Mathematical and Optimization Analysis of a Miniature Stirling Cryo-cooler

Abstract

In the given report, a comprehensive analytical model of the working of a miniature Stirling Cyo-cooler is presented. The motivation of the study is to determine the optimum geometrical parameters of a cryo-cooler such as compressor length, regenerator diameter, expander diameter, and expander stroke. In the first part of the study, an ideal analysis is carried out using the Stirling Cycle and basic thermodynamics equations. Using these equations, rough geometrical parameters are found out.
In the second part of the study, a more comprehensive Schmidt’s analysis is carried out. In this analysis, pressure and volume variations are considered sinusoidal and based on these, various equations regarding efficiency and COP are derived. Various graphs are generated in MATLAB plotting Refrigeration and Work done w.r.t to various geometrical parameters. With the help of these graphs, the net refrigeration obtained is calculated for a given geometry of cryo-cooler.. This model provides a more accurate picture of the cryo-cooler. However in this analysis, regenerator efficiency is considered 100 % which is not true in practical cases.
In the third and final part of the study, optimization of regenerator is carried out. This part is based on Ackermann’s analysis in which various looses taking place inside a regenerator are considered and accounted for. These looses are minimized using an iterative cycle and optimum regenerator dimensions are obtained. Thus the geometrical results obtained from the third part of the study are expected to be most accurate as it accounts for most of the looses taking place inside a cryo-cooler.