Receptivity to free stream acoustic disturbances due to a roughness element on a flat plate
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The boundary-layer receptivity resulting from acoustic forcing over a flat plate with a surface irregularity is investigated. The unsteady free-stream disturbances couple with the steady perturbations resulting from the surface irregularity to form a traveling-wave mode. The resonance condition necessary for receptivity requires a forcing at a wave number equal to that of the Tollmien-Schlichting (TS) eigenmode and a frequency equal to that of the free-stream acoustic disturbance. The basic (mean) flow is calculated using an interacting boundary layer (IBL) scheme that accounts for viscous/inviscid interactions. Then, the method of multiple scales is used to find the total amplitude of the generated wave. Results of this study show how the transition process is significantly stimulated. Also, the dependence of the receptivity on the geometry of the roughness element as well as on the amplitude and frequency of the acoustic disturbance is studied. Application of suction is shown to reduce the receptivity resulting from the roughness element.
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