Wall-Cavity Acoustic Green's Function at Low Mach Number

Abstract

Analytical approximations are developed for the low Mach number, aeroacoustic Green's function for a rectangular or circular cylindrical open cavity in a plane, rigid wall. The formulae can be used to predict the sound radiated into the main flow from a knowledge of the hydrodynamic flow near the cavity. At low Mach numbers the sound is a small by-product of the main flow, whose hydrodynamic properties can first be determined from observation or from a numerical treatment of the incompressible Navier-Stokes equations. Detailed predictions are made of the lowest order, open cavity resonance frequencies, and it is shown how a resonance is excited by the unsteady drag, and also by the lift or drag force experienced by a small bluff body placed in the flow close to the cavity. The cavity resonance frequencies are complex, with imaginary parts depending primarily on radiation damping, which can be sufficiently large for a shallow, open cavity, that a distinct resonance peak is absent from the acoustic spectrum – for a square cavity such peaks are predicted only when the cavity depth exceeds about half the cavity length. For very shallow cavities the efficiency of sound production by volumetric pulsations within the cavity is comparable to that of free field turbulence quadrupoles, and therefore negligible at low Mach numbers.