380:(GM) coolers have found widespread application in many low-temperature systems e.g. in MRI and cryopumps. Fig.5 is a schematic diagram. Helium at pressures in the 10–30 bars (150–440 psi) range is the working fluid. The cold head contains a compression and expansion space, a regenerator, and a displacer. Usually the regenerator and the displacer are combined in one body. The pressure variations in the cold head are obtained by connecting it periodically to the high- and low-pressure sides of a compressor by a rotating valve. Its position is synchronized with the motion of the displacer. During the opening and closing of the valves irreversible processes take place, so GM-coolers have intrinsic losses. This is a clear disadvantage of this type of cooler. The advantage is that the cycle frequencies of the compressor and the displacer are uncoupled so that the compressor can run at power-line frequency (50 or 60 Hz) while the cycle of the cold head is 1 Hz. In this way the swept volume of the compressor can be 50 or 60 times smaller than of the cooler. Basically (cheap) compressors of domestic refrigerators can be used, but one must prevent overheating of the compressor as it is not designed for helium. One must also prevent oil vapor from entering the regenerator by high-quality purification traps.
27:. The term is most often used for smaller systems, typically table-top size, with input powers less than about 20 kW. Some can have input powers as low as 2–3 W. Large systems, such as those used for cooling the superconducting magnets in particle accelerators are more often called cryogenic refrigerators. Their input powers can be as high as 1 MW. In most cases cryocoolers use a cryogenic fluid as the working substance and employ moving parts to cycle the fluid around a thermodynamic cycle. The fluid is typically compressed at room temperature, precooled in a heat exchanger, then expanded at some low temperature. The returning low-pressure fluid passes through the heat exchanger to precool the high-pressure fluid before entering the compressor intake. The cycle is then repeated.
438:
218:
202:
99:
235:
389:
360:
500:
521:(300 K) and the pressure is 200 bars (2,900 psi) (point b). Next it enters the warm (high-pressure) side of the counterflow heat exchanger where it is precooled. It leaves the exchanger at point c. After the JT expansion, point d, it has a temperature of 77.36 K (−195.79 °C; −320.42 °F) and a pressure of 1 bar. The liquid fraction is
351:
provide stiffness in the radial direction and flexibility in the axial direction. The pistons and the compressor casing don't touch so no lubricants are needed and there is no wear. The regenerator in the cold finger is suspended by a spring. The cooler operates at a frequency near the resonance frequency of the mass-spring system of the cold finger.
802:
350:
Another type of
Stirling cooler is the split-pair type (Fig.4), consisting of a compressor, a split pipe, and a cold finger. Usually there are two pistons moving in opposite directions driven by AC magnetic fields (as in loudspeakers). The pistons can be suspended by so-called flexure bearings. They
511:
The Joule-Thomson (JT) cooler was invented by Carl von Linde and
William Hampson so it is also called the Linde-Hampson cooler. It is a simple type of cooler which is widely applied as cryocooler or as the (final stage) of coolants. It can easily be miniaturized, but it is also used on a very large
317:
is the volume between the two pistons. In practice the cycle is not divided in discrete steps as described above. Usually the motions of both pistons are driven by a common rotary axes which makes the motions harmonic. The phase difference between the motions of the two pistons is about 90°. In the
57:
An important component of refrigerators, operating with oscillatory flows, is the regenerator. A regenerator consists of a matrix of a solid porous material, such as granular particles or metal sieves, through which gas flows back and forth. Periodically heat is stored and released by the material.
520:
In Fig.8 the pressures and temperatures refer to the case of a nitrogen liquefier. At the inlet of the compressor the gas is at room temperature (300 K) and a pressure of 1 bar (point a). The compression heat is removed by cooling water. After compression the gas temperature is ambient temperature
420:
From b to c. The HP valve is closed and the LP valve opened with fixed position of the displacer. Part of the gas flows through the regenerator to the LP side of the compressor. The gas expands. The expansion is isothermal so heat is taken up from the application. This is where the useful cooling
346:
It is not so practical to have a cold piston, as described above, so, in many cases, a displacer is used instead of the cold piston. A displacer is a solid body which moves back and forth in the cold head driving the gas back and forth between the warm and the cold end of the cold head via the
58:
The thermal contact with the gas must be good and the flow resistance of the matrix must be low. These are conflicting requirements. The thermodynamic and hydrodynamic properties of regenerators are complicated, so one usually makes simplifying models. In its most extreme form an
371:
are buffer volumes of the compressor. The compression heat is removed by the cooling water of the compressor via a heat exchanger. The rotary valves alternatingly connect the cooler to the high- and the low-pressure sides of the compressor and runs synchronous with the
529:) flows into the cold (low-pressure) side of the counterflow heat exchanger (point f). It leaves the heat exchanger at room temperature (point a). In order to keep the system in the steady state, gas is supplied to compensate for the liquid fraction
427:
From d to a. The LP valve is closed and the HP valve opened with fixed position of the displacer. The gas, now in the hot end of the cold head, is compressed and heat is released to the surroundings. In the end of this step we are back in position
238:
Fig.4 Schematic diagram of a split-pair
Stirling refrigerator. The cooling power is supplied to the heat exchanger of the cold finger. Usually the heat flows are so small that there is no need for physical heat exchangers around the split
347:
regenerator. No work is required to move the displacer since, ideally there is no pressure drop over it. Typically its motion is 90 degrees out of phase with the piston. In the ideal case the COP also equals to the Carnot COP.
806:
399:
The cycle starts with the low-pressure (LP) valve closed, the high-pressure (HP) valve open, and the displacer all the way to the right (so in the cold region). All the gas is at room temperature.
424:
From c to d. The displacer moves to the right with the cold head connected to the LP side of the compressor forcing the cold gas to pass the regenerator, while taking up heat from the regenerator.
403:
From a to b. The displacer moves to the left while the cold head is connected to the HP side of the compressor. The gas passes the regenerator entering the regenerator at ambient temperature
512:
scale in the liquefaction of natural gas. A schematic diagram of a JT liquefier is given in Fig.8. It consists of a compressor, a counterflow heat exchanger, a JT valve, and a reservoir.
536:
When used as a cryocooler it is preferable to use gas mixtures instead of pure nitrogen. In this way the efficiency is improved and the high pressure is much lower than 200 bar.
451:
A so-called
Stirling-type single-orifice PTR is represented schematically in Fig.7. From left to right it consists of: a piston which moves back and forth; a heat exchanger X
40:
are important components of all cryocoolers. Ideal heat exchangers have no flow resistance and the exit gas temperature is the same as the (fixed) body temperature
623:
T. Kuriyama, R. Hakamada, H. Nakagome, Y. Tokai, M. Sahashi, R. Li, O. Yoshida, K. Matsumoto, and T. Hashimoto, Advances in
Cryogenic Engineering 35B, 1261 (1990)
268:
From b to c. The two pistons move to the right. The volume between the two pistons is kept constant. The hot gas enters the regenerator with temperature
85:
Progress in the cryocooler field in recent decades is in large part due to development of new materials having high heat capacity below 10 K.
295:
From d to a. The two pistons move to the left while the total volume remains constant. The gas enters the regenerator with low temperature
507:
of the compressed gas is removed as liquid. At room temperature it is supplied as gas at 1 bar, so that the system is in the steady state.
247:
From a to b. The warm piston moves to the right while the cold piston is fixed. The temperature of compressed gas at the hot end is
243:
The cooling cycle is split in 4 steps as depicted in Fig.2. The cycle starts when the two pistons are in their most left positions:
309:
so heat is taken up from the regenerator material. At the end of this step the state of the cooler is the same as in the beginning.
824:
285:
From c to d. The cold piston moves to the right while the warm piston is fixed. The expansion is isothermal and heat
318:
ideal case the cycle is reversible so the COP (the ratio of the cooling power and the input power) is equal to the
834:
577:
548:
593:
446:
313:
In the pV diagram (Fig.3) the corresponding cycle consists of two isotherms and two isochores. The volume
583:
47:
of the heat exchanger. Note that even a perfect heat exchanger will not affect the entrance temperature
539:
A more detailed description of Joule-Thomson coolers and Joule-Thomson refrigerators can be found in.
473:) where heat is absorbed from the application; a tube, often called the pulse tube; a heat exchanger X
759:
696:
829:
588:
572:
437:
525:. The liquid leaves the system at the bottom of the reservoir (point e) and the gas (fraction 1 −
120:
The basic type of
Stirling-type cooler is depicted in Fig.1. It consists of (from left to right):
785:
728:
604:
102:
Fig.1 Schematic diagram of a
Stirling cooler. The system has one piston at ambient temperature
777:
720:
712:
665:
556:
552:
377:
178:. The work, performed during the expansion, is used to reduce the total input power. Usually
767:
704:
655:
217:
201:
98:
598:
708:
763:
700:
234:
224:
208:
191:
37:
388:
359:
818:
789:
732:
499:
319:
632:
W.E. Gifford and R.C. Longsworth, Advances in
Cryogenic Engineering 11, 171 (1966)
684:
772:
660:
248:
175:
781:
716:
669:
160:
Left and right the thermal contact with the surroundings at the temperatures
643:
20:
747:
724:
484:); a flow resistance (orifice); a buffer volume, in which the pressure
179:
748:"Viewpoint: Compact cryogenics for superconducting photon detectors"
174:
is supposed to be perfect so that the compression and expansion are
127:
a compression space and heat exchanger (all at ambient temperature
560:
23:
temperatures (below 120 K, -153 °C, -243.4 °F) is often called a
396:
The cycle can be divided in four steps, with Fig.6, as follows:
441:
Fig.7 Schematic diagram of a
Stirling-type single-orifice PTR.
392:
Fig. 6 The four stages in the cooling cycle of the GM cooler.
685:"Cryocoolers: the state of the art and recent developments"
547:
Cryocoolers are a key enabling technology for applications
455:(after cooler) where heat is released at room temperature (
417:. Heat is released by the gas to the regenerator material.
555:. Applications include superconducting electronics and
258:
is given off to the surroundings at ambient temperature
810:
503:
Fig. 8 Schematic diagram of a JT liquefier. A fraction
462:) to the environment; a regenerator; a heat exchanger X
75:
zero porosity (this is the volume fraction of the gas);
644:"Basics of Joule–Thomson Liquefaction and JT Cooling"
282:. The gas gives off heat to the regenerator material.
746:
Cooper, Bernard E; Hadfield, Robert H (2022-06-28).
78:zero thermal conductivity in the flow direction;
559:. Compact cryocoolers have been developed for
66:large volumetric heat capacity of the material;
811:National Institute of Standards and Technology
292:is taken up. This is the useful cooling power.
16:Refrigeration system that cools to below 120 K
8:
69:perfect heat contact between gas and matrix;
62:regenerator has the following properties:
771:
659:
363:Fig.5 Schematic diagram of a GM-cooler. V
498:
436:
387:
358:
233:
97:
616:
33:Ideal heat exchangers and regenerators
752:Superconductor Science and Technology
149:a piston (all at the low temperature
7:
689:Journal of Physics: Condensed Matter
642:de Waele, A. T. A. M. (2017-03-01).
302:and leaves it with high temperature
72:zero flow resistance of the matrix;
648:Journal of Low Temperature Physics
109:and one piston at low temperature
54:of the gas. This leads to losses.
14:
19:A refrigerator designed to reach
805: This article incorporates
800:
561:superconducting photon detectors
410:and leaving it with temperature
216:
200:
138:
275:and leaves it with temperature
709:10.1088/0953-8984/21/16/164219
223:Fig.3 pV-diagram of the ideal
1:
683:Radebaugh, Ray (2009-03-31).
851:
444:
189:
661:10.1007/s10909-016-1733-3
578:Adiabatic demagnetization
491:is practically constant.
251:(by definition), so heat
207:Fig.2 Four states in the
773:10.1088/1361-6668/ac76e9
433:Pulse-tube refrigerators
594:Pulse tube refrigerator
533:that has been removed.
447:Pulse tube refrigerator
807:public domain material
508:
442:
393:
373:
240:
182:is the working fluid.
117:
89:Stirling refrigerators
601:(Stirling cryocooler)
584:Dilution refrigerator
502:
477:to room temperature (
440:
391:
362:
237:
101:
495:Joule-Thomson cooler
466:at low temperature (
764:2022SuScT..35h0501C
701:2009JPCM...21p4219R
589:Hampson-Linde cycle
573:Cryogenic processor
825:Cooling technology
605:Entropy production
549:infrared detection
509:
443:
421:power is produced.
394:
374:
241:
146:an expansion space
118:
557:quantum computing
553:superconductivity
81:the gas is ideal.
842:
835:Industrial gases
804:
803:
794:
793:
775:
743:
737:
736:
680:
674:
673:
663:
639:
633:
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621:
355:GM-refrigerators
220:
204:
143:a heat exchanger
850:
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599:Stirling engine
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38:Heat exchangers
35:
17:
12:
11:
5:
848:
846:
838:
837:
832:
827:
817:
816:
796:
795:
738:
695:(16): 164219.
675:
654:(5): 385–403.
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809:from the
808:
791:
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769:
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761:
758:(8): 080501.
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516:Cooling cycle
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384:Cooling cycle
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332:
325:
322:COP given by
321:
316:
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298:
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271:
267:
261:
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246:
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186:Cooling cycle
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105:
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93:
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26:
22:
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751:
741:
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688:
678:
651:
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619:
580:refrigerator
551:and applied
546:
543:Applications
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510:
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119:
110:
103:
84:
59:
56:
48:
41:
36:
29:
24:
18:
139:regenerator
830:Cryogenics
819:Categories
611:References
372:displacer.
249:isothermal
190:See also:
176:isothermal
94:Components
25:cryocooler
790:249534834
782:0953-2048
717:0953-8984
670:1573-7357
21:cryogenic
733:22695540
725:21825399
567:See also
376:Gifford-
124:a piston
760:Bibcode
697:Bibcode
378:McMahon
788:
780:
731:
723:
715:
668:
320:Carnot
180:helium
786:S2CID
729:S2CID
367:and V
239:pipe.
60:ideal
778:ISSN
721:PMID
713:ISSN
666:ISSN
167:and
768:doi
705:doi
656:doi
652:186
343:).
821::
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563:.
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658::
531:x
527:x
523:x
505:x
489:B
486:p
482:a
479:T
475:3
471:L
468:T
464:L
460:a
457:T
453:1
415:L
412:T
408:a
405:T
369:h
365:l
341:L
338:T
334:a
331:T
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324:T
315:V
307:a
304:T
300:L
297:T
290:L
287:Q
280:L
277:T
273:a
270:T
265:.
263:a
260:T
256:a
253:Q
227:.
211:.
172:L
169:T
165:a
162:T
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151:T
134:)
132:a
129:T
116:.
114:L
111:T
107:a
104:T
52:i
49:T
45:X
42:T
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