variable conductance heat pipe

8/7/2019 Variable Conductance Heat Pipe

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VARIABLE CONDUCTANCEHEAT PIPE

TECHNOLOGYResearch Report No. 4

DECEMBER 1973

B.D. MARCUSD.K. EDWARDSW.T . ANDERSON

Contract N o. NA S 2 - 5 5 0 3

P r e ~ a r e dfc rAMES RESEARCH CENTERAERONAUTICS AND SPACE ADMlN

Moffe t t F , e l d , Ccl i l i srn~a 73405

SVSTEM .5 GROUP


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TABLE OF CONTENTSPage

1.0 INTRODUCTTON. . . . . . . . . . . . . . . . . . . . . . . 12.0 ANALYSIS OF THE GROWTH OR COLLAPSE OF SMALL BUBBLESI N GAS LOADED HEAT PIPE ARTERIES . . . . . . . . . . . . . 33.0 ANALYSIS OF THE STABILITY OF LARGE BUBBLES I N GASLOADED HEAT P I P E ARTERIES - REPRIMING OF FAILED

A R T E R I E S . . . . . . . . . . . . . . . . . . . . . . . . . 234.0 SCALING LAWS FOR ACCELERATED LIFE TESTING. . . . . . . . . 45

4 .1 A c c e le r a ted Tes t i ng . . . . . . . . . . . . . . . . . 464.2 Phenomenological Co rros ion Model and An al ys i s . . . . 584 .3 C om pa riso n w i t h L i t e r a t u r e . . . . . . . . . . . . . 674.4 Concl u s i ons and Recommendations. . . . . . . . . . . 72

5.0 DEVELOPMENT OF A VAPOR FLOW MODULATION VARIABLECONDUCTANCEHEATPIPE. . . . . . . . . . . . . . . . . . . 745.7 Excess f l u i d Con t ro l . . . . . . . . . . . . . . . . 745.2 Vapor F low Madulat ion. . . . . . . . . . . . . . . . 765 .3 Con t r o l F lu id s and E x ten s ib le Con ta ine r s . . . . . . 795.4 Excezs F l u i d Con t ro l v s . Vapor F low Modulat ion . . . 895. 5 Des ign o f a P r o to t y pe V apor F low M odu la t i on Hea t P ipe 955 .6 F a b r i c a t i o n o f t h e P r o t o ty p e H e at P i p e . . . . . . . 1365.7 Te s t in g o f the Pro to type Heat P ipe . . . . . . . . . 1105.8 Summarq and Conclusions . . . . . . . . . . . . . . 12 4

6.0 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . 1287.0 NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . 130


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FIGURES

2-1 Danger o f Vapor-Lock Versus Dista nce Alongthe Adi ab at i c Sect icn. . . . . . . . . . . . . . . . 203-1 Ca lcu lat ed Values o f Maximum Re-Priming Load f o r anArtery Containing a Gas-Stabi l ized Vapor Bubblevs. Ar te ry Wall Thickness and Length o f th eAdiabat ic Sec t ion. . . . . . . . . . . . . . . . . . 43

. . . .4-1 Accelerated L i fe Test in g Nic kel -Water hedt Pipe. 47. . . . . . .4-2 Schematic o f Accel erate d L i f e Test Chamber 50

4-3 Gas evo lut i on i n n icke l - water heat p ip e #3 operated. . . . . . . .a t accelerated con di t i on a t 150t 3F 524-4 Gas evo lut i on i n n icke l -wate r heat p ip e # 2 operateda t a cce le ra te d co nd it io n between 250F and 280F . . 534-5 Gas evolut ion i n n ic ke l -water heat p ipes operated a taccelerated isothermal con dit i on s betkeen 135Fand 195F compared w it h t h a t o f h es t pi pe #3operated i n hea t p ipe mode a t 150F. . . . . . . . . 554-6 Gas evo lut i on i n re ference con di t i on n ic ke l -waterheat pipes operated a t 85F f o r 1150 hours and

97F beyond 1150 hours . . . . . . . . . . . . . . . 564-7 Gas evo lu t i on i n acce le ra ted cond i t i on : n i c ke l -waterheat p ipes . . . . . . . . . . . . . . . . . . . . . 594-8 Gas evo lu t ion i n acce le ra ted cond i t i on : n i c ke l -waterheat p ipes . . . . . . . . . . . . . . . . . . . . . 604-9 Gas evo lu t ion i n acce le ra ted cond i t i on : n i c ke l -waterheat p ipes . . . . . . . . . . . . . . . . . . . . . 614-1 0 Temperature dependence of gas evo l u t i o n in n i cke l -waterheat pipes . . . . . . . . . . . . . . . . . . . . . 654-11 Temperature dependence of gas gene rat ion ra t e f o rs ta in less s tee l /water heat p ipes (data f rom [13] ) . . 715-1 Schematic diagram o f excess 1i q u i d c o n t ro l l e d V a r ia b l eConductance Heat Pipes . . . . . . . . . . . . . . . 755-2 Schematic o f Excess Fl u id Con trol Systen, Amenable. . . . . . . . . . . . . . . . . . .t o 1 -g Tes t ing 77


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Page5-3 Vapor Modul at ed Heat Pip e . . . . . . . . . . . . . . . . 785-4 Model f o r D e f l e c t i o n o f B e ll o ws . . . . . . . . . . . . . 805 -5 P r e ssu re - Te m p er a tu r e R e la t i o n sh ip f o r Ex t e n s ib l eCon ta ine r Co n t ro l Us ing a Two-Phase Con t ro l F lu id . . . 865-6 Vapor Modu la t ion Heat P ipe :Schematic o f Pro to ty pe . . . . 975-7 T h r o t t l i n g Val ve - P r o t o t yp e H ea t P ip e . . . . . . . . . . . 10 05 -8 C o n t r o l F l u i d R e se r vo i r a nd Va l ve Ac t u a t o r :Pro to type Hea t P ipe . . . . . . . . . . . . . . . . . . 1025-9 Wick System -Prototy pe Heat Pip e . . . . . . . . . . . . . 10 55-10 Vapor Modula t ion Heat Pipe Components ( inc om ple te) . . . . 10 75-11 P a r t i a l l y Assembled Hea t P ipe . . . . . . . . . . . . . . 1085-1 2 P a r t i a l l y Assembled Heat P ipe . . . . . . . . . . . . . . 1085-1 3 Tes t Con f igu ra t ion and Thermocoup le Loca t ions :Pro to type Vapor F low Modu la t ion Hea t P ipe. . . . . . . 11 15-14 Pr oto typ e Vapor Flow Mod ulat io n Heat Pip eOn Test Stand. . . . . . . . . . . . . . . . . . . . . 11 25-15 Tes t 1 Resu l t s . . . . . . . . . . . . . . . . . . . . . . 11 45-16 Test 2 R e su l t s . . . . . . . . . . . . . . . . . . . . . . 1195-1 7 Opera t ing L i m i t and Tes t Range: Pro to ty pe VaporModu la t ion Hea t P ipes . . . . . . . . . . . . . . . . . 12 7


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TABLESPage

Hen ry's Constant f o r Aqueous Scl u t ions . . . . . . . . . . 5Summary o f Parameters : Numerical Examples . . . . . . . . 19Selectsd Parameters f o r Sample Ca lcu lat ion . . . . . . . . 41Actual and Predicted Gas E vo lut ion i n ReferenceCo ndit ion N icke l -Water Heat Pipe . . . . . . . . . . . 67B oi l in g Po in t o f Cont ro l F l u i d Versus Vapor PressureParam eter TI of Co nt ro l F l ~ i d .. . . . . . . . . . . . 83Vapor P ressure Parameters f o r Some F lu id s. . . . . . . . . 85Comparison Betwee-i Excess F l u i d Con tro l and VaporFlow Modulation Techniques . . . . . . . . . . . . . . 90Vol une t r ic Expans ion fo r Po ten t ia l Cont ro l F l u i ds a tAmbient. Temperatures . . . . . . . . . . . . . . . . . 91.Measured Data - Test 1 . . . . . . . . . . . . . . . . . 115Measured Data - Test 3 . . . . . . . . . . . . . . . . . 122


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1 .O INTRODUCTI O l JFor th e l a s t seve ral ye ars TRW Systems Group, under co nt ra ct

t o NASA-ARC, has performed an extensive research and developmentprogram i n va r ia b le conduc tance heat p ipe techno logy . The t reatmenthas been comprehensive, in vo lv in g th eo re t i ca l and/or exper imentals tud ies i n hy d r os ta t i c s , hyd rody namic s, hea t t r ans fe r i n to and ou t o ft h e p i p e , f l u i d s e l e c t i o n , and m a t e r i a l s c o m p a t i b i l i t y , i n a d d i t i on t ot he p r i nc ip a l s ub jec t o f v a r iab le c onductance c on t r o l t echn iques .

E f f o r t s w ere n o t l i m i t e d t o a n a l y t i c a l w ork a nd l a b o r a t o r yexper imenta t ion , bu t ex tended t o the deve lopment, fa br ic a t io n andte s t o f s pacec ra f t hardware, culm inaJ:i ng i n the s u cc ~ ss fu lf 1i g h t o fthe Ames Heat Pipe Experiment on the OAO-C s pac ec r a f t .

Most o f t he program's accompl ishments have been pre v i ou s l ydocum en ted i n a z e r ies o f r e po r t s and pub l i c a t i o ns . E a r l y t h e o r e t i c a land design developments appear i n References [I, 2, 3 4, 51. L a t e rfundamental work was pub l ish ed i n Feferences [6,7]. Hardware develop-ment and ap pl ic at io n ef f o r t s were clocumented i n References [8, 9, 101,and a computer program f o r des ignir ig and pr e d ic t i n g performance o f gasloaded heat p ipes was presented i n Reference [Ill.

Th is doc um e~ tr ep r es en ts t he f ou r th r es ea r c h r epo r t i s s uedon th is program. I t d e a l s w i t h f u r t h e r a n a l y t i c a l , exper imental anddeve lopmenta l s tud ies per t inent to var iab le conduc tance heat p ipetechno1 ogy .

The p a r t i c u l a r s t u d ie s w hi ch a r e co ve re d i n t h i s r e p o r t f a l li n t o th ree areas, as fo l lows :

1 ) An a na ly s is was per formed on the i n f l ue nc e o f th enonc ondens ib le gas on t h e ope r a t i on o f a r t e r i e s i ngas loaded heat p ipe s. Ana ly t ica l mode ls wered e r i v e d t o a) examine the degree t o which diss olv edgas i n t h e l i q u i d i rl cr ea se s t h e p r o p e n s i t y f o r n u c l e a t i o no f a gas bubb le w i t h in an a r te r y ( S ec t i on 2.0) andb ) e x p l o re th, t a b i1 ; t y o f l a r g e p r e - e x i s t i n g gasb ub bl es w i t h i n an a r t e r y ( S e c t i o n 3.0).


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2) An hn a l j t i c a l and exper imenta l s tud y was per fo rmedt o e xp lo re t h e f e a s i b i l i t y o f e s ta b l is h i n g gasg e ne ra t i on s c a l i n g l aws f o r a c c e le r a te d l i f e t e s t i n go f h ea t p i p e s . ( S e c t i o n 4 .0 ) .

3 ) A d ~ s i g ns t ~ r d ywas c a r r i e d o u t o n t h e u s e o f e x t e n s i b l ec o n t a i n e r s ( e . g . b e l l ow s , b l a d d e rs ) t o p r o v id e v a r i a b l ec onduc t anc e c o t ~ t r o lu s i n - e i t h e r t h e v ap or f l o w m o d u l a ti o no r exc es s f l u i d ?.ondenser f l o od ing t ec hn iques . A vaporf lo w m odu la t ion p r -o to type heat p ip e was fabr - i ca tedand t es t e d . (S ec t i o i i 5.0) .


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2.0 ANALYSIS OF THE GROWTH OR COLLAPSE OF SMALL B U B B LE S I NGAS LOADED HEAT PIPE ARTERIESI n h e a t p i p es c o n t a i n i n g gas i n t he co nd en se r, a r t z r i a l 1 i q u i d

a c t s a s a s o l v e n t a nd c a r r i e s d i s s o l v e d gas w i t h i t i n t o n i g h e r t em pe r-a t u r e , l o w e r 1i q u i d p r es s u re r e g i o n s . The dissolved gas may come out o fs o l u t i o n a t t h e s e h i g h e r t e m p e ra t u re s an d l o w e r p r es s u re s p e r m i t t i n g gasand va po r bu bb le s l a r g e r th a n a c e r t a i n c r i t i c a l s i z e t o g ro w. Suchg r o w th w i l l c au se a h e a t p i p e a r t e r y t o d ep ri me a nd t h e h e a t p i p e t of a i l t o c a r r y i t s de si gn lo ad .

I n w ha t f o l l o w s t h e r e i s an e xa m in a ti on o f t h e a x i a l v 2 r i a t i o no f t h e t e nd en cy f o r b ub bl es t o f o rm i n t h e b u l k o f t h e fluid f l o w in g i nt h e a d i a b a t ic s e c t i o n o f a h e a t p i p e h av in g a c i r c u l a r a r t e r y o f u r l i f or mc r os s -s e c ti o n. T he re i s f i r s t a r e vi e w c f th e la ws fur. t h e b e h a v io r a tt h e i n t e r f a c e o f i d e a l g a s - l i q u i d s o l u t i o n s , E qs . ( 2- 1 ) - ( 2 - 3 ) . Thent h e gas f r a c t i o n i n t h e e v a po r at o r v ap or i s f o un d, n o t f r o n t h e r n lo z t a t ic s ,b u t f r o m s i m p l e c o n s e r v a t i o n o f mass i n t h e s t e a d y - s t a t e , E q. ( 2 - 5 ) .T he re t h e n f o l l o w s a v e r y q u i c k r e v i e w o f f l u i d m e ch an ic s a nd t h e b u b b l eg ro w th ( o r c o l 1apse) c r i t e r i o n f o r a pre- xis t i n g b ub b l e n u c le u s . Counter-.cu r r e n t h e a t a nd mass e xch an g er a n a l ys i s i s t h e n a p p l i e d , a nd two n u me r-i c a l e xa mp le s a r e p r e se n te d a nd d i scu sse d. I t w i l l be shown t h a t t h ep re se nc r o f gas w ~ u l dca u se a g a s l va p o r b u b b l e sma l l e r t h a n t h e p u mp i n gp o r e s i z e t o g r o w , i f one were p resen t i n t h e a d ia b a t i c i e c t i o n .

The p a r t i a l p r e s su r e o f gas P i n t he rmo dyna m ic e q u i 1ib r i u m w i t h9a m i x t u r e o f l i q u i d and d i s s o lv e d gas i s d e s c ri b ed b y He n ry 's L i w f o rd i l u t e s o lu t io n s o f g as i n t h e l i q u i d ,

w+ere C i s H e n r y 's c o n st a nt , h a v in g u n i t s o f p r e s s u r e and b e i n g tem-pe ra t u re dependen t , and x i s t h e m ol ar f r a c t i o n o f t h e gas i n t h e gas-9


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1i q u i d m i x t u re .T he to ta l p ressu re P i s g i ven by Dal to n ' s Law,

where P V and P a r e t h e p a r t i a l p r e s s u r e s o f t h e v o p o r a.:d gas res-9p e c t i v e l y .Raoul t ' s Law g i ves Pv . F o r a b i na ry m i x tu re o f d i ss o l ve d gas

i n a l i q u i d ,

where PS a t i s t h e s a t u r a t i o n p r e s s ur e ( v ap o r p r e s s u r e) i n t he rm od yn am icequ i 1ib r i u m w i t h t h e p u re 1 i q u i d .

T yp i ca l v a lu e s o f H e n ry ' s c o ns t a n t f o r d i l u t e a queous s o l u t i o n sare as shown i n Table 2-1. No te the l a rg e d i f f e re nc es dependi ng uponthe gas spec ies , and no te t h a t C doub les 3oprox i rna te ly over the rangeof tem peratu res f rom 60F t o lSOF. A l a r g e v a l u e o f H e n r y ' s c o n s t a n tdenotes a r e l a t i v e l y ~ n s o lu u ! ~gas a rd v i ce ve rsa .

2.1.2 Steady-Sta ce Dynamic Condi t i o n s a t ;n In te r f ac e :T h e p r e c e e d i n ~r e i b t i o n s h o l d f or 3 s t a t i c c o nd i t i o n a t t h e

i n t e r f a c e . I n a dynamic s i t u a t i o n s uc h as e x i s t s i n a h e a t p i p e ev a-p o r a t o r i ih er e l i q u i d e v a p o ra t es a t an i n te r f ac e , and the vapo r sweepsgas away, conse rv a t i on o f spec ies d i c ta te s th a t ,

where c i s t h e m o l a r c o n c e n t r a t i o n ( d e a s i t y d i v i d e d b y m o l e c u la r w e i g h t ) , V *t h e m ale a vera ge v e l o c i t y n or ma l t o t h e i n t er f a c e& t h e d i f f u s i v i t y o f t h egas i n t h e l i q u i d o r v apor, x t h e m ole f r a c t i o n o f t h e g s p ec ie s on t h e91i q u i d s i d e, y t h e mole f r a c t i o n o n t h e v a po r s id e , and r t he coo rd i na te no rma l9


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SOLUTE

T A B L E 2 -1

HENRY ' S CONSTANT FOR AQUEOUS SOLUTIO!iS

HEN RY'S CONSTANT, ATMOSPHERES


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t o t h e i n t e r f a c e i n q u e st i on . The s u b s c r i p t 2 dcnotes t I t , r ~ h a s e .Theadove e q u a t i o n h o ld s a t a ny p a i r o f va l u e s o f r, one c.,.ue Y tl - l i q u i ds i d e f o r t h e l e f t t e r m and t h e o th e r on t h e gas s i d e . T b u s each z i d ~i sequal t o the same cons tant , namely the molar f lu x o f gas C o i l ; .j l t o t hei n t e r f a c e .

The s o l u t i o n t o Eq . ( 2 - 4 ) shows t h a t , on t h e l i q u i d s i d e ve r ynear the in te r f ac e , a boundary 1a ye r i s e s ta b l i sh e d o f e xp o n e n t i a l d ecay*th i ckness &l/vo. Th is th i ckness i s ra th e r sma l l ; fo r exdmple, f o r N2-8 2d is sc lv ed i n l i q u i d H,O a t 140F, & = 4.29 x 10 f t / s ~ c . , and f o r anL L 2e v a p o r a t i ~ r ~-a te co r respond ing t o 20.0 wa t t s / i n , v, = 0.436 x 1 0 ' ~ f t lsec; the boundary la ye r th ick ness A r i s t h en 0.0 1 2 i n ch e s . A t a d i s -tance of a few such th icknesse s removed f rom the in te r r ac e x i s con-9s t a n t a t t h e b u l k v al ue s o t h a t t h e d i f f u s i o n t e r m d ro ps . On the gass i d e y i s c o n s t a n t so t h a t t h e d i f f u s i o n te rm l i k e w i s e d ro ps . S i r c e9C vA* ; c v * , because th e moles o f s pecies are conserved,L k

where x i s now understood t o be the b u lk va lue a few boundary l aye r9th ickn e sse s f r o m th e i n t e r f a ce .The pressures under dynamic cor~dit i o n s a re then NOT g ive t l by

Eqs. (2-1 ) - ( 2 - 3 ) , when xg i s u n de r s to o d t o be t h e b u l k va l u e. Thee q ua ti on s s t i 11 hol d, of- cou rse , when tr le sub Face val ue o f xg' Xg,s i semployed. Hence,

= Xg,s * 'sat (1-x Q $ 5)and

S u b s t i t u t i n g i n t o t h e p re ce di ng r e l a t i o n y i e l d s-Xg,s'Xg - Xg,s + ' sa t ( l - x )9 s

X = ' C PSatg 9 s /x - C + P9 s a t


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Since y atid P a r e c o n s t a n t i n t h e g as p h as e9P

P = p = C x - ' s a t4 g,S !3 9s - -1 - 1 + P s a tXg C

where terms x and smd l le r have been negle c ted, compared to u n i t y .92 .1 .3 P r e s s u r e - j c t h e A r t e r y f a n A d i a 5 a t i c S e c t i o n :

L e t t k e c o n d i t i o n s a t t h e e nd o f a n e v a p o ra t o r ~ n o f h e a tp i p e a d j o i n i n g t n e b e g i il n in g o f a n a d i a b a t i c s e c t io r . ? , o ted by as u b s c r i p t e . L;t t h e d i s t a n c e down t h e a d i a b a t i c b e c t i o n ( i n t h e d i r -e c t i o n o f t h e v ap or f l o w ) be z. Then t h e p r e s s u r e i n t h e 1i v i d- i n s i d ea u n if o rm a r t e r y i s :

P, ( z ) = P + (dP,/dz) z.L ,ewhere f o r l a m i n a r f l o w i n an a r t e r y o f d ia m et er D

where li p i s l i q u i d v i s c o s i t y , Q h e a t f l o w , pi l i q u i d d e ns i t y ,and 1 l a t e n t h e a t. N ot e t h a t dP, l d z i s c o n s ta n t i n a n a d i a b a t i c s e c t i c n .The p re ss ur e P,,, i s i n t u r n r e l a t e d t o t h e t o t a l (gas p l us

vapor ) p ressu re and rad iu s o f c u r va t u re o f t h e m en is ci i n t h e w i ck ~tt h a t p o i n t .


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S in ce Pe i s e q v : t o t h e sub o f Eqs. (2 -6 ) a n d ( 2 - 7 ) , f r o m E q .( ? - l o ) , we c a n w r i t e

w he re a g a i n t e rm s o f o r d e r x have been neglected. Eq. (2-8) becomesg ,e

2.1.4 -C r i t e r i o n f o r B u b b l e G r o w t h :The c r i t i c a l b u b bl e s i z e i s r e l a t e d t o t h e s u r f ac e t e n s i o n and

the p ressure d i f fe ren ce be tween the gas -vapor m i x t u r e a n d 1iq ~ id .

S u b s t i t u t i n g Eos. (2 -1 ) -( 2- 3) , ( v a l i d f o r t he s t s t i c c on di t i m spresumed a t the bubb le ' n t e r f ac e) and Eq . ( 2 -1 2 1 i n t o ( 2 - 1 3 ) g i v e s


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Tne te rms on the r i g h t hand s id e may be id e n t i f z 3 d as f s ! lows :dP1. - (d$-) Z, t he l i q u i d p re ss ur e r i s e e f f ? i t , good.

2. - - F ) , t n e l i q u i d s u b c oo l in g e f f e c t , good.( 'sat ,e sat3. ( C - P s a t ) x t h e d i b s o l v e d g a s e f f e c t , bad.9 '4. - x P 'sz t ,e( 1 --g ,e s a t y e ) , t he e f f e c t o f d i s s o l v ed cjas on'e t o t a l p res s u re , good bu t s m a l l .

I t remains t o de termine x and T as f i i n c t i on s o f z.9

2.1 . 5 Ccunter -C ur ren t Exchanger R2l a t i o n s h i ps :A t t h e j u n c t' o n o f t h e a d i a b a t i c s e c t i o n a nd co nd en se r z = L,

t he l i q u i d i n t he a r t e r y may be s onew ha t subc3o led a t bu l k t em pera tu reTL a uld i s g a s- r i ch a t mole f r r i t i o n xg,L' The l i q u i d t hen f l ow s downt h e a r t e r y c o u n t e r - c u r r c n t t o va p or sw ee pin g up t h e a r t e r y . The l i q u i dwarms ra th er q s i ck ly due t o a s m a l l am ount o f c ondens a ti on on t he a r t e r yo u t e r s u r fa c e and i s s t r i p p e ! o f g as b y t h e c o u n t e r - f l o w i n g s tr e am o fn e a r l y p u re v ap or . The g o v e rn i n g d i f f e r e n t i a l e q u a t i o n f o r t h e b u l ktemperature is :

where m i s mass f low, c s p e c i f i c he at o f t h e l i q u i d , P p e r i m e t e r , andP kU = h = E R U (2-1 6)


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Fo r e s t a b l i s h e d l a m i n ar f l o w i n a c i r c u l a r a r t e r y Nu = 3.65 and= TD . S i m i l a r l y , t h e go ve r ni ng d i f f e r e n t l a 1 e q u at io n s f o r b u l k mo le

f r a c t i o n i n t h e l i q u i d and v ap or s tr ea ms ? r e , r e s p e c t i v e l y ,

\.:here M i s m o le c u l a r w e i g h t of t h e w or k in g f l u i d , and K i s m ass t r a n s f e rc o e f f i c i e n t .

The i n t t r f ~ i a lc o n d i t i o n s a r e d e te r mi ne d by c o n t i n u i t y o f g asf l o w a c ro s s t t i n t e r f a c e ,

and Hen ry' s and Dal to n ' s Laws

where (dk/dz) i s g iv en b y an e x p re s si o n s i m i l a r t o Eq. ( 2 -9 ) f o r la m i n a r9vapor f l ow on t he gas s i de . The mass t r an s fe r coe f f i c i e n t s a re :

9%n ~ m b ~ ro f r e a l i s t i c s i a p ! i f i c a t i a n s ca n be E G ~ C . F or n e g l i g i b l e( d P I d z ) Eq . (2-20) reduces to :9


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Henry number H i s always qui ie large for cases of in te re st .Whether H is large or cot, Eqs. ( 2 -1 9 ) and (2 -23) can be found t o resulti n :

?'B u t because H i s large and because8 .:.u. . , we have HK > > K;9 9

The r ight hand equality i s based upon neglig ible r es is t 1nce to masstransfer through tne artery wall ; i .e. , a thin porous artery wall.

An additional simplication is, because of large H , and bec~usen = m., and y = x is small,9 A 9 9

For these reasons E q . (2-18) i s of no in te re st , and Eq . (2-17)becomes

Eqs. (2-15) dn d (2-27) are i n identical form, and the solutionsare, assumi n g constant i~usselt numbers,


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where N i s t h e number o f t r a n s f e r u n i t s w i t h t h e s u b s c r i p t s h f o r h e a tt ut r a n s f e r a n d m f o r mass t r a n s f e r ,

N o t e t h a t

F or gas es d i s s o l v e d i n w a te r, t h e f o l l o w i n g v a lu e s p e r t a i n :

T A B L E 2 - 2PROPERTIES FOR DILUTE AQUEOUS

SOLUTIONS OF NITROGEN


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TABLE 2-3SCHMIDT NUMBER AT 68F

F O R SOME AQUEPIIS SOLUTIONS

Species Nh3 c12 CCIL O2 "2 2Sch mid t No. 570 834 559 558 196 613

Un for tun ate ly , Schmidt number exceeds Pr an dt l number. Forexample, a t T = 140F ScN /Pr = 39.9, and the NtU f o r h e at t r a n s fe r i s2n e a r l y f o r t y t im e s l a r g e r t h an t h e Ntu f o r mass t r a n s f e r . The e f f e c t i s

t h a t t h e r eg i on i n wh ich t h e l i q u i d i s h ea te d i s f o r t y t im es s h o r t e r i nl e n g t h th an t h e r e g i o n i n wh ic h t h e i i q u i d i s s t i - ip ps d o f g as. Hencet h e b e n e f i c i a l e f f e c t of s ub co o li ng i s l o s t b e f o r e t h e e f f e c t o f gass t r i p p i n g c a n b e f u l l y r e a l i z e d .

2 .1 .6 The M os t C r i t i c a l A x i a l P o s i t i o n :The f i n a l s o l u t i o n f o r t h e da ng er o f b u bb le g ro w th i s g i v e n by

E q . (2-14) combined w i t h Eqs. (2-28) and (2-29 ) . Le t ,

an d12 8 v L Q L C (2-34)e . sa t ,e

Then


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The quan t i t y 5 i s a meas ure o f t he danger o f bubb le g r ow th, andi t may be p l o t t e d versus z/L t o f 'n d t h e m ost c r i t i c a l a x i a l p o s i t i o n .

We have no te d t h a t Ntu,h tends t o be many t im es l a r g e r tha nN t u , m e Because o f t h i s fac t , T w i l l ra p i d l y approach Te, and, f o r zs l r f f i c i e n t l y s s a l l e r t ha n L , the te rm sse -psat 'psat ,e ) may be app ro-ximated by

M i t h th e C l aus ius -C lapeyron approx imat ionz-Ntu,h (1- L )

'se sa t ,e (2-36a)

IfNtu,h i s l a r g e e nough t h i s t er m may b e n e g l i g i b l e .I f , i n a d d i t i o n t o a l a r g e N tuYh, t h e p ar am e te r S i s s m a i l com-

pa r ed to ;,, wheret he m ost c r i t i c a l spot may be found f rom Eq. (2-35) t o be a t t h e j u n c t i o no f t h e e va p o r a t or and a d i a b a t i c s e c t i o n a t z = 0. A t t h i s l o c a t io n , u nd erthe c ond i t i o ns above , and ne g le c t i ng 1/H~,' c om par ed to un i t y , t h e r er e s u l t s

T h i s r e s a l t i s seen t o b e q u i t e s i mp l e. I t shows that the con-t r o l 1i n g f a c t o r s a r e xL , t h e f r a c t i o n o f g as p i c k e d up i n t h e c on de ns ateand the e-Ntu'm, t h e measure of t h e e f fe c t iv e n e s s o f t h e a d i a b a t i c s e c t i o nas a mass exch ang er. However, as w i l l b e se en i n S e c t i o n 2.2, t he pa r a -meter S i s l a r g e f o r cqueous s o l u ti o n s , and t h i s s l m pl e r e s u l t i s n o tp e r t i n e n t t o t h e m .


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2.1.7 The Determination of xL ard TL:The TRW GASPIPE computer program [11 ] predic ts fa i r ly accura te ly

the temperature in the condenser wall and the vapor wick interface tem-perature as a function of z and the vapor and total pressures. Hencethe molar fraction of gas y as a function of z i s known reaso nab lyaccura te ly . With somewhat 1es s accuracy the program a1 so pr ed ic ts con-densate flow rate m as a function of z.

Under the assumption that the condensate condenses in a saturateds t a t e and lo ses negl sgi ble gas by back di ffu sio n as long as the con-densation ra te i s high, one can calcu late x ( z ) from:

d ( xm) ;,- d m - &d z s a t dz - H dz

where LC is the length of the condenser and L re ta in s i t s meaning fo rnow as the length of the adiabatic section, more explici t ly La.

By the same reasonin g and negle ctin g h eat t r an s fe r t o o r fromthe condensate after i t condenses (which may or may not be jgstified,depending on the condenser wick configuration)

L+LcT - T I/m ( T ~ - T ~ ~ ~ ) ( $ ) ~ z (2-39)

L LEqs. (2-38) and (2-39) conclude the analysis in Section 2 of th i s r epor t .The results are summarized and tw o numerical examples are presented in theremainder of the section.


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2.1 . 8 Summary o f An a l y t ic a l Resu l ts :Eqs. ( 2 -35 ) t oge the r w i t h ( 2 - 36a ) des c r ibe t he bubb le g r ow th pa r a -

meter ( v er su s d i s t a n c e i n a n a d i a b a t i c s e c t i o n . Eqs. (2 -38) and (2-39 )tog eth er wi t h GASPIPE re su l ts f or Te- Tsat and y v e r s n U sz s er ve t o f i xxL and TL needed f o r Eqs. (2-3 5) and (2-36a ). I f t h e iLt er m i n Eq .(2 -35) i s la r ge , then Eq. (2-37) may ho ld . The in eq ua l i t y shown aboveE q . (2 -37) determ ines whether o r n o t cL i s l a r g e enough.

2.2 Two Nu mer ica l Examples :Consider a wa te r hea t p ipe w i t h a 2 f o o t l o n g a d i a b a t i c s e c t i o n

hav i ng an 0 .060 inc h d iam e ter pedes ta l a r t e r y . Two op er a t i ng cond i t i on sare cons idered:

2 ) l ! igh Power: = 745.4 B tu lhr , Te = 740R

The rema inin g assumed co nd i t io ns ar e taken t o be those shown i nTab1 e 6-2 and Fig ure 6-22 o f Referent: [3] .Under the assumption o f con s tan t Hc v a lues o f y L were ob ta ine d

a s i n d i c a t e d by Eq. (2-38) :

For case (1)

W h i le f o r c as e ( 2 )

( 1 . 0 2 8 ~ 1 0 - ' ) = 0 . 0 3 6 4" L = m(These resu l ts are obta ined f rom GASPIPE [I 11).

1 G- - - -- - . -.-.-- - -- -. .. - . -.. - - -- . --. .. - . - .


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Assuming a pumping pore o f 1/200 inches g iv es :se. For case (1 )

For case (2)

Henry number was n o t f ound f o r t he h ig her t empera tu res . I t i st h e r e f o re p o s s i b l e o n l y t o t i i n a t e Hs,/Hs, f o r case ( 1 ) . I n t h i s case:

The NtuYm valu e i s the^ ob t a i ned f r om Eq . (2 -31) . For case (1 )

For case (2)

The remain ing parameter i n Eq . ( 2 -3 5 ) i s r,,. From Eq. (2-34),


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For case (1 )50.4 128(.388 x 10-5 ) ( .~2786 / (32 .2 x= (RW) ( 3.14(0.060/12)~ 3

For case ( 2 )

To see whether o r n o t Eq . (2-37) i s app l ic abl e, we compute:

For case (1)

For case ( 2 )S = (1 .09)(0.0364)(2.2) (434/4.55 x lo-') = 833

Both are much larger than un i ty , and Eq. ( 2- 37 ) i s n o t a p p l ic a b l e .Table 2- 4 summarizes the above re su lt s, and Figure 2-1 shows a p l o t o fEq . (2-35).2.2.1 Discussion:

The f i gu re shows th a t the subcoo l in g e f f ec t p redomina tes thed isso lved gas e f f e c t a t 1- z/L = 0 (where the 1iq u i d condensate en te rst h e a d ia b a t i c se c t i o n ) . I n b o t h cases 6 i s n eg a t ive , wh ich i n d i ca t e stha t a bubb le the s ize o f the pumping pore would co l lap se complete ly .

I n case (1 ) t h e h e a t f l ow and re s u l t i n g ve lo c i t i e s a re sm i l l sot h a t t h e Ntu f o r bo th hea t and mass t rans fe r a re la rze . I n t h i s case


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TABL E 2-4SUHMARY OF PARAHETERS: I I IJ f1ERICAL EXAr lP LES

PARAMETER CASE 1 CASE 2


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t h e f l u i d r a p i d l y l o se s i t s su b co o li ng so t h a t 5 cl imbs and redchespos i tive v a l ! ~e s . However, t he gas s t r ip p in g proceeds ra p i a l y a1 so, andthe va lue o f 6 q u i c k l y dr op s t o t h e s m al l v a lu e a r i s i n g f r om t h e h y d ro -dynamic 1oad.

I n case ( 2) t h e s u bc oo l i ng e f f e c t i s q u i t o s t ro n g i n i t i a l l y andi s on ly gradua1:y lo s t , because the Ntu f o r heat t rans fer (and n .asst r a n s f e r more so ) i s s m al l a t t h e h i g h e r 1io;lL v e l o c i t i e s o c c~ s !o n e dby t he h i ghe r hea t l oad . As th e subcoal i s 1o: t , t.he diss olv ed gascomes i n t o p l a y , d r i v i n g ( p o s i t i v e . t he gas s t r ' , ~ p i n g e f f e c tbecomes s ign i f i can t and 5 reaches a axi in^,,,^^ or13 decreases. The maxinlltmi s seen t o be la rg e enough so th a t a bubb le appre c iab ly srnal l e r thant he pum ping po re s i z e w ou ld g row i n t he a r t e r y c aus i ng f a i 1u re .

I t i s w or th y o f n o t e t h a t c ase ( 2 ) cor responds t o on ly a 4.4%demand on the pumping c ap ac i ty o f the w ick (i,- = 4.4 x i n T ab le2-4). The p o re s i z e a c t u a l l y needed i n t h e e v a po r a to r i s t h cs o v e r 20t imes 1a rge r t han t ha t c hos en i n t he examp le . When the s i ze o f t hep o t e n t i a l l y t ro ub le so m e bu b bl e i s compared t o t h i s l a r g e s i z e , t h e e f f e c to f d i s s o l v e d g as i s se en t o b e l a r g e i n de e d.

The parameter 5 i s an i n v e r s e mea su re o f t h e s i z e o f p re -e x i s t i n g b u bb le s w hi ch w i l l grow ( 9 r c o l la p s e ) a t any p o s i t i o n a l on gt he hea t p i pe . As such, i t i s a m easu re o f t he po t en t i. ? fa: aar lc ; leat iono f va po r b u bb le s fro m p r e - e x i s t i n g gas s t a b i l i z e d n u c l e a t i o n s i t e s w i t h i nan a r t e r y . I f t h e r e a re n u c l e i p r e s e nt i n s i d e t h e a r t e r y l i q u i d , t he nvapor bubbles w i l l grow a t a n u c l e a t i o n s i t e w hen ever 6 g row s s u f f i c i e n t l vl a rg e t h a t t h e c r i t i c a l r ad iu s r = r e + 1 ) i s equal t o o r l e s s t ha nt h e s i z e o f t h e p r e - e x i s t i n g n u cl eu s .

T y p i ca l h e a t p i p e p r a c t i c e i n v o 7ves va lues o f re around 5 x l o - 'inches. However, i t i s d i f f i c u l t t o ea,imate t h e s i z e of n a t u r a l n u c l e iw hic h m ig h t e x i s t i n a h ea t p i p e a r t e r y , I f we draw f r o ~ ne x p ~ r i e n c ew i t hn u c l e at e b o i l i n g fr o m c l e a n s u rf a ce s , s uc h n u c l e i wo ul d h av e r a d ~ jon theo r de r o f inches. Then t w ou ld h ave t o r i s e t o a v a lu e o f o r d e r50 t o p romote bubb le growth . The numer ical examples then suggest thats uc h na t u ra l nuc l e i are genera.'] ly t o 1e rab le ex c ep t perhaps i n s ys temsunder very h i gh load.


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I n s p i t e o f t h e q u an ti t d t i ve u n d e r t a i n L j r e g a r d i n g c o n d i t i o n sf o r b bb b le gr ow th , t h e a n a l y s i s y i e l d s u s e f u l se m i- qu an t i t a t i v e r e s u l t s ,I t demonst rates th a t , f o r a g iv e n lo a d ( g i r e n va lu e o f r e ) , t h e r e e r i s t sa c r i t i c a l p o s i t i o n a l on g t h e p i p e ( t h e maximum i n 5 ) a t w h i ch n u c l e a t i o ni s m ost p robab le . I t a l s o a l l o w s one t o d e te r m in e t h e r e l a t i v e p r o b a -b i 1it i e s of : ~ u c l e a t io n f o r d i f f e r e n t o p e r a ti n g c o n d i t i o n s o r h e a t p i p edes igns by c om par ing t l i e r es u l t s f o r r e + 1 .

I t i s s t r e s s e d t h a t t h e t h e o ry d ev el op ed h o l d s f b r the bul!:.averages ;n the f l u i d . The center1 i n e v ? l ~ so f r p e r s i s t a t l o we rv alue; f o r a l onge r d i s t an c e f r om t he c ondense r and t hen r i s e t o h i gh - .va lues . The w a l l v a l u ~ sa r e c o n s i d e r a b ' c y d i f f e r e n t t h a , ~t h e b u l k v a l u e sa1 so. I f s i z e a b l e n u c l e i a r e p r e s e n t o n l y 011 t h o w a l l s , t h e c i . i t i c a lpos i t ' on w ould seem t o be j u s t a t t he t r an s i t i o n f ro rr l t b? c ondense r t oa d i a b a t i c s e c t i o q . But bubb les cod ld no t g row to 3 v e ry i ;ge s i z ebefo re encou nter i nc subcoe led 1i q u i d d ee pe r w i t h i n t h e . ? r t e r y .


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3.0 ANALYSIS ?F T.:T 5T;idiLITY OF 1-ARGZ BUBBLES I N GAS LOADEDHEAT PISE ARTERIES - REPRIMING OF FAILED ARTERIESA c l os e d a r t e r y h e a t p i p e i s o ne h a v in g a h i g h p e r m e a b i l i t y

l i q u i d c o n d u i t c ap ab le o f b e i ng o p er at ed a t l i q u i d p r e ss u re s l o w e r t h a ncan be s up po rt ed by a v a p o r -- l iq u id i n t e r f a c e o f t h e s i z e o f t h e a r t e r yf lo w pa th . I n i t s s im p l e s t f or m an a r t e r y i s a c y l i n d r i c a l t u b e r u n n in gin s id e t h e h e a t p i p e f r o m t h e con de nser t o t h e e va p o r a t o r . T h e a r t e r ytu be c an d e l i v e r o r r e c e i v e 1i q g id t h r o ~ g na p or ou s web t o w i c k i ~ gont he p i p e w a l l . The wa:l w i c k i n g has a l ow p e m e a b i l i t y h u t a h i g hcap i 113r y pumping ab i 1it y and s er ve s t o d i s t r i b u t e t h e 1iq u i d c i rcum-f e r e n t i a l l y o v e r t h e p ip e w a l l and t o p r o v i d e s t r o ng c a p i l l a r y s u c t i c nt o f o r ce f l o w t h r o u g h t h e con de nser w i ck i n g a nd web, a l o n g t h e a r t e r y ,an d t h ro u g h t h e e va p o r a t o r ke b a nd w i ck in g . The web an d d i s t r i b u t i o nw i c k i n g w i l l be r e f e r r e d t o as s e c on da ry o r b ac ku p w i c k i n g i n t h e r e -n a i n d e r o f t h i s r e p o r t .

S ho uld a va po r b ub bl e c n t e r t h e a r t e r y a t t h e e v a p o r a t ~ rend,f o r exam ple, t hr o ug h t h e C i s t r i b ~ f t o nweb o r t h r o u g h g r o k t h o f a g asbubble nucleated 3s a consequence of g d s i n t h e p i p c , such a bubblew i 1 1 ca u se t h e a r t e r y t o f i i 1 w i t h v ap or , i f the bubble exceeds ac r i t i c a l s i ze . The v a po r p l u g w hi ch t h e n f or ms e l i m i q a t e s l i q u i d f l o wt hr o ug h t h e h i g h p e r m e a b i l i t y a r t e r y p a t h and may cause th e evap ora tort o d r y o u t a nd t n e e va p o r a t o r t em p er at ui -e t o r u n away. It i s o f con-s i d e r a b l e e n g i n e e r in g i m po r ta n ce t o know w he th e r o r n o t t h e a r t e r y w i 11repr ime when t h ? h e a t l o a d o n t h e p i p e i s r e du ce d. I f r e p r i m i n g c c c u r s ,t h e p ip e can on ce m ore be o p e ra t e d a t h i g h h e a t l o a d s w i t h l o w e va p o r a t o rtemperature .

Exper im ents a t TRW Systems Group have shown th a t when a r t e r i e smade o f scree p ri me , a t h i n s h e a th o f l i q u i d fo rm s and r u n s a l o n g t h esc r ee n w a l l a he ad o f t h e m a in 1iqu id -vapor men iscus . When such an arterywas


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some pores must have admi t te d t he a i r . The t h i n s h e a th o f 1 i q u i d p re -v e n t e d t h e a r t e r y f r o m r e pr im i ng by t r a p ~ ' n ga i r w i t h i n i t . Only whenthe sheath was removed by b low ing ho t a i r f rom a hea t gun d i d the a r te ryrepr ime.

One can thus envis 'on the fo l l o w i ng scer :a rio fo r a gas con t ro l le r !h e a t p i p e a A h e a t p i p e a r t e r y f a i l s a t t oo h i g h a b e at l o ad by e n t r yo f vapo r th rough the evapo ra to r web o r a po re on the a r t e r y sc reen wa l l .The evapo ra to r d r i es ou t , and the evapo ra to r tempe ratu re r i s es r ap i d l y .4 senso r de tec ts the evapo ra to r tezpe ra tz re run away and grea t l y rgducesth e hea t l oad . S i nce the open a r te r y and se c~ nda ryw i c k i ~ gc c n t i n u e t odel iver some 1i q u i d even a f t e r f a i l u r e o f t h z a r t e r y , w i t h t h e power r e -dbced s u f f i c i e n t l y t h e e v a po r a t io n o f t h e r e m a in i ng 1i q u i d s u pp ly c o o l sthe evaporato r . As the evapo rator cool s, the secondary wic kin g and opena r t e r y a r e a b l e t o s u p pl y l i q u i d a t a g r e a t e r d i s t a n r e f r c m t h e co nd ens erthus hastening the coo: ing. When s u f f i c i e n t coo l ing has occur red, th eseconda ry w i ck i ng r ep r i n es comp l e te ly , and a sheath o f l i q u i d fo r c i s ove rthe a r te ry screen w a l l . The bubb le o f vapor and nonccndens ib le gzstrapped by the 1i q u i d s he a th p r ev e n t s f u r t h e r r e p r i m i o g ex c e p t as t h eqas d i f f u ses th rough the shea th o f 1i a ~ i dw e t t i n g t h e a r t e r y . d a l l .

C o u nt e ra c ti n g t h e d i f f u s i o n o f g as t hr ou gh t h e a r t e r y s h e a th i st h e e v o l u t i o n o f d i s s o i v e d gas c a r r i e d up t h e 1i q u i d - f i l l e d p o r t i o n o ft h e a r t e r y f r o m t he gas -bl ocked po r t i o n o f t he condense r. A gas-c o q t r o l 1e d h e a t p i p e , p a r t i c u l a r l y a t re du ce d h e at lo a ds , c o n t a in s a nexten s ive se c t io n o f condenser wh ich i s svbcoo led and con ta ins much gas.A sma ll amount o f t he gas i s unavo i dab ly d i sso l ved i n the condensa teand ca r r i ed up the a r t e r y i n the d i sso l ved s ta t e . Some o f the gas i sl o s t by " s t r i p p i n g " t o t h e c o u n t er - f lo w i n g v ap or s t re am i n t h e p ip e ,bu t unavo idab ly the remainder f i o w s w i t h th e l i q u i d t o t h e v i c i n i t yo f t h e vag or p l u g i n t he a r t e r y be fo re t h e l i q u i d i s d i v e r t e d f r o m thea r te ry by the p l uo i n t o the seconda ry w i ck i ng . As the 1i q u i d f lo w so v e r t h e cap o f t h e v a po r bu b bl e p lu g , gas i s t r a n s f e r r e d t o t h ebubbl e cap i n t e r fa ce and evo l ved i n t o the bubb l e .

Whether o r n o t the a r ie ry repr imes comple te ly then depends u p mwhether o r n o t gas d i f f u s e s t h r o ug h t h e a r t e r y s h ea t h f a s t e r t h a n i t i s


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sdpp l ied by the bubble cap . I n what fo l l ow s these mass t ran s f e r ra te sare formalated, and a computer program to determine whether or not af a i l e d a r t e r y w i l l r epr ime a t a g i ven reduced hea t l oad i s desc ri bed .3 .1 L i qu id F low i n the Evaporato r :3.1.1 Object ives:

I t i s d s i re d t o deve lop th e demand upon the pumping pores i m -posed b y a u n i f o r m l y d i s t r i b u t e d h e at t l u x i n an e v ap o ra t or c a n t a i n in ga f a i l e d a r t e r y . The pressure nece tsary t o su s ta in the bubb le cap i sa lso des i red . The f i r s t q u a n t it y w i l l be used to establ ish the maximuml eng th o f evapo ra tor wh i ch can be su pp li ed w i t h c ~ td ry ou t . D ry ou t o fa po r t i on o f the evapo ra to r wou ld p resum ab l ~l e a d t o d r y o u t o f t h ea r t e r y shea th as we l l and would thus l i be ra te the gas b l ock i ng the a r te r y .Then the a r te r y wou ld be f r ee to repr ime u n t i l f o r r~ i a t i ono f a ~ s wsheathagain impeded i t s progress. The maximum le ng th which can be su pp l ie dw i t h o ~ td r j ou t i s thus taken to be the maximum l eng th o f the a r te r ysheath. The second qu an t i t y , the pressure a t the bubble cap, w i l l becompared w i t h t h c s q ~ i libr ium pressure es ta b l i she d by a balance o f themass t r a ns f e r r a tes i n to and ou t o f t he bubble . I f t h i s e q u i l i b ri u rnp re ss u re i s l ow e r than th e p ressure necessary t o s us t a in the bubb le , thebubble w i l l spontaneously reduce i n s i z e and v ic e versa .

Pumping Pore Stress:T he hyd ros ta t i c cond i t i -n of the vapor bubble cap i s an eq ua l i t y

o f the p ressu re and su r face tens i on fo r ces . N i t h the assumpt ion o f ahemi sphe r i ca l i n t e r fa ce the e q~ l a lit y i s

Under cond i t ion s o f ne g l ig ib le vapor s ide p ressure d rop and zero g r ? > it y ,the pumping pore rad ius o f c urva tu re and p ip e p ressure a re re1 ated by


31/137

where P . ( 0 ) i s t he 1 i q u i d p re ssu r e a t z = 0, th e end o f t h e e v a l j r a t o rAfu r thes t removed f rom the condenser . T h e b ~ 5 b l ei s i m a g i r , ~ dt o e r i s tfrom z = 0 t o z = zb . I n t h i s p o r t io n o f t h e e va p o r a t o r a ?arc901 c1i q u i d p r es su re d i s t r i b u t i o n e x i s t s

where

The subscr ip t w r e f e r s t o t h e b acku p o r secon da ry w i ck i n g, and z, i s theevapora to r 1ength .

I n t h e p rim ed p o r t i o n o f the euapora tor , ze > z zb , a p a r a b o l i cl iq u i d p r e s su r e d istri bution a1so e x i s t s , b u t t h e p r e ssa r e g r a d ie n t s a r emuch ;ess s t e e p due t o t h e h ig h p e r m e a b i l i t y o f t h e a r t e r y ,

where


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A t the end of the condenser, assumed to be flooded, thepressure i s

where the last two terms are the adiabatic and condenser sectionpressure drops,

Eq. (3-9) serves t o f ix P, in terms of P, (o) , Q , and zb.Equating Eqs. (3-2) and (3-9) yields an expression for pumping

p o ~demand. Rearrangi ng the expression gives

where


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Since 3PWe i s gr ea te r than ;Pe. th e demand upon th e pumping por e incr ea se s' *w i t h rb*' as wel l as Q .

3.1.3 --Bubble Pressure:I t r e m a in s t o d e t e r m in e t h e b u b b le p r e ssu r e d i f f e r e n ce , P +* * gb

P v b - PV. Eqs. (3 -1 ) to (3 -3 ) combine to g ive a t z = zb

This exp res sion may be combined wi t h Eq. ( 3 -1 2 ) t o g i v e

T h i s e q u a t i o n s t a t e s t h a t Q* m us t be s u f f i c i e n t l y s m a ll so t h a t t h e opena r t e r y p um ping w i 11 exceed the pr imed f low demand,

2"-r [ I7 JP, + A%, + -1 A ] ij*a 2 cs i n c e Pb m us t be p o s i t i v e i n o r d e r t o d r i v e g as o u t o f t h e b u bb le an d

*f o r c e zb t o ze ro .3.2 T r a n s f e r t h r o u gh t h e A r t e r y She at h:

3.2.1 Mass Tr an sf er :The mass t r a n s f e r t h ro u g h t h e a r t e r y s h e at h i s 1i n e a r l y r e l a t e d

t o Pb. and a q u a n t i t a t i v e va lu e o f t h e p r o p o r t i o n a l i t y c o n s t an t i sd e si r ed . The p h y s ic a l s i t u a t i o n l e nd s i t s e l f t o an e x tr e me l y s i m p lemodel . The mass t r an s f e r res i s ta nce i n t h e va po r sp ace i s sm a l l tom -p a re d t o t h e r e s i s t a n c e t h r ou g h t h e l i q u i d sh ea th , c o t h e e n t i r e 1i q u i d


34/137

s i d e on t h e i n t e r i o r va por l i q u i d s he ath i n t e r fa c e i s v i r t u a l l y u nifo rmi n m o l e f r a c t i o n x H e n r y ' s a n d R a o u l t ' s l a w s t h e n g i v egb '

where C i s the Henry cons tant and Pvi i s t he s a tu r a t i on v apor p r es s u r ecorresponding t o the i n t e r io r temperature , wh ich Ts taken t o be i so -thermal . I n general the tempe rature Ti w i l l be v e ry s l i g h t l y l e s s t ha nthe preva i 1ing pip e vapor temperature, because o f th e sl ight subcoo lingo f t he l i q u i d nea r the bubb le cap.

From a simple mass balance i t i s c l e a r t h a t t h e mole f r a c t i o n i nthe vapor ou t s i de t he a r t e r y a t any ax i a l l oc a t i on has bu l k m ole f r a c t i o ny e qu al t o t h e b u l k m ole f r a c t i o n x o f t h e l i q u i d i r i t h e w ic k i n g a t9 9t h a t a x i a l l o c a ti o n . S in ce th e mole f r a c t i o n i n t he l i q u i d j u s t i n s i d et h e e x t e r i o r v ap or l i q u i d s he at h i n t e r f a c e ' s equal t o y d i v i ded by9Henry number H where

and s ince H i s enarmous f o r the f l u i d and noncondens ib le gas p a i rs com-m on ly used i n h e at p ip e s, t h e l i q u i d s i d e m ole f r a c t i o n o n t h e e x t e r i o ro f the sheath i s n e g l i g i b l e . Thus the ra te o f gas w i thdrawal f ram thebubble is , assuming a hemispher ical a r t e ry end cap,

where a, i s t h e a r t e r y w a l l s he at h e f f e c t i v e t h i c kn e s s an d Rsh,m i s t h er es i s tanc e o f t he s hea th t o mass t ransfer ,


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O f course, i f s a i s app r ec iab le compared t- Da , t h e us u al l o g a r i t h m i cc y l i n d r i c a l s h e l l r e l a t i o n s h i p w ou ld be used i n p r e f er e n ce t o t h e s l a br e l a t i o n above.

E q . (3-1 5 ) o f t h e p r e v i o u s s e c t i o n d e f i n e d a q u a n t i t y P b . Wenow form the same pre ssu re di f fe re n c e and emplok Eq. (3-1 8) t o o b t ai n

'he C laus ius -C lapeyron r e l a t i u n may be used t o ob ta in th e magni tude o fsP ,/ aT

3.2.2 Heat Tran sfer :A t the same t im e th a t mass i s f l o w in g t h r ough the a r t e r y s hea th

o u t o f t h e bu bb le , h e a t i s f l o w i n g t hr ou g h t h e a r t e r y s h ea th i n t o t h ebubb le . Aga in employ ing a s imple s l ab model f o r t h i n s he ath s o r t h ec y l i n d r i c a l she1 1 f o r t h i c k s he at hs

- !2 *- - 2P i n a, ( T D,L,z,, + T D, 1 2 ) ( 5 - Ti)

' ( T - T , )oin = sh ,hwhere


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* *N ot e t h a t i n t h e e v a po r at o r s e c t i o n F ( Z ~) i s zb i t s e l f , and i n t h e*a d i a b a t i c s e c t i o n F ( z b ) i s u n i t y . The o t h e r r e s i s t a n c e i s Rbc,,,

T h e q u a n t i t y x w i l l have t o be found fr om an ana ly s i s t o f o l l ow9 3"i n t h e n e x t s e c ti o n. I t i s p o s s i b l e now t o e l i m i n a t e x a n d w r i t e agemore usefu l express ion f o r mb,,

3 . 3 . 2 Heat Trans fer :

where

I n a s i m i l a r m anner, an e x p re s s i on f o r Qbc call be found

From the Co l bu r n r e l a t i o ns h i p one wou ld ex pec t t h a t

= (Sc,lPr,) 1/ 3bcINUh,bc32


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3.4.2 Heat T r a n s f e r :A t a n e q u i l i b r i u m G r q u a s i - e q u i l ib r i dm the rm al s t a t e Qbc -- Q s h '

and E q s . ( 3 -25 j and (3 -33 ) y i e l d

i n a n o n e q u i l ib r i u r n s t a t e , as t t ? e b u bb le s h r i n k s , l a t e n t h e a t i sd e l i ve r e d t o t h e sh ea th w a l l w i t h t h e r e s u l t t h a t

3 .4 .3 Eq u i l i b r iu m Excess P ressure :T he v a l ue o f Pb g i v en by Eq. ( 3 -22 ) w h i c h w ou ld e x i s t i f t h e

b u bb l e w ere i n a ll e q u i l i b r i u m c o r ~ d it i o n i s now deno t ed as t he ex c es sp res s u re Px. Eqs. ( 3 -37 ) and (3-39) t hen may be s u bs t i t u t a d t o ob t a i n

A t e q u i l i b r i u m Px he re w i l l e q u al Pb i n Eq . ( 3 -16 ) .3 .5 Gas S t r i p p in g and Heat i ng :

3 .5 .1 Ad ia ba t i c Se c t i on Mass T ra ns f er :Assume t ha t t he m o le f r ac t i on o f gas i n t h e c on de ns at e l e a v i n g

t he c ondens e r i s know n t o be xgc ' I n t w o c a l c u l a t i ons us i ng t ae G A S P I P E


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program x,, war found to be on ....; o r d er o f l o - * divided by Henry numberH ( s e c t i o n 2 . 2 ) . Thus x i s e xp ec te d t o be q u i t e sm a l l, b u t t h e p r o d u c tgcC x nay be o f P v and i s t h us q u i t e i m p o r t a n t when 2 a/ r. i s o f t h eQC asame order.

As the 1iq u i d f l o w s u p t h e e va p o r a t or some gas i s s t r i p p e d f r o mi t by the cou nte r f lo win g vapor . As remarked pre vio usl y, because o f th zl a r g e v a lu e o f H and t h e e q u a l i t y o f t h e b u l k v a lu es o f 1i q u i d a ndvapor mo le f ra c t io ns a t any ax i a l s ta t io n , the vapor may be cons ide red t obe p u re f o r p ur po se s o f c a l c u l a t i n g mass t r a n s f e r f r o m t h e 1i q u i d .E lementa ry mass exchanger theory then y ie ld s f o r the bu lk va lue o f

x (z) = x e t",m ?9 9" gc - ;.)IL,~I Q*where Ntu i s t h e n umber o f t r a n s f e r u n i t s g i ve n b y

The o v e r a l l mass t r a n s f e r c o e f f i c i e n t e f f e c t i v e p e r im e t e r p r o d u c t i;

Because Hc J9' gr ea t l y exceeds c, afit he l a s t o r " ga s- si de " t er m i s9 9n e g l i g i b l e . F o r t h i s r e as o n K,,P may be wr i t ten


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Agaln, i f 6, i s app reciable comparer to Ca , the c; Iin d r i ca: she1 1r e l a ti o n s hi p i s used for the ar tery u ia l l res is tance.3.5.2 Adiabat ic Sect ion Heat Transfer:

The l i q u i d leaves the condenser w i ti1 an i n i t i a l subcocjlingA T ~ , S . The GASPIPE program was used t c es timate th is s~bc oo l ing , andvaluc. o ? a few degrees Rankine ware found. Th is subco oii ng i s veryrap i d ly l o s t when the a r t e ry w a l i i s t h i n . The remaining subcooling i s

1-Ntv,h [!z~- Z)/L,~] -T - T -0 ) - A T t , ~ Q*where

Because o f the hig h heat transfer ics?ii!cient f o p condensation on theouts ide of the ar tery , t+e l i q u i d s ide governs the heat t ransfer, and

The same proviso regarding sa/Oa made a t ~ v ei s invqked.3.5.3 Evaporato r Sec tio n ?lax Transfer :

In the evaporator sdct lon the s!inpls Ntu re1at ionship must bemodified, because the mass f l o w v a r i z s w i t h z , as l i q u i d i s b l ed o f ftnroi lgh the webs to the evaporator. For t h i s reason th s mass f low i s


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A t any locat ion ze > z > zb i n th e l i q u i d f i l l e d s e c ti o n of t h e ev ap o ra to ra r te r y , t he c ons z r v a t i on o f gas equa t ion takes che form (n eg lec t i ng thee f f e c t o f f lo w in t o the web on KO,) shown below:

dz*

The s o l u t i on t o Eq. (3-49) i s

3.5.4 Evaporator Se ct io n Heat Tra nsfe r :By s i m i l a r r ea s on in g , t h e s u b co ol i n g i n t h e e v a p o r a t o r i s


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3.6 Adiaba t ic Sect ion Re1 at i on sh i ps:3.5.1 Objec t ives :

I t remains to set up re la t ionsh ips for pumping pore s t ress andbubble pressure, should the bubble pro je c t in to an ad iaba t ic sec t ion.These re la t ionsh ips w i l l rep lace Eqs. (3-12) and (3 -16) i n t he even tthat the bubble length does erceed the evaporator length.3.6.2 Pumpinq Pore Str es s:

Eqs . (3-1 ) and (3 -2 ) con t inue i n e f f e c t , bu t Eq. (3-3) becomes

Eq . (3-6) 1 ikewise changes form

Eq. (3-9) becomes

T h i s l a t t e r e xp re s si on t o g e th e r w i t h Eq . (3-2) gives the pumping pores t ress


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3.6.3 Bubble Pres sure :The bubble pr es s l re di f ference Pb i s g iv en by Eqs. ( 3 1 ) ( 3 -Z ),

and (3-54)

Substi t u t i ng i n Eq . ( 3- 57 ) r e s u l t s i n

3.7 C r i t i c a l Deprimed Heat Flow:3.7.1 Def ini t ion:

The c r i t i c a l depr imed hea t f l ow i s t he hea t f l ow which i ss u f f i c i e n t l y h i g h so th a t some va lue o f zb, between 0 and the v alu e whiche x i s t s j u s t a f t e r f o r m at io n o f t h e a r t e r y s he ath , g i ve s r i s e t o a b ub bl ew h i c h c an ex i s t s t ead i l y . A h igher v a lue o f Q would cause tSd c r i t i c a lb u ~ b l eto grow by i nc reas ing t he t ra ns fe r o f gas i n t o t h s bubble and byinc reas in g the l i q u i d f low pressure losses. The former inc reases Pxgi ve n by Eq. (3-4 1 ) by inc reas ing x given by Eq. (3-42) o r (3-50).The 1at ter causes Pb, given by Eq. 9'"3-1 6) o r ( 3- 59 ) t o f a11.

The cr-i t i c a l condi t ion i s t hu s d e f i ned by the re1a t i o n

3.7.2 Method o f Calc ulat i on:*The ra t i o Px/Pb i s c a l c u la ted v ersus zb f o r a t r i a l v alue o f

'*9. The quant i ty Pb i s o b ta i ne d f ro m Eq. (3-16) . Eqs. (3-42) o r (3-50)and (3-45) or (3-52 ) a re us ed ' t o ob ta i n v a lues o f x and T - Tm neededg '=fo r Eq. (3-41 ) . The c omputat ion i s s topped a t z = z, o r a t th e p o i n t


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when Eq . (3-12) fo r the pumping pore st re ss shows back up wi ck in g dryo u t . Ifth e maximtim va lue o f P,/Pb i s gr ea te r than u n i t y a s m a l l e r*va lu e o f Q i s t r l e d and v i c e v er sa .3.7.3 Sample C a ...--...-.-c , . ~ l a t i o n s :--

Sample ca l cu! a t i ons were made f o r se le c ted parameters t a b ~ la t e di n T a bl e 3 -1 . The r es u l t s a re shown graphed i n F ig u re 3 -1 . The samplec a l c u l a t i o n s c l e a r l y show t h e b e n e f i c i a l e f f e c t s o f t h i n a r t e r y h a1 1and l o n g a d i a b a t i c l e n g t h f o r a c h i ev i n g a h i g h v al ue o f c r i t i c a l d ep ri me dh e a t f l o w .

3.8 Conclusions:An a l ys i s a nd ca1 cu ;a ti on s show co n c lu s i ve l y t h a t a t h i n a r t e r y

w a l l a nd an a d i a b a t i c s e c t i o n f o r gas s t r i p p i n g a r e h i g h l y d e z i r a b l e .Even w i th such featu res , however , th e maximum heat l o ad which can bes us ta in ed du r in g r e ~ r i m i n gwas f o u nd t o b e o n l y a b ou t a t e n t h o f t h elo a d w h i ch co u ld be d e l i ve r e d b y an ope n a r t e r y . S in ce t h i s ope na r t e r y c a p a c i t y i s p re su ma bly o n l y a s ma ll f r a c t i o n o f t h e d e si g nca p a c i t y , t h e l o a d wh ich can b e su s t a in e d d u r i n g r e p r i m ing i s verysma l l indeed,

A l o a d i n e xc es s o f t h e r e p r i m i n g l o a d b u t s m a l l e r t h a n t h e o pena r t e r y c a pa c i ty w i l l n o t cause f a i l u r e o f t h e p i p e ( bu r no u t) , b u t w i l la l s o n o t a l l o w t h e a r t e r y t o r e pr im e . A p e r i o d i c d e s t r u c t i o n and r e -f or mi ng o f t h e a r t e r y s he at h w i l l o cc u r. On the ot he r hand, the absenceo f any load w i l l a l so impede p r im i ng because , d t e q u i l i b r i u m , t h ev ap or c o r e i n t h e e v a p o r a to r w i l l no t be swep t o f g as , a nd t h e r e w i l le x i s t v e ry l i t t l e d if fu s io r , p o t e n t i a l f o r t h e gas t o escape t he a r t e r y .

Thus, t h e r e s u l t s j n d i c a t e t h a t , t o p r im e an a r t e r y i n a gas-l oa d ed h e a t p i p e w h i ch co n t a in s a g as s t a b i l i ze d b u b ble, i t i s n ec es sa ryt o o p e r a te t h e h e a t p ip e a t a l o a d su f f i c i e n t t c sweep t h e gas f r o m t h ee v a po r a to r b u t b el ow t h e c r i t i c a l r e p r i m i n g v a lu e . U n f o r t u n a t e l y , t h ea r .a l ys i s d oes n o t y i e l d r a t e d a ta , and i t i s t he r ef o re n o t y e t p o ss i bl e


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TABLE3-1

SELECTEDPARAMETERSFORSAMPLECALCULATIOrl

FLUIDPROPERTIES(WATER):

LATENTHEAT

SURFACETENSION

LIQUID:

DENSITY

CONDUCT1VITY

KINEMATICVISCOSITY

SCHMIDTNUMBER

PRANDTLNUMBER

SPECIFICHEAT

HENRYCONSTANT

VAPORMOLECULARWT

GASMOIECULARWT(I~ITROGEIJ)

ARTERYCHARACTERISTICS:

INSIDEDIAMETER

AREA

PERIMETER

WALLTHICKNESS

BACK-UPWICK:

FLOWPORE

IJLUMEVOIDFRACTION

TORTUOSITY

HFG=9.90000E+02BTU/LB

ST=4.27000E-03LR/FT

RHOL=6.10000E+01LBlFT3

COfJL=3.90000E-01BTU/HRF'TF

VISL-1.40000E-02FT2/HR

SCL=6.41000E+01

PRL=2.16000E+00

CPL=1.00000E+00BTU/LBF

CATM=1.30000E+05ATNS

VWM=1.80000E+01

GWM=2.80000E+01

DAI=6.00000E-02IrdCHES

AAI=2.83000E-03SQINCilES

PA1=1.89000E-01INCHES

DELAI=8.00000E-03INCHES

DBI=1.20000E-02INCHES

VOID=8.00000E-01

TORT=3.d0000E+00


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AREA

MINPUMFINGPOREDIAMETER

TABLE3-1

SELECTEDPARAMETERSFORSAMPLECALCULATIOJ

(CONTINUED)

OPERATIIiGCONDITIONS:

EVAPORATORTEMPERATURE

VAPORPRESSURE

SUBCOOLING

MOLEFRACTOFGASINEQUILWITHCOND

ARTERYNUSSELTNUMBER

BUBBLECAPiiUSSELTNUMBER

NOMINALLOWLEVELHEATFLOW

PIPECHARACTLRISTICS:

EVAPORATORLENGTH

ADIABATICLENGTH

CONDENSERLENGTH

AGI=1.00000E-02SQINCHES

DMINI=1.20000E-02INCHES

TE=6.37600Et02DFER

PV=1.1)3700E+03LB/FT2

TSUB=1.35000E+00DEGR

YCON=2.42000E-02

AilU=3.65003E+00

BCNU=1.00003E+04

QMIN=2.46000E-~01BTU/HR

XLEI=6.00flOOE+00IIiCHES

XLAI=3.00000+00INCHES

XLCI=2.40000Et01INCHES


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-

-

-

I ADIABAT IC OPENLENGTH ARTERYPOWER

8 10 12 14 16ARTERY WALL THICKNESS ,THOUSANOTHS OF INCHES

FIGURE 3-1. Ca lcu lat ed Values o f Maximum Re-priming Load f o r an Ar te ryContaining a Gas - St ab il iz ed Vapor Bubble vs, A rte ry WallThickness and Length o f t h ? Adiabatic Section.


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t o ana ly t i ca l l y evaluate the pra ct ic al i t y o f thi s approach. Someexperimental resu?ts obtai ned a t TRW Systems Group on ammoni a-he1 iurnheat pipes have shown th at very low l ~ a d s(2-4 wat ts) for extendedperiods (16 hours) were necessary t o successful l y achie ve pr imirg .


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4.0 SCALING LAWS FOR ACCELERATED L!FE T t S T I N GW i th t he hea t p ipe r ap id l y becoming a s e r ioas des ign e lem en t i n

the s o lu t i o n o f many s pac ec r a f t t he r ma l c o n t r o l p rob lem s, t he r e ex i s t sa major impetus f o r unders tand ing the mechanisms and deve lop ing sca l in glaws fw l i f e 1 i m i t i ng p r oc es s es . A n e e d f o r a c h i e v i n g v e r y l o n g 1 i v e dh i g h r e l i a b i l i t y h e at p i p e s y st e rs i n a r a p i d l y c ha ng in g t ec hn ol og ynec es s i t a te s t he emp loym en t o f ac c e le r a ted t e s t i r ~ gtechn iques .

W i t h i n t h e r e a l m o f s g a c e c r a f t t em p er at ur e c o n t r o l d e vi c es ,p o t e n t i a l f a i l u r e p ro ce sse s i n d c r i t e r i a c an be d e f i n e d . E f f o r t s o nt h i s t a s k h a l e d i r e c t l y a dd re ssed t h e d e m on st ra ti on t h a t q u a n t i t a t i ver e 1at io ns can be es tab l ishe d between a 1if e 1 i m i t i n g p ro ce ss and s p e c i f i cm a t e r i a l s c om pa ti b i 1it y , t e s t te m pe ra tu re , a nd h e a t t r a n s p o r t r a t e .

I n c o n s i d e r i n g t h e g e ne ra l p ro b le m o f d e ve l u p i n g s c a l ing 1awsf o r a c c e l e r a t e d 1if e t e st i n g, TKd Systems def ined a broad program andapproach which inv o lv ed mu? t i c ; e mate r i a1 s sys tems, ex te ns iv e mat er i a1tes t s , and a s ev e r a l y ea r t im e phas ed e f f o r t . B ecaus e o f f und ing1i m i t a t i o n s , t h e p r e s e n t t a sk was o f r e du ce d s co pe , b u t d i d n o t o b v i a t eany o f t he c oncep ts i nc lu ded i n t he b roade r p rogr am . Ra the r , t h i s t as kr e p re s e n te d a f e a s i b i 1it y s t ud y t o d e t e rm i ne t h e e x t e n t t o w hi ch as c a l i n g l aw m i gh t be deve lo ped f o r a c c e le r at e d l i f e t e s t i n g i n a s p e c i f i cheat p ipe sys tem. I f a s uc c es s fu l s c a l i n g l a w c o u l d b e e s t a b l i s h e df o r a s p e c i f i c s y s t e m , i t m ig ht p r ov id e j u s t i f i c i i ~ i o nf o r u n d e r t a k i n gthe b r oade r p r og ram wh ich would i nc lud e a1 1 m a te r ia l s c om b inat i ons o fi n t e r e s t i n s p a c e c r a f t t h e rm a l c o n t r o l and a1 1 1if e 1i m i t i ng processes.

N i c k e l - w a t e r h e a t p i p e s w ere s e l e c t e d f o r s t u d y f o r a n u mb v o freasons: ( 1 ) i t was o f i n t e r e s t t o a c c u r a t e l y s t u d y h yd ro ge n gas e v o l u t i o nw h ic h oc cu rs d u r i n g c o r r o s i o n w i t h i r t h e h e a t p i pe , and w h ic h oc c ur s i n o t h e rm a t e r i a l s syste ms w i t h p o s s i b l e i m p o r t a n t h e a t p i p e a p p l i c a t i o n s as w e l l ;( 2 ) pas t ex pe rienc e showed t h i s c oup le e x h ib i t e d a h igh er,ough c o r r os ionr a t e t o p e r m i t e xp e ri m en t al s t u d y o f g as g e n e r a t i o n i n a re a s on a b le t i m ep e r i o d ; (3) t h e s i m p l i c i t y o f s t u d yi n g a s ystem c o n s i s t i n g o f p u r e ( un -a l lo y ed ) m a t e ri a l s; and (4 ) t h e c o m e r c i a 1 a v a i l a b i l i t y o f th e m a t e r i a ls .A c t u a l l y , N i 200 was s e le c ted bec ause f i n e s c r een was a v a i l a b l e up t o


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250 mesh, which was de si ra bl e fo r th e study of wic k degr adat ioc. However,i t was found t h a t i n ord er t o comprehensive ly examine th e more imp ort an te f fe c t o f hyd rogen evo l u t i on i n de ta i 1, w i ck deg rdda t i o r~c ou l d n o t bei n c l uded i n the program. Thus, a h i ghe r pu r i t y g rade o f n i ck e l cou1 dhave been employed, bu t t h i s was no t an im por tan t consid erat ion.

The pr imar y ob je ct iv e was t o iorraul i r te Ciii accura te sca l ing lawf o r t h e s p x i f i c exam ple o f t h e w a te r - n ic k e l h e a t p i p e w hi ch p r e d i c t sthe useable 1i f e t i m e a t r e f e r en c e ( l o w ) o p e r a t i n g c o n d i t io n s f ro m da t ataken a t acce l e ra ted (h i gh ) ope ra t i ng cond i t i ons . I t i s emphas ized th a tt h i s task was n o t concsrned w i t h ac h iev ing a water -n i cke l compati b i lit ys o l c t i o n . However, i t was necessary to ma i n ta i n su f f i c i e n t con t ro l ove rthe s ta r t i n g ma te r i a1 s and fa b r i c a t i on techni ques t o 31 l ow the separa t iono f te mp er at ur e and f l u i d c i r c u l a t i o n e f f e c t s .

Acce le ra ted Test ing :4.1 .I Heat P ipe Mater ia l s and Const ruc t ion

A t o ta l o f 16 hea t p ipes were cons t ruc ted f r om n i ck e l 200 ma te r i a l sf o r th e exper imenta l phase of t h i s ps*ogram. Conta ine rs were 17.5" i nl e n g t h w i t h 1 12 " OD and 0.035" wa l l s. Two la y er s o f 250 mesh scree nwere i n s t a l l e d and the end caps and c losur e tubes were machined from1/2" and 1 /4" d iameter rods , res pec t i v e ly . Care was t ake n t o ensuret h a t a l l t h e h e a t p i p es were a s near ly th e same as poss i b l e i n terms ofmat er i a1 s and con st ruc t io n procedures. A1 1 co nta i ners were c ons truc tedf rom n icke l 200 tube of the same heat number and the same was true o fth a screen and rods from which t he erid caps and pi nc h- of f tubes we7.econstru cted. Ef fo r t s were made du r in g weld ing t o use the same temperatureand complete the we ld i n the same l en g th o f t i me f o r each hea t pi pe .A schemat ic d iagram o f t he hea t p i pes sub j ec ted t o acce l e ra ted t es t i ngi s shown i n Figure 4-1,

I n o rd er t o remove the oxide. f i l m produced dur ing TIG weld ingon the i o te rna l su r faces o f the hea t p i pes , a1l 16 heat p ipes werebaked ou t i n vacuum f o r 2 hours and 26 minute s a t 700C and then r e-duced i n hydrogen f o r 30 mlnutes a t 732C. A tes t spec imen sub jec ted


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to t h is re du c t i on procedure showed no ox ide f i l m r e m a i n i n g o n i n t e r n a lsur faces a f t e r process in ! . A f t e r vacuum bake-out and re du c t i on i n hydro-gen , t he hea t p ipes were s to r e d w i t h p l a s t i c c aps ov e r t he f i l l cubes.The h e a t p i p es were f i l l e d w i t h 2 .0 m l o f t r i p l y d i s t i l l e d and degassedw ate r j u s t p r i o r t o t he in i t i a t i o n o f i .e st i ng . Chrome1 /a1 umel the rm o-c oup les were s po t - we lded t o t he ou ts ide o f t h e hea t p ipes and 2" l o n gw i rr wound r es i s tan c e hea te rs were i n s t a l l e d on t he ev apo r a t c r s ec t i on sp r i o r t o f i l l i n g . A er ot ub e p i p e i n s u l a t i n g m a t e r i a l was i n s t a l l e d t oa1 low fo ur d?f f e r en t c o i - dens e r l eng ths L w h ic h p e r m i t t e d o p e r a t i n gc 'w i t h d i f f e r e n t f l o w rat^ a a t th e same tempera ture and v i ce versa.4.1 .? Measurement o f Noncondensi b l e Gas Ev ol u ti on

As g as i s e v o l v e d d u r i n g o p e r a t i o n o f a h e a t p i p e , i t i s c a rr ie dt o the condenser end caus ing a b lockage and consequent temperature pro -f i l e a l on g t h e o u t e r wal: . Assun ing ide a l gas behav ior , the amount c fgas present may be ca lcu la t ed f rom the temperature pr o f i l e . I f the con-d en se r end i s d i v i d e d i n t o e q ua l i n t e r v a l s a nd t h e t e m pe r at u re a t t h ec e n t e r o f ea ch i n t e r v a l i s Ti, t h e n u nd er st e a d y - s t a t e c o n d i t i o n s t h enumber o f 1b .- mo les o f gas n i s g i v en by t h e i d e a l ga s 1avr as:

I n 4 1 , AV i s t h e voll!mr o f ea ch i n t e r v a l , Ru i s t h e gas c o n s t a n t,and

i s t h e p a r t i a l p r c ss u re o f gas a t che ce n te r o f t h e t t h i n t e r r a l . I n(4 -Z ), P,,, i s t h e t o t a l p r e ss u re ( t h e va po r p re s su r e c o rr e sp o n d in g t ot h e t e m pe ra t ur e i n t h e a d i a b a t i c s e c t i o n ) and P Y j i s t he v apo r p res s u r ei n t h e ithi n t e r v a l .

A data re du c t i on computer program was used t o de term ine thoq u a n t i t y o f g as i n a h e a t p i p e a t any g i v e n t i n e f r om t h e me asureds tead y - s ta te wa l l t em per a tu r e p r o f i l e . Th i s m ethod i s bas ed on t he


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assumpt ion t r;at th e : ~ i c k sur face tempera tu re , and hence the vapor -gas11ii : t u r e, i s v e r y c l o s e t o t h e w a l l t e mp e ra t u re i n t h e g as b l o c k e d r e g i a t lo f t h e c o vJ e n se r . T h i s s sump ti on has been found t o be va l ' t h roughc a l c u la t i o n s w i t h t t e TRW Gasp ip e Prog ra m [I11.

I n p r a c t i c e , e ach p i p e wds d i v i d e d i n t o 314" ~ l e m e n t sw i t h achrome1 -a1 crmel the rnl oco upl e p la ce d i n t h e c e n te r o f e ach i n t e r v a l . Thethermocouple tempe rature re ad i ngs were punched d i r ec t l y i n t o t il ec om pu te r p ro gra m, ~ ~ h i c ha ut om at i c a l l y c a r r i e d o u t t h e o p e ra t io n s i n -d i c a t e d b y e q u a t i o n s ( 4 - 2 ) a nd ( 4 - 1 ), a nd p r i n t e d a u t t h e t o t a l n um bero f 1 b. -m ol es o f gas i n th e p i p e . T r i a l c a l c u l a t i o n s i n d i c a t e d + h dt t h ed i sc rep ancy be tween us i ng a 0 .5" e l ement and a 1 .O" eleme nt wds l es sthan one percen t .

4.1 . 3 A c c e l e r a t e d Tes t i na Condi t i on sI t was assun led, based on p rev ious s tu d ie s o f wa te r h ea t p i p es

[12, 1 31 , t r l a t t n e gas g e n e r a t i o n r a t e wo u ld b e a s t r o n g f u n c t i o n o ft h e o p e r a t i n g (v a p o r ) t e m pe r a tu r e. F o r t h i s r e a s o n a c o n s t a n t t e v p e r a t u r e ,c o n t r o l l e d f l o w chamber, i n w hi ch a l l l i f e t e s t i n g and a c c e le r a te dt e s t i n g o f h e a t p i p e s i n t h i s p ro gr am we re c a r r i e d o u t , was d e si gn e da nd b u i l t . Tne chamb er i s shown s c h e m a t i c a l l y i n F i g u r e 4-2. A boxerf a n b lo w s a i r i n t o a h e a t i n g cha mber and t h e n t h r o u gh m i x i n g b a f f l e si n t o a p l e n u m r e g i o n . T he a i r t h e n f l o w s t h r o u g h a 2 0 0 mesh l a y e r o fsc reen an^ a 1 " t h i ck n e s s o f 1/8" c e l l h oney-gmb t o u n i f o r m l y d i s t r i b u t tand s t ra i g h t e n t h e f l o w i n t o t h e t e s t r e g io n . The t e s t r e g i o n i s co ve re dw i t h a spun gl a s s c ov e r t o e l i n l . n a t e d r a f t s f r o m t h e e n v i ro n q e n t. I na d d i t i o n , t h e e n t i r e c ha nb er i s i n s u l a t e d w i t h 1 " o f u r e t h a n e foam t of u r t h e r m - ' n i m ize e n v i r or lm e nt a l e f f e c t s . The t e m pe r at u re o f t h e a i re n t e r i n g .:he t e s t r e g i c : ~ i s m a i n ta i ne d c o n s ta n t a t 80F by m o d u l a t i n gt h e h e a t e r ( 1 i g h t b ul b s ) power t rl l' cugh a p ro po r t i o na l c on t ro l 1e r u s in ga r e f e r e n c e t h e r mo c o up l e . I n t h e c o u r s e o f t h e p r og ra m, t h e ch am be rd em on st ra te d s e t p o i n t c o n t r o l o f a p p ro x im a te l y +- 0.5OF, and was un -a f fec ted oy con~1ec t . ive a i r c ? r ~ .r e n t si n th e room. However , 1a b o r a t o r ytempera tu re changes o f -+ 3"F, w h i c h o c c u r r e d o c c a s i o n a i l y , w er e f o u n dt o r es u l t i n c h an ge s i n t h e ch am be r t c m pe r a tu f 3 e o f -t 1OF. Thus, the


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F IGURE 4 - 2 , Schematic of Accelerated L i f e Test Cha3ber.

50--.-- , , -. -


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cham ber was e f f e c t i v e i n r educ i ng am b ien t t em pe ra t ~ revar i a t i o n s , b u td i d n o t e n t i r e l y e l i m i n a t e them. The t e s t r e g i o n c o n t ai n s t h ree r ac k sa t d i f f e r e n t l e v e l s t o h o l d th e h e a t p ip es .

The acce le ra ted te s t in g phase o f t he program was begun by ope r -a t i n g t h re e hea t p i pes a t t e ! .i pe ra t u res o f app rox im a t e l y !50F, i5O9F,and 350F T h i s i n i t i a l t e s t i n g s ta ge was c a r r i e d o u t i n o r d e r t odetermine approx imate ly the t ime ar,d tem per a t l~ redependents o f t he gasg e n er a ti o n f u n c t i o n i n o r d er t o d raw u p a d e t a i l e d t e s t p l a n . Gasg e n e r a ti o n c u rv e s f o r two o f t h e se h e a t p i p es o p e r a t i n g a t deceleratedt em pe ra tl rr es o f ap p rox i ~n a t e l y150F and 250F are shown i n I-Sgures 4 - 3and 4-4. These d a ta were t ak en d u r i n g t h e i n i t i a l t e s t i n g p e r i o d o f tnsp rogram and t he t empera tu re was no t w e l l c o n t r o l l ed , as t he s c a t t e r i nt h e d a t a i n d i c a t e s . T he c u r v es a re s how n on l y t o i nd i c a t e t he s t r ongtemperature dependence. The apparent pa ra bo l i c beha v ior was no t foundw i t h n lo re ac c u ra t e da t a t ak en ? a t e r i n t ne p rogram .

Based oq :hese i n i t i a l r es u l t s , a t e s t p l an was d rawn up t ob e gi n l i f e t e s t i n g o f t h r e e r e fe r e n c e c o n d i t i o n h e a t p i pe s and f i v eac s el e ra t ed c on d i t i on hea t p i pe s he1d a t h i g h e r t em p er a tu re s . Thet h r ee r e f e r m c e c o n d i t i o n h e a t pi p es were s e t o p e r a ti n g i n t h e 80.0 +-0.5OF c ons t an t t em pera tu re c hamber i n a s l i g h t r e f l u x mode a t 85.0 +-0.5"F and 0.42 w at ts .

The f i v e a c c e l e r a t e d c o n d i t i o n h e a t p ip e s we re h e l d a t c o n s t a n ttemp eratu res o f 135"F, 150F, 1651F~180F, and 195F ( i sotherma: l y )w i t h z er o f l o w r a t e . These isothermal he, r; p i pe s were h e l d t o w i t h i n+ C.5"F o f t he in d i ca te d tempera tures by comp le te ly wrapp i f ig t he o ipes-w i t h hea t t ape and c onv e r i ng w i t h two l a y e r s o f i n s u l a t i o n . The t e n -p e r a t u r e d i f f e r e n c e b etw ee r any t w o po i n t s on a hea t p i pe was le ss [email protected]. Thus, t he f l u i d f l o w ra t e i n t he i s o t he rm a l he a t p i pes w erees s e n t i a l l y ze!.r!. T he on l y t i m e f l u i d f l o w oc c u r red wds du r i n g t heapprox imate ly one hour per iod s when the hea t p ipe s were opera ted a t100F, as heat p ipes , f o r t he purpose o f measur ing the te m pe ra t~ rep r o -f i l e s . I n o rd er t o measure t he amount o f gas genera ted by h igh tem-pe r a t u r e expos ure, t he hea t p i pes mai n t a i ned under iso thermal condi t i~ n sw ere t ak en ou t o f t he c c n s t an t tem pera t u re cham ber t em pora r i l y f o r


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II I I I I I I 1

HEAT P I P E #3

0 20 40 60 8C 100 120 140 160 180 200 220 240 260 280 300 320 346EXPOSURE T IME ( HRS . ) 7 a - 7 - 13

FIGURE 4-3. Gas evolu t ion i n nickel-water haat pipe #3operated a t accelerated condi t ion a t 150 -3OF . The step i n the curve may have resultedf r o m an unrecorded temperature increase.


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EXPOSURE T IME ( HPS . ) 7.1- 7-,I

FIGURE 4-4. Gaz evol uti on i n nickel-water hoat pipe #2operated a t acc elerated condit ion between259'F and 280F. Data scat ter i s probablydue pr i mar i ly t o v ar ia t ion i n temperature.


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removal o f t he h eat t ape dnd p laced back i n th e chamber and opera ted ash e a t p i p e s f o r t h e p ur po se o f r e c o r d i n g t h e t e m pe ra tu re p r o f i 1es . A f t e rr ec o rd i ng t he t em pera t u re p ro f i ! es , these heat p ipes were removed fromthe chamber, wrapped wi th h eat thpe again, and place d i n th e chamber f o rf u r t he r h j gh t em pera t u re ex pos u re .

Ac c e l e ra t ed t es t i ng unde r i s o t he rm a l c o n d i t i o n s was c a r r i e d o u tf o r a nvmber o f reasons. When ope ra ted as a hea t p i ?e (w i t h f l u i d f l ow )t h e g as g e ne ra te d i n a p i p e b u i l d s u p as a f u n c t io n o f t i r e and t h econsequent change i r t he t em pera t ure p r o f i l e a t t he c ondense r means t h a tt h e va po r t em p er at ur e i n t h e a d i a b a t i c s e c t i o n can be h e l d c o n st a n t o ~ l yi f t he pow er i s c on t i nu ous l y decreas ed o r m ore c ondens er l en g t h i s c on -t i n u o b s l y u nc ov er ed . The f i r s t me th od r e q u i r e s a te m p er a tu r e c o n t r o l l e rf o r each hea t p i pe f o r good ac cu rac y and a l l ow s t h e f l o w ra t e t o de -c reas e , w h i l e t he s econd w ou ld r e qu i r e a g rea t amount o f t i m e i n m ai n-tenance i f t he in su la t i on were moved by hand. I t was des i r ed t o s t udythe temperature dependence w i t h t hes e hea t p i pes , independent o f t hef l o w ra t e . Thus, i t was dec i ded t o t e s t under i s o t he rm a l c ond i t i ons( w i t h z e r o f l o w r a t e ) a n d i t was found poss ib le to ho ld the tempera turesa l m os t p rec i s e l y c ons t an t ov e r an ex t ended (1290 hou rs ) pe r i od us i ngon l y t he t empera t ure c on t r o l l e r on t he cham ber.

C on t ra r y t o ex pec t a t ions , a s t rong tempera ture dependence d idn o t a pp ea r w i t h t h e f i v e h e a t p i p e s h e l d a t a c c e l e ra t e d t e m pe ra tu re s o f135"F, 150F, 16!iF, 180F, and 195F und er is ot he rm al (z e ro f l o w r a t e )c ond i t i ons , as shown i n F i gu re 3-5. A i t h t h e s e hea t p i pes t he gene ra lb e h a v io r a pp ea rs t o be i n i t i a l ( p o s s i b l y pa r ab o l ic ) p a s s i v a t i o n , b u ta t much reduced ra te s corn~aredt o h e a t p i p e s o p e r a t e d w i t h n o n- ze rof l ow , The 150F da t a o f F i gu re 4 -3 ( hea t p i p e mode) i s r ep roduced i nF i g u r e 3-5 f o r compar ison . I + th us a p pe ar s t h a t t h e f l o w r a t e i s ani m p o r t a n t v a r i a b l e i c gas g e n e r t t i o n i n n i c k e l -w a t e r h e a t p i pe s .

The g as g e n e r a t i o n i n t h e t h r e e r e f e r e n c e co . i c ns hea t p i pesi s shown as a f u n c t i o n o f t i m e i n F i g u re 4-6. P s C! . - s ~ ?above, theamount o f gas was ca lcu la ted f rom t he tempera ture p ro !' i?e W I_n a computerp rog ram bas ed on i des 1 gas behav i o r. The s c a t t e r i n t ne da t a nayresult f ro m t h e f a c t t h a t t h e r e s b l t s o f t h e co mp ut er p ro gr am a r e q u i t e


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s e n s i t i v e t o s ma ll v a r i a t i o n s i n th e th erm oc ou ple r e a d in g s , p a r t i c u l a r l yf o r smal l amounts o f gas (1 0 x 1 0 - l o 1b. -mole range) . These he at p i peswere operated a t 85.0 -+ 0 .5 "F f o r 11 50 h o ur s, e x c e p t f o r t wo b r i e fp e r i o d s ( o f a p p r ox i m a te l y 2 h o u rs ) a t 97OF. W i t h i n t h e s c a t t e r o f t h edata , on ly a l i n e a r t ime dependence can be dssumed. q u f f i c ie n t accuracywas n o t o b ta i n e d t o d e te rm in e an i n i t i a l p e r i o d o f p a r a b o l i c p a s s i v a t i o n .A f te r 11 50 hou rs a t 85 "F , t he t em per atu re was i nc r e i s ed t o 97'F i n o r de rt o improve t he accuracy o f the gas measurements . A r a p i d i n c re a s e i ngas was no ted beyovd th i s po i n t up t o t he t o ta l 1600 hou rs ex pos u rei n d i c a t i n g a c hange i n t h e c o r r o s i o n b e h a v io r .

H av in g d e t e m i ned t h a t t h e f l o w r a t e i s an i m p o r t a n t v a r i a b l e i ngas g e n e ra t i on i n n ic k e l- w a t e r h e a t p i pe s , i n t h a t t h e gas e v o l u t i o nr a t e i s v e r y l o w w i t h z er a f l o w r a t e , b u t h i g h a t t h e same t e m pe ra tu rewhen t h e h e a t p i p e s a r e o p er a te d n o r m a ll y w i t h f l u i d f l o w , i t was decidedt o c a r r y o u t a c c t o r 3 t e d t e s t i n g w i t h c o n t r o l le d , n on -z er s f l u j d flab;.i n o r d e r t o e xa min e t p e f l o w r a t e d ep en de nce t o g e t h e r w i t h t h e t e m pe r a tu r edependence , e i g h t hea t p i pes were ope r a ted a t ac c e l e r a te d c on d i t i o ns upto 188 hou r s . The hea t p i pes emp loyed i n t h i s phase o f t he p r og ram weret h e f i v e t e s t e d p r e v i o u s l y w i t h z e ro f l o w a nd t h e t h r e e r e f e re n c e co n-d i t i o n s h e a t p i pe s ( f r o m w hi ch s u f f i c i e n t r e fe r e n c e c o n d it i o n s d a t a hadbeen c o l l ec ted ) . A l l t he s e h e a t p i p e s c o n ta i n e d o n l y a s m a l l a mou nt o fgas as a r e s u l t o f p r e v i o t is t e s t i n g . New hez t p ipes were not employedi n t h i s pha se o f t h e p ro gra m, p r i m a r i l y be cau se t h e a v a i l a b l e f u n d i n gwas n o t s u f f i c i e n t t o c o v e r t h e i n s t r u m e n t a t i o n an d p r o c e s si n g c o s t s .I t was i n i t i a l l y i n te n d ed t o o pe ra te one s e t o f f o u r h e a t p ip e s a t t h esame f l o w r a te and d i f f e r e n t t em per a tu r es and a second s e t o f f o u r a tt he same te l l~p i. ra tu r e and d i f f e r e n t f l o w r a te s . These c o n d i t i o n s cculdn o t b e met e x a c t l y i n p r a c t i c e . A f t e r e s t a b l i s h i n g th e a c ce le r at e dte s t i n g con d i t i on s fo r each heat p ipe, th e power was reduced as gas wasg en er at ed a s a f u n c t i o n o f t i m e i n o r d e r t o h o l d t h e t e mp e ra t ur e c o n s t a n tthroughout th e te s t i n g per iod . Th is was done because i t was f e l t t h a tthe temperature dependence would be s t ron ge r than th e f l ow r a t e depen-dence, as was found t o be th e case. The heat p ipes were operate d undert h e f o l l owi ng ac c e l e r a ted c on d i t i o ns , where the power l e v e ls in pa r en -


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t h e s i s a re th e i n i t i a l and f i n a l v alu es , r e s p e c t i ve l y : 177F (9.0 -8. 1 wa tts ), 163F (6.3 - 5.2 w a tt s) , 153F (6.0 - 4.9 w at ts ), 152F(6.7 - 6.1 w at ts ), 15ZF ( 5 . 7 - 5.0 w at ts ), 152F (6.4 - 5.8 wat ts ) ,152F (5 .4 - 4.4 w a tt s) , and 151F (6.0 - 5.6 w a t t s ) . Th e r e s u l t s 2 fthese measurements are shown i n Figu res 4-7, 4-8, and 4-9. I n a l l casesthe t i v e dependence appears t o be l i n e a r w i t h i n the accuracy o f thedata obta insd. Beyond 100 hours o f exposure th e da ta may be gin to be o freduced accuracy because the area exposed to the indicated temperaturebecomes redu ced as gas b u i 1ds up i n th e condenser . The resul t i ng re-duc t i on i n gas gene r a t ion as t he tem per atu re f a l l s a long t h e condenserc ou ld be t ak en in to ac c oun t by an i t e r a t i v e m e thod bu t t he acc ur ac y o fthe data does n o t appear t o warra nt such a t reatmen t. Fo r t h i s r ?as on ,the curves were drawn w i th emphasis on the i n te rv a l below !OO hc u rs o fexposure. D i sp l acements in a number o f the curves ap paren t ly resu l te dfrom unrecorded increases o r dec reases i n the temperature .4.2 Phenomenological Corrosion Model and Analysis:

Phenomenological ModelA phenom eno

variable conductance heat pipe

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