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.
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.
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
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.
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.
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.
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).
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:
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.
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.