Sound propagation in duct shear layers

Abstract

The propagation of sound in a two-dimensional inviscid shear layer is considered for given initial sound pressure profiles. The eigenvalue problem resulting from an assumption of separable solutions of the form φ(y)exp{ik(βx - ct)}, first obtained by Pridmore-Brown, is solved numerically. It is shown that although the resulting eigenfunctions cannot be proven to be orthogonal or complete, they can be combined by a least total error squared method to give a good representation of the initial pressure profile. The acoustic pressure in the duct is then easily calculated. The results verify all the predictions made in an earlier perturbation calculation. Moreover, they show that the refraction effect gets saturated at high subsonic Mach numbers and at high frequencies. The present technique may be used, if necessary, with impedance boundary conditions at the duct walls.