Exact solutions to one-dimensional acoustic fields with temperature gradient and mean flow

Abstract

An exact solution for one-dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper. The analysis is valid for mean Mach numbers such that the square of the mean Mach number is much less than one. The one-dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived. By appropriate transformations, the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile. The developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow. The results obtained using the analytical solution compare very well with the numerical results. The developed solution is also compared with an existing analytical solution.