Shock wave–thermal inhomogeneity interactions: Analysis and numerical simulations of sound generation

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Abstract
In the present paper the interaction of a moving planar shock wave with a cylindrical thermal inhomogeneity is analyzed. Due to the interaction, both vorticity and sound waves are generated. The main focus of the paper is on the generation and propagation of the acoustic waves and their dependence on shock strength and inhomogeneity intensity. An acoustic analogy of the problem has been formulated as a basis of comparison for the structure of the acoustic pressure field in the limit of either weak shocks or weak inhomogeneities. An extensive numerical study has been carried out in order to understand the influence of both shock strength and intensity of the inhomogeneity. The results show that the acoustic field obeys a two-stage evolution that occurs on a time scale that is independent of shock and inhomogeneity intensities. The comparison of the computed far-field pressure with the theoretical result shows that for weak inhomogeneities the sound is well predicted by the acoustic analogy regardless of the shock strength.