Test Program." ,

presented at the NRC Region 3 Workshop on Pressure Locking and I Thermal Binding, November 7,1995. ,

2. Roark, Raymond J., and Young, Warren C., Formulasfor Stress and '

Strain. Fifth Edition, McGraw-Hill Book Company,1975. ,

3.

Liberal use has also been made of a draft of a report being prepared by Mr. Brian Bunte of Commonwealth Edison Company, tentatively titled

" Pressure Locking / Thermal Binding Report."

i

~

\

l l

l l

vec1606 wog 0207961339

?7 Afr Proprietary Class 2C APPENDDC B, Pzg21 Verification of Pressure Locking Analysb Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC 1606 Group: AEE Program PRESLOK, Version 1 Revision 0 December 22,1995 This Mathcad Program is designed to calculate the estimated opening force under pressure locking scenarios for flex-wedge gate valves using a calculational methodology that accounts for wedge stiffness resisting pressure locking forces. This program was prepared by the Westinghouse Owner's Group based upon the calculational methods developed by Commonwealth Edison.

While this information is presented in good faith and bsWyed to t:e accurate, the Westinghouse Owner's Group does not guarantee satisfactory results from reliance upon such information. Nothing contained herein is to be construed as a warranty, express or implied, regarding the performance, merchantability, fitness or any other matter with respect to the product, nor as a recommendation to use any product or process in conflict with any patent. The Westinghouse Owner's Group reserves the right, without notice, to alter or improve the methods described herein.

This section of the program reads the thirteen items of input data from the plinput1.dat file. .

i := 0.12 J

input;:= READ (plinput!)

P bonnet := inputo psi v := inpm g E := input9 psi P up := input3 psi P down := input2 psi D stem : inPutto'I" t := input3 in F po := inpur g lbf a := inputgin VF := input !2 b := input5 'i" Hub length := input6 'i" 0 := inputydeg Westinghouse Owner's Group 218196 9:57:10 AM Page I of 6 PRESLOK. Ver. l. Rev. 0 12122195

Proprietary Class 2C 9 3 / tar APPENDIX B, Paga 2 Vcrification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V-EC-1606 Group: AEE l

Program PRESLOK, Version 1 INPUTS:

Bonnet Pressure P bonnet = 1300 psi Upstream Pressure P up = 200 psi Downstream Pressure P down = 500 psi Disk Thickness t = 1.7 in (taken at centerline of the hub vertically)

Seat Radius a = 7 in (corresponding to mean seat diameter)

Hub Radius (taken at plane of symmetry, b = 1.1 in perpendicular to the hub, radius of circle i

of equivalent area for non-circular hubs)

Seat Angle 0 = 9 deg

?

Poisson's Ratio (disk material at temperature) v = 0.31 Modulus of Elasticity (disk material at temperature) E = 2.9 10 7

psi ' ..

Static Pullout Force F po = 23000 lbf (measured value from diagnostic test)

Close Valve Factor VF = 0.47 Stem Diameter 1 D ste m " I 9 'I" Hub Length Hub length =0.6 in (from inside face of disk to inside face of disk)

PRESLOK. Ver.1. Rev. 0 1212219: Westinghouse Owner's Group 2l8/96 9:57:14 AM Page2 of6

1 99 /I)E j i Proprietary Class 2C APPENDLX B, Page 3 l

Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG 220 Calc. No.: V EC-1606 Group: AEE Program PRESLOK, Version 1 PRESSURE FORCE CALCULATIONS Coefficient of friction between disk and seat: '

cos(0) p = 0.432

= VF=

1 + VF sin (0)

Average DP across disks: ,

P up tP down DPavg = 950 psi DPavg := P bonnet -

2 Disk Stiffness Constants ,

7 E-(t)3 D = 1.31410 Ibf in D :=

2 12-(1 - v ]

7 G := G = 1.107 10 psi 2-(1+v)

Geometry Factors:

C >* : = -- C 2 = 0.221 4 \a/ \ f1 + \2 inf"b//\)

b b* \

+1 In a\It' Ib* -1 C - - -

C 3 =0.0362 3 := 4 a , at b/ (a C 8 := - 1 + v + (1 - v)- C 8 =0.6635 fT 2.

l-v l-v C

b Ini a

+

4 l- ba C 9 = 0.2169 9 := a- 2 (b/

7 l l s2 3 *2 -1 a -1a -1 L >, = 0 i L -

In 3 := 4 a a (a tal i

1+v f 1-V f a

L 9 . = a-- -Ini ai+

4 l - a\2.

L 9=0 2 (a (a/

PRESLOK, Ver.1, Rev. 0 12/22/95 Westinghouse Owner's Group 2I8/96 9:57:26 AM Page3 of6 i

I CD /lR Proprietary Class 2C APPENDIX B, P ge 4 Verification of Pressure Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc No.: V-EC-1606 Group: AEE Program PRESLOK, Version 1 Geometry Factors: (continued) 19\2 4 f yy2 L i. 1,4. f

- 5 I l l- 2+b* (\

i -

In l Ia\

L ii = 0.0113 13:= _64 (a) a (a) (a/ lb/

1 1-v I i4 lb 2 /3-3 L 1 1 .b '

i 1 t (1 + V) Ini- '

37 := 4- 4 \ai \a \b/, L 17 =0.1858 '

Moment 8 2 2 M tb := (a - b )- L 17 M rb =-34193.2 lbf 2 2 Q b := *E (a - b )

Q b = 20636.6 5 2b in Deflection due to pressure and bending:

2 3 a a DPavg a#

y bg '* NI rb'f C 2 L bg =4.0107 in

• Qb 'f C 3- D 11 Deflection due to pressure and shear stress:

K sa '= - 0.3- 2 in -1+ K sa =-0.8178 2 -

K sa DPavg a y 3q :=

tG 59 Deflection due to hub stretch:

2 2 P force := n-(a - b ) DPavg P

force Hub len#

~#

nb 2 (2 E) y snetch = 3.8815 10 in

~

~

Total Deflection due to pressure forces: .'

yq := y bq

• Y sq - Y stretch Yq =-0.0131 in PRESLOK, Ver.1. Rev. 0 12/22/95 Westinghouse Owner's Group 218/96 9:57:39 AM Page 4 of6 .

t IO l/tCil Proprietary Class 2C APPENDIX Bo Page 5 Verification of Pressure Locking Analysis Program PRESLOK ,

Project /S.O. No.: WOG-220 Calc. No.: V EC-1606 Group: AEE ]

i Program PRESLOK, Version 1 l

Deflection due to seat contact force and shear stress (per Ibf/in.)- 1 l f l.21 a\. In1 a) ia

~7 1

ysw '-t G

Y sw =-8.261 10 (d '

! Deflection due to seat contact force and bending (per ibf/in.):

I 3) 'IC M 'la C9) -6 ,

-L 9 C 3 rL 3 Y bw =-5.99210 Y bw * -

l (C .( b /

(in /

Deflection due to hub compression: .l 2na Hub length ~7 y N Pr = -1.197 10 cmpr l

(.2 2C j fibfl (in /

! Total deflection due to seat contact force (per Ibf/in.):

-6 -

in y w := y bw

• Y sw " Y cmpr Y w =-6.938 10 .

I I

Seat Contact Force for which deflection is equal to i previously calculated deflection from pressure forces:

l F s= 2 n a= F s = 82848.8 lbf Yw UNSEATING FORCES l Fpacking is included in measured static pullout Force n

F p ston := i D ste m P bonnet F p ston = 3685.9 lbf 2 -P down) f F ven := n a sin (0)-(2bonnet P -P up F vert =45754.3 lbf I

! F preslock := 2 Fs-( cos(0)- sin (0)) F preslock = 44848 lbf l tF po F po = 23000 lbf F total := - F piston eF ven + F preslock l

F total = 109916.5 lbf j I

PRESLOK, Ver. l. Rev. 0 12122195 Westinghouse Owner's Group 218196 9:57:52 AM Page 5 of 6

IONMb Proprietary Class 2C APPENDIX B. Page 6 I Verification of Pressure Locking Analysis Program PRESLOK l Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE 1

I l This page has been added to present the PRESLOK1 outputs for verification. The only change is to display more significant digits of the calcualted numbers.

! p = 0.4324202 .

-7 y sw =-8.261 10 -

l DPavg =950 psi 7

D = 1.31410 lbf in 7

-6 , m G = 1.107 10 psi Y bw =-5.99210 m

Cy =0.2209773 im/l

~

-7 -

1D Y cmpt =-1.196922 10 C 3 = 0.0361818 C g =0.6635194 \ in /

-6 , m C 9 = 0.2169174 y w =-6.938 10 .

L 3=0 L 9=0 F s = 82848.814 lbf L ii =0.0113379 F piston = 3685.87 lbf l L 17 =0.1857616 M rb =-34193.lS999 lbf Q b = 20636.591 -[bf p presicck =44848.03 lbf m

F po = 23000 Ibf y bq =4.01065772 in K sa =-0.8177681 F total = 109916.47 lbf y sq =-0.002023039 in y stretch = 3.8814905* 10 in l

y q =4.01306891 in  !

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, PRESLOK. Ver.1. Rev. 0 12122/95 Westinghouse Owner's Group 218196 9:58.00 AM Page 6 of 6 i

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• to y/pz1f l Proprietary Class 2C APPENDIX C, Page I Verification of Pressure Locking Analysis Program PRESLOK I Project /S.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE Program PRESLOK, Version 2 i l

! Revision 0 December 22,1995 i This Mathcad Program is designed to calculate the estimated opening force under pressure locking scenarios for flex-wedge gate valves using a calculational methodology that accounts for wedge stiffness resisting pressure locking forces. This program was prepared by the Westinghouse Owner's Group based upon the .

calculational methods developed by Commonwealth Edison.

j While this information is presented in good faith and be4ieved to be accurate, the Westinghouse Owner's Group does not guarantee satisfactory results from reliance '

j upon such information. Nothing contained herein is to be construed as a warranty,

! express or implied, regarcing the performance, merchantability, fitness or any other matter with respect to the product, nor as a recommendeten to use any product or process in conflict with any patent. The Westinghouse Owner's Group reserves the right, without notice, to alter or improve the methods described herein.

This section of the program reads the thirteen items of input data from the plinput2.dat

! file.

i := 0.12 input := READ (plinput2) v := input 8 P bonnet := inputo Psi E := input9 psi

P up

= input3 psi P down := input2 Psi D stem := input 10 m t := input3 in F po := input 11 lbf 1

I a := inputfn i p := input 13 b := mputym i f

Hub len# := mpurgm J l 0 := inputydeg I

l Westinghouse Owner's Group 218196 9:SS:42 AM Page l of 6 PRESLOK. Ver. 2. Rev. 0 12/22:95 l

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/04//Sg' Proprietary Class 2C APPENDLX Co Page 2 j Verification of Pressure Locking Analysis Program PRESLOK .

Project /S.O. No.: WOG-220 Calc. No.: V EC-1606 Group: AEE l i

i Program PRESLOK, Version 2 INPUTS: )

Bonnet Pressure P bonnet = 1300 psi i Upstream Pressure P up = 200 psi i

l Downstream Pressure P down =500 psi {

Disk Thickness t = 1.7 in (taken at center #ne of the hub vertically)

Seat Radius a = 7. in .

(corresponding to mean seat dlameter) l -

i Hub Radius (taken at plane of symmetry, b = 1.1 in l perpendicular to the hub, radius of circle of equivalent area for non-circular hubs)

Seat Angle 0 = 9 deg Poisson's Ratio (disk material at temperature) v = 0.31

~

i . ,

7 Modulus of Elasticity (disk material at temperature) E = 2.9 10 psi Static Pullout Force F po = 23000 lbf  ;

! (measured value from diagnostic test)  !

se.

Coefficient of Friction between disk and seat: p = 0.432

.. t i

Stem Diameter- D ste m = I 9 "I" '~-

t Hub Length Hub length = 0.6 in (from inside face of disk to inside face of disk) i i

PRESLOK. Ver. 2. Rev. 0 12/22/95 Westinghouse Owner's Group 218196 9:55:46 AM Page 2 of6 j l

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I O S'/f0g Proprietary Class 2C APPENDIX C, Page 3 Verificaion of Pressure Locking Analysis Program PRESLOK ProjecdS.O. No.: WOG-220 Calc. No.: V-EC-1606 Group: AEE Program PRESLOK, Version 2 l PRESSUNE FORCE CALCULATIONS i

Average DP across disks; P up eP down DPavg := P bonnet

- DPavg =950 psi 2

Disk Stiffness Constants E-(t'3 i 7 D := D = 1.31410 lbf in 12-(1 - v )

7 G := G = 1.107 10 psi 2-(1 + v)

Geometry Factors:

I 2 la C 3:= -- 1-lb - l'+ 2 ini C ,- = 0.221 1 -

4 ta (b ,

b lb 2 l f)a I32 b

C i - t1 In! -

!+- -

' -1 C 3 = 0.0362 3 := 4 a ,, (a (b/ (a) 1 I b32.

C 1 + v -(1 - v) '

C g = 6.6635 8 := 2- (a) ,

I 2. 7 b 1+v 1-v C In ai + 1-lb C 9 = 0.2169 9 := a- 2 b; 4 . (a j

a .f a3 2 l a) a 32 L i-'-#1 'l" ' " - '-I L 3=0 3"4a , tal (a) al j 1*v l a) 1-v f L

a

-In l+ l - a32' '

L 9=0 9 := a- 2 (aj 4 (al l

i PRESLOK. Ver. 2, Rev. 0 12122195 Westinghouse Owner's Group 218196 9:55:58 AM Page3 of 6 \

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! Proprietary Class 2C APPENDIX C, Paga 4 Verincation of Pressure Locking Analysis Program PRESLOK '

Project /S.O. No.: WOG-220 Calc. No.: V.EC 1606 Group: AEE I

Program PRESLOK, Version 2 l Geometry Factors: (continued)  :

2 l 32 32' f ai  !

L 1

1 + 4 -[b - 5 bi 4 -4'b  !

2+b '

In' l L 3 3 =0.0113 3 3 := 64- \a a) (a) , a) \b).

i I\# I\ f a\ '

1-v b L

1 1 1-'b  !

1 + (1 + v) inl i L 17 =0.1858 i

37 := 4 4 (a/ (a/ (b),

Moment  !

~

8 2 2 M tb := -(a - b )- L 17 M tb =-34193.2 lbf i

Q b:= DPavg (a, - b2 )

Q b = 20636.6 -

Ibf  !

2b :n Deflection due to pressure and bending: [

I 3 4 a'-

DPavg a e Y bq := M rb -C 2 " Q "ab C 3- g L 11 Y bq =-0.0107 in j D

- t Deflection due to pressure and shear stress:

l 2in K sa := -0.3- -1+ K sa = -0.8178 py .s. ..

K sa DPavg a-y sq :=

tG sq # U *  !

Deflection due to hub stretch: .

l

~

2 2 P force := x-(a - b ) DPavg f P force Hub length  !

' Y stretch , 2 -4 xb (2 E) y stretch = 3.8815 10 in  ;

Total Deflection due to pressure forces:  !

yq := y bq

• Y sq - Y stretch Y q =-0.0131 in l  !

PRE 5 LOK. Ver. 2. Rev. 0 12/22/95 Westinghouse Owner's Group 218196 9:56:12 AM Page4 of6 i i

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lo'7)DB Proprietary Class 2C APPENDIX C, Page 5 Verification of Press re Locking Analysis Program PRESLOK Project /S.O. No.: WOG-220 Calc. No.: V-EC 1606 Group: AEE Program PRESLOK, Version 2 Deflection due to seat contact force and shear stress (per Ibf/in.):

1.2- In!*- a

> ysw *~

tG sw "U

• fibf!

(in /

Deflection due to seat contact force and bending (per Ibf/in.):

(23\ 'IC } 'Ia.C9\

~

~l\ a -s in ybw

-L 9

'C 3 +L 3 Y bw =-5.99210

\D) (C g; .\ b ) .'\ b)

Deflection due to hub compression:

2na Hub length ~7 i" Y cmpr :: . --W 97 10 -

CmPr libf (b 2 2E j Total deflection due to seat contact force (per Ibf/in.): .

-6 ,

y , .= y bw ~ Y sw ~ Y cmpt Y w =-6.938 10 Seat Contact Force for which deflection is equal to previously calculated deflection from pressure forces:

F s := 2 n a- F s= 82848.8 lbf Yw UNSEATING FORCES F packing is included in measured static pullout Force F piston := D ; tem P bonnet F p ston = 3685.9 Ibf 2

F vert := n a sin (0)-(2 P bonnet -P up -P down) F vert =45754.3 lbf F preslock := 2 F s -(p c s(0)- sin (0)) F preslock =44848 lbf F total := - F piston + F vert + F preslock + F p F po = 23000 lbf F total = 109916.5 lbf PRESLOK, Ver. 2, Rev. 0 12/22/95 Westinghouse Owner's Grong 218196 9:56:25 AM Page S of 6

/35 //C5 Proprietary Class 2C APPENDDC C Paga 6 Verification cf Pressure Locking Analysis Program PRESLOK ,

Project /S.O. No.: WOG-220 Calc. No.: V-EC.1606 Group: AEE This page has been added to present the PRESLOK2 outputs for verification. Tne only change is to display more significant digits of the calcualted numbers.

p = 0.4324202 ~7 y sw =-8.261 10 -

DPavg = 950 pp D = 1.31410 lbf in .

7

-6 , m G =1.107 10 psi Y bw =-5.992 10 C 2 =0.2209773

~7 -

Y cmpr = -1.196922 10 C 3 =0.0361818 j

C 8 =0.6635194 .

-6 , m C 9 =0.2169174 y w =-6.938 10 L 3 =0 9" F s = 82848.814 Ibf

- L ii =0.0I13379 F piston = 3685.87 Ibf L 17 = 0.1857616

$1 rb =-34193.18999 -lbf p preslock = 44848.04 lbf Q b = 20636.591 -

m lbf y bq =-0.01065772 in F po = 23000 lbf K sa.= -0.817768 i F total = 109916.47 Ibf y sq =-0.002023039 in y stretch = 3.8814905 10'# in y q =401306891 in PRESLOK. Ver. 2. Rev. 0 12:22195 Westinghouse Owner's Group 2:8:96 9:56:33 AM Page 6 of 6

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