Basic Limitations on the Performance of Stirling Cryocoolers

The flow through the regenerator of a Stirling cryocooler is driven by differences in pressure at the warm and cold sides. These differences lead to power dissipation in the regenerator. The pressure distribution in the regenerator is found using linearized theory. Expressions are derived for the rate of refrigeration and for the coefficient of performance (COP) at fixed amplitude of the piston at the warm side. The rate of refrigeration is optimized with respect to the amplitude and the phase of the piston on the cold side. The maximum rate of refrigeration and the corresponding COP are subject to severe limitations. These limitations are independent of the value of the regenerator conductance. In the limit of zero frequency and zero regenerator void volume, the COP at maximum rate of refrigeration is less than half of the Carnot value. The COP decreases as frequency and void volume increase. Results are presented for the piston amplitude ratio and phase difference corresponding to the maximum rate of re...