Modeling of Wall Pressure Fluctuations Based on Time Mean Flow Field

Time-mean flow fields and turbulent flow characteristics obtained from solving the Reynolds averaged Navier-Stokes equations with a $k‐ε$ turbulence model are used to predict the frequency spectrum of wall pressure fluctuations. The vertical turbulent velocity is represented by the turbulent kinetic energy contained in the local flow. An anisotropic distribution of the turbulent kinetic energy is implemented based on an equilibrium turbulent shear flow, which assumes flow with a zero streamwise pressure gradient. The spectral correlation model for predicting the wall pressure fluctuation is obtained through a Green’s function formulation and modeling of the streamwise and spanwise wave number spectra. Predictions for equilibrium flow agree well with measurements and demonstrate that when outer-flow and inner-flow activity contribute significantly, an overlap region exists in which the pressure spectrum scales as the inverse of frequency. Predictions of the surface pressure spectrum for flow over a backward-facing step are used to validate the current approach for a nonequilibrium flow.