Acoustic resonance for contactless ultrasonic cavitation in alloy melts

Contactless ultrasound is a novel, easily implemented, technique for the Ultrasonic Treatment (UST) of liquid metals. Instead of using a vibrating sonotrode probe inside the melt, which leads to contamination, we consider a high AC frequency electromagnetic coil placed close to the metal free surface. The coil induces a rapidly changing Lorentz force, which in turn excites sound waves. To reach the necessary pressure amplitude for cavitation with the minimum electrical energy use, it was found necessary to achieve acoustic resonance in the liquid volume, by finely tuning the coil AC supply frequency. The appearance of cavitation was then detected experimentally with an externally placed ultrasonic microphone and confirmed by the reduction in grain size of the solidified metal. To predict the appearance of various resonant modes numerically, the exact dimensions of the melt volume, the holding crucible, surrounding structures and their sound properties are required. As cavitation progresses the speed of sound in the melt changes, which in practice means resonance becomes intermittent. Given the complexity of the situation, two competing numerical models are used to compute the soundfield. A high order time-domain method focusing on a particular forcing frequency and a Helmholtz frequency domain method scanning the full frequency range of the power supply. A good agreement is achieved between the two methods and experiments which means the optimal setup for the process can be predicted with some accuracy.     

Modeling acoustic cavitation with inhomogeneous polydisperse bubble population on a large scale

A model for acoustic cavitation flows able to depict large geometries and time scales is proposed. It is based on the Euler–Lagrange approach incorporating a novel Helmholtz solver with a non-linear acoustic attenuation model. The method is able to depict a polydisperse bubble population, which may vary locally. The model is verified and analyzed in a setup with a large sonotrode. Influences of the initial void fraction and the population type are studied. The results show that the velocity is strongly influenced by these parameters. Furthermore, the largest bubbles determine the highest pressure amplitude reached in the domain, which corresponds to the Blake threshold of these bubbles. Additionally, a validation is performed with a small sonotrode. The model reproduces most of the experimentally observed phenomena. In the experiments, neighboring bubbles are found which move in different directions depending on their size. The numerical results show that the responsible mechanism here is the reversal of the primary Bjerknes force at a certain pressure amplitude.     

Numerical modelling of ultrasonic waves in a bubbly Newtonian liquid using a high-order acoustic cavitation model

To address difficulties in treating large volumes of liquid metal with ultrasound, a fundamental study of acoustic cavitation in liquid aluminium, expressed in an experimentally validated numerical model, is presented in this paper. To improve the understanding of the cavitation process, a non-linear acoustic model is validated against reference water pressure measurements from acoustic waves produced by an immersed horn. A high-order method is used to discretize the wave equation in both space and time. These discretized equations are coupled to the Rayleigh-Plesset equation using two different time scales to couple the bubble and flow scales, resulting in a stable, fast, and reasonably accurate method for the prediction of acoustic pressures in cavitating liquids. This method is then applied to the context of treatment of liquid aluminium, where it predicts that the most intense cavitation activity is localised below the vibrating horn and estimates the acoustic decay below the sonotrode with reasonable qualitative agreement with experimental data.     

Characterization of acoustic streaming in water and aluminum melt during ultrasonic irradiation

It is well known that ultrasonic cavitation causes a steady flow termed acoustic streaming. In the present study, the velocity of acoustic streaming in water and molten aluminum is measured. The method is based on the measurement of oscillation frequency of Karman vortices around a cylinder immersed into liquid. For the case of acoustic streaming in molten metal, such measurements were performed for the first time. Four types of experiments were conducted in the present study: (1) Particle Image Velocimetry (PIV) measurement in a water bath to measure the acoustic streaming velocity visually, (2) frequency measurement of Karman vortices generated around a cylinder in water, and (3) in aluminum melt, and (4) cavitation intensity measurements in molten aluminum. Based on the measurement results (1) and (2), the Strouhal number for acoustic streaming was determined. Then, using the same Strouhal number and measuring oscillation frequency of Karman vortices in aluminum melt, the acoustic streaming velocity was measured. The velocity of acoustic streaming was found to be independent of amplitude of sonotrode tip oscillation both in water and aluminum melt. This can be explained by the effect of acoustic shielding and liquid density.     

Identification approach of acoustic cavitation via frequency spectrum of sound pressure wave signals in numerical simulation

In a sono-reactor, complex ultrasound pressure wave signal can be detected, containing multiple information related to acoustic cavitation. In this present study, acoustic cavitation in a cylinder is investigated numerically. Via Fast Fourier Transfer (FFT), the sound pressure signals from sonotrode emitting surface are separated into harmonics, sub/ultra-harmonics and cavitation white noise: (1) the appearance of harmonics proved the non-linear propagation of ultrasound, (2) at the vibratory amplitude from 5∼20μm, only harmonics exists in the frequency spectra, corresponding to expansion and compression of non-condensable gas (NCG), (3) at the vibratory amplitude range of 30∼50μm, the occurrence of sub/ultra-harmonics demonstrated gaseous cavitation occurred, and (4) at the vibratory amplitude higher than 55μm, cavitation white noise arose, pointing out the initiation of vaporous cavitation. Based on the combination of frequency spectra and cavitation zones distribution, the acoustic cavitation state in water liquid is determined.     

A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being estimated directly from the fully nonlinear radial dynamics. The use of this model in a mono-dimensional configuration has shown that the attenuation near the vibrating emitter was much higher than predictions obtained from linear theory, and that this strong attenuation creates a large traveling wave contribution, even for closed domain where standing waves are normally expected. In this paper, we show that, owing to the appearance of traveling waves, the primary Bjerknes force near the emitter becomes very large and tends to expel the bubbles up to a stagnation point. Two-dimensional axi-symmetric computations of the acoustic field created by a large area immersed sonotrode are also performed, and the paths of the bubbles in the resulting Bjerknes force field are sketched. Cone bubble structures are recovered and compare reasonably well to reported experimental results. The underlying mechanisms yielding such structures is examined, and it is found that the conical structure is generic and results from the appearance a sound velocity gradient along the transducer area. Finally, a more complex system, similar to an ultrasonic bath, in which the sound field results from the flexural vibrations of a thin plate, is also simulated. The calculated bubble paths reveal the appearance of other commonly observed structures in such configurations, such as streamers and flare structures.     

Ultrasonic cavitation at liquid/solid interface in a thin Ga–In liquid layer with free surface

Cavitation in thin layer of liquid metal has potential applications in chemical reaction, soldering, extraction, and therapeutic equipment. In this work, the cavitation characteristics and acoustic pressure of a thin liquid Ga–In alloy were studied by high speed photography, numerical simulation, and bubble dynamics calculation. A self-made ultrasonic system with a TC4 sonotrode, was operated at a frequency of 20 kHz and a max output power of 1000 W during the cavitation recording experiment. The pressure field characteristic inside the thin liquid layer and its influence on the intensity, types, dimensions, and life cycles of cavitation bubbles and on the cavitation evolution process against experimental parameters were systematically studied. The results showed that acoustic pressure inside the thin liquid layer presented alternating positive and negative characteristics within 1 acoustic period (T). Cavitation bubbles nucleated and grew during the negative-pressure stage and shrank and collapsed during the positive-pressure stage. A high bubble growth speed of 16.8 m/s was obtained and evidenced by bubble dynamics calculation. The maximum absolute pressure was obtained at the bottom of the thin liquid layer and resulted in the strongest cavitation. Cavitation was divided into violent and weak stages. The violent cavitation stage lasted several hundreds of acoustic periods and had higher bubble intensity than the weak cavitation stage. Cavitation cloud preferentially appeared during the violent cavitation stage and had a life of several acoustic periods. Tiny cavitation bubbles with life cycles shorter than 1 T dominated the cavitation field. High cavitation intensities were observed at high ultrasonication power and when Q235B alloy was used because such conditions lead to high amplitudes on the substrate and further high acoustic pressure inside the liquid.     

Enhancement of oscillation amplitude of cavitation bubble due to acoustic wake effect in multibubble environment

Acoustic cavitation occurs in ultrasonic treatment causing various phenomena such as chemical synthesis, chemical decomposition, and emulsification. Nonlinear oscillations of cavitation bubbles are assumed to be responsible for these phenomena, and the neighboring bubbles may interact each other. In the present study, we numerically investigated the dynamic behavior of cavitation bubbles in multi-bubble systems. The results reveal that the oscillation amplitude of a cavitation bubble surrounded by other bubbles in a multi-bubble system becomes larger compared with that in the single-bubble case. It is found that this is caused by an acoustic wake effect, which reduces the pressure near a bubble surrounded by other bubbles and increases the time delay between the bubble contraction/expansion cycles and sound pressure oscillations. A new parameter, called “cover ratio” is introduced to quantitatively evaluate the variation in the bubble oscillation amplitude, the time delay, and the maximum bubble radius.     

Measuring derived acoustic power of an ultrasound surgical device in the linear and nonlinear operating modes

Objective and motivationThe method for measuring derived acoustic power of an ultrasound point source in the form of a sonotrode tip has been considered in the free acoustic field, according to the IEC 61847 standard. The main objective of this work is measuring averaged pressure magnitude spatial distribution of an sonotrode tip in the free acoustic field conditions at different electrical excitation levels and calculation of the derived acoustic power at excitation frequency (f₀ ≈ 25 kHz). Finding the derived acoustic power of an ultrasonic surgical device in the strong cavitation regime of working, even in the considered laboratory conditions (anechoic pool), will enable better understanding of the biological effects on the tissue produced during operation with the considered device.Experimental methodThe pressure magnitude spatial distribution is measured using B&;K 8103 hydrophone connected with a B&;K 2626 conditioning amplifier, digital storage oscilloscope LeCroy Waverunner 474, where pressure waveforms in the field points are recorded. Using MATLAB with DSP processing toolbox, averaged power spectrum density of recorded pressure signals in different field positions is calculated. The measured pressure magnitude spatial distributions are fitted with the appropriate theoretical models.Theoretical approachesIn the linear operating mode, using the acoustic reciprocity principle, the sonotrode tip is theoretically described as radially oscillating sphere (ROS) and transversely oscillating sphere (TOS) in the vicinity of pressure release boundary. The measured pressure magnitude spatial distribution is fitted with theoretical curves, describing the pressure field of the considered theoretical models. The velocity and displacement magnitudes with derived acoustic power of equivalent theoretical sources are found, and the electroacoustic efficiency factor is calculated. When the transmitter is excited at higher electrical power levels, the displacement magnitude of sonotrode tip is increased, and nonlinear behaviour in loading medium appears, with strong cavitation activity produced hydrodynamically. The presence of harmonics, subharmonics and ultraharmonics as a consequence of stable cavitation is evident in the averaged power spectral density. The cavitation noise with continuous frequency components is present as a consequence of transient cavitation. The averaged pressure magnitude at the frequency components of interest (discrete and continous) in the field points is found by calculating average power spectral density of the recorded pressure waveform signal using the welch method. The frequency band of interest where average power spectral density is calculated is in the range from 15 Hz up to 120 kHz due to measurement system restrictions. The novelty in the approach is the application of the acoustic reciprocity principle on the nonlinear system (sonotrode tip and bubble cloud) to find neccessary acoustic power of the equivalent acoustic source to produce the measured pressure magnitude in the field points at the frequency components of interest.ResultsIn the nonlinear operating mode, the ROS model for the considered sonotrode tip is chosen due to the better agreement between measurement results and theoretical considerations. At higher excitation levels, it is shown that the averaged pressure magnitude spatial distribution of discrete frequency components, produced due to stable cavitation, can be fitted in the far field with the inverse distance law. The reduced electroacoustic efficiency factor, calculated at excitation frequency component as ratio of derived acoustic power with applied electrical power, is reduced from 40% in the linear to 3% in the strong nonlinear operating mode. The derived acoustic power at other frequency components (subharmonic, harmonic and ultraharmonic) is negligible in comparison with the derived acoustic power at excitation frequency.Discussion and conclusionsThe sonotrode tip and loading medium are shown in the strong cavitation regime as the coupled nonlinear dynamical system radiating acoustic power at frequency components appearing in the spectrum. The bubble cloud in the strong nonlinear operating mode decreases the derived acoustic power significantly at the excitation frequency.     

声场中双空化泡的运动特性

空化泡的运动特性是声场作用下的动力学行为,受空化泡初始半径,声压幅值,驱动声压频率,液体特性等众多因素的影响,是个复杂工程。本文从双空化泡运动方程出发,考虑到液体粘滞系数、空化泡辐射阻尼项的影响,研究了不同初始半径、驱动声压频率、驱动声压幅值、液体粘滞系数下空化泡泡壁的运动情况,研究结果表明不同初始半径、外界驱动声压频率、驱动声压幅值、液体粘滞系数均会对空化泡的膨胀比和空化泡的溃灭时间有一定影响。     

Effect of dissolved gases in water on acoustic cavitation and bubble growth rate in 0.83 MHz megasonic of interest to wafer cleaning

Changes in the cavitation intensity of gases dissolved in water, including H₂, N₂, and Ar, have been established in studies of acoustic bubble growth rates under ultrasonic fields. Variations in the acoustic properties of dissolved gases in water affect the cavitation intensity at a high frequency (0.83 MHz) due to changes in the rectified diffusion and bubble coalescence rate. It has been proposed that acoustic bubble growth rates rapidly increase when water contains a gas, such as hydrogen faster single bubble growth due to rectified diffusion, and a higher rate of coalescence under Bjerknes forces. The change of acoustic bubble growth rate in rectified diffusion has an effect on the damping constant and diffusivity of gas at the acoustic bubble and liquid interface. It has been suggested that the coalescence reaction of bubbles under Bjerknes forces is a reaction determined by the compressibility and density of dissolved gas in water associated with sound velocity and density in acoustic bubbles. High acoustic bubble growth rates also contribute to enhanced cavitation effects in terms of dissolved gas in water. On the other hand, when Ar gas dissolves into water under ultrasound field, cavitation behavior was reduced remarkably due to its lower acoustic bubble growth rate. It is shown that change of cavitation intensity in various dissolved gases were verified through cleaning experiments in the single type of cleaning tool such as particle removal and pattern damage based on numerically calculated acoustic bubble growth rates.     

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.     

Hydrodynamic cavitation for sonochemical effects

A comparative study of hydrodynamic and acoustic cavitation has been made on the basis of numerical solutions of the Rayleigh-Plesset equation. The bubble/cavity behaviour has been studied under both acoustic and hydrodynamic cavitation conditions. The effect of varying pressure fields on the collapse of the cavity (sinusoidal for acoustic and linear for hydrodynamic) and also on the latter's dynamic behaviour has been studied. The variations of parameters such as initial cavity size, intensity of the acoustic field and irradiation frequency in the case of acoustic cavitation, and initial cavity size, final recovery pressure and time for pressure recovery in the case of hydrodynamic cavitation, have been found to have significant effects on cavity/bubble dynamics. The simulations reveal that the bubble/cavity collapsing behaviour in the case of hydrodynamic cavitation is accompanied by a large number of pressure pulses of relatively smaller magnitude, compared with just one or two pulses under acoustic cavitation. It has been shown that hydrodynamic cavitation offers greater control over operating parameters and the resultant cavitation intensity. Finally, a brief summary of the experimental results on the oxidation of aqueous KI solution with a hydrodynamic cavitation set-up is given which supports the conclusion of this numerical study. The methodology presented allows one to manipulate and optimise of specific process, either physical or chemical.     

声驻波场中空化泡的动力学特性

以水为工作介质, 考虑了液体的可压缩性, 研究了驻波声场中空化泡的运动特性, 模拟了驻波场中各位置处空化泡的运动状态以及相关参数对各位置处空化泡在主Bjerknes力作用下运动方向的影响. 结果表明: 驻波声场中, 空化泡的运动状态分为三个区域, 即在声压波腹附近空化泡做稳态空化, 在偏离波腹处空化泡做瞬态空化, 在声压波节附近, 空化泡在主Bjerknes 力作用下, 一直向声压波节处移动, 显示不发生空化现象; 驻波场中声压幅值增加有利于空化的发生, 但声压幅值增加到一定上限时, 压力波腹区域将排斥空化泡, 并驱赶空化泡向压力波节移动, 不利于空化现象的发生; 当声频率小于初始空化泡的共振频率时, 声频率越高, 由于主Bjerknes 力的作用将有更多的空化泡向声压波节移动, 不利于空化的发生, 尤其是驻波场液面的高度不应是声波波长的1/4; 当声频率一定时, 空化泡初始半径越大越有利于空化现象的发生, 但当空化泡的初始半径超过声频率的共振半径时, 由于主Bjerknes力的作用将有更多的空化泡向声压波节移动, 不利于空化的发生.     

Sound field measurement in a double layer cavitation cluster by rugged miniature needle hydrophones

During multi-bubble cavitation the bubbles tend to organize themselves into clusters and thus the understanding of properties and dynamics of clustering is essential for controlling technical applications of cavitation. Sound field measurements are a potential technique to provide valuable experimental information about the status of cavitation clouds. Using purpose-made, rugged, wide band, and small-sized needle hydrophones, sound field measurements in bubble clusters were performed and time-dependent sound pressure waveforms were acquired and analyzed in the frequency domain up to 20 MHz. The cavitation clusters were synchronously observed by an electron multiplying charge-coupled device (EMCCD) camera and the relation between the sound field measurements and cluster behaviour was investigated. Depending on the driving power, three ranges could be identified and characteristic properties were assigned. At low power settings no transient and no or very low stable cavitation activity can be observed. The medium range is characterized by strong pressure peaks and various bubble cluster forms. At high power a stable double layer was observed which grew with further increasing power and became quite dynamic. The sound field was irregular and the fundamental at driving frequency decreased. Between the bubble clouds completely different sound field properties were found in comparison to those in the cloud where the cavitation activity is high. In between the sound field pressure amplitude was quite small and no collapses were detected.     

Numerical prediction of tip vortex cavitation behavior and noise considering nuclei size and distribution

The tip vortex cavitation behavior and sound generation were numerically analyzed. A numerical scheme combining Eulerian flow field computation and Lagrangian particle trace approach was applied to simulate tip vortex cavitation. Flow field was computed by using hybrid method which combines Reynolds-Averaged Navier-Stokes solver with Dissipation Vortex Model. The trajectory and behavior of each cavitation bubble were computed by Newton’s second law and Rayleigh-Plesset equation, respectively. According to nuclei population data, the cavitation nuclei were distributed and convected into the tip vortex flow. Calculated volume of the cavitation bubble and the trajectory were used as the input of cavitation bubble noise analysis. The relationship of cavitation inception, sound pressure level, and cavitation nuclei size was studied at several cavitation numbers. It was found that cavitation inception of smaller nuclei is more sensitive to the change of cavitation number and cavitation noise due to the cavitated smallest nuclei has the most influence on overall tip vortex cavitation noise.     

FEM simulation of a sono-reactor accounting for vibrations of the boundaries

The chemical effects of acoustic cavitation are obtained in sono-reactors built-up from a vessel and an ultrasonic source. In this paper, simulations of an existing sono-reactor are carried out, using a linear acoustics model, accounting for the vibrations of the solid walls. The available frequency range of the generator (19-21 kHz) is systematically scanned. Global quantities are plotted as a function of frequency in order to obtain response curves, exhibiting several resonance peaks. In absence of the precise knowledge of the bubbles size distribution and spatial location, the attenuation coefficient of the wave is taken as a variable, but spatially uniform parameter, and its influence is studied. The concepts of acoustic energy, intensity, active power, and source impedance are recalled, along with the general balance equation for acoustic energy, which is used as a convergence check of the simulations. It is shown that the interface between the liquid and the solid walls cannot be correctly represented by the simple approximations of either infinitely soft, or infinitely hard boundaries. Moreover, the liquid-solid coupling allows the cooling jacket to receive a noticeable part of the input power, although it is not in direct contact with the sonotrode. It may therefore undergo cavitation and this feature opens the perspective to design sono-reactors which avoid direct contact between the working liquid and the sonotrode. Besides, the possibility to shift the main pressure antinode far from the sonotrode area by exciting a resonance of the system is examined.     

声空化气泡成长及破裂研究

本文对液体内的声空化气泡的成长与破裂过程进行数值计算,得到各种情况下气泡壁的运动情况.通过对不同初始半径、不同频率下声空化气泡运动的计算,得到空化气泡半径小于共振半径,可以增强空化效果,而单一的增强声场的频率并不一定能加强声空化效果,为增强空化效果提供理论依据.研究各种信号作用下声空化气泡成长情况,明确方波信号激励下的...     

声场作用下两空化泡相互作用的研究

建立了声场作用下两空化泡泡壁的运动方程,得出了双空化泡的共振频率,振动半径及空化噪声声压．由频率方程,振动半径和声压方程可以看出两气泡的运动情况与单气泡的运动情况有着明显的不同．共振频率,共振振幅及声压与两气泡之间的间距有关．在一定的简化条件下,运用MATLAB语言对共振频率,共振振幅及空化噪声声压进行了数值求解,发现共振频率和共振振幅随空泡间距的增大而增大,空化噪声声压随距离增大先增大后减小． 关键词： 超声 空化 频率 声压