Nonlinear ultrasonic standing waves: two-dimensional simulations in bubbly liquids

We present the results of numerical predictions for analyzing the behavior of nonlinear ultrasonic standing waves in two-dimensional cavities filled with bubbly liquids. The model we solve accounts for nonlinearity, dissipation, and dispersion of the two-dimensional media due to the bubbles. The numerical simulations are based on a finite-difference scheme. They consider the bubbles evenly distributed in the liquid. Results are shown for high-amplitude signals. They make it possible to observe how the linear modes turn into multi-frequency nonlinear fields.     

Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.     

Electrical detection of the ultrasonic cavitation onset

We propose a new technique for the study of ultrasonic cavitation. This method is based on the quantification of the electrical admittance variations of the emitter in a range around the resonance frequency at different excitation levels. As the cavitation threshold is reached, the state of the fluid is changing; we evaluate these changes. The high-power piezoelectric transducer is modelled through an analytical model, which is used to relate the characteristics of the fluid domain (bubble density, extent) to the electrical admittance (peak value, resonance frequency, and bandwidth). Thus, the admittance we measure allows us to determine the characteristics of the bubbly liquid. The procedure is applied to the inertial cavitation field generated at 24kHz at very high amplitudes. The results obtained show that a very high bubble density layer is formed at the surface of the sonotrode.     

Acoustic cavitation mechanism: a nonlinear model

During acoustic cavitation process, bubbles appear when acoustic pressure reaches a threshold value in the liquid. The ultrasonic field is then submitted to the action of the bubbles. In this paper we develop a model to analyze the cavitation phenomenon in one-dimensional standing waves, based on the nonlinear code SNOW-BL. Bubbles are produced where the minimum rarefaction pressure peak exceeds the cavitation threshold. We show that cavitation bubbles appear at high amplitude and drastically affect (dissipation, dispersion, and nonlinearity) the ultrasonic field. This paper constitutes the first work that associates the nonlinear ultrasonic field to a bubble generation process.     

Nonlinear ultrasonic resonators: a numerical analysis in the time domain

In the framework of the study of nonlinear acoustic phenomena arising in high-power ultrasonic resonators, this paper deals with the numerical prediction of the behaviour of strongly nonlinear waves in resonators. In particular three-dimensional cavities in complex modal configurations are analyzed. The main motivation of this work is the understanding and optimisation of high-power ultrasonic applications in fluids. Based on conservation laws written in Lagrangian coordinates and the isentropic state equation, several evolution equations (one-dimensional, two-dimensional, three-dimensional and axisymmetric) are proposed and numerically solved in the time domain. No restriction on nonlinearity level is imposed. These developments allow the simulation of the time evolution of the pressure distribution inside the cavity, as well as the harmonics distribution. Distortion, nonlinear attenuation and rms pressure can be studied. Periodic (continue) and pulsed signal excitation are possible. Some results referred to complicated nonlinear waves are presented.     

Numerical simulations of three-dimensional nonlinear acoustic waves in bubbly liquids

This paper presents three-dimensional simulations of nonlinear propagation of ultrasonic waves through bubbly liquids, which represent the continuity of our previous works included in the numerical tool SNOW-BL. The behavior of three-dimensional nonlinear acoustic waves in bubbly liquids is analyzed by means of numerical predictions. Nonlinearity, attenuation, and dispersion due to the presence of bubbles in the liquid are taken into account. The numerical solution to the differential problem is obtained by means of a finite-difference scheme. The simulations we present here consider a homogeneous distribution of bubbles in the liquid. Results compare high and low-amplitude waves to detect the nonlinear effects of the bubbles. Results are shown for radiation and enclosure problems.     

On the physical origin of conical bubble structure under an ultrasonic horn

The cavitation field generated by an ultrasonic horn at low frequency and high power is known to self-organize into a conical bubble structure. The physical mechanism at the origin of this bubble structure is investigated using numerical simulations and acoustic pressure measurements. The thin bubbly layer lying at horn surface is shown to act as a nonlinear thickness resonator that amplifies acoustic pressure and distorts acoustic waveform. This mechanism explains the self-stabilization of the conical bubble structure as well as the generation of shock wave and the focusing at very short distance.