Double acting reciprocating magnetic refrigerator: first experiments

To obtain better practical knowledge of a possible refrigeration process, we have designed an experimental magnetic refrigerator which operates between 4.2 K and 1.8 K. The design performance was reached with 1/2 W capacity from two 18 c m 3 magnetic parts. The static and dynamic losses, thermal efficiency, were measured.

Double acting reciprocating magnetic refrigerator: first experiments C. Delpuech, R. Beranger, G. Bon Mardion, G. Claudet, and A.A. Lacaze

Methods of adiabatic demagnetization although common in laboratory practice were limited until very recently to one. shot operations which restricted the length of the experiments. The first superconductor-switch refrigerator constructed by Heer et al in 19541 was to provide the contInuous operating conditions needed by the physicists: low temperature (< 1 K), low power (1 < mW).

The cost of the work necessary to perform the cycle being negligible compared to the cost of the refrigeration near 5 K, a theoretical efficiency of the Carnot cycle can be defined by:

Since then potential uses of high power refrigerators have appeared, in particular for the production of superfluid helium for cooling large cryomagnetic plants such as the TORE SUPRA project 2 : 300 W at 1.8 K.

In the same way, the thermal efficiency of an actual cycle can be defIned by:

The alternating magnetic refrigerator with regenerator proposed by Van Geuns 3 in 1966 has not been built to our knowledge. Steyert and coworkers at LASL devised a rotating, continuously operating system in 1977.4 This system used a Carnot cycle and the prototype was able to reach the helium transition temperature T~, at atmospheric pressure. To date a few machines have been proposed or tested at ambient or at low temperatures. S-9 This paper describes the results of an experiment based on a particular type of reciprocating apparatus operating between 1.8 K and 4.2 K. Our choice was to design a test stand that would in an initial exploratory stage, provide us with information on such aspects as materials, heat transfer and mechanical guiding at low temperature, with a view to preparing the way for a rotating refrigerator. General analysis of magnetic refrigeration

Cycle without internal heat transfer. The principle of a magnetic refrigerator can be illustrated with the Carnot cycle ABCD, plotted in Fig 1, on an entropy temperature diagram of hydrated gadolinium sulphate. We use, for instance, a temperature of the warm source Tw = 5 K and a temperature of the cold source Tc = 1 K. During the isothermal magnetization of the salt from A to B, the heat released to the warm souce is Qw = Tw(SB - SA). During the adiabatic demagnetization, the temperature is reduced to Tc and then, during the isothermal demagnetization, the heat extracted from the cold source is Qc = Tc(SD -- Sc). AAL is at Universit(~Scientifiqueat M~dicalede Grenoble, France, The other authorsare at the CEA-DRFC/SBT-CENG 85 X 38041 Grenoble C~dex, France. Paperreceived 19 May 1981.

77th = QtcI1/Q~ = T¢/Tw

r~ac

=

L~cC/Q~ and 7/

=

f/ac//?th

where r/ac refers to the actual measured performances of the machine. Another parameter which governs the size of the machine is the energy ~ removed from the cold source per unit volume of salt and per cycle. It is a relatively easy matter to study the variations of the parameters 7/and ~b when the magnetization is a Brillouin function of BIT. To illustrate orders of magnitude, the following computation is given for a well known typical compound, gadolinium sulphate Gd2 (SO4)a : Molar mass, M = 602.7 g; Effective number of Bohr magnetons, 7.9; Land6 factor, g = 2; Magnetic quantum number, 7/2; Density, 4.14; Molar volume, 145.62 cm 3 ; Gramme-ion volume, 72.81 cm 3. The temperature of the two heat reservoirs are Tc = 1.8 K and Tw = 4.2 K. The paramagnetic salt is magnetized up to 5 T at Tw + ATw and is demagnetized down to 0.1 T at Tc - ATe. The two diagrams in Fig. 2 show how ~1 and depend on the temperature differences AT needed for heat transfer. It is clear that the effect is stronger at the cold source than at the warm source. With the same area, heat flux transferred to the warm source is always greater than heat flux extracted from the cold source. The thermal conductance is much lower at the cold source than at the warm source.

Cycle with internal heat transfer. It is possible to use a magnetic cycle with internal heat transfer similar, for instance, to the Ericsson cycle for gas cooling (here constant field instead of isobar) in particular when the source temperatures are high and very different. This cycle is justified by the large contribution of the lattice vibrations to the total entropy. We have also plotted

0011-227 5/81/010579-06 $ 02.00 © 1981 I PC Business Press Ltd. CRYOGEN

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T n~ (/)

The paramagnetic material should exhibit a large decrease of specific entropy upon application of a moderate magnetic field, it should also have a good thermal diffusivity. We avoid metals or metallic alloys because of the eddy current losses. As nearly all the useable compounds are good thermal insulators (k ~- 10 -3 W cm -1 K -1) sophisticated technology is required in order to reduce the temperature difference between the salt and the heat reservoir.

I.O

I T=~I

5 Twarm

tO

Temperature, K Fig. 1

Entropy diagram for Gd2(SO4) 3 8H2 O4

I

O~

I

0.5

~T, K

II

c

I

0.5

~T, K

I

I

Fig. 2 Gd2(SO4) 3 - Brillouin f u n c t i o n assumed Tcold = 1.8 K, Twmrm = 4.2 K, Bml n = 0.1 T, Bmax = 5 T; . . . . &Toold murce ATwarm mume; ~ A T w a r m murce = 0, A T o n l y at cold source; . . . . . . . . A Tcold murm = 0, A T o n l y at warm source

in Fig. 1 a theoretical cycle with complete exchange of heat between lines 8tx and fit. It is very difficult to achieve such a cycle in practice, since the variations of the magnetic fields must be very closely correlated to the temperatures of the paramagnetic material in order to obtain a balanced entropy variation.

Comparison o/cycles. Fig. 3 gives the ratio of refrigeration capacity of the Carnot cycle to the refrigeration capacity of the Ericsson cycle. Perfect heat exchange at the reservoirs is assumed. The temperature of the warm reservoir is varied while that of the cold source Tc is kept at 1.8 K. The Ericsson cycle is found to be the more interesting the higher the temperature, but it is more complex to realize. Even, with a magnetic field of 5 T, the Ericsson cycle turns out to be more profitable at temperatures comparable to the warm reservoir and above 10 K. Below 5 K and with a magnetic field of 3 to 5 T, the two cycles give about the same results; in this case, it is preferable to use the Carnot cycle.

Thermal switches. During the cycle, heat has to be periodically exchanged between the salt and the warm or the cold source. Obviously, there is a need of thermal switches. For the on position of the switch, three different heat transfer modes may be envisaged: with gas, with liquid or through contact of solids. The last method, commonly used in laboratory practice with a mechanical, superconducting or magneto resistant switch, seems to be not suitable for high power refrigerators. Heat transfer in helium gas under vapour pressure or supercritical pressure, whether by conduction or by natural convection, is very poor. Turbulent conditions would be required to improve this situation. Heat exchange is easier with liquid helium. A particular feature is the appearance of the superfluid phase which brings about a very marked increase in thermal conduction. In that case losses through thermal shorts in all the possible leak channels between the two sources can become very appreciable and reduce the useful power of the refrigerator. For the off position of the switch, the fluid has to be removed, or the paramagnetic sample has to be extracted from the fluid.

Cryomagnetic system. It must generate a maximum field as high as possible without disturbing the zero or weak field zones for demagnetization. The field profile should be correlated with the temperature profile of the magnetic material so as to reduce temperature differences when heat transfer is concerned and thereby improve thermal efficiency.

Miscellaneous problems. Many problems arise from the use of moving parts at cryogenic temperatures and in a magnetic field. Friction, shocks, electromagnetic losses, must be kept to a minimum. Magnetic interaction forces are considerable and the mechanical systems must be reliably designed.

Magnetic materials. Suitable magnetic ions are mostly found among the transition elements and the rare earth elements. For a long time, these elements were used in mixed salts. In mixed salts such as Gd2 (SO,)3 8H2 O, the interaction is reduced by non magnetic ions or water of crystallization. This dilution is necessary for reaching very low temperature, but dispensable for refrigeration above 1 K. It may be interesting at first sight to choose a salt which has its specific heat maximum at a temperature close to the cold source. Near the specific heat maximum the salt is capable of absorbing large amounts of power without large variation in temperature, but large specific heat also means low thermal diffusivity. Actually, it appears to be most efficient to use a salt whose specific heat maximum lies far below the temperature of the cold reservoir.

580

~o..

I

1.8 Teakl

I

5

i~l I0

;

15 Temperature, K

I

20

r....

Fig, 3 Gd2(SO4) 3 -- Brillouin function assumed, Tcold = 1.8 K, Brnln = 0.1 "1", ATmurcm = 0

CRYOGENICS, OCTOBER 1981

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auxiliary refrigeration is required, the expansion valve is closed and the refrigerating bath circuit is kept under vacuum.

Design of the magnetic bar. The magnetic parts of the piston are alternately in contact with the 4.2 K source and the 1.8 K source. Consequently, the time taken to establish temperature equilibrium in a cylinder subjected externally to these variations, must be known. For the present experiments, we used HoPO4 and Gd2(SO4)s as paramagnetic substances. As the thermal conductivity of these materials is very poor, we increased the heat transfer outwards by incorporating copper filaments. IO

6 II

Copper wires were arranged radially in the bar so as to conduct heat from the centre to the outer surface, by means of the copper stars illustrated in Fig. 5. Due to their shape, eddy currents were reduced since there is no dosed loop whatsoever, once the outer rim is removed by machining the piston. The fan-shaped ends of the wires increase the contact area with the outer medium. These stars were obtained by chemical etching of copper foils 0.1 mm thick. They were deoxidized by heat treatment in a reducing atmosphere before insertion in the bars. The active components are composed of a stack of thin discs of salts and stars in a cylindrical matrix.

Fig. 4 Cross-sectional view of experimental device. 1 -- Expansion valve; 2 -- Level gauge; 3 -- C o p p e r w a l l ; 4 - - He II bath; 5 -- R e f r i gerator bath (saturated He II); 6 - - Insulator; 7 -- Bearing; 8 -- Magnetic bar; 9 -- S u p e r c o n d u c t i n g coil; 10 -- Magnetic elements; 11 -- C o r r e c t i v e s u p e r c o n d u c t i n g coil

Experimental device Our choice was to design a test stand that would provide information on its use in a first stage. The machine had therefore to be simple and well suited for experiments that are amenable to calculated verifications. The experimental unit is illustrated by the cross sectional view in Fig. 4.

Each thin disc is a densely packed mixture of powdered paramagnetic material and araldite. We used a single. component araldite AT1 in powder form. The araldite content was between 20 and 30% of the volume. The stack of 'Saltdiscs and stars' was held under constant pressure (about 3000 bars) and polymerized at 150°C for three hours. After removal from the mould, the active component obtained was compact, non-porous, had good mechanical strength and could be machined. Fig. 6 shows the two active components. By means of screwed and glued stainless steel connecting rods, they were attached to cylinders made of fibreglass reinforced epoxy, sheathed in alumina. The resulting bar was machined with a diamond wheel.

It is essentially a double acting reciprocating magnetic machine with an auxiliary liquid helium refrigerator. It operates immersed in a bath of liquid helium at 4.2 K which forms the warm reservoir of the magnetic cycle. The cold source is a superfluid bath at atmospheric pressure, that can be lowered to a temperature of about 1.6 K, either with the help of the auxiliary refrigerator or through the magnetic refrigerator, or both. The two identical magnetic elements, 10, are moved periodically and subjected to a cycle consisting of magnetization when immersed in the 4.2 K bath, then demagnetization in the middle bath, 4, which constitutes the cold source. The bar slides in the guide bearings, 7, that isolate the central chamber of the 4.2 K bath. The copper wall, 3, surrounding the central chamber permits heat exchange with the auxiliary refrigerating bath, 5, which is controlled by acting on an expansion valve, 1, and measuring the level of the saturated superfluid helium, 2. The auxiliary refrigerator, controlled by a manual valve, can deliver a power of about 1 W at 1.8 K. Through this refrigerator it is possible to measure thermal losses in various geometrical and magnetic configurations. When no

CRYOGENICS. OCTOBER 1981

Fig. 5

C o p p e r star

581

I

2

3

4

L~~I/IP~' -" ~J,i;;iJI',J,;',!i;l;i,i;[l!i ."Y~A'..-. -;;i,~i~r,~i¢'a~i;l~.... :~ ..ll/VU7p~, _

. . . . .

Fig. 6 Magneticbar, 1 -- Epoxy-fibreglass; 2 - Stainless steel rod; 3 -- Alumina tube; 4 - Active component (salt discs and copper stars) This method of construction has been used for implementing many paramagnetic materials, such as: yttrium oxide, dysprosium oxide, holmium oxide, erbium oxide, holmium phosphate, non-hydrated gadolinium sulphate... All these compounds have thermal contraction coefficients of about 2 x I0 -a between 300 K and 77 K. By the use of copper stars, with a pitch of 1 mm on the copper stars, the mean thermal diffusivity is multiplied by a factor of seven to ten according to computation.

Nb ~ cryomagnetic system at 4.2 K. The magnetic induction profile illustrated in Fig. 7 could be obtained without difficulty using two main coils facing each other and two compensation coils also facing each other. In the zero field zone, the field was always less than 10 -2 T; the maximum field was about 5 T with a maximum difference of + 10% over the length of the active component. Note that by the use of two separate electrical power supplies the field profile can be modified at will.

Drive system. Fig. 8 shows the magnetic force that must be overcome in order to move the bar through a half cycle. The position of a hydraulic cylinder, maximum force 3000 N, having maximum linear speeds of 0.5 m s-1 , is controlled by a function generator. It can be used to impart various movements to the bar, in particular a sinusoidal movement and a trapezoidal movement, which is in fact a sequence of plateaux with sinusoidal sides (Fig. 12). The frequency of the movement and the time of exchange at the sources (length of the holding stages) in the case of the so called trapezoidal movement, can be varied through adjustment of the drive system.

Dynamic losses Pal. When the bar is in alternating movement, additional losses occur due to: friction between bar and bearings; movement of liquid helium imparted by the bar; and transfer of enthalpy due to temperature cycling of the bar itself. The curves in Fig. 9 refer to bearings and bar entirely in alumina with a 20/~m clearance and a sinusoidal movement of amplitude 120 mm. As the specific heat of alumina is very low, the enthalpy transferred by the bar is negligible (< 0.1 mW in this case) and the losses measured are due to friction and forced movement of the liquid. In fact, we measure the total losses Ps + Pd. At low frequency the losses increase when the temperature of the superfluid bath decreases. For frequencies greater than about 0.4 Hz, the losses are independent of the temperature of the bath.

Experiments with a bar in HOP04. An exploratory refrigeration was carried out with an available bar in a defective technological condition (alumina sheath split, copper star with a pitch arrangement of 1.25 mm approximately). Holmium phosphate is a promising choice for the bar since it is easy to shape and in addition has a typical 2~anomaly caused by transition to the antiferromagnetic state at 1.39 K. The associated magnetic entropy AS/R is close to 0.73. With the auxiliary refrigerator off-line and under vacuum and the maximum field at 5.5 T, the drive system was put into operation for a sinusoidal movement, amplitude 120 mm, at a frequency of 0.5 Hz. Fig. 10 shows the

_

,

40-45mrq magneticelement

Experimental results

-I D O

-I -Z, mm

Static losses Ps. Firstly, the bearings are replaced by solid plugs in stainless steel, the superfluid bath is f'flled through a capillary tube that can be closed by a valve. The temperature of this bath can be maintained at a value Tc selected by temperature regulation supplying an electric power Pu in an electric resistor. The actual losses due to the cryostat Pc are obtained by measuring the gas flow pumped through the auxiliary refrigerator then deducting Pu.

Table 1 gives the experimental results obtained with bar and bearings both made of alumina for a 20/am clearance when cold.

100

-2--

Fig. 7 Magneticfield

profile

Stroke=119ram

Secondly, the bearings and a bar are positioned, but the bar is at rest. The additional losses measured are therefore due to: heat transport through the liquid contained in the annular spaces between the bearings and the bar, and heat conduction through the bearings and the bar.

Table 1.

246--358

Stroke = 119ram

4O( 5CE 2O( ICE

J ~ ~o-5o

I I -4o -3o

I -2o

I -,o /

-- -leo

Static Ioues

Hqh

---200

T c, K

1.98

1.80

1.70

P=,mW

100+10

110+10

120+10

---~00

Fig. 8 Magneticforce

582

t h r o u g h o u t a half cycle

CRYOGENICS. OCTOBE R 1981

3(X3

power Pu = 0.36 W; total refrigerating power Pt = P u + Pc

+Ps+ed= 0.57

W.

F r o m the measurements o f heat dissipation at the w a r m

reservoir, it was possible to determine the thermal efficiency of the unit, 77, computed with the useful power Pu. It was also possible to def'me the efficiency of the cycle r?cy using the total refrigerating power. The following results were obtained at 5 T.

2O0 E Q-

At 1.9K:71 =

7.5%

r/ey = 15.6%

At 2.1 K: r? = 11.8%

r/cy = 19.0%

÷

Q-=

15C

v

tOO

K)C I O.5

I I

F,, Hz Fig.9 ....

E Q'-

Lossesversus frequency of the movement 1.81 K; . . . . . . . . 1.98 K

1.70 K;

5C

4

3(

J 0 t

I (~2

J 03

I 0.4

I 0.5

I 0.6

F,, Hz

r

Fig. 11 Useful power at 2.10 K with HoPO 4 and 5.5 T (lines are a guide to the eye)

2£--

i¢

I

2 Fig. 10

I

4 t, mn

L

6

ic

O~

I

8

/

First cooling down with HoPO4 - 5.5 T - 0.5 Hz-120 mm

change in temperature observed and the limit reached of 1.98 K. The alternating fluctuations in temperature do not exceed 10 mK despite the small volume of superfluid helium (about 5 cm 3 ). Fig. 11 shows the change in useful power Pu at 2.10 K as a function of frequency for three sinusoidal movements of different amplitude. At 0.3 Hz and for an amplitude of 100 mm, we have obtained: Pu = 120 mW. Experiments with a bar in Gd2(SO4)3. Initially, this bar had all the technological qualities required. The axial pitch of the copper stars was about 0.5 mm and clearance 20/am. All the experiments reported here were carried out with a frequency of 0.3 Hz and an amplitude of 100 mm. On initial refrigerating, a temperature of 1.72 K was obtained after 4 rain at the following settings: Bmax = 5 T, sinusoidal movement.

o.

.t .

2f

/

.!._2t/x

- -

/

_

/

/

/

02

/

x

/ o.1

/

//I{

/ /I

Fig. 12 compares the variation in useful power Pu as a function of bath temperature for these two movements. The trapezoidal movement that extends the time for heat transfer at the sources improved this result and enabled the limiting temperature to reach 1.67 K.

l L t 2.0 T=,K Fig.12 UsefulpowerwithGd2(S04)3,5 T,amplitude100ram,

At 2.10 K, the following results were obtained: useful

F = 0.3 Hz (lines are a guide to the eye)

C R Y O G E N I C S . O C T O B E R 1981

01.5

I

I.

I

/ 1.72

583

Theoretically, the power and the efficiency decrease when the magnetic field is decreased. In fact the limiting tempera. ture stayed constant when the field decreased from 5 to 3 T and then rose slightly. The efficiency improved and for 2 T, we found at 1.9 K: r/ = 15.9%

a temperature below 1.8 K in a bath of superfluid helium at atmospheric pressure was achieved from the first experiments as well as a refrigerating power close to the half watt that was the initial aim.

rTey = 26.5%

It is likely that irreversibility mainly arises from large temperature differences between paramagnetic salt and heat reservoirs.

Conclusion An experimental device has been realised to study the magnetic refrigeration. The choice of a double acting reciprocating machine and the use of liquid helium as warm heat reservoir are due only to the fact that they give more simplicity for construction and more versatility in operation. The use of an auxiliary refrigerator allows the direct measure of some losses. Significant progress has been made in the following technological areas: production of machinable magnetic components with anisotropic thermal conductivity successful guide systems with low friction in cryogenic medium

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improved knowledge of the thermal losses generated by the movement of a surface in a superfluid bath

Future experiments will be devoted to the test of other materials such as holmium phosphate and gadolinium gallium garnet. Particular attention will be paid to enhancement of the thermal efficiency.

References 1 2 3 4 5 6 7 8 9

Heer, C.V., Barnes, C.B., Daunt, J.G. Rev Sc Instrument 25 (1954) 1088-1099 Aymar,R. et al., IEEE Transactions on Magnetics MAG-15 1 (1979) 542 Van Geuns, J.R. Philips Res Rep Suppl 6 (1966) 1 Pratt, W.P., Rosenblum, S.S., Steyezt, W.A., Barclay, J.A. Cryogenics 17 (1977) 689-693 Brown,G.V.JAppIPhys 47 (1976) 3673-3680 Steyert, W.A.JApplPhys 49 (1978) 1216-1226 andJde Phys Colloque C6 39 (1978) 1598-1604 Barclay,J.A., Steyert, W.A., Zzudsky,D.R. Proc. XVth Int Congress Refrigeration(IIR) I(Venezia 1979) 147-153 Barclay,J.A., Moze, O., Paterson, L. JApplPhys 50 (1979) 5870-5877 Barclay,J.A. Cryogenics 20 (1980) 467--471

CRYOGENICS. OCTOBER 1981