Combining COMSOL modeling with acoustic pressure maps to design sono-reactors

Scaled-up and economically viable sonochemical systems are critical for increased use of ultrasound in environmental and chemical processing applications. In this study, computational simulations and acoustic pressure maps were used to design a larger-scale sono-reactor containing a multi-stepped ultrasonic horn. Simulations in COMSOL Multiphysics showed ultrasonic waves emitted from the horn neck and tip, generating multiple regions of high acoustic pressure. The volume of these regions surrounding the horn neck were larger compared with those below the horn tip. The simulated acoustic field was verified by acoustic pressure contour maps generated from hydrophone measurements in a plexiglass box filled with water. These acoustic pressure contour maps revealed an asymmetric and discrete distribution of acoustic pressure due to acoustic cavitation, wave interaction, and water movement by ultrasonic irradiation. The acoustic pressure contour maps were consistent with simulation results in terms of the effective scale of cavitation zones (∼10 cm and <5 cm above and below horn tip, respectively). With the mapped acoustic field and identified cavitation location, a cylindrically-shaped sono-reactor with a conical bottom was designed to evaluate the treatment capacity (∼5 L) for the multi-stepped horn using COMSOL simulations. In this study, verification of simulation results with experiments demonstrates that coupling of COMSOL simulations with hydrophone measurements is a simple, effective and reliable scientific method to evaluate reactor designs of ultrasonic systems.     

Modeling cavitation in a rapidly changing pressure field – Application to a small ultrasonic horn

Ultrasonic horn transducers are frequently used in applications of acoustic cavitation in liquids. It has been observed that if the horn tip is sufficiently small and driven at high amplitude, cavitation is very strong, and the tip can be covered entirely by the gas/vapor phase for longer time intervals. A peculiar dynamics of the attached cavity can emerge with expansion and collapse at a self-generated frequency in the subharmonic range, i.e. below the acoustic driving frequency. The term “acoustic supercavitation” was proposed for this type of cavitation Žnidarčič et al. (2014) [1].We tested several established hydrodynamic cavitation models on this problem, but none of them was able to correctly predict the flow features. As a specific characteristic of such acoustic cavitation problems lies in the rapidly changing driving pressures, we present an improved approach to cavitation modeling, which does not neglect the second derivatives in the Rayleigh–Plesset equation. Comparison with measurements of acoustic supercavitation at an ultrasonic horn of 20 kHz frequency revealed a good agreement in terms of cavity dynamics, cavity volume and emitted pressure pulsations.The newly developed cavitation model is particularly suited for simulation of cavitating flow in highly fluctuating driving pressure fields.     

Characterization of cavitation under ultrasonic horn tip – Proposition of an acoustic cavitation parameter

Acoustic cavitation, generated by a piezo-driven transducer, is a commonly used technique in a variety of processes, from homogenization, emulsification, and intensification of chemical reactions to surface cleaning and wastewater treatment. An ultrasonic horn, the most commonly used acoustic cavitation device, creates unique cavitation conditions under the horn tip that depend on various parameters such as the tip diameter, the driving frequency of the horn, its amplitude, and fluid properties. Unlike for hydrodynamic cavitation, the scaling laws for acoustic cavitation are poorly understood. Empirical relationships between cavitation dynamics, ultrasonic horn operating conditions, and fluid properties were found through systematic characterization of cavitation under the tip. Experiments were conducted in distilled water with various sodium chloride salt concentrations under different horn amplitudes, tip geometries, and ambient pressures. Cavitation characteristics were monitored by high-speed (200,000 fps) imaging, and numerous relations were found between operating conditions and cavitation dynamics. The compared results are discussed along with a proposal of a novel acoustic cavitation parameter and its relationship to the size of the cavitation cloud under the horn tip. Similar to the classical hydrodynamic cavitation number, the authors propose for the first time an acoustic cavitation parameter based on experimental results.     

Realization of cavitation fields based on the acoustic resonance modes in an immersion-type sonochemical reactor

Different modes of cavitation zones in an immersion-type sonochemical reactor have been realized based on the concept of acoustic resonance fields. The reactor contains three main components, namely a Langevin-type piezoelectric transducer (20 kHz), a metal horn, and a circular cylindrical sonicated cell filled with tap water. In order to diminish the generation of cavitation bubbles near the horn-tip, an enlarged cone-shaped horn is designed to reduce the ultrasonic intensity at the irradiating surface and to get better distribution of energy in the sonicated cell. It is demonstrated both numerically and experimentally that the cell geometry and the horn position have prominent effects on the pressure distribution of the ultrasound in the cell. With appropriate choices of these parameters, the whole reactor works at a resonant state. Several acoustic resonance modes observed in the simulation are realized experimentally to generate a large volume of cavitation zones using a very low ultrasonic power.     

PIV quantification of the flow induced by an ultrasonic horn and numerical modeling of the flow and related processing times

The flow in a confined container induced by an ultrasonic horn is measured by Particle Image Velocimetry (PIV). This flow is caused by acoustic streaming and highly influenced by the presence of cavitation. The jet-like experimentally observed flow is compared with the available theoretical solution for a turbulent free round jet. The similarity between both flows enables a simplified numerical model to be made, whilst the phenomenon is very difficult to simulate otherwise. The numerical model requires only two parameters, i.e. the flow momentum and turbulent kinetic energy at the position of the horn tip. The simulated flow is used as a basis for the calculation of the time required for the entire liquid volume to pass through the active cavitation region.     

Designing and characterizing a multi-stepped ultrasonic horn for enhanced sonochemical performance

The commonly used ultrasonic horn generates localized cavitation below its converging tip resulting in a dense bubble cloud near the tip and limiting diffusion of reactive components into the bubble cloud or reactive radicals out of the bubble cloud. To improve contact between reactive components, a novel ultrasonic horn design was developed based on the principles of the dynamic wave equation. The horn, driven at 20 kHz, has a multi-stepped design with a cone-shaped tip increasing the energy-emitting surface areas and creating multiple reactive zones. Through different physical and chemical experiments, performance of the horn was compared to a typical horn driven at 20 kHz. Hydrophone measurements showed high acoustic pressure areas around the horn neck and tip. Sonochemiluminescence experiments verified multiple cavitation zones consistent with hydrophone readings. Calorimetry and dosimetry results demonstrated a higher energy efficiency (31.3%) and a larger hydroxyl radical formation rate constant (0.36 μM min⁻¹) compared to typical horns. In addition, the new horn degraded naphthalene faster than the typical horn tested. The characterization results demonstrate that the multi-stepped horn configuration has the potential to improve the performance of ultrasound as an advanced oxidation technology by increasing the cavitation zone in the solution.     

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.     

A computational modeling approach of the jet-like acoustic streaming and heat generation induced by low frequency high power ultrasonic horn reactors

High power ultrasound reactors have gained a lot of interest in the food industry given the effects that can arise from ultrasonic-induced cavitation in liquid foods. However, most of the new food processing developments have been based on empirical approaches. Thus, there is a need for mathematical models which help to understand, optimize, and scale up ultrasonic reactors. In this work, a computational fluid dynamics (CFD) model was developed to predict the acoustic streaming and induced heat generated by an ultrasonic horn reactor. In the model it is assumed that the horn tip is a fluid inlet, where a turbulent jet flow is injected into the vessel. The hydrodynamic momentum rate of the incoming jet is assumed to be equal to the total acoustic momentum rate emitted by the acoustic power source. CFD velocity predictions show excellent agreement with the experimental data for power densities higher than W(0)/V ≥ 25kWm(-3). This model successfully describes hydrodynamic fields (streaming) generated by low-frequency-high-power ultrasound.     

超声空化及其声流结构实验研究*

超声空化及其声流效应在医学、化工和能源等领域得到广泛应用。本文采用高速摄像和粒子图像测速系统分别研究了超声场下的空化形态和声流场结构的时空演化规律。实验研究了50W,100W,200W和250W等四种不同输入功率对18kHz的超声变幅杆附近空化及其声流场的影响。研究结果表明：（1）在变幅杆下端面处观察到由大量空化气泡均匀分布组成的倒置锥形空泡结构,并且锥形空泡结构为稳态流动结构。（2）在超声变幅杆附近产生了两种不同的声流形式,第一种是变幅杆底端的射流型声流,第二种是变幅杆两侧的回旋流。此外,通过研究空泡与声流场中最大速度点之间的空间对应关系,发现声流是因为空泡流动带动而产生的。（3）空间位置和输入功率能显著影响射流型声流的流场结构,但是对回旋流的影响十分微弱。     

碟形超声变幅杆的设计

优化超声变幅杆的形状结构可有效地提高水域声场分布和空化区域,提升对水域超声空化效果。通过模拟分析发现传统超声变幅杆在水域中具有声场分布均匀性差、变幅杆端部声压高等特征,不利于声波在水域中传播。基于此,提出并优化设计了一种具有碟形结构的变幅杆,位于变幅杆的最大振幅处的碟形结构,有更大的振动位移;模拟表明其水域声场和声压均衡度显著优于传统变幅杆,铝箔空化腐蚀实验进一步证实了其水域中的声压分布均匀性。同时,实验通过铝箔的空化腐蚀、KI剂量测定及工件表面油渍去除对比了传统变幅杆和碟形变幅杆,分析表明碟形变幅杆所在水域中有较大的空化腐蚀区域,腐蚀速率明显提升,声化学反应速率提高,油渍去除程度增强,说明了设计的碟形变幅杆能够促进空化泡的产生,增加水域空化区域。     

Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results

The intensity distribution of the ultrasonic energy is, after the frequency, the most significant parameter to characterize ultrasonic fields in any sonochemical experiment. Whereas in the case of low intensity ultrasound the measurement of intensity and its distribution is well solved, in the case of high intensity (when cavitation takes place) the measurement is much more complicated. That is why the predicting the acoustic pressure distribution within the cell is desirable. A numerical solution of the wave equation gave the distribution of intensity within the cell. The calculations together with experimental verification have shown that the whole reactor behaves like a resonator and the energy distribution depends strongly on its shape. The agreement between computational simulations and experiments allowed optimisation of the shape of the sonochemical reactor. The optimal geometry resulted in a strong increase in intensity along a large part of the cell. The advantages of such optimised geometry are (i) the ultrasonic power necessary for obtaining cavitation is low; (ii) low power delivered to the system results in only weak heating, consequently, no cooling is necessary and (iii) the "active volume" is large, i.e. the fraction of the reactor volume with high intensity is large and is not limited to a vicinity close to the horn tip.     

Numerical 3D flow simulation of ultrasonic horns with attached cavitation structures and assessment of flow aggressiveness and cavitation erosion sensitive wall zones

As a contribution to a better understanding of cavitation erosion mechanisms, a compressible inviscid finite volume flow solver with barotropic homogeneous liquid–vapor mixture cavitation model is applied to ultrasonic horn set-ups with and without stationary specimen, that exhibit attached cavitation at the horn tip. Void collapses and shock waves, which are closely related to cavitation erosion, are resolved. The computational results are compared to hydrophone, shadowgraphy and erosion test data. At the horn tip, vapor volume and topology, subharmonic oscillation frequency as well as the amplitude of propagating pressure waves are in good agreement with experimental data. For the evaluation of flow aggressiveness and the assessment of erosion sensitive wall zones, statistical analyses of wall loads and of the multiplicity of distinct collapses in wall-adjacent flow regions are applied to the horn tip and the stationary specimen. An a posteriori projection of load collectives, i.e. cumulative collapse rate vs. collapse pressure, onto a reference grid eliminates the grid dependency effectively for attached cavitation at the horn tip, whereas a significant grid dependency remains at the stationary specimen. The load collectives show an exponential decrease towards higher collapse pressures. Erosion sensitive wall zones are well predicted for both, horn tip and stationary specimen, and load profiles are in good qualitative agreement with measured topography profiles of eroded duplex stainless steel samples after long-term runs. For the considered amplitude and gap width according to ASTM G32-10 standard, the analysis of load collectives reveals that the distinctive erosive ring shape at the horn tip can be attributed to frequent breakdown and re-development of a small portion of the tip-attached cavity. This partial breakdown of the attached cavity repeats at each driving cycle and is associated with relatively moderate collapse peak pressures, whereas the stationary specimen is rather unfrequently stressed at the end of each subharmonic oscillation cycle by the violent collapse of the complete cavity.     

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.     

Precipitation of calcium carbonate by ultrasonic irradiation

Supersaturated solution of calcium carbonate ([Ca²⁺]=1.2 mmol/L, [HCO₃⁻]=3.2 mmol/L, pH=8.8, T=30±0.5 °C), a scale forming component, was irradiated by an ultrasonic homogenizer (24 kHz, 15–250 W/cm²) to study the factors that affect its precipitation rate. The factors of (1) depth of horn immersion, (2) ultrasonic intensity and horn tip size and (3) cavitation, which can affect the precipitation rate were investigated in this study. Ultrasonic irradiation was observed to accelerate the precipitation of calcium carbonate and it was found that there exists an optimum range of horn immersion depth for maximizing the precipitation rate. The experimental data also established that the precipitation rate was proportional to ultrasonic intensity and diameter of horn tip. These findings were correlated to the effects of physical mixing, that arises due to ultrasonic irradiation. However, the effect of cavitation in accelerating the precipitation rate was found to be small. Thus it is forwarded that the physical mixing effect, especially macrostreaming is the main factor that accelerates the precipitation rate of calcium carbonate during ultrasonic treatment. Further, neither the morphology nor the size of the calcium carbonate crystals formed were found to be affected by the ultrasonic irradiation.     

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.     

Effect of gold nanoparticle size on acoustic cavitation using chemical dosimetry method

When a liquid is irradiated with high intensities of ultrasound irradiation, acoustic cavitation occurs. Acoustic cavitation generates free radicals from the breakdown of water and other molecules. Cavitation can be fatal to cells and is utilized to destroy cancer tumors. The existence of particles in liquid provides nucleation sites for cavitation bubbles and leads to decrease the ultrasonic intensity threshold needed for cavitation onset. In the present investigation, the effect of gold nanoparticles with appropriate amount and size on the acoustic cavitation activity has been shown by determining hydroxyl radicals in terephthalic acid solutions containing 15, 20, 28 and 35 nm gold nanoparticles sizes by using 1 MHz low level ultrasound. The effect of sonication intensity in hydroxyl radical production was considered.The recorded fluorescence signal in terephthalic acid solutions containing gold nanoparticles was considerably higher than the terephthalic acid solutions without gold nanoparticles at different intensities of ultrasound irradiation. Also, the results showed that the recorded fluorescence signal intensity in terephthalic acid solution containing finer size of gold nanoparticles was lower than the terephthalic acid solutions containing larger size of gold nanoparticles. Acoustic cavitation in the presence of gold nanoparticles can be used as a way for improving therapeutic effects on the tumors.     

超声搅拌磁流变抛光液的声场仿真分析

为了探究超声搅拌磁流变抛光液的制备及优化工艺,利用多物理场数值计算方法,建立了超声搅拌磁流变抛光液的声场仿真模型,并进行了频域分析。研究了不同液位深度、超声变幅杆探入深度,不同功率下磁流变抛光液的声场分布。通过测量磁流变抛光液的声场强度对声场仿真进行了验证。结果表明：随着距变幅杆距离的增加,声强逐渐减弱,高声强区域主要分布在换能器轴线附近。声强在距变幅杆20mm范围内急剧衰减,变幅杆最佳探入深度为10mm,增大功率有助于空化区域的扩大。声场仿真结果与实验测量结果基本一致,对磁流变抛光液的制备提供了数值计算基础。     

Qualitative characterization of ultrasound reactors for heterogeneous sonochemistry

Several measurement methods (thermocouple probe, perforation of aluminium foils by cavitation, chemical dosimeter) are used to characterize the sound fields of low and high intensity ultrasound reactors and to find optimal conditions for the ultrasonic irradiation of heterogeneous reaction mixtures. In this Paper it is shown that, due to the formation of standing waves, the local ultrasound intensity in a flask fixed in an ultrasonic cleaner is strongly susceptible to small changes in experimental conditions. It is also shown that high intensity ultrasound sources, such as an ultrasonic horn, tend to uncouple: that is, cavitation only occurs at the radiating surface and only marginal ultrasound intensity can be detected elsewhere in the surrounding liquid.     

Sonodisruption of re-assembled casein micelles at different pH values

Casein solutions with different pH values were sonicated at a frequency of 35 kHz and increasing acoustic powers. As the sonication power increased, turbidity of solutions and particle diameter decreased at any given pH value, suggesting particles disruption due to the ultrasonic treatment. The magnitude of decrease in re-assembled micelles diameter was greater at a higher pH, indicating an interaction between pH and sonication power in sonodissociation. This interaction is attributed to a looser structure of micelles at higher pH values which increases the efficiency of ultrasonic disruption and not directly to the increased cavitation efficiency. We argue that increased cavitation efficiency with increasing sonication power, which enhances shear forces is the most likely reason for sonodisruption of re-assembled casein micelles.     

Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs＇ collision factor theory

Based on Schaaff's collision factor theory (CFT) in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules, several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components. Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel's and Sehgal's laws for liquid binary mixtures.