Boundary-layer noise induced by arrays of roughness elements

Sound induced by arrays of 10 x 4 roughness elements in low-Mach-number turbulent boundary layers at Re-theta = 3065 is studied with Lighthill's theory and large-eddy simulation. Three roughness fetches consisting of hemispheres, cuboids and short cylinders are considered. The roughness elements of different shapes have the same height of 0.124 delta, the same element-to-element spacing of 0.727 delta and the same flow blockage area. The acoustically compact roughness elements and their images in the wall radiate sound primarily as acoustic dipoles in the plane of wall. The dipole strength, orientation and spatial distribution show strong dependence on the roughness shape. Correlations between dipole sources associated with neighbouring elements are found to be small for these sparsely distributed roughness arrays. Correlations and coherence between roughness dipoles and surface pressure fluctuations are analysed, which reveals the importance of the impingement of upstream turbulence and surrounding vortical structures to dipole sound radiation, especially in the streamwise direction. For roughness shapes with sharp frontal edges, the edge-induced unsteady separation and reattachment also play important roles in sound generation. Large-scale turbulent structures in the boundary layer have a relatively low influence on roughness dipoles, except for the first row of elements.