A discrete adjoint framework for trailing-edge noise minimization via porous material

A discrete adjoint framework on the basis of algorithmic differentiation (AD) is developed for trailing-edge noise minimization. Turbulent flow through porous media is modeled based on the conservative transport equations filtered by a local volume-averaging method in which the effect of the porous media is modeled as viscous source terms. This framework is applied to identify the optimal distribution of porous material of a flat plate with a porous trailing edge in subsonic flow resolved with a high resolution large-eddy simulation (LES) method. The AD-based noise adjoint is shown to be highly accurate and allows for efficient evaluation of the entire design sensitivity vector in one stroke, at a cost comparable to that of a single primal LES simulation. Noise minimization is performed to determine the optimal distribution of the design variables that govern the porosity and permeability of the trailing edge. The optimal design obtained is found to attain a maximum noise reduction of 12 dB from a flat plate with solid trailing edge and 3 dB from the baseline design with a linear porosity variation, respectively. Comparison of noise spectra reveals that the optimization has little effect on the broadband noise component compared to its baseline level. The design space of this optimization problem is also shown to be multi-modal.