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B. Dubus1, C. Granger1; P. Mosbah1; A. Moussatov1, H. Schmit1; L. Sztor1; C. Campos-Pozuelo2

1 IEMN département ISEN, UMR CNRS 8520, 41 boulevard Vauban, 59046 Lille Cedex, France email:

2 Instituto de Acustica, CSIC, Serrano 144, 28006 Madrid, Spain email:


A numerical model of ultrasonic cavitation field is described. It is based on a phenomenological description of a cavitating fluid as a non linear fluid whose characteristics (sound speed, density) depend upon the bubble density. To obtain the constitutive relationship between bubble density and acoustic pressure, a real-time measurement method of the bubble density, relying upon the variation of the electrical resistance of the medium, is proposed. The finite element formulation of the model is derived and implemented in the ATILA code. Computational results on the cavitation field created by a cylindrical concentrator are presented.


The development of industrial devices using physical and chemical processes assisted by ultrasonic cavitation is constrained by the limitation of existing modeling. This difficulty is due to the fact that processes involved are highly non linear and the reactions taking place in the fluid cannot be described by simple mathematical relations. More over, the overall efficiency of devices using cavitation is usually low and an oversizing cannot easily compensate for a bad design. Numerical modeling can provide the tools that would help to optimize the design of these devices.

The development of these numerical models involves different scales: the reactor scale corresponding to the parameters (reactor geometry, transducer...) available to the designer, the bubble scale where most physical processes (vibration, rectified diffusion, coalescence, fragmentation, Bjerknes forces...) take place; the particle scale used to describe the cavitating fluid as a continuum. The microscopic non linear phenomena must be translated into a constitutive equation (at the particle scale) in order to be implemented in the numerical model. Existing numerical models [1-4] start from the study of the dynamical behavior of the single bubble. Strong hypotheses (linear vibration [2, 3], isolated bubbles [1-4], prescribed distribution of bubble sizes [1-4], no coalescence or fragmentation [1-4]) are then added. Finally, the Caflish model [5] is used to build up a constitutive equation of the cavitating fluid. Resulting equations are expressed in the time-domain and solved using finite element [1] or finite difference [2-4] methods.

A different approach is presented here. Firstly, it is assumed that the cavitating fluid reaches a steady-state. Physical quantities are described by their average value at the working frequency.

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