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Navier Stokes equation applied to acoustics
Posted 07.09.2010, 10:38 GMT-4 Fluid & Heat, Acoustics & Vibrations, Computational Fluid Dynamics (CFD), Parameters, Variables, & Functions 4 Replies
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I have to model a small hole crossed by an acoustic wave, where some energy is disipated because of the friction on the rigid walls. This problem must take into acount the viscosity of the medium and therefore needs to solve an acoustic wave equation derived from the Navier Stokes equation.
However I can't find a model of Navier Stokes equation able to calculate time-harmonic problems, but only time dependent or stationary analysis. Does anyone know some one?
I'm using the acoustics module, and I tried to add a laplacian term of the velocity field in the wave equation (menu Physics/Equation System/Subdomain Settings) thus becoming the equation right, so I don't know if it is possible or not because of the complexity of such operator. Does anyone know how to insert this laplacian?
Finally I ask whether it is possible to use the PDE model to introduce a vectorial equation (based on the velocity field) involving operators like laplacian or curl.
Thank you,
Victor M.
Hello Victor Garcia
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I would be extremely interested to learn if you ever found a solution to this problem as I'm dealing with a similiar sounding problem of acoustic loss which I've currently attributed to viscous drag within a narrow pipe.
Regards
Alasdair
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I found two ways to solve the problem:
- To introduce the Navier-Stokes equation through its weak form.
- You can add an elastic domain whose Bulk modulus, density and Poisson coefficient are calculated in such a manner that the elastic equation matches with Navier-Stokes equation.
However it is remarkable that Comsol 4.2 has already added thermo-acoustic propagation, so it is the simplest way to simulate your problem.
Regards,
Victor M.
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Would you mind sharing a simple example model with me, what you were doing sounds similiar to what I wish to achieve (modelling the viscous attenuation of sound waves through very narrow slits to observe the affect on standing wave resonances). I'm having trouble with the thermo-acoustic model solving and the sole example I have found on the website isn't a great help.
Regards
Alasdair
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At the moment I haven't had time to use the special features of Comsol 4.2 in this way, although I hope to do this soon.
On the other hand, regarding to Comsol 3.5, I send you a file that test the transmission through a layer of "air" modelled by using a elastic subdomain whose parameters (Young modulus and Poisson ratio) are defined in such a manner that the elasticity equation becomes Navier-Stokes. Note that the incident wave crosses the elastic subdomain without being altered because the viscosity of air is very low.
It is very important to mesh accurately the boundaries between elastic and fluid domains. Otherwise the coupling between these domains will be too poor. Take it into account in your problem.
Regads,
Victor
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