Turbulent Boundary Layer Superstructures Near the Wall and Their Relationship to Wall-Pressure Fluctuations

Abstract

Turbulent boundary layer superstructures are characterized as regions of organized coherent motions that are on the order of several boundary layer thickness long in the streamwise direction and meander in the spanwise direction as they move and evolve within the boundary layer. They are presumed to exist within the outer region of the boundary layer, but studies have shown their presence in the lower part of the logarithmic layer as well. They are hypothesized to induce pressure fluctuations upon their interaction with rigid surfaces of various geometrical shapes, surface roughness and other aerodynamic features. Due to their large sizes, they are attributed to the low-wavenumber pressure fluctuations on aerodynamic surfaces that radiate far-field sound with minimal attenuation in energy, as well as internal noise within vehicles.

This study provides experimental evidence of the existence and statistical nature of the superstructures throughout the various regions of a turbulent boundary layer. They are shown to increase in their streamwise length under favorable pressure gradients, while their spanwise meandering gets pronounced in adverse pressure gradient flows. Results from Particle Image Velocimetry (PIV) have shown that they evolve over time and space, by merging, diverging and branching during their life, making it important to characterize their unique statistics in space and time, separately. Moreover, it is shown that in the lower part of the log-layer ($x_2^+<150$) over 26,000 flow through times are needed to converge the length scales of the streamwise velocity to within 2 standard deviations. The streamwise extent of these superstructures gets attenuated in the vicinity of surface roughness ($x_2/k_s=2.8$ and $delta/k_s=30$) as the streamwise length scales shrink by roughly 35%.

Synchronous measurements of the velocity fluctuations with alias-free surface pressure fluctuations reveal a strong relationship between the two. Specifically, at $x_2^+=250$, a significant coherence between the wall pressure and streamwise and wall-normal velocity for frequencies below 500 Hz dominating over 0.2 m of streamwise distance is shown. This significant coherence is presented as two separate lobes occurring at different bands of frequencies, potentially identifying two dominant features in the relationship. A wavenumber-frequency cross-spectrum of the pressure and streamwise velocity reveals the convective ridge dominating the flow. However, significant spectral levels in the sub-convective region, roughly 20 dB below the convective ridge are shown at low frequencies, confirming their direct relationship. Further analyses are required to reveal the contributions of non-linear Poisson source terms to the low-wavenumber pressure fluctuations with improved uncertainty by enforcing statistical convergence.