Behavior of plane waves propagating through a temperature-inhomogeneous region

Abstract

Description and analysis of acoustic waves in ducts with a region containing temperature-inhomogeneous fluid represent a significant problem of scientific and practical interest. This interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions. Most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature-homogeneous regions smoothly. In our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient. A polynomial character of the used temperature profile ensures smooth connection with constant-temperature regions. The one-dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically. The derived solutions based on Heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient. Due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature-homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method.