Turbulent boundary layer models for acoustic analysis
An analysis of the three types of turbulent boundary layer (TBL) models for acoustic analysis is presented because current preferred models over-predict TBL contributions to aircraft interior noise predictions. The mean square pressure is a measure of the total energy due to the pressure fluctuations beneath a turbulent boundary layer. The single point wall pressure spectrum sorts the energy into frequencies. The normalized wavenumber-frequency spectrum sorts the energy into wavenumbers. The pressure fluctuations beneath a turbulent boundary layer are found by solving the Poisson equation. In this work, the Poisson equation is solved both numerically and analytically using data from an LES/DES simulation. The numerical solution uses the point Gauss-Seidel method and has reasonable results. The analytical solution uses an eigenvalue expansion method that is less successful. The empirical mean square pressure models predict a relatively large spread in the pressure fluctuation values. It is difficult to draw any meaningful conclusions on which mean square pressure model is preferred when compared to data from the Spirit AeroSystems 6x6 duct. The single point wall pressure spectrum models are evaluated and the two more modern models of Smol’yakov and Goody seem to perform the best. These models are also compared to data from the Spirit AeroSystems 6x6 duct. The spectrum at low frequencies rolled off similar to the Goody model. This analysis indicates that the Goody model is the appropriate single point wall pressure spectrum model for aircraft applications. Important features of the normalized wavenumber-frequency spectrum models are presented and can be classified as either separable or non-separable. Separable models in the Corcos normalized wavenumber-frequency spectrum model class tend to over-predict the response for a range of cases. Both the non-separable Chase 1 and Smol’yakov-Tkachenko models appear to match the M.I.T. low noise, low turbulence wind tunnel data throughout the range of comparison. The Smol’yakov-Tkachenko model does not lend itself to straight forward Fourier transforms needed by the acoustic models. But the Chase 1 model can be converted from wavenumber-frequency spectrum to the cross spectrum, so it is the preferred model for aircraft applications. Therefore, the preferred turbulent boundary layer models for aircraft interior noise predictions are the single point wall pressure spectrum model of Goody and the normalized wavenumber-frequency spectrum model of Chase 1.
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