Polydispersed Bubbly Flow Research Articles

Implementation and verification of a Quasi-Eulerian-Eulerian-IATE model for the high-efficient prediction of polydispersed bubbly flows in a continuous casting mold

We implement a new gas–liquid two phase model for the high-efficient prediction of polydispersed bubbly flows in a continuous casting mold. This model shares similarity with the Euler–Lagrange (E-L) method, in which the gas velocity is updated by bubble Lagrangian tracking, and with coupling the phase transport equation in Euler-Euler (E-E) method, thus, it is called the Quasi-Eulerian-Eulerian-IATE (Q-E-E-IATE) model. The local mean bubble size is obtained from solving the interfacial area transport equation (IATE). Various interfacial forces including drag force, lift force, virtual mass force, and turbulent dispersion force are incorporated in this model. This model is verified against published experimental data. Good agreement of gas volume fraction, flow field and bubble size distribution are obtained by adding the virtual mass force and adopting optimized IATE constants. The computational cost of the Q-E-E-IATE model is much lower compared to that of the traditional E-L and E-E models.

Structure of a turbulent bubbly flow and heat transfer in a vertical tube

The results of numerical simulation of the flow structure and heat transfer in a vertical polydispersed bubbly flow are presented. The mathematical model is based on the Euler approach taking into account the effect of bubbles on the mean characteristics and turbulence of the carrier phase. The polydispersed distribution of bubbles size in a two-phase flow is modeled by the method of delta approximation considering the process of bubble break-up and coalescence. Carrier phase (fluid) turbulence is predicted using the Reynolds stress transport model. The simulation results showed good agreement with the experimental data presented in the literature. The measured and predicted thermal-hydraulic parameter distribution indicates that in a turbulent bubbly flow, the wall friction increase is greater than heat transfer enhancement.

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.

Population balance modeling of polydispersed bubbly flow in continuous casting using average bubble number density approach

A new methodology of average bubble number density (ABND) model for handling the evolution of polydispersed bubbly flow in the slab continuous casting mold is presented and evaluated. The average bubble number density transport equation coupled with the Eulerian-Eulerian two-fluid model is employed to describe size distribution of bubbles. Various interfacial forces including drag force, lift force, virtual mass force, and turbulent dispersion force are incorporated in this model. SST turbulence model is used with extra source terms introduced to account for the interaction between the bubbles and the liquid. The coalescence of bubbles is formulated according to the random collision driven by turbulence and wake entrainment, and the breakage of bubbles is formulated through considering the impact of turbulent eddies. The intermediate peak and core peak behaviors of void fraction inside the submersed entry nozzle (SEN) are captured very well. Comparisons of gas void fraction, liquid flow pattern, and local bubble size distribution profiles with experimental measurements are provided, showing the applicability and accuracy of the ABND approach in modeling the polydispersed bubbly flow in the slab continuous casting mold.

Modeling of bubble behaviors and size distribution in a slab continuous casting mold

Population balance equations combined with Eulerian–Eulerian two-phase model are employed to predict the polydispersed bubbly flow inside the slab continuous-casting mold. The class method, realized by the MUltiple-SIze- Group (MUSIG) model, alongside with suitable bubble breakage and coalescence kernels is adopted. A two-way momentum transfer mechanism model combines the bubble induced turbulence model and various interfacial forces including drag, lift, virtual mass, wall lubrication, and turbulent dispersion are incorporated in the model. A 1/4th scaled water model of the slab continuous-casting mold was built to measure and investigate the bubble behavior and size distribution. A high speed video system was used to visualize the bubble behavior, and a digital image processing technique was used to measure the mean bubble diameter along the width of the mold. Predictions by previous mono-size model and MUSIG model are compared and validated against experimental data obtained from the water model. Effects of the water flow rate and gas flow rate on the mean bubble size were also investigated. Close agreements by MUSIG model were achieved for the gas volume fraction, liquid flow pattern, bubble breakage and coalescence, and local bubble Sauter mean diameter against observations and measurements of water model experiments.

The effects of bubbles on the structure of upward gas-liquid flow

The paper presents the results of study of the local structure of turbulent gas-liquid flow in vertical pipe. A mathematical model based on the use of Eulerian description for both phases taking into account the action of different forces of interfacial interaction. Special attention is paid to the development of approaches for the simulation of polydispersed bubbly flows taking into account processes of coagulation and fragmentation. Comparison of simulation results with experimental data showed that the developed approach allows to obtain detailed information about the structures of turbulent gas-liquid flows, the distribution of bubbles by size.

Multiple Size Group Modeling of Polydispersed Bubbly Flow in the Mold: An Analysis of Turbulence and Interfacial Force Models

An inhomogeneous Multiple Size Group (MUSIG) model based on the Eulerian–Eulerian approach has been developed to describe the polydispersed bubbly flow inside the continuous-casting mold. A laboratory scale mold has been simulated using four different turbulence closure models (modified k − ɛ, RNG k − ɛ, k − ω, and SST) with the purpose of critically comparing their predictions of bubble Sauter mean diameter distribution with previous experimental data. Furthermore, the influences of all the interfacial momentum transfer terms including drag force, lift force, virtual mass force, wall lubrication force, and turbulent dispersion force are investigated. The breakup and coalescence effects of the bubbles are modeled according to the bubble breakup by the impact of turbulent eddies while for bubble coalescence by the random collisions driven by turbulence and wake entrainment. It has been found that the modified k − ɛ model shows better agreement than other models in predicting the bubble Sauter mean diameter profiles. Further, simulations have also been performed to understand the sensitivity of different interfacial forces. The appropriate drag force coefficient, lift force coefficient, virtual mass force coefficient, and turbulent dispersion force coefficient are chosen in accordance with measurements of water model experiments. However, the wall lubrication force does not have much effect on the current polydispersed bubbly flow system. Finally, the MUSIG model is then used to estimate the argon bubble diameter in the molten steel of the mold. The argon bubble Sauter mean diameter generated in molten steel is predicted to be larger than air bubbles in water for the similar conditions.

Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach

A population balance model based on the multiple-size-group (MUSIG) approach has been developed to investigate the polydispersed bubbly flow inside the slab continuous-casting mold and bubble behavior including volume fraction, breakup, coalescence, and size distribution. The Eulerian–Eulerian approach is used to describe the equations of motion of the two-phase flow. All the non-drag forces (lift force, virtual mass force, wall lubrication force, and turbulent dispersion force) and drag force are incorporated in this model. Sato and Sekiguchi model is used to account for the bubble-induced turbulence. Luo and Svendsen model and Prince and Blanch model are used to describe the bubbles breakup and coalescence behavior, respectively. A 1/4th water model of the slab continuous-casting mold was applied to investigate the distribution and size of bubbles by injecting air through a circumferential inlet chamber which was made of the specially-coated samples of mullite porous brick, which is used for the actual upper nozzle. Against experimental data, numerical results showed good agreement for the gas volume fraction and local bubble Sauter mean diameter. The bubble Sauter mean diameter in the upper recirculation zone decreases with increasing water flow rate and increases with increasing gas flow rate. The distribution of bubble Sauter mean diameter along the width direction of the upper mold increases first, and then gradually decreases from the SEN to the narrow wall. Close agreements between the predictions and measurements demonstrate the capability of the MUSIG model in modeling bubbly flow inside the continuous-casting mold.

Bubble size distribution prediction for large-scale ship flows: Model evaluation and numerical issues

Prediction of the bubble size distribution in the wake of a ship is important to analyze its acoustic signature. To achieve CFD simulation of dynamic ships with moving control surfaces and rotating propellers in waves, a robust implementation is paramount. In this work a mass conserving multigroup discretization strategy of the Boltzmann transport equation for polydispersed bubbly flows is presented, as well as an analysis of available breakup and coalescence models. Modifications of the discrete equations for the fixed pivot method at the boundaries are introduced that guarantee exact bubble mass conservation. The role of the time stepping scheme in the conservation of mass and number of bubbles is discussed. Though the conservation properties of the discrete system of equations are satisfied provided they are solved exactly, in practice an iterative procedure must be used since the ODE’s are non-linear. Three iterative schemes are proposed and they are analyzed in terms of robustness and efficiency. Breakup, coalescence and dissolution models are analyzed from the numerical point of view. Available models of breakup and coalescence are studied finding appropriate choices for ship applications. Other models are appropriate as well, but are more costly numerically. As appropriate for ship applications, an extension to the model of Prince and Blanch for salt water is proposed and analyzed. The final model is tested against experimental data and computations by other researchers, and convergence properties in bubble size discretization is studied. It is found that for salt water the final steady state is dependent on the initial condition since there is a range of sizes for which coalescence and breakup are both negligible.

Eulerian polydispersed modeling of bubbly flows around ships with application to Athena R/V

The modeling of polydispersed bubbly flows in practical applications requires the resolution of large systems of equations with multiple unknowns. Since the solution to this problem lives in a four dimensional space the number of unknowns increases quickly with finer discretizations. In addition, the problem is highly non-linear, strongly coupled and stiff. In this work a series of novel ideas to solve these issues in a robust and efficient manner is presented. Further, a simulation of the bubbly flow around a real self-propelled ship where the propellers are fully discretized is performed. This highly demanding computation serves as a test for the ideas presented in this work. Comparisons with available experimental data are shown.

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

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

CFD modelling of polydispersed bubbly two-phase flow around an obstacle

A population balance model (the Inhomogeneous MUSIG model) has recently been developed in close cooperation between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD-Code CFX [Krepper, E., Lucas, D., Prasser, H.-M, 2005. On the modelling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611; Frank, T., Zwart, P.J., Shi, J.-M., Krepper, E., Rohde, U., 2005. Inhomogeneous MUSIG Model—a population balance approach for polydispersed bubbly flows, International Conference “Nuclear Energy for New Europe 2005”, Bled, Slovenia, September 5–8, 2005; Krepper, E., Beyer, M., Frank, Th., Lucas, D., Prasser, H.-M., 2007. Application of a population balance approach for polydispersed bubbly flows, 6th Int. Conf. on Multiphase Flow Leipzig 2007, (paper 378)]. The current paper presents a brief description of the model principles. The capabilities of this model are discussed via the example of a bubbly flow around a half-moon shaped obstacle arranged in a 200 mm pipe. In applying the Inhomogeneous MUSIG approach, a deeper understanding of the flow structures is possible and the model allows effects of polydispersion to be investigated. For the complex flow around the obstacle, the general structure of the flow was well reproduced in the simulations. This test case demonstrates the complicated interplay between size dependent bubble migration and the effects of bubble coalescence and breakup on real flows. The closure models that characterize the bubble forces responsible for the simulation of bubble migration show agreement with the experimental observations. However, clear deviations occur for bubble coalescence and fragmentation. The models applied here, which describe bubble fragmentation and coalescence could be proved as a weakness in the validity of numerous CFD analyses of vertical upward two-phase pipe flow. Further work on this topic is under way.

多流体モデルによる気泡塔内多分散気泡流の数値計算(流体工学,流体機械)

Bubble coalescence and breakup models are implemented into the (N+2)-field model, which is a hybrid combination of a multi-fluid model and an interface tracking method to examine the applicability of available bubble coalescence and breakup models to poly-dispersed bubbly flows in bubble columns. The implemented models are a breakup model proposed by Luo & Svendsen and coalescence models proposed by Prince & Blanch and Wang et al. The validation of these models is carried out using experimental data for a coalescence-dominating flow, a breakup-dominating flow, a flow in-between, and a flow with low coalescence-breakup frequencies. Good predictions of void and bubble size distributions for the four kinds of poly-dispersed bubbly flows in bubble columns are obtained. It is also demonstrated that all the possible bubble coalescence mechanisms, i.e. bubble coalescence caused by bubble collisions due to turbulent eddies, the difference in bubble velocities and shear slip, and bubble coalescence due to wake entrainment, should be taken into account for obtaining good predictions.

The inhomogeneous MUSIG model for the simulation of polydispersed flows

A generalized inhomogeneous multiple size group (MUSIG) model based on the Eulerian modeling framework was developed in close cooperation of ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD code CFX. The model enables the subdivision of the dispersed phase into a number of size groups regarding the mass balance as well as regarding the momentum balance. In this work, the special case of polydispersed bubbly flow is considered. By simulating such flows, the mass exchanged between bubble size classes by bubble coalescence and bubble fragmentation, as well as the momentum transfer between the bubbles and the surrounding liquid due to bubble size dependent interfacial forces have to be considered. Particularly the lift force has been proven to play an important role in establishing a certain bubble size distribution dependent flow regime. In a previous study [Krepper, E., Lucas, D., Prasser, H.-M., 2005. On the modeling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611] the application of such effects were considered and justified and a general outline of such a model concept was given. In this paper the model and its validation for several vertical pipe flow situations is presented. The experimental data were obtained from the TOPFLOW test facility at the Forschungszentrum Dresden-Rossendorf (FZD). The wire-mesh technology measuring local gas volume fractions, bubble size distributions and velocities of gas and liquid phases were employed. The inhomogeneous MUSIG model approach was shown as capable of describing bubbly flows with higher gas content. Particularly the separation phenomenon of small and large bubbles is well described. This separation has been proven as a key phenomenon in the establishment of the corresponding flow regime. Weaknesses in this approach can be attributed to the characterization of bubble coalescence and bubble fragmentation, which must be further investigated.

Effects of Inlet Bubble Diameter on Bubbly Flow in a Bubble Column under High Gas Volume Flux Condition

Effects of inlet bubble diameter on void and bubble size distributions in poly-dispersed bubbly flow in a rectangular bubble column under high gas volumetric flux conditions are experimentally investigated. Three types of gas distributors are used to form bubbly flows with different inlet bubble diameters at a constant gas flow rate. The conclusions obtained are as follows : (1) the bubble size distribution reaches an equilibrium state at which the birth rate of bubbles belonging to a bubble group due to bubble breakup and coalescence is equal to the death rate at high gas volumetric flux, (2) distributions of void fraction and bubble diameter are not affected by inlet bubble diameters except for the region close to the air diffuser, and (3) the elevation at which the bubble size distribution reaches the equilibrium state becomes lower as the gas volumetric flux increases.

Numerical Simulation of Poly-Dispersed Bubbly Flow Using a Multi-Fluid Model

Numerical methods for predicting poly-dispersed bubbly flows in bubble columns are indispensable in the design of bubble column reactors. The objectives of the present study are (1) to experimentally investigate the effects of a bubble size distribution on poly-dispersed bubbly flows in an open vessel and (2) to examine the applicability of an (N+2)-field model (NP2) to poly-dispersed bubbly flows. Distributions of void fraction and liquid velocity in air-water bubble plumes in the vessel are measured using an experimental setup with a bubble injection device by which the ratio of the volume flow rate of large bubbles to that of small bubbles is controlled to a desired value. The main conclusions obtained are as follows: (1) experimental data on the effects of a bubble size distribution on air-water bubble plumes are obtained, and (2) NP2 gives good predictions for poly-dispersed bubble plumes.

A Hybrid Method for Predicting Dispersed Gas-Liquid and Liquid-Liquid Multi-Phase Flows

A hybrid CMFD (computational multi-fluid dynamics) method is proposed for the prediction of gas-liquid and/or liquid-liquid dispersed two-phase flows including large-scale interface, poly-dispersed bubbles and drops. The method is the hybrid integration of an interface tracking method (ITM), three kinds of particle tracking methods (PTM) and an averaging method based on a multi-fluid model (MFM). The integration enables us to cover a wide range of d*=d/Δx, where d is the particle diameter and Δx the grid size, and to perform various kinds of multiphase CFD such as standard interface tracking, particle tracking and multi-fluid simulations, and hybrid simulations by making an arbitrary combination of ITM, PTM and MFM. The field equations and numerical solution procedure of the proposed method are described in detail. To demonstrate its potential, a poly-dispersed air-water bubbly flow in a vertical square duct and an air-water bubble plume in an open vessel are computed using the combination of ITM, PTM and MFM.

Qualitative Validity of Volume Tracking Simulation of Bubble Motion with Low Spatial Resolution

The number of computational cells assigned to a small bubble is liable to be small in a volume tracking simulation of a poly-dispersed bubbly flow. The volume tracking method is, therefore, expected to at least give qualitatively reasonable predictions of bubble motion without assigning many cells. In this study, bubble motions in stagnant water and shear flows were simulated with low spatial resolutions using a volume tracking method proposed in our previous study. As a result, we confirmed that (1) the method could yield correct characteristics of rising velocity and lateral motion of bubbles, and (2) the bubble volume and interface sharpness were kept well even after a bubble had experienced a large deformation in a strong shear flow.