A two-port model for wave propagation along a long circular microchannel

Veijola, Timo

doi:10.1007/s10404-007-0159-2

Cited by 9 publications

(22 citation statements)

References 13 publications

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“…• Wave propagation in in-ear hearing aids [1] • The behavior of MEMS devices with thin fluid layers [2,3,4] • The behavior of microphones, consisting of a membrane backed by a thin air layer [5,6,7,8] • The behavior of inkjet print heads, including the wave propagation in narrow ink channels [9,10] • The behavior of plates and double wall panels with a thin fluid layer for reduction of sound transmission [11,12,13,14,15,16,17] • Modeling wave propagation in the cochlea [18] • Modeling wave propagation in the vocal tract, trachea and lungs [19] Note that in many cases where the boundary-layer thicknesses are small compared to the dimensions of the domain, neglecting viscothermal effects leads to a very accurate and efficient description of the fluid behavior. Nevertheless, a second class of problems where the viscothermal effects can become significant, even if the boundary-layer thicknesses are relatively small, is in systems near resonance.…”

Section: Applications Of Viscothermal Modelsmentioning

confidence: 99%

“…Substituting the caloric equation of state (2.8) and the Fourier law (2.4) in equation (2.1c) yields the energy equation for an ideal gas 3 :…”

Section: Energy Equation For An Ideal Gasmentioning

confidence: 99%

“…, the sum of the propagation constants for the tangential direc-52 tions 3 . The sub-matrices P 1 and P 2 are of the form…”

Section: Pilot Vector and Surface Normal Coincidementioning

confidence: 99%

“…For flat 2D waveguide, the components of the different solutions to the Helmholtz equations ψ a i , ψ h i , and ψ v i can be split into a symmetric and mirror-symmetric 3 Examples of the expression for k t are: …”

Section: Symmetry In Flat Waveguidesmentioning

confidence: 99%

“…In almost all instance, the accuracy is assessed by validating individual cases experimentally 3 . In most cases, excellent agreement between measurement and LRF results is obtained.…”

mentioning

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: Applications Of Viscothermal Modelsmentioning

confidence: 99%

“…Substituting the caloric equation of state (2.8) and the Fourier law (2.4) in equation (2.1c) yields the energy equation for an ideal gas 3 :…”

Section: Energy Equation For An Ideal Gasmentioning

confidence: 99%

“…, the sum of the propagation constants for the tangential direc-52 tions 3 . The sub-matrices P 1 and P 2 are of the form…”

Section: Pilot Vector and Surface Normal Coincidementioning

confidence: 99%

Section: Symmetry In Flat Waveguidesmentioning

confidence: 99%

“…In almost all instance, the accuracy is assessed by validating individual cases experimentally 3 . In most cases, excellent agreement between measurement and LRF results is obtained.…”

mentioning

confidence: 99%

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Viscothermal wave propagation

Nijhof¹

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Compact model for a MEM perforation cell with viscous, spring, and inertial forces

Veijola¹

2008

Microfluid Nanofluid

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A compact model for calculating damping, inertial, and spring forces in a perforated squeeze-film damper is reported. The repetitive pressure patterns around each perforation are utilized by analyzing the viscoacoustic wave transmission around the hole in a cylindrical volume, called perforation cell. The model is needed in applications where the acoustic wavelength of the oscillation is comparable with the dimensions of the perforation cell. The model is constructed of acoustic impedance twoports. A novel model is derived for the air gap region, and a published two-port model is used for the hole. The impedances for these two-ports are derived from the low reduced frequency model that is equivalent with linearized, harmonic Navier-Stokes equations for acoustic wave propagation in thin channels. This model considers also the transition from the isothermal conditions at low frequencies to the adiabatic ones at high frequencies. The dimensions of MEMS structures are considered using slip conditions for velocities and temperatures. Also, an easyto-use simplified model for frequencies where the squeeze number and the Reynolds numbers are below unity is derived. The analytical compact model is verified with FEM simulations using a harmonic solver for linearized Navier-Stokes equations with slip boundary conditions in a wide range of perforation ratios. The maximum relative error in the damping coefficient in the simulated cases was 20% upto the first resonant frequency.

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Acoustic components

Beranek¹,

Mellow²

2012

Acoustics: Sound Fields and Transducers

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A two-port model for wave propagation along a long circular microchannel

Cited by 9 publications

References 13 publications

Viscothermal wave propagation

Viscothermal wave propagation

Compact model for a MEM perforation cell with viscous, spring, and inertial forces

Acoustic components

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