Transient Response of the Miniature,Reversed Stirling-Cycle,Cryogenic Cooling Machine—An Empirical Approach

Abstract

By regarding the ideal thermodynamic cycle as being artificially separated from the hardware, and by treating the former as a simple energy flux path, an energy-rate balance is set up for the miniature, reversed-cycle, Stirling cooling machine. Account is taken of thermal energy storage and release rates corresponding to the rates of change of temperature of regenerator and cylinder walls. There results a first-order, linear differential equation. Solutions are obtained numerically using the parameters of a tentative cooler design. The solutions are presented in the form of curves of temperature ratio, τ (=T_c/T_e), against time, t, at uniform angular speed. Regenerator inefficiency, I_e, emerges as the parameter that is most critical in the achievement of desired heat-lifting capacity at cryogenic temperatures. For a machine of given thermal mass, both I_e and η_c (cycle efficiency relative to corresponding Carnot efficiency) strongly influence the cool-down rate. The treatment is capable of application to Stirling machines operating as prime movers.