STABILITY STUDIES OF CABLED CONDUCTORS IN He I AND He II

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STABILITY STUDIES OF CABLED CONDUCTORS IN He I AND He II

S. van Sciver, K. Stocker

To cite this version:

S. van Sciver, K. Stocker. STABILITY STUDIES OF CABLED CONDUCTORS IN He I AND He II. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-519-C1-524. �10.1051/jphyscol:19841106�.

�jpa-00223574�

JOURNAL DE PHYSIQUE

Colloque C l , supplbment a u no 1, Tome 45, janvier 1984 page CI-519

S T A B I L I T Y STUDIES OF CABLED CONDUCTORS I N He I AND He I 1 S.W. Van S c i v e r and K. Stocker

Applied Superconductivity Center, University of Glisconsin-Madison, Madison, Wisconsin 53706, U . S. A.

Resume

-

Des experiences o n t

e t e

e f f e c t u e e s pour e t u d i e r l e s p r i n c i p e s m u e s q u i gouvernent 1 a s t a b i 1 i t e de supraconducteurs composites c 9 b l e s r e f r o i d i s p a r un b a i n He1 ou H e I I .

A b s t r a c t

-

Experiments have been performed t o study t h e p h y s i c a l p r i n c i p a l s governing t h e s t a b i l i t y o f c a b l e d composite superconductors c o o l e d by pool b o i l i n g He I and He 11.

There i s c o n s i d e r a b l e i n t e r e s t i n c a b l e d composite superconductors f o r a p p l i c a t i o n s which r e q u i r e t i m e v a r y i n g magnetic f i e l d s . A few examples o f these i n c l u d e magnets f o r f u s i o n p a r t i c u l a r l y i n t h e Tokamak c o n f i g u r a t i o n and h i g h energy p h y s i c s

d i p o l es.

The s t a b i l i t y o f cabled conductors i s n o t w e l l e s t a b l i s h e d . For f u l l y s t a b l e magnetic systems t h e l i m i t s a r e determined p r i m a r i l y by t r a n s i e n t and steady s t a t e h e a t t r a n s f e r between t h e conductor and bath. One i m p o r t a n t parameter which i s n o t w e l l known i s t h e e q u i v a l e n t c o o l e d p e r i m e t e r f o r a s u r f a c e t h a t c o n s i s t s o f a r e g u l a r bundle o f w i r e s r a t h e r than an i d e a l plane o f known o r i e n t a t i o n / I / . I n an attempt t o answer these questions, t h e p r e s e n t study has c o n c e n t r a t e d on measurements o f heat t r a n s f e r and s t a b i l i t y o f model cab1 e c o n f i g u r a t i o n s . The goals o f t h i s i n v e s t i g a t i o n have been two-fold. F i r s t , t o determine heat t r a n s f e r l i m i t s f o r cables o r bundles which have predominantly c y l i n d r i c a l geometries. Sec- ond, t o use these heat t r a n s f e r l i m i t s t o understand t h e performance o f c a b l e d com- p o s i t e superconductors. I n b o t h cases these measurements a r e c a r r i e d o u t i n He I a t 4.2 K and He 11. P r e l i m i n a r y r e s u l t s o f t h i s work have been r e p o r t e d p r e v i o u s l y /2/.

HEAT TRANSFER STUDIES

The experimental model adopted t o i n v e s t i g a t e t h e heat t r a n s f e r i s a bundle o f seven s t a i n l e s s s t e e l tubes o f diameter 1.25

w

and w a l l t h i c k n e s s 0.15 mm. Several o f t h e tubes w i t h i n each bundle are instrumented w i t h Au(Fe)-chrome1 thermocouples so t h a t t h e i n n e r s u r f a c e temperature can be measured. The tubes a r e heated by passing a D.C. c u r r e n t . Using t h i s c o n f i g u r a t i o n s u r f a c e heat t r a n s f e r c h a r a c t e r i s t i c s can be determined p r o v i d e d t h e temperature drop t h r o u g h t h e s t a i n l e s s s t e e l i s t a k e n i n t o account.

One o f t h e p r i n c i p a l q u e s t i o n s p e r t a i n i n g t o t h i s c o n f i g u r a t i o n i s an e s t i m a t e o f t h e e f f e c t i v e cooled perimeter, P. T h i s q u a n t i t y i s s t r o n g l y a f f e c t e d by geomet- r i c a l c o n s t r a i n t s such as number and diameter o f wires. Since t h e r e i s no u n i v e r - s a l l y accepted approach t o t h i s question, we have somewhat a r b i t r a r i l y chosen t h e c o o l e d p e r i m e t e r t o be a 1 i n e enci r c l i n g t h e e n t i r e bundle. Thus a seven w i r e bundle has a c o o l e d p e r i m e t e r o f 3n$ where $ i s t h e i n d i v i d u a l w i r e diameter.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841106

C 1-520 JOURNAL DE _PHYSIQUE

I n the heat t r a n s f e r experiments, a number o f f a c t o r s a f f e c t the measured tempera- t u r e d i f f e r e n c e and c r i t i c a l heat fluxes. These f a c t o r s include:

1 ) Tube o s i t i o n I n general the heat t r a n s f e r i s best f o r t h e tube a t t h e t o p of the h r s t f o r t h a t i n t h e center. This e f f e c t manifests i t s e l f i n both t h e c r i t i c a l heat f l u x and f i l m b o i l i n g heat t r a n s f e r c o e f f i c i e n t .

2) Spacing between tubes. Heat t r a n s f e r improves when helium i s allowed t o v e n t i l a t e between i n d i v i d u a l components o f the bundle.

3) Bath temperature. The peak heat f l u x e s increase w i t h decreasing b a t h

temperature. This e f f e c t i s i n p a r t due t o the bath being subcooled t o 1 atm (100 KPa) but i s most pronounced i n t h e He I 1 range.

4) Heater ramp rate. The peak heat f l u x increases w i t h the c u r r e n t ramp r a t e because the subcool ed h e l ium bath temperature r i s e s as t h e heat i s appl ied. Thi s e f f e c t i s l a r g e s t i n the He I 1 heat t r a n s f e r r e s u l t s where the e n t i r e bath can be affected.

For t h e case o f He I, extensive measurements o f the heat t r a n s f e r curve f o r t h e seven tube bundle have been c a r r i e d out /3/. I n t h i s study t h e parameters which were v a r i e d i n c l u d e gap between bundle components and bath temperature. For a composite superconductor, t h e r e would be no s i z a b l e gap between components. Further because o f h i g h c o n d u c t i v i t y metals present, the heat t r a n s f e r t o t h e center conduc- t o r could be i n p a r t c o n t r o l l e d by heat conduction t o adjacent components. For ous measurements, the peak heat f l u x t o these r y d e l bundles varied from about 0.3 W/cm f o r t h e center conductor t o c l o s e t o 1 W/cm f o r those on t h e outside.

Heat t r a n s f e r t o subcooled He I 1 has considerably d i f f e r e n t behavior. I n p a r t i c u l a r , the peak heat f l u x i s c o n t r o l l e d by a conduction mechanism and t h e temperature d i f f e r e n c e between the bath and the He 11-He I phase t r a n s i t i o n , (TA

-

Tb).

Because o f t h i s f a c t , heat t r a n s f e r i s l i m i t e d by t h e helium cross s e c t i o n a l area. This problem has been s t u d i e d e x t e n s i v e l y f o r one dimensional channels where f o r p r a c t i c a l systems heat flow obeys t h e Gorter-Mellink r e l a t i o n /4/

where f (T) i s a temperature dependent f u n c t i o n w i t h a minimum around 1.9 K.

The peak heat f l u x i n He I 1 i s obtained by i n t e g r a t i o n o f (1) between t h e bath temperature and Th. I n c y l i n d r i c a l coordinates t h i s r e l a t i o n takes t h e form

where r i s the r a d i u s of the c y l i n d r i c a l heater surface and qo* i s the surface heat f l u x . P f f o r t s t o c o r r e l a t e experimental peak heat f l u x e s i n He I 1 w i t h ( 2 ) have n o t been e n t i r e l y successful. I n p a r t i c u l a r t h e r a t i o of the experimental t o

t h e o r e t i c a l value (qex */qth*) i s always l e s s than u n i t y w i t h t h e d e v i a t i o n i n c r e a s i n g w i t h decreaeing radius /5/.

Measurements o f the normalized peak heat f l u x i n He I 1 q0(r0/2)1/3 f o r several c y l i n d r i c a l t e s t sections are shown i n Fig. 1. A1 so p l o t t e d i s t h e temperature dependent heat c o n d u c t i v i t y f u n c t i o n Z(Tb). The seven tube bundle i s assumed t o have an e f f e c t i v e diameter +eff o f 3.75 mm. The other two sets o f r e s u l t s are f o r a s i n g l e tube

+

⁼ 1.25 mn and a previous experiment on a v e r t i c a l l y o r i e n t e d cyl i n d r i - cal copper sample,

+

⁼ 12.7 mm. The f i r s t c h a r a c t e r i s t i c t o note i s t h a t t h e experimental data a l l f a l l below t h e expected c o r r e l a t i o n based on (2). Further, t h e d e v i a t i o n increases w i t h decreasing e f f e c t i v e diameter. One apparent discrep- ancy i n these r e s u l t s i s f o r the s i n g l e tube where higher than expected peak heat f l u x e s occur. This dependence i s most probably brought on by t h e s e n s i t i v i t y o f c r i t i c a l heat f l u x t o t h e rat'e a t which the c u r r e n t i s ramped. However, i t should be p o s s i b l e t o p r e d i c t t h e maximum heat t r a n s f e r r a t e i n c o n f i g u r a t i o n s dominated by c y l i n d r i c a l geometry by combining ( 2 ) w i t h an empirical adjustment f o r the d e v i a t i o n i n cyl i n d r i c a l geometry.

STABILITY MEASUREMENTS

The t e s t c o n f i g u r a t i o n f o r the s t a b i l i t y measurements c o n s i s t s o f a seven w i r e cable. The s i x outer wires are u n i n s u l a t e d copper-NbTi composites w i t h t h e core

.

+=12.7rnrn

., +

* 1.25 rnm

1

Fig. 1. Normalized peak heat f l u x i n He I 1 f o r c y l i n d r i c a l geometries.

being a r e s i s t i v e heater. C h a r a c t e r i s t i c s o f t h e two cables t e s t e d a r e given i n Table I.

Table I. C h a r a c t e r i s t i c s of cab1 ed conductor sections.

Sample I Sample I 1

Conductor 6 x 0.25 mm 6 x 0.51 mm

Cu:NbTi r a t i o 5 4

Core 0.25 mn Manganin 0.50 mn SS

I (5 T, 4.2 K ) 90 A 296 A

R ~ R Stabi 1 i zer 80

- -

Length (mn) 663 622

I n a d d i t i o n t o the core heater, sample I i s instrumented w i t h a l o c a l heater 12 mm l o n g which a l s o i n s u l a t e s the conductor from the helium bath.

Each t e s t s e c t i o n i s i n d u c t i v e l y wound i n a grooved phenolic c o i l form which allows approximately 50% o f the conductor surface t o be cooled by the he1 ium. This provides a cooled perimeter P o f 1.2 nun and 2.4 mn f o r samples I and I 1 respec- t i v e l y . Normalization of the conductor i s achieved by e i t h e r p u l s i n g the core or l o c a l heater and d e t e c t i n g t h e e x t e n t o f the zone w i t h voltage taps over t h e t e s t s e c t i o n length. This experiment was performed i n f i e l d s between 3 and 7 T a t 4.2 K and 3 and 9 T a t 1.9 K as a f u n c t i o n o f a p p l i e d current.

P l o t t e d i n Fig. 2 are the c r i t i c a l I and recovery c u r r e n t 3 IR f o r sample I. At 4.2 K, t h e recovery c u r r e n t s were obtained f o r a 1.55 J/cm heat pulse which i s s u f f i c i e n t t o d r i v e the conductor f u l l y normal a t zero f i e l d . Recovery currents were defined according t o f u l l recovery o f t h e conductor a f t e r approximately 200 msec.

Cl-522 J O U R N A L DE PHYSIQUE

The recovery currents a t 4.2 K were compared t o the unconditional s t a b i l i t y re1 a t i on,

I R 2 R = qP ( 3 )

Fig. 2. C r i t i c a l and recovery c u r r e n t s f o r sample I i n He I and He 11.

where q i s t h e recovery heat f l u x from f i l m b o i l i n g . Based on t h e measured s t a b i l i z e r resistance and recovery c r r e n t s the equivalen3 recovery heat f l u x i s

?!

c a l c u l a t e d t o vary between 0.38 W/cm a t 7 T t o 0.54 W/cm a t 3 T . The noted f i e l d dependence i s most probably the r e s u l t o f end c o o l i n g e f f e c t s . Values determined from these experiments are w i t h i n t h e range o f those measured f o r t h e model c o n f i g - u r a t i o n employed i n the heat t r a n s f e r study. Also, by d e f i n i n g the e q u i v a l e n t perimeter as a c i r c l e enclosing t h e conductor, we f i n d t h e heat t r a n s f e r and s t a b i l i t y c h a r a c t e r i s t i c s r a t h e r s i m i l a r t o those obtained f o r f l a t surfaces /6,7/.

I n the case o f He 11, t h e behavior i s considerably d i f f e r e n t . F i r s t , t h e energy pulse was only capable o f normalizing t h e conductor i n s u l a t e d by the heater. The recovery c u r r e n t IR' shown i n Fig. 2 i s a c t u a l l y associated o n l y w i t h t h i s e f f e c t , which i s discussed f u r t h e r below. Based on the c y l i n d r i c a l heat t r a n s f e r analysis, we estimate t h e f u l l recovery c u r r e n t a t 1.9 K t o be t h a o f t h e upper curve IR Fig. 2 which corresponds t o a peak heat f l u x o f 9.5 W/cm

8 .

Unfortunately, i t was i n n o t p o s s i b l e t o t e s t t h i s l i m i t i n t h e present experiment because o f t h e i n s t a b i l i t y associated w i t h the i n s u l a t e d region.

The energy density r e q u i r e d t o achieve n o r m a l i z a t i o n of t h e conductor was measured f o r sample I a t 1.9 K and sample I 1 a t 4.2 K. For t h e case o f sample I a t 1.9 K, t h e only normal zone occurred under t h e i n s u l a t e d region. For sample I I a t 4.2 K i t was possible t o quench t h e e n t i r 3 conductor a t c u r r e n t s above 0.5 I by t h e a p p l i c a - t i o n o f a pulse l e s s than 1 J/cm

.

A s u n a r y o f pulse energy d e n s i t i e s versus I/Ic i s shown i n Fig. 3. A1 so p l o t t e d a r e t h e r e s u l t s o f Tsuchiya and Suenaga /8/ f o r s i n g l e conductors o f NbTi a t 5 T and Nb3Sn a t 10 T.

Comparing the r e s u l t s a t 4.2 K f o r NbTi, i t i s i n t e r e s t i n g t o note t h e much g r e a t e r l e v e l o f s t a b i l i t y f o r the cable a t h i g h currents. This e f f e c t could be due t o one o f several f a c t o r s i n c l u d i n g t h e higher copper t o superconductor r a t i o f o r t h e cable, the method by which the heat pulse i s a p p l i e d o r heat t r a n s f e r consider- ations. The l a t t e r explanation appears t o be most probable because t h e hea3 r e q u i r e d t o vaporize the helium w i t h i n the cable represents about 135 mj/cm of conductor which i s comparable t o t h e minimum energy a t t h e highest currents.

The r e s u l t s from sample I a t 1.9 K a t 8 t o 9 T show a much h i g h e r degree o f s t a b i l i t y r e q u i r i n g between f o u r and e i g h t t i m e s t h e energy d e n s i t y n o r m a l i z e d t o t h e conductor t h a n a t 4.2 K. T h i s l e v e l o f s t a b i l i t y i s comparable t o t h a t o b t a i n e d by Tsuchiya and Suenaga /8/ f o r Nb3Sn a t 4.2 K. I n t h a t case t h e h i g h l e v e l o f

L

NbTi CABL

-

⁰ ST. a71 : 4.2 K -,mx cu

-

s t a b i l i t y i s o b t a i n e d because o f t h e h i g h Tc w h i l e i n t h e p r e s e n t case i s due t o enhancement o f heat t r a n s f e r .

0

I n o r d e r t o develop a f u r t h e r u n d e r s t a n d i n g o f t h e t y p e o f normal zone e s t a b l i s h e d i n t h e sample I a t 1.9 K, we have analyzed o u r d a t a u s i n g a model developed by M e u r i s and M a i l f e r t /9/. The model t r e a t s uncooled r e g i o n s o f t h e conductor and c a l c u l a t e s t h e c o n d i t i o n s whereby steady normal zones e x i s t and t h e energy r e q u i r e d t o c r e a t e them. Parameters t h a t determine t h i s c o n d i t i o n are:

, . . * ' , , . , ' * " " "

P

a = ( s t a b i l i t y parameter)

h ~ A (Tc

-

Tb)

0.5 1.0 1.5

I / l c

Fig. 3. Energy d e n s i t y r e q u i r e d t o normal i z e conductor samples.

i = I

T

( n o r m a l i z e d c u r r e n t ) ( 5 )

and

x S = [%j1/2 1 (normal i z e d ha1 f w i d t h ) (6

There i s some u n c e r t a i n t y i n t h i s a n a l y s i s owing t o t h e f a c t t h a t t h e heat t r a n s f e r c o e f f i c i e n t , h, t h e coo'led p e r i m e t e r , p, a r e n o t known and t h e thermal c o n d u c t i v i t y depends on a p p l i e d f i e l d as w e l l as temperature. p w v e r , f o r our experimental c o n d i t i o n s , t h e f u l l r e c o v e r y s h o u l d o c c u r when ai

(

0.5 w i t h some v a r i a t i o n due t o t h e p r o p e r t i e s changing w i t h magnetic f i e 1 d.

We have measured t h e energy p e r u n i t l e n g t h r e q u i r e d t o c r e a t e t h e s e steady normal zones f o r sample I a t 1.9 K and a p p l i e d f i e l d s between 3 and 9 T. These r e s u l t s a r e sh wn i n Fig. 4 n o r m a l i z e d a g a i n s t t h e s t a b i l i t y parameter a. Recovery o c c u r s f o r

a i q

,$

0.5. F o r c u r r e n t s l a r g e r t h a n t h i s , ^a de r e a r i n g s i z e d energy pul r e i s r e q u f r e d t o c r e a t e these normal zones. Foa ai 0.6 t h i s p u l s e i s a p p r o x i m a t e l y c o n s t a n t and c l o s e i n v a l u e t o t h e energy . q u i r e d t o v a p o r i z e t h e i n t e r s t i c i a l

C1-524 JOURNAL

DE

PHYSIQUE

he1 ium, AEH

.

Note t h a t t h e e n t h a l py o f t h e conductor between Tb and T i s a1 s o p l o t t e d i n

fig.

4. T h i s energy AECoOd i s about a f a c t o r o f 20 s m a l l e r t h a n 6EHe and i s n o t expected t o c o n t r o l t h e behavior.

Fig. 4. Energy r e q u i r e d t o c r e a t e steady normal zones i n sample I.

CONCLUSIONS

We have i n v e s t i g a t e d t h e heat t r a n s f e r and s t a b i l i t y o f seven w i r e cable conductors i n He I and He 11. The r e s u l t s can be summarized as f o l l o w s :

1 ) For a cable i n He I, s u r r o u n d i n g t h e conductor i s between 0.3 t o 1 W/cm t h e peak heat f l u x when avera ed over a c i r c l e

P .

2) I n He 11, The peak heat I l u x i s c o n t r o l l e d by r a d i a l heat t r a n s p o r t i n He I 1 and can approach 10 W/cm i n small diameter samples.

3 ) The energy d e n s i t y r e q u i r e d t o quench a cable i n He I i s h i g h e r than t h a t f o r an i n d i v i d u a l w i r e because o f t h e e n t h a l p y o f t h e he1 ium w i t h i n t h e cab1 e.

4 ) I n He I 1 t h e conductor performance was c o n t r o l l e d by a normal zone c r e a t e d under an i n s u l a t e d r e g i o n o f t h e t e s t section.

ACKNOWLE DGNENTS

Work supported by t h e U.S. Department o f Energy under c o n t r a c t E-AC02-82ER52077.

Thanks a l s o go t o A. K h a l i l f o r c o n t r i b u t i n g t o t h e e a r l y stages o f t h i s work.

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KHALIL A., STOCKER K. and VAN SCIVER S.W., IEEE Trans. on Magnetics Mag-19 (1983) 268.

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(1982) 375.

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VAN SCIVER S.W. and LEE R.L., Advances i n Cryogenic E n g i n e e r i n g 25 (1980) 363 and i n Cryogenic Processes and Equipment i n Energy Systems, A S M E ~ U ~ . H00164

(19801 147.

6. CLAUDET G., MEURIS C., PARAIN J., TURCK 0.. IEEE Trans. on Magnetics Mag-15 (19811 340.

7. ~UROWSKI P., Cryogenics

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8. TSUCHIYA K. and SUENAGA M., s u b m i t t e d t o Advances i n Cryogenic E n g i n e e r i n g

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