Discrete Bubble Model Research Articles

Modelling and analysis of bubble entrapment by solidification shell in steel continuous casting considering bubble interaction with a coupled CFD-DBM approach

In steel continuous casting processes, argon gas is usually injected to prevent nozzle clogging. However, some argon bubbles may be captured by solidifying shell and result in defects in the final slab. A mathematic model with a coupled CFD-DBM approach is developed to study the bubbles entrapment behavior in the continuous casting process and bubbles distribution inside the slab. The coalescence and breakup of bubbles are considered in the discrete bubble model (DBM). An advanced bubble capture model based on force balance of bubble in front of the solidifying is used for the determination of bubble entrapment. Close agreements are achieved for the size and number density of captured bubble in the measurement layers of an industrial slab. The results show that most bubbles are captured near the meniscus, but bubbles have a greater tendency to be captured away from the meniscus as their size decreases. The fractions of captured bubbles at different regions of wide and narrow faces in the continuous casting mold are analyzed, as well as the effect of casting speed and gas flow rate. The distributions of number density and average size of bubbles inside the steel slab are obtained under different operation conditions. The results show successfully some known phenomena and other new predictions.

Multiscale modeling and validation of the flow around Taylor bubbles surrounded with small dispersed bubbles using a coupled VOF-DBM approach

This work presents a multiscale three-dimensional CFD model for the simulation of two-phase gas-liquid flows with different interface length scales, with focus on slug flow pattern. The model is based on the coupling of the Volume-of-Fluid (VOF) method, used to model the large-scale interface dynamics, and the Discrete Bubble Model (DBM) for modeling the small-scale bubbles, which allows to simulate two-phase flows with different interface length scales. A validation study is conducted independently for the VOF and DBM methods, by comparing the numerical results with experimental data from the literature, showing a very good agreement. A model for the collision between the VOF interface and Lagrangian bubbles is proposed and also independently validated. The coupled VOF-DBM model is used to study a liquid-gas two-phase flow with different interface length scales, where large Taylor bubbles and small dispersed bubbles are present. The results demonstrate that the presence of the small dispersed bubbles alters the flow structure around the Taylor bubble, increases the terminal velocity of the Taylor bubble and affects the flow structure in the wake region, which is directly related to heat and mass transfer rates in slug flow.

Designing key parameters of bubble plumes to restore water quality by using conceptual models: a case study in a sub-deep reservoir

Abstract Bubble plumes are a popular hypolimnetic reaeration technique in deep-water reservoirs since they have the advantage of delivering direct reaeration to the hypolimnion. Improving the understanding of the integrated reaeration processes is beneficial to optimize the reaeration capacity of the aeration or oxygenation system. In this study, the discrete bubble model was first employed to design an oxygenation system for a sub-deep reservoir (the Aha Reservoir, southwest China, with water depths of 10–30 m). A new approach involving the discrete bubble model was used to determine the initial bubble size of the bubble plume applied. The intrusion models were demonstrated to be useful for designing the gas flow rate of the reaeration system. Using the intrusion models, we predicted the intrusion thickness and intrusion distance during operation for the first time. Subsequently, we verified the predictions and produced more realistic empirical formulas. At present, reports about recommendations on initial bubble size and gas flow rate are rare, and practical verification is absent. Taking the Aha Reservoir as an example, the initial bubble radius of 1 mm and the gas flow rate of 20 m3·h−1 were recommended for bubble plume oxygenation and were found to be successful in the field. Our understanding of the reaeration processes during the operation of the bubble plume system is far from comprehensive, but this study serves to highlight the potential of the discrete bubble model and the intrusion models for designing a bubble plume system in an individual lake.

Performance of Closed Loop Venturi Aspirated Aeration System: Experimental Study and Numerical Analysis with Discrete Bubble Model

In wastewater treatment plants, aeration plays a significant role as it encourages aerobic respiration of microbes, which are necessary to break down carbonaceous matter in the waste stream. This process can account for the majority of energy use in wastewater treatment plants. The aeration process is also necessary in odor control in lagoons and in the aquaculture industry. Generally, the aeration process is accomplished with compressors or blowers which can be of low efficiency due to ideal gas laws. This study introduces the idea of increasing aeration efficiency by looping water from a reservoir through a piping network which includes a venturi aspirator at its inlet. For this purpose, an experimental study has been conducted in a laboratory setup with a pump which pulls water from a tank, passes it through a Venturi aspirator and a helical piping network intended to increase bubble residence time, before depositing it back into the bulk fluid tank. This same process is modeled computationally, using a discrete bubble method (DBM), with good agreement with experiments. The overall purpose here is to determine the optimal configurations for standard aeration efficiency (SAE) and the standard oxygen transfer rate (SOTR). A parametric study has been implemented using the DBM based on different hydraulic and flow parameters. The model is also used to predict the SAE of a hypothetical aeration system. Results indicate that it is possible to achieve SAE values in the range of surface aerators or submersed jet aerators using the proposed aeration system with less complex components, thereby decreasing overall costs.

Parallelization of a stochastic Euler-Lagrange model applied to large scale dense bubbly flows

A parallel and scalable stochastic Direct Simulation Monte Carlo (DSMC) method applied to large-scale dense bubbly flows is reported in this paper. The DSMC method is applied to speed up the bubble-bubble collision handling relative to the Discrete Bubble Model proposed by Darmana et al. (2006) [1]. The DSMC algorithm has been modified and extended to account for bubble-bubble interactions arising due to uncorrelated and correlated bubble velocities. The algorithm is fully coupled with an in-house CFD code and parallelized using the MPI framework. The model is verified and validated on multiple cores with different test cases, ranging from impinging particle streams to laboratory-scale bubble columns. The parallel performance is shown using two different large scale systems: with an uniform and a non-uniform distribution of bubbles. The hydrodynamics of a pilot-scale bubble column is analyzed and the effect of the column scale is reported via the comparison of bubble columns at three different scales.

Quantitative comparison between volume-of-fluid and two-fluid models for two-phase flow simulation using OpenFOAM

This study compared numerical characteristics of volume-of-fluid (VOF) and two-fluid models for the two-phase flow simulation by using open-source computational fluid dynamics software (OpenFOAM). In both models, the pressure-implicit method for pressure-linked equations was solved to obtain transient pressure and velocity fields. For the simulation of subgrid-scale bubbles, the VOF model was coupled with a Lagrangian discrete bubble model (DBM). In the single bubble rising case, kinematic and dynamic parameters predicted by the two-fluid model were poor. However, in the bubbly flow case, this model predicted the gas and liquid velocities well and, similarly, the liquid front position in the free surface flow case. On the other hand, the VOF model was less accurate in describing bubbly flow, despite the inclusion of the DBM. While the two-fluid model is recommended for the simultaneous simulation of separated and dispersed flows, the VOF model is more effective for separated flows.

A hybrid discrete bubble-lattice Boltzmann–discrete element model for gas-charged sediments

This paper presents a hybrid discrete bubble-lattice Boltzmann–discrete element modelling framework for simulating gas-charged sediments, especially in the seabed. A discrete bubble model proposed in chemical engineering is adapted in the coupled discrete element/lattice Boltzmann method to model the migration of gas bubbles in saturated sediments involving interactions between gas bubbles and fluid/solid phases. Surface tension is introduced into the discrete bubble model in this work, so that it can handle the complex gas–fluid–solid interface. The lattice Boltzmann and discrete element methods are, respectively, employed to simulate fluid flows and mechanical behaviours of sediments. A velocity interpolation-based immerse boundary method is utilised to resolve the coupling between the fluid flow and the solid/gas phase. The proposed technique is preliminarily validated using simulations of bubble migration in fluids, which is followed by high-resolution investigations of the transport of a gas bubble in seabed sediments. It is demonstrated that this hybrid method can reproduce, to a certain degree, the characters of bubbles moving in seabed sediment tests.

A comparative study between numerical methods in simulation of cavitating bubbles

In this paper, the performance of three different numerical approaches in cavitation modelling are compared by studying two benchmark test cases to understand the capabilities and limitations of each method. Two of the methods are the well established compressible thermodynamic equilibrium mixture model and the incompressible transport equation finite mass transfer mixture model, which are compared with a third method, a recently developed Lagrangian discrete bubble model. In the Lagrangian model, the continuum flow field is treated similar to the finite mass transfer approach, however the cavities are represented by individual bubbles. Further, for the Lagrangian model, different ways to consider how the fluid pressure influences bubble dynamics are studied, including a novel way by considering the local pressure effect in the Rayleigh–Plesset equation. The first case studied is the Rayleigh collapse of a single bubble, which helps to understand each model behaviour in capturing the cavity interface and the surrounding pressure variations. The special differences between the Lagrangian and finite mass transfer models in this case clarify some possible origin for some limitations of the latter method. The second investigated case is the collapse of a cluster of bubbles, where the collapse of each bubble is affected by the dynamics of surrounding bubbles. This case confirms the importance of considering local pressure in the improved form of the Rayleigh–Plesset equation and illustrates the influence of the liquid compressibility for cavity modelling and appropriate capturing of the collapse pressure.

Multiscale Mathematical Model with Discrete–Continuum Transition for Gas–Liquid–Slag Three-Phase Flow in Gas-Stirred Ladles

Gas–liquid–slag three-phase flow in a gas-stirred ladle is composed of both large-scale interfaces and discrete bubbles, making its modeling and study difficult. In the present work, a discrete–continuum transition model was incorporated into a hybrid Eulerian–Lagrangian model to comprehensively resolve the fluid flow in ladle metallurgy. The volume-of-fluid method was used to capture the large-scale interfaces, while a discrete bubble model was applied to simulate the small bubbles that cannot be resolved using the interface-capturing method. The transition between the small bubbles in Lagrangian coordinates and the large bubbles whose interfaces are captured is included using a newly developed algorithm to further reveal the bubble behaviors. Moreover, the complicated vortex structure is characterized using the large-eddy simulation approach. The present modeling framework enables the most complete analysis of gas–liquid–slag three-phase flow in ladles to date.

Euler–Lagrange Modeling of Bubbles Formation in Supersaturated Water

Phase transition, and more specifically bubble formation, plays an important role in many industrial applications, where bubbles are formed as a consequence of reaction such as in electrolytic processes or fermentation. Predictive tools, such as numerical models, are thus required to study, design or optimize these processes. This paper aims at providing a meso-scale modelling description of gas–liquid bubbly flows including heterogeneous bubble nucleation using a Discrete Bubble Model (DBM), which tracks each bubble individually and which has been extended to include phase transition. The model is able to initialize gas pockets (as spherical bubbles) representing randomly generated conical nucleation sites, which can host, grow and detach a bubble. To demonstrate its capabilities, the model was used to study the formation of bubbles on a surface as a result of supersaturation. A higher supersaturation results in a faster rate of nucleation, which means more bubbles in the column. A clear depletion effect could be observed during the initial growth of the bubbles, due to insufficient mixing.

A Multi-scale Mathematical Model of Growth and Coalescence of Bubbles Beneath the Anode in an Aluminum Reduction Cell

Modeling of bubble shapes is challenging because of the wide range of length scales in aluminum reduction cells. A 3D multi-scale mathematical model was developed to understand the nucleation, growth and coalescence of bubbles beneath the anode and to investigate the transition of bubbles from the micro- to macro level. The motion of micro-bubbles is examined using the discrete bubble model (DBM) within a Lagrangian reference. An algorithm for the transition from discrete micro-bubbles to large bubbles, which are fully resolved by the volume of fluid (VOF) approach, is achieved using a user-defined function. The two-way coupling between discrete bubbles and continuous fluids is achieved by inter-phase momentum exchange. The model involves three kinds of bubble coalescence: micro-bubble coalescence is taken into account by the DBM; large bubbles swallowing up micro-bubbles are solved by the discrete-continuum transition model; the coalescence between large bubbles is handled by the VOF method. Numerical results show that the coverage and thickness of bubbles agree well with the experimental data in the literature. Bubble thickness stops increasing when the bubble elongates with the anode bottom, which is 4.0 to 4.5 mm. Meanwhile, two asymmetrical thick heads can be observed under the anode. Bubble release frequency increases with increasing current density.

Application of Circular Bubble Plume Diffusers to Restore Water Quality in a Sub-Deep Reservoir.

Circular bubble plume diffusers have been confirmed as an effective technology for the restoration of the deep water system, but have never been applied in sub-deep water system. In this study, circular bubble plume diffusers were used, for the first time, to restore water quality in the Aha Reservoir, a typical sub-deep reservoir in Southwest China. Axisymmetric intrusive gravity currents were formed with a horizontal radius of 250 m at the equilibrium depth and the intrusion of oxygen-enriched water occurred within the depth of 10–14 m, while thermal stratification remained intact. A total of 95% of the imported oxygen was dissolved, but most was consumed by organic matter and other reduced substances within the hypolimnion. The oxygen consumption of organic matter, NH4+ and remaining reduced materials, accounted for 41.4–52.5%, 25% and 13.3–24.4% of the total imported oxygen, respectively. Compared with the control sites, dissolved oxygen level in the hypolimnion increased 3–4 times, and concentrations of NH4+, total Fe and total Mn were reduced by 15.5%, 45.5% and 48.9%, respectively. A significant decrease in total phosphorus and nitrogen concentrations was observed in the experimental zone (0.04–0.02 mg/L and 1.9–1.7 mg/L, respectively). This indicates that circular bubble plumes have great potential for oxygenation of the hypolimnion and improving water quality in the sub-deep water system. Nevertheless, further efforts are needed to improve the discrete bubble model to elaborate the oxygen transmission dynamics and the plume formation processes in sub-deep water systems, incorporating oxygen consumption processes.

Effect of Bubble Injection Pattern on the Bubble Size Distribution in a Gas-Solid Fluidized Bed

Three different bubble injection patterns including uniform, center oriented and corner oriented injection patterns over the gas distributor have been studied using a discrete bubble model in a 2-D gas solid fluidized bed. The results show that the bubble size and size distribution evolution through the bed are almost the same for uniform and corner oriented bubble injection patterns, but for the case of center oriented injection pattern, the area weighted average bubble diameter (d b,21) is greater than the others. The results show that in the center oriented injection pattern, many of the small bubbles leave the bed without coalescence and this leads to smaller d b,10 than two other cases. Moreover, in this work the size distribution evolution through the bed height is investigated in detail.

Influence of drag closures and inlet conditions on bubble dynamics and flow behavior inside a bubble column

ABSTRACTIn this paper, the hydrodynamics of a bubble column is investigated numerically using the discrete bubble model, which tracks the dispersed bubbles individually in a liquid column. The discrete bubble model is combined with the volume of fluid approach to account for a proper free surface boundary condition at the liquid–gas interface. This improves describing the backflow region, which takes place close to the wall region. The numerical simulation is conducted by means of the open source computational fluid dynamics library OpenFOAM®. In order to validate the numerical model, experimental results of a bubble column are used. The numerical prediction shows an overall good agreement compared to the experimental data. The effect of injection conditions and the influence of the drag closures on bubble dynamics are investigated in the current paper. Here, the significant effect of injection boundary conditions on bubble dynamics and flow velocity in the studied cavity is revealed. Moreover, the impact of the choice of the drag closure on the liquid velocity field and on bubble behavior is indicated by comparing three drag closures derived from former studies.

Evaluating Dissolved Ozone in a Bubble Column Using a Discrete-Bubble Model

ABSTRACTOzonation has been widely applied in water treatment plants, so it is essential to figure out mass transfer and reaction kinetics in ozone contact tanks. In this study, a discrete-bubble model was established to calculate the dissolved ozone concentration in a countercurrent flow system. Results from batch experiments showed that an exponential relationship was well fitted between ozone reaction rate coefficient and ozone consumption amount, and the relationship was not affected by the ozone dosage. Therefore, it was applied in a discrete-bubble model, which was validated by experiments in a countercurrent bubble column with error less than 15%.

Numerical modeling of carbon dioxide chemisorption in sodium hydroxide solution in a micro-structured bubble column

Gas–liquid flows with solid catalyst particles are encountered in many applications in the chemical, petrochemical, and pharmaceutical industries. Most commonly, two reactor types, slurry bubble column (SBC) and trickle bed (TB) reactors are applied for large scale in the industry. Both of these types of reactors have some disadvantages limiting their efficiencies. To overcome the aforementioned disadvantages, a novel reactor type, micro-structured bubble column (MSBC), is proposed in Jain et al. (2013). In the MSBC, micro-structuring of the catalyst carrier is realized by introducing a static mesh of thin wires coated with catalyst inside the column. Wires also serve the purpose of cutting the bubbles, which in turn results in high interfacial area and enhanced interface dynamics. Moreover, the static catalytic mesh ensures lower cost by avoiding filtration of catalyst particles. In this paper, the MSBC is numerically studied using the hybrid volume of fluid – discrete bubble model (VOF-DBM) presented in Jain et al. (2014). The VOF-DBM is extended with a description of wire–meshes and the bubble cutting algorithm as introduced in Jain et al. (2013). Furthermore, a model for mass transfer with chemical reaction as developed by Darmana et al. (2007) is included in the model to study the impact of the wire–mesh and bubble cutting on the chemical reaction rate. In this work, first the model implementation and results are verified for a wide spectrum of parameters from the data available from previous studies, analytical results and experimental findings. Subsequently the model is applied to carry out a parameter study on the chemisorption of CO2 in a NaOH solution, employing different mesh configurations. Since the reaction chosen here is very fast, mass transfer is the limiting step. It is found that the mass transfer can be considerably increased by stacking multiple meshes in the column.

Numerical study of coalescence and breakup in a bubble column using a hybrid volume of fluid and discrete bubble model approach

In this work, two powerful methods are combined for bubble column simulations namely, the volume of fluid and the discrete bubble model. While the former method takes care of the free surface, the discrete bubble model tracks and handles the dynamics of the dispersed bubbles. The hybrid model presented in this work is verified and validated with existing established experimental results. A model parameter study for bubble break-up and coalescence is performed to find the optimum values of the model parameters, i.e. the critical Weber number and the coalescence calibration factor.

A Novel Model for Predicting the Dense Phase Behavior of 3D Gas‐Solid Fluidized Beds

AbstractA novel phenomenological discrete bubble model was developed and tested for prediction of the hydrodynamic behavior of the dense phase of a 3D gas‐solid cylindrical fluidized bed. The mirror image technique was applied to take into account the effects of the bed wall. The simulation results were validated against experimental data reported in the literature that were obtained by positron emission particle tracking. The time‐averaged velocity profiles of particles predicted by the developed model were found to agree well with experimental data. The initial bubble diameter had no significant influence on the time‐averaged circulating pattern of solids in the bed. The model predictions clearly indicate that the developed model can fairly predict the hydrodynamic behavior of the dense phase of 3D gas‐solid cylindrical fluidized beds.

Discrete bubble modeling for a micro-structured bubble column

Gas–liquid flows with solid catalyst particles are encountered in many applications in the chemical, petrochemical, pharmaceutical industries, etc. Most commonly, two reactor types are applied for large scale in the industry. They are slurry bubble column and trickle bed reactors. Both of these types of reactors have some disadvantages limiting their efficiencies. To overcome these disadvantages, a novel reactor type, micro-structured bubble column (MSBC), is proposed. In the MSBC, the micro-structuring of catalytic material is realized by introducing a static mesh of thin wires coated with catalyst inside the column. Wires also serve the purpose of cutting the bubbles, which in turn results in high interfacial area and enhanced interface dynamics. The static catalytic mesh also ensures lower cost by avoiding filtration of catalyst particles. Numerical formulation of the described reactor is based on the 3-D discrete bubble model (DBM) presented in the previous works of Darmana et al. (2005, 2007). The extended version of DBM presented here introduces wires in the existing model and studies their effect on liquid and bubble dynamics. Bubbles and wires are represented by spherical and cylindrical markers, respectively; and the liquid flow-field is solved in the Eulerian gird cells. An improved drag correlation for bubbles in dense (up to 50%) swarm flow is also incorporated in the model. The model implementation and results are verified for a wide spectrum of parameters from the data available from the previous studies, analytical results and experimental findings. Our results show that the model is able to predict the hydrodynamic behavior and bubble dynamics, including the cutting of bubbles through wire mesh, very well.

Bubble Size Distribution in Two-Dimensional Gas–Solid Fluidized Beds

In this article, the digital image analysis (DIA) technique has been used to study the bubble size and bubble size distribution evolution in a pseudo-two-dimensional gas–solid fluidized bed. In addition, a numerical discrete bubble model (DBM) based on the bubble–bubble interactions was developed and the model predictions were compared with the experimental data. The developed model can predict the bubble size and bubble size distribution through the bed height and the lateral distribution of bubbles. Comparison between model predictions and the result of DIA measurements shows that bubble breakage has a significant effect on the bubble size distribution especially at heights far from the distributor plate. Moreover, lateral bubble distribution of the bed was investigated.