Stirling cryocooler model with stratified cylinders and quasisteady heat exchangers

Abstract

A new one-dimensional model of Stirling cryocoolers is presented. A new rate-dependent heat exchanger model is coupled with our existing stratified, isentropic cylinder model. As before, the regenerator is modeled as isothermal, and pressure is modeled as spatially uniform. The heat exchanger model assumes that the timedependent mass flow rate in the heat exchanger is spatially uniform. This is a fair approximation if the heat exchanger volume is relatively small compared to the displacement. Under that assumption, the conservation laws for mass and energy can be integrated in closed form with respect to the space variable, in all the spaces, including cylinders and dead volumes, heater, cooler, and regenerator. This reduces the problem to a set of ordinary differential equations with respect to time, for pressure, velocity, and temperature, or entropy at the interfaces between the different spaces. We solve these equations numerically. Results are presented, which show that for typical cryocooler designs, losses due to irreversible heat transfer can be limited to a small fraction of the adiabatic loss. In contrast, the adiabatic loss remains roughly constant for all geometric designs with the same compression ratio.