Numerical Simulation of Sound Generated by Vortex Pairing in a Mixing Layer

A numerical code solving the filtered Navier-Stokes equations is developed using special techniques of computational aeroacoustics. This approach allows a direct determination of the compressible field on a computational domain including the acoustic far field. A two-dimensional mixing layer between two flows at M 1 = 0.12 and M 2 = 0.48 is simulated. The Reynolds number built up from the initial vorticity thickness and the velocity difference across the mixing layer is Re ω = 1.28 x 10 4 . An appropriate forcing of the mixing layer is defined to have only one pairing in the computational domain at a fixed location. The sound generation pattern for a single pairing displays a double spiral structure, corresponding to the rotating quadrupole associated to two corotative vortices. Successive pairings produce an acoustic radiation at the frequency of this mechanism. The directly computed far-field sound is then compared to the prediction of Lighthill's acoustic analogy (Lighthill, M. J., On Sound Generated Aerodynamically-I. General Theory, Proceedings of the Royal Society of London, Vol. 211, Series A 1107, 1952, pp. 564-587) based on the aerodynamic fluctuations provided by the large-eddy simulation code. Two integral formulations of the analogy, based on spatial derivatives and time derivatives, respectively, are tested. Results are in good qualitative agreement with the results of direct simulation. The accuracy is, however, greater with the formulation using time derivatives instead of spatial derivatives.