Morton Number Research Articles

A numerical study on the drag law of a gas bubble using dynamic body force method

For a gas bubble rising in quiescent liquid, most previous drag force models correlate the drag coefficient Cd to dimensionless parameters such as the Reynolds number Re, the Eötvös number Eo, and the Morton number Mo. However, it is still an open question if the current models can be applied to non-buoyancy-driven bubbles in a wide range of parameters. In the present study, we investigate the effects of Reynolds number Re and Weber number We on the drag force coefficient Cd of bubbly flows. To obtain a converged drag force, a dynamic body force model is developed, which constraints the bubble at a fixed position. A large number of numerical simulations are carried out, spanning in the (We, Re) parametric space. The correlations of Cd to We and Re are studied, respectively. We find that for low We, as the bubble keeps spherical, its drag coefficients can be well predicted by the previous spherical bubble models. For medium–high We, when Re is low, the viscous force contributes most, and therefore, the bubble deformation or We plays an insignificant role on the drag. In contrast, when Re is high, the pressure force or shape drag becomes dominant, which is strongly dependent of We. Therefore, we can identify three different regions, spherical, We-dependent, and We-independent, in the parametric space. Finally, a new empirical drag force model for a non-buoyancy-driven bubble is proposed based on the Cd-Re and Cd-We correlations obtained by our numerical simulations. The current model is superior to the previous drag models, with predicting errors within 20%, by compared to the direct numerical simulation and experimental data. More profoundly, the current model can apply to a wider range of parameters, that is, 1≤Re≤1000 and 0≤We≤20, particularly for high We, when the bubble deformation cannot be neglected.

On peculiar behaviours at critical volumes of a three-dimensional bubble rising in viscoelastic fluids

In this paper, we carried out an investigation of the dynamics of an air bubble rising in viscoelastic liquids with increasing volumes via volume-of-fluid based direct numerical simulations (DNS) with local adaptive mesh refinement techniques. The exponential Phan-Thien Tanner (EPTT) model is adopted for describing the rheological behaviours of the shear-thinning viscoelastic fluid. The well-known jump discontinuity in the terminal rise velocity at a critical bubble volume is captured, which agrees qualitatively with the experimental observation in the literature. On this basis, the numerical simulations have been performed for different rheological properties in wider flow regimes, providing new insights into the local flow field and the stress distribution around the deformable rising bubbles. A characteristic dimensionless regime map has also been proposed to distinguish the peculiar behaviours of a bubble rising in viscoelastic fluids at different Galilei (Ga) and Eötvös (Eo) numbers. We found that at low Ga and low Eo numbers, the large elastic stresses concentrate in the small region near the bubble’s trailing end, leading to the formation of bubble cusp. The appearance of the negative wake is the main reason for the velocity jump to occur. However, for higher Ga of 10, the viscous forces become less dominating. The fluctuations of the polymeric stresses are substantially intensified with increasing bubble volume, and large bubbles experience a pulsating rising velocity with oscillation shapes. On the other hand, at intermediate Ga and high Eo of 10, the modest surface tension induces a cap with a thin skirt trailing the bubble main body at early times. Due to the polymer stretching, the strong extensional flow behind the small bubble eventually forces the bubble tail to break up. The above analyses on the bubble dynamics at constant Morton (Mo) numbers facilitate the extrapolation of the volume effects at different flow regimes and, therefore, will guide the applications in the future.

Lattice Boltzmann phase field simulations of droplet slicing

AbstractWe have performed two‐ and three‐dimensional phase field simulations using the lattice‐Boltzmann method of liquid drops rising through a continuous phase liquid under the influence of buoyancy. In their upward motion, the drops encounter a knife that is placed with the purpose of slicing the drops in two. A range of scenarios has been observed when the drop hits the knife and it has been investigated how the type of scenario depends on the dimensionless parameters governing the motion and slicing of the drop: the Eötvös number, the Morton number, and the ratio of the droplet size and the width of the knife. We studied symmetric and asymmetric encounters between drop and knife and kept track of the size distribution of the resulting fragments.

Influence of Gas Density and Plug Diameter on Plume Characteristics by Ladle Stirring

The paper presents new results concerning the influence of the gas density and porous plug diameter on the nature of liquid steel stirring with an inert gas in the ladle. The tests were carried out on a cold model of a 30t ladle using particle image velocimetry (PIV) with a high-speed camera to analyse the plume zone formed during the supply of argon and helium as a stirring gas. The similarity criteria for the investigation of stirring processes in cold model in the past were discussed and compared. The modified Morton number was used in this paper to relate the gas flow rate in the model with real objects. The presented results constitute complete documentation of the influence of the plug diameter and gas density on the size of formed gas bubbles and the velocity of gas bubbles rising in different zones of the plume, plume, and spout geometry, including the expansion angle, spout height, open eye area, and gas hold-up.

Passage of a rising bubble through a liquid‐liquid interface: A flow map for different regimes

AbstractThe passage of a rising air bubble through a stratified horizontal interface between two Newtonian liquids is studied numerically. A ternary phase‐field model has been utilized for capturing the interface between three immiscible fluids. According to the previous studies, the density, viscosity, and surface tension of the two liquids, in addition to the bubble diameter, are the effective parameters of bubble interaction with the interface. By changing these variables, three main flow patterns are identified in numerical simulations. Penetration flow regime is observed when the bubble enters the upper liquid alone and does not raise the lower liquid. Entrainment flow regime occurs when the bubble lifts some of the heavier liquid to the lighter liquid but still rises alone. If the bubble holds a film of the denser liquid when it rises in the upper liquid, envelopment flow regime takes place. A flow regime map is represented to distinguish the aforementioned flow patterns using Weber and Morton numbers and determine regime transition criteria based on these two dimensionless parameters. For Weber numbers lower than 30, or Morton numbers higher than 1.7 × 10−2, the penetration regime is observed. On the contrary, when the Weber number is higher than 65 and the Morton number is lower than 7 × 10−5, the envelopment regime occurs. The entrainment pattern happens between these ranges and two additional limiting relations of 320Mo0.18 < We < 1500Mo0.23.

Comparison among drag coefficient models of single bubbles under high and low Morton number regimes

Bubble dynamics analysis is highly dependent on drag coefficient computation, and several models have been proposed to compute it. The present study reviewed some of the correlations for the drag coefficient evaluation, and aims to compare the most successfull models available and how they fit the experimental data, spanning over several orders of Morton number regimes (-10.6⩽log10M⩽0.6), including bubbles with different geometrical shapes: spherical, ellipsoidals and cap-like bubbles. The present study categorized the correlations based on their dependency on the aspect ratio. The aspect ratio-dependent models showed great results for E>0.5, whereas for large departures from sphericity, the independent models fit well the experimental data. To tackle the shortcomings found in these models, a new hybrid correlation was proposed that showed a good compatibility with the experimental results for log10M⩽-1.5,0.1⩽Eo⩽100 and 1⩽Re⩽2000 with a maximum average difference from the experimental values for bubble terminal velocity and aspect ratio within respectively 10% and 15%.

Modeling interaction between a Taylor bubble and small bubble in a rectangular column

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−ρggμ4/ρl2σ3 (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.

Dynamics of rising bubbles in initially quiescent liquids that are later on disturbed by falling drops

Three-dimensional dynamics of rising bubbles in initially quiescent liquids that are later on disturbed by falling drops has been numerically investigated. The effects of various parameters such as Eotvos number (Eo), Morton number (M), size of the falling drop, single and multiple falling drops on the dynamics of three different cases represented as single bubble rising, inline bubbles rising and offset bubbles rising are investigated. From the results, it is observed that the final bubble rise velocity in disturbed liquid (with Eo = 38.8 and M = 9.71 × 10−4) due to the impact of falling drop with 0.01 m diameter is increased by 84.21% when compared to the rising bubble in undisturbed quiescent liquid. The same decreases with an increase in the diameter of falling drop up to 0.02 m and 0.03 m, respectively. For inline and offset bubbles, the disturbance caused by the falling drops reduces the final rise velocity by 110% and 113.4%. For Eo = 10.0 and M = 9.71 × 10−8, the low fluids internal resistance causes the bubble to rise faster and reach the liquid surface quickly. However, in the case of inline and offset rising bubbles, the bubbles reach the liquid surface even before the falling drop impacts.

On the rise characteristics of Taylor bubbles in annular piping

A three-dimensional phase-field lattice Boltzmann method has been applied to investigate the rise of Taylor bubbles within annular pipes. The approach couples the conservative phase-field model with a velocity-based lattice Boltzmann scheme. The implementation uses 27 discrete velocities to resolve both the interfacial dynamics and the hydrodynamics. To assist numerical stability for the high-density ratio, two-phase flows a weighted multiple-relaxation-time collision operator is employed. This paper makes contributions in three areas. First, the model is employed to capture the behaviour of Taylor bubbles in five combinations of vertical annular pipes, with results compared to experimental findings from the literature for air-water flows. From this, shortcomings were identified in the ability of existing correlations to accurately predict rise velocities for bubbles in various liquids. Second, the effect of pipe inclination on the rise behaviour of the bubbles was investigated. From the findings, a preliminary correlation describing the rise velocity was proposed. The first two components of the study were conducted with the Taylor bubble rising in stagnant fluid. The final component of this study imposed liquid flow in a concentric annular pipe to determine the impact of this on the bubble’s dynamics. The liquid velocity was defined through a Reynolds number based on the average inlet velocity up to an absolute value of 10. The viscosity was varied to examine Morton numbers from 2.56e-3 to 6.55e-5. To this end both co- and counter-current flow was analysed and a distribution parameter proposed to capture the liquid-gas interaction. To extend this work, future investigations will look to extend the parameter range assessed to ensure the universality of the correlations identified.

Development of closure relations for the motion of Taylor bubbles in vertical and inclined annular pipes using high-fidelity numerical modeling

This study analyses the flow of Taylor bubbles through vertical and inclined annular pipes using high-fidelity numerical modeling. A recently developed phase-field lattice Boltzmann method is employed for the investigation. This approach resolves the two-phase flow behavior by coupling the conservative Allen–Cahn equation to the Navier–Stokes hydrodynamics. This paper makes contributions in three fundamental areas relating to the flow of Taylor bubbles. First, the model is used to determine the relationship between the dimensionless parameters (Eötvös and Morton numbers) and the bubble rise velocity (Froude number). There currently exists no surrogate model for the rise of a Taylor bubble in an annular pipe that accounts for fluid properties. Instead, relations generally include the diameter of the outer and inner pipes only. This study covered Eötvös numbers between 10 and 700 and Morton numbers between 10−6 and 100. As such, the proposed correlation is applicable to concentric annular pipes within this range of parameters. An assessment of the correlation to parameters outside of this range was made; however, this was not the primary scope for the investigation. Following this, the effect of pipe inclination was introduced with the impact on rise velocity measured. A correlation between the inclination angle and the rise velocity was proposed and its performance quantified against the limited experimental data available. Finally, the high-fidelity numerical results were analyzed to provide key insights into the physical mechanisms associated with annular Taylor bubbles and the shape they form. To extend this work, future studies on the effect of pipe eccentricity, diameter ratios, and pipe fittings (e.g., elbows and risers) on the flow of Taylor bubbles will be conducted.

Dynamics of rising bubbles in gradually mixing fluids due to the effect of Rayleigh–Taylor instability

Three dimensional dynamics of rising bubbles in gradually mixing fluids due to the effect of Rayleigh-Taylor instability have been numerically investigated. The effect of various parameters such as Eotvos (Eo) number and Morton (M) number for three different cases represented as single bubble rising, inline bubbles rising and offset bubbles rising are comprehensively investigated. It is observed that, two raising bubbles either inline or offset exhibits higher terminal Reynolds number (ReT) in quiescent liquids when compared with single rising bubble. They enhances ReT by 120.22% for Eo = 38.8 and M = 9.71 × 10−4. Moreover, in gradually mixing fluids due to the presence of Rayleigh-Taylor instability, single rising bubble also exhibits higher ReT and at earlier time. In fluids with low Eo and high M values, mixing effect is very slow because of the presence of higher value of fluids internal resistance as well as high cohesive forces. This causes a delay in the formation of bubble behind the rising pre-defined bubbles. Whereas, in the opposite case, this bubble forms much quicker. But the rising pre-defined bubble breaks up and gradually vanishes off with time. Due to significant decrement in the fluids internal resistance, it is also observed that; at same Eo = 10, by decreasing the value of M from 9.71 × 10−4 to 9.71 × 10−8, the ReT value is increased by 48.84% for inline and offset bubbles. Furthermore, at same M = 9.71 × 10−4, by increasing the value of Eo from 10 to 38.8, 18.3% lower time is required for single bubble to attain higher velocity. This is due to the presence of low cohesive forces and high fluids internal resistance.

Experimental investigation of the behaviors of highly deformed bubbles produced by coaxial coalescence

In this paper, the highly deformed bubbles produced in the regime of bubbling with coalescence are studied systematically, starting from their formation up to their collapse dynamics. We investigate the bubbling dynamics by performing experiments with various liquids (ultrapure water and silicone fluids), gas flow rates (5–300 ml/min) and nozzle radii (0.18–0.55 mm). The evolution of the coalescing process is analyzed in detail, differentiating among four phases: liquid film drainage, neck formation, wave propagation along the bubble surface and bubble detachment. A phase diagram for coaxial coalescence and no coalescence is established in terms of the Weber (to describe the effects of inertia) and the Morton number numbers (to describe the effects of liquid property). Scaling arguments show that the coalescing dynamics is driven by inertia–capillary and viscosity can be neglected. We then present the interesting experimental investigation of large and elongated bubbles just after pinch-off. We deduce the dependence of the geometrical properties of these highly deformed bubbles on the bubbling conditions and a simple model is derived. Finally, we explore the dynamics of the inertial liquid jets arising from the collapse of such highly deformed bubbles. Regardless of the details of the collapse process, we propose a simple scaling law for the jet velocity and unravel the intricate roles of bubble geometry and liquid parameters.

Effects of fine particles on terminal velocities of single bubbles in a narrow channel between parallel flat plates

Effects of the presence of solid particles on the terminal velocities, VB, of single bubbles in a narrow channel were investigated. The gap thickness of the narrow channel was 3 mm. The bubble diameter, dB, was varied from 7 to 20 mm. Air, purified water and fine silica particles of 4.1 μm diameter were used for the gas, liquid and solid phases, respectively. The volume concentration of the particles, CS, was from 0.20 to 0.40. The apparent slurry viscosity, μSL, ranged from 1.7 to 3.1 mPa⋅s. The applicability of a velocity correlation proposed for bubbles in gas-liquid systems to bubbles in slurry was examined. The following conclusions were obtained under the present experimental conditions: (1) the dependence of VB on dB in slurry is similar to that in glycerol-water solutions, and the bubble Reynolds number in slurry and a glycerol-water solution of the same Morton number are almost the same for CS ≤ 0.35, and (2) the velocity correlation for gas-liquid systems is applicable to slurry with fine particles for CS ≤ 0.35 by using μSL instead of the liquid viscosity in the correlation.

Analyses and modified models for bubble shape and drag coefficient covering a wide range of working conditions

In this paper, the dynamics and dominant parameters of bubble shape deformation and drag coefficient during bubble rising were theoretically analyzed based on fundamental insights into bubble motion. Modified models for the aspect ratio and drag coefficient applying to a wide range including saturate vapor-water conditions under high pressure (6.9–15.5 MPa) were finally proposed based on theoretical analyses and comprehensive evaluations on previous correlations of aspect ratio and drag coefficient. Results showed that the combination of Weber number and Morton number can reasonably characterize the bubble shape deformation, while the combination of Reynolds number, Eötvös number and Morton number can reasonably characterize the drag coefficient. The proposed aspect ratio correlation in this paper predicts 90% of the existing experimental and numerical data within ±20% with a relative mean error of 8.2% for bubble rising in both two-component systems at atmospheric pressure and mono-component vapor-water systems at 6.9–15.5 MPa, while the proposed drag coefficient correlation predicts 93.5% of the data within ±35% with a relative mean error of 13.8% covering a wide range of 10−3 ≤ Re ≤ 105, 10−2 ≤ Eo ≤ 103 and 10−14 ≤ Mo ≤ 107.

On the force competition in bubble columns: A numerical study

Computational Fluid Dynamics (CFD) is nowadays fully accepted in engineering practice as a potential tool for the prediction of flows, conversion rates and process efficiency. The Euler/Lagrange is one of the available approaches for describing dispersed multiphase systems, for example in bubble columns. Hence, the flow field within the bubble column is computed using large eddy simulations (LES) considering full coupling with the bubble phase through momentum source terms as well as sub-grid-scale (SGS) turbulence modification by modelling bubble induced turbulence (BIT). Despite the required point-particle approximation, necessary for computing large-scale technical and industrial systems, bubble dynamics was included in the numerical modelling, through shape (eccentricity) and trajectory oscillations. The performance of the proposed bubble dynamics model is analysed in detail and it is shown that without a bubble dynamics model the bubble fluctuating velocities cannot be predicted correctly. In order to predict the bubble motion accurately it is necessary to account for all relevant acting forces in the calculations, namely, gravity/buoyancy, drag, transverse lift, added (virtual) mass, fluid inertia (part of the pressure term), Basset (history term) force and possibly modifications of these forces due to the presence of walls. Based on the state-of-the-art, instantaneous resistance coefficients for all these forces were elaborated and extended for allowing consideration of the bubble dynamic behaviour and deformation through the eccentricity. The proposed resistance coefficients do not consider any swarm effects and are therefore only applicable to bubbly systems with volume fractions of less than 5%. For the beginning clean systems with mobile bubbles are considered only which are moving in low-viscous systems such as a water-air two phase flows with small bubble Morton numbers. Most important, a lift force coefficient which is valid for such low viscous systems is applied based on recent studies. Consequently, a comprehensive and complete model is introduced for describing bubble motion in a point-particle approximation including bubble dynamics (eccentricity) and therefore using composite formulations especially for drag and transverse lift, and in addition accounting for added mass with bubble deformation and wall effects as well as the Basset force. For the regime of deformable bubbles, the resulting instantaneous resistance coefficients are extracted from bubble column simulations and compared with the mean resistance coefficients. Moreover, the local importance of all considered forces on the motion of bubbles within the bubble column was evaluated in detail in terms of bubble size, column height, radial position and Stokes number without and with bubble dynamics model. The importance of these forces and the correspondent effects on the velocity and volume fraction profiles are explored for a laboratory-scale bubble column. The influence of the bubble dynamics model and the considered interfacial forces on the predicted hydrodynamics of the laboratory bubble column is analysed for validation considering two cases with different bubble size distributions with sizes smaller than about 5 mm. Furthermore, the effect of Basset term on particle dispersion is highlighted in a turbulent pipe flow test case.

Correlating the phase settling behavior of aqueous-organic solvent systems in a centrifugal partition chromatograph

The prediction of the performance of a Centrifugal Partition Chromatography (CPC) is a difficult but desirable task. The partitioning of the sample, as well as the fluid dynamical phenomena dispersion, coalescence, and stationary phase retention have to be individually understood. Therefore, the phase settling behavior of different aqueous-organic solvent systems and with this, the dependency of the stationary phase retention in CPC was investigated in this study. On the one hand, batch settling experiments were performed, and the settling velocity of aqueous-organic solvent systems was investigated. With this it was possible to correlate the stationary phase retention in CPC in both operating modes. For descending mode operation a high settling velocity of the lower phase and for ascending mode a high settling velocity of the upper phase is needed for a stable operation and a high stationary phase retention.On the other hand, the dimensionless numbers Capillary number (Ca) and Morton number (Mo) were used to generate a universally applicable correlation for the stationary phase retention in ascending mode. It was shown, that a high stationary phase retention correlates with low values of Ca and Mo, whereas the influence of Mo is neglectable in the parameter space investigated. Within this correlation, the individual influence of each influencing parameter on the stationary phase retention was included. Moreover, this correlation was compared to descriptions for descending mode given in literature. With this it was shown that the minimal stationary phase retention is correlatable to the point of phase inversion.

Experimental study on drag coefficient of a rising bubble in the presence of rhamnolipid as a biosurfactant

Industrial processes do not often deal with a pure fluid. Impurities can affect physical properties of gas-liquid systems, resulting in change of gas bubbles velocity. Purpose of the study was to determine drag coefficient of a bubble rising through a contaminated fluid. As well as, a comparison was done between conditions of a free rising bubble and a rising bubble in wall-bounded flow. Thus, the behavior of a single air bubble rises in aqueous rhamnolipid solutions within two columns with different dimensions was studied experimentally. The experiments were conducted at high Reynolds numbers compared to other researches. The results revealed that effect of the surfactant in wall-bounded flow was much less than free flow whereas bubble terminal velocity was close to the one in a pure fluid and independent of concentration. Moreover, terminal velocity of the free rising bubble decreased as the solution concentration increased for the one less than critical micelle concentration. After that, it kept constant. Furthermore, resulted drag coefficient did not change significantly in different biosurfactant concentrations. The results showed that in high Reynolds number, drag coefficient was a function of Eötvös number and independent of Reynolds and Morton numbers. Consequently, two empirical correlations were presented to predict the terminal velocity and drag coefficient based on surface tension and Eötvös number, respectively.

Physical modelling of dynamic evolution of metallurgical slag foaming

The dynamic evolution of metallurgical slag foaming is vital for the efficiency and safety of the metallurgical processes. Based on the similarity principle via Morton number, the dynamic evolution of Basic Oxygen Furnace (BOF) slag foaming was studied through physical modelling in this investigation. The steady-state structure characteristics and the dynamic evolution of slag foaming were analyzed under the different of superficial gas velocity (us). It was found that the foaming height increased first and consequently decreased as the us increased, while the four different types of steady-state foam structure characteristics were summarized and the dynamic evolution of slag foaming was analyzed. At 0.08 mm∙s−1 < us ≤ 0.50 mm∙s−1, the foam system presented two-layer structure (called Partial Foaming I), while the foaming height increased linearly with the us increased; following gas supply interruption, the foam decayed at a uniform rate. At 0.50 mm∙s−1 < us < 10.00 mm∙s−1, the foam structure evolved into the Entire Foaming I, which was stacked by the spherical bubbles and the deformed bubbles; also, the decaying rate of the foam decreased as the liquid level decreased following the gas supply stop. When us was 0.60 mm∙s−1, the foam had the maximum stability, because its structure was in close proximity to densest packing of spherical bubbles. At 10.00 mm∙s−1 ≤ us ≤ 16.67 mm∙s−1, the foam structure of Entire Foaming II occurred, while the liquid level fluctuated sharply due to the poor stability of the polyhedral bubbles with high size at the upper levels. Moreover, the foaming height reached the peak value; in addition, the liquid level rapidly decreased due to the polyhedral bubble breakage after gas supply interruption. At 16.67 mm∙s−1 < us < 53.33 mm∙s−1, the foam structure evolved into the Partial Foaming II, due to the strong disturbance of high-speed air flow, while the foaming height decreased with the rise of us. As the us further increased, the high-speed gas flow penetrated the liquid phase, leading to the foam disappearance.

Single bubble rising behaviors in Newtonian and non‐Newtonian fluids with validation of empirical correlations: A computational fluid dynamics study

AbstractThe bubble rising (BR) dynamic is a common phenomenon in numerous processes of industries. Here, a single air BR behavior is studied using computational fluid dynamics (CFD) modelling in a Newtonian fluid (NF) and non‐Newtonian fluid (nNF). The volume of fluid formulation with the continuum surface force equation is used to track the air bubble in a NF, while the viscosity of the nNF fluid is estimated by using the power‐law equation. The bubble terminal velocity and its shape deformation, as well as the influence of different dimensionless numbers on BR characterization are investigated. The bubble rise in NF, the bubble terminal velocity increases with decreasing Morton number, and bubble moves up in a zigzag way with shape oscillation for the case of low Morton number of the NF. The bubble rise in nNF, the bubble terminal velocity increases with the increases in the rheological index, and bubble size as well as its shape transforms from an ellipsoidal to ellipsoidal cap types. It is found that the drag coefficient is high in a low rheological index compared with the high rheological index. The CFD results are compared with experimental results and empirical correlations reported in the literature. Good agreements are found between the CFD and the literature data for both fluids.

An improved subgrid scale model for front‐tracking based simulations of mass transfer from bubbles

AbstractGas–liquid bubble column reactors are often used in industry because of their favorable mass transfer characteristics. The bubble mass boundary layer in these systems is generally one order of magnitude thinner than the momentum boundary. To resolve it in simulations, a subgrid scale model will account for the sharp concentration variation in the vicinity of the interface. In this work, the subgrid scale model of Aboulhasanzadeh et al., Chem Eng Sci, 2012, 75:456–467 embedded in our in‐house front tracking framework, has been improved to prevent numerical mass transfer due to remeshing operations. Furthermore, two different approximations of the mass distribution in the boundary layer have been tested. The local and global predicted Sherwood number has been verified for mass transfer from bubbles in the creeping and potential flow regimes. In addition, the correct Sherwood number has been predicted for free rising bubbles at several Eötvös and Morton numbers with industrial relevant Schmidt numbers (103–105).