- Email: [email protected]
Dilution refrigerator for space applications with a cryocooler
Dilution refrigerator for space applications with a cryocooler* A. Benoit and S. Pujol* Centre de Recherches sur les Tres Basses Temperatures, CNRS, BP166, 38042 Grenoble, France *lnstitut Laue Langevin, BP 156, 38042 Grenoble France
The development of a new type of dilution cryostat with an open circuit for circulating 3He and 4He makes its use in space possible. If a cryogenerator is used as precooler to avoid the 4He bath, it is possible to cool the input gas down to 2 K before the dilution unit, using J o u l e - T h o m s o n expansion of the mixture a t t h e dilution output. This results in a simple refrigerator with a low power dissipation at 4 K and continuous operation below 100 mK. The working lifetime of the cryostat is limited by the quantity of gas. For six years of operation, the gas storage system should contain = 3 0 kg.
Keywords: space cryogenics; dilution refrigerators; cryocoolers
The development of new cryogenic particle detectors (bolometers) makes it of considerable interest to build a cryostat for working at below 1 K in space. The operation of a classical dilution refrigerator (see, for example, reference 1) in weightless conditions is difficult because gravity is used to stabilize the phase separation interfaces in the still and in the mixing chamber. Another problem arises from the complex pumping installation. These two problems can be solved using different techniques, but the result is a complex system with charcoal pumps. To make a simple cryostat that works at 0.1 K in space, we have developed a refrigerator that works without recycling the helium used for dilution 2"3. This system does not require a still or pumping system, and will operate in the absence of gravity. The disadvantage is the necessity to take enough helium for the lifetime of the mission, but with small flow rates, continuous operation for more than five years is possible. The basic design uses Joule-Thomson expansion at the output of the dilution unit. Therefore, the dilution stage only requires a cold source near 4 K instead of the 2 K precooling stage of the previous version 2'3.
Description
The two fluids are then cooled in the continuous heat exchanger (3). At the end of the heat exchanger, they are mixed together, producing cooling due to the enthalpy difference between pure and dilute 3He 4. The mixture is used to cool down the cold plate (4) and it then leaves the cryostat after exchanging heat in the exchanger (3). Up to the end of the heat exchanger, before the impedance (5), the fluids are at a pressure
toni excl
col(
A schematic drawing of the cryostat is presented in Figure 1. The two pure gases are injected under pressure (5bar ¢) and precooled at 4.2K in heat exchangers (1). Further precooling is achieved down to 2 K through heat exchangers (2).
*Paper presented at the 1993 Space Cryogenics Workshop, 20-21 July 1993, San Jose, CA, USA '1 bar = 105N m2
0011-2275/94/050421-03 ~') 1994 Butterworth-Heinemann Ltd
Figure 1 Schematic drawing of cryostat (see text for opera-
tional details)
Cryogenics 1994 Volume 34, Number 5
421
Dilution refrigerator for space applications: A. Benoft and S. Pujol higher than the critical pressure and there is only a small pressure drop due to viscosity. In a state of thermodynamic equilibrium, the 3He concentration decreases with increasing temperature. To extract the 3He at the hot end of the heat exchanger, we must avoid the counterflow diffusion of 3He in the tube. Therefore, the 3He injection flow rate is maintained at a value higher than the solubility limit (ti3/ri4 > 10%) and bubbles of pure 3He are pushed into the output tube of the heat exchanger (3). With tubes of 0 . 1 0.3ram diameter, the surface tension maintains a sequence of concentrated and dilute droplets 4 to avoid 3He diffusion in the dilute phase. As the temperature increases, the bubbles dissolve. Therefore, in the high temperature part of the heat exchanger (3), the mutual friction between 3He and superfluid 4He5 is used to avoid the counterflow diffusion of 3He. This implies a high enough fluid velocity, which is obtained using tubes of small diameter at the exit from the heat exchanger (typically 30/zm). At the output of exchanger (3), the dilute mixture is expanded through the impedance (5). The J o u l e Thomson expansion produces a cooling power of the 1 order of 120J mol- at a temperature between 1.5 and 2K, depending on the pumping pressure of the gas. Part of this power ( = 2 0 J mol- 1) is used to cool the input gas down to 2 K in heat exchanger (2) before the dilution unit. Joule-Thomson expansion is a well established technique which is accurately described by theory. The presence of a small fraction ( < 2 0 % ) of 3He in the 4He introduces only a small correction to the cooling power produced with pure 4He. One limitation of the performance of J o u l e Thomson expansion is due to the presence of a superfluid helium film in the pumping tube. In the 20% mixture, the temperat'ure of the )l point is smaller than in bulk 4He ( T a = 1.87K), but the properties are similar 6. We can show that heating by the superfluid helium film is relatively more important at small flow rates, but we do not need to precool the input fluids below the ,~ point temperature.
Results
To test this method of refrigeration, we have built a cryostat where the input fluids are precooled to 4.2 K by thermal contact with a helium bath through a thermal impedance. The Joule-Thomson expansion cools down the screen (6) to between 1.3 and 1.5 K, depending on the flow rate and the 3He concentration. The temperature of the cold plate is given in Figure 2 as a function of 4He flow rate for a fixed 3He flow rate ofri 3 = 1.5/xmols 1. This corresponds to the minimum 3He flow rate needed to avoid counterflow diffusion. At lower 3He flow rates, the system becomes unstable. Increasing the 3He flow rate even more causes an increase in temperature due to an extra heat load on the heat exchanger. Because the system is operated with an excess of 3He, the amount of 3He diluted is given by the product of the solubility limit (6.4%) and the 4He flow rate. Therefore, the theoretical cooling power of such a
422
Cryogenics
1994 V o l u m e
34, N u m b e r
5
T(mK)
'
I
'
I
'
I
'
,
I 6
,
I 8
,
I 10
,
I
'
120 100 80 60 40 4
I , 12 n4(gmol/s)
Figure 2 Minimum temperature as function of 4He flow rate for 63 = 1.5/~mols 1
cryostat depends only on the 4He flow rate, according to the relation W = 5 T 2 ti 4, where T is the temperature in K and h 4 the 4He flow rate in tool s -1 (reference 3). This explains the increase in temperature (Figure 2) as the 4He flow rate decreases. As the flow rate increases above 10/zmols -~, the heat exchange in exchanger (3) deteriorates and viscous heating becomes more important, thus causing a small increase in the minimum temperature. In conclusion, a 4He flow rate of ti4 6/zmol s -1 is enough to run the cryostat below 100 mK. Figure 3 shows the cooling power as a function of temperature for several flow rates. The cooling power is well represented by a T 2 law but, for unknown reasons, it is reduced by a factor of 2 with respect to the theoretical value. From these curves, we can deduce that the total heat leak on the cryostat is of the order of 100 nW. =
Discussion
Heat load on 4 K precooling stage Using a perfect heat exchanger between room temperature and the input of the cryostat, the input power for precooling the fluid is given by the enthalpy difference between the input and output fluids at 4.2 K. For a flow rate of 10/zmols 1, this gives a typical power of the order of 1 mW. Because of the low flow rates used in this system, an almost ideal heat exchanger can be constructed and the heat load will not exceed the theoretical value significantly. Measurements of the real heat load are in progress.
0.8 0.6
-0.2 0
0.02
0.04
0.06 0.(18T 2(K2)
Figure 3 Temperature variation with applied power for different flow rates. Full lines are linear fits: a, 20/~ms 1 with W= 47T~; b, 12/~ms 1 with W= 207"9; c, 6/~ms -1 with W = 11T 2
Dilution refrigerator for space applications: A. Benort and S. Pujol Working life of system With these flow rates the typical quantities of gas needed are 1000dm 3 per year of 3He and 4000 dm 3 per year of 4He. If we use high pressure titanium spheres (volume 33 dm 3, pressure 260bar, weight 7.2kg) the cryostat needs one 3He sphere and three 4He spheres for six years, corresponding to 28.8 kg.
Sensitivity to absence of gravity In this system, all fluids are confined in small tubes and the surface tension is larger than the forces of gravity. Therefore, the position of the phase separation interface is insensitive to gravity. This result has been confirmed by previous experiments in which the cryostat was rotated to various give orientations around the horizontal axis 2.
working at 4.2 K. The simplicity of the system makes it very reliable and the heat load on the cryogenerator does not exceed a few milliwatts. The refrigerator can be controlled by adjusting the flow rates of the two fluids at the input of the cryostat. The dilution can be stopped and restarted to optimize helium gas consumption. The mass of the refrigerator itself is very small (less than 1 kg) and it does not need any external power supply. A gas storage system of ~ 3 0 k g is needed for continuous operation over six years.
Acknowledgement This work has been done with funding from the Centre National d'Etudes Spatiales, France.
Reliability The system is very simple and does not contain moving parts. The only problem that can stop refrigerator is a leak or a block in the capillary. using clean gas and a cold trap, it is possible for system to run for a long time without blocking.
any the By the
Conclusions With this design, it is possible to cool down detectors to lOOmK in a satellite with a small cryogenerator
References 1 Lounasmaa, O.V. Experimental Principles and Methods below I K Academic Press, London. UK (1974) 2 Benoit, A. and Pujol, S. Proc L T 19 Conf (1989) 3 Benoit, A. French Patent 8801232 (from Centre National d'Etudes Spatiales, Paris, France) (1988) 4 de Bruyn Ouboter, R., van den Brandt, B. and Tierolf, J.W. Physica B+C (1981) 107 557 5 Kuerten, J.G.M., Castelijns, C.A.M., de Waele A . T . A . M . and Gijsman, H.M. Phys Rev Lett (1986) 56 2288 6 Radebaugh, R. US Bureau of Standards Technical Note 362. Boulder, CO. USA (1967)
Cryogenics 1994 Volume 34, Number 5
423
The development of a new type of dilution cryostat with an open circuit for circulating 3He and 4He makes its use in space possible. If a cryogenerator is used as precooler to avoid the 4He bath, it is possible to cool the input gas down to 2 K before the dilution unit, using J o u l e - T h o m s o n expansion of the mixture a t t h e dilution output. This results in a simple refrigerator with a low power dissipation at 4 K and continuous operation below 100 mK. The working lifetime of the cryostat is limited by the quantity of gas. For six years of operation, the gas storage system should contain = 3 0 kg.
Keywords: space cryogenics; dilution refrigerators; cryocoolers
The development of new cryogenic particle detectors (bolometers) makes it of considerable interest to build a cryostat for working at below 1 K in space. The operation of a classical dilution refrigerator (see, for example, reference 1) in weightless conditions is difficult because gravity is used to stabilize the phase separation interfaces in the still and in the mixing chamber. Another problem arises from the complex pumping installation. These two problems can be solved using different techniques, but the result is a complex system with charcoal pumps. To make a simple cryostat that works at 0.1 K in space, we have developed a refrigerator that works without recycling the helium used for dilution 2"3. This system does not require a still or pumping system, and will operate in the absence of gravity. The disadvantage is the necessity to take enough helium for the lifetime of the mission, but with small flow rates, continuous operation for more than five years is possible. The basic design uses Joule-Thomson expansion at the output of the dilution unit. Therefore, the dilution stage only requires a cold source near 4 K instead of the 2 K precooling stage of the previous version 2'3.
Description
The two fluids are then cooled in the continuous heat exchanger (3). At the end of the heat exchanger, they are mixed together, producing cooling due to the enthalpy difference between pure and dilute 3He 4. The mixture is used to cool down the cold plate (4) and it then leaves the cryostat after exchanging heat in the exchanger (3). Up to the end of the heat exchanger, before the impedance (5), the fluids are at a pressure
toni excl
col(
A schematic drawing of the cryostat is presented in Figure 1. The two pure gases are injected under pressure (5bar ¢) and precooled at 4.2K in heat exchangers (1). Further precooling is achieved down to 2 K through heat exchangers (2).
*Paper presented at the 1993 Space Cryogenics Workshop, 20-21 July 1993, San Jose, CA, USA '1 bar = 105N m2
0011-2275/94/050421-03 ~') 1994 Butterworth-Heinemann Ltd
Figure 1 Schematic drawing of cryostat (see text for opera-
tional details)
Cryogenics 1994 Volume 34, Number 5
421
Dilution refrigerator for space applications: A. Benoft and S. Pujol higher than the critical pressure and there is only a small pressure drop due to viscosity. In a state of thermodynamic equilibrium, the 3He concentration decreases with increasing temperature. To extract the 3He at the hot end of the heat exchanger, we must avoid the counterflow diffusion of 3He in the tube. Therefore, the 3He injection flow rate is maintained at a value higher than the solubility limit (ti3/ri4 > 10%) and bubbles of pure 3He are pushed into the output tube of the heat exchanger (3). With tubes of 0 . 1 0.3ram diameter, the surface tension maintains a sequence of concentrated and dilute droplets 4 to avoid 3He diffusion in the dilute phase. As the temperature increases, the bubbles dissolve. Therefore, in the high temperature part of the heat exchanger (3), the mutual friction between 3He and superfluid 4He5 is used to avoid the counterflow diffusion of 3He. This implies a high enough fluid velocity, which is obtained using tubes of small diameter at the exit from the heat exchanger (typically 30/zm). At the output of exchanger (3), the dilute mixture is expanded through the impedance (5). The J o u l e Thomson expansion produces a cooling power of the 1 order of 120J mol- at a temperature between 1.5 and 2K, depending on the pumping pressure of the gas. Part of this power ( = 2 0 J mol- 1) is used to cool the input gas down to 2 K in heat exchanger (2) before the dilution unit. Joule-Thomson expansion is a well established technique which is accurately described by theory. The presence of a small fraction ( < 2 0 % ) of 3He in the 4He introduces only a small correction to the cooling power produced with pure 4He. One limitation of the performance of J o u l e Thomson expansion is due to the presence of a superfluid helium film in the pumping tube. In the 20% mixture, the temperat'ure of the )l point is smaller than in bulk 4He ( T a = 1.87K), but the properties are similar 6. We can show that heating by the superfluid helium film is relatively more important at small flow rates, but we do not need to precool the input fluids below the ,~ point temperature.
Results
To test this method of refrigeration, we have built a cryostat where the input fluids are precooled to 4.2 K by thermal contact with a helium bath through a thermal impedance. The Joule-Thomson expansion cools down the screen (6) to between 1.3 and 1.5 K, depending on the flow rate and the 3He concentration. The temperature of the cold plate is given in Figure 2 as a function of 4He flow rate for a fixed 3He flow rate ofri 3 = 1.5/xmols 1. This corresponds to the minimum 3He flow rate needed to avoid counterflow diffusion. At lower 3He flow rates, the system becomes unstable. Increasing the 3He flow rate even more causes an increase in temperature due to an extra heat load on the heat exchanger. Because the system is operated with an excess of 3He, the amount of 3He diluted is given by the product of the solubility limit (6.4%) and the 4He flow rate. Therefore, the theoretical cooling power of such a
422
Cryogenics
1994 V o l u m e
34, N u m b e r
5
T(mK)
'
I
'
I
'
I
'
,
I 6
,
I 8
,
I 10
,
I
'
120 100 80 60 40 4
I , 12 n4(gmol/s)
Figure 2 Minimum temperature as function of 4He flow rate for 63 = 1.5/~mols 1
cryostat depends only on the 4He flow rate, according to the relation W = 5 T 2 ti 4, where T is the temperature in K and h 4 the 4He flow rate in tool s -1 (reference 3). This explains the increase in temperature (Figure 2) as the 4He flow rate decreases. As the flow rate increases above 10/zmols -~, the heat exchange in exchanger (3) deteriorates and viscous heating becomes more important, thus causing a small increase in the minimum temperature. In conclusion, a 4He flow rate of ti4 6/zmol s -1 is enough to run the cryostat below 100 mK. Figure 3 shows the cooling power as a function of temperature for several flow rates. The cooling power is well represented by a T 2 law but, for unknown reasons, it is reduced by a factor of 2 with respect to the theoretical value. From these curves, we can deduce that the total heat leak on the cryostat is of the order of 100 nW. =
Discussion
Heat load on 4 K precooling stage Using a perfect heat exchanger between room temperature and the input of the cryostat, the input power for precooling the fluid is given by the enthalpy difference between the input and output fluids at 4.2 K. For a flow rate of 10/zmols 1, this gives a typical power of the order of 1 mW. Because of the low flow rates used in this system, an almost ideal heat exchanger can be constructed and the heat load will not exceed the theoretical value significantly. Measurements of the real heat load are in progress.
0.8 0.6
-0.2 0
0.02
0.04
0.06 0.(18T 2(K2)
Figure 3 Temperature variation with applied power for different flow rates. Full lines are linear fits: a, 20/~ms 1 with W= 47T~; b, 12/~ms 1 with W= 207"9; c, 6/~ms -1 with W = 11T 2
Dilution refrigerator for space applications: A. Benort and S. Pujol Working life of system With these flow rates the typical quantities of gas needed are 1000dm 3 per year of 3He and 4000 dm 3 per year of 4He. If we use high pressure titanium spheres (volume 33 dm 3, pressure 260bar, weight 7.2kg) the cryostat needs one 3He sphere and three 4He spheres for six years, corresponding to 28.8 kg.
Sensitivity to absence of gravity In this system, all fluids are confined in small tubes and the surface tension is larger than the forces of gravity. Therefore, the position of the phase separation interface is insensitive to gravity. This result has been confirmed by previous experiments in which the cryostat was rotated to various give orientations around the horizontal axis 2.
working at 4.2 K. The simplicity of the system makes it very reliable and the heat load on the cryogenerator does not exceed a few milliwatts. The refrigerator can be controlled by adjusting the flow rates of the two fluids at the input of the cryostat. The dilution can be stopped and restarted to optimize helium gas consumption. The mass of the refrigerator itself is very small (less than 1 kg) and it does not need any external power supply. A gas storage system of ~ 3 0 k g is needed for continuous operation over six years.
Acknowledgement This work has been done with funding from the Centre National d'Etudes Spatiales, France.
Reliability The system is very simple and does not contain moving parts. The only problem that can stop refrigerator is a leak or a block in the capillary. using clean gas and a cold trap, it is possible for system to run for a long time without blocking.
any the By the
Conclusions With this design, it is possible to cool down detectors to lOOmK in a satellite with a small cryogenerator
References 1 Lounasmaa, O.V. Experimental Principles and Methods below I K Academic Press, London. UK (1974) 2 Benoit, A. and Pujol, S. Proc L T 19 Conf (1989) 3 Benoit, A. French Patent 8801232 (from Centre National d'Etudes Spatiales, Paris, France) (1988) 4 de Bruyn Ouboter, R., van den Brandt, B. and Tierolf, J.W. Physica B+C (1981) 107 557 5 Kuerten, J.G.M., Castelijns, C.A.M., de Waele A . T . A . M . and Gijsman, H.M. Phys Rev Lett (1986) 56 2288 6 Radebaugh, R. US Bureau of Standards Technical Note 362. Boulder, CO. USA (1967)
Cryogenics 1994 Volume 34, Number 5
423