Bubble Breakup Models Research Articles

Bubble breakup criteria for the population balance model of gas–liquid flow simulations

This work presented a critical review of various literature models with focus on the bubble breakup criteria. A general formulation of critical energy for breakup criteria was derived. Based on the framework of Luo and Svendsen (1996), effects of breakup criteria and effective eddy scale on model outputs were examined. Results showed that a joint criterion consisting of surface energy criterion and force criterion (Cf + Wed', Wec = 2) exhibited both reasonable breakup frequency and daughter size distribution (M-shape), and an optimized kernel function was proposed. A correlation between fragmentation ratio and eddy scale was introduced, and a new breakup model with a simplified kernel function was obtained based on the model of Qi et al. (2022). Both kernel functions were implemented in CFD-PBM simulations, and the results agreed with bubble size distributions. The confusions about literature bubble breakup criteria were cleared and two bubble breakup models were suggested.

Simulation of Spatial Distribution of Multi-Size Bubbles in a Slab Continuous-Casting Mold Water Model.

In this paper, a fully coupled large eddy simulation model, including the volume of fluid model, the discrete phase model, the bubble-collision model, and the bubble-breakup model was used to simulate the spatial distribution of multi-size bubbles and its impact on the instantaneous two-phase flow in a slab continuous-casting mold. The influence of the bubble-interaction model on the bubbles' three-dimensional spatial distribution and size distribution, as well as on two-phase flow was discussed. By comparison with the velocity on the meniscus and the average bubble diameter inside a continuous-casting slab water model, the appropriate numerical model was recommended to accurately simulate the two-phase flow and characteristics of discrete bubbles. The submerged entry nozzle and the area around it saw bubble coalescence and breakage more frequently than other areas. The key interaction between the bubbles was their bouncing in the deep region of the mold. In the mold, the average bubble diameter was 0.741 mm, and 44.5% of the total number of bubbles had an approximately average diameter.

Air–water properties of unsteady breaking bore part 2: Void fraction and bubble statistics

Continuing from the part 1 (Shi et al., 2022) this paper presents an experimental investigation of transient void fraction and bubble statistics in a highly turbulent breaking bore with Fr1=2.4. The measurements were conducted using a combination of dual-tip phase-detection probes and an ultra-high-speed video camera. The enclosed bubble detection technique (EBDT) used the synchronised probe and camera signals to provide the contour of instantaneous void fraction in the bore roller. The ensemble-averaged void fraction was derived, and compared to analytical solutions of air diffusion models. The bubble statistics were characterised by the bubble clustering properties, pseudo bubble count rate and bubble size spectrum. The clustering data showed the non-random bubble grouping in the shear layer, and the bubble size distributions N(r) followed a commonly adopted bubble break-up model: N(r)∝r−m, where r was the equivalent bubble radius in the present study. The comparison indicated that, in the breaking bore, its air diffusion process was similar to that in a stationary hydraulic jump, and the bubble break-up process was comparable to that in breaking waves.

Effects of solid particles on bubble breakup and coalescence in slurry bubble columns

Bubble size distribution (BSD) is a crucial parameter in the design and scale-up of slurry bubble columns (SBCs) as it affects the hydrodynamics, heat and mass transfers, and, consequently, the column overall performance. It is necessary to understand the impacts of various parameters on the bubble size to adequately predict the BSD. The population balance model is widely adopted to estimate the BSD by considering the bubble coalescence and breakup rates. Many bubble coalescence and breakup models have been proposed in literature to predict the BSD. However, the available models have been developed for two-phase (gas–liquid) systems. They are, hence, less appropriate for three phase (gas–liquid-solids) systems, as the presence of particles in these systems has considerable impacts on their hydrodynamics. Novel bubble breakup and coalescence models are developed in the present study to predict the effects of solids concentration and particle size on the bubble breakup and coalescence rates. The results showed that the presence of solids can increase both bubble coalescence and breakup rates, while the effect is more pronounced on the coalescence rate. In addition, an increase in the particle size increases the bubble breakup rate and decreases the bubble coalescence rate. An integrated population balance and hydrodynamic model was also developed to estimate the BSD and gas holdup in a slurry bubble column. The developed models in this study were successfully validated by experimental hydrodynamic data from literature and those obtained in our pilot-scale slurry bubble column. A set of parametric studies were accomplished to investigate the effects of solid particles on the bubble breakup, bubble coalescence, and BSD in two common industrial applications of SBCs.

Computational study of bubble coalescence/break-up behaviors and bubble size distribution in a 3-D pressurized bubbling gas-solid fluidized bed of Geldart A particles

A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles. High-resolution 3-D numerical simulations were performed using the two-fluid model based on the kinetic theory of granular flow. A fine-grid, which is in the range of 3–4 particle diameters, was utilized in order to capture bubble structures explicitly without breaking down the continuum assumption for the solid phase. A novel bubble tracking scheme was developed in combination with a 3-D detection and tracking algorithm (MS3DATA) and applied to detect the bubble statistics, such as bubble size, location in each time frame and relative position between two adjacent time frames, from numerical simulations. The spatial coordinates and corresponding void fraction data were sampled at 100 Hz for data analyzing. The bubble coalescence/break-up frequencies and the daughter bubble size distribution were evaluated by using the new bubble tracking algorithm. The results showed that the bubble size distributed non-uniformly over cross-sections in the bed. The equilibrium bubble diameter due to bubble break-up and coalescence dynamics can be obtained, and the bubble rise velocity follows Davidson’s correlation closely. Good agreements were obtained between the computed results and that predicted by using the bubble break-up model proposed in our previous work. The computational bubble tracking method showed the potential of analyzing bubble motions and the coalescence and break-up characteristics based on time series data sets of void fraction maps obtained numerically and experimentally.

A turbulent bubble breakup model with application to LES

We present a new turbulent breakup model that considers a linear combination of the critical energy obtained from the deformation energy and the force criteria. The relative velocity between the bubbles and the liquid, which affects the eddy/bubble collision rate, is introduced for the first time in a turbulent breakup model and is found to play a significant role. To extend use to a wide range of turbulent flows, a full turbulent spectrum is employed in the derivation of mean turbulent eddy velocity. A collision efficiency caused by the contact angle between bubbles and eddies is introduced and an effective eddy velocity is proposed when eddy size is larger than the bubble size. In principle, the model considers all the sizes of eddies in the turbulent flow, removing the need to limit the integration range when computing the contribution of eddy sizes to the breakup rate. Two modeling constants are calibrated with experiments, and then the model is validated against other experiments. Good agreement is found for both breakup rate and bubble size distribution in different turbulent flows. When the model is tested on large eddy simulation (LES) of bubbly homogeneous isotropic turbulence, it is found that the void fraction and the pressure are strongly negatively correlated and the bubble relative velocity is affected by pressure gradients, affecting the local bubbly flow. The predicted mean bubble size distribution is almost the same as Reynolds-averaged Navier–Stokes (RANS) when the dissipation rates are low. For high dissipation rates the bubble relative velocity increases as the pressure gradients increase, playing an important role in determining the size distribution, and supporting the rationale of adding bubble relative velocity to the turbulent breakup model.

Experimental study on breakup of a single bubble in a stirred tank: Effect of gas density and liquid properties

AbstractBubble breakup plays an important role in gas–liquid flows, but detailed studies are still scarce. In this work, the breakup behavior of a single bubble in a stirred tank was experimentally studied with a high‐speed camera, focusing on the effect of gas density, liquid properties, agitation speed, and mother bubble size. The bubble breakup time, breakup probability, breakup rate, and daughter bubble size distribution were determined. The internal‐flow phenomenon that the gas flowed from the smaller part to the larger part of a deformed mother bubble was observed by a high‐speed camera. The results showed that with increasing gas density, agitation speed, mother bubble size and decreasing surface tension, the bubble breakup rate and probability of equal‐size distribution significantly increased. With increasing liquid viscosity, the bubble breakup rate decreased especially in the high viscosity range. An M‐shaped daughter bubble size distribution was observed, which was consistent with our previous bubble breakup model.

ACFD‐PBMcoupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media

AbstractTo account for the effect of liquid viscosity, the bubble breakup model considering turbulent eddy collision based on the inertial subrange turbulent spectrum was extended to the entire turbulent spectrum that included the energy‐containing, inertial, and energy‐dissipation subranges. The computational fluid dynamics‐population balance model coupled model was modified to include this extended bubble breakup model for simulations of a bubble column. The effect of turbulent energy spectrum on the bubble breakup and hydrodynamic behaviors was studied in a bubble column under different liquid viscosities. The results showed that when the liquid viscosity was <80 mPa s, the bubble breakup and hydrodynamics were almost independent on the turbulent spectrum. At liquid viscosity >80 mPa s, the bubble breakup rate and gas holdup were significantly under‐predicted when the inertial turbulent spectrum was used, and when using the entire turbulent spectrum the predictions were more consistent with experimental data.

Forecasting a bubbly-intermittent flow regime transition in helically coiled tubes

Simulations of gas–liquid turbulent flows in helically coiled tubes are conducted by a two-fluid hydrodynamic model coupled with the population balance equation. A model of bubble breakup in a turbulent flow, recently developed by the authors, is incorporated into the ANSYS Fluent CFD code employed as a computational tool. The population balance equation is solved by a discrete method. A realizable k-epsilon turbulence model is used for all computations. Numerous simulations of gas-liquid flows in vertically oriented coiled tubes are conducted. Three different coil diameters are employed for simulations. Computed bubble chord distributions are close to experimental data. Simulated dependencies of the superficial liquid velocity on the superficial gas velocity, corresponding the bubbly-intermittent flow regime transition, are in excelled agreement with measured ones. On the other hand, dependencies, obtained using standard bubble breakup models, significantly deviate from experimental results. Thus, it is demonstrated that employment of the novel bubble breakup model greatly enhances a computational accuracy of gas-liquid flows in helically coiled tubes.

Influence of Interfacial Force Models and Population Balance Models on the kLa Value in Stirred Bioreactors

Optimal oxygen supply is vitally important for the cultivation of aerobically growing cells, as it has a direct influence on cell growth and product formation. A process engineering parameter directly related to oxygen supply is the volumetric oxygen mass transfer coefficient kLa. It is the influences on kLa and computing time of different interfacial force and population balance models in stirred bioreactors that have been evaluated in this study. For this investigation, the OpenFOAM 7 open-source toolbox was utilized. Firstly, the Euler–Euler model with a constant bubble diameter was applied to a 2L scale bioreactor to statistically examine the influence of different interfacial models on the kLa value. It was shown that the kL model and the constant bubble diameter have the greatest influence on the calculated kLa value. To eliminate the problem of a constant bubble diameter and to take effects such as bubble breakup and coalescence into account, the Euler–Euler model was coupled with population balance models (PBM). For this purpose, four coalescence and five bubble breakup models were examined. Ultimately, it was established that, for all of the models tested, coupling computational fluid dynamics (CFD) with PBM resulted in better agreement with the experimental data than using the Euler–Euler model. However, it should be noted that the higher accuracy of the PBM coupled models requires twice the computation time.

Numerical analysis of bubble characteristics in a pressurized bubble column using CFD coupled with a population balance model

The effects of the coalescence coefficient and bubble breakup models used in the numerical modeling of bubble behavior are investigated in this study. Simulations show that variations in the system pressure and superficial gas velocity affect the gas phase density and distribution of “gas holdup” in the form of large and small bubbles in the bubble column. In a pressurized bubble column with a high superficial gas velocity, owing to the churn turbulence in the bubble column, the pressure is the primary parameter that causes bubble breakup; however, previous studies have not sufficiently described the treatment of bubble coalescence under this condition. Therefore, in this work, gas holdup in the form of small bubbles is introduced into Luo’s coalescence coefficient to improve the bubble coalescence model. This optimized bubble coalescence model was found to improve the accuracy of bubble size prediction in a pressurized bubble column.

Modeling Bubble Entrainment and Transport for Ship Wakes: Progress Using Hybrid RANS/LES Methods

This article presents progress on modeling bubble entrainment and transport around ships using hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/ LES) methods. Previous results using a Boltzmann-based polydisperse bubbly flow model show that LES perform better than RANS in predicting transport of bubbles to depth, a very important process to predict bubbly wakes. However, standard DES-type models fail to predict proper turbulent kinetic energy (TKE) and dissipation, needed by bubble entrainment, breakup, and coalescence models. We propose different approaches to obtain TKE and dissipation in LES regions and evaluate them for cases of increasing complexity, including decay of isotropic turbulence, a flat plate boundary layer, and the flow in the wake of the research vessel Athena. An exponential weighted average is used to estimate statistics and obtain the averaged quantities in regions with resolved turbulence. The TKE is satisfactorily predicted in the cases tested. A modified ω equation in the SST model is proposed to implicitly compute the dissipation, showing superior results than the standard DES models, although further improvements are necessary. A hybrid RANS/LES approach is proposed, which focused at conserving total TKE as the flow crosses RANS/LES interfaces, as previously performed for zonal approaches but attempting a DES-like detection of regions suitable for LES, critical for large-scale computations of bubbly flows involving complex geometries. A general form of a dynamic forcing term is derived to transfer the modeled TKE to resolved TKE with a controller to guarantee proper conservation of the energy transferred. It was verified that the model is not sensitive to grid size or time step. Improvements to DDES and the proposed TKE-conserving hybrid RANS/ LES method show encouraging results, although remaining challenges are discussed.

Numerical simulation of local bubble size distribution in bubble columns operated at heterogeneous regime

This work investigates the effect of lift force, turbulent dispersion force, bubble breakup models, bubble coalescence models, and the parameters in the class method for solving PBEs on the simulated local bubble size distribution (BSD) at various radial positions (r/R = 0.0, 0.27, 0.58 and 0.8), and the local Sauter mean diameter (Sd) in bubble columns. The results suggest that the local BSD and Sd are slightly affected by the radial positions but greatly influenced by the lift force and the parameters in the class method (e.g. the minimum bubble diameter and maximum bubble diameter). The prediction of BSD could be promoted by including the lift force. The local Sd increases with the increase of the minimum bubble diameter and the maximum bubble diameter.

Numerical Analysis of Effect of Operation Conditions on Bubble Distribution in Steel Continuous Casting Mold with Advanced Bubble Break-up and Coalescence Models

Numerical Analysis of Effect of Operation Conditions on Bubble Distribution in Steel Continuous Casting Mold with Advanced Bubble Break-up and Coalescence Models

Computational fluid dynamics simulation of two-phase flow and dissolved oxygen in a wastewater treatment oxidation ditch

This study presents a computational fluid dynamics (CFD) model of an aerated wastewater treatment oxidation ditch, taking into account gas-liquid flow, oxygen mass transfer and dissolved oxygen. Especially, the effect of the bubble size distribution (BSD) and the biochemical oxygen demand (BOD) distribution on the dissolved oxygen (DO) distribution has been considered. Species transport modelling predicts the DO and BOD distribution. De-oxygenation of local dissolved oxygen by BOD is modelled by an oxygen sink that depends on the local BOD concentration. Bubble coalescence and breakup models predict the BSD. The behaviour of the ditch is non-ideal, which is indicated by the residence time distribution (RTD), heterogeneous flow pattern and DO distribution. The parameters with the greatest influence on the dissolved oxygen are the BOD and bubble size. There is good agreement between the numerical simulation and the observations of flow pattern and measurements of mean DO. This study identifies that the BOD distribution and the BSD are important parameters for accurately predicting the DO distribution and which have been mostly neglected in the public research.

Numerical Analysis of Effect of Initial Bubble Size on Captured Bubble Distribution in Steel Continuous Casting Using Euler-Lagrange Approach Considering Bubble Coalescence and Breakup

A mathematic model considering the bubble coalescence and breakup using the Euler-Lagrange approach has been developed to study the effect of the initial bubble size on the distribution of bubbles captured by the solidification shell. A hard sphere model was applied for dealing with the bubble collision. Advanced bubble coalescence and breakup models suitable for the continuous casting system and an advanced bubble captured criteria have been identified established with the help of user-defined functions of FLUENT. The predictions of bubble behavior and captured bubble distribution agree with the water model and plant measurements well respectively. The results show that the number of small bubbles captured by solidification shell is much higher than that of large bubbles. What is more, the number of captured bubbles at the sidewalls decreases with the distance from the meniscus. For the case of large gas flow rate (gas flow fraction of 8.2%), the initial size of bubbles has little effect on bubble captured distribution under various casting speeds. When the gas flow rate is small (gas flow fraction of 4.1%), the number density of captured bubbles increases as the initial bubble size increases, and the effect of initial bubbles size on captured bubble number density is amplified when the casting speed decreases. The average captured bubble diameter is about 0.12–0.14 mm. Additionally, for all cases, the initial bubble size hardly affects the average size of captured bubbles.

Effects of bubble coalescence and breakup models on the simulation of bubble columns

This work investigates the effects of coalescence and breakup models on the radial distribution of gas holdup and local bubble size distribution in a laboratory scale bubble column operated at 0.11 m/s, 0.14 m/s, 0.19 m/s and 0.23 m/s. The results quantitatively show the influences of bubble coalescence due to various mechanisms, coalescence efficiency calculated by different models, modification coefficients for coalescence rates, critical energy required for breakup and bubble breakage caused by large scale eddies and viscous shear on numerical simulations. Furthermore, qualitative analysis is performed to analyze the effects of these factors. The performance of various models is evaluated (e.g. Han’s breakup model and Das’s coalescence model). Some optimized combinations of coalescence and breakup models that can be used to accurately predict the local gas holdup and bubble size distribution in laboratory scale bubble columns operated at heterogeneous regime are proposed.

Generality of the CFD-PBM coupled model for bubble column simulation

Computational fluid dynamics coupled with a population balance model (CFD-PBM) combines the use of CFD to calculate the flow field and phase holdup and that of PBM to calculate the local bubble size distribution. However, the generality of the CFD-PBM coupled model for different operating conditions and liquid properties has not been systematically studied. The CFD-PBM coupled model where the PBM used our bubble breakup and coalescence models was shown to give accurate results in wide operating conditions (P = 0.1–3.5 MPa, Ug = 0.02–0.16 m/s), liquid properties (0.02–0.07 N/m, 1–185 mPa·s) with the same set of model parameters. Overall, the coupled model showed good generality when the superficial gas velocity, operating pressure, liquid viscosity and surface tension are the factors in bubble coalescence and breakup and the appropriate mechanism models are used to account for them, and forces at the gas-liquid interface are calculated using the local gas holdup and bubble size distribution.

Update to the MUSIG model in ANSYS CFX for reliable modelling of bubble coalescence and breakup

The MUSIG (Multiple Size Group) model in the commercial CFD code ANSYS CFX is a population balance approach for describing binary bubble coalescence and breakup events. It is widely used in the simulation of poly-dispersed bubbly flows. The purpose of this work is to identify the internal inconsistencies in the discrete method that is applied for the solution of the population balance equation in MUSIG, and to propose an internally consistent one for discretising the source and sink terms that result from bubble coalescence and breakup. The new formulation is superior to the existing ones in preserving both mass and number density of bubbles, allowing arbitrary discretisation schemes and is free of costly numerical integrations. The numerical results on the evolution of bubble size distributions in bubbly flows reveal that the inconsistency in the original MUSIG regarding bubble breakup is non-negligible for both academic and practical cases. The discussion on the effect of internal inconsistency as well as updates to the model presented in this work are necessary and important for calibration of bubble coalescence and breakup models using the MUSIG approach.

Simulation of bubbles behavior in steel continuous casting mold using an Euler-Lagrange framework with modified bubble coalescence and breakup models

A mathematic model considering the interaction of bubbles was developed to simulate bubbles behavior in a continuous slab casting mold. The flow of molten steel is calculated with an Eulerian model coupled with a Lagrangian model for bubbles. Modified bubble coalescence and breakup models are established as user-defined functions of FLUENT software. Collisions between bubbles are described by means of hard-sphere model. The break-up mold is implemented with a break-up constrain based on the critical Weber number augmented a model for daughter bubble size distribution. The daughter bubble fraction is calculated with a tanh function, which has a U-shape distribution with lower bounds. Small bubbles were produced by the breakup of large bubbles. The predicted size and number of captured bubbles obtained with the mathematic model agree well with the plant measurements. The size and number distributions of small bubbles near the advancing solidification shell were obtained with simulation results. The results show that the bubble size and number at both the narrow and wide faces decrease with the increase of distance from the meniscus, and they get close to a constant in the deep region. Meanwhile, the initial bubble size has no obvious effect on the bubble distribution in the mold at the operation conditions in the present work.