Larry R. D'Addario
September 10, 1998
Keywords: receiver, cryogenic, refrigerator, Joule-Thompson, JT
This memo reports a theoretical study of some tradeoffs in the design of cryocoolers for temperatures of about 4K. In particular, it assumes a helium-4 Joule-Thompson (J-T) expander as the final refrigeration stage and considers the effect of the operating parameters of this stage on the total efficiency, including the necessary pre-cooling stage. The operating parameters are the temperature and pressure of the helium gas entering the J-T stage. Other design parameters are also considered, including the efficiencies of the heat exchangers, the efficiency of the pre-cooling refrigerator, and the efficiency of the J-T circuit compressor. It is found that the overall power consumption depends only weakly on the J- T supply pressure, but strongly on the pre-cooling temperature. High efficiency in the recuperative heat exchangers is essential (at least 98%). With perfect heat exchangers and with a precooler operating at 1% of Carnot efficiency, the optimum J-T inlet condition is P = 15atm and T = 17K. Only if the precooler is more efficient does it become worthwhile to pre-cool to significantly lower temperature. Under nearly all practical conditions, the total input power is dominated by that needed to run the precooler rather than that needed to compress the helium in the J-T circuit. With 99% efficient heat exchangers, pre-cooling at 3% of Carnot efficiency, and compression efficiency at 45% of adiabatic (all practical values), the total power required per unit cooling at 3.8K is 2800, of which 2125 is for pre-cooling to 12.5K and 675 is for compressing to 10atm (i.e., for 0.5W at 3.8K, the predicted power consumption is 1400W=1062W+338W). This is substantially better than is usually achieved, and is simply the result of careful optimization.
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Last modified: 09 December, 1999
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