Tutorial: 2D Simulation of a 300 KW BERL Combustor Using the Magnussen Model

Introduction
The purpose of this tutorial is to provide guidelines and recommendations for setting up and solving a natural gas combustion problem. This tutorial demonstrates how to do the following: Use the k-epsilon turbulence model and P-1 radiation model. Use the Eddy Dissipation Finite-rate Reaction model. Set up and solve a natural gas combustion problem. Postprocess the resulting data.

Prerequisites
This tutorial is written with the assumption that you have completed Tutorial 1 from the ANSYS FLUENT 14.5 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. If you have not used k-epsilon turbulence, P-1 radiation, and Eddy Dissipation Finite-rate Reaction models before, it would be helpful to rst refer to the ANSYS FLUENT 14.5 Users Guide.

Problem Description
This problem was modeled after the experiments carried out at the Burner Engineering Research Laboratory (BERL) as part of a large project (Scaling 400 study) for combustors ranging in size from 30 KW to 12 MW. The schematic of the problem is shown in Figure 1. The ow under study is an unstaged natural gas ame in a 300 KW swirl-stabilized burner. The furnace is vertically red. It has an octagonal cross-section with a conical furnace hood and a cylindrical exhaust duct. The furnace walls can be refractory-lined or watercooled. The burner features 24 radial fuel ports and a blu centerbody. Air is introduced through an annular inlet and movable swirl blocks are used to impart swirl. Figure 2 shows a closeup of the burner assuming 2D axisymmetry. Appropriate area adjustments were made to account for the 2D representation of a 3D problem. It has been ensured that the 1

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cross-sectional areas of the model and real furnaces are the same. The input conditions for this case, i.e. wall temperature, inlet boundary conditions, and prole have been derived from this experimental data.

Figure 1: Schematic of the Problem

Figure 2: Closeup of the Burner

Preparation
1. Copy the les, (berl.msh.gz and berl.prof) to your working folder. 2. Use FLUENT Launcher to start the 2D version of ANSYS FLUENT. 3. Enable Double Precision from the list of Options.

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Setup and Solution

Figure 3: Mesh

Step 2: General Settings General 1. Check the mesh. General Check ANSYS FLUENT performs various checks on the mesh and reports the progress in the console. Pay attention to the minimum volume reported and make sure this is a positive number. 2. Scale the mesh to mm. General Scale...

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(a) Select mm from the Mesh Was Created In drop-down list. (b) Ensure m is selected from the View Length Unit In drop-down list. (c) Click Scale. (d) Close the Scale Mesh dialog box 3. Retain the selection of Pressure-Based in the Type list. 4. Select Axisymmetric Swirl in the 2D Space list. 5. Enable Gravity. 6. Enter -9.81 for X under Gravitational Acceleration. Step 3: Models Models 1. Enable the Energy Equation. Models Energy Edit...

2. Select the Standard k-epsilon (2 eqn) turbulence model. Models Viscous Edit...

3. Select P1 from the radiation model list. Models Radiation Edit...

Note: The P1 radiation model is used since it is quicker to run. However, the DO radiation model can be used for more accurate results. An Information dialog box will appear informing that the material properties are changed. Click OK.

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4. Select Species Transport as the species model. Models Species Edit...

(a) Enable Volumetric in Reactions group box. (b) Disable Diusion Energy Source. (c) Select Finite-Rate/Eddy-Dissipation in Turbulence-Chemistry Interaction group box. (d) 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 1. Copy the following uid materials from the database. Materials Fluid Create/Edit...

(a) carbon-dioxide (co2) (b) methane (ch4) 2. Rename methane to fuel, delete its chemical formula, and click Change/Create to overwrite methane. Click Yes in the question dialog box. 3. Modify the properties for mixture-template. Materials mixture-template Create/Edit... 5

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(a) Click on Edit... next to Mixture Species and reorder the species as follows: i. h2o ii. o2 iii. fuel iv. co2 v. n2 A transport equation is not solved for the last species in the list, instead its concentration is determined by dierence. To reduce the round-o error, the species of the greatest quantity should be placed last in the list. In most cases, this is n2. (b) Click on Edit... next to Reaction and dene the following reaction. Reactants Stoich. Coecient fuel 1 o2 2.033 Rate Exponent 1 1 Products Stoich. Coecient co2 1.022 h2o 2.022 Rate Exponent 0 0

(c) Ensure mixing-law is selected from the Cp drop-down list. (d) Select polynomial from the Thermal Conductivity drop-down list. Dene two polynomial coecients with 0.0076736 and 5.8837e-05 as the rst and second coecients. (e) Select polynomial from the Viscosity drop-down list. Dene two polynomial coefcients with 7.6181e-06 and 3.2623e-08 as the rst and second coecients. (f) Select wsggm-domain-based from the Absorption Coecient drop-down list. (g) Enter 1e-09 for Scattering Coecient. (h) Click Change/ Create. 4. Enter 16.313 for Molecular Weight and -1.0629e+08 Standard State Enthalpy for fuel under Material Type mixture. 5. Use the following TUI command to change the specic heat of the species included in the mixture.
(set-ifrf-cp-polynomials mixture-template)

6. Select polynomial from the Cp drop-down list for fuel under Material Type mixture and set the values for the coecients as shown below: Species 1 fuel 2005 2 3 4 -0.3407 2.362e-03 -1.178e-6 5 1.703e-10

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Note: Global reaction mechanisms with one or two steps inevitably neglect the intermediate species. In high-temperature ames, neglecting these dissociated species may cause the temperature to be over-predicted. A more realistic temperature eld can be obtained by increasing the specic heat capacity for each species. Above command sets the Cp polynomial coecient to that mentioned by Peter and Weber (1995). Fuel named as fuel in this tutorial, is not a standard species. Therefore, Cp polynomial coecients for fuel need to be specied manually. 7. Click Change/Create and close the Create/Edit Materials dialog box. Step 5: Boundary Conditions Boundary Conditions

1. Read the prole le (berl.prof). File Read Prole... The CFD solution for reacting ows can be sensitive to the boundary conditions, in particular the incoming velocity eld and the heat transfer through the walls. Here, you will use proles to specify the velocity at velocity-inlet-4, and the wall temperature for wall-9. The latter approach of xing the wall temperature to measurements is common in furnace simulations, to avoid modeling the wall convective and radiative heat transfer.

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2. Set the boundary conditions for velocity-inlet-4 zone. Boundary Conditions velocity-inlet-4 Edit...

(a) Select Components from the Velocity Specication Method drop-down list. (b) Select vel-prof u and vel-prof w for Axial-Velocity and Swirl-Velocity respectively. (c) Select Intensity and Length Scale from the Specication Method drop-down list. (d) Enter 17 % and 0.0076 m for Turbulence Intensity and Turbulence Length Scale respectively. (e) Click the Thermal tab and enter 312 K for Temperature. (f) Click the Species tab and enter 0.2315 for Species Mass Fractions for o2. (g) Click OK to close the Velocity Inlet dialog box.

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3. Set the boundary conditions for velocity-inlet-5. Boundary Conditions velocity-inlet-5 Edit...

(a) Select Components from the Velocity Specication Method drop-down list. (b) Enter 157.25 m/s for Radial Velocity. (c) Select Intensity and Length Scale from the Specication Method. (d) Retain 5 % for Turbulence Intensity. (e) Enter 0.0009 m for Turbulence Length Scale. (f) Click theThermal tab and enter 308 K for Temperature. (g) Click the Species tab and enter 0.97 and 0.008 for Species Mass Fractions for fuel and co2 respectively. (h) Click OK to close the Velocity Inlet dialog box.

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4. Change the Type for outow-3 zone to pressure-outlet. Boundary Conditions outow-3 Edit...

(a) Select Select Intensity and Hydraulic Diameter from the Specication Method. (b) Retain 5 % for Backow Turbulent Intensity. (c) Enter 0.6 m for Backow Hydraulic Diameter. (d) Click the Thermal tab and enter 1300 K for Temperature. (e) Click the Species tab and enter 0.2315 for Species Mass Fractions for o2. (f) Click OK to close the Pressure Outlet dialog box. 5. Set the boundary conditions for wall zones. Boundary Conditions wall-6 Edit...

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(a) Click the Thermal tab and select Temperature from the Thermal Conditions list. (b) Set the following conditions: Zone Name wall-6 wall-7 wall-8 wall-9 wall-10 wall-11 wall-12 wall-13 Temperature 1370 K 312 K 1305 K temp-prof t 1100 K 1273 K 1173 K 1173 K Internal Emissivity 0.5 0.6 0.5 0.6 0.5 0.6 0.6 0.6

(c) Click OK to close the Wall dialog box. Step 6: Solution 1. Set the solution parameters. Solution Methods (a) Select Coupled from the Scheme drop-down list.

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(b) Select PRESTO! from the Pressure drop-down list in the Spatial Discretization group box. This is often useful for buoyant ows where velocity vectors near walls may not align with the wall due to assumption of uniform pressure in the boundary layer. Thus, PRESTO! can only be used with quadrilateral or hexahedral meshes. (c) Enable Pseudo Transient. 2. Deselect P1 from the Equations selection list. Solution Controls Equations... 3. Enable Set All Species URFs Together. Solution Controls 4. Change the time scale factor for species and energy. Solution Controls Advanced

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(a) Click the Expert tab. (b) Enter 0.1 for Time Scale Factor of Turbulent Kinetic Energy and Turbulent Dissipation Rate. (c) Enter 10 for Time Scale Factor of Species and Energy. (d) Click OK to close the Advanced Solution Controls dialog box. Note: Higher time scale size is used for the energy and species equations to converge the solution in less number of iterations. 5. Initialize the ow eld. Solution Initialization (a) Click More Settings... and enable Maintain Constant Velocity Magnitude in the Initialization Options group box. Note: This option will help to rid of the reverse ow from the pressure outlet. (b) Click Initialize. 6. Save the initialized case and data les, berl-mag-init.cas.gz and berl-mag-init.dat.gz. File Write Case & Data 7. Change the time scale factor and start calculation. Run Calculation (a) Enter 0.1 for the Timescale Factor. (b) Start the calculation by requesting 100 iterations (Figure 4).

Figure 4: Scaled Residuals

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8. Save the case and data les, berl-mag-1.cas.gz and berl-mag-1.dat.gz. File Write Case & Data 9. Enter 100 for Time Scale Factor of Species and Energy. Solution Controls Advanced 10. Change the time scale factor and start calculation. Run Calculation (a) Enter 0.5 for the Timescale Factor. (b) Start the calculation by requesting 100 iterations. 11. Save the case and data les, berl-mag-2.cas.gz and berl-mag-2.dat.gz. File Write Case & Data 12. Enter 1 for Time Scale Factor of Turbulent Kinetic Energy and Dissipation Rate. Solution Controls Advanced 13. Start the calculation by requesting 100 iterations. Run Calculation 14. Select P1 from the Equations selection list. Solution Controls Equations... 15. Request for an additional 700 iterations (Figure 5).

Figure 5: Scaled Residuals

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16. Save the case and data les, berl-mag-3.cas.gz and berl-mag-3.dat.gz. File Write Case & Data 17. Compute the gas phase mass uxes through all the boundaries. Reports Fluxes Set Up...

18. Compute the gas phase energy uxes through all the boundaries.

(a) Select Total Heat Transfer Rate from the Options list. (b) Select all the zones from the Boundaries selection list and click Compute. 15

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(c) Close the Flux Reports dialog box. 19. Display contours of ow variables of interest. Graphics and Animations Contours Set Up...

In particular, look at temperature, velocities, and species variables. (Figures 68).

Figure 6: Contours of Static Temperature

Figure 7: Contours of Velocity Magnitude

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Figure 8: Contours of Mass Fraction of O2

Results
Use of the DO radiation model, which is more CPU intensive, and also a second order solution, can help to increase the accuracy of the predictions.

Summary
Inherent limitations in the available models result in inaccuracies while predicting intermediate species. Overall, fairly meaningful results within engineering accuracy are obtained.

References
A. A. A. Peters and R. Weber Mathematical Modeling of a 2.25 MWt Swirling Natural Gas Flame. Part1: Eddy Break-up Concept for Turbulent Combustion, Probability Density Function Approach for Nitric Oxide Formation. Combustion Science and Technology. 110. 67-101. 1995

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