Optimization of thermoacoustic stacks for low onset temperature engines

Standing-wave thermoacoustic engines are typically optimized in order to obtain high system efficiency. However, in applications targeting the utilization of waste heat, it may be necessary to optimize them for a low onset temperature difference instead, so as to enable the engine's self-oscillation using low-grade energy sources. This article focuses on theoretical investigations of the critical temperature gradient in stacks, based on the assumptions of a short stack in a standing-wave acoustic field and an ideal gas. A dimensionless critical temperature gradient factor is obtained on the basis of the linear thermoacoustic theory and the analysis of the viscous and thermal relaxation losses for selected stack geometries. With a simple form, it reveals the effects of the stack geometry, the characteristic channel dimension, and the local acoustic impedance on the critical temperature gradient of the stack. In particular, it is shown that the impedance determines the proportion between the viscous loss, heat relaxation losses, and the power production from the heat energy. Numerical analysis based on this dimensionless factor clearly shows that there is an optimum channel dimension for each given stack location in the acoustic field. There exists a possible optimum combination of these parameters, which leads to the lowest critical temperature gradient.