An acoustic finite element including viscothermal effects

M.J.J. Nijhof, Y.H. Wijnant, A. de Boer

Research output: Contribution to conferencePaperAcademic

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Abstract

In acoustics it is generally assumed that viscous- en thermal boundary layer effects play a minor role in the propagation of sound waves. Hence, these effects are neglected in the basic set of equations describing the sound field. However, for geometries that include small confinements of air or thin air layers, this assumption is not valid. Special models that include viscous and thermal effects are available (for example the Low Reduced Frequency model) but only for a limited number of geometries. To overcome these limitations and provide a solution that can be used for arbitrary geometries, an acoustic finite (2D) element that includes viscous and thermal effects is developed. The model is based on the linearized Navier stokes equations (including shear), the equation of continuity, the equation of state for an ideal gas and the energy equation. The method of weighed residuals is used in combination with a mixed formulation of pressure, temperature and particle velocity degrees of freedom. The results of the developed element code are compared with the results of an existing (analytical) Low Reduced Frequency solution and a viscothermal element that was found in literature.
Original languageEnglish
Number of pages8
Publication statusPublished - Jul 2007
Event14th International Congress on Sound and Vibration, ICSV 2007 - Cairns, Australia
Duration: 9 Jul 200712 Jul 2007
Conference number: 14

Conference

Conference14th International Congress on Sound and Vibration, ICSV 2007
Abbreviated titleICSV
CountryAustralia
CityCairns
Period9/07/0712/07/07

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acoustics
temperature effects
geometry
thermal boundary layer
air
ideal gas
sound fields
sound waves
continuity
Navier-Stokes equation
equations of state
degrees of freedom
shear
formulations
propagation
temperature
energy

Cite this

Nijhof, M. J. J., Wijnant, Y. H., & de Boer, A. (2007). An acoustic finite element including viscothermal effects. Paper presented at 14th International Congress on Sound and Vibration, ICSV 2007, Cairns, Australia.
Nijhof, M.J.J. ; Wijnant, Y.H. ; de Boer, A. / An acoustic finite element including viscothermal effects. Paper presented at 14th International Congress on Sound and Vibration, ICSV 2007, Cairns, Australia.8 p.
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Nijhof, MJJ, Wijnant, YH & de Boer, A 2007, 'An acoustic finite element including viscothermal effects' Paper presented at 14th International Congress on Sound and Vibration, ICSV 2007, Cairns, Australia, 9/07/07 - 12/07/07, .

An acoustic finite element including viscothermal effects. / Nijhof, M.J.J.; Wijnant, Y.H.; de Boer, A.

2007. Paper presented at 14th International Congress on Sound and Vibration, ICSV 2007, Cairns, Australia.

Research output: Contribution to conferencePaperAcademic

TY - CONF

T1 - An acoustic finite element including viscothermal effects

AU - Nijhof, M.J.J.

AU - Wijnant, Y.H.

AU - de Boer, A.

PY - 2007/7

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N2 - In acoustics it is generally assumed that viscous- en thermal boundary layer effects play a minor role in the propagation of sound waves. Hence, these effects are neglected in the basic set of equations describing the sound field. However, for geometries that include small confinements of air or thin air layers, this assumption is not valid. Special models that include viscous and thermal effects are available (for example the Low Reduced Frequency model) but only for a limited number of geometries. To overcome these limitations and provide a solution that can be used for arbitrary geometries, an acoustic finite (2D) element that includes viscous and thermal effects is developed. The model is based on the linearized Navier stokes equations (including shear), the equation of continuity, the equation of state for an ideal gas and the energy equation. The method of weighed residuals is used in combination with a mixed formulation of pressure, temperature and particle velocity degrees of freedom. The results of the developed element code are compared with the results of an existing (analytical) Low Reduced Frequency solution and a viscothermal element that was found in literature.

AB - In acoustics it is generally assumed that viscous- en thermal boundary layer effects play a minor role in the propagation of sound waves. Hence, these effects are neglected in the basic set of equations describing the sound field. However, for geometries that include small confinements of air or thin air layers, this assumption is not valid. Special models that include viscous and thermal effects are available (for example the Low Reduced Frequency model) but only for a limited number of geometries. To overcome these limitations and provide a solution that can be used for arbitrary geometries, an acoustic finite (2D) element that includes viscous and thermal effects is developed. The model is based on the linearized Navier stokes equations (including shear), the equation of continuity, the equation of state for an ideal gas and the energy equation. The method of weighed residuals is used in combination with a mixed formulation of pressure, temperature and particle velocity degrees of freedom. The results of the developed element code are compared with the results of an existing (analytical) Low Reduced Frequency solution and a viscothermal element that was found in literature.

M3 - Paper

ER -

Nijhof MJJ, Wijnant YH, de Boer A. An acoustic finite element including viscothermal effects. 2007. Paper presented at 14th International Congress on Sound and Vibration, ICSV 2007, Cairns, Australia.