Phase shift and attenuation characteristics of acoustic waves in a flowing gas confined by cylindrical walls

Wave propagation in flowing ideal gases confined by cylindrical waveguides is described in the low-frequency range using an iterative Frobenius series expansion method. The primary concern is to present a mathematical model enabling any radial-dependent flow profile to be analyzed. In contrast to previous analytical results, the present model is applicable in the general case where cubic and higher order terms in the axial acoustic velocity become important and to examine the influence of a non-vanishing radial velocity term. As a numerical test case, it is found that a gas flow velocity w(r)—for simplifying reasons assumed to be a linear combination of a flat flow profile and a parabolic flow profile corresponding to a mean flow equal to w̄—is well approximated by a flat flow profile of the same mean flow value w̄ at low shear wavenumbers and at higher shear wavenumbers (calculations were done for shear wavenumbers up to 8). In actual fact, the error introduced by making this mean flow approximation is smaller than the error introduced by neglecting the radial velocity term.