Theoretical study of sound radiation from an inlet duct

Abstract

The sound radiation from an inlet duct is investigated by means of the eigenfunction solutions of the wave equation in the oblate spheroidal (ζ, η, φ) and cylindrical (z, r, φ) coordinate systems. The inlet duct under consideration is composed of a uniform circular duct which opens into a configuration determined as the boundary surface of η=constant, that is the half of the hyperboloid of one sheet. The more important features in this investigation are as follows: (1) The oblate spheroidal eigenfunctions with the finite boundary surfaces have been obtained, these have not been studied previously; unlike the uniform duct modes, the shape of the oblate spheroidal wave mode depends on the frequency; the shape of the fundamental mode is plane only at very low frequencies. (2) The conversion of the duct modes to the radiation modes (the oblate spheroidal wave modes) is accurately evaluated at the inlet of the flange because the surface of ζ=0 coincides with that of z=0.