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RIV000053L Submitted: December 27, 2011

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APPENDIX B

THERMAL ANALYSIS

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APPENDIX. B ·.· ... '1-HERMAI.'":: ANALYSIS ..

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SOLU'I't nrlS •••••••••••••• -........................ · •.••

'i''r::m:zlunt. and Steady :1tate - One, 'l'wo or 'l'hree 1.'1r!lena1CJntll •••. • ...................... · ...... ..

One i>1men a1 on a l .......................... Tt•anatcnt One 1)1mens1onal • • • • a I • t • • •• a a • • I • • • e I

'l'rnrmi.ent .- One Dimensional ................ :·;teady state Orie Dimensional - Heat. Generation ..•.••.•....••••••••••••• I •••••••••••••

'l'hermal Moment . ~ .......... ~ .· ....... . •• e e • + ••• • • II

r.taterial Properties & F1lmCoeff1clents ••••••••••

PLICATIO~ OF GENERAL METHODS OF SOLUTION AND ESUL't':l .,'\'f ~iPRCIFIC LOCATIONS ••••••••••••••••••• . .....

Hcaci nnd Vcssel.Planges .......................... .

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Veaael Supports .................................. ~{F.:F!:-:H i·:~~c; ~~:; ·· ••••••••••••.•••••••••••••••••••••••••••.•••••••

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B-10

13-12

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B-17

B-19

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9-21


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·:-·

~- '' ·' . ~ .. . .

,. ·-] ·;.~·. ~-· ·-~. to< ·-··,- .-.?:~·:~:":.. -.-,_;· .. ~appendix presents a ... auftll'rlary of.·.the the.rmal.analysie of· . ·Point~·· Plant f3 Pretusur1zed.· Water. Reactor Vessel; .

aumptions made;. method or. analysis and. results ot' the . W'IV01lll.,igat1ons are· presented •.. · Temperature distributions

from two-dimensional heat ,'flow. an'alyses are·: pr.e-. ted on cross sections or the componente.consldered.

sulta or the one-dimensional heat flow analyses ·are sented in the form of graphl!l •. The times f':jr which dis

. tions are p1•esented were selected· to present the l.' .. errects of t.he trilns1.ents.

Actual thickness or clad materlal, ft. Cross sectton area, ft2. Dlmenu1on, ft . . . Thermal capacttance of n·::>de j, BTU/)F

·- Speclflc heat, BTU/lb-°F .. - Actu·al thlckness ot baee metal, rt

..;.Equivalent thickness of clad material. ft M"dulus of elast1<:1ty, psi A<:celerat1on of gravity,· ft/sec* Heat· transfer. coeft'ic!ent. BTU;hr-ft2-°F

. . Thermal eonducti vi ty, BTU/hr-tt-Op .. : -. Length along a heat flow path, ft ·

·· ·slope of temperature vs time curve, OF/hr Fourier modulus, dimensionless ·Slope or temperature vs time curve at x~, °F/hr

- Rate ot heat ·tlow, BTU/hr - Heat generation of the node j, M'U/hr - nate of heat generation per unit volume, BTU/hr-rts - Rate or heat. generation per unit volume· at the

surt'a.ce; BTU/hr-tt• D1menst..·m, ft The~al resistance, hr-OF/BTU Temperature, op.

- Uniform initial temperature, op .. Temperature at x•bi · 0 P - Temperature difference, op - Slope or temperature vs time curve at x•b, °F/Hr - Volume• rt• - Dtmenslon, tt - Th~rmal 41ftua1v1t7• tt•lhr - Coett'lcient or thermal expansion, tt/tt-0 P

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. • T·To, · Te.1\p.ertiture change/. 0 p ·... ... · :-:;- ··' ·- Absolute,;v1scos1ty;:_·lb/ft~hr __ ; - Po1sson•a ratio, dimensionless

• ~ , distance ratio, d1meris1_onless · Density, lb/t't3

.. Themal-- stress, psi ·- Time, hr - Time d1fr~rence, hr

CT · · = bi. , temperature ratio, d1r:aens1onles3

- ~atural convection property function, 1/tt~ 0 ?

GENERAL SOLtJTIO:rs

Various procedures were used to determine the thermal inro~a~ . tion presented in this appendix. The following paragraphs describe the techniques used and the conditions under which each ·would be applicable.

·:B.3.1 •.

Transient and steady state temperature d1st:-1bu.tic!1s determined by use o~ a finite difference method p~o-grammed for solution_on a ~g1tal computer. ·

A code has been written which r:aakes use or the gene~al 'heat .balance. equations dertv~d by HelL~a~. n~betle~. and Babrov ( 1}. Throu~h .the us~ or· this code, te:nperature distributions can be obtained in bodies ha.·.,ir.g 1rl"egular geometries and composed or different ::tate::-!.als •.

The obJect being investig~ted is divided into a sys~e~ or blocks or nodes. The thermal capacitance ot each no1e and the thermai resistance between nodes 1s calculated using the physical properties of the material.

The thermal capacitance or node J is:

The thermal resistance between homogeneous· nodes J a."ld 1 ls:


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·. nodes .·J and, 1'~>JA1 :1s;::the·:.:.a~e.a·:-n~~lc,~p:~JLt.'a~d; co~m~o·n,t_:···,; .. to both nodes•· •~,k. 1a ·the· thermal conduct1v1 t~r ot. the ,_-.-. · :' .. :materl.al;:· .: ~- ;· ;' ··: · (:~ _; ::_;. · '.·-· · .-)·:·;:;_/• •: , __ · .. : .':. ~- · ·•• :··:_'<:.',._

' '«. ~

·. ''~e- thermal· resistance -betwee'n· noti-ho~~ceneous n.;)des·· . 'J and 1 in' series is:. . -· ' ·•. . ,.

resistance for a film 1s:.

The equation for the change .1n temperature or a parti. cular node in the time tJ:r is:

:··AT • ~- [q(eonduct~d) + ct(generated)] ' . J . .·

'. . . . ..

rate at which heat is. conducted into, the node is:

1 represents each bordertnc·node and JR1 is the · thermal resistance between the 1 node and tne node

. · :. under consideration.

'Ibus •. the equation for the chanse in temperature of a particular node becomes: ·

The temperature or each node 'is calculated at. succes-. s1ve t1l'!\e intervals thtoo:Jgh the ·use or the .finite dltterence •quat1on:

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.. , ...

...

;''

·.·· ...

... ;'.

~· . . .: '·>- :.'-:~. ·~·· ... ; ' . .. . ..

·where l\T. t·s··~·~b~a~:~~~· .'~~~ ·th:~.: P:;e-~tous .. ·e~~~t1on ·and

. · .. e:alu~ t~ t -~~;::\ 1\~:.:.A·.};~; :;ii~;.• < ,;.;;;[.;,;;;; . ''' ;, .: · ..•.... · .•..... · •........ ·. :- · .·· ·. .. . · Por .a :steady. state .;:problem~'· the.~ term.:fri • bracket;s:.must· ·; -.<.: · ·." ·

·. be. equal t(r zero'::,~ hence~·, .. ·<''. < :,: ':· ~-. ··.::-:>>. :. '. . . . . :.: ... :~;. . · . . ' . . " . ~ ~ ;. '· .. .

. . -

'l'his expression is equivalent to performing a heat balance about node· j .. ·

Trana1ent solution tor a fln1te.sl~b ln .whi~h one . . boun,1nry has. a Uneat" temperature change~ whtle the ·other b .. :'iundat"y is insulated. Initially the slab Ls

1 sotherrnal.

Assumption~: .

l. ·. One-dimensional heat· flow. · ' 2.· Thermal prop.art1es or the mater1al do not vary w1 th

te'mperatut'e and may,be evaluated at the average . tenq)erature o\l'er' the· range cove red.

3 •• · Inflnlte ·heat transfer .coetflctent at x.•o.

Mathematical statement of the. problem:

a~' 1 ~ ~x2 - ; ~ • 0 tor o< x (b , -r>O

ooundary condtuons:.

·. T • T0 at -r· • o ror o< ·x <b


,· :·'.

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,·.

.· ..... · . . ·. :. . ··-: 1···'1)''_:··:. • b f · (T0 + ~1:)dx··'

0 .

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.. · : .. ··

. ''b • · T · + . !.!!! J .cidx • '. ·T0. >.+.·_· ~ ·· · ·. tisT

· o · ... b .. 0 ..... . . mean.··:

....

.,._ l. . . ·. ... -(n+i) a .,.a NFoj . 1 . N .. 5 + 2 ···E e..__·_· ..... ·-...,.--• r Po- b r ·.. . :1. "

Po . . : n•O_. · · (n+i) ' .

·only. cons1de·r~ :slabs of o~e· material~- To :include. elad· on the,:base ne'tal,~·>an. equivalent thickness

· .. ' must be added ,to .be base metal·:th1clmeas.::-. ·.. . . ·• . . ' .. ·' . \"

:·: -~·'·Tl1, ·equa·~io·n·--t-~;r.::the·-~~qu1v~~~~~:··t~I~,~~~·~ or:-ci&~ -~i= ·.· . : ; ... ·

. d. -c·;·:fc••···a•c,--.-:2tl!c.:':_:.·;·:: .. VI . Q:~, .. "·.·· .. '.''." ·.···.· ....

. ... ·. "·· .. ·

.•

~-: .. ........ .. , ·.,_·,,. :· .. : ;:, ~- . •.

., .. :· .. ·:· .... . .· .. ;. · .....

.·,

! ... •


- -~~- ·.

where,·· ~)·~~.. .•' .:.,. -.. . ' ,• . ·,· ..

·' "·

. . ..,_:~~ '--~-t::-_. -~~-~·-::_···>·<;~-·~ . · .. ."-'·_: ,.·. . ·; ·. . .·.· _.\·· :. d ,•. equ1valen't ti•1ckness ·or. clact material · · · · · · · .

. · c -~ actual·thTckness:or base material ,.· ,.··-··: . a:-. actuar·_th1ckn'ess ·or:' clad material:

a1 and ,k1 • diffusivtty and c:onduct1v1ty of clad. a 2 and k 2 • d1ffus1v1ty and conductivity or base metal

. The slab thickness "b" now becomes (d+c)

The flnai graph 6r temperature vs · distan~e can b~ plotted using {d+c) as the total length. The temperatur'es 1n the section d<x<(d+c) are correct for the ba:'3e me~al. However, the temperature d1stribution.from O<x<cl must be "foreshortened'' and replotted from O<x<a wher-e th•: temperature at x•a is the temperature cal~ulated fv~ x=d.

Transient solution for a finite slab with uniform 1n1t1al temperature !.n which one boundary has a linear temperature change while the other boundary is kept at. zero temperature.

)(

Assumptions:

l. · One-dimensional heat rlow. 2. Thermal properties of the material do not vary with

temperature and can.be evaluated at ~he average temperature over the range covered.

3. Infln1te heat transfer coefficient at x•o.

Mathematical Qtatement of the problem:

a:z,. 1 ~ ox2- a~ • 0 for 0< X (b' and T)O


&>~"1~~~,·~~;~~,1::t?~e.C; ''~i&rt~ , .. . . .. · T • .T · .... ·•at" '· -r•O ·.for· 0< · x· (b : ·,\ · .·

•9.- a: ~~;~~~<i·> , ·i,.JA: .v ;·, .. , T : T0 +. m-r .. ·at x..aO for. ~;b"·· · .,

. . . .. . ..

The solution is:

· .. ··where,

e <p = -"" m-r

b . Tmean ... ~· . I (T + qm-r )dx.

o·

Transient solution for a. finite slab with non-unifonn • , 1nlt1al temperature which undergoes a linear temperature · change on. each surface,

.. ·

·Asst;mpt1ons~

l, One-dimensional heat t'low . 2. · Thennal properties or the material do nd't vary with

. temperature and can. be evaluated at the average temperature over the range covered •

. 3. Infinite heat transfer coefficient at x-o .

. 4. u•O forcing the surface at x•b to remain at T1.

Mathematical statement of the problem:

aatr !, ~ • 0 for 0< X (b 3XI .. QO't

..

and 't)O •••••


... >' . ~ ... g

.. ·: ..

Boundary cond1tt.ons: . ' '

' '': T •· r(x) ·&t· T~O .. ror:ix x:<b.' ..... · · · . :.··:r:·· ·-~~:.<:.-~;:.:.;,;<;;:·i'~;::;.~u· ·.-- · .. :·.

·. : T. ··-.~o ... +;.PT,}L~:x.,o.;· to~:~-r>O

T .··~1'·~ u~ at·.·~~~<-~or T)O, -bu·t u-o . : .. · .. ,· . .. ··.

.' .·.:·

The solut1o'n: 1s: .-

. {b sin ":X £ f(x.) sin ": dx.

+ n:a (e an~•, [prr0 - (-1 l"u<T0 }'}

If f(x) == T0 +: (Tl-To} the solution becomes

. . •[ 3 . 2 ] T • pT + T(U-p )~ + ~ (u-p )t- + p~ ~ (u+2p )!

2 · -:;; I e n•l


.-.-. "•'-·

·, •. ~ .

. . , . ·, .. ,:_ .~ .... B~lO · fc_' •

B:~~~~~~1~~~i~~~i1f4~~I~l:l£fo}; . ; . Non11near.grad1ent· at. steady state.resulting from heat generation due to gamma ray capture ·in a two material· finite slab with'one sur!'aee.at a fixed temperature

·. and the othe.r surface perrectl:r insulated. ·

ss c.s

Assumptions:

l. One-dimensional heat flow. 2. Thermal properties c·f the materials do not vary with

temperature and can be evaluated at the mean temperature of the body in question.

3. No contact resistance at the Junction of the two .·materials. ·

4. Heat generation of the form q '" = q 0 111 e-~x..

Mathematical statement or the problem:

-k cs

.. Boundary conditions:

. ··.;. :.l •

•

••• . •


'.··.'

· Ts:, • Tcs

ekss f). a + ~ [! 6-ea1

Tangential thermal stresses at x•a1 and x.=a2 due to this te~erature ~1str1bUtion in a thin walled cyllnder Wi~h ends free to expand axially but restrained from bendi:'lg

are:·

01 • 'I'angent!al thermal stress at x=a1

era ... Tangent!a.l thern\J.l· stress at x .. a.a

E • Modulus of ela.st1e1ty v .. Poisson's ratio

a' • Linear e_,ert1cient of thermal expansion

.. '• .... :.


-:· .. · ···.·.,Thermal mom~nt:· ... · A·: t'em ueed~;in<;the':.strueturai. analysis ' 'generally ~rtt':locat1orns ::or.-;.d1'scont1n\h.ty. whe~e. cuts are ' ' .• , • . . II• ~ . : •', . ;·. if',• .f~··.l " . ' ',•,, · ···: ··', • · ..... • ·", •' ., • '{'"":··· < , 'j.•' •' ' . :...-.. · ' ~· : ... ··

. : :.taken:· · .. The· moment'.1a:::due:~to.;a:::~.rad1e.1: .. temperature . :' ·,. ··gradlent :an'd ~18··.'def'1nei:i'. mathematically.: asc·::.: ·, ' .. ,·.:"?·. ' .'' ' b ' '' .. ;.' ' ·: .. '.·'.:':·.'/ '·.' -..;- ,.· ... :,:·'>· ,: _.::: .. :'-:. ' ".: ::\. :. -·.. ' ">

Ea.' . . . MT ~· r:v ·.·IT (R-r )d (R-r)

. a

.. · :

' I. ~

:·The· equation ror· the mean temperature at a cut through a cyl1nder1cal section is:

whe reJ

b f ·Trdr a

a = Olrnenaion to inside surface b = Dimension to outside eurface r =Dimension (a<r<b) R = Mean radius

a 1 = Coeff'1c1ent of thermal expansion v a Poisson's ratio

Material Properties and Film coeff1c1en~s: ~

Properties or materials used in this appendix are presented below. All were evaluated at 325°F.

stainless Steel

k = 9.8 Btu/hr-ft-°F p = 495 lb/ft3 Cp ... 127 Btu/lb .. 0 P

Alr -k c ,0204 Btu/hr-rt-°F V '"' ).0 X 105

carbon steel

k a 26.2 Btu/hr-ft-°F p = 490 lb/ft 3

c'P = .12 Btu/lb-°F

water

k • .40 Btu/hr-ft-°F t = 4.7 X. 108

. . ' '~

The following equations were used to calculate the heat transfer coeCf1cients used in the analyets of the head and vessel flanges.

. ! I

•

•


i . . •.• ..· .... · . ... . . . .·. ; : ·.~~::t·~~: ' ··Convection tUm coer.rtc1ent in. a· vertically encloaed. .· .... gap: .. ~ ' : .. : .. '. .. ;,·.

~ .. . . :· ;_"

'·. ·.

where,

Convection film coef!1cient in a horizontal enclo~ed gap:

hex fx3p:;a6T (ckP~)J~ T = 0.075 L h 0 = o. 075k [vAT ]i

Convection film off the top of a heated plate:

he L rL 3p 2gf.\AT CpiJ. ] j. ~ = o.l4 L IJ.a c k )

1. h ·a O.l4k[ AT)3

C·

The convection film C¢eff1c1ent on the 'bnttom side of the same plate ls assumed to 'be half that on the .top side.

The equation for the radiation coeff.1c1ent acroe8- .the air s;aps and off the top and bottom or the rerue).~·.~:&,.~~~ plate is as follows: , ··

0.173 X 10-e i(T~1~·-·~T~~~4~) hr • ~--~~--- -...!. + ..!. -1 (TJ.•Ta) «1 Ia

11 • Ill • 0.65


........ :·'·,·: ...•

.. '; ,'.';; ,4;. Head and Vessei Flanges:.· A repre~~ntati'~e:':sectio~·or . . ; jY .::: the vessel t'lange - head tlanse region was .. divided into .• a series of nodes as in Figure. B;.;.l · on. ·Page B- 23. · :Por: .. ·_· .. calculating node volumes ancf.heat. transfer· areas, a · .· cylindrical· sector wi t!i an angle equal to half. the .

. angle between .two studs. ttas taken •. 'Ibis 11l0del considers two dimensional heat·flow (axial and radial) except ln the head flange where the studs pass· through. In this area, a third dimension is considel"ed as heat is transferred between the stud and flange.

Assumptions:

a. Two-dimensional heat flow. b. Heat generation negligible. c. 'l'hennal properties do not vary with temperature.

_d. Natural convection is assumed in the gap between the core barrel and vessel flange.

e •. ~11 other.surraces in contact with primary coolant are assumed to have an infinite hea~ transfer coefficient.

f. OUtside surfaces or flanges, vessel and head are perfectly insulated.

g. Natural convection and radiation is assumed in the annulus between the stud and head flange and ln the gap between the head and vessel flanges.

h. The refueling plate transfers heat· to the sur- · roundings by both radiation am convection.

The head and vessel flanges were analyzed for the tol~ lowl~g the~al cond1t1oris using the method described in B.3.l.

a. Heatup Transient: Inside surfaces are heated from · lOoOF to 547°P at a linear rate or·~ lOOOF/hr while the ~'b1ent condition rema1na.at l20°:P.

•

• •••


. :· ~

·. ·:.·~·~/-

b. St~ady' 'state:. : :-~ns1d€{::sJ:~;i~e:~·.::•n~{ h~·id·· con~f~n • · 547°F ·and. the 'ambient .. at '-120°F~ >. .-::.:-'. i : ·

'• ~: ' • w •• •• • • < • ; ..... •.,·. •

~ ., ·• . . ' . :. --~.: .. __. . : :. ·.: ···.·::-··. :.: " . . . ·•' . . . . . ':. ,, .. ·~ ... •' ' . ·, ... c. Cooldown Transient: --The 'inside· surf.ac~s: are cooled~ . ·

_:.from 547°.F _to ·loOO.F • .-at a :linearfrate:))t:~l00°F/h'r. · -.-- -,· _:·. while :_the: a.:mbi.ent.;is held".··at>l20°'F •. ~c:The '::tni t1al~ . . condition· f'or -~his- transient is· the_.· s-teady. ata·c.·e:..:> cond1t1ori deseri~e~ tn·b~:~-- · · · _ -

Results:

Nodal lay.:>uts or the flanges showing temp~·rai,ur(: ~lt::;- · tr•1 bUt..f.i..\flS_ at tlmeS durtng heatup and Oor;,ld~JIIIO tr~n-__

~ . . '

- s!ent.s plus steady state _are )>resented in: Figures- B.; 1 tt.r'u B- 9, Figure B- 39 is a sketch of .1.ht! f'lange reglon showing the locations of discontinuH.y where thi.: effects of radial grad.ients.were considered. At these locations, the radial gradients were.plott.ed, and from these gradients values were obtained for the mean temperature at. the cut and the thermal moment.. The radial gradients are shown in Figures B..: 40 thru B- 49, and the thermal moments resulting.f'rom th~se gradients are tabulated on Page s-100.

Axial gradients in the flanges were also-plotted from the temperature distributions at times during heatup, <:ooldown and at· steady state, These gradients are pre-:Hmtcd in F1gu:-es B-78 thru B-83. ·

For the Plant Hydrosta't1c. Test (2500 ps1a), the inside surf'aces are heated· from 10oop to 400°'F·-e.t .lOOOF;hr while the plant 1s being pressuri'Zed • ., During plant depressurization, the 1ns1de surfaces· are cooled back to l00°F at l00°F/nr._ The13e heatup and cooldown transients are at the same rate but over a' shorter range thn.n the normal hea'tup and. eooldown. 'l11erefore, 1 t would be conservative t:o use the results 1.1f normal heatup and cooldown for the hyd~ostatic test transients.

Other operating transients applied to-· this region have raater rates than heatup and cooldown; but the range of tnrnperature chnnge' ie much shortf;!lr •. Thererore 1 it was · C~o)tH>cl'vative to consider. the mean temperature of the b,H,ly dtd not change f'ru~ the 1n1tlal cond I t1on while t.h.-i t.P.mpct"ature or the inside eurfaae __ tolluwed the fluld \.randent. D1trerencea _between the mean temperatul't! und tht1 tne1de 13\Jrt~&Qe temperat;\.lf'e R1' times d-ur1ng t..h~tH~ transients are tabulated. on P,.ge B·l21.


.. ·.· . -~· : .. •., ·. .

. ' Inlet Nozzle:. ·>A. cress·. section ·or the' .~.ozzle :was: d1-vided.1nto ··a: eeries:~or.:.nodea·:·as 1n.:Pigure·:a..:lo· on.

:. Page P.;._32. · ,Thia.: mc)del~·':'eorisiating· of a cyl1nd.r1eal 'sector with; an: angle :.or. one _;radiarf,·-~.was .used~ to per- .. form ·a. two-dimensional thermal analysis using the ·

.. technique described 1n B.3.l;·and ·the following . ··: .. ,assumptions.···:: ·

a. b .• c. d.

E' •

Two-dimensional heat flow. Heat generation negligible. · · Thermal properties do not vary with temperature. All surfaces in contact with the primary coolant are assumed to have an infinite heat transfer coefficient.. outside surfaces 'are perfectly 'insulated ..

Results:

Temperature distributions were obtained for times dur-.. ing a lOOoF/hr hea.tup from 100°F to 54-r<>F. These distributions are shown.on. nodal layouts in Figures B-10 thru B-13. Figure B- 50 shows the locations.. of discontimli ty where the effects of radial gradients were considered. At these locations, the radial gradients were 1)10tted, and from these gradients val'tH9s were obtained for the mean temperature at the cut and the thermal moment. The radial.gradient plots are found ,in Figures B- ?l thru B- 55 and the thermal moments are .tabulated on Page B-101.

Gradients in the ax.1al d1reet1on were also plotted for the nozzle at times during the heatup transient. These plot.s are found in. Figures B-84 and B- 85.

Temperature d1atribut1ons were not obtained fo.r the cooldown transient. Since cooldown is over the. same range and at the same rate as heatup, cooldown gradients would. simply be mirror images or thosetor the heatup transient. Also, the values for thermal moments which were obtained for heatup, with Signs reversed, can be used for corresponding times during cooldown~

The results or normal heatup and cooldown'were used for the hydrostat1c test transients 88 described f ... lr the flanges in B ••• l.

Al ~,t~.mdy ~t.at.e. the no:nle will be taothemal at the 1tllt;t. COulant temperature ei.nce there 1B no heat. sink.

••


··.,:.

·-·,·.· ·, .. · . ,-.· .. ·

The op~:r:-ati.ng ·transients .for the lnl~t ·m)zzle wer~ investigated .in the' same manner as' t:'or.th<J .. flange' ' an:J.lya!s _in Section ·s~ 4 ~l ~ ·.nu! ·results ar:-'e·:·p'reeentecr on Page B.;.l22. -.· · -·. - - -

. . .. -· . ~:'. : . ·. . . .. :. . . '~. .. .·

OUtlet·. Noz.zlei - A ·r~prese~~t.at1ve secti~n: ~'f the outlet nozzle. wan divided. into a s·er1e·s-·or· nodes as in ~igtire B-14 . on. Page B-36. This model~: consisting· (lf n

·.cylindrical sector with an angle of one radian, was used to perform a thennalanalysis using the method. described ln B.J.l~ ·

Assumptions:

a. Two~d1mens1onal heat flow. b. Heat generation negligible. u. Thennal properties do n<.)t vary with t.emperat.ur'r.:. d. All. surfaces in contact with the· primary coo lan~.

arc assumed to have an 1nf1n1te heat transfer coef'f'1c1ent.

ll, ·outside surfaces perfectly lnsulaten.

'J'ernpct•ature distributions in the outlet nl)Zzle were t)b

ttl1ned for- the following transient and stt:ady stat.e conditions.

a. Heatup: Inside surfaces are heated fr•om 100°F t-c 547°F at a linear rate of l00°Fjhr. Both inlet and o\ltlet fluids follow the same transient.

b. 100~ Power Steady State: The coolant inside the nozzle is held constant at 613°F while the coolant contacting the vessel shell adjacent to the nozzle ls held at 555°F.

c. Operating Transients: Temperature distributions were 0bta1ned !'or operating transients including plant loading and unloading, step reduction from 100~ .to 50~ load, reactor trip !'rom full power, loss 0f flow, one pump and loss of load. Fluid transients for these cases are found.in the Equipment Spec1f1cat1t:on,

Results!

Nodal layouts of the outlet nozzle showing temperature dtntrlbutlons for. tlmes dur1ns heatup, plant load1nlh · nt 100~ power steady Btate and during plant unloading ar-e pr-esented 1n Figures B-14 thru s..;26, Figur'e B-56


· 1s ·· .• • ske<eh· o; •. t~e· •. no~~n.l~!Jif~t~~J"f[ilt:'~I~~!~i~~~!~l~l:}····· :<: :· _: d1scont.1nu~t:v,:where .. ;ertec.ta .~r.:•rad1al~.grad1e~t8:.'wet~:: .. ·'~.:~·:·;·~!!~·: .

. ··: .•. considered r 1.;At ;:these,:locationsp.rad1al ;..;grad1ent·a;,:·~ere,::. :<<.~·,:-;:::;'~:·< .• ·. ••· · · plot.ted tor:the ·conditions., above' •. ;.-:. Prom . .'these~'gra;.··~.,.· .. ·.".:.:~;~.··::.>:. · :;.;~·

· d1ents, ·values· were ;.obtained ·rar· the .'niean·::::temperat\are .: :. >.··· ; . .. ''?;T· . a.t the eut .-and ·the thermal.·: moment.·· :·The.:.radial. ·.<: ~. . . . . . '

gradient· plots are found:in P1gurea:·a-57.-:thnLB.;.7l•· and the restilting·themal momentsare·tabulated. .on Pages . B- 102 and n.:. 103. .• ·· ·

A.x1al gradients ·were· aiao plotted ·r6r the nozzh~ ~t · ·times dut•ing heatup, plant loading at· 10~ pow~r steady state and during plant unloading~ . They are round in Figures B- a6 thru B· 91.

As !n the inlet nozzl•l analysis, the cooldown transient was not completely analyzed. The gradients are mirror !mages of those for heatup and the thermal moments, with reversed signs, can be used for corresponding times durtng cooldown.

At zerv power steady atate, both inlet and outlet fluids are at 547°F. With the outer surface of the nozzle insulated there is no heat sink. Therefore, at this steady state the.nozzlewill be isothermal at 547°F.

. .

The results of heatup and cooldown were also used for the plant hydrostatic test tranaients as described for the ~lange analysis in B.4.1.

Temp,}rature dista'•ibutions for. operating transients includ:ng step reduction rrom 10~ to 50~ load, reactor trip from full power, loss of .flow, one pump and loss of load are presented 1n Figures B- 27 thru B- 38. Thee~ transients have faster rates than heatup, plant loadlng and plant unloading, and their effects are only seen a short distance from the surface. In view or this, it was conservative to consider the inside surface follows the fluid temperature and calculate the aT between the mean temperature and inside surface· temperature. These temperature differences are tabulated on Pages B-123 and B-124.

For the step load transients of :f: 10; of rull power.and stea."'\ break from hot 'zero power where both inlet and outlet fluids follow the same transient, the 1ne1de surfnce temperature was aesumed to tollow the r~uld temperature while the mean temperature of the no:tz.le dld

••

•


.•·. '.. ~ • ?>

. .·.. . ... · ' > . .· ·'<·;'· . _;;;..,?:;~.}~::-/:::·.: : .. ,. '· ' . ..·. ' · not. chance_: ~rom_,the .1n1t1al_.conCl1t1on.- ,:·-·il1fferences·.;,·., · ... . ·between· the ·mean' ·and ·:aurrao·e~·:temperatu~es ··a:re:-tatiulat.ed · .. ··

·on Pagei'_:-B7 123<8.ru~::·B.;.l2~. .:;-~;?':+?"t~:~<-~:~:~:X::;~f: · .. ;. · ., ·~:::,:~: ·· ... B. 4.4 Closure Head: ·.The: vessel closure .head was analyZed to

determine the mean temperature of.the.head at the. end of the lOOOF/hr. heatup and cooldown _transients between

1000F and 54T>F and at· the end of the hydrostatic test transients during which the vessel is heated and .cooled· between lOOOF and 4ooop at lOOOF/hr. ·

. Results_ or the <~ne-d1mena1onal analyt1cttl nolut~.v!"l e:-:: dcscribed·.in ~>ectlon B.3.2 showed the mc;1n ·temn~:·a.t.i.Jr·r.; or the head to be 518°F at the end ot' h•?atup ar1·.; 1290 fi' at the end of cooldown •. At the end of the hydr'u heutur; and cooldown transients, the·mean temperature ur the head ts 384°F and ll6°F, respectively •.

· B.4.5 Vessel \>lall: . The procedure described in B.3.2 was .used . to perrorm the one~dtmensional analysis or the vessel-. wall in the nozzle. region and in the lower shell reg1ori for the heatup and hydro heatup transients.

Tempei•ature distributions for the. two w-all sections, presented in the form or graphs, for times during heatup and hydro heat up are on pages B-94 thru · R-9'7. U:;;lng t.hene curves, the mean temperature and lnslde and outside surface temperatures were obtained ror the times investigated. Differences between the mean temperaturr~ and t;he temperatures or the inside and outside surface:> are tabulated on Page B-104,

The procedure 1n B.3.5 was used in determining the :naxt~um allowable rate or gamma heating in the thinner sect1o.n or the vessel wall. Th1S rate was calculated by substituting 2 Sm ror 01 in the equation for thermal stress nt :x.::aa1 and sol v1ng for q0 "' • With a = o. 4 in - 1

and 2 Sm • 53,400 psi, the maximum value of q0 '" was determined to be 164~000 Btu/rt•-:hr.

B.-4.6 Bottom Head: The method 1n B.3.2 was also used to detr.rmine. tfle rnean, inside eurtace and. out:s lde surf' ace tumpet"ntureu _in the ))c.lttom head o.t tlmea during the twatufl and hydro heatup trana1ent.a. D1fl'erencn betwcr:n tho m•an tempera~ure and the temperatureo or \he 1nl1d~ and outalde eurtaces dur1ng_theae tran&1ents ar.e prencnted on Page B•l05.


·· .. :.

suppo.rta:·:( .'lbe ;~·esa~~.'·J.~ ~uppo.rted c)rr· -th~ noz-. Four_; noziles;<~-two :1nlet.and ;'two· out1e't:~:are used

the support.' arrangemen't~ ti}J.beae. ,riosz'le's•: have '::1 n t e • . pads. built ·up. on .'the:'~bottom~: sidea--·B:Dd:-'re!\tt 'on ....

SU'l)J)(l!'t Shoes·. '.rhe ·SUpport:· ShOeS: a'i-e:. at·te.·ct1ed to a. girder' which rests on a.· conci'ete ~·.foundation.

though both inlet and ·outlet nozzles are use.d for rts, the geometry of the inlet nozzle presents

case and was used for both nozzles tn .. ,.:. ·.·,.,

. . transients and steady state con11 tiona 'd'!!'"4!:

For all conditions, the back aurrace t!J held at tOOOF. This temperature represents ihP. temperature ut the bottom of the support shoe and 1:. am3umcd to be equnl to the ambient .temperature. ·

Plant Heatup - Inside aurraee ls heated f'l'>rn --1on°F to '47°F at a linear rate or 100°F/hr.

Hydro Heatup - Inside surface 1s heated rrom l00°F to 400°F at a linear rate of l00°F/Hr.

·steady State- at steady state, the temperature distribution through the nozzle wall and pad is aasurn_ed to be linear between the fluid temperature inside the nozzle and lOoPF at.the bottom of the support shoe.

Inside temperatures tor the steady states investigated are:

l. Hydro stvady state M 400°P {inlet and ou~let nozzles}.

2, ~~ero Power Steady State .. 547°F (inlet. nnd out-let nozzles}.

3. 100• Power Steady State - 555°P (inlet. nozzle only).

4. 100' Power St~ady State - · 613° · (outlet nozzle only).

Plant Cooldown .. Inside aurtace 1a cooled from·s4..,0p to l00°P at a linear rate of 100°1'/hr.- 'Ibe initial condition tor this trans1ent·is the zero power steady state d1str1but1on. ·

••

e, HYdi"' Cooldown • This transient atarte trom the bJ'dro ··•··· ... steady atate. The 1natde aurraoe la cooled rro. -~1Pp to 100°P at lOOOP/hr. The cl1atr1button at the end ~r hydro (~onldown la a.esumed to be the a&Mi aa tnat tot" tho end· ot' plant. uoolclown.


.... '.. ~ .. :., : : ' .. ' ' '

. ··. ··~· :.· .. ~:;··,.>_:, .. , ··<' ~ :··· ·:···_. :-:...~.;::~:~-{-~~? ::·/·~· ,; . \-~-~·- ,. The tn·ocodurc·· iri 8.3~3 'was~usecl_, to_":per'form. the.;·one·- ·

· d.tmfms ionaL th'ermal:··analysis:_:'for.··'plant" heatup' ·and' . · ·.· .... hydro hcatup·.- .. /:nte:]P,tartt~:cooldowr\··:t:ransieric·~was~<-':, · ·. · :: analyzc.d\ising~the· .. one·dtmimsional" analyticaL·soiuti.on ·:·described'inB~~~4~:·.·.·· ·:, · ···· · ·

. /.:::.r~mperatu~c'dist~··:~~~tl~~s:;thr~ -~h~.~:~zlc wall and· pad at tho. end. of ·plant·· heatup;. hydro heatup and plant coold.own are prP.sentod in Figure: 8 .. 76 •.. Dhtri.buti.onc;. for hydro, zc:.>ro p01.Jc:.>r":and 100'1. power steady stat.r:!.> are JH·csc:.>nted iri· Figm·c 8•77. From th<.•sc .! t:, Lr i.b·~~ ;r;:-.r; te:::lpcrot:ln·cs: of· the ·irisidc and outside• sm·CtH:es ·1'1'!

,tha.• 01('•111 lc•mpcralurl> \vf..•rn obtained. 'lbe T hl"tW(.'l'rl u·,t mt•an. t.<.•tllJli.H·aturt.' and _the temperatur6 of th .. · insio<· at\<.! IJUt!dd~ S\ll"faces· \J.i~ t.:a lculatcd • ·rht•Sf' n~su l lEi Bl'l:

JlrP~t·Tlt.l·d on Page B-106.

):h~u-r.,an, itnhct;lt.•r, and Babrov, ''Use of Numer·ical Analysis in :Tt.·ans rent 5oludon of 1'wo Dim('nsional Heat 'trans fer ProblQms with Natunll and ForcPd Convection". ASMt; T[i1JS@£;~loq~,. 1956 •

.;·.Hl•J\dams, t,.;, H., Hl?at 1'ra.nsmlssion, Thi.rd C:dition, HcGra\t. /Hill Bvok C1'~•, N~w York, 1954.

;AnLhony, l'l. !..., ''.'rempeJ~ai::ure Distributions in Stabs wi.t:h a : '·LinNU" rt•tnpt.;rature Rlse at One Surface'\ GE:nt;>ral Discussion

.'>On Jleat Tr:ansfe>r, 19.Sl. . . . . . : \t-lac kohl•t·t, 1'. H., SRl.u.>ri,ll Harmonics, 2nd Edition, t9L.6

. ::·,·.Ucstln~.:hnu~w l::quipm~nt Specifications 676245 and 676514. :~ Cu Vt·.nJLns No • .1.::·234•042. '.'.CF. Ora,d.u~~ No. 1::-234·0!•3.

f>ra,.,l.n~ No. t::·23l•-045. Dr a~" lnr. No. £·234·047. · Dra,~ln:.; No. J.::-234-049.


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/)E.TAILED ~SSULTS

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6XEPLWWHG 'HFHPEHU ··· ::::-s;::-:~:' !:·.!*:t::J · 2012-12-06 · The obJect being...

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