General formulation of the dispersion equation in bounded visco-thermal fluid, and application to some simple geometries

Bruneau, Michel; Herzog, Ph.; Kergomard, Jean; Polack, Jean‐Dominique

doi:10.1016/0165-2125(89)90018-8

Cited by 84 publications

(56 citation statements)

References 5 publications

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“…Early BEM implementations relied on the work by Bruneau et al, 7 turned into BEM by Dokumaci 8,9 and Karra and Ben Tahar. 10 Their contributions were either having some restrictions or completely neglecting viscosity.…”

Section: Introductionmentioning

confidence: 99%

A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

Andersen

Henrı́quez

Aage

et al. 2018

J. Theor. Comp. Acout.

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In recent years, the boundary element method has shown to be an interesting alternative to the finite element method for modeling of viscous and thermal acoustic losses. Current implementations rely on finite-difference tangential pressure derivatives for the coupling of the fundamental equations, which can be a shortcoming of the method. This finite-difference coupling method is removed here and replaced by an extra set of tangential derivative boundary element equations. Increased stability and error reduction is demonstrated by numerical experiments.

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Section: Introductionmentioning

confidence: 99%

A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

Andersen

Henrı́quez

Aage

et al. 2018

J. Theor. Comp. Acout.

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“…This model represents the wave equation when viscous and thermal losses are concentrated in a boundary layer near the walls of the duct; averaging the acoustical quantities on the cross-section gives rise to a ∂ 1 2 t equivalent operator (see [3,21]), which also appears in other acoustical contexts, see e.g. [9].…”

Section: Introductionmentioning

confidence: 99%

“…H := L 2 ([0, +∞), dµ(ξ)) andH := L 2 ([0, +∞), ξ dν(ξ)) respectively, and using [1], Stability theorem, we prove Theorem 1.2. Let µ be a positive non-null measure satisfying (3) and such that µ({0}) = 0 and ν be a positive non-null measure satisfying (4). Let p ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic stability of linear conservative systems when coupled with diffusive systems

Matignon

Prieur

2005

ESAIM: COCV

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Abstract. In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also illustrate the sharpness of this condition by exhibiting some systems for which we do not have the asymptotic property.Mathematics Subject Classification. 35B37, 93C20, 93D20.

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“…In Kirchhoff's original work only cylindrical prismatic tubes were considered. The more general derivation of the exact solutions given in this chapter follows the work of Bruneau et al [43] to a large extent. The notation is based on the work of Beltman [10,36] who presented the work of Bruneau et al in the dimensionless form that was introduced in section 2.6.…”

Section: Exact Kirchhoff Solutionsmentioning

confidence: 86%

“…They also demonstrated the existence of a second series of modes that are dominated by viscous effects (vortical or vorticity modes) and indicated that, when thermal effects are included, a third series of modes can be found (entropic or thermal modes). Bruneau et al [43] and Liang and Scarton [44] independently extended the method to include thermal effects.…”

Section: Numerical Solutions To Kirchhoff's Dispersion Equationmentioning

confidence: 99%

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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General formulation of the dispersion equation in bounded visco-thermal fluid, and application to some simple geometries

Cited by 84 publications

References 5 publications

A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

Asymptotic stability of linear conservative systems when coupled with diffusive systems

Viscothermal wave propagation

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