Analytical solution of the regenerator temperature distribution in a thermoacoustic device with mean flow

Previous work by the authors has identified a potential for improvement in the efficiency of a traveling wave thermoacoustic engine by replacing the hot heat exchanger with a steady flow of hot gas. An essential step in determining the feasibility of such an engine lies in determining how the mean flow affects the temperature distribution in the regenerator, which in turn affects its acoustic driving capability. In the current work, the second order time‐averaged thermoacoustic energy equation with mean flow is solved analytically for the mean temperature distribution in the regenerator. The resulting expression accounts for the dependence of the working fluid’s thermal conductivity and viscosity on temperature, and results in a nearly exponential temperature profile. The specific effects of mean flow, axial conduction, acoustic velocity amplitude, and gas property variation on the temperature distribution in the regenerator will be explored. In turn, the effect of the temperature profile on regenerator performance will also be reviewed. In addition to their usefulness in the feasibility study, these results can also be applied to assess losses in existing thermoacoustic engines and refrigerators where acoustic streaming results in unwanted net mass flux through the regenerator.