STIRLING CRYOCOOLER MODEL WITH STRATIFIED CYLINDERS AND QUASI-STEADY HEAT-EXCHANGERS

A new one-dimensional model of Stirling cryocoolers is presented. A ne w rate-dependent heat exchanger model is coupled with our existing str atified, isentropic cylinder model. As before, the regenerator is mode led as isothermal, and pressure is modeled as spatially uniform. The h eat exchanger model assumes that the time-dependent 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 displ acement. Under that assumption, the conservation laws for mass and ene rgy can be integrated in closed form with respect to the space variabl e, in all the spaces, including cylinders and dead volumes, heater, co oler, and regenerator. This reduces the problem to a set of ordinary d ifferential equations with respect to time, for pressure, velocity, an d temperature, or entropy at the interfaces between the different spac es. 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 geo metric designs with the same compression ratio.