Viscothermal wave propagation

Abstract

SummaryIn engineering practice, the simplest, most efficient model that yields the desired level of accuracy is usually the model of choice. This is particulary true if an optimization process is involved, in which case the choice of the underlying models is often a trade-off between efficiency and accuracy. It is therefore important to know not only how efficient a model is, but also how accurate.In this work, the accuracy, efficiency and range of applicability of various (approximate) models for viscothermal wave propagation are investigated in a general setting. Models for viscothermal wave propagation describe the wave behavior of fluids including viscous and thermal effects. Cases where viscothermal effects are significant generally involve small fluid domains, low frequencies, 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.Amongst the various models for viscothermal wave propagation that are considered, a prominent role is taken by the family of approximate models known as Low Reduced Frequency (or LRF) models. These are the most efficient approximate models available and they have been used extensively to model a wide variety of problems involving viscothermal wave propagation. Nevertheless, LRF models are only available for a limited number of geometries and can become inaccurate under certain conditions. A second family of models that is considered consists of exact solutions to the equations describing viscothermal wave propagation. These models, which are less efficient than the LRF models, provide reference solutions which can be used to determine the accuracy of the LRF models. A drawback of the exact models is that they are only available for a small number of geometries. Therefore a third family of models is considered, which is based on a newly developed Finite Element (or FE) approximation of the equations for viscothermal wave propagation. The main attraction of these FE models is that they can be used to model arbitrary geometries and boundary conditions. A drawback is that obtaining a solution requires much more computing power than needed for the LRF or exact models. The vi numerical stability and convergence properties of the developed FE methods are investigated to ensure that they can yield reference solutions of a desired accuracy for cases where an exact solution is not available.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. The gathered data provides a means of estimating the accuracy of simple coupled LRF models a priori.Besides the investigation into the accuracy of LRF models, two engineering applications where viscothermal wave propagation takes a prominent role are described. The first application involves the passive si...

Viscothermal accoustics using finite elements

“…Another thesis on viscothermal acoustics [55] wrien by colleague PhD candidate M.J.J. Nijhof appears in the same period as this thesis.…”

“…Other recommended works on the  model are Beltman's PhD thesis and journal papers [5,6,7]. Nijhof [55] presents the  model in a very general form. Many other authors have wrien articles on the subject, oen without using the name '' coined by Tijdeman. is section presents the basic form of the  model with a focus on two geometries: the uniform layer and the cylindrical tube; see figure 3.5.…”

“…e Navier-Stokes equations can also be used in combination with constitutive equations of a liquid, instead of an ideal gas. Interested readers can find the eqations for liquids in [34,55].…”

“…Nijhof [55] proposes a  model that calculates the solution with a single pressure calculation. He uses an alternative boundary condition that contains the second order spatial derivative of the pressure.…”

“…e literature contains many (semi-)analytic solution methods of these equations that are inspired by this paper. Nijhof [55] elaborates on these methods. is thesis focuses on numerical finite element methods for these equations, starting with a direct implementation in apter 2.…”