Asymptotic wave speed estimation in weakly undulated ducts carrying mean flow

An analytical asymptotic solution for evaluating phase speed of acoustic waves transmitting through two-dimensional duct carrying mean flow and having periodically undulated walls is obtained. The study sheds light on the combined effect of mean flow and geometric periodicity on sound phase speed. Assumption of no fluid flow separation at the corrugated walls is made. The perturbation method of strained parameters is employed with two levels of approximation to provide an analytical expression for the acoustic phase speed. A quantitative assessment of the effect of undulation density, different undulation amplitudes at each wall of the duct, and the degree of wall undulations symmetry about the duct mid-plane are presented. The effect of forward mean flow on the acoustic phase speed in presence of wall undulations is compared to that of backward mean flow. It is found that accounting for the mean flow inside undulated ducts generates results that are significantly different from those obtained when the fluid is considered stationary.