A stirling cycle analysis with gas-wall heat transfer in compressor and expander

Abstract

A cycle analysis that includes the gas-wall heat transfer in compressors and expanders of Stirling cryocoolers is presented. The gas-wall heat transfer in the working spaces is quite different from the conventional convective heat transfer, since the pressure of the working gas inside the spaces oscillates and the heat transfer may not be in phase with the temperature difference between the gas and the wall. Several experimental and theoretical expressions have been published to date to estimate the amount of the gas-wall heat transfer and the so-called hysteresis loss for a gas spring. While most of the expressions for the gas spring are not directly applicable to the working spaces of Stirling coolers, some might be useful in predicting its effect on refrigeration. The conventional adiabatic analysis for Stirling cycle is generalized by adding the heat transfer terms to the energy balance equations for the two working spaces. Of the several existing heat transfer relations for the gas spring, three different relations are used and compared. The results are verified by observing that the cycle asymptotically approaches the Schmidt isothermal limit for very small Peclet numbers and the Finkelstein adiabatic limit for very large Peclet numbers. It is found that the effect of the gas-wall heat transfer on the refrigeration would not be significant except for low-speed miniature coolers. The analyses are repeated for various frequencies, the bore/stroke ratios, the dead volumes and the phase angles between the two pistons, and their effects on the cooler performance are discussed.