Oscillatory compressible flow and heat transfer in porous media : application to cryocooler regenerators
Harvey, Jeremy Paul
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In this study the phenomenon of compressible flow and heat transfer in a porous media is modeled based on fundamental principles. The conservation equations for the two phases are transformed by the method of volume averaging which is an analytic method used to unite the microscale and macroscale effects characteristic to porous media flows. Unique to this analysis is 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 drive 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. In addition to pressure gradients, heat transfer within a porous media occurs due to temperature gradients. 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 and pressure gradients in the porous media 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 pressure gradients and heat transfer generate minimum entropy. This concept of minimum entropy generation is unique. As a result, minimum entropy generation should always be used as the criteria for thermodynamic optimization of thermohydraulic systems.