Predictive Limits of Acoustic Diffraction Theory for Rough Wall Flows

Rough walls can produce noise through local effects such as vortex shedding or through diffraction of the convected turbulent flowfield. It is known that diffraction dominates for hydrodynamically smooth surfaces and self-noise dominates for obstructions many times the size of the boundary layer, but as of yet, the transition between regimes has not been thoroughly investigated. In this paper, the limits of acoustic diffraction theory for rough wall flows are examined by analyzing the unsteady drag inferred from measurement of the far-field noise produced by fetches of discrete roughness elements ranging in size from h/δ=5 to 6% and from 14 to 18%. Measured unsteady drag spectra are compared to theoretically predicted spectra from diffraction theory. It is shown that the effectiveness of diffraction theory is not solely dependent on the relative turbulence and roughness scales, but on the ratio of roughness height to boundary-layer thickness as well. It is also shown that the unsteady drag spectra produced by differing roughness geometries and velocities produce tighter collapse at nondimensional frequencies df/Uc less than one. At higher nondimensional frequencies, the spectra fan out by roughness type and velocity, but this effect is captured by diffraction theory, which works well into the frequencies at which the scale of the dominant turbulent eddies along the convective ridge of the wave-number-frequency wall-pressure spectrum are smaller than the roughness elements.