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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, and coalescence of gas bubbles in a gas-liquid bubble column reactor using a population balance approach coupled with the Eulerian multiphase model. The population balance approach is used to solve for bubble flow and size distribution in an axisymmetric bubble 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 column using the Eulerian multiphase model. Enable and set up 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 is written with the assumption that you have completed Tutorial 1 from ANSYS FLUENT 14.0 Tutorial Guide, and that you are familiar with the ANSYS FLUENT navigation pane and menu structure. Some steps in the setup and solution procedure will not be shown explicitly. This tutorial assumes that you are familiar with the use of the Eulerian multiphase mixture model. This tutorial does not cover the mechanics of using this model, but focuses on setting up the population balance problem for bubble size distribution and solving it. For details on Eulerian multiphase model, refer to Section 26.5, Setting Up the Eulerian Model in ANSYS FLUENT 14.0 User’s Guide. The population balance module is provided as an add-on module with the standard ANSYS FLUENT licensed software. A special license is required to use the population balance module. For a comprehensive overview of the ANSYS FLUENT population balance model and its application in solving multiphase flows involving a secondary phase with a size distribution, refer to ANSYS FLUENT 14.0 Population Balance Model Manual. c ANSYS, Inc. March 7, 2012 1

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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. The population balance approachis used to solve for bubble flow and size distribution in an axisymmetric bubble column fora 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.

• Enable and set up 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 is written with the assumption that you have completed Tutorial 1 fromANSYS FLUENT 14.0 Tutorial Guide, and that you are familiar with the ANSYS FLUENTnavigation pane and menu structure. Some steps in the setup and solution procedure willnot be shown explicitly.

This tutorial assumes that you are familiar with the use of the Eulerian multiphase mixturemodel. This tutorial does not cover the mechanics of using this model, but focuses onsetting up the population balance problem for bubble size distribution and solving it. Fordetails on Eulerian multiphase model, refer to Section 26.5, Setting Up the Eulerian Modelin ANSYS FLUENT 14.0 User’s Guide.

The population balance module is provided as an add-on module with the standard ANSYSFLUENT licensed software. A special license is required to use the population balancemodule. For a comprehensive overview of the ANSYS FLUENT population balance modeland its application in solving multiphase flows involving a secondary phase with a sizedistribution, refer to ANSYS FLUENT 14.0 Population Balance Model Manual.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Problem Description

Figure 1 shows the schematic representation of the air-water bubble column of diameter of0.29 m and height of 2 m. Air is injected into the water column through an inlet at thebottom, which has a diameter of 0.23 m, with a constant velocity of 0.02 m/s. The initialdiameter of the injected air bubbles is 3 mm. Model this column as a 2D, axisymmetriccolumn.

Figure 1: Problem Schematic

Strategy

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 andcollisions 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 in ANSYSFLUENT.

1. In this tutorial, you will set up the two phase flow problem using the Eulerian mixturemultiphase model.

(a) Enable the population balance model using the TUI commands.

(b) Use the specialized dialog box for this model to define the size distribution prob-lem.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(c) Select the discrete method with six size bins to represent the the bubble sizedistribution.

(d) Set the volume ratio to 4 with a minimum size of 0.001191 m or 1.191 mm. Thesix size bins correspond to the bubble diameters 0.012, 0.00756, 0.004762, 0.003,0.00189, and 0.001191 metres respectively.

(e) Choose the size bins such that the inlet bubble size of 3 mm, i.e. 0.003 m, liesin the middle of the bin sizes.

(f) Enable the aggregation and breakage kernels and choose the Luo model.

(g) Set up and solve the flow and population balance problem in transient modeuntil an equilibrium solution is reached.

(h) Finally, use the postprocessing capabilities to analyze the flow and resulting sizedistribution.

2. Use the population balance model for solving multiphase flow problems where thesecondary phase has a size distribution such as droplets, bubbles or crystals, whichevolves and changes with the flow due to phenomena like nucleation, growth, aggre-gation or coalescence, and breakage.

The population balance model uses a balance equation, similar to the mass, energy andmomentum balance, to track the changes in the size distribution. The size distributioncan be determined using one of the four approaches:

• The discrete method.

• The inhomogenous discrete method.

• The standard method of moments.

• The quadrature method of moments.

3. Use the discrete method to compute the bubble size distribution. Here, the range ofparticle sizes in the particle size distribution is divided into a finite number of intervalsor discrete bin.

• The bubble sizes chosen for the bins have to be in geometric progression with theratio of bubble volumes of adjacent size bins, or volume ratio, set to an integerpower of 2. Thus the bubble diameters are in geometric progression with a sizeratio which is the cube root of an integer power of 2.

• A transport equation is solved for each bin with a corresponding scalar, whichrepresents the volume fraction of gas in that bin. Thus, the sum of the scalarsfor all the discrete bins is equal to the gas phase volume fraction.

• Source terms in the transport equation account for the birth and death of bubblesin each size bin, when they enter or leave the bin due to breakup and coalescence.These terms are computed using specific models or kernels which are published inthe scientific literature. In this tutorial, you will use the breakup and coalescencekernels for bubble columns developed by Luo et.al. [1]

• After solving the transport equations for the scalars, calculate the value of thenumber density function for each size bin. This is the volume fraction of eachbin i.e. the scalar value, divided by the volume of a single bubble, yielding the

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

number of bubbles per unit volume or number density. The values of the numberdensity function for all size bins give the bubble size distribution.

• The transport equations from the population balance model and the momentumequations are coupled due to user-defined drag based on Sauter mean diametercomputed from the obtained size distribution. Both the number density functionand the Sauter diameter are available in ANSYS FLUENT for postprocessing.Specialized postprocessing functions for the population balance model have beenadded to ANSYS FLUENT.

4. Report and plot volume and surface averages of the size distribution. You will alsocompute the statistical moments of the size distribution, which represent aggregatequantities such as the total number of bubbles or the total bubble surface area perunit volume.

For details about the population balance model and its application to bubble columnreactors, refer to [1] and [2].

Setup and Solution

Preparation

1. Copy the mesh file (bubcol new2.msh.gz) to your working folder.

2. Use FLUENT Launcher to start the 2D double precision 2ddp version of ANSYS FLU-ENT.

For more information about FLUENT Launcher see Section 1.1.2, StartingANSYS FLUENT Using FLUENT Launcher in ANSYS FLUENT 14.0 User’s Guide.

The Display Options are enabled by default. Therefore, after you read in the mesh, itwill be displayed in the embedded graphics window.

Step 1: Mesh

1. Read the mesh file (bubcol new2.msh).

File −→ Read −→Mesh...

As the mesh file is read, ANSYS FLUENT will report the progress in the console.

Step 2: General Settings

1. Define the solver settings.

General

(a) Select Transient from the Time list.

(b) Select Axisymmetric from the 2D Space list.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

2. Check the mesh.

General −→ Check

3. Rotate the mesh display.

Display −→Views...

(a) Select axis from the Mirror Planes list to enable the symmetry.

(b) Click Camera... to open the Camera Parameters dialog box.

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

Figure 2: Mesh Display

ii. Click Apply and close the Camera Parameters dialog box.

(c) Click Apply and close the Views dialog box.

4. Close the Mesh Display dialog box.

Step 3: Models

1. Enable Eulerian multiphase model.

Models −→ Multiphase −→ Edit...

(a) Select Eulerian from the Model list.

(b) Click OK to close the Multiphase Model dialog box.

2. Enable turbulence model.

Models −→ Viscous −→ Edit...

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

(b) Click OK to close the Viscous Model dialog box.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Step 4: Materials

1. Copy a new material from the materials database.

Materials −→ Create/Edit...

(a) Click FLUENT Database... to open the FLUENT Database Materials dialog box.

i. Select water-liquid (h2o<l>) from the FLUENT Fluid Material list.

ii. Click Copy and close the FLUENT Database Materials dialog box.

(b) Click Change/Create and close the Create/Edit Materials dialog box.

Step 5: Phases

1. Define the primary phase (water-liquid).

Phases −→ phase-1-Primary Phase −→ Edit...

(a) Enter water-liquid for Name.

(b) Select water-liquid from the Phase Material drop-down list.

(c) Click OK to close the Primary Phase dialog box.

2. Similarly, define the secondary phase (air).

Step 6: Operating Conditions

1. Specify the following operating conditions

Boundary Conditions −→ Operating Conditions...

(a) Enable Gravity and set the Gravitational Acceleration to a value of -9.81 m/s2 inthe X direction.

(b) Enable Specified Operating Density and retain a value of 1.225 kg/m3 for Oper-ating Density.

(c) Click OK to close the Operating Conditions dialog box.

Step 7: Population Balance Model Setup

1. Enable the population balance model.

(a) Enter the TUI command, define models addon-module, in the console.

(b) Enter 5 for the module number to enable the Population Balance model.

The GUI now changes and an item is added to the Models menu.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

2. Set the parameters for the population balance model.

Models −→ Population Balance −→ Edit...

(a) Ensure that Discrete is selected from the Method list.

(b) Ensure that Geometric Ratio is selected from the Definition list.

(c) Ensure that air is selected from the Phase drop-down list.

(d) Enter 6 for Bins, 2 for Ratio Exponent, and 0.001191 m for Min in the Bins groupbox.

(e) Click Print Bins to print the discrete bubble sizes for each bin.

(f) Enable Aggregation Kernel and Breakage Kernel from the Phenomena group box.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(g) Select luo-model from the Aggregation Kernel and Frequency drop-down lists.Leave the surface tension requested by the model as default.

(h) Click OK to close the Population Balance Model dialog box.

In the Secondary Phase dialog box, the Diameter property changes to sauter-meani.e. the Population Balance model is automatically set to calculate the Diameterfor the mean bubble size.

Step 8: Boundary Conditions

1. Set boundary conditions for inlet.

Boundary Conditions −→ vinlet

(a) Select air from the Phase drop-down list and click Edit....

i. Click the Momentum tab.

A. Select Magnitude, Normal to Boundary from the Velocity SpecificationMethod drop-down list.

B. Enter 0.02 m/s for the Velocity Magnitude.

ii. Click the Multiphase tab.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

A. Enter 1 for the Volume Fraction.

B. Ensure that Specified Value is selected from the Boundary Condition drop-down lists for all the Population Balance variables.

C. Enter 1 for Bin-3-fraction and retain the default value of 0 for the othervariables in the Boundary Value group box.

D. Click OK to close the Velocity Inlet dialog box.

(b) Select mixture from the Phase drop-down list and click Edit....

i. Click the Momentum tab and select Intensity and Hydraulic Diameter fromthe Specification Method drop-down list.

ii. Enter 5 % for Turbulent Intensity and 0.145 m for Hydraulic Diameter.

iii. Click OK to close the Velocity Inlet dialog box.

2. Set the boundary conditions for the outlet.

Boundary Conditions −→ outlet

(a) Select air from the Phase drop-down list and click Edit....

i. Click the Multiphase tab and enter 1 for Backflow Volume Fraction.

ii. Set the value of Bin-3-fraction to 1 and retain 0 for the other variables in theBoundary Value group box.

iii. Click OK to close the Pressure Outlet dialog box.

(b) Select mixture from the Phase drop-down list and click Edit....

i. Select Intensity and Hydraulic Diameter from the Specification Method drop-down list.

ii. Enter 5 % for Backflow Turbulent Intensity and 0.145 m for Backflow HydraulicDiameter.

iii. Click OK to close the Pressure Outlet dialog box.

Step 9: Solution

1. Set the solution method parameters.

Solution Methods

(a) Ensure that Phase Coupled SIMPLE is selected from Scheme drop-down list inPressure-Velocity Coupling group box.

(b) Retain the default settings for the Spatial Discretization parameters.

2. Retain the default values for Under-Relaxation Factors.

Solution Controls

3. Initialize the solution.

Solution Initialization

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(a) Enter 0.1 (m2/s2) for Turbulent Kinetic Energy and 0.25 (m2/s3) for TurbulentDissipation Rate in the Initial Values group box.

(b) Enter 1 for air Bin-3-fraction.

(c) Click Initialize.

4. Mark the region for adaption.

Adapt −→Region...

(a) Retain selection of Inside from the Options list and Quad from the Shapes list.

(b) Enter the values for the coordinates as shown in the following table:

Parameter ValueX Min 1.8X Max 2.0Y Min 0Y Max 0.145

(c) Click Mark to select the region for adaption.

(d) Close the Region Adaption dialog box.

5. Patch the selected regions.

Solution Initialization −→ Patch...

(a) Select air from the Phase drop-down list.

(b) Select Bin-3-fraction from the Variable list and enter 1 for Value.

(c) Select hexahedron-r0 for Registers to Patch.

(d) Click Patch.

(e) Select Volume Fraction from the Variable list and set Value to 1.

(f) Click Patch and close the Patch dialog box.

6. Set surface point.

Surface −→Point...

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(a) Enter x0 (m) = 1.5 and y0 (m) = 0.

(b) Keep New Surface Name as point-5 and click Create.

7. Create a surface monitor for Bin-0-fraction.

Monitors (Surface Monitors)−→ Create...

(a) Enable Plot and Write.

(b) Enter surf-mon-1.out for the File Name.

(c) Select Time Step from the X Axis drop-down list.

(d) Select Time Step from the Every drop-down list.

(e) Select Vertex Average from the Report Type drop-down list.

(f) Select Population Balance Variables... and Bin-0-fraction from the Field Variabledrop-down list.

(g) Select air from the Phase drop-down list.

(h) Select point-5 from the Surfaces list.

(i) Click OK to close the Surface Monitor dialog box.

8. Create a surface monitor for Bin-3-fraction.

Monitors (Surface Monitors)−→ Create...

Set the parameters as shown in the following dialog box.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

9. Create a surface monitor for Bin-5-fraction.

Monitors (Surface Monitors)−→ Create...

Set the parameters as shown in the following dialog box.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

10. Save the initial case file (bubcol new2-initial.cas.gz).

When using the population balance model, the settings do not get applied to the solver.In order to get appropriate results, you need to exit ANSYS FLUENT and read the casefile in a new session (so that the settings are applied).

11. Exit ANSYS FLUENT.

Step 10: Calculation

1. Read the case file (bubcol new2-initial.cas.gz) in a new ANSYS FLUENTsession.

2. Initialize the solution and patch the regions. Repeat Step 9: 3–5.

3. Set the time stepping parameters.

Run Calculation

(a) Enter 0.01 s for Time Step Size.

(b) Enter 5000 for Number of Time Steps.

(c) Enter 100 for Max Iterations/Time Step.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(d) Click Calculate.

The scaled residuals are as shown in Figure 3. Figures 4-6 show the plots of con-vergence history of Bin-0-fraction, Bin-3-fraction, and Bin-5-fraction, respectively.

4. Save the case and data files (bubcol new2.cas/dat.gz).

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 3: Scaled Residuals

Figure 4: Convergence History of Bin-0-fraction

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 5: Convergence History of Bin-3-fraction

Figure 6: Convergence History of Bin-5-fraction

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Step 11: Postprocessing

1. Display the filled contours of air volume fraction.

Graphics and Animations −→ Contours −→ Set Up...

(a) Select Phases... and Volume fraction from the Contours of drop-down list.

(b) Select air from the Phase drop-down list.

(c) Disable Auto Range from the Options list and enter 0 for Min and 0.1 for Max.

(d) Click Display (see Figure 7).

Figure 7: Contours of Volume Fraction of Air

The changes in phase from inlet to outlet, and areas with low volume fraction aswell as dead zones can be observed.

2. Create a vector plot for water velocity and observe the recirculation patterns.

Graphics and Animations −→ Vectors −→ Set Up...

(a) Select Velocity and water-liquid from the Vectors of and Phase drop-down listsrespectively.

(b) Click Display (see Figure 8).

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 8: Water Velocity Vector Colored by Velocity magnitude of Water

3. Create a contour plot of population balance for air phase.

(a) Select Population Balance Variables... and Bin-0-fraction from the Contours ofdrop-down lists.

(b) Select air from the Phase drop-down list.

(c) Click Display (see Figure 9).

Figure 9: Contours of Bin-0-fraction for Air Phase

4. Calculate the moments of the bubble size distribution for the fluid region and theoutlet.

Report −→ Population Balance −→Moments...

(a) Increase Number Of Moments to 4.

(b) Ensure that fluid is selected from the Cell Zones list and click Print. The valuesof the moments are printed in the ANSYS FLUENT window are as shown:

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

>

Population Balance Moments over Surface(s) (default-interior)Moment Number Moment

------------------------- ------------------------0 1539977.11 5773.34182 28.0914443 0.19237414

Population Balance Moments over Volume(s) (fluid)Moment Number Moment

------------------------- ------------------------0 1533654.11 5757.65172 28.0882993 0.19286639

5. Plot the volume averaged discrete number density function distribution for differentbubble sizes for the fluid volume.

Report −→ Population Balance −→Number Density...

(a) Select Volume Average from the Report Type list.

(b) Select Discrete Number Density from the Fields list.

(c) Select Histogram from the Plot Type list.

Histogram is enabled only after you select Discrete Number Density from the Fieldslist.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(d) Select fluid from the Cell Zones list.

(e) Click Print to print the values in the ANSYS FLUENT console. The values printedin the console are as shown:

>

Number Density for Discrete MethodParticle Diameter Number Density

------------------------- ------------------------0.012004528 61481.7770.0075623785 90768.764

0.004764 130437.590.0030011319 1221509.50.0018905946 15388.33

0.001191 14068.122

(f) Click Plot to plot the histogram of the volume averaged number density distri-bution with bubble diameter (see Figure 10).

Figure 10: Volume Averaged Number Density Distribution Histogram

You can also plot the length and volume based number density distribution.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

6. Create a surface x=1 with x-coordinate equal to 1.

Surface −→Iso-Surface...

(a) Select Mesh... and X-Coordinate from the Surface of Constant drop-down list.

(b) Enter 1 for Iso-Values.

(c) Enter x=1 for New Surface Name.

(d) Click Create.

(e) Close the Iso-Surface dialog box.

7. Plot the surface averaged discrete number density function distribution for differentbubble sizes for the surface at x=1.

Report −→ Population Balance −→Number Density...

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(a) Select Surface Average from the Report Type list.

(b) Select Discrete Number Density from the Fields selection list.

(c) Select Histogram from the Plot Type list.

(d) Select x=1 from the Surfaces list.

(e) Click Print to print the values in the ANSYS FLUENT console.

The values printed in the console are as shown:

Number Density for Discrete MethodParticle Diameter Number Density

--------------------------------- ------------------------0.1941455 14224.253

0.077046692 24425.0060.030576 39920.434

0.012134094 79730.2580.0048154183 1146.9032

0.001911 1920.4554

(f) Click Plot to plot the histogram of the surface averaged number density distri-bution with bubble diameter (see Figure 11).

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 11: Surface Averaged Number Density Distribution Histogram

8. Plot the distribution along the central axis of the bubble column for each scalar.

Plots −→ XY Plot −→ Set Up...

(a) Select Population Balance Variables... and Bin-3-fraction from the Y Axis Functiondrop-down lists.

(b) Select air from the Phase drop-down list.

(c) Select axis from the Surfaces list.

(d) Click Axes... to open the Axes - Solution XY Plot dialog box.

i. Disable Auto Range from the Options list.

ii. Enter 1.8 for Maximum and click Apply.

iii. Close the Axes-Solution XY Plot dialog box.

(e) Click Plot (see Figure 12).

You can see the initial bubble size distribution.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 12: Distribution of Bubble Size Along the Axis for Bin-3-fraction

The Bin-3-fraction (initial bubble size) decreases from inlet to outlet.

(f) Close the Solution XY Plot dialog box.

Breakup and coalescence are irrelevant in the freeboard region, which does notcontain water.

9. Create and plot a custom field function that calculates the fraction of air containedin a bubble size corresponding to Bin-3-fraction.

Define −→Custom Field Functions...

(a) Select Population Balance Variables... and Bin-3-fraction from the Field Functionsdrop-down lists.

(b) Select air from the Phase drop-down list.

(c) Click the Select button to include this variable.

(d) Click the multiplication sign x.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(e) Select Phases... and Volume fraction from the Field Functions drop-down list andclick the Select button.

(f) Enter discrete-size-3-fraction for New Function Name.

(g) Click Define to create the function.

(h) Close the Custom Field Function Calculator dialog box.

10. Plot the contours of the custom field function discrete-size-3-fraction.

Graphics and Animations −→ Contours −→ Set Up...

(a) Select Custom Field Functions... and discrete-size-3-fraction from the Contours ofdrop-down list.

(b) Disable Auto Range and enter 0 for Min and 0.04 for Max.

(c) Click Display (see Figure 13).

(d) Close the Contours dialog box.

11. Plot contours of the distribution of the Sauter diameter.

Graphics and Animations −→ Contours −→ Set Up...

(a) Select Properties... from the Contours of drop-down list.

(b) Select air from the Phase drop-down list.

(c) Select Diameter from the Contours of drop-down list as the fluid property forplotting.

The Diameter option is available only after selecting air.

(d) Click Display (see Figure 14).

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 13: Contours of Custom Field Function discrete-size-3-fraction

Figure 14: Contours of Sauter Diameter

12. Similarly, plot the histogram of the Sauter diameter distribution in the fluid volume.

Plots −→ Histogram −→ Set Up...

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

(a) Select Properties... from the Histogram of drop-down list.

(b) Select air from the Phase drop-down list.

(c) Select Diameter from the Histogram of drop-down list as the fluid property.

(d) Click Plot (see Figure 15).

The plot shows the distribution of the length number density of bubbles with Sauterdiameter. You can also click Print to print the distribution in the ANSYS FLUENTconsole.

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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Figure 15: Histogram of Sauter Diameter Distribution

Suggested Exercises

1. Calculate the gas hold-up in the column using the volume integration tools in ANSYSFLUENT and knowing the initial dimensions of the water column.

2. Rerun the case for a finer bubble size distribution using a geometric volume ratio of2 around the inlet bubble diameter of 3 mm.

Summary

This tutorial used the population balance approach to solve the bubble size and flow dis-tribution in an axisymmetric bubble column and illustrated the setup, solution process andpostprocessing of gas-liquid multiphase flows with a size distribution. It used the discretemethod to calculate the bubble size distribution for the population of six different bubblesizes.

References

[1] Luo, Hean; Svendsen, Hallvard F., Theoretical model for drop and bubble breakup inturbulent dispersions, AIChE Journal v. 42, no. 5, May 1996, pp. 1225-1233.

[2] Sanyal, J.; Vasquez, S.; Roy, S.; Dudukovic, M.P., Numerical simulation of gas-liquiddynamics in cylindrical bubble column reactors, Chemical Engineering Science, v. 54, no.21, 1999, p. 5071-5083.

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