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

Gilles Tissot 1, * Robin Billard 2 Gwenael Gabard 2
* Corresponding author
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique , INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Abstract : 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.
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Gilles Tissot, Robin Billard, Gwenael Gabard. Optimal cavity shape design for acoustic liners using Helmholtz equation with visco-thermal losses. Journal of Computational Physics, Elsevier, 2020, 402, pp.109048. ⟨10.1016/j.jcp.2019.109048⟩. ⟨hal-02335784⟩

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