Application of vortex sound theory to vortex-pairing noise: sensitivity to errors in flow data

Aeroacoustical analogies allow one to extract acoustical information from limited information about the flow. In the particular case of low Mach number compact flows, vortex sound theory has been quite successful. In the present paper, different formulations of the vortex sound theory are compared on the basis of their ability to provide realistic results for vortex-pairing sound when approximate flow models are used. In particular, these theories do not perform equally well when applied to a flow model in which the effective conservation of momentum and kinetic energy is not respected, as it should be in the absence of external forces and neglecting viscous dissipation and compressibility effects. A conservative form of the vortex sound theory is obtained by reiterating the assumptions of conservation of these flow invariants. This alternative form of the analogy allows one to obtain more robust results when applied to perturbed analytical flow models and experimental data.