Impact of turbulence on the prediction of linear aeroacoustic interactions: Acoustic response of a turbulent shear layer

A powerful model to predict aeroacoustic interactions in the linear regime is the perturbed compressible linearized Navier–Stokes equations. Thus far, the frequently employed derivation suggests that the effect of turbulence and its associated Reynolds stresses is neglected and a quasi-laminar model is employed. In this paper, dynamic perturbation equations are derived incorporating the effect of turbulence and its interaction with perturbation quantities. This is done by employing a triple decomposition of the instantaneous variables. The procedure results in a closure problem for the Reynolds stresses for which a linear eddy-viscosity model is proposed. The resulting perturbation equations are applied to a grazing flow in a T-joint for which strong shear layer instabilities at certain frequencies are experimentally observed. Passive scattering properties of the grazing flow are validated against the experiments performed by Karlsson and Åbom and perturbation equations being quasi-laminar. We find that prediction models must include the effect of Reynolds stresses to capture the aeroacoustic interaction effects correctly. Neglecting its effect naturally results in the over prediction of vortex growth at the frequencies of shear layer instability and therewith in an over prediction of aeroacoustic interactions.