Bubble Centroid Research Articles

Research on cavitation bubble behaviors between a dual-particle pair

The interactions between particle clusters and cavitation bubbles play an important role in several industrial applications, e.g., the abrasive erosion of hydraulic machinery, the efficiency improvement of ultrasonic cleaning, and the mineral flotation. This paper explores the influence of a dual-particle pair of unequal sizes on the bubble collapse dynamics based on a Kelvin impulse model and high-speed photography. The impact of the radius ratio of the dual-particle pair (ranging from 1.0 to 3.0), defined as the ratio of the large-particle radius to the small-particle radius, on the bubble interface deformation, collapse jet, and the translational movement of the bubble is analyzed. The main findings are as follows: (1) the Kelvin impulse based on the Weiss theorem can effectively predict the asymmetric bubble behaviors in terms of the moving distance and the direction of the bubble centroid during the bubble collapse; (2) the particle radius ratio is a key parameter affecting the intensity and direction of the Kelvin impulse, as well as the bubble centroid moving distance; and (3) the zero-Kelvin-impulse point is always biased toward the smaller particle in the dual-particle pair.

Polarization and CEP dependence of the transverse phase space in laser driven accelerators

We present experimental results which show a laser polarization-dependent contribution to electron beam pointing jitter in laser wakefield accelerators (LWFAs). We develop a theoretical model for the polarization dependence in terms of the transverse dynamics of trapped electrons, resonantly driven by bubble centroid oscillations. The latter are generated by the carrier wave phase evolution at the self-steepened laser pulse front. In the model, the polarization-dependent jitter originates from shot-to-shot fluctuations of the laser carrier envelope phase (CEP). The model is verified by particle-in-cell simulations and suggests that CEP stabilization of the driving lasers might be necessary to achieve ultimate electron pointing stability in LWFAs. Published by the American Physical Society 2024

Bubble rising near a vertical wall: Experimental characterization of paths and velocity

Trajectories of a single bubble rising in the vicinity of a vertical solid wall are experimentally investigated. Distinct initial wall-bubble distances are considered for three different bubble rising regimes, i.e., rectilinear, planar zigzag, and spiral. The problem is defined by three control parameters, namely, the Galilei number, Ga, the Bond number, Bo, and the initial dimensionless distance between the bubble centroid and the wall, L. We focus on high-Bond numbers, varying L from 1 to 4, and compare the results with the corresponding unbounded case, L→∞. In all cases, the bubble deviates from the expected unbounded trajectory and migrates away from the wall as it rises due to the overpressure generated in the gap between the bubble and the wall. This repulsion is more evident as the initial wall-bubble distance decreases. Moreover, in the planar zigzagging regime, the wall is found to impose a preferential zigzagging plane perpendicular to it when L is small enough. Only slight wall effects are observed in the velocity or the oscillation amplitude and frequency. The wall migration effect is more evident for the planar zigzagging case and less relevant for the rectilinear one. Finally, the influence of the vertical position of the wall is also investigated. When the wall is not present upon release, the bubbles have the expected behavior for the unbounded case and experience the migration only instants before reaching the wall edge. This repulsion is, in general, more substantial than in the initially present wall case.

Interactions of a collapsing laser-induced cavitation bubble with a hemispherical droplet attached to a rigid boundary

We investigate experimentally and theoretically the interactions between a cavitation bubble and a hemispherical pendant oil droplet immersed in water. In experiments, the cavitation bubble is generated by a focused laser pulse right below the pendant droplet with well-controlled bubble–wall distances and bubble–droplet size ratios. By high-speed imaging, four typical interactions are observed, namely: oil droplet rupture; water droplet entrapment; oil droplet large deformation; and oil droplet mild deformation. The bubble jetting at the end of collapse and the migration of the bubble centroid are particularly different in each bubble–droplet interaction. We propose theoretical models based on the method of images for calculating the Kelvin impulse and the anisotropy parameter which quantitatively reflects the migration of the bubble centroid at the end of the collapse. Finally, we explain that a combination of the Weber number and the anisotropy parameter determines the regimes of the bubble–droplet interactions.

Experimental study of underwater explosions below a free surface: Bubble dynamics and pressure wave emission

The current work experimentally studies the complex interaction between underwater explosion (UNDEX) bubbles and a free surface. We aim to reveal the dependence of the associated physics on the key factor, namely, the dimensionless detonation depth γ (scaled by the maximum equivalent bubble radius). Four typical bubble behavior patterns are identified with the respective range of γ: (i) bubble bursting at the free surface, (ii) bubble jetting downward, (iii) neutral collapse of the bubble, and (iv) quasi-free-field motion. By comparison of the jet direction and the migration of the bubble centroid, a critical value of γ is vital for ignoring the effects of the free surface on UNDEX bubbles. Good agreements are obtained between the experimental data and Zhang equation [Zhang et al., “A unified theory for bubble dynamics,” Phys. Fluids 35, 033323 (2023)]. Additionally, the dependence of the pressure signals in the flow field on γ is investigated. The peak pressure, impulse, and energy dissipation in the UNDEX are investigated.

Experimental Study on Three-Dimensional Bubble Rising Behaviours by Virtual Stereo Vision

This study addresses the measurement of three-dimensional (3D) bubble rising behaviour in still water with bubble equivalent diameters ranging from 2.61 mm to 5.11 mm using high-speed imaging and virtual stereo vision technology. The bubble shape, 3D trajectory/velocity, displacement angular frequency and terminal velocity of bubbles are analysed. The bubble equivalent diameter is obtained by the elliptic volume method. The bubbles are divided into small and large bubbles with a critical equivalent diameter of 4.49 mm, according to whether they are accompanied by deformation. The small bubbles (deq<4.49 mm) are spherical or ellipsoid, while the large bubbles (deq≥4.49 mm) exhibit ellipsoid, mushroom and hat shapes. The 3D trajectory is obtained by 3D reconstruction of bubble centroid coordinates. The rising trajectory of small bubbles shows 3D spiral motion, while the pitch increases gradually with the increase in the equivalent diameter. The trajectory of large bubbles is a two-dimensional (2D) zigzag. The bubble displacement curves in x- and z-directions are evaluated with third-order Fourier fitting. The results show that the bubble displacement frequency in the x and z-directions decreases with the increasing bubble diameter, and the displacement frequency in the xdirection is larger than that in the z-direction. The relative proportions of the viscous force, buoyancy, surface tension and inertial force on bubbles with different equivalent diameters are different, which leads to three trends in the vertical velocity of bubbles within the diameter range of this study. Finally, the bubble terminal velocity in still water is investigated. The terminal velocity first decreases and then increases with the increase in the equivalent diameter. The minimum value is 16.17 cm/s when the diameter of the bubble equivalent diameter is 4.49 mm. Moreover, the applicability of some classical prediction models is discussed.

An Experimental Study of Cavitation Bubble Dynamics near a Complex Wall with a Continuous Triangular Arrangement

The mechanism of cavitation cleaning of complex surfaces has received more and more attention. In the present paper, with the help of a high-speed photography experimental system, the dynamic behavior of a cavitation bubble in symmetrical positions near a complex wall with a continuous triangular arrangement is investigated. In terms of the bubble size and the initial wall–bubble distance, the non-uniform shrinkage of the bubble collapse and the movement characteristics of the bubble centroid are revealed. The main conclusions are as follows: (1) The collapse dynamic behavior of the bubble near a complex wall with a continuous triangular arrangement can be divided into three typical cases. (2) According to a large number of experimental results under different parameters, the parameter ranges corresponding to the three cases and the critical values between different cases are given. (3) The larger the bubble size is, or the smaller the initial wall–bubble distance is, the more significant the effect of the complex wall is, and the greater the movement distance towards the complex wall during the collapse stage.

Investigation on the cavitation bubble collapse and the movement characteristics near spherical particles based on Weiss theorem.

In this paper, the cavitation bubble dynamics near two spherical particles of the same size are investigated theoretically and experimentally. According to the Weiss theorem, the flow characteristics and the Kelvin impulse are obtained and supported by the sufficient experimental data. In terms of the initial bubble position, the bubble size and the distance between the two particles, the collapse morphology and the movement characteristics of the bubble are revealed in detail. The main findings include: (1) Based on a large number of experimental results, it is found that the Kelvin impulse theoretical model established in this paper can effectively predict the movement characteristics of the cavitation bubble near two particles of the same size. (2) When the initial bubble position is gradually away from the particles along the horizontal symmetry axis near two particles of the same size, the movement distance of the bubble centroid in the first period increases first and then decreases. (3) When the initial position of the bubble centroid is at the asymmetric position near the two particles, the movement direction of the bubble centroid is biased towards the particle closer to the bubble, but not towards the center of this particle.

Experimental investigation on dynamic behaviour of bubbles emerging from micro‐capillary orifice in a flow channel

AbstractThe flow phenomenon of liquid with bubbles is widespread in various industrial fields, which determines the mass transfer characteristics of the equipment. In this work, the dynamic behaviour of bubbles emerging from micro‐capillary orifice in a flow channel was studied by a visualization experiment, while the effects of gas flow rate and liquid flow rate on these processes of bubble growth, departure, and inrush were explored. The experimental results showed that one bubble formation cycle can be divided into three stages: Waiting, departure, and inrush, as well as the dynamic behaviour of bubble emerging from micro‐capillary orifice in a flow channel, were significantly affected by gas flow rate and liquid flow rate. At a higher gas flow rate, the growth time and the departure time were shorter, as well as the departure volume of the leading bubble and the inrush volume of the trailing bubble were smaller, while the transverse longitudinal ratio fluctuated more violently, and the swing amplitude of the bubble centroid was greater. With an increasing liquid flow rate, the growth time, the departure time, and the inrush time shortened, while the departure volume of the leading bubble decreased and the fluctuation of the bubble centroid weakened. These findings are conducive to improving the performance of the equipment by optimizing the design of the aerator to regulate the dynamic behaviour of bubbles.

Dynamics of cavitation bubbles near granular boundaries

We study the dynamics of a cavitation bubble near beds of sand of different grain sizes. We use high-speed imaging to observe the motion of the bubble and the sand for different values of the stand-off parameter $\gamma$ (dimensionless bubble-boundary distance) between 0.3 and 5.3. Compared with a rigid boundary, we find that a granular boundary leads to bubbles with shorter lifetimes and reduced centroid displacements. Above $\gamma \approx 1.3$ , the behaviour of the bubble is almost independent of the granularity of the sand. When the stand-off parameter lies between $0.6$ and $1.3$ , a mound of sand develops beneath the bubble, which can force the latter to assume a conical shape as it collapses. For $\gamma \lesssim 0.6$ , the bubble develops a bell-shaped form, leading to the formation of thin and surprisingly fast micro-jets ( $v_{jet} > 1000\,{\rm m}\,{\rm s}^{-1}$ ). Moreover, between $\gamma \approx 1.3$ and $\gamma \approx 0.3$ , granular jets erupt from the sand surface following the bubble collapse. We additionally develop a simple numerical model, based on the boundary integral method, to predict the dynamics of a cavitation bubble near a bed of sand, which we replace by an equivalent liquid. The simulations are remarkably consistent with experimental observations for values of $\gamma$ down to $1.3$ . We also show how the anisotropy parameter $\zeta$ , a dimensionless version of the Kelvin impulse, can be adapted for the case of a nearby bed of sand and predict the displacement of the bubble centroid for $\zeta \lesssim 0.08$ .

Theoretical investigation and experimental support for the cavitation bubble dynamics near a spherical particle based on Weiss theorem and Kelvin impulse

In the present paper, the laser-induced cavitation bubble dynamics near a fixed spherical particle is comprehensively investigated based on the Weiss theorem, the Kelvin impulse theory and the high-speed photography experiment. Firstly, the applicability range of the theoretical model in the time and the space is statistically obtained based on sufficient experimental results. Then, the in-depth theoretical analysis is carried out in terms of the liquid flow field and the bubble Kelvin impulse with the corresponding experimental results as the reasonable support. In addition, the theoretical prediction model of the bubble movement is established and experimentally fitted from the analytic expression of the Kelvin impulse. Through our research, it is found that: (1) the applicability range of the Kelvin impulse theory for the bubble near the spherical particle is approximately the dimensionless distance between the bubble and particle (γ) greater than 0.50. (2) The effect of the particle on the liquid velocity between the bubble and the particle is mainly manifested in the form of the image bubble, which always causes the liquid velocity in this region to be significantly lower than other surrounding regions. (3) The average movement velocity of the bubble centroid can be reasonably predicted by establishing a directly proportional function between the Kelvin impulse and the velocity with the relationship constant (α) equal to 3.57×10−6 ± 1.63×10−7 kg.

Dynamics of a gas bubble penetrating through porous media

Porous media have been widely used for liquid-gas separation, benefiting from the strong capillary force generated from the micro/nanoscale pores. Understanding the flow characteristics in pore scale is significant for the design of porous structure. In this study, a numerical model was established to investigate the dynamics of a bubble penetrating through porous media at the pore scale. The two-phase interface was captured using the diffuse interface method. The influence of pore shape, width, and height on the bubble deformation, velocity, and critical pressure was investigated. For the same pore size, the largest bubble centroid velocity and the highest critical pressure exist in the quadrilateral pores compared rather than in the circular or triangular pores. As the pore width decreases, both the average velocity of the bubble centroid and the critical pressure increase. However, the critical pressure is independent of the pore height. As the pore height increases, the average velocity of the bubble centroid increases. A new correlation of the critical pressure for bubble penetration has been proposed, which is a function of the shape factor, the pore width, and the bubble diameter. The findings of this work can contribute to improving the design of porous media for two-phase separation.

A numerical study of a bubble pair rising side by side in external magnetic fields

The motion of a pair of bubbles rising side by side under the influence of external magnetic fields is numerically examined. Through solving the fully three-dimensional Navier–Stokes equations, the results reveal that the bubble interactions are rather sensitive to the field direction and strength. At first, we identify that, in a hydrodynamic flow, whether the two bubbles will bounce or coalesce depends on the developments of the counter-rotating streamwise vortices during the collision. In particular, for an originally bouncing bubble pair, a streamwise magnetic field tends to promote their coalescence by weakening the strengths of the standing streamwise vortices, and such a weakening effect is caused by the asymmetric distribution of the Lorentz force in the presence of another bubble such that a torque is induced to offset the original streamwise vortices. Under a horizontal magnetic field, on the other hand, the influences are highly dependent on the angle between the bubble centroid line and the field: a transverse field or a moderate spanwise field always leads the bubble pair to coalescence while a strong spanwise field has the opposite effect. This anisotropic effect comes from the Lorentz force induced flow diffusion along the magnetic field, which not only produces two pairs of streamwise vortices at the bubble rear, but also homogenizes the pressure along the magnetic lines. As the competition between the two mechanisms varies with the magnetic direction and strength, the interaction between the bubble pair also changes. We show that the external magnetic fields control the bubble interaction through reconstructing the vortex structures, and hence the core mechanisms are identified.

Effect of a single air bubble on the collapse direction and collapse noise of a cavitation bubble

Studying the influence of a single air bubble on the noise intensity of cavitation bubble collapse has great significance for understanding the mechanism of air entrainment to alleviate cavitation in hydraulic engineering. A cavitation bubble is generated by an underwater low-voltage electric discharge device and interacts with a rising air bubble. Only the cases where the cavitation bubble centroid, air bubble centroid, and hydrophone probes are located approximately on the same horizontal line are analyzed. The results show that the roundness, size and distance of an air bubble have a very important effect on the collapse direction and collapse sound pressure of the cavitation bubble. The findings also reveal that the direction of collapse is closely related to the collapse sound pressure, while the dimensionless distance γ and dimensionless radius roundness ratio ε’ are important parameters that determine the collapse direction of the cavitation bubble.

Study on the transient characteristics of pulsation bubble near a free surface based on finite volume method and front tracking method

The pulsation bubble dynamics near a free surface have significant engineering applications. Based on the finite volume method, a front tracking method coupled with an extrapolation technique is applied to study the transient characteristics of the pulsation bubble near the free surface with the different stand-off distance parameter γ and buoyancy parameter δ (the parameters are defined in Sec. II D). By comparison, the numerical results agree well with the results from the spark-generated bubble experiment. For the cases with small δ, (i) the phenomenon that the bubble top is elongated is no longer obvious while γ > 2.0, (ii) with the decrease in γ, the bubble centroid at the minimum volume is gradually away from the free surface except for migrating upward while 0.85 < γ < 1.0, and (iii) while γ > 1.2, the free surface begins to fall with the bubble collapse after rising during the expansion stage and almost falls back to its original position while γ > 2.4. For the cases with γ = 1.0–1.13, (i) while δ > 0.2293, the jet penetrates the bubble before the bubble reaches its minimum volume, and both are contrary while δ < 0.2293, (ii) while δ > 0.4636, the free surface begins to fall with the bubble collapse after rising during the expansion stage, and (iii) the bubble is always migrating toward the free surface while δ > 0.4109. Meanwhile, the phenomena such as the inward jet formed inside the toroidal bubble, the toroidal bubble split, and the water skirt are also analyzed.

Collapsing dynamics of a laser-induced cavitation bubble near the edge of a rigid wall.

In the present paper, the collapsing dynamics of a laser-induced cavitation bubble near the edge of a rigid wall is experimentally investigated with a high-speed photography system. For a symmetrical setup, the two primary control parameters of the bubble collapsing behavior include the equivalent maximum bubble radius and the distance between the bubble and the edge of the rigid wall. Based on the bubble interface deformation during the collapsing process, three typical cases are identified for the categorization of the phenomenon with the influences of the parameters revealed. Through a quantitative analysis of the obtained high-speed photos, the motions of the bubble interface in different directions are given together with the calculations of the bubble centroid. The primary findings of the present paper could be summarized in terms of the bubble-edge distance as follows. When the bubble is close to the edge, the movement of the bubble interface near the edge will be restricted with a clear neck formation in the middle part of the bubble. For this case, the edge could delay the bubble collapsing time up to 22% of the Rayleigh collapsing time. When the bubble is of the medium distance to the edge, the differences of the expansion or shrinkage of the bubble interface among different directions will be reduced with an olive-shaped bubble formed during the collapsing process. For this range of parameters, the bubble moves rapidly toward the edge especially during the final collapsing stage. When the bubble is far away from the edge, the bubble will be a nearly spherical one.

Retardant Effects of Collapsing Dynamics of a Laser-Induced Cavitation Bubble Near a Solid Wall

In the present paper, the dynamic behavior of cavitation bubbles near a wall is experimentally investigated with a focus on the retardant effects of the wall on the collapsing dynamics of the bubble. In the present experiments, a cavitation bubble is generated by a focused laser beam with its behavior recorded through high-speed photography. During the data analysis, the influences of non-dimensional bubble–wall distance on the bubble collapsing dynamics are qualitatively and quantitatively investigated in terms of the interface evolution, the velocities of the poles, and the movement of the bubble centroid. Our results reveal that the presence of the wall could significantly affect the collapsing characteristics, leading to a dramatic difference between the moving velocities of interfaces near and away from the wall. With the decrease of the bubble–wall distance, the effects will be gradually strengthened with a rapid movement of the bubble centroid during the final collapse. Finally, a physical interpretation of the phenomenon is given based on the bubble theory, together with a rough estimation of the induced water hammer pressure by the bubble collapse.

Thermal hydraulic characteristics of unstable bubbling of direct contact condensation of steam in subcooled water

The study of direct contact condensation (DCC) of steam is important owing to the diverse range of DCC applications, including uses in power plants, heat exchangers, and steam ejectors. In this study, an experimental investigation was performed to study the thermal hydraulic characteristics of the DCC of steam in an unstable condensation regime. Deionized water was used as the working fluid obtained with the use of a reverse osmosis method. The experiments were performed with pool temperatures in the range of 70 to 92 °C ± 2 °C, with different steam mixture mass fluxes in the range of 5 and 64 kg/m2 s, and with a gas injection nozzle with an inner diameter of 9.525 mm. The pool temperature was measured using thermocouples, and the surface area of the bubble and the volume flow rate were evaluated with high-speed camera image acquisitions. Subsequently, image processing was used to obtain the heat-transfer coefficient and other thermal hydraulic characteristics, such as the bubble condensing frequency and the bubble centroid velocity. The calculated condensation heat-transfer coefficients were found to be 24.57–179.78 kW/m2⋅K. According to the experimental results at various boundary conditions, a unified correlation of the heat-transfer coefficient was identified at the bubbling frequency in the unstable condensation regime, regardless of the pool subcooling temperature and steam mass flux. It was also found that the characteristic frequency of the steam bubble can be determined based on the boundary conditions to allow the determination of the heat-transfer coefficient with the given boundary conditions.

Experimental study of influences of a particle on the collapsing dynamics of a laser-induced cavitation bubble near a solid wall

In the present paper, the collapsing dynamics of a laser-induced cavitation bubble between a spherical particle and a solid wall is fully revealed using a high-speed camera based cavitation experimental system. For the purpose of comparisons, experiments of cases without the presence of the particle are also conducted and demonstrated. Influences of several paramount parameters (including the bubble radius, the particle radius, and the relative positions among the bubble, the particle and wall) on the bubble collapsing dynamics, the motions of bubble boundaries and the positions of the bubble centroid are all investigated. Based on the directions of the micro-jets during the bubble collapse, the bubble collapsing behavior could be categorized into three cases with their primary characteristics revealed. Furthermore, the transitions among three different cases are clearly demonstrated using several examples in terms of high-speed photography. Based on a large amount of experimental data, quantitative discussions on the parameter zone of the identified three typical cases are given in terms of the three non-dimensional parameters. Generally speaking, the particle scale does not show significant influences on the bubble dynamics behavior except some special positions of the bubble.

Numerical study on the effect of the concave rigid boundaries on the cavitation intensity

In this paper, we study the motion of a cavitation bubble near a concave boundary from a theoretical perspective. To illustrate the e ect of the surface concavity of the boundary, boundary integral and nite di erence methods are utilized to investigate the more detailed process of jet formation. Bubble shapes and its lifetime, movement of the bubble centroid, pressure contours, and velocity vectors are used to demonstrate thenumerical results. The velocity of a liquid jet impacting on the far side of the bubble surface tends to increase with decreasing boundary concavity. This result suggests that higher pressures can occur when cavitation bubbles collapse near a concave boundary. With the increase of boundary concavity, the time evolutions of the bubble growth and collapse tend to increase, and the liquid jet is formed later.