Impact of viscous and heat relaxation loss on the critical temperature gradients of thermoacoustic stacks

A stack with a small critical temperature gradient is desirable for a standing wave thermoacoustic engine to obtain a low onset temperature difference (the minimum temperature difference to start engine's self-oscillation). The viscous and heat relaxation loss in the stack determines the critical temperature gradient. In this work, a dimensionless critical temperature gradient factor is obtained based on the linear thermoacoustic theory. It is indicated that the impedance determines the proportion between the viscous loss, heat relaxation losses and the power production from the heat energy. It reveals the effects of the channel dimensions, geometrical configuration and the local acoustic impedance on the critical temperature gradient in stacks. The numerical analysis shows that there exists a possible optimum combination of these parameters which leads to the lowest critical temperature gradient. Furthermore, several different geometries have been tested and compared numerically.