ML20071D667
| ML20071D667 | |
| Person / Time | |
|---|---|
| Site: | Turkey Point  |
| Issue date: | 09/15/1981 |
| From: | Kaza R HENRY PRATT CO. |
| To: | |
| Shared Package | |
| ML17345A980 | List: |
| References | |
| NUDOCS 8303110292 | |
| Download: ML20071D667 (99) | |
Text
{{#Wiki_filter:m , . A ar wa. :.c. ; e
- y +::;ngpg 4ggw_.6_ Q.a \l*]
x
.... M.%_ '_ ,g. ;. n_ y :n_.f{Y.
uM %_.. r;. ;; . ~; e m . .m ..-_..m . .-
.M, 3.Y ;. ;. .
j " ^' K' , ,L,< E lN.EW ' ,* Q .
- f. lG 4 h73**?"'Y-. 3_.q y .1,; . Q* , '; ',
-l '. .% *
. ;g.- : _
-, .g /.49...'*/.'N-h.?.-4.'w.-iXa. 'p&*'ch+ ,- 4:- -
;?
. .' ,. ;O . '- .;.; '/"*f t,i,1,.<\ .h '9. n.m_,y-m ,fi'Qi1~a. -7.
,, -] J~', '"
- $ Mh,m.. %g,ld.' C[; ,.'. ,"@('j N.,
wnw -. . 3 m.,.
- g. .y. x....
- y. .,
7s.~.. .,._ 7 ,.,.~...:.. n. m.7<_. ~
. c.
s.
- "=
.. a. .,,.: .m-m ;
. .p.mm,%.. . y- - - .
. .i. ... .;m. _~ --:.a. w a. ., w,,a.r.,
,n.
a- m. w )sspa.:
. n ..:.g;a ,fy:.
, .g n.
/a.'.'._s.. . r.,;
-.<>n _--
c.. ; 7
~ -:. .
S.
<. -1, .s
.,._.7,-a..,.L.-- ,;
- ;n
- p. ; ;.s . n q .c - w - > g . < ;g' .
m .- .. . ~ . , . m:%r,.
- a. .:(: mz..y: ra a t . _.. , m' gy :- w::yw: y .%+ 3.z.Q.;. "..: ym; .. m
- .c
- q f ~:w
, a .3.y
;;,: : J' .? '
L,_ 'y x ~. .' ..: .. Ju=3.: m n:-:m
; ];' 3, ; ;
.," p % . W:y f?l~~q.' ,\ ,,,: $3 ' .. v.- x.3
- , y , .r es.. - L. : ~~- ?. , . .xe y": ..e.
. ... -? ::
~ %:. ', w ;; ,, . . . ~ y _ _ ;\ L.9.. .. L; ;i'y
. ,,8,:-. ...%. -:s g.
~.
'. :.. _y , . .
.. a a g ,, p
.c
- p:. .m,
,. ,w. , -,u. n: . . ;.~ ;4n,yrd . m ~.r p .y :: yyw - _ c.;. g .. ,
-m g:_n, ,w;
~
. , 5.c2 +
s w ,-- %e. . 2-
,.e, m .m x, s 7a ,~w,'
.~
q:pm;
- c. y m 4..v x w;
- ~ g.
.w, L, .
. . ~
m,em,. my ., m , N,.,..> x w. m m n- < ;* w.p. . :.m .. .c , - .; .
.: p
=[.d I
- a- E w' _. .' '
I
,.', _ g&
y .
, s_
x..1- x. Y.,.n.,,. m
$mQ
,md &. . ,
.,N,s. w* $.s
.s.. . .
- .. q' n
- ,
/*% -g Q .tp
.n.
g.
,M is '
s
'f5.y I IIC N I W l'i t Vl"I' ( 1 n11 t \ N y M
, m,-
- y. ,.. n... 3%;
v 4
. .~ e
* . 'ni/ s l, i
- -*e
'M,$ '
- .d.*. '.,t - - . '* 0 f - . 1;.:.- T%* J:g
,. c Q #
~-?,.. ~
i?QQ
' , ,1 4
. -.r ,s' .y.-.i et .e -
h d
..=.8.' * ~ k -. ' (( ;;,.y *
) +A'.5? ., ,'A :,'M.
, J% ; y'
. . , . . , ,e . .
- c '1 , i l ) ,' ,* }
..j n . -m
. . p
%, .CT.y u
.n.a" , .x"..r .
',, ?
. .s.
-'S
- _ ,., y s.ye + -
lh ;' r-
,f Q' ; fl0h*Y'W4'.y;.f
.s c. ~-i$
#.b
./4 w
/6 e~-
,1:43 9
^ . .y,% p- c. ' *r i
's
* ,.,n,,~., e
- 5 , )<'. . . ur.g d. ..
'. . J =.- ut l,.
. . ** 3@s4 R:, N. ,. ~ .,,,,. 4
,,' ;,g . .p*.--b. & ' ' y.. : . 'f* -.4 , ..g',.-,e
, ..o-fgG y -
,- . wm,
,.s gg r,c%" w 4 v[ . ';:.. k.
. ~ F.
esY : '. n Q: j .& ,l f*R1a% n t;f9. - l {~. f~vL
.3,.y t w.v....s , '-c. m;r 2 a. . c o
%'p r f h ((. o $ b.
- C-W s' WY.IU , Y.m.....-w';nm 5
~
A.,~5* x%W2. QRlLSD W T Q5',Q. m st
,; y w m*P TI Y
~. K.cQ. m~5 . m . &.W..p we ,,M m.,~.];n?Q'Q.~ a.iO.w.,kmC.h&y.Q~.MQWM
- v. , -
mm:m..nb,e.cm p. - e roMy 3 h**M ak'h&m
% .Q.).g .m
#.*Q^@k %t*!%$:.s
'ny.N&~ Qy ha d ~,.-Q-:ur. g 9. g g%m_..m a 2 M ' q?' #%.g,Mu13 w Md?.9 Wi-.2 @mr4.p mw@.w hdGHr m$ @G wWp M A; -);$w 3 gib%
x W %.#: W mpy e~ Mm%ig;C:sF y&, $6;ge;.B.R@bgd'W.MRmMQgi% y w R _ L f % m Q&WMEG m % g w w& l Q &m Q W !s%w& w@y$ wMMA n% awM.c. si &gWE e p e%aM M p h @ E,R g n% @A:,o v - a M n hMMWi Ma I
# n n&w u -, ig
%S.wv.m h1W.SgM w
Q# p ce ',.p.s ,a 6 ' t A~7 - i "p %:.. w : p %. h .,.~ = R y.u. u -- ,. s- W a-5 b A - Y' *' $
&mqc.:m$ h $$
pp.
?-
AL.a. sman 1w w4sw - m 1 ::.
. y# h_ M m e n .tm: m m ,
t u R.m3. pa y w.n+4 p
%p M M**L sw.e w+ GAT.d~,R@<ylW Y.lb i
L. a e m t fe wu
" .,Q:W~
g~ Y &.: % 4f. :'. n . vW e.. % nm . w .,..r n,
- g w
m $y m% zw WENRW.e&56 j< k p;? M w w:n M $ w UTE w;W:5 % "_ J.
-:N syMB&.; +na n >
N. 4wW ~g F F;. s SWWWW
&xmmm. ue mm ww rw~ws:M ;gx.,ys.,
m.- gw&~r?.mc
& 62f5
- - mmy . p t ,4gx _g. m.g m .z,,.M n m.n..:. m ug. ., u.g;wg w%w p 4 => w n .s . u m %~s..s%.. -
h g;.qn h*g'* a 19 --u x.-,M y Oi D h NNN e y s % c'N M[ a' N k. N E k NDdh m m$h mum w mmmt
- e[d h kk h *.h Qp % pNb W y Q % W it
,m.y- w w . mu.xyW Qn.-r#.M.,w g
%yw:M fQQtv f 6e.%n%+hk" w qwnX.
nm nc a. n-- hgM%%%y: M G.R W ~ %: i f w:.ks e n.- m~ NRM ~ wm wg%a. k , SW.5Qf i G u;&s$&,m *:;?%% R ,& Qe? %m. .hf ?vaN!2ll$$b t fk W.W Q Q2N..%.%n 6 WlEh!..'8.Y W,? gg U2 Q s. W ' gg fxE'%gp&$, ggp4 e g&gg%gg&[&g se MN#WRMMMMMARWN$$g$m@IMi$MMNb p%E cw%w&x R
-..-Revision 1 _
STPES3 REPORT FOR-f 48" RIA WITH BETTIS ACTUATOR i i Project Site Turkey Point Units 3 & 4 Cus tomer Florida Power & Licht Co. Engineer Bechtel Power Corcoration Original Specification 5610-M-83 j Original Purchase Order 5610-M-83 - Original Pratt Job No. 7-3071-1 & 7-3071-2
- Valve Tag Nos. POV-3-2602 POV-3-2603 POV-4-2602 POV-4-2603 General Arrangement Drawing E-586 pey, 1-Prepared by
- -OJ N. OM v fismt""oni,,,
g v. a '
- . Date: @-15--2l S
/\,C -
""~
39S60 '- m ,k&,', - S Reviewed by: __ /'. 9 - [6A' #}Gf _ $ / REGISTEFED f 5 ' PRCIE55CNAL : 5 . Date: s/ W~ /d ~ N hW., E'" "EER CF .- lk?= Certified by: ! / e- d' M %,,, g/' Date: ( C) - / A - 8 / .
*[-
. . _ . . . . - . . - _ .. - - . - - - . . - ~ ~ ~ - _ _ _ . . -. . . _ _ _ - . .- .. _ - . _ _ .-.. .- - .. ..-
i
! CONTEUTS ?
l ! Page l ' l I. Introduction 1 ) j II. Considerations 2 i III. Method of Analysis 4 A. Torque Calculation 6 i i S. Valve Stress Analysis 8 1 l C. Operator Evaluation 9 IV. Conclusion 10 i V. Additional Information 11 l Attachments (1) Input Documents j (A) Pressure vs. time graph l (B) Pratt letter regarding additional t l ,, information (C) Customer / engineer response to request for information ! (2) Valve Assembly Stress Report (3) Supplemental Torque Calculations l l (4) General Arrangement and Cross-Section Drawings l l t b {
'ww-w.wwww,.w,.e,s.---w-r-e.-ie-w-w- y ew m-w. v m.-wg-----e--.i%,,mwg ::ww---.--,- y,, --pmy,m.----,,---e,-----<w-mywm-vT--.t-v-w---m.
. . - . _ _ - . -- - - . =
I. Introduction This investigation has been made in response to a request by the customer / engineer for evaluation of containment isolation / purge valves during a faulted condition arising from a loss of coolant accident (LOCA), The analysis of the structural and operational adequacy of the ()valveassemblyundersuchconditionsisbasedprincipallyupon containment pressure vs. time data, system response (delay) time, piping geometry upstream of the valve, back pressure due to ventilation components downstream of the valve, valve orientation and direction of , valve closure. i The above data as furnished by the customer / engineer forms the basis for the analysis. Worst case conditions have been applied in the absence of definitive input. O e k s
II. Considerations The NRC guidelines for demonstration of operability of purge and vent valves, dated 9/27/79, have been incorporated in this evaluation as follows: A. l. Valve closure time during a LOCA will be less than or equal to the no-flow time demonstrated during shop tests, since , T fluid dynamic effects tend to close a butterfly valve. Valve [O closure rate vs. time is based on a sinusoidal function.
- 2. Flow direction through V&lve contributing to highest torque; namely, flow toward the hub side of disc if asymmetric, is used in this analysis. Pressure on upstream side of valve as furnished by customer / engineer is utilized in calculations.
Downstream pressure vs. loca time is furnished by cus tomer/ engineer or assumed to be worst case.
- 3. Worst case is determined as a single valve closure of the inside containment valve, with the outside containment valve fixed at the fully open position.
- 4. Containment back pressure will"have no effect on cylinder oper-ation since the same back pressure will also be present at the f- g inlet side of the cylinder and differential pressure will be,the U .
same during operation.
- 5. Purge valves supplied by Henry Pratt Company do not normally include accumulators. Accumulators, when used, are for opening the valve rather than closing.
- 6. Torque limiting devices apply only to electric motor operators
/T which were not furnished with purge valves evaluated in this i report.
l
-~g 7&8. Drawings or written description of valve orientation with respect to piping immediately upstream, as well as direction o f valve closure, are furnished ' yccustomer / engineer. In lieu of input, worst case conditions have been applied to the analysis; namely, 900 elbow (upstream) oriented 900 out-of-plane with respect to valve shaft, and leading edge of disc closing toward fm s
1 outer wall of elbow. Effects of downstream piping on system
-# back pressure have been covered in paragraph A.2. (above).
B. This analysis consists of a static analysis of the valve components indicating if the stress levels under combined seismic and LOCA conditions are less than 90% of yield strength of the materials used. A valve operator evaluation is presented based on the operators (J) u ability to resist the reaction of LOCA-induced fluid dynamic torques. C. Sealing integrity can be evaluated as follows: Decontamination chemicals have very little effect on EPT and stainless steel seats. Molded EPT seats are generically known to have a cumulative radiation resistance of 1 x 108 rads at a maximum incidence temperature of 350 F. It is recommende'd that seats be visually inspected every 18 months and be replaced periodically as required.
/ Valves at outside ambient temperatures below 00F, if not properly
( ,N) adjusted, may have leakage due to thermal contraction of the elastomer, however, during a LOCA, the valve internal tempera ture would be expected to be higher than ambient which tends to increase
, sealing capability after valve closure. The presence of debris or damage to the seats would obviously impair sealing.
i
4_ 4 III. Method of Analysis Determination of the structural and operational adequacy of 1 l the valve assembly is based on the calculation of LOCA-induced l to rque , valve stress analysis and operator evaluation. A. Torque calculation The torque of any open batterfly valve is the summation of , ! fluid dynamic torque and bearing friction torque at any given disc angle. Bearing friction torque is calculated from the following l equation: i TB=PxAxUxd7 where P = pressure differential, psia 2 A = projected disc area normal to flow, in , U = bearing coefficient of friction d = sh. aft diameter, in. , Fluid dynamic torque is calculated from the following equations: For subsonic flow I P ! R CR > * #EE'O**
- P -
2 l 3 T =D x K xF D xCTl
- E2 1.4 RE l
For sonic flow - 2 - - P > R i 1 - CR l V
- _2 _,
3 T * * (s D" T2
- 2* l.4 RE (F RE 2 1)
Where T = flui dynamic torque, l'.-lbs. D
p Fpg = Reynold number factor R CR
= critical pressure ratio, (f (d) )
Py = upstream static pressure at flow condition, psia P 2
= downstream static pressure at flow condition, psia D = disc diameter, in.
CT1 = subsonic torque coefficient
-~
CT2 = sonic torque coefficient (' K = isentropic gas exponent ( Tf 1.2 for air / steam mix)
*4 = disc angle, such that 90 = fully open; O = fully closed Note that C Tl and C T2 are a function of disc angle, an exponential function of pressure ratio, and are adjusted to a 5" test model using a function of Reynolds number.
i fs Torque coefficients and exponential factors are derived from (%/ ) analysis of experimental test data and correlated with analytically predicted behavior of airfoils in compressible media. Empirical and analytical findings confirm that subsonic and sonic flow conditions across the valve disc have an unequal and opposite effect on dynamic torque. Specifically, increases in up-stream pressure in the subsonic range result in higher torque values, while increasing P y in the sonic range results in lower torques. Therefore, the point of greatest concern is the condition of initial sonic flow, which occurs at a critical pressure ratio. The effect of valve closure during the transition from subsonic to sonic flow is to greatly amplify the resulting torques. In fact, the maximum dynamic torque occurs when initial sonic flow occurs
~'
coincident with a disc angle of 72 (symmetric) or 63 (asymmetric)
~ '{a) from the fully closed position.
-,- ~ . . - .
, 1 l The following computer output summarizes calculation data and torque results for valve opening angles of 90 to 0 .
1 1 i I l i i i l i i i i j j . f
- l O 1 i
I 1 I I l i r 1 ,i i
9 D-27256-2 TOROUE TAELE 1 9 / 14 / 31 f'~' L JOE: FLOP.PMF TUPVE"-PT P2-VAPI AELE ; ICE ADJU;TED <FEYriLD'. NO.FNCiti!) CAT. 0 TEAM AIP MIMT'.F E I,IITH 1.4 LEO OTEAN FEP 1-LEO AIP 1 SPEC.GP.= . 728255 MOL.WT.= 21.3??2 F AF A (I!ErtT. EXP.) = 1.19775 R= 72.1972 GAS CCrl TAtlT-C ALC. 50ti!C : PEED (MOVING MIMTR.)= 1371.29 FEET /!EC AT 283 DEG. CRIT.CA!E IriLET VELOCITY IS 1.48516 TIME! HIGHER A0 AIF CRIT.CA E ItiLET V1-CF , 5 INCH MODEL MAX. 70POUE 10 AT THE CPITICAL PFE00.F ATIO(.535-(5 IN)MODEL OR APPX .692271 ( 47.375 Iro u!TH OTMIX.)FIP!T Cri!C e G 72 DEG.V. A.) ABSOL. MAX. TOFOUE (FIP!T !CtlIC) AT 72-68 DG.VLY. At G. = 514276 IN-LEO .D 72 DEG. MAX.TOPOUE IriCLUDEO OICE EFFECT GE'rttCLDO ttu.ETC) AFPX. X 1.30269 FDP 47.375
's IriCH EA;IC LINE I.D.
1 ALL PFE!2UPE: UOED 0TATIC(TAP)PPEIO.-AE CLUTEIP2 ItiCL.PECOVEPY PFESO. (TOROUE) CALC' VALIDITY:P1/P2>1.0Ti
. VALVE TYPE: 48"-PIA 513/7.5 CLASS 75 DISC OICE: 47.062 INCHE0 OYMMETRICAL DISC SHAFT DIA.: 4 INCHE0 BRG. COEF. OF FPCTN. 5.00000E-03 SEATIrlG FACTCP 15
. IriLET PPE00.VAP. MAX. 60.2 POIA DUTLET FFE!!UFE.P6): 33.93 PSIA (72 DEG. ACTUAL PFE00.CriLY(VAP.))
MAX.AtlG. FLOW PATE: 550564 CFM 1092962 OCFMi 60077.6 LE/ MIN e CRIT.50NIC FLOM-90DG 67628.4 LE<M!ti AT 37.234 IriLET P!IA VALVE IriLET DEri!!TY: .10912 LB/FT
- 3-M iti. .157531 LE/FT^3-MAX.
- FULL OPEN DELTA P: 9.58431 POI SY0 TEM CCriDITION!:
PIPE IN-PIPE-OUT -Arid- AIP/0 TEAM MIXTUPE SERVICE 9 283 DEG.F
' \[n MINIMUM 0.75 DIAM. PIPE DOWri3TFEAM FROM CEtiT.LIriE CHAFT.
P1 ABO. PPE!!UPE(ADJ.)FDLLOWS TIME /PPE00.TPAliOIENT CURVE. AB00 LUTE NAX.TOFOUE IO DEPEriDEffT Ott DELAY TIME AfiD 3.43 TO 2.15-TH P0uEP OF (P1/P2)Ifi !JOFOT PAriGE X LIttEAR Cutt 0TAfiT X Durt;TP.PFE00. P6-ABO. G5-6 0 LEG. ) Ifl SUB50tlIC PANGE LIMITO-0!iLYi2EE FCPMULAT10r10.-PER TECTS H.FCATT THIO TO. AT 72 DEG.0YMM. DIOC (68=0FF0ET SHAFT)CT=T/D^3/P2(ABC)
--5 IN.MODEL EQUIV.VALUEO------ACTUAL SICE VALUE0-----
AriGLE P1 P2 DELP PPE!O. FLCW Fluil TD TB+TH TIME (LCCA) APPPX. PSIA PSIA PSI RATIO (OCFM) (LIeMIN) ----INCHLBO---- TD-TB-TH CEC. g 90 41.70 29.38 12.32 .704 CP1092863 60077 0 1430 -1430 :.00 85 44.29 30.93 13.36 .698 1153003 63383 123955 1449 127506 3.39 80 46.31 31.38 14.93 .678 1158249 63672 189597 1496 188100 3.77 75 48.07 30.60 17.47 .637 1145101 62949 307545 1587 305957 4.13
. 72 49.01 28.67 20.34 .585 CP10!4664 57977 489099 1727 487371 4.21
-- 70 49.59 27.99 21.61 .564 CP1029718 56606 474955 1716 473238 4.4!
) 65 50.86 25.10 25.77 493 CP 92?246 51028 43713 442434 369699 1691 440742 368063 4.72 433 CP 795188 16?5 s ,/ 60 51.87 22.47 29.40 4.95 55 52.61 19.97 32.64 .380 CP 668253 ?6735 361006 1647 3593!S 5.11 50 53.05 13.37 34.68 .346 CP 546199 30026 277?66 1700 275666 5.22 45 53.20 17.21 35.99 .323 533747 29341 244600 1744 242936 5.;5
40 53.33 16.45 36.98 .308 369400 20306 170489 1737 176700 !.29 35 53.72 15.67 38.04 .292 296493 15749 135682 1918 133563 5. 39 30 54.34 15.22 39.12 .230 213264 11723 73408 1950 71557 5.55 25 55.16 14.97 40.19 .271 147567 8112 46702 1977 44625 5.75
-20 56.15 14.82 41.32 .264 91239 5015 32506 1932 30574 6.05 15 57.23 14.72 42.50 .257 51981 2657 11G99 2015 9863 6.08 10 58.34 14.F1 43.63 .252 25970 1427 7606 2113 5494 4.7S 5 5.5.40 14.70 44.69 .248 G656 475 4063 2209 1858 ~.11
, 0 60.20 14.70 45.50 .244 0 0 35307 2141 30665 7.50 i
d ,
~EATIrlG + EEAPING + HUP EAL TCPOUE >M/M)=
MAX.DYN. - IEAPirlG - HUB EAL TCFOUE .M + = 37948 I ri-L E.! D 0 DEG. 489099 IN-LBC D 72.DEG.
B. Valve Stress Analysis The Pratt butterfly valve furnished was specifically designed for the requirements of the original order which did not include specific LOCA conditions. The valve atress analysis consists of two major sections: 1) the body analysis, and 2) all other components.
~~g The body is analyzed per rules and equations given in paragraph NB 3545 of Section III of the ASME Boiler and Pressure Vessel Code.
The other components are analyzed per a basic strength of materials type of approach. For each component of interest, tensile and shear stress levels are calculated. They are then combined using the formula: Smax = 1(T1+T2) +1, (T1+T2) + 4(S l+S2) 2 2 CI where S max = maximum combined stress, psi Ti = direct tensile stress, psi i T2 = tensile stress due to bending, psi Si = direct shear stress, psi S2 = shear stress due to torsion, psi The calculated maximum valve torque resulting from LOCA condit~ ions is used in the seismic stress analysis, attachment #2, along with "G"
. loads per design specification. The calculated stress values are compared to code allowables if possible, or LOCA allowables of 90%
of the yield strength of the material used. 1
! 9 C. Operator Evaluation 0'4 Model: Bettis 2744A-2SR-45
-Ra ting : 125,000 in-lbs open and closed positions only 87,000 in-lbs intermediate positions Max. valve torque: 489099 in-lbs !
The Bettis cylinder operator furnished was specifically designed for ths requirements of the original order which did not include LOCA conditions. i The maximum torque generated during a LOCA induces reactive forces in the load carrying components of the actuator. The operator model furnished has an approximate rating which exceeds the calculated valve torque for the following i valve angles: 35 degrees open to O degrees (fully closed) Listed in the attachments section of this report are the following documents used in evaluating the structural and operationai adequacy of the actuators.
- Supplemental Torque Calculations (attachment 43) l -
4
- I i
l
10 l
. I IV. Conclusion ,
It is concluded that neither the valvo structure (with present materials) nor the valve actuator are adequate to withstand the defined LOCA-induced loads based on the calculated torques developed in this analysis except for restricted valve opening as described below:
; Specifically, the valve top shaft, disc pins, thrus t bearing adjusting screw, trunnion bolts, operator bolts , and bonnet are shown to be overstressed except at valve disc
) angles of 50 or less. (See attachments #2 and #4.) I
- In addition, the calculated torques exceed the rating for the actuator except at valve disc angles of 35 or les s .
9 I e k f i f, 4 i -
11 4 4 V. Additional Information The following items are presented to describe how system factors affect torques developed in this analysis for your consideration and are informational only. Further analysis by the customer / engineer is recommended prior to implementation. ( l. An important factor governing the magnitude of the dynamic torque is delay time from the start of a LOCA incident to activation of the pressure sensing mechanism, which in turn initiates valve closure. Careful re-evaluation by the customer / engineer of the pressure sensing / timing sequence may render the present valve assembly functional through
. a significantly greater range of angles.
- 2. Installation of a convergent-divergent section downstream of the outside containment valve with a throat area sufficient to allow unrestricted ventilation during normal operation, but which will choke LOCA-induced flow while the valve is closing, through the critical range of 80 -60 l open, could resultantly reduce the flow through the valve to subsonic levels.
- 3. An orifice plate installed similar to #2 above can also
, choke the system downstream and reduce flow through the valve to subsonic levels.
- 4. Mechanically restrict or block the valve disc to a maximum disc opening angle. (See attachment #3 for further g illus tra tion. ) ,
l 7---- -- ~~ w a - , - , - - , -.v---,-_--- , , , , , , -,---,--,n- ,-,------..,.--n... - - - , - - - - - - , , -
t k l . 1 4 I
. -4 -
i l l
. i ATTACHMENT 1A .
I PRESSURE vs. TIME GRAPHS . 9 9 i l f 1 1 l 4 4 1 I . l t t
,-e-e-- v'e
10 - 3
' j .- t--
;_ ..- I
/.-- _ . __; . _j m 5 i
- t !8 - ' - '
4 y t i .
- e. . .
---l . . ; .
if. g. i. 1 g r i ; _e.~8-: 1-
- f :
- _. . . :-- .- . ~ -. i i - , :- ; ;; .- : -
f . '
.i
.f.
1
.g ? *
. : - . - ::. n. ..==.: . =_ . . : = =.
g
, . . ._- .u . .. .-
= ~_.
. . . . . . _. -...- : . . . . .= _ = y : . . . ..=...
.y. ,
. . . _ . - - -. s' i I e
_ _ , __ ,. l- . g- - r - t . .
- - [ _ _ j '_ L__
.. .L.. N -t -: . ! - - - ---! -. _ l -
I- .. i; . ( s-
. -- ; .e -s. . a .. .:.__. . i .: ' .. ..L.- . .
. t -g .
I _--.. .=.,,4. 7=' ..._. :._ _ :.. ._; - .: . r :_ _: .-_-_' :_ _ L_2: _ _ _ .. _: - .: .: ._:--_ _ _ .-. .; _ - .- ; . - _ _:-...:-. r:: ._.,._-M------ A.---: 8 .
, ,_ . . ._. .u_. .. .: :_ : .2. - : w .. .
p =_ ; . _ -' - L : -- _- __ F---- _ . C. _ - !- :.-_ -I. - _-: :.; ._ ;. ' :..- : ; .- :- -' 1 _- ---_--.-....J*--
. - _. i 7
,__ y . ._ . g/ f _.,.___ .y. , .
j-.......,----.. 7..
. . - ,~...
_ - - -- - ----._-__.e..,,a.--s._.__- - - - . . . . . ... . _. . --- . . . . .
;n . . - _ ._ _ . .
.- . . p ..
- c. -
; _y -,s., - - . _ . . _ _ . . _ ._ .___.__ . - .
e . . _ - , - . E # **& n i ..w . I I M ' n- . e
,, e
~,'./
i 6 . 6 . i i . t
' u= , i w i . .
f.< # '- 3
, s. .- 7 w...=.,."-.a:.--
. . ..- . .a : : -- =.: - . . . . _ -_:. -p.- . =.:. =.. . ._. .s g . .
...-__-:-.h.=-: _- m =. - =:. ,*.a. : . e .a :- _ . .:: -
7 " -{Q1 [ % = ._.. _- + = "is- ~_j-1:-i- : ; ~ = _ _- ::6 E_ =:- -. =- /;Y-- P f- i- _25 '- ;- -~.:.. : . L . a .= : : . a_ . -1 a , : _ ; : . _
=- :-- - . .: : - - .:. - :: :; z . . _ .
a -.=_t-- - -- -- - :- -- e / "--- = : := =r-'= - = :-~~ =. - t r " -- M { .:n- -- _-- -_.-----.__:: -. :__==:.-=------=-- - ==_:.
-. .-: -_ .. ; -. _ .. .__ = _ _.__;.
_ ..y.. _L : . _ . . ; = ;.:.2_ - - s-+ -;- = = -1 7.-; u n ', . p -- a .~ .
.__=-.._--+=...
, _= d'hg. u. = .i -+= ;- z_ = -- - - _- - c.n.u .sp ; . -// r :- . =.i .=_ i _:. :: L :=. _ y _::_.= ._ M. ;-- . F :-. . E : . _ - - .
tid- F,- - : =_ = == - -- - =--G E=
^
==__M:
==a :-. - ::.
- .= ; =L
_ :. . _ = = i ==. ? .a-_-_._.--;.;_. _WE - -. :=+T :.n== : =.~_.=. ;=E- ~ =5 : ! - __ w -_;__.___.-_-__ _ . - . - - . _ _ -
. . _ _ . = _ _
- . _- . _ ,=,_- -. - -_- _ _ . _ .
=_-t-----
___._ __ = =_ rr ._---- __ ___ _ _ _ . . _ . . Rre _ . _ , . --~~----j d - ~
-= tx ,C. _
*% _ e. - 3 m -i r. . !
i e i # J t i i I l w '_n % x -
- c, 3 ,.
, ni , e . s , . ~.
.u ._m 3
. . _w. u .:. _z_- .:= = .- i.- = - : -- t i i .:-- + .--- -:m- m = :- += m m -
- a a_ : - .-- i c-m . 2.: =- =. ,. = ._ z - - _ . _.-
. '. % Q M_.
_.n
..":===.-J=--2.-_-
r = = _= e :-- . = c _ F =- + :' ' :-t -t r e:
- O y E.W(__ Z:M'e . M Z_~1 _._ . -? =
=5F W=_"-
=
M 3 =f- ' I - E Edi _ ..-Ms.--- .__- _:- . .T _ -6:4,_. ;;. ', _ __r _. El Rs a ._- __.__2:._. - : : --- .,=-_ _-- -__ - = _; : r _._-- .r b r.r__I t- x.t.* _ . _ - _ . _ - - _ . . _ _ _ . _ _ _ _ _ . _ _*
. - - - _ - __ yJ
-_.e - _ _ _ - :.- _ . . _ . _ .
q_.: g y __ .. . . .-
- -y =__- -- - .j g + ;- - .8-y
=--- ew .2y-- y. , =- n: - -- - - -y -
a a . _ _ , . . . . _. . .._. . _ .. ,:,-_=. :--.=.=_==.=.=. .=-_.--=..._:. . _ _ . - - - - - - . = = . _ - - - - - - . , 7-. _ h-r=--tbD =' _-r--- E3 21.-_'i-__. _ .__,_ __ ---- $W . .. bf.
-d - b-~ .s IN1 =i 21.r-5Cb".k- 5
$~NI-(
,- . . _ . ;;-__ ; . .__ . ._ ; ' =. -2
_~-~ - . - b : ;_ ' f .g y., ,;. . ,.; :=k,-,: -- =--- -- _ _ _ _ . _ . _ . __=_:-.__------.__.-.==,=-_---=---.: ..__. , ,.j,,
;_._r_..._______. _ , _y, _ ..
. - = _ . _ _ - ;~
,_ _ _ - -_.-------:c_ -
,~.
_._.-__-._- _...._____._a _ .. . __ _ . _ i%
. g,_ . . :~
I I i _ em l , e N l 4 [ X ! I
._1 %. r T
, ~. l
.i t , N_ . 6
-w.T_ i l e
. .. . N .
N_ , . . N. ' a y
, p 2..:: : - ..:- - . . _. : N; .N-- i-o_1 5
l
'N ' _a l < g _ p.c= : r: --.---r...: .: n. -- ,* \ .N 3 .- - - . .- N _.. ... - _ : . s r. r
. :..: N- .. i l* . 7 f-5:N- *:"'- = -' -- i-7 ! - % I EU L\ . i . '+ 'N r r @ - E N ' " ' - ' ' I =: '
- L ' '- _ : J
~ 4 I-r _.__I-5"E" * "_~ INN I- E *I
. _ . N__~ 5' P__
~
g_ ,- . .%. . __ ._ .-_ p_._..._.n_ _. _. n-. . _ ; ' _._ ..e._ __._
.' 's_ ..._' _' : *5'E s.
l".'_ .g N~ Ni- _E - M .' .#.#." I'#- U ~" '.._: . _ " * . .-' ~" - _.__'"_N; .; .= __._: _%,;- _ . _ . .L : _.=.:.. ---_:*=.__._=;.___.._..r L. t __ __ g . . . _ . .- (-. . ._2= . L. %.."l
- '.. -1 . . s i .- .--.
',,,_f , ,
-- g-i,,,,,,
p_M Q. - ) 6 - : -- l - - e - .: . .r-4.1 L,.;,_, _. ,_,,,K,_,,,,,, ;_,; _ 4 - ia - . ;
'a,., .
N- I. N - - - - t ,.- l
._._. u _ . p . - . ._ p ._
. j . - ;
r: ....-L
- - i. p - - K
,. N
..gs: [N ._!...e r.!.- -,\sr . . f
.:.... L..:2 =_ =. . L :: :._ : _ ; i - - . : . \. - -. !. .-- - . _ . ..
i_ ___._....g_..._....____.._......._.._......-__1.;:.-
... . . . . . . i 3_
r ; rr p~ _r {. ---- e
. ; s . . L. _ : . _: c: .;_ :,.:. :. . :: ._ : . :_ = :- . - u.:_-_-_ : : .
- -.: ...t..N s:: -~r - . . !. .
. . .. t
, _ _ - - - - -
- t _.--- _-- : -- -- r . . ;_ .: - .:: . ::- . . r _ :- . :. .'%. :. N_ ;- _$._e.; - -
.t.._.
_ .. .. -_ _,. ..~.____.._..____.._____....._.__.._._..___._._~.._._r.._ __....s ,. .. .... . . .. . ,. ., _- _ .. ___ .. _ . - _ . _ .. .. ..... . .._. s __ . , s ,. r _-~ . . --. . .s _. l _ . . . _ . _ . . . . _ . _ . . . . _ _ _ _ .p
, . . _ . . . ,_.._ _ _ _ . , s -
i l g
,_-_7.
_ ..y s . , , - ss , _ . . , _ ~ .s _ _%.,
.s_.s,
-,4 t .
_4-__- .... -- . . . _ _ . . . ~ . _6..._.__ 7-.... .. _ _ _ . -.3 , . i
%; i r p--" r-* -
.__6....__.__t.._.-__g____,__
._ _ ._ }
g.__, 7. - ,. j.__~ F. .
. . . . - - . e.
_ . . . _ . . . p . . _ . - ,N - 4.- . w s t, e
, , , , r--- ~ r -- - 6
- - - -i , -f- *--**---!--- " - ~ - ~-
&lfe) < 3 WC.T.kJ .L N:rus s VL rwo') y g _ , y__ , _
1 1 l l i 1 i 1 ATTACHMENT 1B PRATT LETTER REGARDING ADDITIONAL INFORMATION i ) . l .I ao e 4 e e
- G sw ,,
. - - - -. - . . = . . - .
PRATT HENRY l'R.i':'T C( B 11).\.N Y f It al N )L T!! Il! Gill.\ND.\\ i'N! M .\l 114 4.1 \. I! J J M bl- . s.~ C T e ~~
" - "e=- .- v_ 16, _331
. 'y.'.
. E c ..... u' .' ' v- .. e _- C w' - e . G .a i ". h. e _ e--.h " ,~ c. o"., _'_- D _4 v 4 s .4 o.". 15743 Shady Grovo P. cad C-a _4... _. e- o,uu 3, - - m.- _0/oO a .m. a..,.. . _4 , . v ..
.. c_,
- w. < B a- l e. - w.4..,
I
Subject:
43" and 54"
- o. . .- ,e. y o _, ve .:... , _1, r s e =- .
m, i_.e _-g u.; , 3o _4 .". '. P_o ;" e C '. Florida Power & Light Co. Prat No.: D-27256 Dem ... - :
. - . l c.a. 4. .. . .
.s Conf'rmine our recent relechene conversation, the 'enry d Pratt Com.oanv kiilaa r.urnish a revisec cur 9e valve anal sls uron
. 1 -
- _4 _4 m. , . 2 , .me .w... _4 . m, ., . me.,.
- 2-_
.ecc.4p.. c. _-
Our general analysis of purge vclves suhjected to LCCA ccnditions
; a . . _c.... _ u. , _. . .u. _4 -s aa24_4on-1 c- a u ..,s , s i g n _4 .= 1 ,... . . .4. --
. - ,- c . . _.
_ n m _4 .. -. the maxicam :orque and resultant stresses in the valve assembly. I
- _' _e , -.5. e _ e _# ^ - = , .eq"es.=d
- b..a". .he _4."_o...a.io.
. _ cv.44='-- 'o c- + -
accurate as poss1cte. i IYe k'_4 l_' ~ _ c g 'm' .4 _ e *. i
- 1. .s.e CC~w_4ne4 - _- n. -e _ts.,.CG
- .m.. Cmo.s:
. .._4 - _4an_
u
.:w.- ,1-_
ventilation system . - como.onents downstream or 4 One VaeVe (one Ior eacn valve s1Ze), or 3 ' 7"^ a' g = D. b. o .# b a c k .C "e e s "--a.
~'
. s. - - .3 '_ _i. ..C 5 - - =
4 a4
- b. . .a _.L,
_n_ 4 ,- w _4 -... m..b. ._ D c.-. u _w, o _: ...L . - w ._ ...s.e._,,,b-... w - = = _Wg 9 J
. . .m . , -_ e , ,=
. .4. _
. . , o_ A. .b. s.
! ..,7.pc.
.-.. .. . s _4-
- a. .e 4 -.
(! I 7.y. 4 . 4 .g g,e J
.. 4 , _. o _w . a ---.
.e.- .a 4.. v__ mw_
,,7w .1..
. .- . "es_'s.
b
- 4 .m.A_6 w
- A =L.3 c , c 4. .m. w%,n'* _ W .N w + p * : . _V 3. .
y....w i t 4 5
---w- - -
m- - - - --
_ _ .___ _ , .__ . . . . _ _ . _ . _ . _ . _ . .m. - . ._ ~. - es v.. ,.m
- 4. . -
e -
.A . --
-Lw'.3 s o 3 .-.
,1 D. C..,..a., r Cv n
- ~
. C a-su=.; v . , -. w. r er '. f,, *d1.
Paqu 3:a
.O . eww., n. 4 4 .- . . . .e a. 4
+n w..
L -
...w .
/ . 1
.-- /3. . .
.4
. ..L
.c.,C 7 r.yw.c. ,.
2 -2
,...: . .. . . . , ~. . , . -
4,4 -
.O
. ...w d .V,. a.. .fs s.
s - .A w . v . _ .s ... d.,,.,g y v w .,. C S ,
- c. . O , :. A. n. . ; .... .: 1 . , . , ~ ~
a .~..4 . . . . . . . ., u..s....v, u .e. ._. 1
".h.ie w w" a "w 4 v. .d .' .1 ' n.
D "36- 4 . . - " . . ' .^
- . ~v wrw .'; .3.'."....w.o.s".
.i...#^'....'...'c..
- w. -w ^a
,,.r 1
a, g .e . nw . m..
- .,.. q ..
. . .an,...., .
- . . - . ...:. , . . .s6, ..+...
- . , a .3 . ,,
-. . , 1. ,;. .a e . r= ...A.
C D, e ." .' w O " eYal L' ' . 4 v^ n .' o- -
." 3.2 ". .' " '. " .
t.r.3 ..1., w . .;, ..u.; ,_., C .m.. ,,. S ,
- . . . . y
.. ..... ..9 :.. m. .n vs.. 2. .: ... .
i l
/
sf s 9 < * *
- m. .
-9 :n..2 u . . . -
. =. .m. ...,.
.. c.
o
~
%.C U"...* c-w ^ . c'l. . wd ."'. .". c;4 . ". c c . . . ."#"<-
~
O. '" O fw " " s u~* 7. l
/kk l l
Co. . ta . - . . =, c ca . ;e-
! n ." l 1
I l, I l l 1 l l l i l l I J l l l .I l i j I l
*f i .
, I i I
- i j
l
)
I
- i l
l l
1 j ll o l i 1 i l i 1 i I I i I ATTACHMENT 1C * ! I l CUSTOMER / ENGINEER RESPONSE TO REQUEST FOR INFOPS. TION l . l l . I i I i
- l l
O e
--w-,- - - ,.--n, - - , - , . , , - . . - - - - . ~ - - ~ -_r_, - - , ,.,,
l l Bechtel Power Corporation Engineers-Constructors t 15740 Shady Grove Road I V Gaithersburg, Maryland 20760 h~' 301-258 3000 i March 26, 1981 l l Mr. T. J. Wrona Henry Pratt Company 401 South Highland Avenue Aurora, Illinois 60507
Dear Mr. Wrona:
x) Turkey Point Units 3 & 4 Bechtel Job 5177-152 REA-TPN-31 Purge Valve Analysis
. Bechtel Files: A-21, S-77.1 V-241 In response to the engineering data requirements listed in your letter dated February 16, 1981, we feel certain assumptions and considerations must accompany the numerical values and thus we answer as follows:
[ Regarding "The combined resistance coefficient of all ventilation components Q] 1) downstream of the valves (one for each valve size) . . . ." We consider the conservative approach to be that conditien which would pass the most Post Accident Flow. For that condition, all ductwork, except the seismically qualified and Q listed porcions, would be removed in such a way as to not impede the accident flow path. The only qualified duct is the ten-foot penetration pipe between the two valves of any pair, which is the same diameter as the valve. Furthermore .one of the two valves could be con-sidered to fail in its blocked open position due to signal malfunction. Flow resistance coefficients vary considerably with valve angle. The entrance and exit coefficient for the penetration pipe also contributes to the total system resistance although the ten feet of pipe is essentially insignificant. p) The flow medium is a mixture of air (k = 1.4) and steam (k = 1.3) with the ( steam portion increasin;; as ec.e accident progresses. The conservative approach NM would then be to use the lowcr friction of steam. ~ Using 1979 Crane Technical Pmr No. 410 - Flow of Fluids through Valves Fittings and Pipe, and 19-~ J.E Handbook of Foundamentalsywe compile the following flow resis tance uf:.cients: PIPE ITEM COEF. REF. Entry 0.78 Crane A-29 Length 0.03 Crane 3-4 & A-22 Exit 1.00 Crane A-29
- m. T. ,, woo, Bechtel Power Corporation Page 2 V-241 VALVE OPEN VALVE ANGLE ANGLE COEF. REF.
0 90 0.17 '79 ASHRAE 31.35 10 80 0.52 20 70 1.6 30 60 3.9 ~ 40 50 10.8 50 40 33. 60 30 118. 70 20 751. 1 J NOTE: Take one valve at blocking angle selected during closure time and the other valve to vary from that angle to fully closed. For example assuming a 30 degree blocking angle and the failure of the outboard valve to close, the inboard valve would have the following down-stream flow resistance coefficients: at 30 degrees 0.03 + 118 + 1.00 = 119.03 say 119 at 20 degrees 0.03 + 118 + 1.00 = 119.03 say 119 total system resistance coefficient, restricting the flow is: at 30 degrees 0.78 + 118 + 0.03 + 118 + 1.00 = 237.81 say 238 at 20 degrees 0.78 + 751 + 0.03 + 118 + 1.00 = 870.81 say 871 the downstream resistance coefficient of the outboard valve is 1.00. If both the valves were to operate and the recom= ended blocking angle were to be 50 degrees, the downstream resistance coefficient of the inboard valve would be tables as follows: - at 50 degrees 0.03 + 10.8 + 1.00 = 11.83 say 12 at 40 degrees 0.03 + 33 + 1.00 = 34.03 say 34 at 30 degrees 0.03 + 118 + 1.00 = 119.03 say 119 O at 20 degrees total system resistance coefficient would then be: 0.03 + 751 + 1.00 = 752.03 say 752 at 50 degrees 24
- at 40 degrees 67 I
at 30 degrees 238 at 20 degrees 1,504 Assuming the generic k coefficients of butterfly valves are applicable to the specific Pratt valves' supplied to Turkey Point, we have developed l.. a family of curves to indicate mini =um valve back pressure with maximum Post LOCA flow. (See Enclosure 1) l U l l i l
ar. r. J. urona Bechtel Power Corporation Page 2 O V-241
- 2) Regarding the " Confirmation that maximum delay time from LOCA to initiation of valve rotation is 4.2 seconds. Provide a minimum delay time as well."
Minimum delay times would certainly be more realistic. However, we must conservatively consider only one time for each accident containment pres-sure curve. Three of the four curves can be grouped together and the worst case envelope considered. The delay time for the envelope curve /7 which is the double ended break is 2.7 seconds. The delay time for the U 0.5 ft2 pressure curve is approximately 5.3 seconds. Delay time is found by adding 1.5 seconds to the point on the graph when 6 psi is reached. Time of full closure will vary with blocking angle, however, we would expect an approximate linear relationship in regards to the maximum 90 degree closure interval of 5 seconds. The figure of 4.2 seconds mentioned in your letter is not a starting time for the Turkey Point curves and thus cannot be confirmed. If there are any further questions, please contact us. Yours very truly, [' 5 A. W. Wilk Project Engineer AWW/RVB:mfa
Enclosure:
Curves cc: W. H. Rogers, Jr., w/o . H. D. Mantz, w/o S. G. Brain, w/3 G. R. Gram, w/l p F. A. Panzani, w/l . g
'j R. J. Acosta/R. Li, w/l M. Crisler, w/1 D. W. Haase, w/1 D. T. Hughes, w/l D. E. Douthit, w/l i
I i
ENCLOSURE 1 V-2M 2 OS M7-w2 Cn c. sin- ! 7 _ n.. g, '.'. ". '~ P 7.: .=. . .==. . - .-- _. ~ii-~ ~~ ~ . . -~r. -M M C- h * ' *I l ' C T.~- - . " ' _.3 ggu. _ . , . ~. n_._- : ..-- ::=. _5_. . . . [. ~_: _'i.-~.!.. i, 3
.3...,.
7, j . . _
=: Le aum*33
- t - - + *.1 - - -- e_ .s
.____.r
_.a6~ m n. .s2nt
* (a tm -
, . , . . r . .r-, . . : . ,
?--
..._... -,c a.t 4
; - . - - - - ._, . : r ; ;_- . := =
. .;. .1...- :.;;==: ,.-" - L*v:,__...
*-a : ; j .a ; . ;'. '.~ .h ._:.s._
.- - - - . . ee
- p. _ - : .-% u. g g _4 ._ . . .: : . . . ._ a;.. : :( r.=:n:..% 4 N - I - .! )m i; . i q (==:; .d
-* 3 , -- -.=D _: n
-- = :r : _
n --- - ( fm
) .i__.."..=,-u:._..._....-_._..,;.,;._:.%.m
. _-- L i ,.
g a _ _ =- v.,r --.:.--
\ i -___...,.:-- g ..
g ,. . ut
. n :. _n. ' ...-.... : . , . . ~ _ y j :....--- *-
- ' ~ -
-t..;*t.q: N. a.t:
t, Y/
= :f: _ ::; 22--- -- - . .:. n _=_ .: . - * , . .
f =__ ..i q-
.*%. . _ _ . . _ . 5* 15
. - - . . . . .Tf . - __.[3-jj 'i - ot+-*n .,- . I; _...,- *y.%3 -D
_3_g',;,.._...___...__.. __ ;g;-- ,g--=._ - -- ;;];- --*= " -- - W_y j _ _ __- _ _ . . _ .. .{t3y. .=-._.iw
'a-*,__ -~;:~: ---- --
- N;
+ ,_
y^;t. -_ - ._ . . _ . _ . _ . . _ . _ . ._ . _ _ . _ _ _ _ . _ _ _ . _ . . _ _ _ . . _ _ _ _ s r;.as. .%. *_;; J. .;. . i ,
- ::g.;. -; a _;M, n. r.Lt.;;*; c;;;;r; . =;.;n;uJ[':- ---~',%. _' - , F* *:
J t . __. __. O : s -- - a W m,7 f! C 1 ; N_ _ . _ _ _ _ - - - - - - -----. r % g - _y...--: . . : ~. ' J. - *..- .- ~ . *
^ ^^
{. . o -.g,p. .
- -..1 cs
- -m, _ .:. ._~. _ ::- 3n4 t.n . ___ ._.Qm . . ;. q.:"_ t: "m - -.:.r_.
, . . ..3 s .tcy_:. . - ;.s _. _ =: . . , _ . . . .: n=
riE~ n---
!l . _ _. . _. _ .c. . : ,: . q - . _ ..
_ . ._. .d, . Ei =. 44. ' %. 1. '_'.i _i,- s . E. .l _ _ _ _ __ _ . _ .. .__ _ . . . t ._, ._. .. ._. . . _. . ._ . . =_ . :
.d l_T. 7 -
r-- ..?=
.. x T ;.: ., ., 'r,.,- _, ._ .";*. _. nm#. .-- ._._... ;QQ. M;y N ,$7 s: -x;,; =9 ' . :A 'D
; w Y y . e -.t " ' .*- .6 2 L ---- - - - ._.._=.
L -- ; t.. W.4- ._r=1 rTZ2T 3 y.. ,, '-- ,q N N.h _' __.. :-- :
'T_ .;. . ; ' --~-. . . _ . . . . _ .
I*
- m. .
- -t--", I -
g,,,.
. m --af 4
_._.4
- :.t-._ .- g:: = 4 .9..:. :=.J.;
- Ct'. - .
_p._---------
%3. w Ah _. %
_m =s w r_: v.Ar=~
,, = _ gi 6 2== ._
( \ *:n . : 2.;W-' w tr. ;=--~ t- ^
+ -. ~ ~
~
f d
. (.e ;.J 4 -*3_*aL T,."t-'*" -'--~
- g /
KW"T.2*d _ . . _ _
- 5 ,;;j i , . _ . _ _ ,
-- ./
x%._=. . f m= ~c p.y _s (O y v f sp - N.. ~s -* -- ~~ s t_ s 1~;
;. b .) . .a sj -y : l_ w -
uJ . q . --
-_ . e i _.
,m.
W
% V .___.=2_
?
Q 5:.-gy a U,. M n
=.e u) ~ m.~. .. 3 i* '
- 6
-b
_- _ :.e.- - -
=il. -
__- g n- f - =- 9. =-; .:._ m -v -- y 5 .,a : n tJ +
-_-. y : :.s. . . . .; C y' _ f w
O . _ s _-_. ., <
- _ f .
"-p=---
'y'-_.*M'
-,' e, {
s., 4 - r ? } ,-.cm1
%y a --
/ ., .-- - / x._ y _.g.e . _%
u a __. - : p .- - z p . _z-
- /--.
.s asm ww., __.-- q sa 4 **-
. - =
u ,. _* / :_
- -- p --
_s r f~~~--__p f ;6 y k=~
.f.g .
-----.:, - 7 =_.= & 3~ 4 . X
.-- .= %a oa f~~' w-f ;.^.,M~__-- ~~~_ p +
E!
,s u p____,_
~ E-[f*-~
y<
._-- -- i%.D
.- =3--
.h.:. #:
q . y y ___.._."_"'*P _ _ _ . . r.-~.O.
.-u. .N--.m_ m.
,_ _,;y-- .-x.--.._;.y.-_.._....._..
_;. .._..._._.,7__ -
.._.t.
.__ . . _ . _ _ _ _ _ _ . ._..w..___
~ . . _ _ . _ - .. ~- g. >- y -
._s_---__. * .; =n :_._ _ a - . - t : == : x = _ un . . += u.;: .a- ^/r : 'O $
~~
~~ 2 -
- -- u _a u -
---+s_:u( .-
- . - . . . -.. _ _ , , .[_ ~ _ -[ UI m
r--~- . u__.- . __:.j_ . _ _; _ - ....._._; ,
.., a
?.
~ _ ~__. ~L_._. _. . '; _: :. . _. . . . . . . _ . _ _ . . . . . . _ . . . . . . _ . . . . . . _ _ _ . . . . N 4 --
1----
. _. } _ .. .R.__. .. .1_=.. n .;;.; : : n.=_;_;. ;.c_
..=._t._. . :._: _: _. ... :;: :..: -. : n_r. _. . ._ .._
1 ::::. ."_.:. ........_g
..:_;. . . __ .;. . .. . ~ . . _: _.. _ . . .. -.=_
4
- . - -_ _n _
. . . . ..r uu ::
7
,,\ ^*~~1-.;'._.. . _ !. :.; . J i. **- ;* .:j -- ~ ; * -- - - . . . . . a. : : ._ . :
-t-*;*.*-*-
.. . ... . _r: . = . :=; u_n : i. a r : .;; ; . :.f * : .; _.;: * :- ;_ :f _;11.:** :;-1.* .* -- ** --
- T . .;. . ..; ;; ; ; .;_; ,_;;
(s - j --. .gr n-n . ;; = n = :. u p. n u --- - :p._r u agu-- :- :r : ;;;_ x;=;:: ch=. g .... q 2n._. . - . 3 ];. 2_- 95 ,.g.; 9_:: -}_ . : 2; 2]d' :, [ ':::l _.g=::.:-i -
- j - j. ]:.3 .;,_.di-%i_.p ; '
=.- . . . .
---: .. ..m-... .
...:.g . ; ._
g .,,,............_., N O n g" h \r) N
,< h h Q ~9 P
e_t f-*
- s,2 =O 8 M.,, N
_r- o W$d 530SS M :.G V3 .M JM .MG
kB um-1-m CAL C. Sm- l 1 e
.. _. . _ _ _ . . . . .. . _ . . .. . . .t ,
m.3,,
. .___c_
i . ; .i . . . . _n
= - . . . . . .---: - - - -
- 4. . , :
E.__ ;
- -53e_( h_. ._.
. ...... _ . _ .. .. ..._ .s.. .
.. . 3
_.. ..t,
.I .. . . , . .. .
t _.-
. Q 3 %; @ b* 3 'A
;=.-*t-+
*.?
d L .*) I* .e ; .. % -*.g
- i v- **
- I P- .dj,-- - ._'.-*;?-'*-- .
- g6-
- g. .
%- &-- ,.; . . a, e
. a _%. -.- .:..g...... ..
, . , .glt
___..}._....,.
- _n _ - t . 9q ..: - . .. x l ._ <, . :, s q,,*---.-* , , . . _ . _ . - :-- ::: .-- u- -- ;..:%_s g .
+
- u. ,s-
- -.:.=--=:u-~....,._
~.7 71;
* --"A*"Q_.---_..
O...- a
. . .N
*-:. .- .r : ._c . ' - : . .
. . : ~. . ;
^
._e. . _. ... . . , . . . ... .. . . .-* . " ' " - " " *
/>/N ,
_. ._ L: _. . .-
,.a. ta .. ,
- s. . :. g.-'._~,'******
t
, -- l m,,- .n. . ..- . ...- . .. ... _ - . - . ...- -- - ._ - . _ . _-.
, ,j
._-,,,s._.... .._..s. . .. ._.. ... _ ... ....
-.. ..... . ,... _. .. ._ . . . .._ .. %:: r . . . _
_ . . . . . _ . . _ _ _ . . . . . .. . . . _ . . . . ___ _. . . . - ..._ . _ . .._ ._.__-.__c
- --- ; - ; ..' : - _ n - - u;; c.m . .-
3 y f -.- . . ( _ . . . , . .. .. _ w/ ~;. . 7:: . . . . , . ..7 % ;. --..q---- -----:--"----
-5 .~._h. .
t' . ;_-
~ "-
. . ,. . . . . . .. .. _....._..._..___n.._1,,*F..;..._.%_h..,:
_ . ! ~_' _- _,T_ . _ __'%._ -. . _ . .. ..N.... - _ . ..._ .L.. .__..'_._._.1,._;_;-
!: .&. W .Q r :2.: __. . :.C ,, ::.. .. J.,
- ~
- f. .; *% . fs :_ .. i . =..,.'"',M,__--..
a
- _ - .' . . -_._~_..-.""..- ~. . - _.". . _-.4--. . . . _ _ . _ =
g, ..-e a -
*. . . ._ . ._ . _ _ . . . ._n;;._ O__.P.. %: i : -.-C.-
~_-.n__;1...'._.._._._:._--__--
- 1. ;. _- 4 .__
. . ._.A. 2_.P. . __ . ....- . _ _ _. . . . _ - - _ _ - ._. _...f. t ..s.._;,.. . . _ ... .. _. _ . . _ . _ . . . . . - .. . . . .
.' j . _ . b _. .
_ . . 1. : . f 6
-- r . _ :----""-
1 ;I- ___ :: .M. 7 _ ..sm
%. ? .N. -
! .J.%-.
...--.-----*t..._.
. . . . . -... .._.a_--....-.__
,Q ; ** -* _ . -t
...A.. ..,.
. ~ - *
- _6 _ . _ _ . . _ . _. . _ _.
- . . , ~O : -*---'.;.-
. - .' ~~>
r_. ; md.. . ;.'.,a._ r.. _.._ ._.: .,.._.^.. _ , _- '__~ *. _ ;- .*,.,',...
* ~-
_ ' _ . _ , ' _ _ .- - - ~ ~ _ ' ~_ _ . _ _- _ _ .. __ . ,. -.. __ . _ . . ...t..1...... . ... ._.__.1
. .. . ....~ ._,
__.._..____ . . , gf %.
,,,,, ,. ___ f Q .. . . --~~~-~--~~'.2.__.. __.. _ . . _ .
__.: - ._: .- ~.*_.%g _2 - - - -- ; . r n _ a _. n_ : ----- - - - - - -
- . _ , ._ .__4__L_._. _.
. c _ - _: -'. -: .-_ - . ;- ; in.. -- -- T.; ...g* . i .:.C_ _-- t..h . .E [: .- : ;.;w ~ ._ _
-_.T..,*,,..._._..____
...-,Ln..._.__3_.__._._._ .
_. . , _ . _ . . - _ . . .-..__.__,,..4*_J.'%w.. .
,.m
..__ ._w. . _ . . . , .
n_._,_. ..,,,__..,,,,,.
.,.,.,w.--~M__._ ....
g . . .. _
/<j g . . .- .,
g .
,x -
L._ .. _ _.. -.. .~. . _, _ , .._ % . _ y = ,
}
\ ..-_am.~'s s..-
N , _ . . ;J
- I4* __.
_._ .. *%-- ..: -._ _ ~ ._ g . g.. . . , , , a _ . - . . _ . . ~ . _ . _ ._ K
...m.-. .+
e_ _ _ _ aq- _r p .;-- - . g _, _ . . _ . d _ g t
- Id
*K "i>=
q r--
. .dm
.. _ ..4
.s.
__.,. ~. . -
- ~ .
(. W. _
..** _h W
~__.
. _ - ._.. . r+ . - _ - __.
-# ~ _ . _ _ _ . . _ , _. _ _ . .-
.w _ _- .
O I _ _ _ _ a -e 7 .' U _ . . ,
~
. . x__-.. . . ___- - ._
2 _
-p' _ , y ~.- _. _ - . - . ,.
es ,e ,, _ _ - -, .. . . _ __._,nr ---- - C* n -- p~ ' g w *==,
- - - -.-=.,e-.e gg _,s -
- , = -
W
-._P mg_.._-".,,.._#
,,,,f,/__,..~.,.
yT , , , , _ .
.I i -
a""'--_pf Z ^- - " ' ~ un g ___ _? _ ,__ g _= - ) 5 *** .f - - v
,_,.___f____f _ _ - - _
=.
- _ .
-*-~~;,-;;a _*_ _;".*,, ; "'""'~ --" . J
_~ -
"""-[__..,,,--I . - --- _. --"---"-*-'"A--- .
pe
=
6
.__.,-r".
. _ _ _*_g,-j-.==_..,,,,- _
O4 .
- - . , . .-e _. m_.
a_ __ n, r-..r,,, w
*:,, 3 = ,,_ ~ ~ ~ - -- - --
ma
-=.
p _-,Nm e
.r s~
=,. -.';*__--_.__..
- _ . . - - - _ . . _ ._ _.,g ;, M ,,_., W.- _
MN g -. _ h g C*,,
'\
e _.=,,,J. i .
/
, ,k n ,__.. __ . . _ ___..%. * ***
s / . __ owe __ __ _- _._
. . . _ _ . _ _ _ , . . _ . ._ . . _ _ __ ,__ _ . . . -. _ . . _ . _ , . . _ . . . . _ _. ., -_'.. . . ._ _,, ____.-b
-_-* - _ . . __*g m-
. _ . . . _.. : .__.__.. ._._. ._......-..-*4..sj.= . --
/
g _ _ _ . . . . . . _ . . . . . _ - . . . _ . . . _ . . . . . _ _ . - . 3.. . . . . . . .. . . . . . . . ....__.L . . . . s
.. . . .A r's
%, yy y. _._ .
a 2 . . ._; . 9 t1Ws==%. _;
. _ . _ . . . _ . . _ _ _ _ _ ~ . _ - - - - - . - . . ._. _ . . - - - " ~ - -
* - - - - * - - - - - - _ . _ - ~ _ . _ . . . ;*- ^ . y e., N -
--------=:.n=---._. __ _ . _ _ ..
___.._..u":--_.===-. - _. - -- u::. . . .* - - e T y '7 ---
. N 3'Em a _; -,
; _n:
hr._. : . ..n. :. 2 :~ .- -_ . --. _:
-....x._.2__,_.-..;u.._:.
. ._ r . ' . ;;
. . . c.. ..=_L.. .. ..n_ . .._._ _. . .:. _. _. .. -._.. ... . :_ ._r.:=.
. . .. .: : . .;. ..: =._.
* .' **T .... . _ . ___ ,
l'- .. .J: . _ ._ ; .; ; ; *. e x w s - ( e 3 p_.....~..._,, p-_. ..._._. ..
..-*-- .- ta
%/<;
p __ .
- . ._. . - - .- _. _._1- -. .. ._.
- ._.. i - - ..: -r :.
_.N O g n so e-n g e- H Q Q ---
- e u o--
r--
- ~
N
~ ~
n N YM -: 605 3m *;A*) VS .W 1rA MJ. J l
g
.' g 7 i
0 05 W-!52 m , CM C. Sn~!" g__.. . . _ . _ . . . _ _ . _ . . . ..
....__.u_.3._.,._ g --; y . g n g:- :gg.g,,,,,-- _ .p q ; .,-;-
c=~_ m -
.r n . ;-
= n_..h r_.e y __:, e:: - - -
- ~- a_._.:
9.:.
-. :I M .L b- - ,. I
% w "}-
r- e 'b*. -t u t t - 0 ----4 t- -- - d :=::_: __:: ~ x -- - -
- + - - - - - ~
t--.. p m. % o.a : - re we c r wrr-- . . . . . . . , . - m it ,e a e ,- A,V O.i MU. ydj:- ~~~9 ~r" ~- -Y 1 i ___.b M.u i. M 5_dfid.* G 'h ~Y E 'd v,., t-
! M
- =u H . ::.r p _ 2::.: _n . .: :. = m :: ..= u ;-- y.. .n =.: 3::.w
= q ,_ . : r- e
[m3
- -- : - " .*. : , s. . s.; . . _ . N d === ::._---
= u. .:. = : . _- =.:.- :. - .. _ : . . _ ._c
- ~n u; ' . .:y.. .-i y, ~~~. .-Q; ~-r%,-"':: .2; w .~-e . y ::.r ,n.: -xe. w-- . . i: =.:rn'_ -4 ..4_:_n:
- 1
- .2
.: m .:---:= -- .= - - - - - -
tv! E :-d.
- g. . _ s.-,
._ .m. : _ " :2 ,....1 - : - --- .nn . = : - - - - = _ _--- .
r r --- - _ . . _ _ - t . '_\,e3 c%. . -. *% , - . ..--_..__:=---. ___._.- __ _=..=:.==---._==. E, _ _ _ __-
. - .c
.r.__ ..r ._. : a = =. _u. . . =:.=. r. . . ,;^;
. g . _ . . .
. s ""L*!7l- . . .. ,
- q1
.f -._4 ,
7._.... -. . . _ . _
. , . ....:. : s. . 4 ==. _=...r. x =. . =.. . . . _ . . . _ . . . .. - *% r =._. _ ____.: .- .,; y =_ ...
v._C'**.*3=..- . - . 2 . . _ . . ._ : __. -_---
. . .~ r ; -__..lg- .I . . . . . ., .
- i. ~ . t*- .
T . .
. ;_._.y, ]-f
- g -
*;P - C{! .*~~ :-' : ._ ..._ ::.:
q _e} : -.+ , :. =. _ . ._
. - . ; ; . _- _. __ . y q , _. D, g.'e". Q._ / . . ; _-- *., : . , . . _ .- .
__ _ . _ _ y. .-m_.. -
+. ..a. ye-g
.:( 2x-- -- : 2_.,;; _; .J; p _r- .;.m. : -, . e. -
u c
" av_: __: . __ .s - .: - . u. . - _ L. _
. . : . 2= - 4. 9 . -. ga w.:r .::c : _- : . _. --- ==_ . :._ n _3-. : _ _x_=_=_:
- . . :r-_ 2. ==
p 7:r _: . . ~ ._ .;' -. _ _- -- : y - _.-_; j e _: M l p- ..% . . , _ D :_, { .._:Z: r;r _ _ _ __ .__.:=:-
-.,=,_=
mp ht-u'~ . . _ . . . _ . . , 7.- - _ r--- T , 32-_ 3 ., .C')=2. - M__j;]-
= g ti. -... @ ]i,_f@M TQ%.
- - .. 7.), _ _ _ _ . . . =: a_ n __ . .. _ . _2; s . e . ...=_.._,w
. - a w . __. _._r-;
- : = =r _.::. 6, m
.. m.._ _ - ~._ _ _.. _
.. , __.2_.. .a ..._ _ % . . , - _ . _ _ . _ _ _ _ _ ..
.tr_=;,-
__ _ . :. ._:: j 4.5 3 ;._- f =4 i.f._ _2 " - _. _ % 4,- ; gj . + ,~. .. . _ . . ." . ' '_M 1.--* fN " - + -
'v- =*
- -* _ M . v --*r
.~.__.c _ ::: - ---d> = N ; , :: . _._ ;s l . .:=ur
- t* 4 1 . - _ . i . - _ _ _*- 4. ,.a__.
s, -
)
~ c,C'**
; : 9_rry---- M'r= t:-*: * - --- -t '. ; -- :t __
3 : ~_,; . v "_- _- =-; - gw. _-_% - 40
- n _ .
N..
._z---' -_---
W g s s.;- - - N . _%: - - - - - - - -
, . ._;n-
; ,-. : c -~
_- - _ -- =: :: d :- ._ _ m _
- f. _ _ __
q _ d 0 _.{ 5 R en a.- . _ . . _ . = ,
..____.r. - - - - -
h ,
.:=y;;; . -
= ;.8 - _
/m s
/
\)N p
s- _
- g. ,.r ;: - y-_' _ _
-----{,_ g- : . -=
2 0 -_.
~ -
y Q , _ '_s -&_ , _e C G ,- - N cT - ___ V ;;;*._ k ; -- - e
~
; ,"pd..
E*
,,r-- :.
r: :s- --*v
~
w, -- - _ / P " Wg _- _wes -_ -,,--- 1a X; y _, _. . _p . , " _.__v.,.w'~.--=--
~..e- _ :-
=
__r_'.__,__r."m"~__.--
^ _ . . - _
_ ,;:s- - : 3 _._
,.c",,.*-'"_
y'- -,
-z._-'"
---,,,,r-' 3-- : vg* :-
d t' _: __ _ tl% c -- _;r 7.__---;,f;;e._y__---_".,.==*"""' " - :- '~-~ -_-- ~--
,., ,c _ _ _ _
_.J.. . . g;_ ,,,, .
-/ _ _ _,.:;;,f .,7._,d--^ & ^W - ~ -,
- ~
.; -n =
Og N n .- - - - - - . ;_,,7_
- s.-u,;;;-----c - - -
._. e_-
y s (. .. %.. _ .
,-._,,;,.._____.____ s; g,.*,.---
9..= e.a, - _ _ . . _ _ . - -r%.. - -
- 3. :: ._ -
._.o . __ _
_ . ._. ._.....~,.,..____ . J, L_ -
._-EE5.f ~ ~ ~ "=
._ _. _ _ _,. _ _ . . . . . .-_..__.-.y .
y.____..;_.____..__._.______. . _ . . _ .
,, . _ _ _ ._,-- > ..,e.
{- [:. ==1.=:=_==r=.====--=-=---------v------
- -- m ,,, s . s~- . . . -
- -- -~
., ,- '~~' ;
i _t--- :------
..- : - r: _ - -
_ N. ,.- n .#~.:
..y
-+y.
_~ p a__. . . ._;_:- u.__; _.____.:. . . __ . _ c;q _ c :e____,. _
- . . .. ._. . . _ . . . . . .... _.._._ .. .m-% ' - - -
=i 2 . n a ;.E i - =1 ._ :: _ = i -~ E . - i-- M - "i -'.i". . b =i- __i. :.. _- .rn_ n_ ._-_*-_ ". . . _ _ . . .~ :=: = =i ". : 2- :. '
[ ,N :- , .
, - . _ - - . . . . . .u- - - -
n_.=. . . . . . . . _ = : :_._.: =---===_.._: . &: ~'--- --
! I p r- : __c:. -- . _ = _ _ : =r - -
- n=. - ;: =: - :2 ; .:= : rn u_ ==n . . .
(.) p- = = .i nn i . . w : = =: : . 2 - : m aj.= = : = n =.= "_ :- _. mu ;:=j.1__ U -- rg _ p . t__- o _ : --. . =- _- -_-.-. -. -_-_- _- ..._.:
-.__-_._._..=__- : :
- = - - - - - : - - .: ._. ...._._.-n:.u_._...._a.
- ~ - - _ -._ .:_...._. :
_r.: -- { .. .. ..:_.:
._'r!".._' * :- '-_ ; ;.~.; : ~ . ' ' ' : ; . .1'.' '
- T.* " C . . .- . ! *;*" ' J' CI -- "? .._ ...
@ 4 D o
es "1 E-
% ~ g M
x Q *d Q Q CF-
- e_n.
r-s.9
~ M_1 8
i'O N
~
Y/ %;d 2:MS Sn;;i "M*i v2 3A 7rA .:W1 -)
dos m-m .. Cn c. se t ~---~ l _.......:=....-. )
-- Q -
..*------'..."_.'.'_..'_~__-_.9'*..'~%qW:.. - .n. A;;. - --- : - - -
u
- .- l *c . _. .. . g .._.,. .----
- ._.Tn'--- l 1
t N i:- .._. I N ,; ti D Ui b8
- r2605 ..a O 1.:"! l'.* C 1 t.T 't !'t 2
- -- [* ] - - - - - +
s 2{ e 0 .-
--~ 1. :i:.i!. A g ] , M F.. S. :. r m..*.:._..
. -. . . _ y s. I; c, ,- s.s :.:. _.. . _ . . _ . . , .c s , I
" ' ' -M M.'Dhh ~2CM v.l EMO i ' --'.~ R3 - --
. . . . .M C '_' _ d, ,-_
_a -
.-4..a- I ;--
n_;- = .% . ..N.,] _ .y.*&
-- _n f f - : m 4 g =: w:--
l'
. . .:.:: .. . . .u n=- .. u .
a
, .. ; ; :.1 ;:; } .- . ., s .; ;; ; -- . ;;;- - - - - - -- : , - . . . . . . ,
. J. r ; :. a _.
/'D ; --- 4. -. ;. . ;r :4- =: ;- :,.. ;-~,: : -v. 7 . !: - % C . Q --', _: '*
- .- .-. ;r.,,_ N %.q.. l'. .--e g - - - ; n. .;; ..
c
, =: n..::-.. -= 4
- g _=. 1..;u:.
4.s v ~?= : .: .
"*;_, 'm. U . . .,,.u : .J : :
s:
.... = - - " . :, s
< tt 2 :=::{ : ! . - _3 ..;-.-........-----:;-... .= _ ; . . : = = .
<,v _
T- -
=c : : -
. .; . . _: ,.i.y p .1c o,:;=t.m.. .--.
.7_._.".._.a=---,:=_..=... -
_. 1, dW . _ , . . .
- p. _"l..*. :...;. g__.'LC I'" -@_ . .%-..* .,..._1- _ .. _ _ _ . . _ . . ."._'.M..,.,,= *
. .'%..,y i *%. , * --**.* 7.!__.__._..._ . _ . _. .. .._.;;. _ . _ . _ = _ .*.:-'-._.;...'.;;_.;._.
, y: ~1. : $ 'J k I"4I :: _ L'.. - - " -
__.~~- *.; ** ! 7 & ve i1.N.1. _-* .I**,
. ., . .o. : m: _:.u_.--
_ . . . . - y 2- - u - ._, : ~. - .- : : . r, : = . , . _ _ . ----"_--;=.*.:r..C-..__.__..:
.g N T^.... . _ _ _ - - - - . . . - - . . . . - . . .. . . . .
_4.,.a -
--- =
- > = . m :: : : --- :- :--: n _ _... .e: =_,",:%. .a. c - : =: ..!:_ 2. u == = 2.= : -- _=
..r ~~*'*w-~*----~-----*- _ _ _ - n ~- : . .._c t".__-. .-------
- ;.,,,
- .=,- , ' h_ i .=. ..;-
_. .tl l- _ P.. r. . . _ _ _ . . . _ . ..:;.;. :;.;; . ; n- : - -- ;; . _ . ---; _. 1 _. w,c, . _,
,d_ _ m. J b. .,.__.a_.,--....-
=*..:
.,,.r.~,c.e w::
- ..._c.
, ._.2
.,3 :_.
,. 4 _ .
m.. % . _ _ _ _...._.._.._..__. . g ; ; - .7 %r n -% ~, =__,. _ _:------_.. -
. ; n. _, _. _ m
,N__.,,..__,..._;.
..._.3._,._ . _ _ _ _ . ._ _ . _
_ __4. - : g_ ~. =~:- . ._ . .._2 -- _" a -- = una;a _;;_ _
--- n_. _ .-w_ __,s m-:: _v. a: =, , . . . . . - --
. =::
t__
- 1. = . ~:m _
a!-=- -=-----
,m ~
~
"--4:..
; _=, : .
-&_w_.~._.._.__=-=--_ ___. ~ : :- .'%v ..: .: _an
----->Z--
j *r :c =-- =. . =::=: _*. =. -_;;_*: .:----- _ } = s:s:; %. . ( i: __ 4 -- Qc --* - . - .~ --
^~n.
, ! ::;.,~m - - - - - - -
% .J ':2.- . ._. . . .
Q ng s - ..,-,;---- - - - - . -
- _ . ~, , , . . . - . _ . - - - .
v -
- c. .~.a.--- :.--
, - - , % g a ;; .___- --
g - td . q _- .' . t . l.1J y q .,-- V. _
=: /=- - - = = .
. ; ,: = :- -
= a.:-_- -
~ _=-
m .- - _-- ...r. . _ _ . . _ . .;;. O(g
- r A g.
-4
+ ...___..~.
-=-
. m- -
- - --- u : : ._
__ m __.__-= =: _
=
- y . _.
q,) t -
../__.__ _.
u .: _. y.d==- ,.d.L--- r -- m
-_s--- : -- .::-r _.- c:
1.d - - _c.. : e n: y _-- ./ . . , . __ t-q ,-
--__..~--
_ . .r_:
=-
h y ,- < -
.~--w__z . f_ - -
e
.~-
. _ w" v:.
- . .. =< .. >. . __ _ . . ---:_._ .
G e --
,: y;, i _._. _
^
- e-- ._ :_ --
_ x-.w--_f 9 __ _
- =" s-
/ ^_ :;:.e _ r -- "_ /. -__. _ - ,- -_ # :-. _ . . --
- d.
- g.
r_. a- e-1'*_a-=- W -m.-
=._------..=-,_.:- -=_._ ...
- - - = _ -,, -
** ~ - - : ; - "-
03 __?
.s'._a_"_.r
, ,.;:= -..
- - - - - -_ . . ._.~ ^ . . , . . _ '- 3
- e. . t .:;- -Q~ -- ..g e ,
s.__ = r.,-' u
.2 n ,,, m p ,w v e ,___ __ . _ _ _m_ -_
s . s fs \ s . - . _ _ . . . . , . . _ .
> 1 _ _ _ _ . . _ . _ _ _ . .-.. --- __. . . - w : __.___
/ . . . - _
v. me
- _ _ = . = _ . :. ... - .. _. . . = _ . _
. . . . .._.n----
_ _ _ _ _ . - .= r: 4. .-y _........____.s .
-_ nc; .,._37_-- r -- --- - - : _= ~- - - - " " - -
y .'.i.lQ TI~ {:b 7] 1 . w
- d--
=Eiv._. . . . -_. . b., P --
__ .. _. _f :-- 3 ._.2 = : == = n . ..__--:_,--:=----._=n.u=_n-- .__ :_;:: - _, _._._. 7. 3 . -y M- _ _ _ . _ . . ._ .- .----------:._. _.---= . _ _ - --- _ . . _ - _ . __=----~~.~ qa%- na ._ .: _ - .___ . .c_ : __; ; u: . _ . : _ ._. : -- -
.___. c; 3 .,
a/- _a. _ =. a r:: 77
= _ ~ ..-:- - = .. :-:- :___. . . a . . . . . . t _ . .a =: == = = . . . : ._. . - - : . . - - :: a = ._2. = - . ...
=
i - ._
.: .= _: =. = . = :-- - - = =_ = :- -- . : . - .:-
---r-.
. .: = :..: : m. ; n _ n x- . . n :._ .: n : . : . : :__ : . 2.
_ - - - - . - - - - =
--=;
-9 .
s - 3 ._; _. : -._:_u :. _ n __ :.= u =.n_ r u n r_ .: =. : ==. = : x . : := = ..: = x= u == - - , 2 . j
= jn - 75 i@-i":.i=i ri =i==ri '"".. ;".== r= = -i2- :-- r - =!=i.=iii ,:uin :
"' - ~~
( )
': ~i - - - :. R :i ;=.i: ". E E.i 22 - .:_.a ;; H :"i
_ - . _ . E. : ._ --d : : =i = :- = . ::i.=. =.i.i_:1. u-m .u. :
~I ~~
; . . . .. - --- : : n _ : - -- .--:. .. _ . . . . u_. ; _ , .r---....n.. I
._= i _2..-:ncu =: r 2: = . _. : .=:- . cr. - _ - - - =.; : = r n.--
._. - . e D & % d 0 o x w x .. - - - - I_$ $
e m M . W M. .htDS 3m '.G G .?MrA .Lw.!. 2
e if 4 o O i a l I 4 e . 3..- , , ll M' A y[V U_ ,__ c 5 o NUCIGa!7
<n
; a up u w o
(b I I Ik o A11 ele}fSiS Th
*)
h i , k> o I l
:lal S tress P 18900 ed 25/4 Bending P eb /,7 7 3 Torsion P et 4173 IJB-3545.2 Thermal Secondary 38 ASTtt A-36 Stress Q ggg Sm 12600 NB-3545.2 Primary Plus Secon- S 38 ASTM A-36 3Sm dary Stress b9bb 37800 tJB-3545.3 tiormal Duty Patigue S 39 ASTtt A-36 1.5Sm Stress P ~/ I O I 18900
!!a -.>
2000 m Dine Nil-3546.2 combined Bending S (l) 40 ASTit A-36 1.5Gm j Stress in Disc '76 6 U 18900 e o Sh: f t tJB-3 5 4 5. 3 : ombined S tross .; ( 4 ) 41 ASTM A-276 g 1.SSm e- in fihaft Type 316 3.. 30000 e Condition A i; tu
. g tab t;u 1 STRESS LEVEnd POR VALVE COMPONENT #
- ALLOilAT CODE REF. REP. STRESS STRESS LEE j cot 4 pot 1Et3T PARAGRAPil SYMBOL & NAME PAGE MATERIAL LEVEL, PSI PSI DISC ( .9) ( .6)1 Shear Stress in S (20A) 43A ASTr1 A-276 16200 PItJS Top Pin . Type 316 d.- 730 Bearing Stress on S (20B) 43A ASTM A-276 9SY Top Pins in Shaft Type 316 l1847 27000 Shaft Compressive Stress S(21) 45 (SKP-#23222C) 125,000 Bearings on Shaft Roller -
7bbbb Bearings - Thrunt Bearing Stross on S(22) 46 ASTil B-164 Sm Bearing Thrust Collar Condition A 49I 13600 Shear Stress in S(24) 46 ASTM B-164 (.9) (.6): Adjusting Screw Condition ^ 3 72il 16 w Threads Combined S tress in S(28) 48 ASTr1 B-164 .9Sv Retainer Bolts Condition A )86Ib 27000 1 , Shear Tear out of S(31) 48 ASTit B-164 736 (.9) (.6)! Thrust Bearing Condition A 16200 Retainer Bol ts
*v o
N v l
. - - - - -- - O
, _t ,-
TABLE
, ./
]
1 L/ \ -l STRESS LEVELS FOR VALVE CO!!PONENTS
\j N.)
A L LO'.-1 A D L CODE REF. ~ REF. STRESS STRESS LEV C O M P Otl E!J T PARAGRAPII SYP1BOL & NAME PAGE MATERIAL LEVEL, PSI PSI Bottom Shear Tear Out of S(33) 49 ASTM A-36 .6Sm Cover Bolts in Bottom l624 7560 Trunnion Shear Tear Out of S(34) 49 ASTM A-36 .6Sm Cover Bolt llead l 3 6C 7560 Through Bottom Cover Combined S tress in S(35) 49 ASTM A-193 Sm Cover Bolts GR.B7 7iN 25000 Combined Stress in S(38) 49 ASTM A'36 Sm Cover ICbb 12600 Operator Shear Tear Out of S(42) 51 ASTtt A-36 .6Sm Mounting Trunnion Bolts Thru gg 7560 Tapped IIole in Trunnion Bearing S tress on S(43) 51 ASTtt A-36 Sm Tapped floles in j 3 33C 12600 Trunnion Bearing S tress of S(44) 51 ASTM A-36 Sm Trunnion Bolt on
, j g c7 74 12600 Through I! ole in Bonnet Shear Tear Out of S(45) 53 ASTM A-36 Sm Trunnion Bolt IIcads 7C1 1260C Through Bonnet y Combined Stress in S(46) 53 SAC GR.2 .9sy u
a Trunnion Bolt 53 E '/.3 ?s?00 o _ i f Shear Tear Out. of S(51) 53 ASTtt A-36 . 6 S r.. Oparator Bolt IIcad 71I 7 r. r,0 Thru Bonnet
EE LV BE ALI U S 0 OSP 0 0 0 0 LS 0 y0 0 m0 n0 0 LE 6 s2 6 S0 S0 6 AR m2 95 m2 62 62 m2 T S1 .2 S1 7 7 S1 S I 7 - S g k SP 7 e S E ,
'g b 7
- 6 3_
cy RL
- y. 9 1 s 3
TE (. (- g SV g E L y - L A I S R T E 6 6 6 N T 3 2 3 3 E A - - N M - . . A O A R A P G M t t t i M O T E T T C S A S S A S A A E V L .E A FG 3 3 5 7 7 8 V EA 5 5 5 5 5 5 RP R O ) ) ) ) ) )
'r
' 2 5
3 5 8 5 3 6 7 0 7 7 S ( ( ( ( ( ( L S S S S S S E V t E e . L E n n m n n M n i i o n i S A on t o S N i s s t B s
- ? E s -
ss s ro r s R & ss et e aB ap ey T ee rl r e eo rd S L rl to t y hn hT t o O t o SB Sd Si S SB B SI I o n M dr dB ds di dn Y S gh eo e ee e eo ngt nt nt ns ns ni i ue ia ie iss i s in _ ron arn br me bn mn bed mrl bed mrl bn mu - eho op oo ot e ot e or _ BTB CO CB CSW CSW CT _ i
.l FP EA RR G
EA DR OA CP 1 T r g)
! ond E ti '
E l t att i L O rnn B P euo _ A M poC _ T O Ot t - ( _ C - t .a
' i l
Y _ LC) o ANZ RET (- f- 6 6 _ UUR ] l _ TQE 4 ] c _ _ AEl NR( l 6 l M F _ OU S T L A N A 6 E I 6 7 n 6 N R 3 26o 3 % O E - 1i - - P T A A3t A A M A i O M M Med M M C T Tpn T T S Syo S S E A ATC A A V L A V F O .E FG 3 4 4 5 S EA 6 6 6 6 E RP I ._ C N E U Q Y E LC . - R ANL y 2 3 4
. F REO N
': UUB N N N L TQM F F F F A AEY .
R NRS U F T A N T P _ A N . 2 E C NE T E Ot 1 O R E L PA Y J E l l B MN D N V l t A O O A O O T C B B C B 0aO i<
7,...,..,... -i
. n Job !; umber: 3 1.7 a 5 G Va1.c 5 ire: Af. R';A C operator Mounting: p .,n w operator: EE , , .c .: 7u._ n - u. ,n -4S'
] Ag l A C, e /. Bg 5, l L( F d A It* , ( 7 , 3 6,11 (. F x m_ ) c e 9 Ay N/A C 3 F n)ec A ,%7 2, C 3 1 F 2 #. c c 2 A 3
,M4 C p 3 G b M 1#' E A , % c 9. C 2
- d' U'- Od D' 4
A 5
, (. e 6 C 3 'M U t 7 # 5'
- S' A
6
'5SI 6 1^9 9x 3 A7 . A N1. C7 A, (.2q- g 3 Ag . Ae1 C 8 A'b E 9z A Ag 1 AA Dy d Hy ,m A
10
- I 2
A H 2 II' A yy . C o (. , D 3 i,25 H 3 7 ' O ' ^ A , c6F D4 % ,W H J 1, E q 12 4 A 13 , D 5
- U S
NIA B 1 & > I D_f D 6
.W H 6
B & D ,7 f H 11,375 2 7 7 1 B 6e6 Dg ,T H 8 b 3 OU B 4
.m Dg j Hg 1. ) n_.9 l B
5 1e,11 D 10 'I I l M30 ! B 6 MA D yy il I 2 IM*75 B 7 NJA F b (~ 1 I 3 D 9'#4 l i 27 f l l
Dimensional Data (Con t. ) I ~74. C/ L 11 , >> 7 f R 4 1%,931 4 , 1 IfI * ' 5 1 5 I 6 I1' TA l-3 "x 9, e 7 R 6
#1 ' j Zy 3*%'t. C1 M, I~cr7 Ry I . C*r I I'119 M z
O E m 2^' 8 3 7 l. LT K 2 f-l F 7 5 o,e c e t J 2 J. 1 26l 7 t e }'7 J 3
) .1 T { 16lS7 t m
- RN A7 AT A-J4 j .1 W
{ 2 J N 2c cc Ty 1 5 a J 1 T 2
#' 1 <
6 Ky A eW N 2 b 3
- D' S K
2 1 N 3 A T 4 l* K %, Mp P d 7C T 5 N ' 3 K l A ,7 C P 6 4 r K l A,7 P 7 I 5 s K 6
- O Tl T 8* bM#W Ly 10 Q1 f. T Tg .A36 L2 } O2 4, 5" T 10 I
L I'37 03 A, T 11 1,7 s 3 L4 i , /- 1 Q4 2.o T ! 12 L A 05 2, ( A S U 1 19 5 L *SO 06 ' I 6 2
~
L7 #A 07 A ,115 U 3
- . Lg *41 r 4* hT U 4_ N14 L
9 IC.6 ry 1*?,, ( R/ f U S NI' L 0 *b3 6 20 10 2
am - -J. 24 - .- ._m._.., , _-, . .. _ _ ', Dimoncional Da ta (Co n t . ) I V 1 NIA - V N 1 #2 2 , V l'3 M 3
- V 4 NiA V
- 5 V
6 A ' I' ' V 7 9.366 Vg i C , ~T ; 4 w1 (eccc w 2 I?Ce w 3 We ; w lic 4 w .,r e W7 I
~
wg 34 E i X O O'O - l
- r o
c.c .
~
Z 0 3' bl3 Z i 181 z 2 71 z S c. f i 3 1 z 4 6 c . s-Zy Nln Z
- I 8
- - l 1
l l l 29 i
)
ANALYSIS INTRODUCTION 73 Described in the following pages is the analysis used ( in verifying the structural adequacy of the main elements of the air purge butterfly valve. The analysis is structured to comply with Paragraph ND-3550 of Section III of the AStic Boiler and Pressure Vessel Code (hereafter referred to as the code). In the analysis, the design rules for Class 1 valves are used. Since the requirements for this class of valve is much more explicit than for either Class 2 or 3 design rules. The design rules for Class 2 and 3 are exceeded by the rules for Class 1 valves. The air purge valve is designed in accordance with Code Case 1678 of the code. Valve components are analyzed under the assumption that I the valve is either at maximum fluid dynamic torque or seating against the maximum design pressure. Analysis temperature is 300 F. Seismic accelerations are simultaneously
. . - applied in~each of three mutually perpendicular directions.
Seismic loads are made an integral part of the analysis by the inclusion of the acceleration constants gx, g, y g'z The symbols g x ' y9'9 z represent accelerations in the x, y p,, (ms/ and z directions respectively. These directions are defined with respect to the valve body centered coordinate system as illustrated in Figure 1. Specifically, the x axis is along the pipe axis, the : axis is along the shaf t axis, and the y axis is mutually perpendicular to the x and z axes, forming a right hand triad with them. 30
~
Analysis Introduction i Valve orientation with respect to gravity is taken () into account by adding the appropriate quantity to the seismic loads. The justification for doing this is that a gravitational load is completly equivalent to a lg seismic load.
- The analysis of each main element or sub-assembly of i the butterfly valve is described separately in an appropriately titled section. In addition to containing sketches where appropriate, each section contains an explanation of the basis for each calculation. Where i
applicable, it also contains an interpretation of code requirements as they apply to the analysis. Figure 2 is a cross-section view of the butterfly valve, and its associated components. Detailed sketches are provided throughout the report to clearly define the geometry. , i 4 LO I l 31 1
I \ . . . . D ._ }O 5 .-
. +Z .-
A
. , 1. . I
.I
[- Q O\ * *
/& Rj- l
. . .L e c> . . ,
'r& '.h i.'/l ' X
- /
A ,) O i. 4..u-j;%'b,5.'s.[ 9,f a'-
', ' . 3b CJ Q /d i$ ! \
/
/
\
@ (f' N.N NGs /- \ O
/ ..'
/ N',- , .
>~,
. ,x./4' -.
N. . ,. Y,,, .. er~
,. . .\.
d 1.-1l/,.: // N
/,, I . ,. '
*l
-{Lfl*l i.:. - i
*'}:' '.k5 'j. .,...%~--
. . i , . , 4 )'
p .
. . .. . .. 'j k:.
q.) -. - . . . . - ,, , Q w. g
, UF UMJU /6bL!!dLY
& ?
.- l
. l
. i SHAFT RETAll!ER SLIPS lilTO GROOVE A!'O 15 BOLTED TO HUS BLOCK.
~
~ TOP STUS SHAFT OPE".N! GR KEY'.!AY
,) ~
HUB B LOCK KEY'..'.'.Y ls l O!' LC.",E OF TOP 1:13 c DETA SHAFT ,
/ [i[ j \
# . BLOCi' 0:LY
,< s
; p..> v' O .
A U LJ l lp __d p 1 HUD SHAFT RETAlliER SHAFT DLOCKS ( 00LTS h RETAl :ERS fn I Im O O I DISC L
- Z
( C O La _- o y ._. BOTT0ft STUS SHAFT l ,
- n
~Q .*' g. , *r s
e e e e
l l
- FLANGE ANALYSIS 1 i ,
i I The flange analysis is in accordance with appendix II, para. VA-56 of section VIII, division I of the ASME codes for pressure vessels and AWWA C-207
~
\
l i i t ; t i i O l l l ,l 0
-4 84 , '
e I e 34 4 4 ww,--. y,<v --v---e--- ,y.
I BODY ANALYSIS
-s The body analysis consists of calculations as detailed
\m/ in Paragraph NE-3540 of Section III of the code. Paragraph NB-3540 is not highly oriented to butterfly valves as related to various design and shape rules. Therefore, certain of the design equations cannot be directly applied for butterfly valves. Where interpretation unique to the calculation is necessary, it is explained in the sub-section containing that calculation description.
Figure 3 illustrates the essential features of the body geometry through the trunnion area of the valve. The symbols used to define specific dimensions are consistent with those used in the analysis and with the nomenclature used in the code.
- 1. Minimum Body Wall Thickness s
Paragraph NB-3542 gives minimum body wall thickness requirements for standard pressure rated valves. The actu.a1 minimum wall thickness in the purge valve occurs behind the seat retaining screws. l' C\ (j 2. Body Shape Rules The air purge valve meets the requirements cf Paragraph I NB-3544 of the code for body shape rules. The external fillet at trunnion to body intersection must be greater than thirty percent of the minimum body wall thickness. O 35
Body Analysis (Cont. )
- 3. Primary Membrane Stress Due to Internal Pressurg, Paragraph NB-3545.1 defines the maximum allowable
< stress in the neck to flow passage junction. In a butterfly valve, this corresponds with the trunnion to body shell junction. Figure 3 shows the geometry through this section.
The code defines the stresses in the crotch area i (N using the pressure area method. The equation presented U is found in paragraph NB-3545.1. Pm = (Af/Am + .5) Ps 1 Applying the code rules to the crotch region results in a membrane stress considerable less than if applied to the region not containing the trunnion. The I
- trunnion increases the metal area (Am) which decreases the Af/Am ratio and reduces the result. For a section not containing the trunnion, the fluid area to metal area ratio (Af/Am) r6 duces to the body inside radius to the shell thickness (Rm/Hg), since the depths are the same. The resulting membrane stress equation is then
Pm = ( Rm/Hg + . 5 ) Ps
\ This equation results in the highest stressed area s-and complies with the intent of the code.
- 4. Secondary Stresses A. Body Primary plus secondary stress due to internal f s. pressure.
t 36
DVUI ,litec e;" s GL I S v.s Figure 3 , O . e O nz_d!h -
~
L
~
s x
,N O
4N . N kN ' O e O O O O . 37
Body Analysis (Cont.) Paragraph NB-3545.2 (a) of Section III of the code 4 defines the formulas used in calculating this stress.
\ Q p =C p Ei t
+ .5 P s ,
e B. Secondary stress due to pipe reaction - Para. NB-3545.2 (b) gives the formulas for finding stress due to pipe reaction: P 5 = Direct or axial load effect
- ed " d
- { G d
P eb = C3bF S = Bending load effect G b P = Fb S = Torsional load effect et Gg C. Thermal secondary stress - Para. NB-3545.2(c) of f e Section III of the code gives formulas for I determining the thermal secondary stresses in the pipe. 07=OT1 + OT2
+a~ ..
ere 0 OT2 = C62 2 D. Primary plus secondary stresses - This calculation is per Para. NB-3545.2 and is the sum of the three previous secondary stresses:
+ O t2 #- 3 Sn"O p ed + m
- 5. Valve fatigue requirements - Para. NB-3545.3 of Section III of the code defines requirements for normal duty ,
I valve fatigue. The allowable stress level is found l from Figure I-9.0. Since the number of cycles is l unknown, a maximum value of 2000 is assumed. The 38 W w -
,_,- g --,.- - , - ,--7 %
l Body Analysis _ (Cont. ) allowable stress can then be found from Figure I-9.1 for carbon steel. This then gives an allowable s. tress j of 65000 psi. l +P eb ! Sp y = 2/30 p *OT3 + 1*30T1 1 S p2 " '40 p *2eb + 20T3 I where: OT3 = C63 C aT2 9 ; 1 I i I I l i l l l
- j. .
l 9 I O l l
. l l
i 1
) ! 1 29 f.
e - 1
DISC ANALYSIS Section NB-3546.2 defines the design requirements of the v '_ iisc. Both primary bending and primary membrane stre .
.ioned in this section. For a flat plate such ;
; as *- ,
; . valve disc, membrane stress is not defined ur.- '
s
'Jp
.l js. tion of the disc reaches one-half the disc s
since total deflection of the disc is much less th; . than one-half the thickness, membrane stresses are not applicable to the analysis. Figure 5 shows the disc for the air purge butterfly valve. The disc is designed to provide a structurally sound pressure retaining component while providing the least inter-ference to the flow. . Primary Bending Stress Due to the manner in which the disc is supported, the disc experiences bending both along the shaf t axis and about the shaft axis. The combined bending stress is maximized at the disc center where the maximum moment occurs. The moment i . is a result of a uniform pressure load. Combined bending stress in disc: S (l) = (S (2) 2 , g (3) 2) h where S (2) = .90413 PsE1 C 7
= Bending stress due to moment along shaft axis, psi
'4 3
S (3) = .6666 PsR4 C g = Bending stress due to moment about shaft axis, psi 7 3
.O 40
SHAFT AU7tL'l3 !3 The shaft is analyzed in accordance wi th para. MD-3346.3 of section III of the code. The shaft loading is a combination of seismic, pressure, and opera ting loads. Maximum torsional loading is either a combination of seating and bearing torque or bearing and dynamic to rque . Columnar stress is not considered in the shaft loading due to its negligible effe,ct on the stress levels. Figure 2 shows the banjo assembly with the stub shafts. Shaft stresses due to pressure, seismic, and operating loads: , s S (4) = S (5) + (S (5) 2 + 4 S (6)') h 2 2 Where: 7 2 S(5) = (S (7) 2 + S (8) ') 3 = combined bending s tr ess , PSI 2 S(7) = (n R 4 P +W 2 9) x .25 B y R = Dending tensile s 5 stress due tri 4 n .25 R pressure & s i.v i 5 loads along x - axis, P5' S (8) = .25 W 2 9 y By Rg = Bending tensile stress due to seismic loads along
. 2 5, w R4 5 y - a is, PSI
'2 S(6) = (S ( 9 ) 2 + S (10 ) ') 'I = combined shear stress, PS1
-l S (9) =T 8 R. = Torsional shear stress, PSI
_3 _ j .
- R
, , ,t S(10 = 1. j J.3 .5n R 4 P_=
.5N, ..
( g ,,
*g,') '
= L' i r ec *
,, n.
2 Stress 3 R 5 PC!
~
41 s 42 (
DISC PIN ANALYSIS ! l
\
The valve assembly or cross-section drawing shows the two stub shaf ts and the disc pins. The top disc pins are subjected to torsional load as they transmit the operating torque. , Combined Shear Stress in Top Disc Pin: T g .5 U S S (20A) = 2 2N y R . D 5 12 Bearing Stress on Top Pins in Shaft: k T .5 U S S (20B1 = 'gR+
, 5
.5 K 2 2D12"1 Where D = Disc Pin Diameter, i. .
.- . 12
. P = Actual Shut Off Pressure, psi. O U = .785 (2R 4) PUR g 35 4 U S =U4+W9* 2 35E moem Oe e ew 6 e d on
~
43 & 44 4 % .A e
i ! I- ? SHAFT BEARING ANALYSIS L i > i { The roller bearings in the trunnion are subjected to both seismic and pressure loads. R4 2+W 2 (gx 2+g 2) b , u P ! s y S(21) = = Compressive load ; 2 j on shaft bearing, I lbs. 1 1 _a i l } i ! 1
*4 6,
- s l
l i, . I O l i I i l 45 i }
1 THRUST BEARING ANALYSIS a As shown in figure 5, the thrust bearing assembly is located in the bottom trunnion. It provides res traint for the banjo in the z direction, assuring that the. disc edge remains correctly positioned to maintain optimum sealing. Formulas used to analize the assembly are given below.
- 1. Bearing stress on thrust collar due to seismic load.
W 2 9' ' i S(22) =
.785 (D 4 2 -D 10 2}
- 2. Shear stress in adjusting screw head due to seismic load.
W2 9z S(23) =
- D T lo 2 -
() 3. Combined stress in adjusting screw. S(25) (S (25) 2 + 4 S (26) 2)h S(24) = 2 2 Where: - W
"' 2 9z S(25)'= = Direct tensile stress due to seismic 2
l
~
load. 16 U 6 S(26) = 3
= Torsional shear stress due to thrust xD bearing seismic friction torque.
10
)
J U " U } 2 9z (.5 D10 +
- 6 3 4 - 10
- 4. Shear stress in adjusting screw threads due to seismic loads.
W 9- l 2 S(27) =
.9 n D T i 10 10 i
\
' 46 ;
l l
\
i
~
\
ermswrp% vu mta w [. .
. 1 Tl! RUST DET tii'C A5SEliULY e
VALVE BODY s . . . O- . S!!rie r
. .T. .I_R.U S T '. 'r. . . .
r
/
s
,r - ---
- 7. [ ,
.xs \ N s :
ca f r:/ (i&
.x
, g\x ' s Ns
\
W , O sN - 7= s
~\
1- -- N NNx\ N.
.J;M-./_.._. _.ig /~Qs%.
N Ns . Yi --- i,j'e4. .__ 5 ' M'C- E.; ,
/T,'Mi=-'l '
[N NN - N N\g .2.sk\
~-~ ' \ '
h s h_
. um w u o A= w,,
; ! h h
-E- -I k bl b O. W k .
\ _ RET A l'N I UC S CRE'./
h ,Nh M M GOTTOM ccyrit i.
- AD.Ill3T I !r, c.cn nf Cavin car 1
0 . a I
\
t i i { 5. Combined stress in retainer bolts due to seismic loads. ! ,b S(29) + (S (29) + 4 S ( 30) ') S(28) = 2 2 i j Where: W," 9 Z S(29) = 6A 13 = Tensile stress due to seismic load. i 4 U - 6 i S(30) = 6R A
= Shear stress due to seismic load.
, 7 12 4 i I v l 6. Shear tear out of thrust bearing retainer bolts. W i S(31) = 2 9z i 6w D 5 i i 4 i s 9 < l C 4 . e4 4 i
- s. ,
J a 9 : i - t
- i l
l l i l l 4h 4 1
BOTTOM CO"ER ANALYSIS Figure 5 shows the bottom trunnion assembly, including 'the bottom cover and bottom cover bolts.
- 1. Bottom Cover Bolt Stresses The bottom cover experiences loading from the weight of the banjo and from pressure loads. In determining stress levels, the, bolts are assumed to share torsional and tensile loading equally.
Shear tear out of bolts through tapped holes in trunnion: 2 W -+w P R 2 9z 6 8( }
- 4L
~
(2.83) D 6 3 Shear tear out of bolt heads through bottom cover, PSI. 2 W2 g, + n P s R 6 4T 1 (5.2) D 6 Combined stress in bolts, PSI 8( } (S (37) 2 , 4 g g. ;) 2) h , S(35) = + 2 2 Where:.- U S(36) = 707 3 4 ^4 torsional load. W2 g, + n P s
~
R 6 S(37) = = Tensile stress in bolts 3 due to seismic and pressure loads, PSI.
. 2. Bottom Cover Stresses The combined stress in the bottom cover is calculated I
using the following formulas: b l S 9 +S 0) , ( (S ( 39) + S(40) + 4 S(41) ) J S(38) = 2 2
~O 49
_ ~_ _ ..- - ... . -.- _ _ . - . . - - - = - . - -. . .. . _ . _ - .. _- - . a Where: P +W 2 9'* 3( 785) (D4+ .25) s = Radial s tress { S(39) = 2 i 4 xT 4 i 3 P +w 2 92 (. 785) (D4+ .25) s = Tangential stress
. S(40) =
m 4 w i'4 i i P +W 2 92 785 -(D4+ .25) s = Shear stress S(41) = x (o + .25) T 4 / ) 4 4 1 f l i n ll *
- i. .
i*
- t l
l I 1 I
-e--w e-w- w w s--w--.--<m. ,e.-,%-ww..- .e ey w w -c _ __y., ----y-q ._w,,, ,
OPERATOR MOUt: TING ANALYSIS The operator mounting consists of the top trunnion, the bonnet, ( )the operator housing and the bolt connections as shown in Fig.
- 1. Bolt Stresses and Localized Stress Due to Bolt Loads.
The following assumptions are used in the development of the equations: A. Torsional, direct shear, and direct tensile loads are shared equally by all bolts in the pattern. B. Moments across the bolt pattern are opposed in such a way that the load in each bolt is proportional to its distance from the neutral bending axis.
- a. Shear tear out of trunnion bolt through tapped hole in top trunnion.
/ 2 Fg+W4 gg 2+gy2+g g
+ Mx(J 2+H2) "y I"1+H2}
S(42) =
? 2
% 4 2J 2 +2(J2+H2 )2 + 2J y +2(J +H2} y 2-
.9uL 47 D
^
- b. Bear'ing stress on' tapped holes in trunnion.
4 (M +T 8 x
+F ) 'W4(g x +gy b
+ V +
- S(43) =
4 4 4(.707H2) Db 74 i
- c. Bearing stress on through hole in bonnet.
i - M +T Z 8 (F X +F,! ) + W4(g* 'gY) I s(44) = + 4 4 i 4(.707H2} DT j 76 1 i
- 51 l
a i
ADAPTER PL ATE l V 11 _h ', N -1 N \ 7'
~Y K x o .
pg N V s x
? FIL L E T k'EL D
'T5 ALL AROUND v A -x, j t
. . c. v, h . .
c k Th J
~'
n BONNET' ( TOP TRUNNION
~
VAL VE BODY h TRDNNION BOL TS b . . TOP TRUNNION MOUNTING - G l
- d. Shear tear out of trunnion bolt heads through bonnet.
== -
# 2I S(45) =
* * +
x 2) , bl2 2J2 +2(J 2+N2) 2Jy +2(J y+H2} 5.2 0 7T 6
- e. Combined stress in trunnion bolts (Fig. 8)
S(47)#EI48} + ( (S (47) +S (4 8) ) + 4 (S (49) +S (50) ) )b S(46) = Where, Fz + W4 9, S(47) =
~
= Direct tensile stress, psi 43 5
M (J 2+H2) M y(J y+H2) Tensile stress due to 2J2 +2(J 2+H2) 2J1 +2(J 1+H2 ) momenu, psi (F x +F 2) ,g (gy 2,g 2) , _ Direct shear stress, ps.1 S(49)
=
43 M +T S(50) = ( 707H2)4A6
- f. Shear tearout of operator bolt head through bonnet.
F .,
' (M*+My )V4 +
S(51) =
}
2(V1 +V2 +v3 4 5.2 D g7 T
- g. Bearing stress on through holes in bonnet.
M 3 +T g
. S(52) =
.5H7 8T 7 Dg
- h. Combined stress in operator bolts (Fig. 10)
+ 4 (S ( 56) +S ( 57) )
S(53) = S(54)+S(55) + ((S (54) +S (55)) 2 2 8
)
53 i l l
-- l
ov ,g
. pY O
t 9 0 O
. II2
- g J,2 "5 H2 v ?;
. O t a
r I 21
/
TOP TRUNNION BOLTING liigu r c 6 O O 4 , 54 esemp .e. we m m-,
Where, F, S(34) = 4j = Direct tensile stress, psi. 7 (M*+MY ) V 4 Tensile stress due to bending S(55) = 2 2 2 2
=
moment, psi. 2(V1 ,72 ,73 ,74 )g7 (F* +F Y )b Direct shear stress, psi
'S(56) = -
4A
=
8 M,+T g
- S(57) = = ear stress due to torsion, psi
.5H78A g BONNET STRESSES The bonnet stresses are calculated with the assumption that loading is through the bolt connections as previously defined,
- a. The maximum combined stress in the bonnet was calculated pm using the following formulas:
( )+ ( 0) , ( (S ( 59 ) +S ( 60) ) + 4(S(61)+S(62))2)h S(58) = 2
= Combined stress in bonnet legs.
Where, F*+W g,4* S(59) = = Direct tensile stress, psi
, ,, B 5
S(60) = x8+'v9 y g
= Tensile stress due to bending moment, psi 1 2 (F * +F Y )b + W4(g* +g Y )b = Direct shear stress, psi S(61) =
B : 5 TC 8O S(62) = = Shear stress in bonnet body due to torsional l g 0 load, psi J Ss l l
. E cd-Y b
t D . i 11 b j;' \ i \ \ T V4 D I\,i V)
. /
- s. N N,[ Vz ,
\~~.. - - V V V Y OPERATOR BOLT PATTERN i
Figurc 8 l l
- i i e . l
.O ee l 1
Where, k" Tg = Operating torque, in-lbs. s C0 = Torsional cons tant for non-circular cross-section 4 K0 = Function of cross-section, in .
- b. The maximum combined shear stress in the bonnet mounting plate to body welds was calculated using the following fo rmulas :
BOTTOM BONNET WELDS S(63) = ((S(64) + 4(S(65))2) ,
= Combined shear stress in bottom 2
bonnet weld, psi ! Where, S(64) = S (66) + S (67) = Total tensile stress, psi F +W 4gg 3 S(66) = = Direct tensile stress, psi U 1
== ==
M M" S(67) =3 5 + 3 Bending tensile stress, psi
. "I 2 S(65) = S(68) + S(69) = Total shear stress, psi - - - +W (g* +gY) l S(68) = (F* +FY) = Direct shear stress, psi g
1 M +T
- S(69) = = Torsional shear stress, psi 3
! 3 I l l TOP BONNET WELDS IISI III ^ 4 IS II II = Combined shear stress in top S(70) = 2 bonnet weld, psi Where, ff S(71) = S(73) + S(74) ! 57 l .I g ege m - e **w w + =
. - _ . _ - _ . ~ _ - . _ - . _ _ _ - . . _ . , _ - - - - _ .- . . . , . _ . . , - _ . . . _ . . . . _ _ . , - - - .
;+
I 4 F
-- 2 d S(73) - -
Direct U 2 tensile stress, psi 4 y .(/~ m M S(74) =x E+ME =
*1 ~*2 Bending tensile stress, psi J
S(72) = S(75) + S(76) = Total shear stress, psi f S(75) = (Fx +F y) = Direct shear stress, psi I ' M +T S(76) = ,
- 3 4 = Torsional shear stress, psi TRUNNION BODY STRESS The trunnion body stresses are calculated using theof ll owing assumptions.
1. Operator loading is through the bolt connections . 2. There is an equal and opposite reaction to the bolt loads at the body. The combined stress in"the trunnion body was calculated using the'following formulas: S(77) =S( 8) S(79) ,_(S(78)+S(79))
+ 4 (S (80) +S (81) ) 2) h Where, F* + W4g2 S(78) =
, s KK.4S 85B 2 = Direct tensile stress, psi 2 S(79) =- (Mx +F-yK 6) . 5K 4 (My +Fx6K ) .5K 5
-nB 4' 3 =
.0833K 3 4 Bending tensile stress, psi 54 2 45 ~"3 2 64 64
)
9 i 1 1 58 w , - - -
- - - . - - - - - .--r--.- , - - , . -
t 2' l (F x +F v )b+W4(c'x +gv); = Direct shear stress, psi ) S(80)
=
i 2 ! KK. 4S SB 2 l (M.,+T 8
) .5(K. +K5)
S(81) =
~
= Torsional shear stress, psi 3 4
.0833(K 45 K 3+K54)nB2
' 32 i i b I l L. . 59 i i i q-w--,:,,w .----m- -- - , - ,
TOP TRUICIO*I ASSEMBLY f~ %wd ' (S ) The top trunnion assembly consists of the top trunnion plate, the t,
' ' top trunnion, the welds and the body material immediately adjacent to the trunnion. Fig. 10 illustrates the elements of the assembly.
- 1. Combined shear stress in the top trunnion plate welds is a maxi-mum due to seismic and torsional loads.
<N
\
S(77) = (S (78)' + S (79) 2) s Y Where, 2 4(g=2,g=Y ) F S(78) = 2+ = Shear stress due to operator
.707 (.5) nD yy nD L ll ly eccentricity gmR 4(Mg+Tg) (3Dyy+2Tyy) = Torsional shear due to operator S 79) = ,
eccentricity and operator 3(1.41)nL11(D11+2T11)3 torque
/N
\
l2. Combined stress in base of trunnion body due to combined bending, torsion and seismic loads.
(S 81) +S ( 8 2) (S (81) +S (82) ) 2 + 4 (S (3 3) +S ( 8 4) ) 2) h S(80) = 2
+
2 Where,
+
~ 49 z S(81) =
2
= Direct tensile stress, psi.
()S (, .25n(D y1 -B22)
==
32((M x
+FK)2+y
- 6 IM v
^ K x 6) )
7 D y1 S(82) = 4 n(D 1 -32)
= Bending tensile stress, psi
[ ) (/ ' 60
1 s D,1
- ^
Trunion Plate
. W elci r T 71 -
B, m 1 - l t f~ . !
\\\
' \ !
),
\ Trunion Plate N <
*- p x 13 earing K U# '
Trunion
,g N ,
Trunien E.'.ase
.s W//MW/h
~
"b h JH s .n Vll2N/E0/04 Dociy Shell i . .
t D
*een e W
61
. f
* *****e* **
- mee-..= = . ,
e-m-e- - ,,,,-,.w----- - - , , , - - . , -,-nr.
Top Trunnion Assembly Cont'd
. (F * *F " ) +W +g" )
S(83) = f (g* 9 = Direct shear stress, psi
/
.25n(D g -B ~)
2 16 (M' +T8) D yy S(84) = 4 = Torsional shear stress, psi n(D yy -B24)
- 3. Combined shear stress in top trunnion to shell weld is a maxi-mum due to seismic and torsional loads.
d S(85) = (S(86) + S (87) 2) h Where, 4((27 * + FYK )
+ (I+FK Y * ) )
F S(86) = + nD yy Lyy
.707(.5)nD yy
= Shear stress due to operator eccentricity b) 4 (M.,+T8)
" ( Dyy+2Tyy) Torsional shear due to operator S(87) =
= eccentricity and operating 3 (1. 41) nLyy(Dyy+2Tyy) 3 torque
+
LJ p 62
FREQUENCY I.NALYSIS i ! A. Introduction i To calculate the natural frequency of the various I components of the Triton NXL valve, a model system with a single degree of freedom is constructed. The individual components and groups of components are modeled and analyzed as restoring spring forces which act to oppose the respective weight forces they are , subjected to. The static deflection of the component is calculated and is related to natural frequency as: K F" = 177 5 H or Fn"b 2r % L oy () or F = 9.8 n 3y The analysis details the equations and assumptions
, used in determining the natural frequencies listed in the summary table. Sketches are provided where appropriate.
i () B. Valve Body Assembly The body shell, as seen in Figure 1, is assumed to experience loading due to the entire valve weight. Natural Frequency of the body shell: FN1 *
- AY1 63 f
- m. -_- _ ._
Frequency Analysis l l Where 3 ay y=WLyy = Maximum d'eflection of body shell ue va ve we g , nches. 48 E I 5 C. Banjo Assembly Figure 2 shows the banjo assembly in the body. The I natural frequency of the banjo assembly is calculated , using the following: b FN2 = 9. 8 OY 2 Where
! 3 ay2 " w 7By = Maximum deflection of shaft, inches 12 E I 6
D. Cover Cao Assembly As seen in Figure 6, the cover cap supports the banjo. i The natural frequency of the cover cap is calculated as follows: f h F -
... ,N3=C9.8 OY3 Where - +
2 ay3 = 3 (m -1) W 2 ( . 5D4+ .12 5 ) 2 = Maximum deflection of ver cap 16sE T 4 3m2 l
. ) E. Bonnet Assembly I
Figure 7 shows the top trunnion assembly. The follow-ing asseumptions are made in calculating the bonnet natural frequency: l l l I 64
,w ,c. g,. _ . , _ . . . p -- - - , - --c,.,., ,,y,_,--__
Frequency Analysis t . 1. The wors t valve assembly mounting position is where the bending moment is predominant in producing ! deflection.
- 2. The bonnet is assumed fixed at the top trunnion.
! 3. The adapter plate is assumed to be integral with ! and have a cross-section the same as the component i i it mounts to. - Natural frequency of bonnet: i h FN4 = 9.8 - aY 4 { Where i ay4 = W H38+4 3 + WZH3o8 3EI y 2EI i t
,4 * %
Es e v e 4 l I
)
i 5 i l I 1 d. 4 1 i o 4
+ - - - - - - - - _ . _ , , - - _ .
,.,.-n,-,--,__,,,e m,-.n.n...__,,,a,-.~~-+n m ,,, m- _.-m v ~ r - n
. - _ ___ _ - _. _= . - . . . . . _ .
l l
?
i f
- l l
A 1 ATTACHMENT 3 i. SUPPLEMENTAL TORQUE CALCULATIONS I f I l i l l I I I l i i
! l l l 1
I 1 1
ATT.'sCHMENT 3 The following pages illustrate the combined effects l l of disc blockage and delay time on dynamic torque. In each case, the delay time is fixed at that which produced the worst case torque for the full open, unblocked condition. The initial disc angle is reduced by blocking to illustrate the resultants of several different initial angles of lf l opening. i i 6 I l l i l r
a ' 6 , 4 n.
. D-27256-2 TORQUE TABLE 2 9 / 14 / $1
. JOB: FLOP.PMP;TUPVEY-PT P2-VARIABLE OIZE ADJUOTED*FEYNLDO NO.FNCTN!)
SAT.0 TEAM /AIP MIXTUPE MITH 1.4 LEO TEAM PEP 1-LEO AIP OPEC.GP.= . 738255 MOL.WT.= 21.3872 K AP A (IOENT. EXP. ) = 1.19775 R= 72.1972
. GAS Curt TAffT-CALC.
SutlIC 0 FEED <. MOVING MIXTP.) = 1371.29 FEET /5EC AT 293 DEG. CRIT. CASE IriLET VELOCITY 10 1.57264 TIMES HIGHER AS AIR CPIT. CASE IriLET V1-CF [- g t 5 INCH MODEL
. MAX. TOPOUE 10 AT THE CRITICAL PPESO. PATIO (.585-(5 Itt> MODEL OP APPX .692271
( 47.375 IrDWITH ITMIX.)FIPOT OutiIC(S 72 DEG.V.A.) i ABOOL. MAX.TOFOUE(FIPST 00tiIC) AT 72-68 DG.VLV. AfiG. = 179419 Iri-LES S 35 DEG. MAX.TOFOUE INCLUDE 0 OIZE EFFECT(REYNOLD0 NO.ETC)APPX. X 1.23418 FOR 47.375 INCH EAIIC LIffE I.D. ALL PPEOSURES UOED: STATIC (TAP)PPESS.-ABOOLUTE:P2 INCL.PECOVERY PRESS. (TORQUE) CALC'S VALIDITY:P1/P2> 1. 07; VALVE TYPE: 48"-R1A5:3/7.5 CLASO 75 a DIOC IIZE: 47.062 ItiCHES SYMMETRICAL DISC SHAFT DIA.: 4 IflCHES ERG. CCEF. OF FFCTN.: 5.00000E-03 SEATIrfG FACTCR: 15 INLET PPESS.VAP. MAX.: 51.191 POIA
.,[T CUTLET PFE000PE(P6): 33.93 PSIA (72 DEG. ACTUAL PPE00.ONLY (VAP. ) >
( _,) MAX.AfiG. FLOW FATE: 108209. CFM: 214793. OCFM: 11807.7 LE/MIri CRIT.!OrlIC FLOW-90DG: 57551. LB/ MIN AT 31.6857 INLET PSIA VALVE INLET DEfl0ITY: .10912 LE/FT^3-MIN. .133956 LE FT^3-MAX. FULL OPEtt DELTA P: 13.4092 PSI SYSTEM COfiDITIOriO: PIPE IN-PIFE-CUT -AND- AIR / STEAM MIXTUFE CERVICE S 283 DEG.F MIrlIMUM 0.75 DIAM. PIPE DOWtt0TFEAM FPOM CErlT..LIrlE 3 HAFT. P1 ABS. PRE!!UPE ( AD J. ) FOLLOW TIME /PFESO.TPAti;IEtiT CUFYE. ABSOLUTE MAX. TOPQUE 10 DEFEriDEtiT Ori DELAY TIME AND 3.43 TO 2.15-TH FOWEP e OF (P1/P2)IN WOPST PAriGE X LINEAP COftSTAtti X DuriOTR.PFESS. P6-AES.<75-60DEG.) ') Iti SUE 00rilC PAriGE LIMITS-OriLY: 0EE FDFMULATIOrl!.-FEP TEITI H.PPATT THIS TO. AT 72 DEG.0YMM. DIOC (68=OFFIET OHAFT) CT=T/D^3/P2 '. ABS) b
--5 IN.MODEL EQUIV.VALUE0- ACTUAL OICE VALUE0- --
- ANGLE P1 P2 DELP FPE00. FLOW FLOW TD TE+TH TIME (LOCA)
APPRX.POIA POIA POI PATIO (OCFM) (LE/MITO ----INCHLES---- TD-TE-TH ;EC. 05 41.70 22.36 19.34 .536 214792 11807 51642 1586 50055 3 00 30 44.03 15.04 23.99 .342 172255 9469 47548 1716 45831 3.28 25 45.55 14.89 30.66 .327 122772 6749 30708 1759 28949 ?. . d 5 20 46.34 14.78 31.56 .319 75817 4167 21406 1808 19597 3.35 15 46.59 14.72 31.88 .316 42217 2320 8815 1964 6950 5.90: 10 47.69 14.71 32.98 .308 21243 1167 d323 1947 4376 4.07'
. 5 49.50 14.70 34.80 .297 6992 384 3823 2019 1804 4.37) 0 51.19 14.70 36.49 .287 0 0 35650 1984 33665 4.75
- _ - - .a 5EATIriG + EEAPIrfG + HUE IEAL TOFOUE *M/M)= 37635 IN-LEO 4 0 DEG. )
MAX. DYrt. ,EEAPING - HUB IEAL TCFOUE (M'M) = 51642 Iri-LE; S 35 DEG. ;
., . - ~4
% q s_ / .
l 9
P
,s ..+...........................-.....
SUMMAFY TOPOUE TABLE-VALVE ELDCFED TO: 40 DEG. MAX.ANG. FLOW PATE: 157316 CFM8 312270. SCFM; 17166.4 L3/ MIN
. SEATING + EEAPING + HUB CEAL TOFOUE (M/M)= 37674 IN-LB0 S 0 DEG.
MAX.DYN. - EEAFING - HUE SEAL TOPOUE IM/M) = 91788 IN-LEO d 35 DEG. AT 3 IEC. DELAY TIME TD 5 CLD;ED VLV. (LOCA) TIME ( 41.7 TD 52.3009 PSIA UPSTR. FFE00. ) , REYNLDO NO. F ACTCP ( MULT I PL. ) = 1.02458 TOTAL TDF0. INCFEAIE-FACTOR (TD MODEL EACIS)-F (PE) * (P6/P2) +J9= 1.45002 s ,- m ................................. .
SUMMARY
TORQUE TABLE-VALVE ELDCKED TO: 45 DEG. MAX.ANG. FLOW FATE: 219543. CFM: 435791. OCFM; 23956.6 LB/ MIN SEATING + EEAPING + HUE SEAL TDRCUE (M/ M) = 37705 IN-LB0 & 0 DEG. MAX.DYN. - EEAPING - HUE SEAL TDFOUE (M/M) = 129383 IN-LEC @ 40 DEG. AT 3 OEC. DELAY TIME TD 5.25 CLDOED VLV.<LDCA> TIME ( 41.7 TD 53.2 POIA e UPSTR.FFESO.) REYNLDS NO.FACTOF (MULTIPL.)= 1.29674 TDTAL TDRO. INCREASE-FACTOR (TD MODEL EACIC)-F (RE).(P6/P2).J9= 1.41954
SUMMARY
TDRQUE TABLE-VALVE ELDCKED TU: 50 DEG. MAX.ANG. FLOW RATE: 213950. CFM; 424688. SCFMi 23346.3 LE/ MIN SEATING + EEAPING + HUB OEAL TOFOUE (M/M)= 37736 IN-LES & 0 DEG. MAX.DYN. - EEAPING - HUE SEAL TDFOUE (M M/ = 176303 IN-LIC S 45 IEG. I AT 3 OEC. DELAY TIME TD 5.5 CLD5ED VLV. (LUCA> TIME ( 41.7 TD 54. 0939 POIA UPSTR.PPE00.) REYNLDO NO. FACTOP (MULTIPL. ) = 1.26153
~s TDTAL TOPO. INCFEASE-FACTDP (TD MODEL EAOIO)-F (RE).(P6 P2) +J9= 1.381
)
%./ .
l
. SUMMAPY TDFOUE TABLE-VALVE ELDCKED TD: 55 DEG.
6 MAX.ANG. FLOW FATE: 264052 CFM: 524140. CCFM; 28810.4 LE/ MIN _. SEATING + EEAPING + HUB OEAL TCFOUE (M/M)= 37766 IN-LIO & 0 IEG. MAX.DYN. - EEAPING - HUB OEAL TDFGUE (MeM) = 200052 IN-LIO 3 50 IEG.
- AT 3 IEC. DELAY TIME TD 5.75 CLDOED VLV. (LDC A) TIME ( 41.7 TD 54.9701 P SIA UPOTP.FFE00.)
PEYNLD; NO. F ACTOP MULTIF L. ) = 1.26097 (x' . TOTAL TOFO.INCFEAIE-FACTCPsTD MDIEL EALIO)-F(:E) .
- P6 P2) .J9= 1. 33 038 I
e
-,r - - - - ,
w - .-
6 .
. . jf
.....++ .........................+..
SUMMARY
TOROUE TABLE-VALVE ELOCKED TO: 60 DEG. MAX. ANG. FLOI.1 PATE: 318087. CFMi 631399 2CFMi 34709.7 LE/ MIN SEATING + EEAFING + HUE OEAL TOPOUE (M/M) = 37796 IN-LB5 & 0 DEG. MAX.DYN. - EEARING - HUB OEAL TORGUE (M/M) = 275702 IN-LE! & 55 DEG. s AT 3 SEC. DELAY TIME TO 6 CLOOED YLV. (LOC A> TIME < 41. 7 TO 55.8265 PSIA
, UPSTR. PRESS.)
REYNLDS NO.FACTOP(MULTIPL.)= 1.24212 TOTAL TORQ. INCREASE-FACTOR (TO MODEL P ASIS)-F (FE) . (P6 P2) .J9= 1. 35975
.+.+++++ + ..................++.....
e
SUMMARY
TOPOUE TAELE-VALVE ELOCVED TO: 65 DEG. MAX.ANG. FLOW RATE: 379236. CFMI 752778. SCFMi 41382.3 LE/ MIN SEATING + EEAPING + HUE !EAL TOFOUE (M M) = 37825 IN-LES @ 0 DEG. MAX.DYN. - EEARING - HUE IEAL TOPQUE (M M) = 357203 IN-LEO 9 65 DEG. AT 3 SEC. DELAY TIME TO 6.25 CLOSED VLV.<LOCA) TIME ( 41.7 TO 56.6602 P SIA UPOTP.PRESO.) REYNLDS NO.FACTOP(MULTIPL.)= 1.21566 .
~
TOTAL TOFO. INC F EA!E-FACTOR (TO MODEL PAIIS)-F (PE) + (P6/P2) .J9= 1. 33078
+++++.............+.......+...... . 5 b
SUMMARY
TOROUE TABLE-VALVE ELOCKED TO: 70 DEG.
, MAX.ANG. FLOW PATE: 430453. CFMi 854443. OCFMi 46971.1 LE/ MIN SEATING + EEADING + HUB 3EAL TOPOUE (M/M) = 37853 IN-LEO & 0 DEG.
,_ / MAX.DYN. - EEAPING - HUE !EAL TORQUE (M/M) = 390847 IN-LEO & 65 DEG.
AT 3 SEC. DELAY TIME TO 6.5 CLO!ED VLV.<LOCA> TIME ( 41.7 TO 57.4675 ' POIA UPOTR.PFESS.) e' PEYNLD NO. FACTOP (MULTIPL. ) = 1.21019 TOTAL TOFO.1NCFEACE-FACTOR (TO MODEL EAOIS)-F (FE) (P6eP2) *J9= 1. 3248 - 4 O I
e t O .
+++.+....++ .+++......++.....+......
SUMMARY
TCROUE TAELE-VALVE ELOCKED TO: 75 DEG. MAX.AffG.FLCU PATE: 494335. CFMi 981249. OCFMi 53942. LB/MIri SEATING + BEAPItfG + HUE !EAL TCFOUE (M/M)= 37890 Iff-LEO S 0 DEG. MAX.DYN. - EEAPIffG - HUB SEAL TGFOUE (M MT = 430363 Iri-LES & 70 DEG. AT 3 OEC. DELAY TIME TO 6.75 CLO!ED VLY.(LOCA> TIME ( 41.7 TO 58.2428 P SIA UPOTR.PPE00.) PEYtiLDS fiD. FACTCP (MULTIPL.) = 1.19917 9 TOTAL TOFO. ItiCFEACE-FACTDP (TO MODEL BASIO)-F(RE) +(P6/P2) +J9= 1. 31273
+++++...+ +........ +. .++++.+......
SUMMARY
TCPOUE THELE-VALVE ILOCNED TO: 30 DEG.
. MAX. AffG.FLOU PATE: 518135. CFMi 1028492 SCFMi 56539. LB MIti ,' OEATIrlG + EEAPIrlG + HUE SEAL TCPOUE (M/M)= 37906 Iti-LEO P 0 DEG.
MAX.DYti. - EEAPIt!G - HUB OEAL TORQUE (M/M) = 449227 Iri-LES S 70 DEG. I AT 3 ?EC. DELAY TIME TO 7 CLCOED VLV.(LOCA) TIME ( 41.7 TO 58.9771 PSIA UPSTR.PPE00.) PEYNLD; fiO. F ACTCP (MULTIPL. ) = 1.19521 ' TOTAL TCFQ. ItICFEAIE-FACTOP (TD MODEL EASIC)-F (FE) +(P6eP2) .J9= 1. 3084 s ss++e++..s+e.e+ese ss++e ++.*++++e++ , } OUMMARY. TCPOUE TAELE *JALVE ELCCKED TU: 85 DEG. MAX.AfiG. FLOW PATE: 547259. CFMi 1086302 SCFMi 59717.1 LE/ M Iri
, SEATIriG + EEARItiG
- HUE SEAL TCFOUE <M/M) = 37929 IN-LEO S 0 DEG.
MAX.DYri. ,EEARIffG - HUB !EAL TOFOUE (M M) = 463889 Irt-LB0 S TO DEG. AT 3 OEC. DELAY TIME TO 7.25 CLDIED VLV.(LOCA) TIME ( 41.7 TG 59.6528 P
+- SIA UPOTR.PFE00.)
PEYNLDO ffD. FACTCP (MULTIPL. ) = 1.19221 TOT AL TOFQ. IfiCFEAC E-FAC TCP (Tu MODEL I AOIS)-F (PE) + <P6/P2) .J9= 1. 30511
~
9
- 9 e
9
. , , . - - , - - . - - - - . . _ - , ... --.,n., , , - , - , .-,..-,.-,..m,,,,.__ . - - , . - , - - - - - - , . . - . , - - . .
-"b---- - -a b-A - , m ,- . - a ,,_m
_ .=___,_,m _,, ,_ _ l 4 e n l i i ATTACHMENT 4 1 GENERAL ARRANGEMENT f AND CROSS-SECTION DRAWINGS i l-t l I l 0
+e l
l I i i e w-wea-t -w w y m,
--Mw-+er s ,, ,ww.M--+r- wp-g-,-yw+-v e - w w -ww yw eywww_ w w-ww -
e me w - em w w m-m-we-~9e-v w*+N:}}