Adiabatic losses in Stirling cryocoolers: a stratified flow model

Abstract

A numerical model of Stirling cryocoolers is presented in which the machine is divided into spaces that are either fully isothermal or fully adiabatic. In adiabatic spaces, the flow is one-dimensional and stratified. Pressure is time-dependent, but spatially uniform. The model includes two conservation laws, namely for mass and energy. With respect to space, the conservation laws are integrable in closed form, so that numerical, iterative integration is required only with respect to time. The program implementing the proposed solution is fairly simple and very fast, because numerical integration with respect to space has been eliminated and replaced by the closed-form solution. Results are presented for two sets of assumptions regarding the expansion space. In both cases, the compression space is assumed to be adiabatic and stratified, while the heat exchangers are isothermal. Small cryocoolers may not have a freezer, in which case heat exchange occurs mainly in the expansion space which, in this situation, can be approximated by an isothermal model. For larger cryocoolers, the ratio heat exchange area/volume in the expansion space deteriorates; eventually, a separate freezer become necessary and the expansion space becomes nearly adiabatic. The adiabatic losses for these two cases are compared. Results are presented for temperature ratios between 0.1 and 0.95 and phase angles between 0 and 180°. Three different geometries are studied, in which the ratio of the swept volumes is varied between 0.5 and 1 † † The source code is available for inspection and non-commercial use as per the conditions specified in the program copyright notice. Please direct inquiries to the author .