Topology optimization for acoustic structures considering viscous and thermal boundary layers using a sequential linearized Navier-Stokes model

This paper proposes a level set-based topology optimization method for designing acoustic structures with viscous and thermal boundary layers in perspective. It is known that acoustic waves propagating in a narrow channel are damped by viscous and thermal boundary layers. To estimate these viscothermal effects, we first introduce a sequential linearized Navier-Stokes model based on three weakly coupled Helmholtz equations for viscous, thermal, and acoustic pressure fields. Then, the optimization problem is formulated, where a sound-absorbing structure comprising air and an isothermal rigid medium is targeted, and its sound absorption coefficient is set as an objective function. The adjoint variable method and the concept of the topological derivative are used to obtain design sensitivity. A level set-based topology optimization method is used to solve the optimization problem. Two-dimensional numerical examples are provided to support the validity of the proposed method. In addition, the mechanisms that lead to the high absorption coefficient of the optimized design are discussed.