Theoretical model of a Stirling/Pulse tube hybrid refrigerator and its verification

Abstract

Stirling/pulse tube hybrid refrigerator, a novel refrigerator composed of Stirling refrigerator as the first stage and pulse tube refrigerator as the second stage, has great potential in space detection applications. This kind of hybrid refrigerator exhibits outstanding comprehensive performance in reliability, efficiency and compactness due to its unique structure. However, there is usually a contradiction between revealing the reality accurately and giving an analytical expression for the existing models. Focusing on accuracy and analyticity, a theoretical model is purposed. In the theoretical model, the major factors affecting the overall performance, including the acoustic inertance, the acoustic compliance, the viscous resistance, the axial temperature gradient and the thermodynamic process in the working chambers, are taken into consideration. By adopting the thermoacoustic equations and the chamber equations, the theoretical model is able to give analytical expressions which can reveal the underlying mechanism mathematically. The theoretical model is verified numerically and experimentally. The cooling capacity of both stages, pressure and acoustic power among the theoretical model, the numerical model and the experiment are compared, and a good trend consistency with respect to the displacer phase is achieved. Based on the theoretical model, the inter-stage cooling capacity allocation characteristics can be explained as the change of phase distribution. Compared with the existing models, the theoretical model is able to reflect the reality in a satisfactory way as well as provide a way to explicitly study the thermodynamic characteristics of Stirling/pulse tube hybrid refrigerator mathematically with analytical expressions, which will provide a better insight to its appropriate design.