Eulerian–Lagrangian 3-D simulations of unsteady two-phase gas–liquid flow in a rectangular column by considering bubble interactions

This work discusses the development of a three-dimensional Eulerian–Lagrangian CFD model for a gas–liquid flow in a rectangular column. The model resolves the time-dependent, three-dimensional motion of small gas bubbles in a liquid to simulate the dynamic characteristics of the oscillating bubble plume. Our model incorporates drag, gravity, buoyancy, lift, pressure gradient and virtual mass forces acting on a bubble rising in a liquid, and accounts for two-way momentum coupling between the phases. We use MUSIG model that provides a framework in which the population balance method together with the break up and coalescence models can be incorporated into three-dimensional CFD calculations. We use turbulent flow to describe liquid flow field. The standard κ–ε of turbulence is selected for calculating the properties of turbulent flow. The effect of aspect ratio of the column on the flow pattern, liquid velocity and gas hold-up profiles is discussed.     

Injection de bulles en paroi d'un écoulement cisaillé visqueuxBubble injection at the wall of a viscous shear flow

Air bubble injection at the wall of a viscous shear flow is filmed using a high speed video camera. The temporal evolution of the bubbles equivalent radius and the position of their centre of mass throughout their growth are determined from image processing. The experimental results are then used to validate a model of forces acting on the bubbles during their growth and after their detachment within the limit of small bubble Reynolds numbers. To cite this article: G. Duhar, C. Colin, C. R. Mecanique 331 (2003).     

Liquid flow patterns about barbotage bubbles

This paper summarizes the results of a flow visualization study on the liquid motion around barbotage bubbles during growth and departure. Flow patterns, as well as for the first time, instantaneous velocities, are reported as a function of time and location about the bubbles. The experiments, employing the hydrogen-bubble technique and high-speed cine photography, were with: water as the liquid, air as the bubbled gas, orifice diameters of 0.116 and 0.252 cm, and different air flow rates; the two limiting cases of constant supply pressure and constant volumetric flow rate were covered. It was found that the liquid around a barbotage bubble assumes two velocity maxima, the first an outward maximum during bubble growth and the second in the opposite direction approximately at the time of bubble departure; further, liquid velocities were found to be higher close to the bubbling site. Certain differences in liquid velocities between the constant pressure and constant flow cases are explained in terms of available theoretical solutions to the bubble growth rate. Qualitative comparisons of the barbotage liquid flow patterns and those recently reported for boiling flow patterns are also presented.     

Experimental investigation of horizontal air–water bubbly-to-plug and bubbly-to-slug transition flows in a 3.81 cm ID pipe

The present study seeks to investigate horizontal bubbly-to-plug and bubbly-to-slug transition flows. The two-phase flow structures and transition mechanisms in these transition flows are studied based on experimental database established using the local four-sensor conductivity probe in a 3.81 cm inner diameter pipe. While slug flow needs to be distinguished from plug flow due to the presence of large number of small bubbles (and thus, large interfacial area concentration), both differences and similarities are observed in the evolution of interfacial structures in bubbly-to-plug and bubbly-to-slug transitions. The bubbly-to-plug transition is studied by decreasing the liquid flow rate at a fixed gas flow rate. It is found that as the liquid flow rate is lowered, bubbles pack near the top wall of the pipe due to the diminished role of turbulent mixing. As the flow rate is lowered further, bubbles begin to coalesce and form the large bubbles characteristic of plug flow. Bubble size increases while bubble velocity decreases as liquid flow rate decreases, and the profile of the bubble velocity changes its shape due to the changing interfacial structure. The bubbly-to-slug transition is investigated by increasing the gas flow rate at a fixed liquid flow rate. In this transition, gas phase becomes more uniformly distributed throughout the cross-section due to the formation of large bubbles and the increasing bubble-induced turbulence. The size of small bubbles decreases while bubble velocity increases as gas flow rate increases. The distributions of bubble size and bubble velocity become more symmetric in this transition. While differences are observed in these two transitions, similarities are also noticed. As bubbly-to-plug or bubbly-to-slug transition occurs, the formation of large elongated bubbles is observed not in the uppermost region of bubble layer, but in a lower region. At the beginning of transitions, relative differences in phase velocities near the top of the pipe cross-section to those near the pipe center become larger for both gas and liquid phases, because more densely packed bubbles introduce more resistance to both phases.     

Injection and coalescence of bubbles in a quiescent inviscid liquid

Time periodic generation and coalescence of bubbles by injection of a gas at a constant flow rate through an orifice at the bottom of a quiescent inviscid liquid is investigated numerically using a potential flow formulation. The volume of the bubbles is determined for different values of a Weber number and a Bond number. Single bubbling and different regimes of coalescence are described by these computations. The numerical results show qualitative agreement with well-known experimental results for liquids of low viscosity, suggesting that bubble interaction and coalescence following gas injection is to a large extent an inviscid phenomenon for these liquids, many aspects of which can be accounted for without recourse to wake effects or other viscosity-dependent ingredients of some current models.     

The minimum in-line coalescence height of bubbles in non-Newtonian fluid

The minimum in-line coalescence height of bubbles generated from a submerged nozzle was investigated experimentally in shear thinning non-Newtonian fluid at lower Reynolds number (2∼60). Carboxymethyl cellulose sodium (CMC) aqueous solution and carbon dioxide were used as the liquid phase and the gas phase, respectively. The process of the formation, movement and in-line coalescence of bubbles was visualized and recorded by a high-speed digital camera. The influences of bubble size, bubble generation frequency and liquid property on the minimum in-line coalescence height of bubbles were investigated by changing nozzle diameter, gas flow rate and the mass concentration of CMC aqueous solutions. For a given liquid, the generating frequency and size of bubbles increased but the minimum coalescence height of in-line bubbles decreased when the nozzle diameter and gas flow rate were increased. When the nozzle diameter and gas flow rate were fixed, the shear-thinning effect of CMC aqueous solution became stronger with increasing CMC mass concentration, which led to the increase in both the terminal rise velocity and average acceleration of the trailing bubble, consequently, the minimum in-line coalescence height of bubbles decreased. An empirical correlation for estimating the minimum in-line bubble coalescence height was proposed, the calculating values accords well with experimental data with a mean relative deviation only 7.6%.     

Bubble formation in co-fed gas–liquid flows in a rotor-stator spinning disc reactor

The gas–liquid flow in a rotor-stator spinning disc reactor, with co-feeding of gas and liquid, is studied for high gas volumetric throughflow rates and high gas/liquid volumetric flow ratios. High speed imaging and spectral analysis of pressure drop signals are employed to analyse the flow. Two mechanisms of bubble formation are observed, one due to gas overpressure leading to large irregular bubbles, and one due to liquid turbulent vortices leading to small, well-defined bubbles. The two mechanisms lead to three distinct gas dispersion regimes, distinguished by their characteristic oscillations in pressure drop. At low rotational Reynolds numbers (Re_ω < 0.4 · 10⁶), in the gas spillover regime, the gas is dispersed as large bubbles only. Above this critical Re_ω, small bubbles are sheared off as well, thus forming a heterogeneous dispersion. At sufficiently high Re_ω, depending on the gas flow rate, the gas is homogeneously dispersed as small bubbles. The maximum gas flow that can be dispersed as small bubbles is linearly proportional to the local energy dissipation rate. The understanding of the bubble formation mechanisms and pressure signature allows prediction and detection of the prevailing hydrodynamic regime in scaled up spinning disc reactors and for different reaction fluids.     

Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles

In this work, we present a numerical study to investigate the hydrodynamic characteristics of slug flow and the mechanism of slug flow induced CO₂ corrosion with and without dispersed small bubbles. The simulations are performed using the coupled model put forward by the authors in previous paper, which can deal with the multiphase flow with the gas–liquid interfaces of different length scales. A quasi slug flow, where two hypotheses are imposed, is built to approximate real slug flow. In the region ahead of the Taylor bubble and the liquid film region, the presence of dispersed small bubbles has less impacts on velocity field, because there are no non-regular intensive disturbance forces or centrifugal forces breaking the balance of the liquid and the dispersed small bubbles. In the liquid slug region, the strong centrifugal forces generated by the recirculation below the Taylor bubble lead to the effect of heterogeneity, which makes the profile of the radial liquid velocity component sharper with higher volume fraction of dispersed small bubbles. The volume fraction has a maximum value in the range of r/R = 0.5–0.6. Meanwhile, it is usually higher than 0.35, which means that larger dispersed bubbles can be formed by coalescences in this region. These calculated results are in good agreement with experimental results. The wall shear stress and the mass transfer coefficient with dispersed small bubbles are higher than those without dispersed small bubbles due to enhanced fluctuations. For short Taylor bubble length, the average mass transfer coefficient is increased when the gas or liquid superficial velocity is increased. However, there may be an inflection point at low mixture superficial velocities. For the slug with dispersed small bubbles, the product scales still cannot be damaged directly despite higher wall shear stress. In fact, the alternate wall shear stress and the pressure fluctuations perpendicular to the pipe wall with high frequency are the main cause for breaking the product scales.     

Gas dispersion in horizontal pulp-fibre-suspension flow

Dispersion of gas into pulp-suspension horizontal flow was investigated downstream of 90° tees for ranges of fibre mass concentrations (0–3.0%), superficial liquid/pulp velocities (0.5–5.0 m/s) and superficial gas velocities (0.11–0.44 m/s) based on a gas mixing index, derived from the standard deviation of cross-sectional local gas holdup obtained from electrical resistance tomography. Mixing for dilute suspensions was similar to that for water, but differed significantly for higher suspension concentrations. Mixing worsened with increasing fibre mass concentration for the bubble flow regime, likely due to dense fibre networks in the core of the pipe causing bubbles to congregate near the wall. When buoyancy was significant, gas uniformity improved with increasing pulp concentration, since robust fibre networks caused liquid/pulp slugs to flow at the top of the pipe, whereas stratified flow was approached at lower concentrations. Mixing was less dependent on superficial liquid/pulp velocity at higher pulp concentrations, due to less variation in flow regimes.     

Spray features in the near field of a flow-blurring injector investigated by high-speed visualization and time-resolved PIV

In a flow-blurring (FB) injector, atomizing air stagnates and bifurcates at the gap upstream of the injector orifice. A small portion of the air penetrates into the liquid supply line to create a turbulent two-phase flow. Pressure drop across the injector orifice causes air bubbles to expand and burst thereby disintegrating the surrounding liquid into a fine spray. In previous studies, we have demonstrated clean and stable combustion of alternative liquid fuels, such as biodiesel, straight vegetable oil and glycerol by using the FB injector without requiring fuel pre-processing or combustor hardware modification. In this study, high-speed visualization and time-resolved particle image velocimetry (PIV) techniques are employed to investigate the FB spray in the near field of the injector to delineate the underlying mechanisms of atomization. Experiments are performed using water as the liquid and air as the atomizing gas for air to liquid mass ratio of 2.0. Flow visualization at the injector exit focused on a field of view with physical dimensions of 2.3 mm × 1.4 mm at spatial resolution of 7.16 µm per pixel, exposure time of 1 µs, and image acquisition rate of 100 k frames per second. Image sequences illustrate mostly fine droplets indicating that the primary breakup by FB atomization likely occurs within the injector itself. A few larger droplets appearing mainly at the injector periphery undergo secondary breakup by Rayleigh–Taylor instabilities. Time-resolved PIV is applied to quantify the droplet dynamics in the injector near field. Plots of instantaneous, mean, and root-mean-square droplet velocities are presented to reveal the secondary breakup process. Results show that the secondary atomization to produce fine and stable spray is complete within a few diameters from the injector exit. These superior characteristics of the FB injector are attractive to achieve clean combustion of different fuels in practical systems.     

Experimental investigation of single helium bubbles rising in FLiNaK molten salt

An experimental investigation of single helium bubbles rising in a stagnant molten fluoride salt mixture was conducted in a 25.4 mm quartz tube at 600 °C and atmospheric pressure. The fluoride salt chosen for this research was the eutectic mixture of LiF-NaF-KF (46.5–11.5–42%), also known as FLiNaK. The images obtained using a high-speed camera were processed to estimate the bubble size, rising velocity, trajectory and shape. The shape of the bubble showed typical characteristics of wobbling bubble corresponding to published classifications. The trajectory of the rising bubble showed complex path oscillations and combinations of rectilinear, zig-zag and helical motion. The projected area-equivalent diameter and experimental terminal velocity varied from 5.26 to 6.23 mm and 232.35–259.57 mm/s, respectively. Several important dimensionless numbers were calculated and reported based on the experimental results, which are closely related to the phenomena involving a gas bubble rising in liquid. The measured terminal velocity was compared with the predictions of existing correlations that include the dimensionless numbers and showed reasonable agreement. The Particle Image Velocimetry (PIV) technique was applied to complement the experimental data set with high-fidelity measurements of the velocity field of the liquid molten salt surrounding the bubble. The paper presents a unique set of PIV and two-phase experimental data capturing the behavior of rising helium bubbles in molten FLiNaK and its surrounding flow field.     

Flow around a flexible cylindrical shell by a plane stream of an ideal liquid

The flow by a plane stream of an ideal liquid around a cylindrical shell of zero flexural stiffness (a soft cylindrical shell), or a gas bubble on the boundary of which forces of tension act, was studied in [1–6]. The flow around an elastic plate in a linear formulation was considered in [7, 8]. We consider the flow, around a flexible cylindrical shell which possesses a flexural stiffness and at the same time admits large displacements, by a plane system of an ideal incompressible liquid. An application of methods of the theory of functions of a complex variable leads to an effective solution of the problem. The shape of the shell, the forces in it, the forces acting on the shell, and the field of velocities of the flow of the liquid are determined.     

Direct 2D simulation of small gas bubble clusters: from the expansion step to the equilibrium state

A numerical strategy, based on an adaptive finite element method, is proposed for the direct two‐dimensional simulation of the expansion of small clusters of gas bubbles within a Newtonian liquid matrix. The velocity and pressure fields in the liquid are first defined through the Stokes equations and are subsequently extended to the gas bubbles. The liquid–gas coupling is imposed through the stress exerted on the liquid by gas pressure (ruled by an ideal gas law) and by surface tension. A level set method, combined with a mesh adaptation technique, is used to track liquid–gas interfaces. Many numerical simulations are presented. The single bubble case allows to compare the simulations to an analytical model. Simulations of the expansion of small clusters are then presented showing the interaction and evolution of the gas bubbles to an equilibrium state, involving topological rearrangements induced by Plateau's rule. Copyright © 2006 John Wiley & Sons, Ltd.     

Prediction of mono-disperse gas–liquid turbulent flow in a vertical pipe

A two-fluid model in the Eulerian–Eulerian framework has been implemented for the prediction of gas volume fraction, mean phasic velocities, and the liquid phase turbulence properties for gas–liquid upward flow in a vertical pipe. The governing two-fluid transport equations are discretized using the finite volume method and a low Reynolds number $k-\varepsilon$ model is used to predict the turbulence field for the continuous liquid phase. In the present analysis, a fully developed one-dimensional flow is considered where the gas volume fraction profile is predicted using the radial force balance for the bubble phase. The current study investigates: (1) the turbulence modulation terms which represent the effect of bubbles on the liquid phase turbulence in the k–ε transport equations; (2) the role of the bubble induced turbulent viscosity compared to turbulence generated by shear; and (3) the effect of bubble size on the radial forces which results in either a center-peak or a wall-peak in the gas volume fraction profiles. The results obtained from the current simulation are generally in good agreement with the experimental data, and somewhat improved over the predictions of some previous numerical studies.     

A numerical strategy for the direct 3D simulation of the expansion of bubbles into a molten polymer during a foaming process

In the framework of the foam process modelling, this paper presents a numerical strategy for the direct 3D simulation of the expansion of gas bubbles into a molten polymer. This expansion is due to a gas overpressure. The polymer is assumed to be incompressible and to behave as a pseudo‐plastic fluid. Each bubble is governed by a simple ideal gas law. The velocity and the pressure fields, defined in the liquid by a Stokes system, are subsequently extended to each bubble in a way of not perturbing the interface velocity. Hence, a global velocity–pressure‐mixed system is solved over the whole computational domain, thanks to a discretization based on an unstructured first‐order finite element. Since dealing with an Eulerian approach, an interface capturing method is used to follow the bubble evolution. For each bubble, a pure advection equation is solved by using a space–time discontinuous‐Galerkin method, coupled with an r‐adaptation technique. Finally, the numerical strategy is achieved by considering a global mesh expansion motion, which conserves the amount of liquid into the computational domain during the expansion. The expansion of one bubble is firstly considered, and the simulations are compared with an analytical model. The formation of a cellular structure is then investigated by considering the expansion of 64 bubbles in 2D and the expansion of 400 bubbles in 3D. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamics of two-phase downwards flows in submerged entry nozzles and its influence on the two-phase flow in the mold

Gas–liquid flows inside the submerged entry nozzle (SEN) of a slab mold and its influence in the flow field in the mold were studied using video recording, mathematical simulations and particle image velocimetry (PIV) approaches. Bubbly and annular flows in the SEN yield structurally-uncoupled and structurally coupled flows in mold, respectively. High gas loads (ratio of mass flux of gas and mass flux of liquid) at high casting rates lead to increases of bubble population and bubbles sizes due to coalescence processes whose rate exceeds that of their breakup. The presence of gas bubbles or gas layers inside the SEN lead to periodical twisting of the liquid flow that induces biased flows through both ports yielding uneven flows in the mold. A multiphase mathematical model predicts acceptably well the flow dynamics of two-phase flows inside the SEN.     

Formation of bubbles at submerged orifices - Experimental investigation and theoretical prediction

The present work reports an experimental investigation on bubble release through submerged orifices. Bubble frequency has been measured as a function of gas flow rate for three different orifice sizes at various pool heights. Needle type conductivity probe has been used for bubble count. Analysis of probe signal not only gives the bubble frequency but also indicates a transition from bubbling to jetting regime. Further, to validate the experimental observations a simple mechanistic model has been developed considering the evolution of non-spherical bubbles at the orifice mouth. Reasonable agreement between the model prediction and the experimental result has been observed.     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.