Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

Beltman, W.M.

doi:10.1006/jsvi.1999.2355

Cited by 75 publications

(71 citation statements)

References 63 publications

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“…For small values (k/s ≪ 1) the free wavelength is large compared to the viscous boundary layer thickness. For most gases and liquids, the ratio is small in the frequency and dimensional ranges that do not conflict with the assumptions of continuum mechanics [36]. For free waves,k/s ≪ 1 leads to the assumption of inviscid wave propagation.…”

Section: Dimensionless Groupsmentioning

confidence: 98%

“…All models were rewritten in a convenient dimensionless form and he demonstrated that only the LRF model could be used for the entire range of narrow to wide tubes. Two decades later, Beltman [5,10,36] compared the available models for layer geometries using a similar dimensionless notation (see section 2.6). He demonstrated that the relatively simple LRF models, which are computationally very efficient, are highly accurate for most fluids under standard atmospheric conditions under the same assumptions required for continuum mechanics.…”

Section: (Lrf) Model With a Numerical Solution Tomentioning

confidence: 99%

“…The characteristic length is given for a few cross sections of simple geometric shape in figure 2.1. Note that in many publications that involve the definition of a shear wave number (for instance [10,19,36]), the chosen (or implied) characteristic length for a layer/slit is half its width, while the characteristic length of the other geometries is as defined here. This 'inconsistent' choice of the characteristic length hinders a straightforward comparison of the results for different waveguide cross sections with that of a layer/slit.…”

Section: Characteristic Lengthmentioning

confidence: 99%

“…The most prominent reduced (analytical) models for viscothermal wave propagation were put in perspective by Tijdeman [35] and Beltman [36]. Their reviews of the different models showed that LRF models are highly accurate and most efficient to describe viscothermal wave propagation in isothermal, rigid waveguides of simple geometry structure for most fluids under standard atmospheric conditions.…”

Section: (B)(c)(d) Lrf Modelsmentioning

confidence: 99%

“…In the literature (semi) analytical LRF models can be found for square, circular, annular or triangular prismatic tubes [20,66,67,68,69] and rectangular, circular and elliptical air layers [10,22,25,36]. An LRF model for wave propagation in a curved air layer is given in section 4.2.2.…”

Section: (B)(c)(d) Lrf Modelsmentioning

confidence: 99%

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Viscothermal wave propagation

Nijhof¹

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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...

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Section: Dimensionless Groupsmentioning

confidence: 98%

Section: (Lrf) Model With a Numerical Solution Tomentioning

confidence: 99%

Section: Characteristic Lengthmentioning

confidence: 99%

Section: (B)(c)(d) Lrf Modelsmentioning

confidence: 99%

Section: (B)(c)(d) Lrf Modelsmentioning

confidence: 99%

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Viscothermal wave propagation

Nijhof¹

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A non‐conforming finite element formulation for modeling compressible viscous fluid and flexible solid interaction

Guilvaiee

Tóth

2022

Numerical Meth Engineering

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In modeling fluid–solid interaction (FSI), considering the impact of fluid compressibility is necessary to describe sound propagation. Furthermore, in micro‐scale, fluid viscosity is important. We present a finite element formulation for modeling a flexible solid coupled to a compressible viscous fluid. We use the linearized Navier–Stokes equations for a Newtonian fluid and describe the linear elastic solid using the linearized balance of momentum. For coupling between fluid and solid, we develop a non‐conforming finite element formulation, and propose an estimation for the necessary penalty factor by applying a scaling approach. The formulation is validated based on several test cases for various material combinations and shows good agreement with analytical solutions. Further, Nitsche‐based and symmetrization‐free formulations are compared, and spatial convergence is studied. Finally, we present an application example of a miniature Helmholtz resonator, which depicts a notable impact of the solid interaction on the viscous flow. In sum, our study indicates the potential for widespread use of the presented numerical approach in modeling FSI in miniature systems.

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FEM‐Modeling of thermal and viscous effects in piezoelectric MEMS loudspeakers

Guilvaiee

Tóth

2023

Proc Appl Math and Mech

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Loudspeakers based on piezoelectric micro‐electro‐mechanical system (PMEMS) are attracting an increasing interest due to their small size, low electronic power consumption, and easy assembly. These aspects are particularly advantageous in applications like earphones, mobile phones, and in‐ear hearing aid devices. However, creating sufficiently high sound pressure levels challenges many existing MEMS loudspeakers. Furthermore, their small dimensions require the consideration of additional physical phenomena like thermoviscous losses, which are often negligible in large loudspeakers. We model and characterize a 3D piezoelectric MEMS loudspeaker in this work using our open‐source finite element method (FEM) program openCFS. We use the linearized conservation of mass, momentum, and energy (thermoviscous acoustic PDEs) for a compressible Newtonian fluid (air) and describe the linear elastic solid using the linearized balance of momentum. The coupling between flow and solid fields is then applied using a non‐conforming FEM formulation. The standard acoustic partial differential equation (PDE) is used in the far‐field, where the thermal and viscous effects are negligible. We study the viscous effects on the displacement and the sound pressure levels (SPLs) of the loudspeaker by parameter studies. These results indicate that at a distance of 13 mm, an SPL of 55 dB at 5 kHz is achieved by a single PMEMS loudspeaker with a footprint of 1.7×1.7 mm2 under a low driving voltage of only 1 V, which is promising considering its dimensions.

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Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

Cited by 75 publications

References 63 publications

Viscothermal wave propagation

Viscothermal wave propagation

A non‐conforming finite element formulation for modeling compressible viscous fluid and flexible solid interaction

FEM‐Modeling of thermal and viscous effects in piezoelectric MEMS loudspeakers

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