Characterization of sound radiation by unresolved scales of motion in computational aeroacoustics

Abstract

Evaluation of the sound sources in a high Reynolds number turbulent flow requires time-accurate resolution of an extremely large number of scales of motion. Direct numerical simulations will therefore remain infeasible for the forseeable future; although current large eddy simulation methods can resolve the largest scales of motion accurately, they must leave some scales of motion unresolved. A priori studies show that acoustic power can be underestimated significantly if the contribution of these unresolved scales is simply neglected. In this paper, the problem of evaluating the sound radiation properties of the unresolved, subgrid-scale motions is approached in the spirit of the simplest subgrid stress models: the unresolved velocity field is treated as isotropic turbulence with statistical descriptors evaluated from the resolved field. The theory of isotropic turbulence is applied to derive formulas for the total power and the power spectral density of the sound radiated by a filtered velocity field. These quantities are compared with the corresponding quantities for the unfiltered field for various filter types and widths.