The Sound Generated by a Two-Dimensional Shear Layer: A Comparison of Direct Computations and Acoustic Analogies

Abstract

The sound generated by vortex pairing in a two-dimensional mixing layer is studied by solving the Navier-Stokes equations (DNS) for the layer and a portion of its acoustic field, and by solving acoustic analogies with source terms determined from the DNS. Predictions for the acoustic field based on Lilley's equation are in excellent agreement with the DNS results giving detailed verification of Lilley's acoustic analogy for the first time. We show that parts of the full source term which arise when the left-hand-side of Lilley's equation is linearized should not be neglected solely because they are attributable to refraction and scattering, nor because they are proportional to the dilatation. Lilley's source, -2u_(i,j)u_(j,k)u_(k,i), appears to be mainly responsible for the overall directivity of the acoustic field produced by the vortex pairings, which is highly focused at shallow angles to the streamwise axis. Scattering of the waves by the flow appears also to be significant, causing the directivity to be more omnidirectional than the Lilley source alone would predict. We also show how small errors in determining the sources, especially those due to scattering, can sometimes lead to large errors in the predictions.

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