Shape optimization of micro-acoustic devices including viscous and thermal losses

Since the late 1980s, numerical shape optimization has been applied successfully to improve the design and development of novel acoustic devices. Most often, viscous and thermal dissipation effects are neglected in the optimization process, as this is an acceptable assumption in e.g. room acoustics, etc. However, in many acoustic devices, ranging from hearing aids to metamaterials, dissipation can significantly influence the acoustic wave behaviour. In this paper, we propose a numerical acoustic shape optimization technique and we demonstrate it using two-dimensional quarter-wave and Helmholtz resonators including accurate modelling of viscous and thermal dissipation. By combining a dissipative boundary element method with shape optimization, the sound absorption capability of the resonators located at an impedance tube termination is maximized. Numerical experiments demonstrate the importance of viscothermal dissipation and its impact on the optimization outcome. The resulting resonator shapes, optimized using a lossy assumption, yield significantly better performance compared to their lossless counterpart, with near-perfect absorption at the desired optimization frequencies.