Near-isothermal regenerator - A perturbation analysis

Abstract

We develop a perturbation model for regenerators of the type used in Stirling and Gifford-McMahon cryocoolers. The model is valid in the near-isothermal limits, which is usually a quite good approximation for these devices, because typically, the flow passages are small compared to the conductive heat penetration depth in the gas, and because the thermal mass of the heat-storing matrix is large compared to the thermal mass of the gas. Our model is one dimensional and it uses a conventional, empirical model for heat transfer. Our approach can yield solutions for arbitrary heat transfer correlations, which makes it suitable for incorporation in computer models. We also present complete solutions for the important case corresponding to the laminar limit, when the Nusselt number is a constant. Results include the longitudinal temperature distribution and the enthalpy flux through the regenerator. In some conditions, which are more representative of pulse-tube refrigerators than of typical Stirling cryocooler operation, and for which the model remains valid, we obtain multiple solutions, some of which are associated with a sharp temperature peak, in a region in the regenerator where the amplitude of the mass flow rate oscillation exhibits a minimum