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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 13.0 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 Section26.5, Setting Up the Eulerian Modelin ANSYS FLUENT 13.0 Users 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 13.0 Population Balance Model Manual.

c ANSYS, Inc. January 24, 2011 1


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Modeling Bubble Breakup and Coalescence in a Bubble Column Reactor

Problem Description

Figure1 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 initial

diameter 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 ANSYS

FLUENT.

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.

2 c ANSYS, Inc. January 24, 2011


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(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 0.001911 m or 1.911 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, lies

in 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 birthand deathof 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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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 diameter

computed 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 toANSYS 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 ofANSYS FLU-ENT.

For more information aboutFLUENT Launcher see Section1.1.2, StartingANSYS FLUENT Using FLUENT Launcher inANSYS FLUENT 13.0 Users Guide.

TheDisplay 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) SelectTransient from the Time list.

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



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2. Check the mesh.

General Check

3. Rotate the mesh display.

Display

Views...(a) Selectaxis 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 Applyand close the Camera Parameters dialog box.

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

4. Close theMesh Displaydialog box.

Step 3: Models

1. Enable Eulerian multiphase model.

Models Multiphase Edit...

(a) SelectEulerian from the Model list.

(b) Click OK to close the Multiphase Modeldialog 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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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)from the FLUENT Fluid Material list.

ii. Click Copyand 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-liquidforName.

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

(b) Enable Specified Operating Density and retain a value of1.225 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 theModels menu.



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2. Set the parameters for the population balance model.

Models Population Balance Edit...

(a) Ensure thatDiscrete is selected from the Method list.

(b) Ensure thatGeometric Ratiois selected from the Definition list.

(c) Ensure thatairis selected from the Phase drop-down list.

(d) Enter6 for Bins, 2 for Ratio Exponent, and0.001191m forMin in theBinsgroupbox.

(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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(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 theSecondary Phase dialog box, theDiameter property changes to sauter-mean

i.e. the Population Balance model is automatically set to calculate theDiameterfor the mean bubble size.

Step 8: Boundary Conditions

1. Set boundary conditions for inlet.

Boundary Conditions vinlet

(a) Selectair 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. Enter0.02 m/s for the Velocity Magnitude.

ii. Click the Multiphase tab.

A. Enter1 for the Volume Fraction.

B. Ensure thatSpecified Valueis selected from the Boundary Conditiondrop-down lists for all the Population Balance variables.

C. Enter1forBin-3-fraction and retain the default value of0 for the othervariables in the Boundary Value group box.

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



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(b) Selectmixture 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 Intensityand 0.145m for Hydraulic Diameter.

iii. Click OKto close the Velocity Inlet dialog box.

2. Set the boundary conditions for the outlet.

Boundary Conditions outlet

(a) Selectair 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 ofBin-3-fractionto 1 and retain 0 for the other variables in theBoundary Value group box.

iii. Click OKto close the Pressure Outletdialog box.

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

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

ii. Enter5% forBackflow Turbulent Intensityand0.145m forBackflow HydraulicDiameter.

iii. Click OKto close the Pressure Outletdialog 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 Couplinggroup box.

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

2. Retain the default values forUnder-Relaxation Factors.

Solution Controls

3. Initialize the solution.

Solution Initialization

(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) Enter1 for air Bin-3-fraction.

(c) Click Initialize.

4. Mark the region for adaption.

Adapt Region...



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

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

Parameter Value

X Min 1.8

X Max 2.0Y Min 0

Y Max 0.145

(c) Click Markto select the region for adaption.

(d) Close the Region Adaptiondialog box.

5. Patch the selected regions.

Solution Initialization Patch...

(a) Selectair from the Phase drop-down list.

(b) Select Bin-3-fraction from the Variable list and enter 1 for Value.(c) Selecthexahedron-r0 for Registers to Patch.

(d) Click Patch.

(e) SelectVolume 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...

(a) Enterx0 (m) = 1.5andy0 (m)= 0.

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

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

Monitors (Surface Monitors) Create...

(a) EnablePlotand Write.



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

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

(d) SelectTime Step from the Everydrop-down list.

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

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

(g) Selectair from the Phase drop-down list.

(h) Selectpoint-5from the Surfaces list.

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

8. Create a surface monitor forBin-3-fraction.

Monitors (Surface Monitors) Create...

Set the parameters as shown in the following dialog box.

9. Create a surface monitor forBin-5-fraction.

Monitors (Surface Monitors) Create...Set the parameters as shown in the following dialog box.



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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 exitANSYS FLUENT and read the casefile in a new session (so that the settings are applied).

11. ExitANSYS FLUENT.

Step 10: Calculation

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

2. Initialize the solution and patch the regions. RepeatStep 9: 35.

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 forMax Iterations/Time Step.

(d) Click Calculate.

The scaled residuals are as shown in Figure3. Figures4-6show the plots of con-vergence history ofBin-0-fraction, Bin-3-fraction, andBin-5-fraction, respectively.

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



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Figure 3: Scaled Residuals

Figure 4: Convergence History ofBin-0-fraction



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Step 11: Postprocessing

1. Display the filled contours of air volume fraction.

Graphics and Animations Contours Set Up...

(a) SelectPhases... and Volume fractionfrom the Contours ofdrop-down list.

(b) Selectair from the Phase drop-down list.

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

(d) Click Display(see Figure7).

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) SelectVelocity and water-liquid from the Vectors of and Phase drop-down listsrespectively.

(b) Click Display(see Figure8).



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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) Enter 0 for Min and 1forMax.


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.



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Report Population Balance Moments...

(a) IncreaseNumber Of Moments to 4.

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

>

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

Moment Number Moment

------------------------- ------------------------

0 1489889.2

1 5600.0782

2 27.479965

3 0.19211298

Population Balance Moments over Volume(s) (fluid)

Moment Number Moment

------------------------- ------------------------

0 1483171.4

1 5582.8814

2 27.470498

3 0.19260043

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

Report Population Balance Number Density...

(a) SelectVolume Average from the Report Type list.

(b) SelectDiscrete Number Density from the Fields list.



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(c) SelectHistogramfrom the Plot Type list.

Histogramis enabled only after you selectDiscrete Number Densityfrom theFieldslist.

(d) Select fluid from the Cell Zones list.

(e) ClickPrintto print the values in theANSYS FLUENTconsole. The values printedin the console are as shown:

>

Number Density for Discrete Method

Particle Diameter Number Density

------------------------- ------------------------

0.012004528 66031.477

0.0075623785 76371.661

0.004764 114764.32

0.0030011319 1216879.3

0.0018905946 4335.91130.001191 4788.7544

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

Surface Iso-Surface...

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

(b) Enter1 for Iso-Values.

(c) Enterx=1forNew Surface Name.

(d) Click Create.

(e) Close theIso-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...

(a) SelectSurface Average from the Report Type list.

(b) SelectDiscrete Number Density from the Fields selection list.



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(c) SelectHistogramfrom the Plot Type list.

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

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

The values printed in the console are as shown:

Number Density for Discrete Method

Particle Diameter Number Density

--------------------------------- ------------------------

0.1941455 0.65229802

0.077046692 125.01903

0.030576 2729.8223

0.012134094 29808.771

0.0048154183 2617.7323

0.001911 940.51139

(f) Click Plot to plot the histogram of the surface averaged number density distri-

bution with bubble diameter (see Figure 11).

Figure 11: Surface Averaged Number Density Distribution Histogram



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

Plots XY Plot Set Up...

(a) SelectPopulation Balance Variables... andBin-3-fractionfrom theY Axis Function

drop-down lists.(b) Selectair from the Phase drop-down list.

(c) Selectaxis from the Surfaces list.

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

i. Disable Auto Range from the Options list.

ii. Enter 1.8for Maximumand clickApply.

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

(e) Click Plot(see Figure12).

You can see the initial bubble size distribution.

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

TheBin-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...



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


(c) Click theSelectbutton to include this variable.

(d) Click the multiplication signx.

(e) SelectPhases... andVolume 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 functiondiscrete-size-3-fraction.


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

(b) Disable Auto Range and enter 0forMinand 0.04forMax.

(c) Click Display(see Figure13).

(d) Close the Contours dialog box.

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


(a) SelectProperties... from the Contours ofdrop-down list.


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

TheDiameter option is available only after selectingair.




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

Figure 14: Contours of Sauter Diameter



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

Plots Histogram Set Up...

(a) SelectProperties... from the Histogram ofdrop-down list.


(c) SelectDiameter from the Histogram ofdrop-down list as the fluid property.

(d) Click Plot (see Figure15).

The plot shows the distribution of the length number density of bubbles with Sauter

diameter. You can also clickPrintto print the distribution in theANSYS FLUENTconsole.



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Figure 15: Histogram of Sauter Diameter Distribution

Suggested Exercises

1. Calculate the gas hold-up in the column using the volume integration tools in ANSYSFLUENTand 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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