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Tutorial: Premixed Combustion in a Conical Chamber using the Zimont (mean progress variable based) Model

Purpose
The purpose of this tutorial is to provide guidelines and reco

mmendations for setting up and solving a premixed gaseous mixture using the premixed combustion (Zimont) model. Both, adiabatic and non-adiabatic premixed combustion models will be used.

Prerequisites
This tutorial assumes that you are familiar with the FLUENT interface and that you have a good understanding of the basic setup and solution procedures. Some steps will not be shown explicitly. In this tutorial, you will use the premixed combustion model. This tutorial does not cover the mechanics of using this model. Instead, it focuses on the application of this model to solve the problem. If you have not used this model before, refer to Section 16: Modeling Premixed Combustion in the FLUENT 6.2 User’s Guide.

Problem Description
The conical combustor considered is shown in Figure 1. A small nozzle at the center of the combustor introduces the lean methane/air mixture (equivalence ratio = 0.6) at 60 m/s and 650 K. The high speed ?ow reverses direction in the combustor and exits through the co-axial outlet. Chemical reaction for equivalence ratio of 0.6 is: CH4 + 3.33(O2 + 3.76N2 ) = CO2 + 2H2 O + 1.33O2 + 12.53N2

c Fluent Inc. June 3, 2005

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Premixed Combustion in a Conical Chamber using the Zimont Model

Some related parameters are as follows:

Table 1: Premixed Mixture Properties Parameter Mass of air (for equivalence ratio 0.6) Mass of fuel Mass fraction of fuel Heat of combustion (j/kg) Adiabatic Temperature(K) Critical Strain Rate (1/s) Laminar Flame Speed (m/s) Value 2 × (32 + 3.76 × 28)/0.6 = 457.6 16 0.0338 3.84e+07 1950 5000 0.35

Figure 1: Problem Schematic

Preparation
1. Copy the ?le, conreac.msh to your working directory. 2. Start the 2D version of FLUENT.

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c Fluent Inc. June 3, 2005

Premixed Combustion in a Conical Chamber using the Zimont Model

Setup and Solution
Step 1: Grid 1. Read the mesh ?le (conreac.msh). 2. Check and display the grid.

Grid

FLUENT 6.2 (2d, segregated, lam)

Figure 2: Grid Display

Step 2: Models 1. De?ne the solver settings. (a) Under Space, select Axisymmetric. (b) Retain the default settings for other parameters. 2. Enable the standard k-epsilon (2 eqn) turbulence model. 3. De?ne the Species model. (a) Under Model, select Premixed Combustion. (b) Under Premixed Combustion Model, retain the selection of the Adiabatic model. (c) Set the Turbulent Flame Speed Constant to 0.637.

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Premixed Combustion in a Conical Chamber using the Zimont Model

Step 3: Materials 1. Create a new ?uid material called premixed-mixture with the physical properties shown in Table 2. Table 2: Premixed Mixture Material Parameter Density (kg/m3) Density of Unburnt Reactants (kg/m3) Temperature of Unburnt Reactants (k) Adiabatic Temperature of Burnt Products (k) Laminar Flame Speed (m/s) Critical Rate of Strain (1/s) Value premixed-combustion 1.2 650 1950 0.35 5000

For the adiabatic model, the temperature is calculated from the temperature of the unburnt mixture and the adiabatic temperature of the burnt products. For more information, refer to Section 16.2.4: Calculation of Temperature in the FLUENT 6.2 User’s Guide. Step 4: Operating Conditions 1. Retain the default operating conditions. Step 5: Boundary Conditions 1. Set the boundary conditions for ?uid-6. (a) Select premixed-mixture in the Material Name drop-down list. 2. Set the boundary conditions for velocity-inlet-5. (a) Set the Velocity Magnitude to 60 m/s. (b) Select Intensity and Length Scale as the Turbulence Speci?cation Method and specify the Turbulence Length Scale as 0.003 m. (c) Retain the default values for the other parameters. 3. Set the boundary conditions for pressure-outlet-4. (a) Select Intensity and Length Scale as the Turbulence Speci?cation Method. (b) Set the Back?ow Turbulence Length Scale and Back?ow Progress Variable to 0.003 m and 1 respectively. (c) Retain the default values for the other parameters. 4. Retain the default adiabatic boundary conditions for wall-1.

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c Fluent Inc. June 3, 2005

Premixed Combustion in a Conical Chamber using the Zimont Model

Step 6: Solution 1. Solve for ?ow and turbulence equations. (a) In the Solution Controls panel, select the Flow and Turbulence equations. (b) Enable the plotting of residuals during calculation. (c) Initialize the ?ow ?eld and compute from all-zones. (d) Save the initial case and data ?les. (e) Start the calculation by requesting 250 iterations. 2. Solve using all the equations. (a) In the Solution Controls panel, select the Premixed Combustion equation. (b) Request an additional 200 iterations or perform iterations until the solution converges (Figure 3).

Residuals continuity x-velocity y-velocity premixc k epsilon

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05 0 50 100 150 200 250 300

Iterations

Scaled Residuals

FLUENT 6.2 (axi, segregated, ske)

Figure 3: Scaled Residuals

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Premixed Combustion in a Conical Chamber using the Zimont Model

Step 7: Postprocessing 1. Display the velocity vectors in the domain (Figure 4). Display ?→Vectors... (a) Set Scale to 10 and click Display.

6.49e+01 6.16e+01 5.84e+01 5.52e+01 5.19e+01 4.87e+01 4.54e+01 4.22e+01 3.90e+01 3.57e+01 3.25e+01 2.93e+01 2.60e+01 2.28e+01 1.96e+01 1.63e+01 1.31e+01 9.86e+00 6.62e+00 3.39e+00 1.54e-01

Velocity Vectors Colored By Velocity Magnitude (m/s)

FLUENT 6.2 (axi, segregated, ske)

Figure 4: Velocity Vectors

2. Display contours of stream function (Figure 5). Display ?→Contours... (a) Select Velocity... and Stream Function in the Contours of drop-down lists. 3. Display ?lled contours of mean progress variable (Figure 6). (a) Under Options, select Filled. (b) Select Premixed Combustion... and Progress Variable in the Contours of drop-down lists. 4. Display ?lled contours of static temperature (Figure 7). (a) Select Premixed Combustion... and Static Temperature in the Contours of dropdown lists.

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c Fluent Inc. June 3, 2005

Premixed Combustion in a Conical Chamber using the Zimont Model

1.26e-03 1.20e-03 1.14e-03 1.07e-03 1.01e-03 9.48e-04 8.85e-04 8.22e-04 7.58e-04 6.95e-04 6.32e-04 5.69e-04 5.06e-04 4.42e-04 3.79e-04 3.16e-04 2.53e-04 1.90e-04 1.26e-04 6.32e-05 0.00e+00

Contours of Stream Function (kg/s)

FLUENT 6.2 (axi, segregated, ske)

Figure 5: Contours of Stream Function

1.00e-00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Progress Variable

FLUENT 6.2 (axi, segregated, ske)

Figure 6: Contours of Mean Progress Variable

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Premixed Combustion in a Conical Chamber using the Zimont Model

1.95e+03 1.88e+03 1.82e+03 1.75e+03 1.69e+03 1.62e+03 1.56e+03 1.49e+03 1.43e+03 1.36e+03 1.30e+03 1.23e+03 1.17e+03 1.10e+03 1.04e+03 9.75e+02 9.10e+02 8.45e+02 7.80e+02 7.15e+02 6.50e+02

Contours of Static Temperature (k)

FLUENT 6.2 (axi, segregated, ske)

Figure 7: Contours of Static Temperature

Step 8: Setup for Non-Adiabatic Premixed Combustion 1. Change the species model (Premixed Combustion Model) from Adiabatic to Non-Adiabatic. 2. In the Materials panel, modify the following properties of the premixed-mixture material: Parameter Heat of Combustion Unburnt Fuel Mass Fraction Value 3.85e+07 0.0338

For the non-adiabatic model, FLUENT solves an energy transport equation to account for heat losses or gains within the system. The temperature is calculated from the heat of combustion and the fuel mass fraction. For more information, refer to Section 16.2.4: Calculation of Temperature in the FLUENT 6.2 User’s Guide. 3. Set the Temperature for velocity-inlet-5 to 650 k.

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c Fluent Inc. June 3, 2005

Premixed Combustion in a Conical Chamber using the Zimont Model

Step 9: Solution (Non-Adiabatic Premixed Combustion) 1. Solve for ?ow and turbulence equations. (a) In the Solution Controls panel, select the Flow and Turbulence equations. (b) Set the Under-Relaxation Factors for Density, Energy, and Turbulent Viscosity to 0.8. (c) Set the discretization for Pressure to PRESTO! and retain the default settings for the other parameters. (d) Initialize the ?ow ?eld and compute from all-zones. (e) Start the calculation by requesting 250 iterations. 2. Solve using all the equations. (a) In the Solution Controls panel, select all the equations. (b) Set the Under-Relaxation Factors for Density, Momentum, and Progress Variable to 0.5. (c) Set the Under Relaxation Factor for Energy to 0.9. (d) Request for 1500 iterations or perform iterations until the solution is converged (Figure 8). (e) Save the case and data ?les.

Residuals continuity x-velocity y-velocity premixc energy k epsilon

1e+00 1e-01 1e-02 1e-03 1e-04 1e-05 1e-06 1e-07 1e-08 0 100 200 300 400 500 600 700 800 900

Iterations

Scaled Residuals

FLUENT 6.2 (axi, segregated, ske)

Figure 8: Scaled Residuals

c Fluent Inc. June 3, 2005

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Premixed Combustion in a Conical Chamber using the Zimont Model

Step 10: Postprocessing 1. Display the velocity vectors in the domain with a scale factor of 10 (Figure 9).

6.49e+01 6.17e+01 5.84e+01 5.52e+01 5.20e+01 4.87e+01 4.55e+01 4.23e+01 3.90e+01 3.58e+01 3.25e+01 2.93e+01 2.61e+01 2.28e+01 1.96e+01 1.63e+01 1.31e+01 9.85e+00 6.61e+00 3.37e+00 1.33e-01

Velocity Vectors Colored By Velocity Magnitude (m/s)

FLUENT 6.2 (axi, segregated, ske)

Figure 9: Velocity Vectors

2. Display ?lled contours of stream function (Figure 10). 3. Display ?lled contours of mean progress variable (Figure 11). 4. Display ?lled contours of static temperature (Figure 12). Display contours of static temperature by selecting Temperature... and Static Temperature in the Contours of drop-down lists.

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c Fluent Inc. June 3, 2005

Premixed Combustion in a Conical Chamber using the Zimont Model

1.27e-03 1.21e-03 1.14e-03 1.08e-03 1.02e-03 9.53e-04 8.89e-04 8.26e-04 7.62e-04 6.99e-04 6.35e-04 5.72e-04 5.08e-04 4.45e-04 3.81e-04 3.18e-04 2.54e-04 1.91e-04 1.27e-04 6.35e-05 0.00e+00

Contours of Stream Function (kg/s)

FLUENT 6.2 (axi, segregated, ske)

Figure 10: Contours of Stream Function

1.00e-00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Progress Variable

FLUENT 6.2 (axi, segregated, ske)

Figure 11: Contours of Mean Progress Variable

c Fluent Inc. June 3, 2005

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Premixed Combustion in a Conical Chamber using the Zimont Model

1.94e+03 1.88e+03 1.81e+03 1.75e+03 1.68e+03 1.62e+03 1.56e+03 1.49e+03 1.43e+03 1.36e+03 1.30e+03 1.23e+03 1.17e+03 1.10e+03 1.04e+03 9.73e+02 9.09e+02 8.44e+02 7.79e+02 7.15e+02 6.50e+02

Contours of Static Temperature (k)

FLUENT 6.2 (axi, segregated, ske)

Figure 12: Contours of Static Temperature

Results
Postprocessing results can be used to study the application of the premixed combustion model in FLUENT.

Summary
Application of premixed combustion model (Zimont model) in a premixed gaseous mixture case has been demonstrated.

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c Fluent Inc. June 3, 2005


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