A finite element for viscothermal wave propagation

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Abstract

The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that describes viscothermal wave propagation is needed to model such devices. For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately described by the low reduced frequency model. This model’s major drawback is that it is only defined for simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries. To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to the LRF model, the viscothermal finite element can be used to analyze complicated geometries. This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in which the results of the finite element models are compared to measurements.
Original languageEnglish
Title of host publicationProceedings of ISMA2008
Subtitle of host publicationInternational Conference on Noise and Vibration Engineering
EditorsP. Sas, B. Bergen
Place of PublicationLeuven
PublisherKatholieke Universiteit Leuven
Pages4271-4278
Number of pages8
ISBN (Print)978 9073802865
Publication statusPublished - 15 Sep 2008
Event2008 International Conference on Noise and Vibration Engineering, ISMA 2008 - Leuven, Belgium
Duration: 15 Sep 200817 Sep 2008
http://past.isma-isaac.be/isma2008

Conference

Conference2008 International Conference on Noise and Vibration Engineering, ISMA 2008
Abbreviated titleISMA
CountryBelgium
CityLeuven
Period15/09/0817/09/08
Internet address

Fingerprint

wave propagation
Stokes flow
propagation
acoustics
boundary layers
geometry
loudspeakers
inertia
wave equations
compressibility
viscosity
tubes
formulations
air

Keywords

  • IR-70026
  • METIS-255513

Cite this

Kampinga, W. R., Wijnant, Y. H., & de Boer, A. (2008). A finite element for viscothermal wave propagation. In P. Sas, & B. Bergen (Eds.), Proceedings of ISMA2008: International Conference on Noise and Vibration Engineering (pp. 4271-4278). Leuven: Katholieke Universiteit Leuven.
Kampinga, W.R. ; Wijnant, Ysbrand H. ; de Boer, Andries. / A finite element for viscothermal wave propagation. Proceedings of ISMA2008: International Conference on Noise and Vibration Engineering. editor / P. Sas ; B. Bergen. Leuven : Katholieke Universiteit Leuven, 2008. pp. 4271-4278
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title = "A finite element for viscothermal wave propagation",
abstract = "The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that describes viscothermal wave propagation is needed to model such devices. For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately described by the low reduced frequency model. This model’s major drawback is that it is only defined for simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries. To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to the LRF model, the viscothermal finite element can be used to analyze complicated geometries. This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in which the results of the finite element models are compared to measurements.",
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Kampinga, WR, Wijnant, YH & de Boer, A 2008, A finite element for viscothermal wave propagation. in P Sas & B Bergen (eds), Proceedings of ISMA2008: International Conference on Noise and Vibration Engineering. Katholieke Universiteit Leuven, Leuven, pp. 4271-4278, 2008 International Conference on Noise and Vibration Engineering, ISMA 2008, Leuven, Belgium, 15/09/08.

A finite element for viscothermal wave propagation. / Kampinga, W.R.; Wijnant, Ysbrand H.; de Boer, Andries.

Proceedings of ISMA2008: International Conference on Noise and Vibration Engineering. ed. / P. Sas; B. Bergen. Leuven : Katholieke Universiteit Leuven, 2008. p. 4271-4278.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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T1 - A finite element for viscothermal wave propagation

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AU - de Boer, Andries

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N2 - The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that describes viscothermal wave propagation is needed to model such devices. For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately described by the low reduced frequency model. This model’s major drawback is that it is only defined for simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries. To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to the LRF model, the viscothermal finite element can be used to analyze complicated geometries. This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in which the results of the finite element models are compared to measurements.

AB - The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that describes viscothermal wave propagation is needed to model such devices. For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately described by the low reduced frequency model. This model’s major drawback is that it is only defined for simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries. To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to the LRF model, the viscothermal finite element can be used to analyze complicated geometries. This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in which the results of the finite element models are compared to measurements.

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PB - Katholieke Universiteit Leuven

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Kampinga WR, Wijnant YH, de Boer A. A finite element for viscothermal wave propagation. In Sas P, Bergen B, editors, Proceedings of ISMA2008: International Conference on Noise and Vibration Engineering. Leuven: Katholieke Universiteit Leuven. 2008. p. 4271-4278