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This paper proposes an adjoint sensitivity analysis method that enables the evaluation of the sensitivities of far-field sounds with respect to object shapes. In this method, flow-induced sounds are directly simulated based on the lattice Boltzmann equation (LBE) with an athermal model under low-Mach-number conditions. In addition, wall boundaries of complex geometries are considered using the interpolated bounce-back (IBB) condition, which also allows the adoption of arbitrary parameters that define object geometries as design variables in the sensitivity analysis. The sensitivities of far-field sounds to numerous design variables can be evaluated by solving the adjoint equation, which is derived from the LBE with the IBB condition. This study demonstrates the validity of the proposed method using two test problems. In these tests, the sensitivities evaluated by the adjoint method are compared with those evaluated by the finite difference method. Furthermore, this paper presents new shapes optimized to suppress the generation of the Aeolian tone using the sensitivity analysis method. |
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