Bubble Dynamics Model Research Articles

Analysis of multi-frequency ultrasound effect on acoustic microcavitations in [formula omitted]-dimensional fluid

Acoustic microcavitation and associated mechanical effects, such as stress and strain, are significant in decreasing cavitation thresholds and improving cavitation effects at multiple (i.e., single, dual, and triple) frequencies. Ultrasonic excitation and the introduction of microbubbles as cavitation nuclei are both extremely successful techniques. Besides, the enhancing effects brought on by a dual and triple frequency approach, the cavitation dynamics of microbubbles in viscoelastic tissues under the influence of dual and triple frequency excitation are poorly known. This work deals with the modelling and numerical investigation of acoustic cavitation in N-dimensional fluid based on the multifrequency of ultrasound fields. The mathematical model of ultrasonic microcavitation bubble dynamics is formulated by continuity and Navier-Stokes equations in N-dimensions and the equation of pressure due to acoustic multifield. The proposed model is solved and investigated numerically based on the hybrid-B-Spline method. The numerical results illustrate that the behaviour of the microcavitation bubble dynamics increases with a decrease of the value of the N-dimensional fluid. Moreover, the results of the numerical simulation show the importance of the effect of different multifrequency on the behaviour of the microbubble dynamics, as the results obtained showed that in the case of a single frequency, the radius of the microbubbles is higher than in the cases of dual and triple frequency. Additionally, at different initial radii values for cavitation microbubbles, the growth and departure rates for microcavitation dynamics were examined. Finally, in the proposed model, numerical solutions are studied, their stability is verified, and they are compared with previous theoretical works.

Bubbles Counting Using Organic Pollutants Degradation as a Probe

Relying on the fact that both of chemical and physical impacts of sonication are in strong relation to the number of acoustic cavities, the present paper introduces an innovative technique for the estimation of the number of active bubbles using the degradation of nonvolatile pollutants in the bulk liquid as a probe. The internal (gas pages) and external (liquid) bubble sonochemistry were simulated to track the radicals generation and use for nonvolatile pollutants degradation (in the liquid phase). To this end, COPASI® chemical kinetics software has been used for optimizing the acoustic bubble number density by linking the instantaneous bubble gas reaction (described by a bubble dynamic model accounting for the radical dissolution mechanism) and the aqueous free radicals degradation kinetics [i.e. concentration vs. time] of several nonvolatile organics (phenol, 4-chlorophenol, dyes…). Based on this strategy, the number density of active bubbles was determined for different operating circumstances (i.e. acoustic intensity, frequency, liquid temperature and saturation gas type). The performance of our method was evaluated by comparing our findings to those available in the literature, where an excellent agreement was established. Our technique showed that the number density monotonously goes up with increasing ultrasound frequency from 200 to 1140kHz, regardless of the experimental conditions used in this investigation. The opposite behavior has been obtained with the increase of the liquid temperature and acoustic intensity. Additionally, it has been noticed that the variation in the number of cavities with respect to the nature of saturating gas is frequency-dependent. At a frequency of 200kHz, the number of bubbles is in the order: O2>Ar>air. However, over this frequency (>200kHz), the number of acoustic bubbles is in the order: O2>air>Ar. On the other hand, it has been shown that below a frequency of ~860kHz, the variation of void fraction (ε) is synchronized with change in number density (N); nevertheless, over this value (>860kHz), these two parameters (N, ε) are no longer closely connected. As a result, in this case (>860kHz), the evaluation of number density from the total volume fraction of bubbles could not be directly performed without more information regarding the bubbles population, (e.g. size distribution, bubble-bubble interactions, bubbles deformation…etc.). Finally, the current proposed technique is flexible and can determine the number density of active bubbles for a wide range of operating conditions and circumstances.

Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning

The intricate process of bubble growth dynamics involves a broad spectrum of physical phenomena from microscale mechanics of bubble formation to macroscale interplay between bubbles and surrounding thermo-hydrodynamics. Traditional bubble dynamics models including atomistic approaches and continuum-based methods segment the bubble dynamics into distinct scale-specific models. To bridge the gap between microscale stochastic fluid models and continuum-based fluid models for bubble dynamics, we develop a composite neural operator model to unify the analysis of nonlinear bubble dynamics across microscale and macroscale regimes by integrating a many-body dissipative particle dynamics (mDPD) model with a continuum-based Rayleigh–Plesset (RP) model through a novel neural network architecture, which consists of a deep operator network for learning the mean behavior of bubble growth subject to pressure variations and a long short-term memory network for learning the statistical features of correlated fluctuations in microscale bubble dynamics. Training and testing data are generated by conducting mDPD and RP simulations for nonlinear bubble dynamics with initial bubble radii ranging from 0.1 to 1.5 micrometers. The results show that the trained composite neural operator model can accurately predict bubble dynamics across scales, with a 99% predictive accuracy for the time evolution of the bubble radius under varying external pressure while containing correct size-dependent stochastic fluctuations in microscale bubble growth dynamics. The composite neural operator is the first deep learning surrogate for multiscale bubble growth dynamics that can capture correct stochastic fluctuations in microscopic fluid phenomena, which sets a new direction for future research in multiscale fluid dynamics modeling.

Numerical study of cavitation shock wave emission in the thin liquid layer by power ultrasonic vibratory machining

In the field of power ultrasonic vibration processing, the thin liquid layer nestled between the tool head and the material serves as a hotbed for cavitation shock wave emissions that significantly affect the material's surface. The precise manipulation of these emissions presents a formidable challenge, stemming from a historical deficit in the quantitative analysis of both the ultrasonic enhancement effect and the shock wave intensity within this niche environment. Our study addresses this gap by innovatively modifying the Gilmore-Akulichev equation, laying the groundwork for a sophisticated bubble dynamics model and a pioneering shock wave propagation model tailored to the thin liquid layer domain. Firstly, our study investigated the ultrasound enhancement effect under various parameters of thin liquid layers, revealing an amplification of ultrasound pressure in the thin liquid layer area by up to 7.47 times. The mathematical model was solved using the sixth-order Runge–Kutta method to examine shock wave velocity and pressure under different conditions. our study identified that geometric parameters of the tool head, thin liquid layer thickness, ultrasonic frequency, and initial bubble radius all significantly influenced shock wave emission. At an ultrasonic frequency of 60 kHz, the shock wave pressure at the measurement point exhibited a brief decrease from 182.6 to 179.5 MPa during an increase. Furthermore, rapid attenuation of the shock wave was found within the range of R0-3R0 from the bubble wall. This research model aims to enhance power ultrasonic vibration processing technology, and provide theoretical support for applications in related fields.

Numerical investigation of hydroxyl radicals produced by a single bubble in jet pump cavitation reactor

Jet pump cavitation reactors (JPCRs) have significant potential to be used in water treatment applications. During their operation, the hydroxyl radicals generated by cavitation collapse produce a strong oxidation capacity, which is one of the key mechanisms in disrupting algal cells. In this paper, we investigate the hydroxyl radicals produced by single cavitation bubble in a JPCR. The numerical method includes a bubble dynamic model, molecular diffusion model, energy balance equation, and chemical reaction model for predicting the hydroxyl radical production. Additionally, the pressure distribution within a JPCR is tested and used to analyze the single-bubble performance. The effects of the JPCR operating conditions and structure parameters on hydroxyl radical production are further discussed. Our results indicate that, when the flow rate ratio is positive, the number of hydroxyl radicals is closely related to the development and collapse of the cavitation bubble and reaches a peak value under the critical condition. When the flow rate ratio is negative, the maximum production of hydroxyl radicals appears under backflow stagnation condition. In general, increasing the throat length–diameter ratio and diffuser angle encourages the production of hydroxyl radicals, whereas increasing the area ratio inhibits their generation.

Energy-efficient bubble aeration guided by bubble dynamics model: From bubble formation at submerged orifice to oxygen utilization during uprising

Bubble aeration is a significant consumer of energy in wastewater treatment processes. Optimizing oxygen transfer, from an energy usage perspective, is crucial in the development of clean production techniques and for the stimulation of the circular economy. Although large efforts have been made in enhancing this process, particularly in ameliorating bubble diffusers, a main problem lies in energy wastage due to over-pursuing ultra-fine bubble generation. In this study, a dynamic model, that integrated both bubble expansion and detachment at submerged orifices, and consequential oxygen utilization during the uprising, was developed in order to better facilitate energy savings during the control of bubble generation. We demonstrate through calibrated models that bubble formation is governed by many factors including gas flow rate, orifice radius, surface tension, liquid viscosity, and surface wettability. Small bubbles are more prone to form when subjected to conditions of high wettability, small orifice size and low flow rate, since the bubbles are easily detached by the increasing upward forces in these scenarios. The oxygen transfer during the rising process was calculated as a function of bubble size, gas type and water depth. Bubbles with a radius smaller than a threshold value can shrink and collapse while below the water surface and thus provide 100% oxygen utilization. The threshold values of bubble radius are determined to be 150 μm and 250 μm at 5 m and 15 m initial water depth, respectively. The parameter set for bubble generation in order to obtain the desired bubble size may then be inversely determined by our bubble formation model, and it's considered as optimal aeration strategy to realize precise aeration. With these results, our study highlights the viability of the approach employing the proposed model in order to direct energy-efficient bubble generation.

Analysis of multi-bubble pulsations by the finite element method and bubble dynamics equations

Bubbles are widely used in industrial production, biomedical engineering, and many other fields. The analysis of the response of bubble clusters under acoustic waves is significant for the application of bubbles. In this paper, different bubble dynamics models are used to calculate the instantaneous radius of multi-bubbles, and the results corresponding to the different models are compared with those by the finite element method. In addition, the effect of bubble interactions on bubble pulsation is analyzed at different distances, and the effect of incident acoustic direction on the bubble's instantaneous radius is also investigated. The results show that time delays, which have often been neglected in previous work, should be considered except when the bubble spacing is minimal. The results calculated by the finite element method indicate that the attraction and repulsion between bubbles are alternating, which is related to the velocity field between bubbles. Moreover, the suppression or promotion of bubble interactions for bubble pulsation is affected by bubble distance under the same acoustic excitation conditions. Finally, for a bubble cluster with large bubble distances, its total scattered field relating to the incident acoustic wave can be approximated as the interference field of multiple secondary acoustic sources with the same waveform and different phases. If these bubbles are in random motion, the total scattered sound intensity of the bubble cluster is proportional to the number of bubbles.

Numerical prediction of cavitation nuisance on hydrofoils: Combined analysis of cavity dynamics and the aggressiveness of collapsing cavitating structures

The unsteady cavitating flow past a three-dimensional twisted hydrofoil is numerically investigated by a large eddy simulation to obtain in-depth insight into the bubble dynamics near the cavitation erosion region. Macroscopic cavity evolution is captured by a multiphase flow computing frame, while the bubble oscillations in the cavitating flow are computed by solving the Gilmore bubble dynamic model, in which the driving force for the bubble movement is exported through the application of a discrete phase model. The cavitation erosion potential is then computed by a robust indicator developed based on the energy balance hypothesis. The relevance between the dynamics and the destructive essence of a cavitation bubble and the erosion intensity is thoroughly analyzed. The results show that the unsteadiness involved in the turbulent cloud cavitation is well reproduced, and the main cavitation erosion risk in the middle region of the hydrofoil is also accurately predicted comparing with the painting test results. A localized high-pressure region is identified near the rear part of the attached cavity where the mainstream encounters the primary reentrant jet flows. The peak bubble internal pressure can reach 487 MPa near the middle plane of the hydrofoil, during the stage when the surrounding liquid pressure is continuously increased. The bubbles with the smallest radius, ranging from 23.1 to 26.3 μm after compressing from their initial sizes (R0 = 100–700 μm) in the near wall region, are associated with the extremely high internal pressure, and they are responsible for the cavitation erosion damage on the hydrofoil surface.

Viscosity effects and confined cochlea-like geometry in laser-induced cavitation dynamics

On the path to an optoacoustic hearing implant for stimulation of residual hearing, one possibility for tone generation in liquids is the concatenation of acoustic click events, which can be realized i. a. by the acoustic transients that accompany an optical breakdown. The application of a viscous gel is helpful in this context, as this results in an attenuation of the distortion of tone quality caused by higher harmonic components. To further understand the underlying cavitation bubble dynamics both in the viscous gel and in a confined volume that is dimensioned similarly to the human cochlea, a numerical model built in OpenFOAM was adapted and compared to additional experiments. Experimentally, the acoustic transients were generated by optical breakdown by nanosecond laser pulses with a pulse duration of 0.7 ns and a wavelength of 1064 nm. The pulses were focused on a viscous gel inside a water container. The pressure transients were measured by a needle hydrophone. The comparison of the bubble dynamics in different viscosities between the model and the experiment shows that, except for high viscosities, the experimental observations could be modeled by the simulation. We assume that the maximum size of the cavitation bubble strongly decreases with increasing viscosity, which can be used for high-frequency attenuation as reported in our previous research. In conclusion, this study aims at an application-oriented realization of the numerical cavitation bubble dynamics model to understand the experimental findings on the pathway to an optoacoustic hearing implant.

Numerical Method to Determine the Inception of Propeller Tip Vortex Cavitation Based on Bubble Dynamics

Due to the scale effect, tip vortex cavitation (TVC) is the earliest type of cavitation that occurs on real ship propellers. As a result, experts in the ship field have been paying close attention to the accurate prediction of propeller TVC inception for a long time. The motion and growth of the microscopic nuclei in the water have a significant influence on TVC inception. However, the minimum pressure coefficient method—a common method at present—based on the traditional Eulerian framework, neglects the influence of microscopic nuclei and therefore cannot accurately predict the cavitation inception. Moreover, the numerical prediction method for cavitation inception, which is based on bubble dynamics models and considers the influence of nuclei, has not established a set of unified and specific discrimination criteria applicable to propeller cavitation inception. In order to make up for the shortcomings of traditional prediction models and the existing methods based on bubble dynamics in the prediction of TVC inception, we propose a new discrimination method for propeller TVC inception based on bubble dynamics in this paper. The comparison with experimental results demonstrates that our proposed method allows us to predict propeller TVC inception more accurately. In addition, the effect mechanism of tip vortex flow characteristics on nuclei evolution is further investigated, and it is found that when approaching the low-pressure region at a vortex core under the influence of tip vortex suction, nuclei grow explosively under the continuous action of the low pressure at the vortex core until they reach their maximum sizes and then collapse rapidly.

Large-scale molecular dynamics simulations of bubble collapse in water: Effects of system size, water model, and nitrogen

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 106 and 4.5 × 109 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L−1. Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. We also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

Application of the unified equation of bubble dynamics for simulating the large-scale air-gun bubble with migration effect

How to effectively reduce the high-frequency output caused by excessively steep initial peak slope and enhance the low-frequency output generated by bubble oscillation has become present research interest in seismic source design. The most effective way to improve the low-frequency content of a seismic source is to increase its chamber volume. However, the size of air-gun bubbles generated by large-volume air-gun sources has increased by several hundred times compared to traditional high-pressure air guns, which has made the migration phenomenon of bubbles no longer negligible. The previous air-gun bubble dynamics models did not comprehensively account for the effects caused by bubble migration phenomenon. In this paper, we have developed an air-gun bubble dynamics model based on unified equation for bubble dynamics, and the newly established model demonstrates a closer alignment with experimental data compared to models based on the Gilmore and Keller equations. Based on this, the influence of the design parameters of air-gun seismic source on the bubble migration is studied. It explores the ramifications of migration on the dynamic properties of air-gun bubbles and the signatures of seismic sources. Additionally, we examine how incoming flow velocity magnitude and air-gun design parameters influence the signatures of air-gun seismic sources. Finally, we investigate the impact of both the spacing between dual guns and the horizontal movement of bubbles caused by mutual attraction on the signatures of dual-gun sources.

3D model for inertial cavitation bubble dynamics in binary immiscible fluids

The physics of cavitation bubbles in water has been extensively studied for over a century. However, our understanding of bubble dynamics in binary immiscible fluids, such as a water-oil system, is limited. These systems have recently gained a lot of interest due to their relevance in modern medical treatment, emulsification, and the food industry. In this study, we establish an accurate and inexpensive three-dimensional boundary integral (BI) model for inertial cavitation bubble dynamics in binary immiscible fluid systems. Our novel scheme for solving velocities on the flow boundaries, expressed in a matrix form, can be easily extended to complex situations where multiple bubbles are generated in different phases. Additionally, we employ a density potential method and a weighted moving least-squares method to maintain a high level of mesh regularity. Our results demonstrate that the proposed 3D model is comparable in accuracy to a 3D axisymmetric model by comparing it against analytical solutions and the results obtained from an axisymmetric model. Furthermore, we compare our numerical simulations against a purposely conducted experiment for the bubble-droplet interaction, and excellent agreement is achieved. For the first time, we present simulation results of two-bubble interactions with an initially flat fluid-fluid interface and inside a droplet surrounded by a second fluid. We also reveal the dependences of the two-bubble morphologies, flow patterns, and jet velocities on the density ratio between the two phases. Finally, we find a significant difference in the mechanism of fluid mixing by multiple bubbles compared to that of a single bubble case.

Investigation of the effect of a multi-frequency ultrasound signal on the inertial cavitation threshold is various viscoelastic mediums

The objective of the present study is the numerical investigation of the inertial cavitation threshold in soft tissue under different multi-frequency signals of high intensity focused ultrasound (HIFU). For the modeling of bubble dynamics, the Gilmore-Akulichev-Zener model was used. The inertial cavitation threshold was calculated for different criteria, for different signal modes (single-, dual-, and triple-frequency), and for different viscoelastic mediums. Effect of nonlinear wave propagation and mechanical effects of acoustic caviation have been also studied. The obtaining results demonstrated that a criterion, based on bubble size, gives lower threshold values than a criterion using bubble collapse velocity. An increase in the values of viscosity and elasticity leads to a rise in the threshold amplitude. Analyzing threshold values for dual- and triple-frequency signal modes, it can be seen that the inertial cavitation threshold can be sufficiently reduced when a multi-frequency signal with the correct frequency combination is applied. However, the inertial cavitation threshold also depends on the initial bubble size. This dependency was also investigated in the current study.

Study on the Dynamic Evolution of Bubbles in Oil/Pressboard Insulation

Power transformer may generate bubbles in the transformer oil due to various factors such as internal insulation winding vibration and pressure change. Bubbles distort the spatial electric field, which makes the discharge breakdown along the gas channel, accelerate the discharge breakdown of insulating medium. Therefore, in order to prevent the arc discharge induced by micro bubbles inside the transformer from increasing the risk of transformer combustion damage, it is necessary to conduct in-depth research on the dynamic law of suspended bubbles before insulation breakdown from the source by combining experiments and simulations. In this paper, the bubble dynamic model of needle plate electrode under the multi coupling physical field of transformer is established in terms of the migration and deformation of suspended bubbles in liquid phase. By comparing the migration trajectories of single suspended bubbles obtained from experiments and simulations, the reliability of the model is verified. The variation of velocity component of voltage amplitude and the change of shape stretching of single suspended bubble in power frequency period are simulated, and the fluctuation law of pressure formed by electrostriction force inside and outside the bubble during migration is analyzed. The capacity absorption process of multi bubbles in the strong field region near the needle electrode was simulated. The changes of the surrounding liquid pressure and the spatial electric field distribution during the formation of the gas channel were analyzed, and the internal relationship between the gas channel and the formation of the discharge breakdown was revealed.

Enhancing medical ultrasound imaging through fractional mathematical modeling of ultrasound bubble dynamics

The classical mathematical modeling of ultrasound acoustic bubble is so far using to improve the medical imaging quality. A clear and visible medical ultrasound image relies on bubble’s diameter, wavelength and intensity of the scattered sound. A bubble with diameter much smaller than the sound wavelength is regarded as highly efficient source of sound scattering. The dynamical equation for a medical ultrasound bubble is primarily modeled in classical integer-order differential equation. Then a reduction of order technique is used to convert the modeled dynamic equation for the bubble surface into a system of incommensurate fractional-orders. The incommensurate fractional-order values are calculated directly, by using Riemann stability region. On the basis of stability the convergence and accuracy of the numerical scheme is also discussed in detail. It has been found that the system will remain stable and chaotic for the incommensurate values α1<0.737 and α2<2.80, respectively.

Nonlinear modeling of sparkling drink bubbles using a physics informed long short term memory network

Bubble dynamics exist in many physical phenomena from the interaction between atmosphere and ocean, to food science of champagne bubbles. Bubble sound has recently been found to be a new way to understand bubbles and bubble dynamics. In this paper, we collect bubble sounds of different types of sparkling drinks, namely, sparkling water, beer, and champagne, and use the experimental data to construct a data driven model for sparkling bubbles. We apply dynamical reconstruction theory to the measured data and use false nearest neighbor, correlation dimension, and largest Lyapunov exponent to verify that the sparkling drink bubble dynamic is nonlinear and chaotic. Based on the derived physical principle on bubble pressure, we propose a novel physics informed long short term memory (PI-LSTM) neural network as a time series predictor to form a data driven with physics guidance model for bubble dynamics. It is shown here that the proposed PI-LSTM is effective in modeling the bubble sound data with improved accuracy compared to standard predictors including LSTM, multi-layer neural network and decision tree. The predictive analysis supports the nonlinear behavior of the bubble sound signals and demonstrates results consistent with the chaotic analysis.

Modelling of bubble dynamics on vertical rough wall with conjugate heat transfer

The wall temperature distribution and wettability greatly influence the bubble dynamics and heat transfer process. In this work, lattice Boltzmann (LB) method is implemented to investigate the bubble dynamics on the vertical rough heating wall, where the conjugate heat transfer process is taken into consideration. The interaction between bubble dynamics and boiling heat transfer characteristics is revealed. The results reveal that the bubble motion and the gas–liquid interface are dependent on the wall thermal conductivity. A high wall thermal conductivity will cause the gas film to cover the wall surface and hinder the heat transfer process. Moreover, the influence of the wall mixed wettability on the conjugate heat transfer behaviors is also analyzed. The findings demonstrate that the step wall wettability can promote the nucleation efficiency so as to achieve the enhancement of the wall heat transfer.

Jet characteristics of the three-dimensional explosion bubble in a compressible fluid

In this study, a three-dimensional model for underwater explosion bubble dynamics is established using a weakly compressible theory implemented in the boundary integral method. To validate its accuracy and reliability, we compare the model's results with theoretical solutions, an axisymmetric model, and experimental data. First, we systematically study the jet characteristics of an underwater explosion bubble in the free field and reveal the power laws for the height, width, and velocity of the liquid jet of the bubble with respect to the buoyancy parameter δ. It is important to note that, in addition to δ, the strength parameter ε also plays a significant role in determining the height of the jet, particularly when δ≲ 0.3. Furthermore, we investigate the impact of an inclined wall on jet features and provide an analytical expression for the jet angle for bubbles near a vertical wall, utilizing the Kelvin impulse theory.

Research on the dynamics of a restricted cavitation bubble near a symmetric Joukowsky hydrofoil

In the present paper, the restricted cavitation bubble dynamics near a symmetric Joukowsky hydrofoil are researched theoretically and experimentally. Using Kelvin impulse theory, the Joukowsky transformation, and the circle theorem, a theoretical model for restricted bubble dynamics is established to analyze the collapse jet characteristics. The validity of this model is then verified using high-speed photographic experiments. The velocity and direction of the collapse jet at specific position angles are quantitatively analyzed. Furthermore, the spatial characteristics of the Kelvin impulse direction near the symmetric Joukowsky hydrofoil are revealed by theoretical results. The main conclusions include the following: (1) the new theoretical model is proven to be effective in predicting the direction of the collapse jet for a restricted bubble near a symmetric Joukowsky hydrofoil. (2) As the distance between the bubble and hydrofoil increases, the collapse jet direction changes from pointing toward the nearest wall to pointing toward the center of the hydrofoil. (3) The variation rate of the Kelvin impulse direction for the restricted bubble is very sensitive to the bubble position near the two ends of the symmetric Joukowsky hydrofoil.