Eulerian Species

Tutorial: Using the Eulerian Multiphase Model with Species

Transport

Introduction

Fluidized beds are used in processes where gas/solid mass transfer is of importance. The de-composition of ozone (O3), using particles as a catalyst, creates a suitable low-temperatureenvironment for mass transfer. This tutorial solves a gas/solid flow with a simple one-stepozone decomposition reaction in a fluidized bed.

The reaction equation is

O3 → 1.5O2 (1)

This tutorial demonstrates how to do the following:

• Use the granular Eulerian multiphase model with species transport.

• Define the rate of reaction with a user-defined function (UDF).

• Define the Syamlal-O’Brien drag correlation with a user-defined function (UDF) usingappropriate parameters.

• Set boundary conditions for internal flow.

• Define the fluid and solid phases.

• Calculate a solution using 2D planar geometry in conjunction with the pressure-basedsolver.

• Solve a time-accurate transient problem with data sampling for time statistics.

Prerequisites

This tutorial assumes that you are familiar with the FLUENT interface and that you have agood understanding of basic setup and solution procedures. Some steps will not be shownexplicitly.

In this tutorial you will use the Eulerian multiphase model with species transport. If youhave not used this feature before, refer to the FLUENT 6.3 User’s Guide.

c© Fluent Inc. October 30, 2006 1

Using the Eulerian Multiphase Model with Species Transport

Problem Description

The problem involves the transient startup of ozone decomposition in a fluidized bed. Thefluid phase is a mixture of ozone and air, while the solid phase consists of sand particleswith an 87.75 micron diameter. A schematic of the fluidized bed is shown in Figure 1. Thedomain is modeled as a 2D planar cylindrical case.

volume fraction

0.52

of solids

pressure outlet

uniform velocity inletu = 0.08 m/s

0 Pa gauge

Figure 1: Problem Specification

2 c© Fluent Inc. October 30, 2006


Preparation

1. Copy the files 2-D-FBed Ozone.msh.gz, rrate.c, and bp drag.c to your workingfolder.

2. Start the 2D double-precision (2ddp) version of FLUENT.

Setup and Solution

Step 1: Grid

1. Read the grid file (2-D-FBed_Ozone.msh).

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole. Make sure the minimum volume reported is a positive number.

3. Display the grid using the default settings.

Display −→Grid...

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

Figure 2: Grid Display

4. Rotate the view so that the inlet of the fluidized bed is at the bottom.

Display −→Views...



(a) Click the Camera... button 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 (-90◦) is displayed (Figure 2).

ii. Close the Camera Parameters panel.

(b) Click the Save button in the Actions group box in the Views panel to save theupright view.

When you do this, view-0 will be added to the list of Views.

(c) Close the Views panel.

You can use the probe mouse button to check which zone number corresponds to eachboundary. If you click the probe mouse button on one of the boundaries in the graphicswindow, its zone number, name, and type will be printed in the FLUENT console. Thisfeature is especially useful when you have several zones of the same type and you wantto distinguish between them quickly.



Step 2: Models

1. Specify a transient, 2D model.

Define −→ Models −→Solver...

(a) Retain the default selection of Pressure Based from the Solver list and 2D fromthe Space list.

The pressure based solver must be used for multiphase calculations.

(b) Select Unsteady from the Time list.

(c) Click OK to close the Solver panel.

2. Define the multiphase model.

Define −→ Models −→Multiphase...

(a) Select Eulerian from the Model list.

The panel will expand to show the inputs for the Eulerian model.



(b) Retain the default value of 2 for Number of Phases.

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

3. Define the species model.

Define −→ Models −→ Species −→Transport & Reaction...

(a) Select Species Transport from the Model list.

The Species Model panel will expand.

(b) Enable Volumetric from the Reactions group box.

(c) Disable Diffusion Energy Source from the Options group box.

(d) Click OK to close the Species Model panel.



FLUENT will list the properties required for the models that you enabled, in theconsole. An Information dialog box will appear, reminding you to confirm theproperty values that have been extracted from the database.

(e) Click OK in the Information dialog box to continue.

Step 3: Materials

Define −→Materials...

1. Create a new material called air+ozone.

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

i. Select fluid from the Material Type drop-down list.

ii. Select ozone (o3) from the Fluent Fluid Materials selection list.

iii. Click Copy to copy the information for ozone to your model and close theFluent Database Materials panel.

(b) Select mixture from the Material Type drop-down list.

(c) Enter air+ozone for Name.

(d) Click Change/Create.

When you click Change/Create, a Question dialog box will appear, asking you ifmixture-template should be overwritten. Click No to retain mixture-template andadd the new material, air+ozone, to the list. The Materials panel will be updatedto show the new material name in the Fluent Mixture Materials list.



2. Click the Edit... button to the right of the Mixture Species drop-down list to open theSpecies panel.

You will select the species that are involved in the decomposition of ozone. The orderof the species in the Selected Species list is important.

Perform the following steps to achieve the proper order:

(a) Select water-vapor (h2o) from the Selected Species selection list and click theRemove button to move it to the Available Materials selection list.

(b) Similarly, remove n2 from the Selected Species list.

(c) Select ozone (o3) from the Available Materials selection list and click the Addbutton.

(d) Similarly, add n2 back in the Selected Species list.

The Selected Species list should now contain o2, o3, and n2, respectively.

(e) Click OK to close the Species panel.



3. Click the Edit... button to the right of the Reaction drop-down list to open the Reac-tions panel.

(a) Select o3 from the Species drop-down list in the Reactants group box and enter1 for both Stoich. Coefficient and Rate Exponent.

(b) Select o2 from the Species drop-down list in the Products group box and enter1.5 for Stoich. Coefficient and 0 for Rate Exponent, respectively.

There is no need to modify the Arrhenius Rate constants, as a UDF will be usedto define them in Step 4.

(c) Click OK to close the Reactions panel.

4. Retain the default settings in the Reaction Mechanisms panel.

5. Select volume-weighted-mixing-law from the Density drop-down list.

Thermal properties do not need to be specified since this is an isothermal case.

6. Retain the default value of 1.72e-05 for Viscosity.

7. Click Change/Create.



8. Create a new material called solids.

In the fluidized bed the solid particles (treated as a fluid) are held in suspension by theair+ozone mix injected at the bottom of the bed.

(a) Select fluid from the Material Type drop-down list.

(b) Select water-vapor (h2o) from the Fluent Fluid Materials drop-down list.

(c) Enter solids for Name.

(d) Enter silica for Chemical Formula.

(e) Enter 2650 kg/m3 for Density.

(f) Click Change/Create and close the Materials panel.

When you click Change/Create, a question dialog box will appear, asking you ifwater-vapor (h2o) should be overwritten. Click No to retain water-vapor (h2o)and add the new material, solids, to the list. The Materials panel will be updatedto show the new material name in the Fluent Fluid Materials list.

You can remove materials that are not required to run this case by selecting mix-ture in the Material Type in the Materials panel. Under Fluent Mixture Materials,select mixture-template from the drop-down list and click the Delete button. Simi-larly, select fluid in the Material Type and delete all Fluent Mixture Materials otherthan O2, O3, N2, air and silica.

9. Specify the species for the gaseous phase (phase-1) and the sand bed phase (phase-2).

Define −→ Models −→ Species −→Transport & Reaction...

(a) Select phase-1 from the Phase drop-down list and click the Set... button to openthe Phase Properties panel.



i. Select air+ozone from the Material drop-down list.

ii. Click OK to close the Phase Properties panel.

(b) Select phase-2 from the Phase drop-down list and click the Set... button to openthe Phase Properties panel.

i. Select solids from the Material drop-down list.

ii. Click OK to close the Phase Properties panel.

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

Step 4: User-Defined Functions

1. Compile the user-defined functions.

Define −→ User-Defined −→ Functions −→Compiled...

(a) Click the Add... button in the Source Files group box to open the Select Filepanel.

(b) Select the files, rrate.c and bp drag.c and click OK.

The bp drag.c source code is a routine for customizing the default Syamlal-O’Briendrag law in FLUENT. In the solid phase, the default drag law uses coefficientsof 0.8 (for voids ≤ 0.85) and 2.65 (for voids > 0.85), for minimum fluid ve-locities of 0.25 m/s. The current drag law has been modified to accommodate aminimum fluid velocity of 0.08 m/s. The source code, rrate.c, defines a customvolumetric reaction rate for the decomposition reaction of ozone.

(c) Click Build to build the library.

(d) Click Load to load the UDF.

FLUENT will build a libudf folder and compile the UDF.

A dialog box will appear warning you to make sure that UDF source files are inthe folder that contain your case and data files. Click OK in the dialog box.

(e) Close the Compiled UDFs panel.



2. Specify the volume reaction rate function.

Define −→ User-Defined −→Function Hooks...

(a) Select rrate::libudf from the Volume Reaction Rate Function drop-down list.

(b) Click OK to close the User-Defined Function Hooks panel.



Step 5: Phases

1. Define the granular secondary phase.

Define −→Phases...

(a) Select phase-2 and click the Set... button.

i. Enable Granular.

ii. Define the properties of the solid phase as shown in the table:

Parameters ValuesDiameter 8.775e-05 mGranular Viscosity syamlal-obrien

Granular Bulk Viscosity lun-et-al

Frictional Viscosity schaeffer

Angle of Internal Friction 30 degreesGranular Temperature algebraic

Solids Pressure syamlal-obrien

Radial Distribution syamlal-obrien

Elasticity Modulus derive

Packing Limit 0.53

Note: You will have to scroll down the Properties list to see the remainingoptions.



iii. Click OK to close the Secondary Phase panel.

2. Specify the drag law to be used for computing the interphase momentum transfer.

(a) Click the Interaction... button to open the Phase Interaction panel.

i. Select user-defined from the Drag Coefficient drop-down list to open the User-Defined Functions panel.

A. Select custom drag syam::libudf and click OK to close the User-DefinedFunctions panel.

ii. Click the Collisions tab and enter 0.8 for Constant Restitution Coefficient.

iii. Click OK to close the Phase Interaction panel.

3. Close the Phases panel.

Step 6: Operating Conditions

Set the gravitational acceleration.

Define −→Operating Conditions...

1. Enable Gravity.

The panel will expand to show additional inputs.

2. Enter -9.81 m/s2 for Gravitational Acceleration in the X direction.

3. Enter 297 K for Operating Temperature.

4. Click OK to close the Operating Conditions panel.



Step 7: Boundary Conditions

Define −→Boundary Conditions...

1. Set the conditions for the gaseous phase (phase-1).

(a) Select Inlet from the Zone selection list.

(b) Select phase-1 from the Phase drop-down list and click the Set... button to openthe Velocity Inlet panel.

i. Enter 0.08 m/s for Velocity Magnitude.

ii. Click the Thermal tab and enter 293 K for Temperature.

iii. Click the Species tab and enter 0.2097 and 0.1 for o2 and o3 respectively.

iv. Click OK to close the Velocity Inlet panel.

2. Define the boundary conditions for leftwall.

(a) Select leftwall from the Zone selection list.

(b) Select phase-2 from the Phase drop-down list and click the Set... button to openthe Wall panel.

i. Select Specularity Coefficient from the Shear Condition list and enter 0.5 forSpecularity Coefficient.

ii. Click OK to close the Wall panel.

3. Define the boundary conditions for the rightwall zone identical to that of the leftwall.

4. Close the Boundary Conditions panel.

Step 8: Adaption

A small region will be adapted in order to create a register so that the solid volume fractioncan be patched.

1. Adapt the the regions to be patched.

Adapt −→ Region...

(a) Enter 0 and 0.115 for X Min and X Max respectively.

(b) Enter 0 and 10 for Y Min and Y Max respectively.

(c) Click Mark.

FLUENT will report the number of cells marked for adaption in the console.

Clicking the Manage... button will open the Manage Adaption Registers panel.The name of the register created will be hexahedron-r0.

(d) Close the Region Adaption panel.



Step 9: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Deselect Energy from the Equations selection list.

(b) Enter 0.7 and 0.3 for Pressure and Momentum respectively.

Note: You will have to scroll down Under-Relaxation Factors to see the remainingparameters.

(c) Enter 1.0 for Granular Temperature.

(d) Select Second Order Upwind from the Momentum, Energy, phase-1 o2 and phase-1o3 drop-down lists.

(e) Select QUICK from the Volume Fraction drop-down list.

(f) Click OK to close the Solution Controls panel.

2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

3. Initialize the solution.

Solve −→ Initialize −→Initialize...

(a) Change the initial phase-1 X Velocity to 0.01.

(b) Change the initial phase-1 o2 to 0.233 (composition of oxygen in air).

(c) Retain all other default initial values.

(d) Click Init and close the Solutio Initialization panel.

4. Patch the initial sand bed configuration.

Solve −→ Initialize −→Patch...



(a) Select phase-2 from the Phase drop-down list.

(b) Select Volume Fraction from the Variable selection list.

(c) Select hexahedron-r0 from the Registers To Patch selection list.

(d) Enter 0.52 for Value.

(e) Click Patch and close the Patch panel.

After initializing the entire domain of your flow field, you can enter different initial-ization values for particular variables into different cells. This is known as patchingand is generally used if you have multiple fluid zones that you want to patch withdifferent values.

5. Set the time stepping parameters.

Solve −→Iterate...

(a) Enter 0.001 for Time Step Size and 10000 for Number of Time Steps.

(b) Select Fixed from the Time Stepping Method list.

(c) Enable Data Sampling for Time Statistics.

This will allow you to sample data at a frequency that is set by you.

(d) Enter 40 for Max Iterations per Time Step.

(e) Click Apply.



6. Save the initial case and data files (ozone fluidbed.cas.gz andozone fluidbed .dat.gz).

File −→ Write −→Case & Data...

7. Save the data files every 1000 time steps.

File −→ Write −→Autosave...

(a) Enter 1000 for Autosave Data File Frequency.

(b) Enter ozone fluidbed %t.dat.gz for Filename.

(c) Click OK to close the Autosave Case/Data panel.

8. Click Iterate to run the calculation for 10 seconds in the Iterate panel.

Step 10: Postprocessing

You will now examine the progress of the sand and ozone/air mixture in the fluidized bedafter a total of 10 seconds. The fluidized bed should have reached a steady flow solution atthis time.

1. Plot contours of mass fraction for oxygen and ozone species.

Display −→Contours...

(a) Select Species... and Mass fraction of o3 from the Contours of drop-down list.

(b) Enable Filled from the Options list.

(c) Click Display.

The O3 mass fraction contours are shown in Figure 3.

(d) Similarly plot the mass fraction contours of O2.

The mass fraction contours of O2 is shown in Figures 4.

In Figure 3 you can see that O3 is almost fully decomposed as it approaches the outletof the fluidized bed.



Figure 3: O3 Mass Fraction

Figure 4: O2 Mass Fraction



2. View the phase motion by displaying plots of velocity vectors for the gas and solidphases.

Display −→Vectors...

(a) Select Velocity from the Vectors of drop-down list and phase-1 from the Phasedrop-down lists.

(b) Select Velocity... and Velocity Magnitude from the Color by drop-down list andphase-1 from the Phase drop-down list.

(c) Enter 5 for Scale and 2 for Skip to improve visualization of the velocity vectors.

(d) Click Display.

The phase-1 velocity vectors are shown in Figure 5.

(e) Select phase-2 from the Phase drop-down list to plot the phase-2 velocity vectors.

The phase-2 velocity vectors are shown in Figure 6.



Figure 5: Velocity Vectors for Phase-1

Figure 6: Velocity Vectors for Phase-2



3. Display filled contours of Phases... by Volume fraction for phase-1.

Display −→Contours...

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

(b) Select phase-1 from the Phase drop-down list.

(c) Click Display. The contours of volume fraction for phase-1 are shown in Figure 7.

Figure 7: Volume Fraction for Phase-1



4. Compare the mass fraction of O3 and O2 at the pressure outlet of the fluidized bed.

Plot −→XY Plot...

(a) Display an XY plot of mass fraction of O2.

i. Select Species... and Mass fraction of o2 from the Y Axis Function drop-downlist.

ii. Retain the default selection of Direction Vector from the X Axis Functiondrop-down list.

iii. Select outlet from the Surfaces selection list.

iv. Enter 0 for X Plot Direction and 1 for Y Plot Direction.

v. Click Plot.

(b) Similarly, display an XY plot of mass fraction of O3 by selecting Mass fraction ofo3 from the Y Axis Function drop-down list.

(c) Compare the O2 and O3 XY plots for mass fraction in Figure 8 and Figure 9.



Figure 8: XY Plot of Mass Fraction of O3

Figure 9: XY Plot of Mass Fraction of O2



Summary

This tutorial demonstrated how to set up and solve a granular multiphase problem usingthe Eulerian multiphase model with species transport and reaction. The problem involvedthe 2D modeling of particle suspension in a fluidized bed, and postprocessing showed thenear-steady-state behavior of the sand in the fluidized bed, under the assumptions made.Such cases should be typically run for a total of 40 seconds of operation, however, as thisis very computationally intensive, this case was only run for 10 seconds for demonstrationin this tutorial.


Eulerian Species

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