Liquid jet and droplet deformation induced by non-uniform acoustics radiation pressure distribution
Résumé
The present work focuses on non linear acoustic effects on an elliptic cylinder or an ellipsoid. These effects are encountered in acoustic levitation, ultrasonic standing wave atomization or two-phase flow combustion instabili-ties. Theoretical approaches mainly paid attention on the total radiation force, but a modeling of the distribution of acoustic radiation pressure around the object is needed to predict liquid object deformation. In the present study, a semi-analytical model is presented in order to compute the local radiation pressure as the only reason for liquid jet or droplet deformation. The method used here imposes an incident field to, a posteriori, compute the scattered field as a function of the object geometrical properties. A partial wave decomposition(PWD) model is developed to express incident and scattered fields by and immovable object with rigid boundary conditions. Radiation pressure is computed for progressive and standing wave fields. Validation of our method is done by comparing with the radiation force results from the literature. Results show that the larger the deformation, the higher the acoustic effects in a direction perpendicular to the acoustic wave axis. Introduction Non linear effects of acoustics are encountered in applications such as acoustic levitation, ultrasonic standing wave atomization or two-phase flow combustion instabilities occurring in rocket engines [1-4]. Most of the studies dealing with interaction of acoustics and spherical [5-9] or cylindrical [10-14] objects focused on the stationary radiation force. The main objective was there to determine the displacement of these objects. However, their deformation is also of a great interest in applications dealing with liquid objects. In studies on acoustically levitating droplets, some authors considered the radiation pressure distribution as the source of the stationnary deformation of the free surfaces [2, 15, 16]. They showed that spherical droplets became oblate when exposed to the radiation pressure. For cylindrical objects, it was experimentally proven that cylindrical liquid jets subjected to a low frequency standing wave were susceptible to be deformed into elliptic cylinders [17]. Thus, by relying on those results it appeared that knowing radiation pressure distribution around elliptic objects was necessary to correctly analyze the interaction between acoustics and deformed objects. Hasheminejad et al. [18, 19] developed an approach based on elliptic functions, namely Mathieu functions, to describe the acoustic scattered field. This is a powerful method, but limited in its applications due to the occurrence of Mathieu polynomials instability. Other authors considered a theoretical approach based on the expression of the incident and scattered waves by means of the formal cylindrical or spherical functions [17, 20-22]. All the studies cited above focused only on the modeling of the radiation force computed with the far field assumption avoiding the computation of radiation pressure distribution. To tackle the problem of object deformation induced by acoustics, it is needed to model the radiation pressure distribution. This is done here for elliptic cylinders and ellipsoids. The two-way coupling between incident acoustic harmonic plane waves and these objects is explored by computing the radiation pressure field and resulting radiation force. In the first section is presented the method used to compute the acoustic velocity potential field scattered by elliptic objects and the consequent computation of the radiation pressure and radiation force. Results showing the convergence of the method, its validation and the radiation pressure distribution are presented in the second section. Finally, the last section is dedicated to some conclusions.
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