Sound extrapolation methods for turbulent flows based on indirect acoustic variables

In computing sound radiation from a turbulent flow, the far-field directivity solutions based on sound extrapolation methods can be contaminated if the expensive volume integrals are neglected while the non-acoustic fluctuations are collected on the integration surface. In earlier work by the first two authors, a sound extrapolation method was developed by filtering out the eddies before the far-field computation. A convection operator D_c was applied on the pressure fluctuation p′ under the assumption that the motion of the eddies is mainly convected by the mean flow, as indicated by Taylor's hypothesis. Good results were obtained when the method was applied to typical aeroacoustic problems. In this work, we develop two more formulations using alternative indirect acoustic variables. The first method is based on the convection operator D_c to the velocity fluctuation u′ that seems to be more relevant to Taylor's hypothesis. The second method uses u′ = ∇ ·u′ as the acoustic variable based on the fact that the sound waves are related to the compressive process of a fluid medium. The methods are studied using different benchmark problems and practical aeroacoustic applications. It is shown that all methods work well for the two-dimensional (2D) convecting vortex, an acoustic monopole in uniform flow and the at plate - gust interaction problem. However, when the three methods are applied to vortex- shedding noise and to co-owing jet noise, the original method based on D_cp′ shows least sensitivity to choice of integration surface, and results obtained using different integration surfaces with the variables v′ and D_cu′ are inconsistent. It is found that the reason for the poor performance is that non-acoustic components are also contained in the indirect variables v′ and D_cu′ on the integration surfaces.