The Influence of Mean Flow on the Acoustic Properties of a Tube Bank

The theory of sound propagation through a bank of rigid parallel tubes in the presence of a nominally steady, low Mach number cross flow is discussed. A detailed diffraction analysis is given for the idealized but mathematically tractable case of a bank of strips set at zero angle of attack to the mean flow. Various approximations for the dispersion equation governing the propagation of long waves are derived, including the influence of acoustically induced vortex shedding from the strip trailing edges and of hydrodynamic interactions between neighbouring strips. The sound is attenuated by a transfer of energy to the kinetic energy of the essentially incompressible field of the shed vorticity. It is shown how the principle of conservation of energy and a Kramers-Kronig dispersion relation can be combined to yield an alternative derivation of the dispersion equation. This procedure is applicable to a simplified model of propagation through a bank of rigid tubes of circular cross section, and an approximation to the dispersion equation is obtained in this case. The relevance of these results to bound resonances in tube bank cavities is discussed.