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Tutorial: Premixed Flow in a Conical Chamber using the

Finite-Rate Chemistry Model

Introduction

The purpose of this tutorial is to provide guidelines and recommendations for setting upand solving the combustion of a lean, premixed gaseous fuel mixture of methane and air ina conical reactor. Combustion is modeled using the finite-rate chemistry model in ANSYSFluent.

This tutorial demonstrates how to do the following:

• Set up and solve the combustion problem of a premixed gaseous fuel mixture ofmethane and air in a conical reactor.

• Use the species transport model with finite-rate chemistry.

• Set up and solve the case with appropriate solver settings.

• Postprocess the resulting data.

Prerequisites

This tutorial is written with the assumption that you have completed Tutorial 1 from ANSYSFluent 14.5 Tutorial Guide, and that you are familiar with the ANSYS Fluent navigationpane and menu structure. Some steps in the setup and solution procedure will not be shownexplicitly.

This tutorial uses the species transport model with finite-rate chemistry and volumetricreactions. A basic understanding of the combustion processes is desirable. For more infor-mation on species transport and finite-rate chemistry relating to volumetric reactions, seeSection 15.1 Volumetric Reactions in the ANSYS Fluent 14.5 User’s Guide.

Problem Description

The conical combustor considered is shown in Figure 1. A small nozzle at the center ofthe combustor introduces the lean methane-air mixture (equivalence ratio = 0.6) at 60 m/sand 650 K. Combustion involves several complex reactions between CH4, O2, CO2, CO,H2O, and N2. The high-speed flow reverses direction in the combustor and exits throughthe co-axial outlet.

c© Fluent Inc. January 28, 2013 1

Tutorial: Premixed Flow in a Conical Chamber using the Finite-Rate Chemistry Model

Figure 1: Schematic Figure

Setup and Solution

Preparation

1. Copy the file (conreac.msh) to your working folder.

2. Use FLUENT Launcher to start the 2D version of ANSYS Fluent.

3. Enable Double-Precision in the Options list.

Step 1: Mesh

1. Read the mesh file (conreac.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 −→ Axisymmetric

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

2 c© ANSYS, Inc. January 28, 2013


2. Check the mesh (see Figure 2).

General −→ Check

Figure 2: Mesh Display

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

Step 3: Models

1. Enable the Energy Equation.

Models −→ Energy −→ Edit...

2. Define the k-epsilon turbulence model.

Models −→ Viscous −→ Edit...

(a) Select k-epsilon in the Model list to open Viscous Model dialog box.

(b) Retain the default settings and click OK to close Viscous Model dialog box.

c© ANSYS, Inc. January 28, 2013 3


3. Define the species model.

Models −→ Species −→ Edit...

(a) Select Species Transport from the Model list to open Species Model dialog box.

i. Enable Volumetric from the Reactions group box.

ii. Select methane-air-2step from the Mixture Material drop-down list.

iii. Select Finite-Rate/Eddy Dissipation from the Turbulence-Chemistry Interactiongroup box.

iv. Click OK to close the Species Model dialog box.

An Information dialog box will appear informing that the material properties are changed.Click OK.



Step 4: Materials

Materials −→ Fluid −→ Create/Edit...

1. Copy nitrogen-oxide (no) from the database.

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

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

ii. Select nitrogen-oxide (no) from the Fluent Fluid Materials list.

iii. Click Copy and close the Fluent Database Materials dialog box.

iv. Click Change/Create and close the Create/Edit Materials dialog box.

2. Modify the mixture material, methane-air-2step.

Materials −→ Mixture −→ Create/Edit...

(a) Enter 0.0241 for Thermal Conductivity in the Properties group box.

(b) Click the Edit... to the right of the Mixture Species to open the Species dialogbox.

i. Add nitrogen-oxide (no) to the Selected Species list.

ii. Reorder the species so that nitrogen (n2) appears last in the Selected Speciesselection list.



iii. Click OK to close the Species dialog box.

(c) Specify the reactions in the Reactions dialog box.

i. Click the Edit... to the right of the Reaction to open the Reactions dialogbox.

A. Increase the Total Number of Reactions to 5.

B. Define the reactions as shown in the following table:

where,PEF = Pre-Exponential FactorAE = Activation EnergyTE = Temperature Exponent



ReactionID

1 2 3 4 5

Number ofReactants

2 2 1 3 2

Species ch4, o2 co, o2 co2 n2, o2, co n2, o2

Stoich. ch4 = 1 co = 1 co2 = 1 n2 = 1 n2 = 1Coefficient o2 = 1.5 o2 = 0.5 o2 = 1 o2 = 1

co = 0Rate ch4 = 1.46 co = 1.6904 co2 = 1 n2 = 0 n2 = 1Exponent o2 = 0.5217 o2 = 1.57 o2 = 4.0111 o2 = 0.5

co = 0.7211Arrhenius PEF=1.6596e+15 PEF=7.9799e+14 PEF=2.2336e+14 PEF=8.8308e+23 PEF=9.2683e+14Rate AE=1.72e+08 AE=9.654e+07 AE=5.1774e+08 AE=4.4366e+08 AE=5.7276e+08

TE = −0.5Number ofProducts

2 1 2 2 1

Species co, h2o co2 co, o2 no, co no

Stoich. co = 1 co2 = 1 co = 1 no = 2 no = 2Coefficient h2o = 2 o2 = 0.5 co = 0Rate co = 0 co2 = 0 co = 0 no = 0 no = 0Exponent h2o = 0 o2 = 0 co = 0Mixing default default default A = 1e+11 A = 1e+11Rate values values values B = 1e+11 B = 1e+11

ii. Click OK to close the Reactions dialog box.

(d) Click the Edit... to the right of the Mechanism to open the Reaction Mechanismsdialog box.

i. Select all the reactions from the Reactions list.

ii. Click OK to close the Reaction Mechanisms dialog box.

(e) Ensure that mixing law is selected from the Cp (Specific Heat) drop-down list formixture.

(f) Ensure that piecewise-polynomial is selected from the Cp (Specific Heat) drop-down list for all the species.

3. Click Change/Create and close the Create/Edit Materials dialog box.



Step 5: Boundary Conditions

Boundary Conditions

1. Set the boundary conditions for pressure-outlet-4.

Boundary Conditions −→ pressure-outlet-4 −→ Edit...

(a) Enter the values as shown in the following table:

Parameters ValuesSpecification Method Intensity and Length Scale

Backflow Turbulent Intensity 10 %Backflow Turbulent Length Scale 0.003 mBackflow Total Temperature 2500 KSpecies Mass Fractions o2 = 0.05, co2 = 0.1, and h2o = 0.1

(b) Click OK to close the Pressure Outlet dialog box.

2. Set the boundary conditions for velocity-inlet-5.

Boundary Conditions −→ velocity-inlet-5 −→ Edit...

(a) Enter the values as shown in the table:

Parameters ValuesVelocity Magnitude 60 m/sSpecification Method Intensity and Length Scale

Turbulent Intensity 10 %Turbulent Length Scale 0.003 mTemperature 650 KSpecies Mass Fractions ch4 = 0.034

o2 = 0.225

(b) Click OK to close the Velocity Inlet dialog box.

3. Retain the default boundary conditions for wall-1.



Step 6: Solution

1. Modify the species model.


(a) Disable Volumetric from the Reactions list.

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

This is a non-reacting simulation. It is good practice to solve for flow and mixingreactions (species transport) and then enable the reactions.

2. Set the under-relaxation factors.

Solution Controls

(a) Enter 0.95 for all the species and for Energy in the Under-Relaxation Factorsgroup box.

3. Initialize the solution.

Solution Initialization

Hybrid Initialization is the default Initialization Method in ANSYS Fluent 14.5. Refer tothe section 28.11 Hybrid Initialization, in the ANSYS Fluent 14.5 User’s Guide.



(a) Click More Settings....

i. In the Species Settings tab enable Specify Species Parameters.

ii. Enter 0.01 for all Species Fraction.

iii. Click OK and close the Hybrid Initialization dialog box.

(b) Click Initialize.

4. Save the case file (5step cold.cas.gz).

File −→ Write −→Case...

5. Solve for 200 iterations (see Figure 3).

Run Calculation −→ Calculate



Figure 3: Scaled Residuals

6. Save the data file (5step cold.dat.gz).

File −→ Write −→Data...

Step 7: Postprocessing

1. Display the velocity vectors in the domain (see Figure 4).

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

(a) Enter 10 for Scale and click Display.

Figure 4: Velocity Vectors

(b) Close the Vectors dialog box.



2. Display contours of stream function (see Figure 5).

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

(a) Select Velocity... and Stream Function from the Contours of drop-down lists andclick Display.

Figure 5: Contours of Stream Function

(b) Close the Contours dialog box.

Step 8: Reacting Flow Case Setup

1. Enable volumetric reactions.


(a) Enable Volumetric from the Reactions list.

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

2. Patch an initial temperature field to initiate the combustion process.

Solution Initialization −→ Patch...

(a) Select Temperature from the Variable list.

(b) Enter 1000 for Value.

(c) Select fluid-6 from the Zones to Patch list.

(d) Click Patch.

(e) Close the Patch dialog box.

3. Save the case file (5step final.cas.gz).

File −→ Write −→Case...



4. Solve for an additional 1000 iterations (see Figure 6).

Run Calculation −→ Calculate

Figure 6: Scaled Residuals After 1000 Iterations

5. Save the data file (5step final.dat.gz).

File −→ Write −→Data...

6. Compute the gas phase mass fluxes through all the boundaries.

Reports −→ Fluxes −→ Set Up...

(a) Calculate the Mass Flow Rate with velocity-inlet-5 as boundary.

i. Select velocity-inlet-5 from the Boundaries list.

ii. Click Compute.

(b) Calculate Mass Flow Rate with pressure-outlet-4 as boundary.

i. Select Pressure-outlet-4 from the Boundaries list.

ii. Click Compute.

Both these figures should be equal and opposite in sign to each other.

7. Compute the gas phase energy fluxes through all the boundaries.

Reports −→ Fluxes −→ Set Up...

(a) Select Total Heat Transfer Rate from the Options list.

(b) Select all the zones from the Boundaries list and click Compute.

(c) Close the Flux Reports dialog box.



Step 9: Postprocessing

1. Display velocity vectors in the domain with a scale factor of 10 (see Figure 7).

Figure 7: Velocity Vectors

2. Display contours of stream function (see Figure 8).

Figure 8: Contours of Stream Function



3. Display filled contours of static temperature (see Figure 9).

Figure 9: Contours of Static Temperature

4. Display contours of species mass fractions of ch4 (see Figure 10).

Figure 10: Contours of Mass Fraction of CH4



5. Display contours of species mass fractions of co2 (see Figure 11).

Figure 11: Contours of Mass Fraction of CO2

6. Display contours of species mass fractions of co (see Figure 12).

Figure 12: Contours of Mass Fraction of CO



7. Display contours of species mass fractions of h2o (see Figure 13).

Figure 13: Contours of Mass Fraction of H2O

8. Display contours of species mass fractions of no (see Figure 14).

Figure 14: Contours of Mass Fraction of NO



9. Display contours of species mass fractions of o2 (see Figure 15).

Figure 15: Contours of Mass Fraction of O2

Results

The finite-rate chemistry model in ANSYS Fluent can be used to predict the temperaturefield and species mass fractions.

Summary

Application of the finite-rate chemistry model using a 5-step global chemical reactionmechanism has been demonstrated. The 5-step global mechanism by Nicol [1] for methaneoxidation and NO formation is tuned specifically for lean, premixed combustion applications.The mechanism is valid for a pressure of 1 Atm, inlet temperature of 650 K, and a fuel-airequivalence ratio range of 0.45 to 0.70. Quantities presented below are in units of kmoles,cubic meters, seconds, and Kelvin.

1. CH4 + 1.5O2 → CO + 2H2O

R1 = 1015.22[CH4]1.46[O2]0.5217exp(−20643/T )

2. CO + 0.5O2 → CO2

R2 = 1014.902[CO]1.6904[O2]1.57exp(−11613/T )



3. CO2 → CO + 0.5O2

R3 = 1014.349[CO2v]exp(−62281/T )

4. N2 +O2 → 2NO

R4 = 1023.946[CO]0.7211[O2]4.0111exp(−53369/T )

5. N2 +O2 → 2NO

R5 = 1014.967T−0.5[N2][O2]0.5exp(−68899/T )

References

[1] Nicol, D.G. “A Chemical and Numerical Study of NOx and Pollutant Formation inLow-Emissions Combustion,” Ph.D. Dissertation, University of Washington (1995).


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