Prediction of supersonic jet noise from a statistical acoustic model and a compressible turbulence closure

Acoustic radiation of shock free supersonic jets is modified in comparison with subsonic jet noise because of Mach wave emission. Intense noise is radiated when turbulent structures are convected supersonically relative to the ambient sound speed. Using the framework of Lighthill's equation, Ffowcs Williams and Maidanik developed an approximation of Lighthill's term for a supersonically convected acoustic source in a turbulent shear layer. From this result, a model can be deduced for axisymmetric jets. One then shows that the local knowledge of the mean flow and a characteristic time of turbulence in the source volume may be used to calculate the spectral directivity of Mach wave noise. As a consequence of this local formulation of the acoustic source term, the noise model contains a single unknown multiplicative constant. It also requires a calculation of the mean flow which may be carried out with a k - ∈ compressible turbulence model. Two cold jet cases at M = 1·7 and M = 2·0 and a hot jet at M = 2·0 and T_j/T₀ = 2·5 are analyzed. Comparisons with available experimental data and Tam's calculations based on an alternative description in terms of instability waves travelling at the convection speed show a good agreement between calculations and measurements.