Modeling the Surface Pressure Spectrum on Rough Walls in Pressure Gradients

Models for surface pressure spectra beneath rough wall boundary layers are assessed, with particular emphasis on prediction from steady, Reynolds-averaged Navier-Stokes (RANS) data. RANS roughness boundary conditions are shown to have qualitatively good trends between roughness function and roughness Reynolds number, but model-to-model discrepancies remain and the universality of an equivalent sandgrain roughness height for turbulence models is doubtful. Existing empirical models for the surface pressure spectrum show good agreement in some spectral regions and a newly proposed model shows good matching across the spectrum in a variety of pressure gradient conditions. Adjustments are made to existing TNO analytical models to incorporate rough wall effects, including changes to the velocity spectrum model and the inclusion of a wall-shift, shown to be independent of local Reynolds number, pressure gradient, or turbulence model. The mathematical character of the rough wall spectrum has been revealed, but challenges remain to implement both flow and spectral modeling without a priori knowledge of the flow.