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On compressibility assumptions in aeroacoustic integrals: a numerical study with subsonic mixing layers.

Two assumptions commonly made in predictions based on Lighthill's formalism are investigated: A constant density in the quadrupole expression and the evaluation of the source quantity from incompressible simulations. Numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two-dimensional mixing layer at Re = 400. Published results of the direct noise computation (DNC) of the flow are used as reference and input for hybrid approaches before the assumptions on density are progressively introduced. Divergence free velocity fields are obtained from an incompressible simulation of the same flow case, exhibiting the same hydrodynamic field as the DNC. For the tested values of the Mach number, hybrid predictions reproduce correctly the reference acoustic field, validating both assumptions in the source region. However, in the observer region, the inclusion of flow effects in the Lighthill source term is not preserved, which is illustrated through a comparison with the Kirchhoff wave-extrapolation formalism, and with the use of a convected Green function in the integration process.