10 Pbed Reactor

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Tutorial: Modeling Flow and Heat Transfer in Packed Bed

Reactor

Introduction

The purpose of this tutorial is to provide guidelines and recommendations for setting upand solving 2D axisymmetric flow and heat transfer in a packed bed reactor.

In this tutorial, you will:

Use the porous media model in ANSYS FLUENT. Use the physical velocity formulation for modeling flow through porous media.

Use user-defined functions (UDF) and a user-defined scalar for modeling thermal non-equilibrium between solid (packing) and fluid.

Set boundary conditions for modeling convective heat transfer.

Calculate the transient solution using the pressure based solver.

Display contours of velocity, solid, and fluid temperature for visualization.

Prerequisites

This tutorial is written with the assumption that you have completedTutorial 1 from theANSYS 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.

In this tutorial, you will use the porous media model and model convective heat transfer.For more information on these functionalities, refer to the ANSYS FLUENT 13.0 UsersGuide.You will also use user-defined functions and user-defined scalars for modeling thermal non-

equilibrium between solid (packing) and fluid. For more information on these functionalities,refer to the ANSYS FLUENT 13.0 UDF Manual.

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Modeling Flow and Heat Transfer in Packed Bed Reactor

Problem Description

The schematic of the packed bed reactor to be modeled is shown in Figure1. Flow and heattransfer through the reactor will be simulated as 2D axisymmetric model. The thermal non-equilibrium between the solid (packing material) and the fluid is modeled by solving a scalar

transport equation for the packing material temperature. The scalar transport equation fordetermining the temperature distribution in the packing material is implemented throughthe user-defined function, thermal-non-equ.c.

The reactor is 0.032 m in diameter and 0.25 m high. Air flows into the reactor via a topinlet and is vented out to atmosphere. The air velocity is 0.2085 m/s and inlet temperatureis 320.15 K. The reactor is packed with 0.00683 m spherical glass particles and is heatedby a steam jacket. This maintains the external wall temperature at 383.15 K. The externalwall heat transfer coefficient is estimated to be 70 W/m-K.

Inlet

0.25 m

0.0

32m

Packing Size = 0.00683 m

Packing Material : Glass

External Heat Transfer Coefficient = 70 W/mK

Wall Temperature = 383.15 K

Outlet

Figure 1: Schematic of the Packed Bed Reactor

Preparation

1. Copy the files, reactor.msh and thermal-non-equ.cto your working directory.

2. Use FLUENT Launcher to start the (2DDP) version ofANSYS FLUENT.

For more information aboutFLUENT Launchersee Section1.1.2 StartingANSYS FLU-ENT UsingFLUENT Launcher in theANSYS FLUENT 13.0 Users Guide.

3. Click the UDF Compiler tab and make sure that Setup Compilation Environment for

UDF is enabled.

The path to the .bat file which is required to compile the UDF will be displayed as

soon as you enableSetup Compilation Environment for UDF.

If theUDF Compiler tab does not appear in theFLUENT Launcherdialog box by default,click theShow Additional Options>> button to view the additional settings.

Note: The Display Options are enabled by default. Therefore, after you read in themesh, it will be displayed in the embedded graphics window.

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Setup and Solution

Step 1: Mesh

1. Read the mesh file (reactor.msh).

File Read Mesh...

AsANSYS FLUENT reads the mesh file, messages will appear in the console reportingthe progress of the conversion.

Figure 2: Mesh Display

Step 2: General Settings

1. Check the mesh.

General Check

ANSYS FLUENT will perform various checks on the mesh and report the progress inthe console. Make sure that the minimum volume reported is a positive number.

2. Scale the mesh.

General Scale...

(a) Selectmm from the Mesh Was Created In drop-down list.

(b) Click Scale and close the Scale Mesh dialog box.

Confirm that the maximum x and y values are0.25 m and0.016 m, respectively.



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3. Define the solver settings.

General

(a) SelectAxisymmetric from2D Space selection list.

(b) Select Transient from Time selection list.

Step 3: Models

1. Enable the Energy Equation.Models Energy Edit...

Step 4: Compile UDFs

1. Define the thermal non-equilibrium condition between the packing and the fluid.

In order to model this condition, you need to solve an additional scalar transport

equation. This scalar transport equation is defined using the user-defined function,

thermal-non-equ.c.



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(a) Compile the user-defined function.

Define User-Defined Functions Compiled...

i. Click the Add... button in the Source Files section to open the Select Filedialog box.

ii. Select the file thermal-non-equ.c.

iii. Enter reactor-libas the Library Name.

iv. Click the Build button.

v. Click the Loadbutton.

(b) Define an additional scalar by enabling the user-defined scalar equation.

The additional scalar represents the packing temperature.

Define User-Defined Scalars...

i. Set the Number of User-Defined Scalars to 1.

ii. Select none from the Flux Function drop-down list.

iii. Select pm scnd order::reactor-lib from the Unsteady Function drop-down list.

iv. Click OKto close the User-Defined Scalars dialog box.



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An information dialog box will open reminding you to confirm the property values

that have changed. ClickOK.

In the thermal non-equilibrium model, you will only consider transient cooling

or heating of the porous matrix. Heat transfer by conduction is not taken intoconsideration.

(c) Hook the UDF function.

Define User-Defined Function Hooks...

i. Click the Editbutton next to the Adjust.

ii. Select pm adjust::reactor-lib from the Available Adjust Functions.

iii. Click the Add button.

pm adjust::reactor-lib will now be available in the selected adjust functionslist.



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iv. Click OKto close the Adjust Functions dialog box.

(d) Click OK to close the User-Defined Function Hooks dialog box.

Step 5: Materials

1. Modify the properties ofair.

Materials air Create/Edit...

(a) Modify the properties ofair as per the following table:

Properties Values

Density 1.1

Cp 1010

Thermal Conductivity 0.0276

Viscosity 1.95e-05

(b) Retain selection ofdefined-per-uds in the UDS Diffusivity drop-down list.

(c) Click theEdit... button next to the UDS Diffusivity drop-down list.



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i. Select uds-0 under User-Defined Scalar Diffusion in the UDS Diffusion Coeffi-

cients dialog box.

ii. Enter 1.84 for Coefficient.

iii. Click OKto close the UDS Diffusion Coefficients dialog box.

2. Copy copper from the ANSYS FLUENT material database.

(a) Click FLUENT Database... in the Create/Edit Materials dialog box.



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

(c) Selectcopper (cu)from the FLUENT Solid Materials list.

(d) Click Copy and close the FLUENT Database Materials dialog box.

3. Create a new solid materialglass.(a) Enter glass for Name and delete the entry for Chemical Formula in the Cre-

ate/Edit Materials dialog box.

(b) Enter 2250kg/m3 for the Density.

(c) Enter 0 J/kg-k for Cp.

Cp is nullified to remove heat absorption by the packing material from the heattransfer calculations. The packing material will conduct heat with the surround-

ing fluid, but will not absorb any heat in this transient analysis.

(d) Select orthotropic from the Thermal Conductivitydrop-down list.

i. Retain the default settings forDirection 0 Components.

ii. Enter 1.31 w/m-K for Conductivity 0and 0.53forConductivity 1.

iii. Click OKto close the Orthotropic Conductivity dialog box.

(e) Click Change/Create.

A Question dialog box will appear asking if you want to overwritecopper. Click

No.

4. Close theCreate/Edit Materials dialog box.



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Step 6: Cell Zone Conditions

1. Set the cell zone conditions forzone1.

Cell Zone Conditions zone1 Edit...

(a) Enter packingas the Zone Name in the Fluid dialog box.(b) Enable Porous Zone andSource Terms.

(c) Click theSource Terms tab.

i. Click the Edit... button next to the Energydrop-down list.

A. Set the Number of Energy (w/m3) sources to 1.

B. Selectudf energy source::reactor-lib from the drop-down list.



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C. Click OK to close the Energy (w/m3) sources dialog box.

ii. Click Edit button next toUser Scalar 0.

A. Set the Number of User Scalar 0 sources to 1.

B. Selectudf uds source::reactor-lib from the drop-down list.C. Click OK to close the User Scalar sources dialog box.

(d) Click thePorous Zone tab.

i. Ensure that Relative Velocity Resistance Formulation is enabled.

ii. Enter 1.41e+07 1/m2 for Direction-1 and Direction-2 in Viscous Resistancegroup box.

iii. Enter 4181 1/m for Direction-1 and Direction-2 in Inertial Resistance groupbox.

iv. Enter 0.423 for Porosity in Fluid Porosity group box.

v. Select glass in the Solid Material Name drop-down list.(e) Click OK to close the Fluid dialog box.

Step 7: Boundary Conditions

1. Set the boundary conditions forinlet.

Boundary Conditions inlet Edit...



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(a) Enter velocity-inlet as the Zone Name.

(b) Enter 0.2085 m/s for the Velocity Magnitude.

(c) Click theThermaltab and enter 320.15 k for the Temperature.

(d) Retain the default settings for the other parameters.

(e) Click OK to close Velocity Inlet dialog box.

2. Set the boundary conditions for external-wall.

Boundary Conditions external-wall Edit...

(a) Click Thermal tab and selectConvection fromThermal Conditions group box.

(b) Select copper from the Material Name drop-down list.

(c) Enter 70w/m2-k for the Heat Transfer Coefficient.

(d) Enter 383.15 k for the Free Stream Temperature.

(e) Click OK to close the Wall dialog box.



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Step 8: Solution

1. Set the solution parameters.

Solution Methods

(a) SelectPRESTO! from the Pressure drop-down list in Spatial Discretization groupbox.

(b) SelectSecond Order Upwindfrom the drop-down lists forMomentum,Energy, andUser Scalar 0.

2. Enable the plotting of residuals during the calculation.

Monitors Residuals Edit...

(a) EnablePlot in Options group box.

(b) Click OK to close the Residual Monitors dialog box.



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3. Initialize the flow field.

Solution Initialization

(a) Selectvelocity-inletfrom the Compute fromdrop-down list.

(b) Enter 383forUser Scalar 0 in Initial Values group box.

(c) Click Initialize.

4. Save the case file (pbr-1.cas.gz).

File Write Case...

5. Set the iteration parameters.

Run Calculation

(a) Enter 10s for the Time Step Size.

(b) Enter 200for the Number of Time Steps.

(c) Enter 40for the Max Iterations/Time Step.

(d) Click Calculate.



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Figure 3: Scaled Residuals

6. Save the data file (pbr-1.dat.gz).

File Write Data...

Step 9: Postprocessing

Display Contours...

1. Display filled contours of static temperature (Figure4).

Figure 4: Contours of Static Temperature

2. Display filled contours ofUser Scalar 0 (Figure5).

The difference in the fluid static temperature values and the values of the user-defined

scalar represents the bed or packing temperature.



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Figure 5: Contours of User Scalar 0

Summary

This tutorial demonstrated the application of the porous media model in ANSYS FLUENTfor a packed bed reactor. In this tutorial, you used the physical velocity formulation andmodeled convective heat transfer for the packed bed reactor. You also used user-definedfunctions and a user-defined scalar to model the thermal non-equilibrium between the solid(packing) and the fluid.

16 ANSYS I J 24 2011

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10 Pbed Reactor