Multi-frequency sonoreactor characterisation in the frequency domain using a semi-empirical bubbly liquid model

Recently, multi-frequency systems were reported to improve performance in power ultrasound applications. In line with this, digital prototyping of multi-frequency sonoreactors also started gaining interest. However, the conventional method of simulating multi-frequency acoustic pressure fields in the time-domain led to many challenges and limitations. In this study, a multi-frequency sonoreactor was characterised using frequency domain simulations in 2-D. The studied system consists of a hexagonal sonoreactor capable of operating at 28, 40 and 70 kHz. Four frequency combinations were studied: 28–40, 28–70, 40–70 and 28–40–70 kHz. A semi-empirical, modified Commander and Prosperetti model was used to describe the bubbly-liquid effects in the sonoreactor. The root-mean-squared acoustic pressure was compared against experimental validation results using sonochemiluminescence (SCL) images and was noted to show good qualitative agreement with SCL results in terms of antinode predictions. The empirical phase speed calculated from SCL measurements was found to be important to circumvent uncertainties in bubble parameter specifications which reduces error in the simulations. Additionally, simulation results also highlighted the importance of geometry in the context of optimising the standing wave magnitudes for each working frequency due to the effects of constructive and destructive interference.     

Investigation of acoustic and geometric effects on the sonoreactor performance

In this work, three design configurations of a sonoreactor are considered under various operating conditions, and the acoustic characteristics during water sonication are investigated while using an immersed-type ultrasonic flat transducer probe in a sonoreactor model. Numerical models are also developed to simulate the sonication process, and they are successfully validated and compared with available data in the literature. Several sets of numerical investigations are conducted using the finite-element method and solved by the computational acoustics module in the COMSOL Multiphysics. The effects of the acoustical and geometrical parameters are investigated, analyzed, and reported, including the ultrasonic frequency, acoustic intensity, and scaling-up the reactor. The present study includes a parametric investigation examining the change of the ultrasonic frequency, intensity, and probe immersion depth on the performance. The results of the parametric study show that the highest cavitation energy corresponds to the maximum magnitude of negative pressure that takes place in the range of 60–80 kHz. The cavitation energy analyses are conducted under the conditions of 20 kHz of frequency and at 36 W input power. It is found that the cavitation energy of 15.87 W could produce 2.98 × 10⁻¹⁰ mol/J of sonochemical efficiency. In addition, the effect of altering the transducer probe depth changes the acoustic pressure field insignificantly. Furthermore, a recommendation is made to improve the sonochemical efficiency by introducing more considerable ultrasound input power while operating the sonoreactor at an ultrasonic frequency lower than 60 kHz. The results presented in this paper provide a comprehensive assessment of different sonoreactors and the feasibility of scaling-up their production rate.     

Investigation of sonochemical activities at a frequency of 334 kHz: The effect of geometric parameters of sonoreactor

In this study, the effect of the dimensions of the bottom plate and liquid height was investigated for high-frequency sonoreactors under a vertically irradiated system. The dimensions of the bottom plate did not significantly influence sonochemical activity considering power density. However, as the bottom plate was increased in size, the hydroxyl radical generation rate decreased because of a decrease in power density. It is therefore recommended that sonoreactors with bottom-plate dimensions close to those of the ultrasonic transducer module be used. Liquid height had a significant effect on sonochemical activity, but the trend of the activity considering power density changed as the initial pollutant concentration changed. In the case of low initial concentration of As(III) (1 mg/L), the maximum cavitation yield for As(III) oxidation was observed at liquid heights of 150 mm.     

A comparative study on the modeling of sound pressure field distributions in a sonoreactor with experimental investigation

In sonochemical reactors the effect of emerging cavitation bubbles has significant influence on the amplitude and structure of the developing sound field. Calculations show that the damping parameter and the phase velocity may, depending on the pressure amplitude, change by several orders of magnitude. For example, the sound velocity in water comes to 1500 ms⁻¹, whereas in a bubbly liquid it may decrease to 20 ms⁻¹, which is much below the velocity of sound in air (about 340 ms⁻¹). In this paper, a method of calculating the time dependent three-dimensional pressure field in sonochemical reactors of various shapes is presented. It takes into account inhomogeneous distributed wave parameters which are a function of the spatial depending pressure amplitude. The modeled results are then compared with experimentally measured values of a certain kind of reaction vessel. The agreement is found to be satisfactory.     

Visualization and optimization of cavitation activity at a solid surface in high frequency ultrasound fields

Despite the increasing use of high frequency ultrasound in heterogeneous reactions, knowledge about the spatial distribution of cavitation bubbles at the irradiated solid surface is still lacking. This gap hinders controllable surface sonoreactions. Here we present an optimization study of the cavitation bubble distribution at a solid sample using sonoluminescence and sonochemiluminescence imaging. The experiments were performed at three ultrasound frequencies, namely 580, 860 and 1142 kHz. We found that position and orientation of the sample to the transducer, as well as its material properties influence the distribution of active cavitation bubbles at the sample surface in the reactor. The reason is a significant modification of the acoustic field due to reflections and absorption of the ultrasonic wave by the solid. This is retraced by numerical simulations employing the Finite Element Method, yielding reasonable agreement of luminescent zones and high acoustic pressure amplitudes in 2D simulations. A homogeneous coverage of the test sample surface with cavitation is finally reached at nearly vertical inclination with respect to the incident wave.     

FEM Modal Analysis on the Gravity Support System of ITER

The three-dimensional finite element method model with 20 degree sector of the ITER overall gravity support system was built by the ANSYS software. The modal analysis of the gravity support system was made and first ten natural frequencies and vibration modes of the gravity support system were calculated by using Block Lanczos method. The results of modal analysis on ITER represent that the stiffness of flexible plates has influenced greatly for the natural frequency of the system.     

The effects of liquid height/volume,initial concentration of reactant and acoustic power on sonochemical oxidation

Even though much knowledge on acoustic cavitation and its application has been accumulated over the past decades, further research is still required to develop industrial uses of acoustic cavitation. It is because the available information is mainly based on small-scale sonoreactors and the design and optimization of sonoreactors for large-scale applications have not been widely studied. In this study, the effects of liquid height/volume, initial concentration of the reactant and input acoustic power on sonochemical oxidation reactions including iodide ion oxidation, As(III) oxidation, and hydrogen peroxide generation were investigated using a 291 kHz sonoreactor with various liquid height/volumes (50, 100, 200, 300, 500, and 1000 mL) and input powers (23, 40, and 82 W). As the liquid height/volume and the input power changed, the power density varied from 23 to 1640 W/L and the maximum cavitation yields of triiodide ion for 23, 40, and 82 W were observed at 0.05, 0.1, and 0.2/0.3 L, respectively. It was found that low power was more effective for the small volume and the large volume required high power level and the moderate power density, approximately 400 W/L, was suggested for the sonochemical oxidation of iodide ion in the 291 kHz sonoreactor in this study. Similar results were observed in the generation of hydrogen peroxide and the sonochemical oxidation of As(III) to As(V). It was also revealed that KI dosimetry could be applicable for the estimation of the sonochemical reactions of non-volatile compounds such as As(III).     

偶极声波换能器振动特性计算

利用ANSYS有限元软件计算了声波测井中使用的偶极子换能器在不同机械边界条件下的振动模态和频率响应。计算结果显示,偶极子换能器在一定的频率范围内有多个振动模态,不同的机械边界条件不仅影响振动模态的个数而且还影响同一振动模态的谐振频率;从频率响应曲线上还可以看出此结构的偶极子换能器在做弯曲振动时的频带较窄,这对在不同地层井眼中进行的偶极子声波测井非常不利。通过多个不同主频的偶极子换能器组合工作可以从根本上拓宽偶极声波换能器的频带宽度。     

由波模频移确定矩形管道沉积层的厚度

提出了用波模的频率偏移求矩形管道中沉积层厚度的方法。在已知无沉积层矩形管道内横截面的情形下,将测量的波模频率与用有限元计算得到的波模频率进行比对,确定沉积层的厚度。给出了有限元计算结果以及实验结果(长15m,截面为449mm×425mm的矩形管道,沉积层厚度分别为40mm和60mm)及其相对误差。实验和有限元计算的结果有很好的一致性,验证了本方法的正确性。     

Simulations of a full sonoreactor accounting for cavitation

In spite of the increasing interest in ultrasound processing applications, industrial scale-up remains limited, in particular by the unavailability of predictive computer tools. In this study, using a previously published model of cavitating liquids implementable as a non-linear Helmholtz equation, it is shown that a full sonoreactor can be modelled and simulated. The model includes the full transducer and the vibrations of the vessel walls, using the physics of elastic solids and piezo-electricity. The control-loop used by the generator to set the optimal frequency is also accounted for. Apart from the geometry, the unique input of the model is the current feeding the transducer whereas the dissipated electrical power, transducer complex impedance and working frequency are available as outputs. The model is put to the test against experiments realized in different geometries, varying either the input current or the transducer immersion depth. Despite the overestimation of the power dissipated in the liquid, the evolution of the acoustic load in both cases is reasonably well reproduced by simulation, which partially validates the method used.     

环筋对水下平底圆柱壳的声振特性影响

本文建立了计算两端带平底板的有限长圆柱壳水中声辐射的FEM／BEM三维模型，探索了加筋的高度、宽度、数目对平底圆柱壳的辐射功率、辐射效率、法向声强、声场指向性的影响规律。计算方法是在有限元软件ANSYS中做加筋平底圆柱壳建模、模态分析基础上，将有关数据（网格、模态）导入边界元软件SYSNOISE中计算流体结构耦合状态下的辐射声场特性。结果表明：（1）随着环筋高度、宽度增大，激励点声压峰和法向声强峰在0-400Hz频率范围内数目减少且峰向高频方向移动，同时辐射声功率在减小（除个别模态峰值外），而辐射效率随筋高增大而增大。（2）环筋数目的增加使激励点辐射声压和法向声强峰数目明显减少，使辐射声功率明显低于无筋圆柱壳的辐射声功率，辐射效率随环筋数目增大而增大。（3）环筋宽度变化对声场指向性影响不大；圆柱壳声场指向性随环筋高度和数目增加出现较大变化，尤其是在研究的频段内的f=51Hz和f=301Hz上。这对于水下结构辐射噪声预报以及噪声抑制具有重要意义。     

Interpreting the influence of liquid temperature on cavitation collapse intensity through bubble dynamic analysis

The violent collapse of inertial bubbles generates high temperature inside and emits strong impulsive pressure. Previous tests on sonoluminescence and cavitation erosion showed that the influence of liquid temperature on these two parameters is different. In this paper, we conducted a bubble dynamic analysis to explore the mechanism of the temperature effect and account for the above difference. The results show that the increase of vapor at higher liquid temperatures changes both the external compression pressure and the internal cushion and is responsible for the variation of bubble collapse intensity. The different trends of the collapsing temperature and emitted sound pressure are caused by the energy distribution during the bubble collapse. Moreover, a series of simulations are conducted to establish the distribution map of the optimum liquid temperature where the collapse intensity is maximized. The relationship between the collapse intensity and the radial dynamics of the bubble is discussed and the reliable indicator is identified. This study provides a clear picture of how the thermodynamic process changes cavitation aggressiveness and enriches the understanding of this complex thermal-hydrodynamic phenomenon.     

Memory effect and redistribution of cavitation nuclei in a thin liquid layer

Temporal evolution and spatial distribution of acoustic cavitation structures in a thin liquid layer were investigated experimentally with high-speed photography. The inception and disappearance processes of cavitation bubble cloud revealed that the metastable cavitaton structures formed in the thin liquid layer caused a long-term “memory effect”. A factor which weakens the memory effect was identified. The distribution of cavitation nuclei was investigated by changing the temporal decay of the memory effect.     

热声回热器结构频率的数值研究

介绍了声波在结构中的几种表现形式,综合考虑结构声传播过程中的色散现象会影响结构和流体的声耦合,将结构声理论运用于热声系统回热器内结构振动的分析。通过采用Ansys软件对回热器中薄板建立模型并分析其振动模态。结果显示:(1)回热器中薄板结构主要受弯曲波作用,振动时发生弯曲变形;(2)薄板振动模态的固有频率随板厚度减小而降低,随长度减小而增加;(3)薄板振动模态随阶数升高而趋于复杂,相应的固有频率值由数十赫兹发展到数千赫兹,包含热声系统谐振频率的工作区间。     

Acoustic emission spectra and sonochemical activity in a 36 kHz sonoreactor

During ultrasound-induced cavitation in liquids, acoustic emissions at fundamental and harmonic frequencies can be detected. The effect of acoustic emissions at harmonic frequencies on the sonochemical and sonophysical activities has not been explored, especially in large-scale sonoreactors. In this study, the acoustic emissions in the range, 0-250 kHz in a 36 kHz sonoreactor with varying liquid heights were studied and compared with the sonochemical activities. The acoustic pressures at both fundamental and harmonics decreased drastically as the liquid height was increased due to the attenuation of sound energy. It was observed that the increase in input power resulted in only an increase in the acoustic emissions at derivative frequencies such as, harmonics and subharmonics. The sonochemical activity, evaluated in terms of sonochemiluminescence and H₂O₂ yield, was not significantly enhanced at higher input power levels. This suggests that at higher power levels, the “extra” acoustic energy is not effectively used to generate primary cavitation activity; rather it is converted to generate acoustic emissions at harmonic and subharmonic frequencies. This is an important observation for the design of energy efficiency large-scale sonochemical reactors.     

Cavitation erosion by shockwave self-focusing of a single bubble

The ability of cavitation bubbles to effectively focus energy is made responsible for cavitation erosion, traumatic brain injury, and even for catalyse chemical reactions. Yet, the mechanism through which material is eroded remains vague, and the extremely fast and localized dynamics that lead to material damage has not been resolved. Here, we reveal the decisive mechanism that leads to energy focusing during the non-spherical collapse of cavitation bubbles and eventually results to the erosion of hardened metals. We show that a single cavitation bubble at ambient pressure close to a metal surface causes erosion only if a non-axisymmetric energy self-focusing is at play. The bubble during its collapse emits shockwaves that under certain conditions converge to a single point where the remaining gas phase is driven to a shockwave-intensified collapse. We resolve the conditions under which this self-focusing enhances the collapse and damages the solid. High-speed imaging of bubble and shock wave dynamics at sub-picosecond exposure times is correlated to the shockwaves recorded with large bandwidth hydrophones. The material damage from several metallic materials is detected in situ and quantified ex-situ via scanning electron microscopy and confocal profilometry. With this knowledge, approaches to mitigate cavitation erosion or to even enhance the energy focusing are within reach.     

Turbulent structures in cylindrical density currents in a rotating frame of reference

Gravity currents are flows generated by the action of gravity on fluids with different densities. In some geophysical applications, modeling such flows makes it necessary to account for rotating effects, modifying the dynamics of the flow. While previous works on rotating stratified flows focused on currents of large Coriolis number, the present work focuses on flows with small Coriolis numbers (i.e. moderate-to-large Rossby numbers). In this work, cylindrical rotating gravity currents are investigated by means of highly resolved simulations. A brief analysis of the mean flow evolution to the final state is presented to provide a complete picture of the flow dynamics. The numerical results, showing the well-known oscillatory behavior of the flow (inertial waves) and a final state lens shape (geostrophic adjustment), are in good agreement with experimental observations and theoretical models. The turbulent structures in the flow are visualized and described using, among others, a stereoscopic visualization and videos as supplementary material. In particular, the structure of the lobes and clefts at the front of the current is presented in association to local turbulent structures. In rotating gravity currents, the vortices observed at the lobes front are not of hairpin type but are rather of Kelvin-Helmholtz type.     

Polaron self-energy and effective mass in a freestanding cylindrical quantum wire

The polaron self-energy and correction to the electron effective mass in a freestanding quantum wire is investigated by the perturbation approach.The polaron effect of the electron-confined longitudinal optical (LO) phonon and surface optical (SO) phonon interactions are separately worked out. Numerical calculation on a GaAs quantum wire shows that the confined LO phonon contribution to the polaron self-energy is relatively small for a narrow wire and gradually approach that of the bulk material when the radius of the wire increases. While the contribution of the SO phonon modes is big for small wire radius and then decreases as the radius increases.