Turbulent Boundary Layers over Rough Surfaces: Large Structure Velocity Scaling and Driver Implications for Acoustic Metamaterials

Abstract

Turbulent boundary layer and metamaterial properties were explored to initiate the viability of controlling acoustic waves driven by pressure fluctuations from flow. A turbulent boundary layer scaling analysis was performed on zero-pressure-gradient turbulent boundary layers over rough surfaces, for 30,000≤〖Re〗_θ≤100,000. Relationships between fluctuating pressures and velocities were explored through the pressure Poisson equation. Certain scaling laws were implemented in attempts to collapse velocity spectra and turbulence profiles. Such analyses were performed to justify a proper scaling of the low-frequency region of the wall-pressure spectrum. Such frequencies are commonly associated with eddies containing the largest length scales. This study compared three scaling methods proposed in literature: The low-frequency classical scaling (velocity scale U_τ, length scale δ), the convection velocity scaling (U_e-U ̅_c, δ), and the Zagarola-Smits scaling (U_e-U ̅, δ). A default scaling (U_e, δ) was also selected as a baseline case for comparison. At some level, the classical scaling best collapsed rough and smooth wall Reynolds stress profiles. Low-pass filtering of the scaled turbulence profiles improved the rough-wall scaling of the Zagarola-Smits and convection velocity laws. However, inconsistent scaled results between the pressure and velocity requires a more rigorous pressure Poisson analysis. The selection of a proper scaling law gives insight into turbulent boundary layers as possible sources for acoustic metamaterials. A quiescent (no flow) experiment was conducted to measure the capabilities of a metamaterial in retaining acoustic surface waves. A point source speaker provided an acoustic input while the resulting sound waves were measured with a probe microphone. Acoustic surface waves were found via Fourier analysis in time and space. Standing acoustic surface waves were identified. Membrane response properties were measured to obtain source condition characteristics for turbulent boundary layers once the metamaterial is exposed to flow.