Practical modeling of acoustic losses in air due to heat conduction and viscosity

To cite this version:Bérengère Lebental, Frédéric Bourquin. Visco-acoustic modelling of a vibrating plate interacting with water confined in a domain of micrometric size. Journal of Sound and Vibration, Elsevier, 2012, 331 (8) AbstractIt is well established that concrete durability strongly depends on the capillary porosity of the material. Hence, structural health monitoring of concrete structure could take advantage of concrete microporosity monitoring. To this end, a new method for the in situ non-destructive testing of capillary porosity in cementitious materials has been proposed. A sensing device that seems well suited to this application is a capacitive ultrasonic transducer with a characteristic size of 1 µm. It is to be embedded in the material. Its vibrating membrane is made of aligned carbon nanotubes forming a thin layer with a typical thickness of 1 nm. It generates acoustic waves of micrometric wavelength into water-filled micropores, aiming at measuring their properties.The present paper focuses on the numerical simulation of the embedded sensor. In order to properly account for viscous effects in fluids at the micrometric scale, we have developed a specific computational method for the visco-acoustic modelling of a microplate vibrating between 10 MHz and 2 GHz in a water-filled domain of micrometric size. Our approach is based on the condensation of the fluid part of the fluid-structure problem on the structure by a finite element method, and on a spectral approximation of the structural equations.The numerical results indicate that the fluid domain is resonant despite the viscous terms, which causes a frequency downshift of the resonances and a decrease of the quality factor. In the coupled sys- the pore width, which makes the device a good candidate as a porosity sensor.

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“…Several numerical methods based on finite elements [14,15] and boundary elements [18,19] are also available.…”

Section: Visco-thermal Elasto-acousticsmentioning

confidence: 99%

Visco-acoustic modelling of a vibrating plate interacting with water confined in a domain of micrometric size

Lebental

Bourquin

2012

Journal of Sound and Vibration

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“…Cheng et al [78] eliminate the energy equation and temperature variable by using an equation of state that relates pressure directly to density (thus the effects of a thermal boundary layer are not taken into account). 18 In the work of Christensen et al [26], it is not explicitly mentioned which degrees of freedom are discretized to obtain the presented results.…”

Section: (H) Bem/fem Full Lnsf Modelsmentioning

confidence: 99%

“…Due to the ongoing increase in memory, cpu-power and solver efficiency, the attention of researchers has gradually being drawn to such FE models over the last few years. Literature on such models is scarce, however [24,25,26,27]. The numerical stability of FE methods for viscothermal wave propagation has not been investigated previously.…”

Section: Finite Element Modelsmentioning

confidence: 99%

“…For instance if linear shape functions are used for a velocity only FE approximation of the Stokes equations, the inf-sup condition is not satisfied for the associated mixed problem, suggesting that such an FE method is numerically unstable. In practice, such elements are indeed known to suffer from locking 26 . The tendency of primal methods for the Stokes problem to be susceptible to locking transcends to FE methods for the LNSF equations in the case of velocity/temperature-based methods.…”

Section: Velocity-temperature Based Elementsmentioning

confidence: 99%

“…Exceptions where full LNSF models are compared with LRF results for systems of more complex geometry, are found in the recent work of Kampinga [1] and Christens et al [26]. Kampinga uses the FE models that are presented in chapter 5 to verify the LRF solution and the solution of a new method called the Sequential Linear Navier Stokes Model.…”

Section: Literaturementioning

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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A finite element model of perforated panel absorbers including viscothermal effects

et al. 2015

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Practical modeling of acoustic losses in air due to heat conduction and viscosity

Cited by 6 publications

References 12 publications

Visco-acoustic modelling of a vibrating plate interacting with water confined in a domain of micrometric size

Visco-acoustic modelling of a vibrating plate interacting with water confined in a domain of micrometric size

Viscothermal wave propagation

A finite element model of perforated panel absorbers including viscothermal effects

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