Acoustic radiation due to scattering of T-S wave by the mean-flow distortion induced by steady local suction

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Substantial sound waves can be generated by boundary-layer instability modes when the latter are scattered by a rapid mean-flow distortion. This is a rather generic mechanism and operates when an oncoming T-S wave is scattered by a steady local suction slot. This paper focuses on this problem by extending a recently developed Local Scattering Theory (Wu & Dong, J. Fluid Mech. submitted), where a so-called transmission coefficient, defined as the ratio of the T-S wave amplitude downstream of the scatter to that upstream, is introduced to characterize the effect of a local scatter on boundary-layer instability and transition. As in the earlier work, the mathematical formulation is based on triple-deck formulism, but in order to accommodate the acoustic far field, which was not considered in the paper mentioned, the unsteady terms in the upper deck, which play a leading-order role in radiation, are retained, and the influence of the radiated sound on the near-wall perturbation is included. The upper deck equation for the pressure is the Helmholtz equation rather than the Laplace equation. This leads to a modified pressure-displacement relation, which is coupled with the linearized boundary-layer equations in the lower deck. Discretization of the whole system formulates a generalized eigenvalue problem, which is solved numerically. It is found that suction suppresses oncoming T-S waves, and this effect increases with the suction velocity and the slot width. The directivity is ndependent of the flow parameters only when the Mach number is low. The intensity of the radiated sound in general increases with the frequency, the suction velocity and the width of the suction slot. Interestingly, for O(1) suction velocities, the radiated sound is very weak, indicating that the gain of stabilizing effect does not cause aeroacoustic penalty.