Developing an augmented onset model for a thermoacoustically-driven, pulse tube cryocooler

Abstract

This paper aimed to develop an augmented onset model for a looped-branched, thermoacoustically-driven, pulse tube cryocooler based on the transfer matrix model, introducing a reliable, uncomplicated prediction of the onset features compared to a full transient simulation of the thermoacoustic field. Disciplined successive multiplication of the element's matrices extracted from the linear thermoacoustic equations along with the joint, boundary and periodic conditions establish an eigenvalue onset problem. The corresponding problem solutions are in line with the earlier experimental results for a looped-branched thermoacoustic system. Investigating multiple layouts with specific startup characteristics indicated the ability of a four-stage cryocooler driven by two engines at each stage to reach an onset temperature difference of 45 K at liquid nitrogen temperature. Furthermore, the Morris screening method was adopted to rank the uncertain input factors, followed by the Sobol sensitivity analysis to quantify the uncertainty of model outcomes. The sensitivity quantification highlights that the uncertainty in the gas equation-of-state, specific heat capacity, and the cold regenerator mesh number predominantly affect the onset features. Other influential factors include the dimensions of the hot and cold segments of the unit that respectively affect the onset temperature and the frequency.