CHAPTER III Closed cycle refrigerators and cryocoolers 1. Introduction In Chapter II we described the principles of liquefaction of gases to produce low temperatures. A second method of producing low temperatures is by using a closed cycle cooling system. When the cooling power is in the range of kilowatts the cooling system is referred to as a Cryorefrigerator. If, on the other hand, the cooling power produced is below a few watts, the cooling system is generally called as a Cryocooler. 2. Helium Refrigerator The helium liquefier circuit described in Chapter II can be used with some simple modifications as a Closed Cycle refrigerator . Here the liquid helium after Joule Thomson expansion is circulated through the part to be cooled. The vaporized helium then passes through the cold side of the train of heat exchangers and returns back to the compressor. In large size charged particle accelerator systems as well as in thermo- nuclear fusion devices, big size superconducting magnets are used. They need refrigeration power in kilowatts at 4.2 K or lower. Closed cycle helium refrigerators are then the only option available for cooling these devices. A schematic of a 1 kW helium refrigerator system planned to be used in the Institute for Plasma Research at Ahmedabad for the Superconducting Tokomak project is described by Sarkar et al. (1) in the Proceedings of the 18 th International Cryogenic Engineering Conference held in 2000. This will be a helium refrigerator producing 650 W of refrigeration along with a liquefaction capacity of 200 l/hr. Larger helium refrigerators have been built and are operating successfully at various accelerator laboratories all over the world. The discussions on large-scale helium refrigeration systems are not discussed hereafter since this is beyond the scope of this book. 3. Closed cycle cryocoolers Like a heat engine, a cryocooler also makes use a working substance, which undergoes a thermodynamic cycle of operations. However, the cooling cycle is in the reverse direction to that of a heat engine. In a closed cycle cryocooler the working substance absorbs a certain amount of heat, Q c , from the sample at the cold temperature Tc and rejects a greater amount of heat, Q W, at a warm temperature T W. Since Q W is larger than Q c, external work W has to be done on the working substance in each cycle. 25 The amount of work needed to extract unit quantity of heat at the cold temperature T c, or in other words, the ratio W/Q c is a measure of the effectiveness of the refrigerator. The cryocooler based on Carnot cycle is the ideal refrigerator in which all processes are reversible. For this ideal Carnot refrigerator, (W/Q c) Carnot = (T W −Tc )/T c (III.3.1) The performance of an actual cooling cycle is compared with that of the ideal Carnot cycle. The efficiency of an actual cycle is defined as η = (W/Q c) Carnot / (W/Q c) actual (III.3.2) and is expressed as a percentage. The higher the value of η the more efficient is the cycle. A closed circuit cryocooler can be multi-staged. The principle of operation of a two- stage cryocooler is shown in Figure III.1. In the second stage of the cooler, heat Q c is absorbed at a temperature T c and work W 2 is done on the working substance to raise its temperature from T c to an intermediate temperature T i. Figure III1 Multi-staged cryocooler system This now acts as the cold end of the first stage of the cryocooler. At this intermediate temperature a quantity of heat Q i may be absorbed from another object. The total energy in the working substance at Ti will be Q = Q c + W 2 + Q i (III.3.3) 26 Further work W i is done on the working substance and heat Q w is rejected at the warm temperature T w. The working substance in most cryocoolers is helium gas. In a single stage system, these cryocoolers can reach a temperature of around 50 K and in the two stage system, the second stage cold end (also known as cold head) can reach a temperature around 10 K. These are the temperatures obtained, when there is no heat load on the cold head of the cryocooler except for the minimal heat leak from the warm parts of the cryocooler. If an additional heat load Q is supplied at the cold head (say by activating a heater), the cold head temperature rises. The higher the applied heat load, the higher is the cold end temperature. In the following we will use the words cryo-refrigerators and cryocoolers interchangeably.. There are many different thermodynamic cycles for a closed circuit refrigerator. We will describe here, only two most popular cycles, namely the Stirling and Gifford McMahon (GM) cycles. The cryorefrigerators built on these cycles have found worldwide acceptance. In both these cycles, the refrigerator consists of the following essential components. (i) a compressor to compress the gas, (ii) a displacer to move the gas from the cold to the warm end and vice-versa and (iii) a regenerator, to enable the gas to exchange heat with the same. But unlike the recuperative type heat exchanger, discussed in Chapter II , this is regenerative type heat exchanger, which means the following. At any instant of time, there is only one stream of gas, either warm or cold, passing through the regenerator. The regenerator serves as a repository of heat from the warm gas when it passes through the regenerator and as a supplier of heat when the cold gas passes through it. This will be discussed further in a later part of this chapter. The pulse tube cryocooler has been under development over the last two decades and has reached a stage where it can now compete with the other refrigerators for some applications. It differs from the above two cryorefrigerators, in that it has no displacer. A gas piston in the tube shuttles back and forth and serves the purpose of the displacer. The principle of operation of the pulse tube refrigerator will be briefly described in this chapter. In contrast to the above refrigerators, the Joule Thomson Cryocooler working down to 77 K usually operates in an open cycle. Although it needs a high pressure source of gas, it does not use a compressor. Though its efficiency is poor compared to Stirling and GM cycles, it finds limited applications. 27 4. Regenerator The regenerator should have the following characteristics. It should allow a relatively free passage for gas flow to ensure a low-pressure drop in the regenerator. The regenerator material must have a high thermal capacity in the temperature range in which it is used so that it can store the heat efficiently. Also, it should have a sufficiently large thermal conductivity so that temperature uniformity in a direction perpendicular to fluid flow is achieved quickly . But there should be high resistance to heat flow in the direction in which the fluid is flowing. This can be achieved either by using spacers of low thermal conductivity between layers of the regenerator material or by the suitable design of the regenerator material itself. For a single stage cryocooler operating down to ~ 30 K, the regenerator material will be a mesh of fine stainless steel or phosphor bronze wire. These metallic wires are 30 to 100 µm in diameters with mesh openings of the same size. Around 80 K, the thermal capacity of these materials is large and comparable to the classical value, 3R per gram mole. But below this temperature the specific heat decreases rapidly. For two stage cryorefrigerators, in which the second stage temperature is below 20K, one should use a material with a lower Debye Temperature than copper. Lead is a suitable material. It is used in the form of small spherical balls (with diameters of the order of a few hundred µm). Below 10 K, the thermal capacity of conventional regenerator materials is small compared to the thermal capacity of the working substance, namely, helium gas. This makes the regenerator efficiency quite low. This is the reason why the temperature range of operation of Stirling or GM refrigerators is usually limited to above 10 K. Newer magnetic materials, which have a large magnetic specific heat at very low temperatures, have been developed for use as regenerator material in the second stage of the refrigerator. These materials order magnetically in the temperature range 4 to 15 K. Such an ordering is associated with a large peak in specific heat. Of these materials, ErNi, besides having a large enough specific heat anomaly is chemically stable and also insensitive to oxidation. Using spheres of ErNi as regenerative material, it is possible to build two stage cryorefrigerators to provide refrigeration down to 4.2 K. 5. Stirling cycle cryorefrigerators The Stirling cycle heat engine was first patented by Stirling brothers in 1816. The use of reversed Stirling cycle for cryorefrigeration was the brain child of Kohlers in the Phillips Research Laboratories in Eindhoven, Holland. In the Stirling cryogenerator, a piston and a displacer are mounted on the same shaft. The ideal cycle of operations consist of two isothermal and two isochoric processes. The four phases of the reverse Stirling cycle are shown in Figure III.2. 28 Phase 1 : The displacer is at the top of the stroke and the piston is at the bottom of the stroke. The piston moves up while the displacer is stationary. The gas is compressed. Phase 2: Piston is at the top of the stroke and the displacer is moving down.