ADIABATIC LOSSES IN STIRLING CRYOCOOLERS - A STRATIFIED FLOW MODEL

A numerical model of Stirling cryocoolers is presented in which the ma chine is divided into spaces that are either fully isothermal or fully adiabatic. In adiabatic spaces, the flow is one-dimensional and strat ified. Pressure is time-dependent, but spatially uniform. The model in cludes two conservation laws, namely for mass and energy. With respect to space, the conservation laws are integrable in closed form, so tha t numerical, iterative integration is required only with respect to ti me. The program implementing the proposed solution is fairly simple an d very fast, because numerical integration with respect to space has b een eliminated and replaced by the closed-form solution. Results are p resented for two sets of assumptions regarding the expansion space. In both cases, the compression space is assumed to be adiabatic and stra tified, while the heat exchangers are isothermal. Small cryocoolers ma y not have a freezer, in which case heat exchange occurs mainly in the expansion space which, in this situation, can be approximated by an i sothermal model. For larger cryocoolers, the ratio heat exchange area/ volume in the expansion space deteriorates; eventually, a separate fre ezer become necessary and the expansion space becomes nearly adiabatic . The adiabatic losses for these two cases are compared. Results are p resented for temperature ratios between 0.1 and 0.95 and phase angles between 0 and 180-degrees. Three different geometries are studied, in which the ratio of the swept volumes is varied between 0.5 and 1.