A finite element for viscothermal wave propagation


Kampinga, W.R. and Wijnant, Y.H. and Boer de, A. (2008) A finite element for viscothermal wave propagation. In: ISMA2008, International Conference on Noise and Vibration Engineering, September 15-17, 2008, Leuven, Belgium.

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.
Item Type:Conference or Workshop Item
Engineering Technology (CTW)
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Link to this item:http://purl.utwente.nl/publications/70026
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