Discussion Forum

There is a very interesting and surprisingly still underutilized discovery made by Timothy S. Lucas at al. about the “Resonant Macrosonic Synthesis” patent number US5515684 issued in 1996. The main feature of the invention is that by using an acoustic resonator of appropriate shape (which has got anharmonic higher modes), one can obtain much higher pressure amplitudes than what the acoustical saturation in cylindrical resonators would allow.

Young-Doo Chun and Yang-Hann Kim have discussed the modelling of such resonators in their paper “Numerical analysis for nonlinear resonant oscillations of gas in axisymmetric closed tubes”. I am interested in modelling this resonator using both gases and liquids, but primarily liquids.

Would it be possible to simulate such resonators in nonlinear regime, having asymmetrical pressure amplitudes in one of the COMSOL predefined models?

Since the amplitude is very high compared to the average pressure, we can not use the linear acoustics interfaces. The closest model I could find is the “Nonlinear Acoustics: Modeling of the 1D Westervelt Equation”. Unfortunately, this approach does not take into account the wave distorting influence of the average pressure vs. pressure amplitude ratio. Although the positive pressure is not limited and consequently it can rise way above the average pressure level, the negative pressure is limited. In gases it can not get lower than 0 Pa, while in liquids the cavitation pressure sets the lower pressure amplitude limit. Thus, due to this amplitude asymmetry the average pressure will be different at the two ends of the resonator, and an average overpressure can drive a unidirectional pumping bulk flow through the resonator openings even without any valves. The above mentioned Westervelt model can not do such modelling, since it does not take the bulk flow into account.

If we would use one of the aeroacoustic interfaces by adding the nonlinear term of the Westervelt equation (if it is even possible), then I would have to give the bulk flow velocity in advance, which I don’t know, because it depends on the acoustic pressure asymmetry, and on the size of the openings etc.

I have read in one of the papers that the nonlinear resonator can be accurately modelled by solving the compressible Navier-Stokes equations. I have attempted to simulate this in one of the CFD interfaces using the “Turbulent Flow, k-ep” with the “Compressible flow ma ~0.3” setting enabled, but it doesn’t model it correctly. The pressure disturbance doesn’t propagate with the speed of sound, but it is transmitted instantaneously over the whole domain as if the fluid would be incompressible, thus it seems to be useless for acoustic simulations.

Does anybody know how to model this system in COMSOL with one of the predefined interfaces (even by using some modifications like adding a nonlinear term)? If not, then would it be possible to solve it using the PDE interfaces (if yes then how)?

Appreciate your comments.

George