Page 40 - Summer 2021

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Simulation of Perforates: An Application of
Nonlinear Thermo- viscous Acoustics
M. Herring Jensen
Whether designing a concert hall, an earbud microspeaker, or virtual reality sound (Vorländer, 2020), acoustics sim- ulation has gained a foothold in many commercial and academic settings. For electronic products especially, the competition between companies is fierce, because con- sumers have many options to choose from when they are looking to spend money on the latest and greatest devices. Product experts race to design the next viral product in a market where even a small competitive advantage can have a big impact on a company’s success. In this climate, many teams turn to simulation to develop that advantage.
Simulation is becoming even more important as new design challenges arise. Optimizing designs, minimizing weight, and making devices as small and compact as possible are some
examples. And where many designs would previously rely on analytical inputs, like Webster's horn equation used for a tweeter waveguide design, it is now pos- sible to include more details in the simulation model and explore new designs. One example is the ability to conduct a numerical simulation of all relevant physics and how they interact, to simultaneously study electro- magnetics, structural deformation, and acoustic fields in multiphysics simulations of loudspeakers. Another example is how simulation and better computers allow the inclusion of smaller-scale or microfeatures.
The example studied here is microperforated plates (MPPs) or perforates, used in many acoustics applications where controlled damping is necessary. Perforates are found in room acoustic treatments for sound control and absorption, in duct acoustics for muffler systems, in various micro- phone applications, and in grills in front of loudspeakers.
Damping occurs as a result of thermal and viscous dissipa- tion in the acoustic boundary layer. In microperforated plates, the boundary layer thickness is comparable to the perfora- tion diameter, which leads to a larger amount of damping.
A full thermoviscous acoustics description is necessary to capture the losses in detail. In general, as sound pressure levels increase in the devices, nonlinear effects start to kick in. An increase in dissipation occurs and the value of the trans- fer impedance becomes level dependent. The importance of nonlinear effects can be related to the Strouhal number,
Figure 1. Acoustic velocity magnitude in a tapered perforate showing the onset of vortex shedding: 3D view (left) and cross section (right) with acoustic temperature fluctuations and velocity.
40 Acoustics Today • Summer 2021 | Volume 17, issue 2