Numerical Study of Wall Pressure Fluctuations for Zero and Non-Zero Pressure Gradient Turbulent Boundary Layers

Abstract

Turbulent boundary layers on a flat plate configuration are simulated using synthetic 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. Wall pressure fluctuations are obtained by calculating a Poisson equation including both the mean-shear turbulence interaction source term and the turbulence-turbulence interaction source term. The Poisson equation is solved by means of Hockney's method. Wall pressure fluctuations for zero and adverse pressure gradient boundary layers are calculated. The adverse pressure gradient is realized by placing an airfoil above the flat plate. Simulated one-point spectra and two-point statistics are analyzed. The results are compared to the experimental results, which were measured in the Acoustic Windtunnel Braunschweig for the same configurations. Good agreement with the experimental results is obtained.

An acoustic model of a Helmholtz resonator under a grazing turbulent boundary layer

“…6. At around ωδ * /u 0 ≈ f δ 99 /u 0 ≈ 0.3 the convection velocity over the frequency exhibits a typical maximal curvature in accordance with Viazzo et al [25], Gloerfelt and Berland [26] and Hu et al [27], where δ * is the displacement thickness. Above this maximal curvature, the convection velocity remains approximately constant.…”

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

“…This can be explained by the fact that the APG boundary layer has a larger mean ow gradient ∂U 1 /∂x 2 in the region 0.1 < x 2 /δ < 0.3 than the ZPG boundary layer, where the contribution plays a major role on the spectral peak, and a larger ∂U 1 /∂x 2 leads to a larger level of p ms . Note, the level of p tt for isotropic turbulence from the previous work of Hu et al 40 is smaller than the present calculation. The reason is that the mirrored source or Green function should be antisymmetric mirrored when dealing with terms including derivative in the wall-normal direction, otherwise the contribution from these terms will be canceled by the source and the mirrored source.…”

“…Note that, for frozen turbulence the slope at low frequencies should be ω 2 , however, due to the temporal turbulence decay the slope becomes much atter for non-frozen turbulence. 13,39,40 In contrast to p ms , spectra of p tt show a rather at behavior at lower frequencies, which is due to the contribution of terms with no derivative in streamwise direction, i.e. ∂/∂x 2 ∂x 2 , ∂/∂x 2 ∂x 3 and ∂/∂x 3 ∂x 3 .…”

“…25,28,38,39 Although the turbulent boundary layer can be simulated by DNS and LES, due to the extremely expensive computational resources, applications are generally restricted to generic studies at low and medium Reynolds numbers. A more ecient approach for the simulation of turbulent boundary layers was published by Hu et al, 39,40 which is also applicable for computations at higher Reynolds numbers. Turbulence within the boundary layer is not resolved by this approach, but generated by the Fast Random Particle-Mesh Method (FRPM).…”

Three-dimensional flow field over a trailing-edge serration and implications on broadband noise

“…However, in the presence of trailing-edge serrations at an angle of attack, the strong three dimensionality of the flow 21 and the adverse pressure gradient 35 may strongly modify the statistical properties of the turbulent boundary layer approaching the trailing edge. A description of the flow features is then essential to uniquely identify the noise emission and eventually reduction obtained by the device.…”