Analytical investigation of compressible oscillating flow in a porous media: A Second-order successive approximation technique

In this paper the field equations of compressible oscillating flow in the regenerator of Pulse Tube Refrigerators (PTRs) are solved. To obtain an analytical solution, successive approximation technique is applied to continuity, momentum, gas and matrix energy equations and ideal gas equation of state. In this respect, the flow field variables are expanded to second-order unsteady terms. To introduce the influence of consecutive terms in the expansions, a comparative study is conducted on first unsteady, second steady and second unsteady terms. The proposed model presents a powerful analytical tool, applicable to oscillating flow analysis in porous media and rapid optimization of the pulse tube cycle. Results proved that expanding the terms to second-order ones can enhance the solution precision considerably. Friction factor and Nusselt number for different meshes are proposed based on the second-order analytical solution.