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Pressure uctuations within turbulent boundary layers on a at plate con guration are simulated using synthetic isotropic and anisotropic turbulence generated by the Fast Random Particle-Mesh Method. The averaged turbulence statistics needed for the stochastic realization is provided by a Reynolds averaged Navier-Stokes calculation. Di erent integral length scales in di erent directions are used to realize the anisotropy of the turbulence length scales. Reynolds stress anisotropy is implemented by relating the anisotropic Reynolds stresses obtained from the Reynolds averaged Navier-Stokes calculation and the respective isotropic Reynolds stresses realized from the Fast Random Particle-Mesh Method. Wall pressure uctuations are obtained by solving a Poisson equation including both the mean-shear turbulence interaction source term and the turbulence-turbulence interaction source term. The Poisson equation is solved using the convolution theorem in wavenumber domain and with a free-space Green function. For an exact realization of the Green function in conjunction with a Fourier transform method on a nite domain, Hockney's method is applied to the Poisson problem. Wall pressure uctuations for zero and adverse pressure gradient boundary layers are calculated. The adverse pressure gradient is realized by placing an airfoil above the at plate. Simulated one-point spectra and two-point statistics are analyzed. Simulated results for the wall pressure one-point spectra show that spectra from both the mean-shear term and the turbulence-turbulence term have the same order of magnitude. The results are compared to the experimental results, which were acquired in the Acoustic Windtunnel Braunschweig for the same con gurations.

elib (german aerospace center)

Numerical investigation of wall pressure fluctuations for zero and adverse pressure gradient turbulent boundary layers using synthetic anisotropic turbulence