Optimal cavity shape design for acoustic liners using Helmholtz equation with visco-thermal losses

摘要

This paper presents a shape optimisation strategy to design a cavity for acoustic liners, that approaches at best a target impedance over a given frequency range, penalising too large shape displacements from an initial guess. A model based on the Helmholtz equation is used, where the visco-thermal losses are taken into account by an equivalent impedance boundary condition. Using an adjoint-based method, the gradient of the cost functional with respect to shape variations is calculated, and regularised by a Sobolev gradient. A finite element method is employed with XFEM cut elements, that allows to consider an immersed boundary which is localised by a level-set function. We show that with this method, we are able to obtain a cavity shape leading to an almost perfect absorption for a frequency in the prescribed optimisation range.