Viscothermal wave propagation

Abstract

In this work, the accuracy, efficiency and range of applicability of various (approximate) models for viscothermal wave propagation are investigated. Models for viscothermal wave propagation describe thewave behavior of fluids including viscous and thermal effects. Cases where viscothermal effects are significant generally involve small fluid domains, lowfrequencies, or fluid systems near resonance. Examples of practical applications of these models are, for instance, describing the behavior of in-ear hearing aids, MEMS devices, microphones, inkjet printheads and muffler systems involving acoustic resonators. Three different types of models for viscothermal wave propagation are studied: The first family consists of Low Reduced Frequency (or LRF) models, which are the most efficient approximate models available. Nevertheless, LRF models are only available for a limited number of geometries and can become inaccurate under certain conditions. The second family of models consists of exact solutions to the equations describing viscothermal wave propagation. These models are less efficient than the LRF models, and are only available for a small number of geometries. The third family of models consists of Finite Element (or FE) approximations of the equations for viscothermal wave propagation. Solving these FE models, which can be used to model arbitrary geometries and boundary conditions, requires much more computing power compared to the LRF or exact models. The numerical stability and convergence properties of these newly developed FE methods are investigated extensively. Using these three families of models, a number of parameter studies are carried out that yield detailed information on accuracy of the highly efficient LRF models for a range of geometries and boundary conditions. In addition, two engineering applications where viscothermal wave propagation takes a prominent role are described. The first application involves the design of a (passive) silencer involving acoustic resonators for a speed controlled cooling fan in a personal computer. Measurements indicate that a reduction of the noise level between 3.5 to 7 dB(A) is achieved. The second application involves the modeling of a resonator system for sound absorption in aircraft cabins. For this application, the accuracy of the FE model offers a significant improvement over that of the LRF model.