General formulation of thermoacoustics for stacks having arbitrarily shaped pore cross sections

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Abstract
Theoretical treatments of thermoacoustics have been reported for stacks with circular pore and parallel plate geometries. A general linear formulation is developed for gas‐filled thermoacoustic elements such as heat exchangers, stacks, and tubes having pores of arbitrary cross‐sectional geometry. For compactness in the following, F represents the functional form of the transverse variation of the longitudinal particle velocity. Generally, F is a function of frequency, pore geometry, the response functions and transport coefficients of the gas used, and the ambient value of the gas density. Expressions are developed for the acoustic temperature, density, particle velocity,pressure, heat flow, and work flow from knowledge of F. Heat and work flows are compared in the short stack approximation for stacks consisting of parallel plates, circular, square, and equilateral triangular pores. In this approximation, heat and work flows are found to be greatest for the parallel plate stack geometry. Pressure and specific acoustic impedance translation theorems are derived to simplify computation of the acoustical field quantities at all points within a thermoacoustic engine. Relations with capillary‐pore‐based porous media models are developed.

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