The regenerator of a travelling-wave thermoacoustic engine must have small enough passages for the gas to be in close thermal contact with the material. The material can then maintain a steady temperature profile through its thickness, while the temperatures of the gas parcels oscillate as they are displaced, to a greater extent than adiabatic compression dictates. Ideally, the parcels should follow the temperature of the adjacent surfaces. However, the narrower the passages are, the greater is the acoustic pressure loss and any potential gains in the enhancement of acoustic power are offset by these losses. Reducing the regenerator thickness ameliorates this effect but leads to higher heat flux requirements due to loss by thermal conduction down the temperature gradient. Thus the optimisation of regenerator material and thickness is a complex process, particularly when the cost of the regenerator is also an important consideration. In this paper, a fundamental analysis of regenerator performance in terms of a time constant, relating the heat transfer coefficient and the thermal capacity of the gas, provides a quantitative measure for arbitrary geometry. For regenerators with straight-through passages, the equivalence of this analysis to one involving solution of the boundary layer equations and the ratio of the hydraulic radius to the thermal penetration depth is demonstrated. The sensitivity of the generation of acoustic energy to the frequency, the time constant and the temperature ratio across the regenerator is calculated for a number of cases. Experimental data for the acoustic pressure loss of randomly-orientated, woven steel meshes, can also be related to the time constant, so the analysis is applicable to regenerators made from that type of material, as well. Its advantage is that it can also be used to describe inhomogeneous materials.
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