Exact solutions for modeling sound propagation through a combustion zone

Abstract

Exact analytical solutions for one-dimensional sound propagation through a combustion zone, taking the effects of mean temperature gradient and oscillatory heat release into account, are presented in this paper. The wave equation is derived starting from the momentum and energy equations. Using appropriate transformations, solutions are derived for the case of an exponential mean temperature gradient in terms of Bessel functions. For the case of a linear mean temperature profile, solutions are derived in terms of confluent hypergeometric functions. Example calculations show that the accuracy in modeling combustion–acoustics interactions can be significantly increased by the use of these solutions.