Oscillatory compressible flow and heat transfer in porous media: Application to cryocooler regenerators

In this study the phenomena of compressible flow and heat transfer in porous media are modeled based on fundamental principles. The conservation equations for the two phases are transformed by the method of volume averaging which is an analytical method used to unite the microscale and macroscale effects characteristic to porous media flows. Unique to this analysis is the fact that the model is valid for oscillatory, cryogenic flows such as that occurring in a regenerative cryogenic refrigerator such as a Pulse Tube Cryocooler (PTC.); In a PTC the forced flow driven oscillations in the regenerator create Reynolds numbers high enough such that microscale inertial effects dominate the momentum equation. This phenomenon, known as the Forchheimer Effect, can be predicted and modeled based solely on fundamental principles and the method of volume averaging. The coefficients that characterize the Forchheimer momentum equation are determined experimentally.; Heat transfer within a porous medium occurs due to temperature gradients in the gas and solid phases. Conduction within the solid and fluid phases is made evident by volume averaging, but the determination of the conductivity coefficients requires numerical experiments and is unique to the geometry and conductivities of the two phases. Convection between the two phases is the dominant mode of heat transfer within the porous media. Determination of the convective heat transfer coefficient for a porous media requires physical experiments.; Heat transfer due to temperature gradients and flow friction in the regenerator are always competing effects leading to a model which requires coupling of the momentum and energy equations. These competing effects are united with the concept of entropy generation which relies on the second law of thermodynamics. All real processes generate entropy, and the most efficient processes which balance flow friction and heat transfer generate minimum entropy.; The theoretical model is presented with a numerical solution technique. These numerical solutions are compared with similar solutions existing in the literature. The uniqueness of this model is the completeness of the theoretical development and the flexibility of use for a variety of applications. Numerical solutions are compared with experimental data for an operating cryocooler.