Heat transfer in subcooled liquid cryogens

Experimental study o f heat transfer in helium, hydrogen and nitrogen has been carried out over a wide range o f pressures and subcooling. Empirical correlations are obtained to calculate heat transfer coefficients at nucleate boiling, film boiling and single-phase convection. Conditions are determined for transitions from one heat transfer mode to another.

Heat transfer in subcooled liquid cryogens Y u . A . Kirichenko, K.V. Rusanov and E.G. Tyurina Key words: helium, liquid nitrogen, liquid hydrogen, heat transfer

Nomenclature Ra =

a

thermal diffusivity, m 2 s -~

A, B, C

constants

Cp

isobaric heat capacity o f liquid J kg-1 K-l

d

typical size, m

g

acceleration, m s-2

gd3~AT (va)l , Rayleigh number

g[3c

R a , = (va--~ "

Ts

Pi -- Pv p,,

, modified Rayleigh number

saturation temperature, K

A T s = T H - Ts

K = qmax/L X/Pv [Gg(Pl - Pv)] ¼, stability criterion

TH

heating surface temperature, K

l c = 2rr [o/g(Pl - Pv)] 1/2, critical wavelength, m

o~ = q / A T =

heat transfer coefficient, W m-2 K-1

L

evaporation heat, J kg-x

fl

thermal expansion coefficient, 1/K

k, m, n

exponents

¢ = Ts - T 1 = subcooling, K

N u = ad/~l

Nusselt number

0 - Cp~ L

dimensionless subcooling

X

thermal conductivity coefficient, W m-lK-1

v

kinematic viscosity coefficient, m 2 s-1

p

density, kg m-3

o

surface tension, N m-1

N u . = odc/~v modified Nusselt number

P

pressure, Pa

q

heat flux density, W rn-2

qo

corresponds to 'convection-developed boiling' transition

qmax

corresponds to nudeate-film boiling transition

In thermal calculations of cryogenic cooling systems for modern instruments and devices (eg eryoturboalternators) it is often essential that the liquid subcooling effect on the heat transfer characteristics should be allowed for. There is no generally accepted method of such calculations as yet; experimental data concerning pool boiling o f subcooled liquid cryogens are few 1-4 and lack some essential information. Heat transfer between a solid surface and a liquid may proceed generally in three modes: single-phase convection, nucleate boiling or f'drn boiling. In thermal calculations one has to be able to determine the heat transfer coefficient at a present combination of operating conditions: q, p, ¢; for various heat transfer modes the calculation formulas are different. Therefore, it is necessary to know the positions of boundaries between the modes (qo, qmax) as a function of pressure and subcooling. The

Subscripts v and 1 relate to vapour and liquid

purpose of this work was to obtain empirical correlations to estimate the above characteristics of heat transfer. Heat transfer was studied in subcooled liquid cryogens using a fiat horizontal copper heater with diameter d = 20 mm over a wide range o f pressures and subeooling: for helium, p = 0.1 - 0.2 MPa, ~ = 0 - 2.2 K; for hydrogen, p = 0.1 - 0.65 MPa, ~ = 0 - 12.5 K; for nitrogen, p = 0.0125 - 0.9 MPa, ¢ = 0 - 38 K. The studies were carried out using a stainless steel cryostat with two vessels. A copper working vessel with a test section at the bottom was enclosed in an external vessel; both vessels were filled with liquid. To set up and maintain the necessary subcooling and pressure conditions, the working vessel was pressurized with helium gas, while the pressure in the external vessel was maintained below this value. The experimental apparatus was described in detail previously: The heater and liquid temperatures were measured by ger-

0011-2275/83/004209-03 $03.00 © 1983 Butterworth & Co (Publishers) Ltd CRYOGEN ICS . APRI L 1983

209

Table 1.

C and n values in (1)

Liquid

p, MPa

Helium

0.1 0.125 0.15 0.175 0.2

C 159 40.5 157 742 409000

0.463 0.690 0.542 0.376 -0.412

13.6 60.4 84.9 389

0.665 0.544 0.524 0.353

0.1 0.2 0.4 0.65

Hydrogen

0.0125 0.05 0.1 0.2 0.4 0.6 0.9

Nitrogen

n

0.95 1.42 2.27 4.46 4.45 1.90 6.76

Table 2.

Rangeof Ra numbers, A and m values in (3)

Liquid

Ra

A

Helium

5 x 108 +4 x 101°

0.107(1-1.6 x 10"6p) 0.330

Hydrogen 8 x 10s +2.5 x 108

0.048

0.419

Nitrogen

0,836

0.259

6 × 107 +6 x 108

At film boiling of helium the heat transfer coefficient is also independent of subcooling. Typical data are shown in Fig. la (1 - p = 0.1 MPa, q = 9 x 103 W m-Z; 2 - p = O . 1 MPa, q = 2 x 1 0 4 W m - Z ; 3 - p = 0 . 2 M P a , q = 104 W m-Z). A similar result was obtained previously at film boiling of subcooled hydrogen (p = 0.1 - 0.8 MPa, ~o= 0 - 8 K). Criterion data processing performed by the authors is shown in Fig. lb; the standard deviation from

0.81 0.79 0.76 0.70 0.72 0.78 0.68

(2)

N u , = O. 115 Re°, "412 manium resistance thermometers. During the experiment the subcooling of liquid in the working vessel was changed at constant supercharging pressure and heat flux density. In the case of developed nucleate boiling (qo < q < qmax) the heat transfer coefficient as = q/ATs does not depend on ¢ and can be found as o~ = Cq n

(1)

where C and n values were found experimentally and are presented in Table 1. The standard deviations are from 20 to 35%.

(3

E

d

<>

Because of small temperature differences the data obtained under single-phase convection mode feature a considerable spread in values; this might be the reason why their criterion processing as Nu = A R a m

(3)

yields the values of A and rn that are somewhat different from those typical of noncryogenic liquids and gases (,4 = 0.56, m = 0.25 at Ra < 2 x 107 and A = 0.14, m = 0.33 at Ra/> 2 x 107) as presented inTable 2. For helium, coefficient A decreases with the growth of pressure (and subcooling) at m = const, and the experimental values of a are smaller, than those calculated by Nu = 0.14 Ra °'33; for hydrogen and nitrogen the experimental data are located above this calculated straight line. The position of the convection-developed nucleate boiling boundarfline can be described by the relation qo = BOk

I O

0,5

I

I

1.O

1.5

102

4

2

lo' Lb 2

I 4

,

I

,

10 6

2

4

(4)

Experimental results are shown in Fig. 2 (nitrogen: points 1-6 correspond to p = 0.05; 0.I ; 0.2; 0.4; 0.6 and 0.9 MPa; 7 - calculated by (4) with B = 2.19 x lOS W rn-2, k = 1.11; hydrogen: points 8-11 correspond to p = 0.1; 0.2; 0.4 and 0.65 MPa; 12 to B = 2.63 x 104 W rn-2, k = 0.91; helium: points 13-17 correspond to p = 0.1; 0.125; 0.15; 0.175 and 0.2 MPa; 18 - to B = 1.14 × 103 W m-:, k = 0.95). The dependence of qo on 0 is close to linear one. The range of parameters studied previously' (helium) is also indicated in Fig. 2 (hatched area 19); no appreciable effect of ~0on a s (developed nucleate boiling) was observed' which matches the intermode boundary data obtained in this work. The position of the nucleate-film boiling boundary for helium and hydrogen with a standard deviation of -+ 11% is specified by the formula 6

~,K

I

K

= qmax/L ~/Pv [og(pl -- Pv)] z/4

10 7

Re Fig. 1 F i l m boiling of subeooled h e l i u m , a - - o -- 1, A - - 2 , ¢ -- 3 ; b - - • - - 0.1 M P a , • ~ 0 . 1 5 M P a , • - 0 . 2 M P e s t r a i g h t l i n e c a l c u l a t e d by (2)

210

is -+ 16%.

4

2

m

(5)

= Kx [1 + ~(pl/pv) 3/4 0]

withK 1 = 0.2; ~ = 0.15 (see Fig. 3).

C R Y O G E N I C S . A P R I L 1983

10 5 /k-1

0.3 4

I~-2

-"

O

V-4

~0.1

2

I

~

E]

•

[]

All,

[]

-

104

(~-6

0

I 0

O-

4

• ~.

2

8 - 9

-

<~ - 10 ~10 ~

i

I 1.0

I

I

I

1.5

0 (Pe/Pv)3/4 Fig. 3 Dimensionless subcooling dependence o f stability criterion helium, o -- 0.1 MPa, • -- 0.15 MPa, a -- 0.2 MPa, Hydrogen, • - 0.1 MPa, A -- 0.2 MPa, 0 -- 0.4 MPa, • -- 0.65 MPa. Straight line calculated by (5)

-

ql' - 11

-13

O

Z~- 14 •

- 15

V-

10 2

16

o f low Temperature, UkrSSR Academy o f Sciences, Kharkov, USSR. Paper received December 1982. References

1 2

~-17

3

e / 10 -2

2

4

1 0 "1

2

4

10 °

4

e Fig. 2

I 0.5

Dimensionless subcooling dependence of q0

Authors

6

The authors are at the Physico-Technical Institute

CRYOGENICS.

5

APRIL

1983

Ib~him, E.A., Boom, ILV., Mclnto~h, G.E. Heat transfer to subcooled liquid heliumAdv CryogEng 23 (1978) 151-158 Verld~ B.I.,Kirichenko, Yu.A. Levehenko, N.M. Heat transfer during subcooled hydrogen boilingAdv Cryog Eng 25 (1980) 467--475 Sindt,C.F. Heat transfer to slush hydrogen Adv Cryog Eng 19 (1974) 427--436

Kurilenko, A.A., Dymenko, 8.1L Heat transfer including plug film boiling of hydrogen in tubes lnzhenerno-Fizicheskii Zhurnal40 (1981) 586-591 Verkin, B.I., Kiriehenko, Yu.A., Kozlov, S.M. Rusanov, K.V. Heat transfer during pool boilihg of subcooled helium Proc 8th Intern Cryog Eng Conference, Genova, (1980) 256-260 Kutateladze, S.S. Fundamentals of heat transfer theory M. Atomizdat (1979) 416

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