Generation of subharmonics in acoustic resonators containing bubbly liquids: A numerical study of the excitation threshold and hysteretic behavior.

In this paper we study the generation and behavior of subharmonics in a bubbly liquid confined in an acoustic resonator, through numerical simulations carried out at finite-amplitude acoustic pressure. Several configurations in terms of resonator length and driving frequency are considered here. Our results show that these frequency components, created from a higher-frequency signal at the source (ultrasound), are due to the nonlinearity of the medium at high acoustic-pressure amplitude and to the configuration of the resonator (geometry and boundaries).

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field.

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown.

Nonlinear Maximization of the Sum-Frequency Component from Two Ultrasonic Signals in a Bubbly Liquid.

Techniques based on ultrasound in nondestructive testing and medical imaging analyze the response of the source frequencies (linear theory) or the second-order frequencies such as higher harmonics, difference and sum frequencies (nonlinear theory). The low attenuation and high directivity of the difference-frequency component generated nonlinearly by parametric arrays are useful. Higher harmonics created directly from a single-frequency source and the sum-frequency component generated nonlinearly by parametric arrays are attractive because of their high spatial resolution and accuracy.

Numerical models for the study of the nonlinear frequency mixing in two and three-dimensional resonant cavities filled with a bubbly liquid.

The objective of this work is to develop versatile numerical models to study the nonlinear distortion of ultrasounds and the generation of low-ultrasonic frequency signals by nonlinear frequency mixing in two and three-dimensional resonators filled with bubbly liquids. The interaction of the acoustic field and the bubble vibrations is modeled through a coupled differential system formed by the multi-dimensional wave equation and a Rayleigh-Plesset equation. The numerical models we develop are based on multi-dimensional finite-volume techniques and a time discretization carried out by finite differences.

Two-Dimensional Numerical Simulations of Ultrasound in Liquids with Gas Bubble Agglomerates: Examples of Bubbly-Liquid-Type Acoustic Metamaterials (BLAMMs).

This work deals with a theoretical analysis about the possibility of using linear and nonlinear acoustic properties to modify ultrasound by adding gas bubbles of determined sizes in a liquid. We use a two-dimensional numerical model to evaluate the effect that one and several monodisperse bubble populations confined in restricted areas of a liquid have on ultrasound by calculating their nonlinear interaction. The filtering of an input ultrasonic pulse performed by a net of bubbly-liquid cells is analyzed.

A numerical model for the study of the difference frequency generated from nonlinear mixing of standing ultrasonic waves in bubbly liquids.

The aim of this paper is the study of the behavior of nonlinear standing ultrasonic waves in bubbly liquids and the generation of the difference frequency by nonlinear mixing of several signals. To this end we present a new numerical model based on the finite-volume method and the finite-difference method. This model solves the differential system formed by the wave equation and a Rayleigh-Plesset equation coupling the acoustic pressure field with the bubble vibrations.

A two-dimensional nonlinear model for the generation of stable cavitation bubbles.

Bubbles appear by acoustic cavitation in a liquid when rarefaction pressures attain a specific threshold value in a liquid. Once they are created, the stable cavitation bubbles oscillate nonlinearly and affect the ultrasonic field. Here we present a model developed for the study of bubble generation in a liquid contained in a two-dimensional cavity in which a standing ultrasonic field is established.

Nonlinear frequency mixing in a resonant cavity: numerical simulations in a bubbly liquid.

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared.

An acoustic switch.

The benefits derived from the development of acoustic transistors which act as switches or amplifiers have been reported in the literature. Here we propose a model of acoustic switch. We theoretically demonstrate that the device works: the input signal is totally restored at the output when the switch is on whereas the output signal nulls when the switch is off.

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.

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.

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.

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.

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.

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.

Nonlinear ultrasonic propagation in bubbly liquids: a numerical model.

In this paper, we investigate the problem of ultrasonic propagation in liquids with bubbles. A new numerical algorithm is constructed to solve the acoustic field-bubbles vibration coupled system. For this purpose, a second-order equation written in a volume formulation is considered for bubbles vibration and coupled with the linear nondissipative wave equation, i.

Numerical analysis of strongly nonlinear extensional vibrations in elastic rods.

In the framework of transduction, nondestructive testing, and nonlinear acoustic characterization, this article presents the analysis of strongly nonlinear vibrations by means of an original numerical algorithm. In acoustic and transducer applications in extreme working conditions, such as the ones induced by the generation of high-power ultrasound, the analysis of nonlinear ultrasonic vibrations is fundamental. Also, the excitation and analysis of nonlinear vibrations is an emergent technique in nonlinear characterization for damage detection.

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.

Comparative study of the nonlinear behavior of fatigued and intact samples of metallic alloys.

A method and an experimental setup to study the nonlinear behavior of fatigued and intact metal samples under high-frequency stresses has been developed and tested. The method is based on the measurement of the vibration velocity of stepped bar samples flexurally and/or extensionally vibrating at resonance. The vibration velocity signal, picked up by a laser vibrometer, is automatically acquired and analyzed by classical fast Fourier transform (FFT) methods for different excitation levels.

Experimental and theoretical investigation of the mean acoustic pressure in the cavitation field.

The cavitation field radiated by a 20 kHz sonotrode-type transducer is experimentally and theoretically analyzed. Special interest is paid to the origin of the strong fluid streaming appearing in low frequency sonoreactors. A new experimental procedure is proposed to evaluate the mean acoustic pressure inside the fluid.