Investigation of bubble breakup and coalescence in a packed-bed reactor – Part 1: A comparative study of bubble breakup and coalescence models

In a packed-bed reactor a comparative study of bubble breakup and coalescence models has been investigated to study bubble size distributions as a function of the axial location. The bubble size distributions are obtained by solving population balance equations that describe gas–liquid interactions. Each combination of bubble breakup and coalescence models is examined under two inlet flow conditions: (1) predominant bubble breakup flow and (2) predominant bubble coalescence flow. The resulting bubble size distributions, breakup and coalescence rates estimated by individual models, are qualitatively compared to each other. The change of bubble size distributions along the axial direction is also described with medians. The medians resulting from CFD analyses are compared against the experimental data. Since the predictions estimated by CFD analyses with the existing bubble breakup and coalescence models do not agree with the experimental data, a new bubble breakup and coalescence model that takes account of the geometry effects is required to describe gas–liquid interactions in a packed-bed reactor.     

Investigation of bubble breakup and coalescence in a packed-bed reactor – Part 2: Development of a new bubble breakup and coalescence model

A mechanistic model of bubble breakup and coalescence has been developed for a packed bed. Bubble breakup and coalescence models are developed for two coalescence and three breakup mechanisms by taking account of geometry effects and local flow conditions. The bubble size distribution estimated with the present bubble breakup and coalescence models are compared with the experimental data. Change of bubble size distributions along the axial direction is studied with the median bubble size. Median bubble size as a function of the axial location is estimated under two inlet flow conditions: (1) bubble breakup dominated flow and (2) bubble coalescence dominated flow. The predictions of the median bubble size with the present model result in the best among other existing bubble breakup and coalescence models. However, the prediction of the median bubble size for the bubble coalescence dominated flow is still significantly larger than the experimental data. Breakup and coalescence coefficients need to be adjusted in order to predict more accurate bubble size distributions and median bubble size for both flow conditions. For the bubble breakup dominated flow, the breakup and coalescence coefficients are found to be 0.35 and 0.4, respectively. For the bubble coalescence dominated flow, the breakup and coalescence coefficients are found to be 0.35 and 0.01, respectively.     

Bubble–wall interaction and two-phase flow parameters on a full-scale boat boundary layer

Full scale bubbly flow experiments were performed on a 6 m flat bottom survey boat, measuring the void fraction, bubble velocity and size distributions as the bubbles naturally entrained at the bow of the boat interact with the boat’s boundary layer. Double-tip sapphire optical probes capable of measuring bubbles down to 50 μm in diameter were specifically designed and built for this experiment. The probes were positioned under the hull at the bow near the bubble entrainment region and at the stern at the exit of the bottom flat plate. Motorized positioners were used to vary the probe distance to the wall from 0 to 50 mm. The experiments were performed in fresh water (Coralville Lake, IA) and salt water (Panama City Beach, FL), at varying velocities with most data analysis performed at 10, 14 and 18 knots. The results indicate that the bubbles interact significantly with the boundary layer. At low velocity in fresh water, bubble accumulation under the hull and coalescence are evident by the presence of large bubbles at the stern. At high speeds bubble breakup dominates and very small bubbles are produced near the wall. It is also observed that salt water inhibits coalescence, even at low boat speeds. The void fraction increases with speed beyond 10 knots and peaks near the wall. Bubble velocities show slip with the wall at all speeds and exhibit large RMS fluctuations, increasing near the wall.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

On the role of the lateral lift force in poly-dispersed bubbly flows

An extensive experimental database comprising air–water as well as steam-water upwards vertical pipe flows for a pressure up to 6.5 MPa was used to investigate the effect of the lateral lift force on turbulent poly-dispersed flows with medium or high gas volume fraction. It was clearly shown that the lift force plays an important role also in such flows. Several effects such as bubble coalescence and breakup as well as fast rising large bubbles which push small bubbles towards the pipe wall superpose the effect of the lift force but can be separated from this effect. The critical bubble diameter, at which the lift force changes its sign, predicted by using Tomiyama’s correlation agrees well with experimental data obtained for turbulent air–water and steam-water flows with medium and high void fraction and a broad spectrum of bubbles sizes. The values for this critical bubble diameter are confirmed by the experimental data within the frame of the uncertainty of the data. Consequences of the action of the lateral lift force on flow structures in different flow situations are discussed. From the investigations it can be concluded that the lift force including the bubble size dependent change of its sign should be considered in a proper numerical 2D or 3D-simulation on flows in which bubbles in the range of several millimeters are present.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

On the breakup of bubbles at high Reynolds numbers and subcritical Weber numbers

In this paper we propose a simplified two-dimensional model to describe some aspects of the turbulent breakage of bubbles at subcritical Weber numbers. In particular we focus on the breakup of bubbles owing to their interaction with an array of successive eddies, modeled by a train of straining flows. Our simulations show that, under certain conditions, a bubble accumulates energy due to its interaction with a sequence of turbulent structures until it eventually breaks, even if none of the eddies is sufficiently energetic to split the particle by itself. It is also shown that the different strain directions of the eddies acting on the surface of the bubble, and the resonance effect between their characteristic frequency and the natural oscillation frequency of the bubble immersed into the straining flow are the two key factors in the bubble deformation, and subsequent breakup mechanism. Moreover, the breakup patterns obtained from our simulations seem to agree qualitatively well with the experimental observations.     

Experimental Study on Bubble Movement Characteristics during Underwater Pyrotechnic Combustion

High-speed photography was used to study bubble movement characteristics during underwater pyrotechnic combustion. The results show that bubble behaviors include bubble formation at the nozzle, departure from the nozzle, bubble coalescence, and bubble breakup. Compared with cavitation bubbles and fluidization bubbles, the nozzle bubbles formed during underwater pyrotechnic combustion feature larger diameters, up to centimeters, and darker, and more irregular shapes. During large bubble coalescence, two bubbles approach each other, generate a channel for transfer of mass and heat, and finally coalesce. The bubbles contain high-temperature gases and solid residues generated during pyrotechnic combustion, which lead to non-uniform forces on the bubble surface and make the bubbles more prone to breakup. Because of the high-temperature solid grains, the surrounding liquid vaporizes to form bubbles.     

Modeling of aerated stirred tanks with shear-thinning power law liquids

Detailed simulations of aerated stirred tanks with shear-thinning power law liquids are presented. The lattice-Boltzmann scheme was used to discretize the filtered conservation equations of the liquid phase. The motion of bubbles was tracked based on the Euler–Lagrange approach with a bubble cluster concept. The collision, breakup and coalescence of bubbles were modeled as stochastic events. The predicted flow field of a single-phase stirred tank with shear-thinning power law liquid shows reasonable agreement with experimental data. For aerated systems, qualitatively similar gas holdup distribution was achieved when comparing the predicted result with experiments. Using the proposed modeling approach, it was found that a change in rheology alters the number mean diameter, Sauter diameter and the shape of bubble size distribution.     

Effects of hydrophilic particles on bubbly flow in slurry bubble column

To investigate the effects of hydrophilic particles on slurry bubble flows in a bubble column, distributions of the local gas holdup and the bubble frequency are measured using an electric conductivity probe. Particles are made of silica and their diameter is 100 μm. The particle volumetric concentration C_S is varied from 0 to 0.40. The measured data imply that the presence of particles promotes bubble coalescence. The film drainage time for two coalescing bubbles in a quasi two-dimensional bubble flow in a small vessel is also measured to quantitatively evaluate the particle effect on coalescence. A particle-effect multiplier is introduced into a coalescence efficiency model by taking into account the data of film drainage time and is implemented into a multi-fluid model. The main conclusions obtained are as follows: (1) the local gas holdup and bubble frequency in slurry bubble flows decrease with increasing the particle concentration, (2) the hydrophilic particles enhance bubble coalescence and the enhancement saturates at C_S ≃ 0.45, (3) the particle effect on coalescence is well accounted for by introducing the particle-effect multiplier to the film drainage time, and (4) the multi-fluid model can give good predictions for the distribution of the local gas holdup in the slurry bubble column.     

Modeling and computation of cavitation in vortical flow

The paper presents an investigation of Euler–Lagrangian methods for cavitating two-phase flows. The Euler–Euler methods, widely used for simulations of cavitating flows in ship technology, perform well in regions of moderate flow changes but fail in zones of strong, vortical flow. Reasons are the strong approximations of cavitation models in the Euler concept. Alternatively, Euler–Lagrangian concepts enable more detailed formulations for transport, dynamics and acoustic of discrete vapor bubbles. Test calculations are performed to study the influence of different parameters in the equations of motion and in the Rayleigh–Plesset equation for bubble dynamics. Results confirm that only Lagrangian models are able to describe correctly the bubble behavior in vortices, while Eulerian results deviate strongly. Lagrangian formulations enable additionally the determination of acoustic pressure of cavitation noise. Two-way coupling between the phases is required for large regions of the vapor phase. A new coupling concept between continuous fluid flow and discrete bubble phase is developed and demonstrated for flow through a nozzle. However, the iterative coupling between the phases via volume fractions is computationally expensive and should therefore be applied only in regions where Eulerian treatment fails. A corresponding local concept for combination with an Euler–Euler method is outlined and is in progress.     

Curvature induced flow pattern transitions in serpentine mini-channels

Experimental investigation of the phase interactions in two-phase mini-channel serpentine systems is performed with a focus on determining the effect of radius of curvature of the serpentine on two-phase flow pattern transitions. The initial formation of two-phase flow patterns in T-junction contactors and the resulting effect on the flow through serpentine geometries are studied to predict the initiation of bubble breakup and/or coalescence in planar serpentine arrangements. Bubble breakup maps are developed for each of the serpentine geometries, identifying curvature-induced shifts in the transitions between flow patterns.     

Three-dimensional CFD simulation of bubble–melt two-phase flow with air injecting and melt stirring

This paper reports on progress in developing CFD simulations of gas bubble–metallic melt turbulent flows induced by a pitched-blade impeller with an inclined shaft. Foaming process of aluminum foams, in which air is injected into molten aluminum composites and the melt is mechanical stirred by the impeller, has been investigated. A two-fluid model, incorporated with the Multiple Reference Frames (MRF) method is used to predict the three-dimensional gas–liquid flow in the foaming tank, in which a stirring shaft is positioned inclined into the melt. Locally average bubble size is also predicted by additively solving a transport equation for the bubble number density function, which accounts for effects of bubble breakup and coalescence phenomena. The computed bubble sizes are compared with experimental data from our water model measurement and reasonable agreements are obtained. Further, simulated results show that the volume averaged total and local gas fractions are generally increased with rising impeller speed and gas flow rate. The local averaged bubble size increases with increasing gas flow rate and orifice diameter and decreasing liquid viscosity, and decreases also with rising rotation speed of the impeller.     

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

In this paper we present a three‐dimensional Navier–Stokes solver for incompressible two‐phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third‐order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second‐order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first‐order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three‐dimensional results with those of quasi‐two‐dimensional and two‐dimensional simulations. This comparison clearly shows the need for full three‐dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd.     

A conservative semi‐implicit method for coupled surface–subsurface flows in regional scale

A semi‐implicit method for coupled surface–subsurface flows in regional scale is proposed and analyzed. The flow domain is assumed to have a small vertical scale as compared with the horizontal extents. Thus, after hydrostatic approximation, the simplified governing equations are derived from the Reynolds averaged Navier–Stokes equations for the surface flow and from the Darcy's law for the subsurface flow. A conservative free‐surface equation is derived from a vertical integral of the incompressibility condition and extends to the whole water column including both, the surface and the subsurface, wet domains. Numerically, the horizontal domain is covered by an unstructured orthogonal grid that may include subgrid specifications. Along the vertical direction a simple z‐layer discretization is adopted. Semi‐implicit finite difference equations for velocities and a finite volume approximation for the free‐surface equation are derived in such a fashion that, after simple manipulation, the resulting discrete free‐surface equation yields a single, well‐posed, mildly nonlinear system. This system is efficiently solved by a nested Newton‐type iterative method that yields simultaneously the pressure and a non‐negative fluid volume throughout the computational grid. The time‐step size is not restricted by stability conditions dictated by friction or surface wave speed. The resulting algorithm is simple, extremely efficient, and very accurate. Exact mass conservation is assured also in presence of wetting and drying dynamics, in pressurized flow conditions, and during free‐surface transition through the interface. A few examples illustrate the model applicability and demonstrate the effectiveness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

In this research, the co-axial coalescence of a pair of gas bubbles rising in a viscous liquid column under the effects of an external uniform magnetic field is simulated numerically. Considered fluids are dielectric, and applied magnetic field is uniform. Effects of different strengths of magnetic field on the interaction of in-line rising bubbles and coalescence between them were investigated. For numerical modeling of the problem, a computer code was developed to solve the governing equations which are continuity, Navier–Stokes equation, magnetic field equation and level set and reinitialization of level set equations. The finite volume method is used for the discretization of the continuity and momentum equations using SIMPLE scheme where the finite difference method is used to discretization of the magnetic field equations. Also a level set method is used to capture the interface of two phases. The results are compared with available numerical and experimental results in the case of no-magnetic field effect which show a good agreement. It is found that uniform magnetic field accelerates the coalescence of the bubbles in dielectric fluids and enhances the rise velocity of the coalesced bubble.     

Opposed bubbly jets at different impact angles: Jet structure and bubble properties

The structure of two colliding water jets containing small gas bubbles is studied experimentally. The effects of the separation distance between jets, as well as the orientation angle, on the spatial distribution of bubbles have been considered. Results on the global structure of the final jet and bubble properties have been obtained using a high-speed video camera, and measurements of the positions of coalescence events are presented. Jets are introduced through inclined pipes (with a diameter of 0.7 mm) into a large water tank to avoid wall effects. Inclination angle has been changed from 0° to 45° with respect to the horizontal, resulting in a 0° up to 90° impact angle between jets. Generation of bubbles is controlled by a T-junction device where a regular slug-flow is created prior to injection. Bubble sizes have been measured, and a mean diameter of around 1 mm has been obtained using high values of the liquid flow rate. In the studied range of separation distances between the bubbly jets, a more homogeneous dispersion of bubbles is created as the distance between jets is decreased and the momentum flux of each jet is increased. Higher numbers of coalescences are observed when using smaller distance between jets, and the obtained measurements revealed that the number of bubble coalescence events is reduced significantly using high values of liquid flow rates.     

Numerical simulation of shock propagation in a polydisperse bubbly liquid

The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.     

Consistent discretization for simulations of flows with moving generalized curvilinear coordinates

We develop a consistent discretization of conservative momentum and scalar transport for the numerical simulation of flow using a generalized moving curvilinear coordinate system. The formulation guarantees consistency between the discrete transport equation and the discrete mass conservation equation due to grid motion. This enables simulation of conservative transport using generalized curvilinear grids that move arbitrarily in three dimensions while maintaining the desired properties of the discrete transport equation on a stationary grid, such as constancy, conservation, and monotonicity. In addition to guaranteeing consistency for momentum and scalar transport, the formulation ensures geometric conservation and maintains the desired high‐order time accuracy of the discretization on a moving grid. Through numerical examples we show that, when the computation is carried out on a moving grid, consistency between the discretized scalar advection equation and the discretized equation for flow mass conservation due to grid motion is required in order to obtain stable and accurate results. We also demonstrate that significant errors can result when non‐consistent discretizations are employed. Copyright © 2009 John Wiley & Sons, Ltd.     

A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid

The breakup of an axisymmetric viscous jet is considered in the lubrication approximation. The discretised equations are solved on a fixed equidistant one-dimensional Eulerian grid. The governing equations are implemented in a conservative second order accurate total variation diminishing (TVD) scheme, preventing the numerical diffusivity. Singularities that occur at pinchoff and coalescence are regularised by a small modification on the surface tension. The modification is of the order of the spatial step Δx. This regularisation ensures that the solution of the presented numerical model converges to the exact solution of the breakup of a jet in the lubrication approximation. The results of the presented numerical model agree quantitatively with the analytical solution of the Rayleigh–Plateau instability, and with experimental results on the final stage of the Rayleigh–Plateau instability.