Numerical Model for Pulse Tubes Using Method of Lines

Abstract

An accurate two-dimensional (2D) numerical model is necessary to calculate fundamentally 2D pulse tube loss mechanisms such as momentum streaming and radial gas-to-gas heat transfer. Scale analysis provides clear direction that consideration of nonlinear terms is essential for the accurate determination of the 2D pulse tube equations. The results of the scale analysis provide insight on how to solve the 2D model without having to perform mathematical “tricks” at the pulse tube ends as found with a previous nonlinear 1D model. An enhanced version of that model has been developed in which particular attention is paid to the end effects to improve the energy balance and to improve solution accuracy and convergence. Identified weaknesses in previously performed analyses are addressed with emphasis on viscosity and conductivity effects at the ends. The improved 1D model is an important and necessary step towards the next phase of the research, the solution of the 2D nonlinear pulse tube equations.