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The singularity issue arising from the phase fraction approaching zero in multiphase flow can significantly intensify the solution difficulty and lead to nonphysical results. By employing the conservative form of momentum equations in high-phase-fraction and discontinuity regions and the phase-intensive form of momentum equations in low-phase-fraction regions, computational reliability can be assured while avoiding the singularity issue. Regarding the proposed adaptive momentum equation method, the form of momentum equations for each cell is determined by a conversion bound and a phase fraction discontinuity detector. A comparative analysis is conducted on this method and other singularity-free methods. For discontinuities of dispersed phases, an error estimation method of the conversion bound is presented through theoretical analysis. Computational results demonstrate that the discontinuity detector accurately captures discontinuities in high-phase-fraction regions while disregarding pseudo-discontinuities in low-phase-fraction regions. Compared to the conservative form corrected by the terminal velocity method, the method yields higher-quality flow fields and potentially exhibits an efficiency improvement of over 10 times. Compared to the phase-intensive form, the method benefits from the physical quantity conservation, providing higher computational reliability. When encountering discontinuities, the expected error from the error estimation method aligns well with the actual error, indicating its effectiveness. When the conversion bound is below 1/10 000 of the inlet phase fraction, the errors of the adaptive method are essentially negligible. [ABSTRACT FROM AUTHOR]

The three-dimensional motion trajectories of bubbles in liquid metal have been extensively measured under a horizontal magnetic field (HMF) using ultrasonic phased array technology. This study focuses on the case of a streamwise magnetic field (SMF). Experimental results show that the anisotropy of bubble oscillation in HMFs is not observed in the SMF. Under a weak SMF, single bubbles exhibit zigzag oscillation motion whose axis is along the streamwise direction. The oscillation frequency and amplitude decrease as the SMF intensity increases. As the SMF becomes stronger, the bubble suddenly begins to exhibit low-frequency oblique oscillations, the main axis of which deviates from the streamwise direction. Further increases in the SMF intensity produce an oblique straight-line motion, with the oblique oscillations suppressed by the magnetic field. Under the SMF, the terminal velocity of the bubbles initially increases when the magnetic interaction parameter is N < 1 , with the attenuation of the oscillation frequency being the dominant cause. However, the magnitude of velocity growth under the SMF is smaller than that in the case of an HMF. When N > 1 , the bubble terminal velocity steadily decreases and exhibits a similar trend to that under the HMF, along with an increase in the drag coefficient. [ABSTRACT FROM AUTHOR]

This study employs laboratory experiments and a fluid/solid coupled numerical model to investigate the path instability of a falling sphere near a vertical sidewall. The falling trajectory of an acrylic sphere resembles a zigzag curve when the initial gap between the sphere and the sidewall is smaller than the sphere diameter D. The maximum lateral displacement of an acrylic sphere was about 0.85D, while the steel sphere falls nearly in a rectilinear path under the same gap distance. The Reynolds number, based on the diameter and terminal velocity of the sphere, is in the range of Re = 1.88 × 104–4.16 × 104. The flow fields and forces on the falling spheres were simulated by a turbulence model and the immersed boundary (IB) method. The simulated trajectories agree with the experimental results, and the simulation results demonstrate that the periodic vortex shedding only occurs in the wall-normal direction, not in the wall-parallel direction. The terminal velocity, drag, and lateral force are all affected by the vortex shedding. The vortex-induced lateral force coefficients vary in the range of CL = −0.30–0.30, regardless of the sphere density and the initial gap. Moreover, a dimensionless force ratio between the gravitational force and vortex-induced lateral force is proposed herein to measure the effect of vortex shedding on the sphere trajectory in high Reynolds number flows. [ABSTRACT FROM AUTHOR]

This paper analyzes experimentally and numerically the steady bubble rising in water with a surfactant dissolved at very low concentrations. We explain how traces of surfactant can significantly change the bubble dynamics. The tiny surface tension variation produced by the surfactant monolayer has a negligible effect on the capillary pressure. However, this variation occurs within an extremely thin diffusive boundary layer, which produces a Marangoni stress three orders of magnitude larger than the tangential viscous stress in a surfactant-free bubble. Although the Marangoni stress is confined within the surface boundary layer, it manages to immobilize most of the bubble's south hemisphere. The increase in skin friction and the reduction of the terminal velocity cannot be attributed to the viscous stress exerted on the immobilized interface but to the stress in the diffusive surface boundary layer. The stagnant-cap approximation applies despite the small surfactant concentration considered. [ABSTRACT FROM AUTHOR]

The reduction of carbon emissions has become a critical global issue, and the use of monoethanolamine (MEA) solution for CO2 absorption is prevalent in industry. To elucidate the mass transfer mechanisms in reactive multiphase flow, we employed high-speed photography and digital image processing to examine the dynamics and mass transfer behavior of CO2 bubbles in a Hele-Shaw cell. The results indicate that as the MEA solution concentration increases, oscillations during bubble ascent diminish, and the terminal velocity decreases. Based on changes in the mass transfer coefficient, the reaction process can be segmented into a phase of intensified mass transfer, marked by a rapid decrease in bubble equivalent diameter, and a phase of deteriorating mass transfer, where the diameter stabilizes. Additionally, we introduced a dimensionless mathematical model for the Sherwood number based on experimental findings, and its reliability was confirmed. [ABSTRACT FROM AUTHOR]

Off-gas systems are implemented in molten salt reactor designs to control the release of gaseous fission products. Two-phase flow in molten salt must be studied to understand how the system will behave in comparison to traditional working fluids like water. Flow visualization experiments and particle image velocimetry measurements were performed for three argon bubble sizes injected into a co-current stream of molten salt in a natural circulation loop facility. Similar bubble sizes were injected in experiments with water to compare the bubble shape, trajectory, and wake flow behavior of the fluids. The bubble region of interest was used to calculate the equivalent diameter and terminal velocity. Results for water showed a wobbling bubble surface and less stable bubble trajectory due to lower surface tension and viscosity compared with molten salt. Particle image velocimetry results demonstrated the increased viscosity of salt dampens turbulent fluctuations for the smaller bubble size. For a cap bubble, turbulent fluctuations were larger and longer lasting than in results for the wake flow of an argon cap bubble in water. [ABSTRACT FROM AUTHOR]

The settling of solid particles in fluid constitutes a fundamental and crucial aspect with applications spanning various natural phenomena and engineering processes, including sediment transport and wastewater treatments. This paper delves into an experimental investigation aimed at comprehending the settling dynamics and self-organization of multiple spherical particles settling side by side at intermediate Reynolds numbers. The study employs an electromagnetic release device, previously developed for controlled settling of particles under gravity, ensuring simultaneous release with zero initial rotation and velocity. This research captures settling trajectories and provides insight into the flow fields surrounding particles by utilizing particle tracking and particle image velocimetry. The experiments systematically investigate the influence of the settling patterns, the flow fields, the velocities of particles, and their dependence on Reynolds number Re (Re = 52–258), the number of particles n (n = 3–8), as well as the initial spacing between particles l0* (l0* = 0–2). The results consistently reveal a left–right symmetry about the centerline in settling patterns, flow fields, and particle rotations across all values of n, l0*, and Re. The final settling pattern exhibits distinct shapes dependent on l0*: a "V" or "M" shape for l0* < 0.2, a "concave-downward" shape for 0.2 < l0* < 2, and a "straight-line" shape for l0* ≥ 2. The lateral spread of particles increases with time, particularly pronounced with smaller l0* and larger Re, attributed to strong repulsive forces between neighboring particles. Correspondingly, the maximum of horizontal velocities reduces from outside to inside and increases with decreasing l0* and increasing Re. The inner vortices are smaller than the outer vortices, which causes the lateral spread. The vertical spread increases with n but remains insensitive to Re. The average terminal settling velocities for all particles in the array are consistently smaller than those for single particles, as a portion of kinetic energy contributes to horizontal motions. [ABSTRACT FROM AUTHOR]

The onset of secondary wake instability is generally predicted via experiments, linear stability analysis, and three-dimensional direct numerical simulations. The current work stems from an open question that is very intriguing and fundamental: Can the upper bound of a two-dimensional flow be predicted purely on the basis of two-dimensional computational results? It is found that spatial distribution of a field variable, i.e., streamwise velocity in the vortex formation region, aids in determining the upper limit of a two-dimensional flow regime of a symmetric object. The vortex formation length attains its least value at the second critical Reynolds number. In addition, streamwise extents of mean wake and vortex formation region along wake axis become the same. Under this circumstance, the streamwise velocity at the terminal point of vortex formation region is such that its mean value vanishes while intensity of fluctuations or corresponding Reynolds stress becomes the maximum. The predicted values of critical Reynolds numbers for circular, square, and diamond cross sections exhibit excellent agreement with the results available in the literature. [ABSTRACT FROM AUTHOR]

The dynamics of perforated disks falling freely in a large expanse of viscous fluid at rest is investigated numerically. This complex fluid–structure interaction is solved via large eddy simulation. This numerical algorithm is verified and validated with available experimental results. The influence of Archimedes number expressing the ratio between the gravity-buoyancy and viscosity effects is discussed thoroughly, including kinematics and dynamics. Two critical Archimedes numbers are identified, A r cr 1 ≈ 450 and A r cr 2 ≈ 950 , respectively. At these two critical Archimedes numbers, both kinematic and dynamic variables change trends. In this paper, we focus on the statistics of free-falling perforated disks. With the Archimedes number Ar increasing, the average angle of attack ⟨ AoA ⟩ and descent velocity ⟨ U z ⟩ decrease gradually, and they arrive at a fixed value finally (here, ⟨ · ⟩ represents a time-average result); On the contrary, the other kinetic variables change violently when Ar is around 900, for example, terminal velocity ⟨ U t ⟩ . Additionally, phase differences of kinematic and dynamic variables are analyzed. A constant phase difference between the nutation angle θ and normal force FN is identified, about 66 ° , which is independent of Ar. Vortex structures are visualized using Q-criterion, and triangular vortex is omnipresent around holes. During the descent, a helical vortex always attaches to the perforated disk outer edge. With Ar increasing, complex vortex interaction appears, for example, merging and stretching. Some unusual behaviors in the numerical results are analyzed from the perspective of wake dynamics. [ABSTRACT FROM AUTHOR]

We use a novel experimental setup to obtain the vertical velocity and acceleration statistics of snowflakes settling in atmospheric surface-layer turbulence, for Taylor microscale Reynolds numbers (R e λ ) between 400 and 67 000, Stokes numbers (St) between 0.12 and 3.50, and a broad range of snowflake habits. Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of St. Ensemble-averaged snowflake root mean square (rms) accelerations scale nearly linearly with St. Normalized by the rms value, the acceleration distribution is nearly exponential, with a scaling factor for the (exponent) of −3/2 that is independent of R e λ and St; kurtosis scales with R e λ , albeit weakly compared to fluid tracers in turbulence; gravitational drift with sweeping is observed for St < 1. Surprisingly, the same exponential distribution describes a pseudo-acceleration calculated from fluctuations of snowflake terminal fall speed in still air. This equivalence suggests an underlying connection between how turbulence determines the trajectories of particles and the microphysics determining the evolution of their shapes and sizes. [ABSTRACT FROM AUTHOR]

Settling of non-spherical particles is poorly understood with previous studies having focused mainly on spherical particles. Here, a series of particle-resolved direct numerical simulations are conducted using FLOW-3D (commercial computational fluid dynamics software) for spheres and five regular, non-spherical shapes of sediment particles, i.e., prolate spheroid, oblate spheroid, cylinder, disk, and cube. The Galileo number varies from 0.248 to 360, and the particle Reynolds number R e p ranges from 0.002 77 to 562. The results show that a non-spherical particle may experience larger drag and, consequently, attain a lower terminal velocity than an equivalent sphere. If R e p is sufficiently small, the terminal velocity is less affected by particle shape as characterized by the particle aspect ratio. For relatively large R e p , the shape effect (represented by the Corey shape factor) becomes more significant. Empirical correlations are derived for the dimensionless characteristic time t 95 ∗ and displacement s 95 ∗ of particle settling, which show that t 95 ∗ remains constant in the Stokes regime (R e p < 1) and decreases with increasing R e p in the intermediate regime (1 ≤ R e p < 103), whereas s 95 ∗ increases progressively with increasing R e p over the simulated range. It is also found that in the Stokes regime, particle orientation remains essentially unchanged during settling, and so the terminal velocity is governed by the initial orientation. In the intermediate regime, a particle provisionally settling at an unstable orientation self-readjusts to a stable equilibrium state, such that the effect of initial orientation on the terminal velocity is negligible. Moreover, an unstable initial orientation can enhance the vertical displacement and may promote vortex shedding. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study on air-bubble entrainment in quiescent water by translating circular turbulent jets. The jet diameters, plunging heights, impact velocities, and translating velocities were varied during the experiments to investigate their relative effect on the bubble characteristics. The experimental observations reveal that the jet translation affects the air bubble entrainment mechanism and the distribution of bubble size. A rotating cavity forms around the plunging jet due to the translation of the jet. Depending on the translating velocity, the air bubble emanates from the cusp of the cavity and the downstream water surface meniscus with the jet. The bubble swarm produced by the translating jet exhibits vortex shedding with Strouhal numbers between 0.22 and 0.27, comparable to a circular cylinder in cross-flow. The peak of the bubble size distribution varies between 0.5 and 1.5 mm, while the Sauter mean diameter varies between 1.8 and 2.8 mm. The maximum penetration depth of bubbles is found to be a function of the jet impact to translating velocity ratio, and the Capillary number of the air–water interface. The spatial distribution of bubbles along the plume cross section exhibits Gaussian distributions. Finally, the terminal rising velocity of the bubbles shows no obvious effect of the jet translation. [ABSTRACT FROM AUTHOR]

The experimental investigation of the wall effect on the cluster particle settling in the Newtonian and non-Newtonian fluid medium is carried out in three different diameter flow channels. The cluster usually forms during the sedimentation of particles in a fluid medium, so it becomes necessary to study the behavior of the cluster particles. Different cluster particles are considered depending on the number of spheres (N) attached to the cluster and the cluster's shape. The present experiment covers the following range of conditions: 0.05 ≤ deq/D ≤ 0.24, 2 ≤ N ≤ 7, 0.64 ≤ n ≤ 1, and 0.14 ≤ K ≤ 1.81. The results reveal that the terminal velocity varies with the blockage ratio (deq/D), N, and cluster shape. For a particular deq/D ratio and the same N, the terminal velocity of polyhedron particles is high compared to the planar and chain shape particles. The blockage ratio and the Reynolds number affect the wall factor of the cluster particles. However, from the experiment, it is observed that the wall effect also depends on the orientation of the particles. The impact of the wall on the cluster particle is high in Newtonian fluid when compared to cluster particles in non-Newtonian fluid. The present work additionally investigates the influence of drag on cluster particles in the presence and absence of the wall effect. The numerical relationships are developed to predict experimental results in Newtonian and non-Newtonian fluid mediums. [ABSTRACT FROM AUTHOR]

Some plant species (e.g., dandelions) have evolved plumed seeds made of thin filaments to assist their dispersal, while some other plants (e.g., maples) opt for winged seeds that autorotate after release, which could effectively prolong their descent. Inspired by these plants, in this paper, we designed a series of autorotating sub-1 mm three-dimensional passive microfliers comprising conic spiral filamentous wings and conducted computational fluid dynamics analysis on their autorotation kinetics. The effects of flier density (ρs = 0.1 × 103–2.7 × 103 kg m−3), wing number (n = 2–4), wing shape (Archimedean- or Fibonacci-spiral), and relative airflow velocity (V = 0.1–1 m s−1) were systematically investigated. We found that (1) at a given V, the terminal rotation speed (ST) is almost invariant with ρs; (2) during natural descent, a flier with larger n would fall faster yet spin slower, while the wing-tip speed is only marginally dependent on n; (3) an Archimedean flier would fall slower yet spin faster than its Fibonacci counterpart, resulting in a lift-to-drag ratio more than doubled. The angular momenta and kinetic energies during natural descent were also compared between the Archimedean and Fibonacci fliers, which could serve as metrics for flight stability. It was found that the Archimedean fliers outperform the Fibonacci counterparts in both stable flight and prolonged descent. Our results here could offer guidance for the design of miniaturized fluid-immersed (aerial/aquatic) vehicles and robots featuring rotary modules working passively or actively in low-Reynolds-number regime. [ABSTRACT FROM AUTHOR]

Understanding particle settlement in channeled fluids has wide applications, such as fine particulate matter, coronavirus particle transport, and the migration of solid particles in water. Various factors have been investigated but few studies have acknowledged the channel's effect on settlement dynamics. This study developed a coupled interpolated bounce-back lattice Boltzmann-discrete element model and examined how a channel's width affects particle settlement. A factor k denoting the ratio of the channel's width and the particle diameter was defined. The terminal settling velocity for a single particle is inversely proportional to k, and the time that the particle takes to reach the terminal velocity is positively related to k. When k is greater than 15, the channel width's effects are negligible. For dual particles of the same size, the drafting-kissing-tumbling (DKT) process occurs infinitely in a periodic pattern, with the two particles swapping positions and settling around the channel's centerline. The smaller the k, the sooner the DKT process occurs. The particles collide with the channel wall when k <= 10. For dual particles of different sizes, the DKT process occurs once so that the bigger particle leads the settlement. Both particles settle along the channel's centerline in a steady state. The bigger the k, the bigger the difference in their terminal settling velocities until k = 15. The small particle collides with the channel wall if released under the big particle when k = 6. The findings of this study are expected to inform channeling or pipeline design in relevant engineering practices. [ABSTRACT FROM AUTHOR]

An in-depth analysis of the kinetics of the collision between freely rising oil droplets in water in the range of Re = 4.64–463.3 was carried out to understand the physical mechanism and detailed kinetics of the interaction between the oil droplets and wall. The results show that when oil droplets with Re ≥ 27.8 hit the wall vertically at terminal velocities, a "dimple-like" water film is formed near the wall, which significantly affects the pressure distribution within the water film, the oil–water interfacial shear force, and forces on oil droplet. A coupled model describing water film thickness and pressure accurately captures the kinetic behavior of water film drainage near the wall. The film-induced force based on lubrication theory can reasonably predict the motion trajectory of oil droplets near the wall and dominate the motion of oil droplets colliding with the wall. The motion phase diagram with (Re, We) as the control parameter was established to quickly identify the droplet motion rule under different liquid–liquid density ratios. [ABSTRACT FROM AUTHOR]

Adding a small amount of surfactant to a gas–liquid two-phase flow can markedly change the dynamic behavior of its bubbles. In this study, the lateral motion of a single bubble (deq = 1.99–3.33 mm, Reb = 200–420) contaminated by surfactant and rising in a linear shear flow is experimentally studied. Sodium dodecyl sulfate (SDS) is chosen as the surfactant with concentrations ranging from 10 to 50 ppm. A curved screen is used to generate a stable linear shear flow, and particle image velocimetry is used to measure the quality of the flow field. Bubble motion parameters, including trajectory, aspect ratio, instantaneous velocity, and terminal velocity, are captured using the shadow method with charge-coupled device cameras. The lift coefficient C L is obtained by a quasi-steady-state analysis. The results show that the presence of surfactant inhibits the lateral migration of bubbles rising in a shear flow and that increasing the SDS concentration and bubble equivalent diameter strengthens this inhibition effect. That is, the C L and the net lateral migration distance decreased with SDS concentration and bubble equivalent diameter. In addition, the variation trends of the quasi-steady drag coefficient, bubble terminal velocity, and bubble oscillation frequency with bubble equivalent diameter and SDS concentration also were analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the behaviors of single bubble in shear-thinning viscoelastic fluids were investigated using OpenFOAM. The volume-of-fluid method was used to capture the interface, and the Giesekus model was adopted for describing the rheological behaviors of shear-thinning viscoelastic fluids. The bubble cusp, negative wake, and velocity jump phenomenons in viscoelastic fluids were obtained, and the effects of wall effect, mobility factor α, and Weissenberg number (Wi) on bubble behaviors were investigated. The results showed that the viscoelastic stress is the main reason for the formation of bubble cusp, the relaxation of polymer macromolecules leads to the formation of negative wake, and the negative wake may be the main reason for the velocity jump. The open angle θ of the negative wake decreases and the distribution region in the vertical direction increases with the increasing Reynolds numbers (Re). In addition, the magnitude of the maximum negative velocity increases with Re and appears further away from the bubble cusp. Moreover, decreasing the wall effect can accelerate the formation of viscoelastic stress and make the bubble cusp appear earlier. As the mobility factor α increases, the viscosity and viscoelastic stress of the fluid near the bubble decrease; this causes the terminal velocity of the bubble to increase. As the Wi increases, both the maximum velocity and terminal velocity of the bubble increase, and the time lag occur. The viscoelastic stress τyy has a longer linear distribution at the tail of the bubble with the increase in Wi. [ABSTRACT FROM AUTHOR]

A single-winged maple seed (samara) is dispersed laterally by a crosswind in contrast to simply descending straight down (zero dispersion) in quiescent air. This article presents the general kinematic response of a particular type of samaras (Acer buergerianum) in stable autorotation to the disturbance of a concentrated crosswind (simulated via slot jet) with the crosswind strength varied distinctively from weak to strong. A relatively weak crosswind slower than the tip velocity of the stably autorotating samara causes only damped undulations of its descent trajectory. In contrast, we demonstrate that the samara exhibits a bi-modal response when disturbed by a relatively strong crosswind (velocity greater than samara tip velocity). The strong crosswind enables the samara either to float laterally with the crosswind or drop-out through the crosswind with the switching of its rotational direction. Regardless of crosswind strength, stable autorotation is re-established after the samara leaves the crosswind zone, albeit accompanied by large-scale undulations in its descent trajectory. More importantly, before landing, the samara regains its original terminal descent velocity achieved in quiescent air. [ABSTRACT FROM AUTHOR]

In this study, a computational fluid dynamics simulation was used to study single bubble flow in liquid metal. Until now, bubble trajectory and shape [Mougin, G. and Magnaudet, J., "Path instability of a rising bubble," Phys. Rev. Lett. 88, 014502 (2002)] stability problems in liquid metal have only been insufficiently analyzed in the literature. Because of the difficulty of such an experimental validation, no universal correlations on terminal velocity, shape aspect ratio, and drag force coefficient have been produced to date. The existing bubble shape parameter and terminal velocity correlations with dimensionless numbers are still debatable, mostly because experimental validation is very challenging. The objective of this study was to develop new correlations between bubble stability and bubble deformation in liquid metals. An in-house code, PSI-BOIL, has been used for the simulations. A single bubble rising in a quiescent liquid has been simulated for three different sets of materials (nitrogen+mercury, argon+GaInSn, and argon+steel). The obtained results suggest that shape instability phenomena take place in the bubble dynamics in liquid metals for Eötvös numbers >1.7. Small bubbles (Eo < 1.7) maintain a stable ellipsoidal shape, while the shape and velocity of larger bubbles (Eo > 1.7) tend to oscillate with bubbles rising via non-rectilinear trajectories. The inviscid approximation works well for bubbles in liquid metals. It has been confirmed that the dynamics and the shape of small bubbles (Eo < 1.7) in liquid metals are only controlled by the Weber number. [ABSTRACT FROM AUTHOR]

In this work, we proposed a facile underwater air cavity generation strategy based on rough microstructured spheres and explored its water entry dynamics and drag reduction characteristics. Under the assistance of microstructures, the three-phase contact line is pinned near the sphere equator and inhibits the wetting of the liquid film along the sphere surface, so that leading the formation of air cavity. The water entry process is mainly divided into four stages: flow formation, cavity opening and stretching, cavity closure and entrapment, and cavity collapse. With the Froude number Fr, the pinch-off depth of air cavity obviously increases, and the pinch-off time is also delayed, which contributes to the formation of a longer bottom air cavity. In addition, the spheres with a larger impact velocity would fall faster in water during the initial falling period, while the terminal velocities are nearly the same for all the spheres when they are in a stable falling period. It is worth noting that for a same sphere, the larger impact velocity could not only contribute to the formation of a longer air cavity but also makes the generated air cavity keep in a stable and streamlined shape at different underwater depth, which is vitally important for achieving continuous drag reduction. Finally, we demonstrated numerically that the stable streamlined sphere-in-cavity structure could reduce the hydrodynamic resistance levels up to 91.3% at Re ∼ 3.12 × 104, which is related to the boundary slip caused by an air layer trapped in the microstructures. [ABSTRACT FROM AUTHOR]

We report the characteristics of Rayleigh–Taylor instabilities (RTI) occurring at the interface between a suspension of granular particles and a clear fluid. The time evolution of these instabilities is studied numerically using coupled lattice Boltzmann and discrete element methods with a focus on the overall growth rate ( σ ¯ ) of the instabilities and their average wave number ( k ¯ ). Special attention is paid to the effects of two parameters, the solid fraction (0.10 ≤ ϕ 0 ≤ 0.40) of the granular suspension and the solid-to-fluid density ratio (1.5 ≤ R ≤ 2.7). Perturbations at the interface are observed to undergo a period of linear growth, the duration of which decreases with ϕ 0 and scales with the particle shear time d / w ∞ , where d is the particle diameter and w ∞ is the terminal velocity. For ϕ 0 > 0.10 , the transition from linear to nonlinear growth occurs when the characteristic steepness of the perturbations is around 29%. At this transition, the average wave number is approximately 0.67 d − 1 for ϕ 0 > 0.10 and appears independent of R. For a given ϕ 0 , the growth rate is found to be inversely proportional to the particle shear time, i.e., σ ¯ ∝ (d / w ∞) − 1 ; at a given R , σ ¯ increases monotonically with ϕ 0 , largely consistent with a linear stability analysis (LSA) in which the granular suspension is approximated as a continuum. These results reveal the relevance of the timescale d / w ∞ to the evolution of interfacial granular RTI, highlight the various effects of ϕ 0 and R on these instabilities, and demonstrate modest applicability of the continuum-based LSA for the particle-laden problem. [ABSTRACT FROM AUTHOR]

We investigate the flow characteristics and kinetic behaviors of particles in turbulent Rayleigh–Bénard convection particulate flows. Direct numerical simulations combined with a Lagrangian point-particle strategy were carried out in the range of Stokes numbers 2 × 10 − 4 ≤ S t L ≤ 7.3 × 10 − 2 for Rayleigh numbers from 2 × 10 6 to 10 8 at the Prandtl number P r = 0.678. A two-way coupling model is employed in which the momentum exchange between the dispersed particles and the carrier fluid is taken fully into account. Based on various patterns of particle motion, we find three transport modes of inertial particles which are labeled as the circling transport (CCT) mode, the channel transport (CNT) mode, and the downpour transport (DPT) mode, respectively. These modes can switch to each other when Stokes numbers and Rayleigh numbers vary and exhibit different effects of particle motions on the flow field and heat transfer. For the CCT and DPT modes, compared with the CNT, a weakening alteration of flow structures and thermal plumes leads to no significant effect on the transport of momentum and heat. For the CNT mode, a pronounced effect of particles on enhancements of the turbulent momentum transport and heat transfer relates to the strong interaction between the particle clusters and the chaotic structures of eddies. What is more, the particles tend to homogeneously distribute for the CCT and DPT modes, although the particles exhibit different transport states. As for the CNT mode, under both preferential sweeping and centrifugal effects, particles accumulate into clusters that hover toward the region of high strain rate and the edges of eddies. We found that the averaged particle settling speeds are almost proportional to the Stokes number. The particle settling speeds are larger than the terminal velocity of Stokesian particles for the CCT and CNT modes as particles tend to settle in the downward fluid. In contrast, it becomes smaller than the terminal velocity for the DPT mode due to the drag of the upward fluid. [ABSTRACT FROM AUTHOR]

We investigate numerically the dynamics of freely rising gas bubbles driven by buoyancy at low Reynolds numbers, focusing on two distinct characteristics: the clustering morphology and the probability density functions (p.d.f.) of the velocity fluctuations for bubbles. A modified Volume-of-fluid (VOF) method is implemented in our direct numerical simulations to circumvent the nonphysical coalescence between bubbles. Four values of the gas fraction are studied: 5%, 10%, 15%, and 20%. The Eötvös number and the Galileo number are fixed at Eo = 2 and Ga = 855, respectively. For a single rising bubble, the Reynolds number according to the terminal velocity and the bubble diameter is around 27, displaying an ellipsoidal shape. For a swarm of bubbles, both irregular and regular clustering configurations are observed in our numerical simulations as we vary the gas fraction, which can only be realized at high Reynolds numbers in the previous experiments due to the low gas fraction limit. Moreover, we find that the p.d.f.s for bubble velocity fluctuations exhibit distinctly different behavior from the high Reynolds number experiments. The horizontal components for these p.d.f.s approach Gaussian distributions only when the gas fraction is high, i.e., α = 15 % and 20%. It suggests that the strong bubble–bubble interaction through their flow wakes is an efficient way to trigger the flow into turbulent states. [ABSTRACT FROM AUTHOR]

Despite the large effort devoted to the study of single bubbles rising in a stagnant liquid, the complex phenomena involved have resulted in a large scatter in the terminal velocity. Providing new experimental data where the statistical uncertainty is thoroughly evaluated is therefore necessary. Single bubble experiments were conducted in a tall vertical column containing stagnant liquid at ambient conditions. To track the bubbles over the spatial range, high-speed cameras were mounted on a linear unit drive. The tall column allowed us to study the effect of hydrostatic pressure and late developed bubble dynamics on the bubble motion. The bubble properties, i.e., the bubble velocity, size, shape, and trajectory, were evaluated using an image analysis processing method. The analysis includes a quantitative evaluation of important parameters involved in the handling of the raw data. Several of the existing correlations for the terminal velocity were validated against the experimental data. The data are well predicted by the correlation proposed by Tomiyama et al. ["Terminal velocity of single bubbles in surface tension force dominant regime," Int. J. Multiphase Flow 28, 1497–1519 (2002)]. The uncertainty in the experimental data has been emphasized, providing a quantitative evaluation based on several statistical methods. The number of experimental events necessary to obtain statistical significance was evaluated using a 95% confidence interval. Satisfying precision is found to be fulfilled for 10–15 bubble rise events. For bubbles of comparable size, the statistically significant terminal velocity data were found to exhibit a small scatter. [ABSTRACT FROM AUTHOR]

In this paper, direct numerical simulations (DNS) are performed to investigate the inline rise of a pair of three-dimensional (3D) air bubbles in a viscoelastic liquid using the volume-of-fluid approach with an adaptive mesh refinement technique. The exponential Phan-Thien–Tanner model is used as the non-linear viscoelastic constitutive equation for the liquid. The numerical model has been validated by comparison with previously published results, including the terminal velocity jump discontinuity of an isolated bubble rising in a viscoelastic fluid, when its volume exceeds a certain critical value. Focusing on the inline rising bubble pair in such a viscoelastic medium with different configurations, we found that the wake of the small leading bubble attracts a larger trailing bubble, whereas for a supercritical bubble in front of a subcritical bubble, they tend to further separate. Before reaching a critical volume, the two subcritical bubbles remain close to each other after approaching each other, forming a stable chain. For pairs containing a supercritical trailing bubble, however, a drafting–kissing scenario occurs before the bubble–bubble coalescence. The long-range repulsion and the short-range attraction due to fluid elasticity are critical to the aforementioned bubble pair interactions. Interestingly, the terminal rise velocities of the stable bubble chain and the coalesced bubble both increase with the initial spacing. The squeezing flow near the growing bubble neck seems to delay the coalescence process. The capillary wave propagating down to the coalesced bubble tip together with the extensional flow behind the stretched bubble determines the generation of satellite microdroplets along the tail of the coalesced bubble. To the best of our knowledge, this is the first 3D DNS on a bubble pair ascending in viscoelastic fluids. [ABSTRACT FROM AUTHOR]

The concept of added (virtual) mass is applied to a vast array of unsteady fluid-flow problems; however, its origins in potential-flow theory may limit its usefulness in separated flows. A robust framework for modeling instantaneous fluid forces is proposed, named Energized Mass. The energized-mass approach is tested experimentally by acquiring the fluid kinetic-energy history around an accelerating sphere at both subcritical and supercritical terminal velocities. By tracking the energized-mass volume, the force response is shown to be related to changes in shear-layer growth as a function of acceleration moduli and Reynolds number. The energized-mass framework is then used to develop a low-order force model, requiring only body geometry and kinematics as input. An analytical expression for the instantaneous force on a sphere due to energized-mass growth is derived based on shear-layer mass flux arguments. Instantaneous forces determined experimentally, and modeled using the energized-mass approach, show strong agreement with direct force measurements. The results of this investigation thus demonstrate that the energized-mass framework provides a viable low-order modeling approach, and in tandem, can provide new insights into the origin of forces on accelerating bodies. [ABSTRACT FROM AUTHOR]

We experimentally study the dynamics of two identical air bubbles rising side-by-side in water by varying two parameters, namely, the radius of the bubble and center to center distance between them. The bubbles follow a three-dimensional spiraling motion, and their path and shape oscillations are observed in both the front and top views by using a high speed camera with a back-lit illumination and a mirror arrangement. Bubbles of different sizes are created by using a dumping cup mechanism, and the center to center distance between the two bubbles is varied by using telescopic joints. The dynamics of the two side-by-side bubbles is compared and contrasted with that of a single rising bubble. We found that the bubbles act independent of each other, like a single bubble, when the center to center distance is greater than seven times the radius of the bubbles. For similar separation distances, increasing the size of the bubbles results in a smaller terminal velocity and also lesser deviation from a spiral path due to high inertia. [ABSTRACT FROM AUTHOR]

The settling dynamics of falling spheres inside a Laponite suspension is studied. Laponite is a colloidal synthetic clay that shows physical aging in aqueous suspensions due to the spontaneous evolution of inter-particle electrostatic interactions. In our experiments, millimeter-sized steel balls are dropped in aqueous Laponite suspensions of different ages (i.e., time elapsed since sample preparation). The motion of the falling balls is captured using a high-speed camera, and the velocities of their centroids are estimated from the images. Interestingly, we observe that balls of larger diameters fail to achieve terminal velocity over the entire duration of the experiment. We propose a mathematical model that accounts for rapid structural changes (expected to be induced by the falling ball) in Laponite suspensions whose aging time scales are much slower than the time of fall of the ball. For a range of ball sizes and Laponite suspension ages, our model correctly predicts the time dependence of the ball velocity. Furthermore, fits to our model allow us to estimate the rates of destructuring of the thixotropic suspensions due to the passage of the falling ball. [ABSTRACT FROM AUTHOR]

The slip of a small bubble (SB) from the annular film of the slug/Taylor bubble (TB) is often encountered in the chemical reactors and has intrigued many researchers. A combined experimental and numerical study has been performed to investigate the interaction of the SB and the slug bubble in a rectangular column with viscous fluids. The interaction behavior of the SB depends upon its diameter, deq, and thermo-physical properties of the fluid. The SB sprints away from the slug bubble at low Morton numbers, Mo = [(ρl − ρg)gμ 4 ]/[ρ1²Ïƒ ³ ] (sprint-away regime). On the other hand, SB interacts with TB due to its lower terminal velocity at higher Mo (bubble slip regime). The SB behaves independently ahead of the TB nose but accelerates linearly into its annular film. A regime map has been proposed to differentiate between the bubble slip and the sprint-away regime. The entrapped film between TB and SB is continuously fed from the annular film and avoids the coalescence. An ad hoc pressure jump model has been proposed to explain the repulsion of SB in the annular film. Furthermore, a modified lubrication theory based model predicted the stability of the entrapped film due to interfacial velocities and curvature. [ABSTRACT FROM AUTHOR]

The behavior of the pressure along the trajectories of finite-sized nuclei in isotropic homogeneous turbulence is investigated using direct numerical simulations at Reλ = 150. The trajectories of nuclei of different sizes are computed by solving a modified Maxey–Riley equation under different buoyancy conditions. Results show that larger nuclei are more attracted to the vortex cores and spend more time at low-pressure regions than smaller nuclei. The average frequency of pressure fluctuations toward negative values also increases with size. These effects level off as the Stokes number becomes greater than 1. Buoyancy, characterized by the terminal velocity w , counteracts the attraction force toward vortex cores while simultaneously imposing an average vertical drift between the nuclei and the fluid. Computational results indicate that weak vortices, associated with moderately low pressures, lose their ability to capture finite-sized nuclei if w ≥ u′. The attraction exerted by the strongest vortices on the largest of the considered nuclei, on the other hand, can only be overcome by buoyancy if w ≥ 8u′. The quantitative results of this study are shown to have a significant impact on modeling cavitation inception in water. For this purpose, the Rayleigh–Plesset equation is solved along the nuclei trajectories with realistic sizes and turbulence intensities. The simulations predict cavitation inception at mean pressures several kPa above vapor pressure. [ABSTRACT FROM AUTHOR]

Dynamics of a single porous, rigid, two-dimensional (2D) elliptic particle settling in a narrow vertical channel filled with a Newtonian fluid is numerically studied using the lattice-Boltzmann method. The main objective of the work is to investigate the role played by the particle's permeability on its trajectory, orientation, and terminal velocity when released from the rest state with prescribed initial conditions. Assuming that the flow induced in the fluid surrounding the particle is laminar, incompressible, isothermal, and two-dimensional, numerical results could be obtained over a wide range of parameter settings suggesting that permeability can strongly affect the modes of sedimentation reported in the literature for impermeable elliptic particles provided that the particle's permeability is larger than a threshold. Above this threshold, permeability is predicted to increase the terminal velocity of the particle with its severity depending on the blockage ratio. It is also predicted that a permeable particle is less sensitive to initial orientation and position as compared with an impermeable particle. [ABSTRACT FROM AUTHOR]

Sedimentation of a single, two-dimensional, rigid, elliptic particle in a biviscous fluid contained in a finite, closed-ended channel is studied in this work using the lattice-Boltzmann method. The main objective of the work is to numerically investigate the role played by a fluid's yield stress on the trajectory, orientation, and terminal velocity of such a particle for different density and aspect ratios. Numerical results suggest that a new mode of settling might emerge for yield-stress fluids, which is nonexistent for Newtonian fluids. That is, a particle released from the rest state at the midplane with a prescribed, nonzero, inclination angle (with respect to the horizontal line) migrates toward the left side-wall (if the inclination angle is positive) soon after it is released but changes course after a short while and moves back toward the centerline where the voyage started. However, while for Newtonian fluids the particle eventually returns to the centerline and continues its free fall with a horizontal orientation, for yield-stress fluids, the particle might finally lodge at a specific distance away from the centerline and continue its fall assuming a nonhorizontal orientation. The offset position is predicted to be a function of the Bingham number and the density ratio but independent of the initial inclination angle. [ABSTRACT FROM AUTHOR]

We present an experimental study of buoyancy-driven flows of two immiscible Newtonian liquids in a vertical tube where initially the heavier and more viscous one is placed on the top of the lighter one. Flow visualization was performed using a digital camera, and inversion velocities were determined through image analysis. The influence of the governing parameters on the speed and flow regime was examined for pairs of liquids with small density differences. Two different flow regimes were observed, namely, falling drops and falling slugs. In the first regime, spherical and ellipsoidal drops are obtained, depending on the ratio between the drop and tube diameters. The falling slug regime is a core-annular flow pattern above a critical value of interfacial tension, while no flow is noticed below this critical value. The experimental results are in good agreement with model predictions from the literature. Indeed, the results showed that terminal velocity can be estimated by empirical correlations for falling spheres. [ABSTRACT FROM AUTHOR]

A force balance model has been developed to predict the terminal velocity of a submillimetric bubble as its rises in water under buoyancy. The dynamics of repeated collisions and rebounds of the bubble against a horizontal solid surface is modeled quantitatively by including forces due to buoyancy, added mass, drag, and hydrodynamic lubrication--the last arises from the drainage of water trapped in the thin film between the solid surface and the surface of the deformable bubble. The result is a selfcontained, parameter-free model that is capable of giving quantitative agreement with measured trajectories and observed collisions and rebounds against a solid surface as well as the spatio-temporal evolution of the thin film during collision as measured by interferometry. [ABSTRACT FROM AUTHOR]

We rigorously derive a formula for the terminal velocity of a small bubble in a vertically vibrated viscous incompressible liquid starting from the full Navier-Stokes equations and the exact boundary conditions at the bubble surface. This formula is derived using a perturbation analysis in which the small parameter is the nondimensional amplitude of the pressure oscillation. The analysis does not assume that the bubble remains spherical but does assume that the bubble is axisymmetric. It is shown that the bubble terminal velocity can be computed to second order while computing the full solution only to first order by applying a compatibility condition on the first-order solution. To second order, the bubble terminal velocity is shown to be the net value from an upward steady term and a rectified term that can be downward or upward. The perturbation formula depends on the vibration frequency nondimensionalized by the bubble radius and the liquid kinematic viscosity. We show that our perturbation formula links two heuristically developed formulas for the rectified component, which we denote the velocity-averaged and force-averaged formulas. Our perturbation formula reproduces the velocity-averaged formula for low frequencies and the forced-averaged formula for high frequencies and varies monotonically between these limits for intermediate frequencies. We furthermore develop a high-resolution spectral code specifically to simulate this type of bubble motion. Results from this code verify that the perturbation formula is correct for infinitesimal oscillating pressure amplitudes and suggest that it provides an upper bound for finite amplitudes of the pressure oscillation. [ABSTRACT FROM AUTHOR]

We studied the terminal velocity of a packed array of bubbles, a bubble cluster, rising in different fluids: a Newtonian fluid, an elastic fluid with nearly constant viscosity (Boger fluid), and a viscoelastic fluid with a shear dependent viscosity, for small but finite Reynolds numbers (1 × 10-4 < Re < 4). In all three cases, the cluster velocity increased with the total volume, following the same trend as single bubbles. For the case of clusters in elastic fluids, interestingly, the so-called velocity discontinuity was not observed, unlike the single bubble case. In addition to the absence of jump velocity, the clusters did not show the typical teardrop shape of large bubbles in viscoelastic fluids and the strength of the negative wake is much weaker than the one observed behind single bubbles. Dimensional analysis of the volume-velocity plots allowed us to show that, while the equivalent diameter (obtained from the total cluster volume) is the appropriate length to determine buoyancy forces and characteristic shear rates, the individual bubble size is the appropriate scale to account for surface forces. [ABSTRACT FROM AUTHOR]