On the validity of numerical models for viscothermal losses in structural optimization for micro-acoustics

Abstract

The increasing interest in miniaturizing acoustic devices has made accurate and efficient models of acoustic viscous and thermal losses progressively more important. This is especially the case in micro-acoustic devices such as hearing aids, condenser microphones and MEMS devices. Using the full linearized Navier Stokes equations to numerically model losses comes at a high computational cost. An approximate boundary layer impedance boundary condition representing acoustic losses has therefore become popular due to its high computational efficiency. This is especially true in the context of optimization where an efficient numerical method is required due to the many repeated analyses needed. However, the boundary layer impedance is only valid in the computational region where boundary layers are non-overlapping. Applying the boundary layer impedance can therefore lead to poor optimization results or limit the possible design space if the optimization violates this limitation. Therefore, the benefit of losses in narrow regions cannot be exploited if the boundary layer impedance is used. This work investigates two shape optimization test cases for maximizing the absorption properties of Helmholtz-like geometries based on the Boundary Element Method. The test cases are used to compare and validate the boundary layer impedance against a full viscothermal implementation revealing the benefits of the boundary layer impedance but also its limitations in a structural optimization setting. Based on the numerical experiments it is recommend to avoid the use of the boundary layer impedance in cases where any theoretical boundary layer overlap exists or at least verify simulation and optimization results with a full-losses implementation.