Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation

The use of a top-mounted electromagnetic induction coil has been demonstrated as a contactless alternative to traditional ultrasonic treatment (UST) techniques that use an immersed mechanical sonotrode for the treatment of metals in the liquid state. This method offers similar benefits to existing UST approaches, including degassing, grain refinement, and dispersion of nanoparticles, while also preventing contact contamination due to erosion of the sonotrode. Contactless treatment potentially extends UST to high temperature or reactive melts. Generally, the method relies on acoustic resonance to reach pressure levels suitable for inertial cavitation and as a result the active cavitation volume tends to lie deep in the melt rather than in the small volume surrounding the immersed sonotrode probe. Consequently, (i) with suitable tuning of the coil supply frequency for resonance, the treatment volume can be made arbitrarily large, (ii) the problem of shielding and pressure wave attenuation suffered by the immersed sonotrode is avoided. However, relying on acoustic resonance presents problems: (i) the emergence of bubbles alters the speed of sound, resonance is momentarily lost, and cavitation becomes intermittent, (ii) as sound waves travel through and reflect on all the materials surrounding the melt, the sound characteristics of the crucible and supporting structures need to be carefully considered. The physics of cavitation coupled with this intermittent behaviour poses a challenge to sonotrode modelling orthodoxy, a problem we are trying to address in this publication. Two alternative approaches will be discussed, one of which is in the time domain and one in the frequency domain, which couple the solution of a bubble dynamics solver with that of an acoustics solver, to give an accurate prediction of the acoustic pressure generated by the induction coil. The time domain solver uses a novel algorithm to improve simulation time, by detecting an imminent bubble collapse and prescribing its subsequent behaviour, rather than directly solving a region that would normally require extremely small time steps. This way, it is shown to predict intermittent cavitation. The frequency domain solver for the first time couples the nonlinear Helmholtz model used for studying cavitation, with a background source term for the contribution of Lorentz forces. It predicts comparable RMS pressures to the time domain solver, but not the intermittent behaviour due to the underlying harmonic assumption. As further validation, the frequency domain method is also used to compare the generated acoustic pressure with that of traditional UST using a mechanical sonotrode.     

高能超声制备碳纳米管增强AZ91D复合材料的声场模拟

建立了高能超声制备碳纳米管增强AZ91D复合材料的声场计算模型, 并采用有限元方法计算了20 kHz超声直接作用下AZ91D熔体的声场分布, 熔体声场呈辐射状分布, 距离声源越远, 声压幅值越低. 采用超声作用下单一气泡变化模型描述超声作用下AZ91D 熔体中的空化效应, 通过对Rayleigh-Plesset方程的求解, 得到了不同声压作用下气泡的变化规律, 获得了声压幅值与熔体空化效应的关系, 声压幅值越大, 气泡溃灭半径阈值越小, 熔体发生空化效应越容易. 计算了固定坩埚尺寸、不同超声探头没入熔体深度情况下的声场, 得到了超声探头最优没入深度为30 mm左右. 将声场计算结果以及AZ91D熔体中空化效应的发生规律进行综合分析, 得到了超声功率对有效空化区域的影响规律, 超声功率较大时, 有效空化区域体积随超声功率近似成线性增大. 最后, 通过甘油水溶液超声处理实验, 验证了模拟计算的准确性.     

Sonoluminescence

Sonoluminescence (SL) is the name given to the light emitted when a liquid is cavitated in a particular (rather violent) manner. The appropriate cavitation conditions can be realized by using high intensity ultrasound, a spark discharge, a laser pulse, or by flowing the liquid through a Venturi tube. SL occurs in a wide variety of liquids, its intensity and spectrum depending on the nature of the solvent and the solute (including dissolved gas). The intensity, but apparently not the spectrum, also depends on the frequency of the sound and on the temperature and hydrostatic pressure of the liquid. In a standing wave sound field the SL originates from bubbles attracted to the pressure antinodes and has its maximum intensity when the bubble volume is a minimum. The phase of the sound cycle at which this occurs depends on the amplitude and frequency of the sound field. Spectral measurements show that SL originates mainly from the recombination of free radicals created within the high temperature and high pressure environment of a bubble undergoing an adiabatic compression, as may happen either during transient cavitation or during highly non-linear, but stable, cavitation. In discussing these, and other, attributes of SL this review emphasizes developments over the past 20 years. Because of the importance of the dynamical theory of bubbles to a full understanding of SL, it includes an account of bubble dynamics. In addition, it describes the various experimental techniques employed in the creation and analysis of SL. Although the review lays particular stress on the SL produced via acoustic cavitation, it also examines the characteristics of the SL produced using other methods of cavitation.     

A high-temperature acoustic field measurement and analysis system for determining cavitation intensity in ultrasonically solidified metallic alloys

A high-temperature acoustic field measurement and analysis system (HTAFS) was self-designed and developed to achieve real-time acoustic field analysis and quantitative cavitation characterization within high-temperature liquids. The acoustic signal was acquired by a high-temperature resistant waveguide and calibrated by separate compensation of line and continuous spectra to eliminate frequency offsets. Moreover, a new method was proposed to derive from the continuous-spectrum sound intensity and line-spectrum sound intensity in the frequency band above 1.5 times the fundamental frequency to characterize the intensity of transient cavitation and stable cavitation. The acoustic field characteristics within solidifying liquid Al-7 %Si alloy were successfully determined by this system. With the increase of ultrasound amplitude, the acoustic pressure in the alloy melt increased to be stable, the transient cavitation intensity first rose and then declined, and the stable cavitation intensity remained unchanged. Combined with the structural evolution of the primary α(Al) phase, the transient cavitation intensity was determined to be the dominant factor for the ultrasound-induced grain refinement effect.     

Properties of sound attenuation around a two-dimensional underwater vehicle with a large cavitation number

Due to the high speed of underwater vehicles,cavitation is generated inevitably along with the sound attenuation when the sound signal traverses through the cavity region around the underwater vehicle.The linear wave propagation is studied to obtain the influence of bubbly liquid on the acoustic wave propagation in the cavity region.The sound attenuation coefficient and the sound speed formula of the bubbly liquid are presented.Based on the sound attenuation coefficients with various vapor volume fractions,the attenuation of sound intensity is calculated under large cavitation number conditions.The result shows that the sound intensity attenuation is fairly small in a certain condition.Consequently,the intensity attenuation can be neglected in engineering.     

Measurement of acoustic power in studying cavitation processes

A comparative calorimetric method for measuring the acoustic power generated by a sound source under cavitation conditions and the power absorbed by a liquid with bubbles is developed. The conditions under which the whole of the generated power is absorbed by the liquid with bubbles are determined experimentally. An instrument for power calibration of sound sources operating under cavitation conditions is designed. The instrument is found to provide a high measurement accuracy (3% or better). The requirements on the dimensions of the vessel and on the volume of the liquid in which the sound source operates are formulated to make the power generated under cavitation conditions independent of these parameters. For the first time, it is shown experimentally (by the example of the reaction of nitric oxide formation under the action of sound) that, if these conditions are satisfied and the sound intensity exceeds the threshold intensity, the rate of a number of sonochemical reactions is proportional to the sound intensity in the range from 1.7 to at least 47 W/cm². It is shown that the dependence of the rate of cavitation processes on the sound intensity with a maximum at 8.6 W/cm² and a sharp decrease in the rate with a further intensity increase is determined by the fact that the measured quantity was the electric power at the transducer rather than the acoustic one.     

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。     

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 new type of high power composite ultrasonic transducer

A new type of high power composite ultrasonic transducer was proposed and studied. The composite transducer consists of a sandwich longitudinal piezoelectric transducer, an isotropic metal hollow cylinder with large radial dimension, and the front and back metal radiation mass. By means of its special structure and Poisson’s effect, the composite transducer can produce vibrations both in its longitudinal and radial directions, and therefore, it can radiate sound waves in three-dimensional space. The electro-mechanical equivalent circuit of the composite transducer was derived and the resonance frequency equation was obtained analytically. Numerical methods were used to simulate the vibration of the composite transducer, and the vibrational displacement distribution, the resonance frequency and the radiation sound field are given. Some composite transducers are designed and manufactured; their resonance frequencies and the radiation acoustic field are measured and compared with the analytical and numerical results. It can be seen that the measured frequencies and acoustic field contour are in good agreement with the analytical and numerical results. It is expected that this kind of composite ultrasonic transducer can be used in more and more power ultrasonic applications, such as ultrasonic cleaning, ultrasonic extraction, ultrasonic sonochemistry and other ultrasonic liquid processing, where high ultrasonic power and large ultrasonic processing space are needed increasingly.     

Unilateral MRI using a rastered projection

Unilateral magnetic resonance techniques, where magnet and radio frequency (RF) coil are placed on one side of the sample, can provide valuable information about a sample which otherwise cannot be accommodated in conventional high spectral resolution magnetic resonance systems. A unilateral magnetic resonance imaging approach utilizing the stray field from a disc magnet and a butterfly geometry RF coil is described. The coil excites spins in a volume centered around an arc through the sample. Translating the RF coil relative to the magnet and recording the signal at each translational location creates a projection of the signal in a tomographic slice through the sample. Rotating the RF coil relative to the sample and repeating the translation creates projections through the sample at different angles. Backprojecting this information yields an image. A proof of concept device operating on this principle at 12.4 MHz was constructed and characterized. Projections through three phantoms are presented with a 1.2-4 cm field of view, thickness of 102 microm, and at a distance of 3mm from the RF coil and 14 mm from the magnet. The edge spread function (ESF) was measured resulting in a 4mm full width at half maximum (FWHM) line spread function (LSF) estimation using a Gaussian model. An example of one reconstructed image is presented.     

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.     

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     

Acoustic noise simulation and measurement of a gradient insert in a 4 T MRI

High speed switching of current in gradient coils within high magnetic field strength magnetic resonance imaging (MRI) scanners results in high acoustic sound pressure levels (SPL) in and around these machines. Many studies have already been conducted to characterize the sound field in and around MRIs and various methods have been investigated to attenuate the noise generated. In the work presented here a computational vibro-acoustic model was developed based on an iteratively modified and validated finite element (FE) model to characterize the acoustic noise properties of the gradient coil. The simulation results from the computational model were verified through experimental noise measurement for the gradient coil insert in a 4 T MRI scanner by using swept sinusoidal time waveform inputs. Comparisons show that the computational model predicts the noise characteristic properties extremely accurately. There are three dominant frequency bands where the SPL is much higher than those at other frequencies. The SPL in the horizontal direction is much higher than that in the vertical direction due to the excitation to the horizontally placed X coil. The SPL to the inner surface of the coil is higher than far from the inner surface, which proves that the acoustic noise is radiated from the inner surface and primarily caused by the normal vibration of the inner surface. Further verification was conducted by using two types of trapezoidal sequence inputs usually used, which is to simulate real scanning sequences for small animals. Again the accuracy of the developed model is verified. The validated acoustic computational model could be used as an effective method to predict the noise that would be produced by a coil in the design stage. Modification of the structural design or the excitation pulse could be performed to reduce the acoustic noise when the gradient coil is in scanning.     

声波在含气泡液体中的线性传播

为了探讨含气泡液体对声波传播的影响, 研究了声波在含气泡液体中的线性传播. 在建立含气泡液体的声学模型时引入气泡含量的影响,建立气泡模型时引用 Keller的气泡振动模型并同时考虑气泡间的声相互作用,得到了经过修正的气泡振动方程. 通过对含气泡液体的声传播方程和气泡振动方程联立并线性化求解,在满足 (ω R₀)/c << 1 的前提下,得到了描述含气泡液体对声波传播的衰减系数和传播速度. 通过数值分析发现,在驱动声场频率一定的情况下,气泡含量的增加及气泡的变小均会导致衰减系数增加和声速减小;气泡的体积分数和大小一定时, 驱动声场频率在远小于气泡谐振频率的情况下,声速会随驱动频率的增加而减小; 气泡间的声相互作用对声波传播速度及含气泡液体衰减系数的影响不明显.最终认为气泡的大小、 数量和驱动声场频率是影响声波在含气泡液体中线性传播的主要因素. 关键词： 含气泡液体 线性声波 声衰减系数 声速     

液体材料超声处理过程中声场和流场的分布规律研究

针对合金熔体等液体材料的超声处理过程,选取水作为透明模型材料,采用数值模拟计算和示踪粒子实验方法,研究了20和490 kHz两种频率超声作用下水中的声场和流场分布.结果表明,增大变幅杆半径能够提高水中声压水平,扩大空化效应的发生区域.当超声频率为20 kHz时,水中声压最大值出现在超声变幅杆下端面处,且声压沿传播距离的增大而显著减小.如果超声频率增加至490 kHz,水中的声压级相比于20 kHz时明显提高,且声压沿着超声传播方向呈现出周期性振荡特征.两种频率超声作用下水中的流场呈现相似的分布特征,且平均流速均随着变幅杆半径增大表现出先升高后降低的趋势.变幅杆半径相同时,20 kHz频率超声作用下水中的平均流速高于490 kHz频率超声.采用示踪粒子图像测速技术实时观察和测定了水中的流速分布,发现其与计算结果基本一致.     

超声珩磨区实际气体的单空泡动力学分析

为进一步揭示功率超声振动的珩磨机理,以珩磨液为工作介质,研究了功率超声珩磨环境中实际气体的单空泡动力学特性。基于Rayleigh-Plesset方程,应用实际气体绝热方程和范德瓦尔斯方程对其进行了修正,建立了功率超声珩磨环境中实际气体的单空泡动力学方程以及实际气体单空泡共振频率方程。并运用4~5阶RungeKutta法模拟了不同超声条件(声压幅值、空泡初始半径、振动频率)对泡壁的运动以及运动速度的影响。结果表明:较高的声压幅值,空泡理论共振半径R'0与初始半径R0的比值为102数量级以及较低的超声频率有利于超声珩磨磨削区空化效应的发生。     

Critical current measurement in superconducting rings using an automatic inductive technique

A measurement technique was developed to identify the critical current of superconducting rings. It is based on the detection of the voltage on a secondary coil when the current induced in the superconductor by a primary one go beyond to the critical value. The technique uses a DC power supply to control the AC current circulating by the primary circuit. Such circuit mainly consists on an AC power supply which gives a constant AC voltage, a primary inducting coil and a control coil with iron core. The AC current circulating by this circuit is modified with the change in the impedance of the control coil due to the fact of the DC current supplied by the power supply in parallel with it.