INSTABILITIES IN SUBCOOLED He II CHANNELS

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INSTABILITIES IN SUBCOOLED He II CHANNELS

A. Khalil

To cite this version:

A. Khalil. INSTABILITIES IN SUBCOOLED He II CHANNELS. Journal de Physique Colloques,

1984, 45 (C1), pp.C1-511-C1-514. �10.1051/jphyscol:19841104�. �jpa-00223572�

J O U R N A L DE PHYSIQUE

Colloque C1, supplement a u n o I , Tome 45, janvier 1984 page CI-511

I N S T A B I L I T I E S I N SUBCOOLED H e I 1 CHANNELS

A . Khalil

C a i r o U n i v d i ~ s i t y , EgypL

Resume - Les i n s t a b i l i t e s de tempPrature e t de f l u x s o n t 6 t u d i 6 e s p o u r l e s c a n x s o u s - r e f r o i d i s

a

l ' h e l i u m I 1 a y a n t un r a p p o r t & l e v 6 l o n g u e u r

s u r d i a m e t r e . Des o s c i l l a t i o n s de temperature ii basse frPquence r e s u l t a n t d ' u n c h a u f f a g e uniforme o u l o c a l s o n t anslysees sous d i f f e r e n t e s c o n d i - t i o n s de f l u x .

A b s t r a c t

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Temperature and f l o w i n s t a b i l i t i e s a r e s t u d i e d i n subcooled h e l i u m I 1 channels o f l a r g e l e n g t h t o d i a m e t e r r a t i o . Low f r e q u e n c y tem-

p e r a t u r e o s c i l l a t i o n s a r i s i n g f r o m u n i f o r m o r l o c a l h e a t i n g a r e analysed a t d i f f e r e n t f l o w c o n d i t i o n s .

The i n v e s t i g a t i o n o f temnerature and f l o w i n s t a b i l i t i e s i n l i q u i d h e l i u m i s impor- t a n t f r o m t h e p o i n t o f v i e w o f t r a n s i e n t o r steady s t a t e suoerconducting maqnet s t a - b i l i z a t i o n . These i n s t a b i l i t i e s o r p e r i o d i c temperature e x c u r s i o n s occure a t c e r t a i n combinations o f geometry, f l o w c o n d i t i o n s and h e a t f l u x . A l t h o u g h s e v e r a l s t u d i e s have been r e p o r t e d on f o r c e d f l o w h e l i u m I i n s t a b i l i t i e s i n c l u d i n g s u p e r c r i t i c a l h e l i u m /1,2/ and two-phase h e l i u m / 3 , 4 / , l e s s e f f o r t has been d i r e c t e d t o t h e s t u d y o f p o s s i b l e i n s t a b i l i t i e s i n h e l i u m I 1 l o o p s . G e n t i l e and F r a n c o i s / 5 / r e p o r t e d tem-

p e r a t u r e f l u c t u a t i o n s o f a few rnK and f r e q u e n c i e s o f 0.01 t o s e v e r a l Hz i n a c l o s e d s a t u r a t e d He I 1 G o r t e r - M e l l i n k d u c t heated a t one end.

I n t h e p r e s e n t work, c o n d i t i o n s l e a d i n g t o p e r s i s t a n t p e r i o d i c l o w f r e q u e n c y tempe- r a t u r e e x c u r s i o n s a r e s t u d i e d i n subcooled He I 1 channels o f l a r q e l e n g t h t o diame- t e r r a t i o w i t h and w i t h o u t n e t f l o w . Heat i s a p p l i e d u n i f o r r n e l y a l o n g t h e whole channel l e n g t h o r a t a l o c a l s p o t t o s i m u l a t e a l o c a l d i s t u r b a n c e h e a t i n g up t h e su- p e r c o n d u c t o r .

To s i m u l a t e l o n g and narrow channels, two t e s t s e c t i o n s a r e made o f s t a i n l e s s s t e e l tubes 210 cm l o n g w i t h i n s i d e d i a m e t e r s o f .079 and 0.12 cm. Each o f t h e t e s t sec- t i o n s i s i n s t r u m e n t e d w i t h a l o c a l copper b l o c k h e a t e r i n t h e m i d d l e o f t h e channel and a u n i f o r m h e a t e r e x t e n d i n g o v e r a l e n g t h o f 200 cm. The t e s t s e c t i o n s a r e wound i n t o a 3 cm d i a m e t e r c o i l and surrounded by a h i g h vacuum can. L i q u i d h e l i u m a t 0.11 MPa i s subcooled t o 1.8 t o 2 K by passing t h r o u g h a h e a t exchanger immersed i n a s a t u r a t e d He I 1 b a t h /6/. Both ends o f t h e t e s t s e c t i o n a r e h e a t sunk t o t h e s a t u - r a t e d He I 1 bath. Temperature i s measured a t f i v e l o c a t i o n s a l o n g t h e channel u s i n g .carbon r e s i s t a n c e thermometers. The measurements a r e c a r r i e d o u t a t b o t h steady

s t a t e and t r a n s i e n t c o n d i t i o n s ( w i t h a s t e p power h e a t i n p u t ) a t n e t f l o w r a t e s of 0 t o .04 g/sec.

I

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UNIFORY HEATINS CONDITIONS

When t h e He I 1 channel i s heated u n i f o r m l y , l o w f r e q u e n c y temperature f l u c t u a t i o n s d e v e l o p when t h e temperature i n t h e m i d d l e (TG) approaches t h e lamda temperature.

When Tb'< Ti, t h e h e a t t r a n s f e r process i s governed b y mutual f r i c t i o n i n b o t h t h e a x i a l and r a d i a l d i r e c t i o n s , and a s m a l l t e m p e r a t u r e g r a d i e n t develops a l o n g t h e channel w i t h t h e maximum t e m p e r a t u r e o c c u r i n g a t t h e m i d plane. As t h e steady h e a t i n p u t i s s l o w l y i n c r e a s e d t o Qo a t which Tb- approaches Tx ( F i g . l ) , a t h i n He I . l a y e r forms a l o n g t h e channel w a l l . The t h i c k n e s s ( 6 ) o f such l a y e r v a r i e s f r o m a maximum a t p o i n t b ' t o z e r o a t t h e ends of t h e channel. As t h e h e a t f l u x i s i n c r e a s e d 5 i n c r e a s e s and t h e f r e e c o n v e c t i o n h e a t t r a n s f e r i n t h e He I l a y e r changes t o sub- c o o l e d n u c l e a t e b o i l i n g as bubbles n u c l e a t e a t t h e s u r f a c e and r i s e v e r t i c a l l y u n t i l t h e y c o l l a n s e i n t h e subcooled l a y e r o r r e a c h t h e channel e x i t . Temperature o s c i l l a -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841104

CI-512 JOURNAL DE PHYSIQUE

t i o n s may t h e n d e v e l o p a t p o i n t a*, a l t h o u q h t h e steady b u l k t e m p e r a t u r e i s s t i l l below T

.

The He I l a y e r keeps on i n c r e a s i n g , u n t i l a t a c e r t a i n c r i t i c a l h e a t f l u x , t h e whoie c r o s s s e c t i o n a t p o i n t b, i s f i l l e d w i t h He I . As t h e s u r f a c e h e a t f l u x i s f u r t h e r i n c r e a s e d t h e subcooled He I zone propaqates up and downstreams o f p o i n t

6

and i t s average temperature i n c r e a s e s u n t i l t h e s a t u r a t i o n temperature (4.3 K) i s reached. Then, two-phase s a t u r a t e d b o i l i n g s t a r t s and c o n t i n u e s u n t i l complete d r y - o u t .

F i g . 1

-

D i f f e r e n t h e a t t r a n s f e r r e - gimes i n a u n i f o r m l y heated He I 1 channel.

F i g . 2

-

Steady s t a t e t e m p e r a t u r e p r o - f i l e s as a f u n c t i o n o f u n i f o r m h e a t i n p u t . S i n c e t h e e x p e r i m e n t a l d a t a f o r t e s t s e c t i o n s I and I 1 a r e q u a l i t a t i v e l y s i m i l a r i n most aspects, t h e f o l l o w i n g d i s c u s s i o n w i l l be focussed on some o f t h e t e s t s p e r - formed on t e s t s e c t i o n I (d = .079 cm and 1 = 220 cm).

F i g u r e 2 shows t h e i n c r e a s e o f T3 and T a s a f u n c t i o n o f t h e a p p l i e d u n i f o r m h e a t f l u x Q a t z e r o f l o w and w i t h n e t f l o w 08 .014 and .03 g/sec ( c o r r e s p o n d i n g t o v e l o c i t i e s o f 19.8 and 42 cm/sec). A t z e r o n e t f l o w c o n d i t i o n s , a sharp temperature r i s e occures c l o s e t o Ti caused b y t h e f o r m a t i o n o f a t h i n He I l a y e r . T h i s second o r d e r phase t r a n s i t i o n i s u s u a l l y s h a r p and smooth i f t h e h e a t f l u x i s i n c r e a s e d s l o w l y . Otherwise, l a r g e amp1 i t u d e p e r s i s t i n g t e m p e r a t u r e f l u c t u a t i o n s c o u l d develop.

The t e m p e r a t u r e a t p o i n t s 2 and 4 shows l o w f r e q u e n c y f l u c t u a t i o n s ( - - 5 Hz) even when t h e b u l k t e m p e r a t u r e i s l e s s t h a n

Ti.

The u n s t a b l e zone f o r T 4 , i s enclosed between i c ( c o r r e s p o n d i n g t o t h e b u l k t e m p e r a t u r e ) and i d as shown i n F i g . 2 a t z e r o f l o w . As t h e mass f l o w r a t e i s i n c r e a s e d f r o m 0 t o .014 g/sec., T3 i s r e p r e s e n t e d by t h e l i n e 0 j k f o l l o w e d by an u n s t a b l e zone o f slow temperature e x c u r s i o n s . Be- cause, a t l o w v e l o c i t i e s t h e He I l a y e r i s u n s t a b l e when s u b j e c t e d t o s m a l l f l o w and h e a t f l u x p e r t u r b a t i o n s . However, t h i s u n s t a b l e zones c o m p l e t e l y d i s a p p e a r as t h e mass f l o w i s f u r t h e r i n c r e a s e d t o .03 g/sec o r h i g h e r . T h e h i g h v e l o c i t i e s r e s u l t i n a. t h i n n e r and s t a b l e He I l a y e r and b e t t e r t u r b u l e n t m i x i n g i n t h e r a d i a l and a x i a l d i r e c t i o n s .

The b e h a v i o u r o f t e s t s e c t i o n I 1 ( d = . 1 2 cm) i s s i m i l a r i n most aspects, except f o r the,end temperatures w h i c h showed no o s c i a l l a t i o n s below T T h i s i s due t o t h e r e - l a t i v e l y l a r q e r d i a m e t e r compared t o t h e b u b b l e d e p a r t u r e Aiameter. I n t h i s case a l l bubbles formed a t t h e m i d d l e o f t h e channel c o l l a p s e i n subcooled He I 1 b e f o r e r e a c h i n g t h e end p o i n t s .

The t r a n s i e n t t e m p e r a t u r e p r o f i l e s f o r T3 and T a t t h e a p p l i c a t i o n o f a s t e p h e a t i n p u t i s i l l u s t r a t e d i n F i g . 3. The t r a n s i t i o n f r o m He I 1 t o He I i s accompanied b y p e r s i s t i n g o s c i l l a t i o n s which decrease i n a m p l i t u d e as t h e s a t u r a t i o n temperature

( T ) i s anproached. I n d u c i n q a n e t f l o w lo\.rers t h e averaqe temperature a t p o i n t 3, buz a t t h e same t i m e slow f l o w and t e m p e r a t u r e e x c u r s i o n s develops due t o t h e sudden h e a t f l u x p e r t u r b a t i o n . The same c o n c l u s i o n a p p l i e s a l s o t o t h e temperature t r a c e s a t channel ends.

Tb

-

^{1.87 K}

6=.079 cm

time , S

O b l b

2b 30

^O;

50

^{6b 70}

F i g . 3

-

T r a n s i e n t temperature response t o a s t e p u n i f o r m h e a t i n p u t .

I 1

-

LOCAL HEATING CONDITIONS

When t h e He I 1 channel i s heated l o c a l l y a t p o i n t 3, one dimensional S . X . h e a t t r a n s - p o r t develops u n t i l a c r i t i c a l h e a t f l u x i s reached when T3 approaches

TA.

The h e a t t r a n s p o r t i n subcooled He I1 open channels has been i n v e s t i g a t e d by G e n t i l e / 7 / and L o t t i n /8/. However, t h e w i d t h o f t h e channels used i n t h e i r i n v e s t i g a t i o n s was n o t s m a l l enough t o r e s t r i c t b u b b l e c i r c u l a t i o n o r cause severe o s c i l l a t i o n s upstream and downstream of t h e l o c a l h e a t e r .

F o r t e s t s e c t i o n 11, no o s c i l l a t i o n s a r e observed i n T p and T4 f o r heat f l u x e s as h i g h as t h e c r i t i c a l h e a t f l u x , and t h i s confirms t h e r e s u l t s r e p o r t e d e a r l i e r /6/

f o r t h e same channel s i z e . On t h e o t h e r hand, t h e steady s t a t e temperature p r o f i l e s o f T2 and T showed l a r g e a m p l i t u d e i n s t a b i l i t i e s i n t e s t s e c t i o n I as i l l u s t r a t e d i n F i g . 4. f h e s e i n s t a b i l i t i e s d e v e l o p because t h e channel r a d i u s i s c l o s e t o t h e b u b b l e d e p a r t u r e d i a m e t e r . As t h e f l o w v e l o c i t y i s increased, an u n s t a b l e two-phase s i t u a t i o n r e s u l t s when t h e channel c r o s s s e c t i o n i s f i l l e d b y a l t e r n a t i n g vapor p l u q s .

CONCLUSION

The p r e s e n t s t u d y demonstrates t h e i n f l u e n c e of f l o w , h e a t i n p u t and g e o m e t r i c a l con- d i t i o n s on t h e c r e a t i o n o f thermal and hydrodynamic i n s t a b i l i t i e s i n open subcooled

JOURNAL DE PHYSIQUE

time , S

F i q . 4

-

Temperature i n s t a b i l i t i e s r e s u l t i n g f r o m l o c a l h e a t i n g .

He I 1 channels. Such t r i p l e o r two-ohase o s c i l l a t i o n s c o u l d be p e r s i s t a n t i n l o n g channels w i t h d i a m e t e r s c l o s e t o b u b b l e d e p a r t u r e d i a m e t e r a t z e r o o r l o w f l o w ve- l o c i t i e s . Under s t e a d y s t a t e u n i f o r m h e a t d e p o s i t i o n , v e l o c i t i e s h i g h e r t h a n 40 cm/s and s u b c o o l i n g below 1.8 K t e n d t o e l i m i n a t e t h e t r i p l e p h a s e o s c i l l a t i o n s and s t a b i l i z e t h e f l o w .

ACKNOWLEDGEMENTS

T h i s work was c a r r i e d o u t a t t h e U n i v e r s i t y o f Wisconsin-Yadison w i t h t h e s u p p o r t o f t h e Wisconsin E l e c t r i c U t i l i t i e s .

REFERENCES

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1 ) Daney, D.E., L u d t k e , P.R., and Jones, M . C . , J. Heat t r a n s f e r 101 ( I ) (1979) 9 .

2 )

H o f f e r , J.K., and Dean, J.W., ASME paper 77-14T-76 (1977)

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3 ) K h a l i l , A., i n "Heat and Mass F l u i d F l o w i n Power Systems Components", A. R i z k , Perqamon Press. ( 1 9 7 9 ) , 157.

4 ) Matsubara, Y., Sugawara, A., and Yasukochi, K., Adv. Cryogenic Eng. 25 (1980) 521.

5 ) G e n t i l e , D., and E r a n c o i s , V . , Adv. Cryogenic Eng. 27 (1982) 467.

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6 ) K h a l i l , A . , and Van S c i v e r , S.W., Proc. ICEC 9, Kobe, Japan ( 1 9 8 2 ) , 273.

7 ) G e n t i l e , D . , and F r a n c ~ i s ~ M . X . , Cryogenics 21 (1981) 234.

8 ) L o t t i n , J.C., and Van S c i v e r , S.bl., Proc. I C E 9 , Kobe, Japan ( 1 9 8 2 ) , 269.