Dependence of Sound Amplification on Temperature Distribution in Annular Thermoacoustic Engines

The aim of this paper is to study the influence of the shape of the temperature distribution on the thermoacoustic amplification in an annular thermoacoustic prime mover. An analytical model is presented and the acoustic field in the whole device is computed for an arbitrary temperature distribution. The obtained results demonstrate dependence of the thermoacoustic amplification not only on the maximum temperature difference but also significantly on the details of the spatial temperature distribution, which influence the structure of the acoustic field throughout the thermoacoustic core. These results provide the opportunity to predict qualitatively the variation of the thermoacoustic amplification, when the temperature distribution is modified by acoustic streaming or acoustically enhanced thermal conductivity. It may be of primary importance when trying to explain the complicated, experimentally observed dynamics of the transient process of acoustic wave amplification and saturation.