Spheroidal Bubbles Research Articles

Experimental investigation on the effect of direct contact condensation regime on thermal stratification

Direct contact condensation affects the performance of a small modular reactor with pressure suppression system. Since the heat and mass transfer varies with the condensation regimes as well as steam-water interface shapes, the identification and classification of the condensation regimes are important. The experiment of steam direct contact condensation was carried out and the corresponding condensation regimes were studied. Specifically, the experiment was studied by injecting steam vertically into a wet well with subcooled water. The physical process of steam condensation phenomenon with varying undercooling degree of wet well was recorded by high-speed camera. According to the location of the steam-water interface and the shape of the steam bubble, the four condensation regimes were studied, namely chugging, external necking, spheroidal upward bubble and T-shaped upward bubble. Besides, it is found that thermal stratification occurs in the wet well at low steam mass flux, the influence of each condensation regime on the thermal stratification of wet well was studied. The experimental results show that the internal chugging and external necking cause a large downward circulation of subcooled water, which enhance the flow mixing around the discharge tube and the bottom of the wet well. Consequently, the thermal stratification phenomenon does not happen in those condensation regimes. However, the regimes like spheroidal upward bubble and T-shaped upward bubble cause the upward circulation of subcooled water in wet well, which cause the thermal stratification. The critical Richardson number (Ri) determines the condensation regimes. Furthermore, when the Ri is smaller than 1, the condensation regime is external necking. Besides, when the Ri is greater than 1, the condensation regimes are spheroidal upward bubble and T-shaped upward bubble.

Collision rates of small solid particles with rigid spherical and spheroidal bubbles in laminar flow

The interaction and impact of solid particles from a dilute suspension with fixed spherical and deformed bubbles (i.e., oblate spheroids) with rigid interface was analysed numerically, a situation found for example in flotation or three-phase chemical reactors. The flow field about the bubbles was computed for laminar flow and the particles were considered as point masses incorporating all forces as there are drag, added mass, fluid inertia, transverse shear-lift, and gravity/buoyancy. Particle sizes were varied up to about 200 µm allowing for a wide range of interaction Stokes numbers. The impact efficiency was evaluated for a wide range of bubble Reynolds numbers and bubbles having different shape and size, as well as eccentricity and orientation. The volume equivalent diameter of the bubbles was between 2 and 4 mm. The bubble deformation was varied up to an eccentricity of 1.8 and the bubble orientation was modified until 45 degrees. The effect of different forces on the impact efficiency was studied in detail. Added mass, fluid inertia (part of the pressure term), and slip-shear transverse lift force cannot be neglected in liquid environments, especially for larger particles. The obtained results were also compared to the composite model of Schulze (1989), well established in the field of flotation. Finally, also the particle impact statistics (i.e., location and velocity) was evaluated.

Акустика и гидродинамика импакта капли: два режима излучения звуковых пакетов

The paper studies acoustic signals in two modes of merging with water in a freely falling water droplet by the matched optical and acoustic methods. Only the primary sound packet was observed in the intrusive mode at the low drop speed, when the cavity was formed with a delay in the colored wake of the inflowing liquid. Experiments demonstrated the drop speed influence on the primary signal parameters. At the high droplet speed, the cavity started to form from the moment of the initial contact. The flow pattern became more complicated, the droplet substance was distributed over the emerged cavity surface and the grown crown in the form of separate fibers forming the line and mesh structures. The falling section of the primary acoustic signal was formed by a group of pulses with the complex spectral composition. Further, one or more low-frequency sound packets were registered after the pause. Spectral portrait of the secondary packets was related to the shape of the detached gas cavity. Smooth axisymmetric cavity was radiating the monochromatic packet. The complex-shaped cavity was transforming into a gas bubble and emitting the multi-frequency signal. Duration and amplitude of the secondary sound signals were depending on the transformation rate of the separated gas cavity into a smooth spheroidal bubble. The acoustic signal parameters were changing nonmonotonically with increasing velocity of the merging drop

Control of electron beam polarization in the bubble regime of laser-wakefield acceleration

Electron beam polarization in the bubble regime of the interaction between a high-intensity laser and a longitudinally pre-polarized plasma is investigated by means of the Thomas–Bargmann–Michel–Telegdi equation. Using a test-particle model, the dependence of the accelerated electron polarization on the bubble geometry is analysed in detail. Tracking the polarization dynamics of individual electrons reveals that although the spin direction changes during both the self-injection process and acceleration phase, the former has the biggest impact. For nearly spherical bubbles, the polarization of electron beam persists after capture and acceleration in the bubble. By contrast, for aspherical bubble shapes, the electron beam becomes rapidly depolarized, and the net polarization direction can even reverse in the case of a oblate spheroidal bubble. These findings are confirmed via particle-in-cell simulations.

Trajectory Analysis of Rising Spheroidal Bubbles in a Rolling Column

The rise of spheroidal bubbles is emulated using a hexapod with periodic angular perturbations to mimic bubble paths in columns onboard seagoing vessels. Bubble trajectories are determined using high-speed camera imaging/ultrasound Doppler velocimetry in vertical, inclined, and rolling columns. The performances of the measurement techniques are compared based on the bubble rise velocity time series and frequency spectra. A hierarchy of reference frames is developed to relate the bubble velocity/acceleration components in the (non-)Galilean frames and to infer from trajectography the lift and drag forces applying to the bubble in the moving-bubble frame. Wall disruption during bubble flights in the rolling column is scrutinized using various geometric/dynamic metrics to underline the dissimilarities between near-wall and centerline bubble path oscillations. Although Coriolis, centrifugal, and Euler accelerations play roles neither on the bubble streamwise rise nor the bubble accelerations, the time-varying character of the buoyancy force brings in dynamic features to the bubble rise in a rolling column that are distinct from those observed in static inclined columns.

Path instability of a no-slip spheroidal bubble in isotropic turbulence

Path instability of a millimetric spheroidal bubble in isotropic turbulence is investigated by direct numerical simulation combined with an immersed boundary method. The zigzag frequency and the degree of obliquity of the bubble are enhanced with the strength of the background turbulence.

Dynamics of a spheroidal gas bubble near a rigid surface

Non-spherical dynamics of a bubble during its axisymmetric collapse near a planar rigid wall is considered. The liquid surrounding the bubble is ideal incompressible, its flow is potential. The pressure in the bubble is uniform, and varying with respect to adiabatic law. At the beginning of collapse, the bubble is spheroidal, the liquid is motionless. A numerical technique is applied, which is based on a stepwise method in time for calculating the bubble surface movement and on the boundary element method. The initial stage of the bubble collapse till the moment of contact between some parts of the bubble surface (i.e., till losing its one-connectedness) is considered. The effect of the ratio of the semi-axes of the spheroidal bubble and the initial thickness of the liquid layer between the bubble and the wall on the bubble shape, the pressure and velocity fields in liquid are investigated. The region of the problem parameters (the distance from the wall, the bubble non-sphericity) is outlined, in which the bubble collapses with formation of a cumulative liquid jet impacting on the bubble surface part nearest to the wall. The liquid pressures resulting from the impact are estimated.

Modeling of Turbulent Flow around Bubbles in Molten Steel

Turbulent flow around bubbles in the molten steel is predicted by using a two‐dimensional axisymmetric model. The dependence of bubble terminal velocity and bubble shape on its size is taken into account. The recirculation region is not observed for the free spherical and spheroidal bubbles, while it is found at the rear of the free spherical‐cap bubbles and the rigid bubbles. For the free spherical and spheroidal bubbles, the velocities at the rear of bubbles and at the bubble surface are raised with increasing turbulence kinetic energy. For free spherical‐cap bubbles and rigid bubbles, the wake flow is more easily formed in the weaker turbulence and the recirculation volume increases as the turbulent kinetic energy decreases.

Grain‐Displacive Gas Migration in Fine‐Grained Sediments

AbstractGas migration mechanisms control the release of gas from seafloor sediments. We study underlying phenomena using transparent sediments subjected to controlled effective stress; this experimental approach allows high‐resolution real‐time monitoring of gas migration through cohesionless granular materials under 3‐D boundary conditions. Observed migration patterns depend on the effective stress at the time of injection and the stress history. Gas migration transitions from pore invasive to grain displacive when the capillary pressure for air entry ΔPAE is greater than the effective stress σ′. This study focuses on grain‐displacive gas migration. The morphology of grain‐displacive gas bodies changes with depth as the sediment stiffness G increases and the effect of surface tension γ vanishes: spheroidal gas bubbles form in the near‐surface, faceted cavities further down, and eventually open‐mode fractures develop at depth. The gas injection pressure is proportional to the effective stress in grain‐displacive migration. Preloading and overconsolidation cause the rotation of principal stresses and gas‐driven openings align with the new minimum principal stress direction. Cyclic loading promotes the upward migration of gas‐filled openings, and there is mechanical memory of previous gas pathways in sediments.

Numerical Simulation of the Evolution of a Gas Bubble in a Liquid Near a Wall

A numerical technique based on the application of the boundary element method is proposed for studying the axially symmetric dynamics of a bubble in a liquid near a solid wall. It is assumed that the liquid is ideally incompressible and its flow is potential. The process of expansion and contraction of a spheroidal bubble is considered, including the toroidal phase of its movement. The velocity and pressure fields in the liquid surrounding the bubble are evaluated along with the shape of the bubble surface and the velocity of its displacement. The numerical convergence of the algorithm with an increase in the number of boundary elements and a refinement of the time step is shown, and comparison with the experimental and numerical results of other authors is performed. The capabilities of the technique are illustrated by solving a problem of collapse of a spheroidal bubble in water. The bublle is located a short distance from the wall.

Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

We report on a series of results provided by three-dimensional numerical simulations of nearly spheroidal bubbles freely rising and deforming in a still liquid in the regime close to the transition to path instability. These results improve upon those of recent computational studies [Cano-Lozano et al., Int. J. Multiphase Flow 51, 11 (2013); Phys. Fluids 28, 014102 (2016)] in which the neutral curve associated with this transition was obtained by considering realistic but frozen bubble shapes. Depending on the dimensionless parameters that characterize the system, various paths geometries are observed by letting an initially spherical bubble starting from rest rise under the effect of buoyancy and adjust its shape to the surrounding flow. These include the well-documented rectilinear axisymmetric, planar zigzagging, and spiraling (or helical) regimes. A flattened spiraling regime that most often eventually turns into either a planar zigzagging or a helical regime is also frequently observed. Finally, a chaotic regime in which the bubble experiences small horizontal displacements (typically one order of magnitude smaller than in the other regimes) is found to take place in a region of the parameter space where no standing eddy exists at the back of the bubble. The discovery of this regime provides evidence that path instability does not always result from a wake instability as previously believed. In each regime, we examine the characteristics of the path, bubble shape, and vortical structure in the wake, as well as their couplings. In particular, we observe that, depending on the fluctuations of the rise velocity, two different vortex shedding modes exist in the zigzagging regime, confirming earlier findings with falling spheres. The simulations also reveal that significant bubble deformations may take place along zigzagging or spiraling paths and that, under certain circumstances, they dramatically alter the wake structure. The instability thresholds that can be inferred from the computations compare favorably with experimental data provided by various sets of recent experiments guaranteeing that the bubble surface is free of surfactants.

Collapse of a spheroidal cavitation bubble near a solid wall

Dynamics of a gas bubble in a liquid near a solid wall is studied. The influence of the initial spheroidal disturbances of the bubble shape and the distance to the wall on the dynamics of the bubble–liquid system is analyzed. The pressure in the bubble is initially greater than that of the surrounding liquid. An algorithm based on the Euler scheme and the boundary element method is applied in the calculations.

A global stability approach to wake and path instabilities of nearly oblate spheroidal rising bubbles

A global Linear Stability Analysis (LSA) of the three-dimensional flow past a nearly oblate spheroidal gas bubble rising in still liquid is carried out, considering the actual bubble shape and terminal velocity obtained for various sets of Galilei (Ga) and Bond (Bo) numbers in axisymmetric numerical simulations. Hence, this study extends the stability analysis approach of Tchoufag et al. [“Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble,” Phys. Fluids 25, 054108 (2013) and “Linear instability of the path of a freely rising spheroidal bubble,” J. Fluid Mech. 751, R4 (2014)] (which considered perfectly spheroidal bubbles with an arbitrary aspect ratio) to the case of bubbles with a realistic fore-aft asymmetric shape (i.e., a flatter front and a more rounded rear). The critical curve separating stable and unstable regimes for the straight vertical path is obtained both in the (Ga,Bo) and the (Re,χ) planes, where Re is the bubble Reynolds number and χ its aspect ratio (i.e., the major-to-minor axes length ratio). This provides new insight into the effect of the shape asymmetry on the wake instability of bubbles held fixed in a uniform stream and on the path instability of freely rising bubbles, respectively. For the range of Ga and Bo explored here, we find that the flow past a bubble with a realistic shape is generally more stable than that past a perfectly spheroidal bubble with the same aspect ratio. This study also provides the first critical curve for the onset of path instability that can be compared with experimental observations. The tendencies revealed by this critical curve agree well with those displayed by available data. The quantitative agreement is excellent for O(1) Bond numbers. However, owing to two simplifying assumptions used in the LSA scheme, namely, the steadiness of the base state and the uncoupling between the bubble shape and the flow disturbances, quantitative discrepancies (up to 20%–30%) with experimental threshold values of the Galilei number remain for both small and large Bond numbers.

Deformation of a shock wave under strong compression of nonspherical bubbles

The deformation of a radial convergent shock wave appearing inside a spheroidal cavitation bubble under strong compression is studied. It is shown that the shock wave in the course of its convergence can be deformed strongly. In particular, initially the most convex parts of the contour of the surface of the shock wave in its axial cross section can first become rectilinear and then be transformed into concave regions. Along with the formation of concave regions in the contour, sharpenings appear in it. Further small rectilinear regions can be formed instead of sharpenings. In the considered cases of initially elongated and flattened bubbles, the closure of the shock wave begins in the center of the bubble, just as under the closure of a spherical shock wave in an ideal spherical bubble.

Radiation damping of an arbitrarily shaped bubble

Large encapsulated bubbles have recently been used for abating low-frequency anthropogenic underwater noise [J. Acoust. Soc. Am. 135, 1700–1708 (2014)]. The use of encapsulation allows for the possibility of bubbles that are significantly nonspherical in their equilibrium state. Strasberg [J. Acoust. Soc. Am. 25, 536–537 (1953)] investigated the resonance frequency of an ideal bubble with arbitrary shape and found that the dependence of resonance frequency on the shape of the bubble reduced to a well-known problem in electrostatics. The present work extends that analysis to include the effects of radiation damping on the oscillation of a bubble, and does so by including a loss term due to Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837–2841 (1992)] in the volume-frame dynamical equation for the bubble. An expression is given for the amplitude of the acoustic field scattered from the bubble, and it is shown that radiation damping scales as resonance frequency cubed for arbitrarily shaped bubbles having the same volume. Comparisons are made with previous work on scattering from spherical and prolate spheroidal bubbles, and various new bubble shapes are considered. [Work supported by AdBm Technologies, the ARL:UT McKinney Fellowship in Acoustics and ONR.]

Heat and mass transfer across interfaces in complex nanogeometries.

Heat and mass transfer in nanodevices depends much on the geometry due to the strong influence of curvature on interfacial properties, such as the Kapitza resistance. We present a method which combines nonequilibrium square gradient theory and nonequilibrium molecular dynamics simulations to obtain the coefficients in a curvature expansion of the interface transfer coefficients. The expansion can be used directly to describe heat and mass transfer in complex nanogeometries. As examples of complex nanogeometries, we consider an oblate spheroidal droplet, a prolate spheroidal bubble, and a toroidal bubble. Depending on the sign and magnitude of the curvature, transfer is enhanced or reduced significantly. The presented method is applicable to many types of interfaces and substances, and we expect it to contribute to the understanding and design of future nanodevices.

Mass transfer from single carbon dioxide bubbles in contaminated water in a vertical pipe

Mass transfer from single carbon dioxide bubbles rising through contaminated water in a vertical pipe of 12.5mm diameter was measured to investigate effects of surfactant. The bubble diameter was widely varied to cover various bubble shapes such as spheroidal, wobbling, cap and Taylor bubbles. The gas and liquid phases were 99.9% purity carbon dioxide and a surfactant solution made of purified water and Triton X-100. Comparison of mass transfer rates between contaminated and clean bubbles made clear that the surfactant decreases the mass transfer rates of small bubbles. The Sherwood numbers of small bubbles in the extreme cases, i.e. zero and the highest surfactant concentrations, are well correlated in terms of the bubble Reynolds number, Schmidt number and the ratio, λ, of the bubble diameter to pipe diameter. The Sherwood numbers at intermediate surfactant concentrations, however, are not well correlated using available correlations. The mass transfer rates of Taylor bubbles also decrease with increasing the surfactant concentration. They however increase with the diameter ratio and approach those of clean Taylor bubbles as λ increases. The main cause of this tendency was revealed by interface tracking simulations, i.e. the surfactant adsorbs only in the bubble tail region and the nose-to-side region is almost clean at high λ.

Linear instability of the path of a freely rising spheroidal bubble

AbstractPath and wake instabilities of buoyancy-driven oblate spheroidal bubbles with a prescribed shape rising freely in a viscous fluid otherwise at rest are studied using global stability analysis, following the technique recently developed for a coupled fluid $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}+$ body system by Tchoufag, Fabre & Magnaudet (J. Fluid Mech. vol. 740, 2014, pp. 278–311). The essential role of the wake on the path instability is evidenced by comparing the shape of the global stability diagram with that obtained in the case of a fixed bubble. However, dramatic differences are also found, since the critical curve of the coupled system mostly involves low- and high-frequency oscillating modes, whereas that of a fixed bubble only involves stationary modes. Comparison of the present predictions with results obtained through direct numerical simulation is achieved in several regimes, confirming the predictions of the linear approach but also highlighting some of its limitations when the system successively encounters several unstable modes.

Mass transfer from a bubble in a vertical pipe

Mass transfer from single carbon dioxide bubbles in vertical pipes is measured using a stereoscopic image processing method to develop a mass transfer correlation applicable to a wide range of bubble diameters in standard pipe sizes. The diameters of pipes used are 12.5, 18.2, and 25.0mm and the bubble diameter ranges from 5 to 26mm. The ratio, λ, of the bubble diameter to the pipe diameter is varied from 0.2 to 1.8, which covers various bubble shapes such as spheroidal, wobbling, cap, and Taylor bubbles. Measured Sherwood numbers, Sh, strongly depend on bubble shape, i.e., Sh of Taylor bubbles differs from that of spheroidal and wobbling bubbles. The Sherwood numbers are correlated in terms of the Peclet number Pe and λ. The applicability of the proposed correlation to long-term bubble dissolution process is examined through comparisons between measured and predicted dissolution processes. The predictions are carried out by solving mass conservation equations not only for carbon dioxide but also for nitrogen and oxygen. Good agreements are obtained in the dissolution processes for various bubble sizes and the three pipe diameters.

On the resonance frequency of an ideal arbitrarily shaped bubble

Large encapsulated bubbles have recently been described for use in abating low-frequency anthropogenic underwater noise [J. Acoust. Soc. Am. 130, 3325–3332 (2011)], and the use of encapsulation allows for the possibility of bubbles that are nonspherical in their equilibrium state. For the purpose of more accurately determining such bubbles’ resonance frequencies, a lumped-element model of the linear oscillation of an ideal, arbitrarily shaped gas bubble in an incompressible liquid is presented. The corresponding boundary-value problem required to predict the resonance frequency of the bubble is seen to be equivalent to a classic problem in electrostatics [J. Acoust. Soc. Am. 25, 536–537 (1953)]. Predictions made for the resonance frequency of prolate and oblate spheroidal bubbles using this model are tested against a finite-element model of the full acoustic scattering problem. Particular attention is then paid to the case of an ideal toroidal bubble of arbitrary thickness, and predictions made for the resonance frequency of such a bubble using the lumped-element approach are compared to a finite-element model of the full acoustic scattering problem as well as to existing approximate models for the dynamics of thin toroidal bubbles. [Work supported by AdBm Technologies, LLC and the ARL:UT McKinney Fellowship in Acoustics.]