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    Tutorial: Modeling Bubble Breakup and Coalescence in a

    Bubble Column Reactor

    Introduction

    The purpose of this tutorial is to provide guidelines for solving the flow break-up, andcoalescence of gas bubbles in a gas-liquid bubble column reactor using a population balanceapproach coupled with the Eulerian multiphase model in FLUENT 6.3. The populationbalance approach is used to solve for bubble flow and size distribution in an axisymmetricbubble column, for a population of six different bubble sizes.

    This tutorial demonstrates how to do the following:

    Set up a two-phase, unsteady bubble column problem for an air-water bubble columnusing the Eulerian multiphase model.

    Activate and setup a population balance model with six bubble sizes.

    Solve the case using appropriate solver settings and solution monitors.

    Postprocess the resulting data for bubble size distribution.

    Prerequisites

    This tutorial assumes that you are familiar with the FLUENTinterface, basic setup, solutionprocedures, and the use of the Eulerian multiphase mixture model. This tutorial does notcover the mechanics of using this model, but focuses on setting up the population balanceproblem for bubble size distribution and solving it.

    The population balance module is provided as an add-on module with the standard FLUENTlicensed software. A special license is required to use the population balance module.

    If you have not used the Eulerian multiphase model before, refer to the FLUENT UsersGuide and the FLUENT Tutorial Guide. Also, refer the Population Balance Model Man-

    ual [2] for a comprehensive overview of the FLUENT population balance model and itsapplication in solving multiphase flows involving a secondary phase with a size distribution.

    Problem Description

    Figure 1 shows the schematic representation of the air-water bubble column of diameterof 0.29 m and height of 2 m. Air is injected into the water column through an inlet atthe bottom, which has a diameter of 0.23 m, with a constant velocity of 0.02 m/s. The

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    Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

    initial diameter of the injected air bubbles is 3 mm. You will model this column as a 2D,axisymmetric column.

    The injection of air causes the development of a turbulent flow pattern in the liquid column,which transports the bubbles throughout the column. Due to the effects of turbulence and

    collisions between individual bubbles, the bubbles breakup and coalesce with each other.As a result, bubbles with a range of sizes are formed in the bubble column. The sizedistribution of the bubbles, plays a critical role in any mass transfer and reactions thatmay occur between the air and the liquid, as in a Fischer-Tropsch synthesis process. Henceresolving the bubble size distribution is an important task in the CFD analysis of bubblecolumn reactors. This can be accomplished using the population balance model inFLUENT.

    Figure 1: Problem Schematic

    Solution Strategy

    1. In this tutorial, you will set up the two phase flow problem using the Eulerian mixturemutiphase model. The population balance model will be activated using TUI com-mands. The specialized panel for this model will be used to define the size distribution

    problem. you will select the discrete method with six size bins to represent the thebubble size distribution. The volume ratio will be set to 4 with a minimum size of0.001911 m or 1.911 mm. The six size bins correspond to the bubble diameters 0.012,0.00756, 0.004762, 0.003, 0.00189, and 0.001191 metres respectively. The size bins willbe chosen such that the inlet bubble size of 3 mm, i.e. 0.003 m, lies in the middle ofthe bin sizes. You will also activate the aggregation and breakage kernels and choosethe Luo model. The flow and population balance problem will be setup and solvedin transient mode until an equilibrium solution is reached. Finally, you will use thepostprocessing capabilities to analyze the flow and resulting size distribution.

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    Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

    2. The population balance model is used for solving multiphase flow problems wherethe secondary phase has a size distribution such as droplets, bubbles or crystals,which evolves and changes with the flow due to phenomena like nucleation, growth,aggregation or coalescence, and breakage.

    The population balance model uses a balance equation, similar to the mass, energyand momentum balance, to track the changes in the size distribution. The size dis-tribution can be determined using one of the three approaches: the discrete method,the standard method of moments and the quadrature method of moments. [2]

    In this tutorial, you will use the discrete method to compute the bubble size distribu-tion. Here, the range of particle sizes in the particle size distribution is divided into afinite number of intervals or discrete bins. The bubble sizes chosen for the bins arerequired to be in geometric progression with the ratio of bubbles volumes of adjacentsize bins, or volume ratio, set to an integer power of 2. Thus the bubble diameters arein geometric progression with a size ratio which is the cube root of an integer powerof 2.

    A transport equation is solved for each bin with a corresponding scalar, which repre-sents the volume fraction of gas in that bin. Thus, the sum of the scalars for all thediscrete bins is equal to the gas phase volume fraction. Source terms in the transportequation account for the birth and death of bubbles in each size bin, when theyenter or leave the bin due to breakup and coalescence. These terms are computedusing specific models, or kernels, which are published in the scientific literature.In this tutorial, you will use the breakup and coalescence kernels for bubble columnsdeveloped by Luo et.al. [3]

    After the transport equations for the scalars have been solved, the value of the numberdensity function for each size bin is calculated. This is simply the volume fractionof each bin i.e., the scalar value, divided by the volume of a single bubble, yielding

    the number of bubbles per unit volume or number density. The values of the numberdensity function for all size bins gives the bubble size distribution. The transportequations from the population balance model and the momentum equations are cou-pled due to user-defined drag based on Sauter mean diameter computed from theobtained size distribution.

    Both the number density function and the Sauter diameter are available in FLUENTforpostprocessing. Specialized postprocessing functions for the population balance modelhave been added to FLUENTYou will report and plot volume and surface averagesof the size distribution. You will also compute the statistical moments of the sizedistribution, which represent aggregate quantities such as the total number of bubblesor the total bubble surface area per unit volume. Please refer to[2], [3], and[4] for

    details regarding the population balance model and its application to bubble columnreactors.

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    Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

    Preparation

    1. Copy the file bubcol new2.msh.gz into your working folder.

    2. Start the 2D double precision (2ddp) version ofFLUENT.

    Setup and Solution

    Step 1: Grid

    1. Read the mesh file bubcol new2.msh.

    2. Check the grid.

    Grid Check

    3. Display the grid.

    Display Grid...

    4. Rotate the grid display.

    Display Views...

    (a) Selectaxis from the Mirror Planes selection list to enable the symmetry.

    (b) Click Camera... to open the Camera Parameters panel.

    i. Drag the indicator of the dial with the left mouse button in the counter-clockwise direction until the upright view is displayed (Figure 2).

    GridFLUENT 6.3 (2d, dp, pbns, lam)

    Figure 2: Grid Display

    ii. Click Applyand close the Camera Parameters panel.

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    Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

    (c) Click Apply and close the Views panel.

    5. Close theGrid Display panel.

    Step 2: Models

    1. Define the solver parameters.

    Define Models Solver...

    (a) SelectAxisymmetric from the Space list.

    (b) SelectUnsteadyfrom the Time list.

    (c) Click OK to close the Solver panel.

    2. Enable the Eulerian multiphase model.

    Define Models Multiphase...

    (a) SelectEulerian from the Model list.

    (b) Click OK to close the Multiphase Modelpanel.

    3. Enable turbulence model.

    Define Model Viscous...

    (a) Select standard k-epsilon (2 eqn) from the Model list.

    (b) SelectMixture from the k-epsilon Multiphase Model list.

    (c) Click OK to close the Viscous Model panel.

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    Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

    Step 3: Materials

    1. Copy a new material from the materials database.

    Define Materials...

    (a) Click Fluent Database... to open the Fluent Database Materials panel.

    (b) Select water-liquid (h2o) from the Fluent Fluid Material list.

    (c) Click Copy and close the Fluent Database Materials and Materials panel.

    Step 4: Phases

    1. Define new phases.

    Define Phases...

    (a) Set water-liquidas the primary-phase.(b) Set air as the secondary-phase.

    Step 5: O