A linear 1D model for the thermoacoustic effect in the presence of mean flow

In thermoacoustic devices, the interaction of thermo-viscous boundary layers and axial temperature gradients causes conversion of thermal energy to acoustic power and vice versa. In this publication, an improved model for thermoacoustic boundary layer effects in the presence of moderate mean flow is derived and analyzed. In contrast to existing (implicit) models, the acoustics are not only influenced by the profile of the axial mean temperature, but also the steady flow conditions, which are explicitly taken into account in the perturbation equations. For a slab stack pore the three dimensional thermoacoustic equations are derived and reduced to a transversally averaged system of differential equations, invoking the Green's fiinction technique and suitable simplifying assumptions. The results of the new model are compared to those of an established implicit modeling approach on the one hand and a full CFD computation on the other. It is shown that for a wide range of mean flow Mach numbers the new formulation predicts the acoustic behavior more accurately than the established implicit model. Finally the Mach number limits of the model are investigated and discussed.