Subgrid-scale contribution to noise production in decaying isotropic turbulence

An estimation of the noise generated by subgrid scales provided by a large- eddy simulation (LES) calculation is performed based on a priori tests, The derivation of Navier-Stokes equation to obtain Lighthill's equation (Light hill, M. J., "On Sound Generated Aerodynamically, Part I: General Theory:" Proceedings of the Royal Society of London, Vol. A211, 1952, pp, 364-587; L ighthill, M. J., "On Sound Generated Aerodynamically, Part II: Turbulence a s a Source of Sound," Proceedings of the Royal Society of London, Vol. A222 , 1954, pp. 1-32) is presented for both the direct numerical simulation (DN S) and the LES Navier-Stokes equations. The Lighthill tensor is split into several parts: a high-frequency part that is not resolved by LES calculatio n, the filtered Lighthill tensor computed from basic filtered variables, an d a subgrid-scale tensor. A DNS of decaying isotropic turbulence is carried out to evaluate the contribution of each term to the noise production. It is confirmed that the high-frequency part of Lighthill's tensor does not co ntribute significantly to noise production for the usual cutoff wave number value of LES. The subgrid-scale contribution cannot be neglected and requi res the use of a subgrid-scale model to recover reliable results dealing wi th the acoustic field. The acoustic contribution computed using a subgrid-s cale model of scale similarity type is compared to the acoustic contributio n of the exact subgrid-scale tensor.