Figure 1 shows the schematic of the bluff-body combustor geometry and the 2D axisymmetric grid used here, along with a table containing the major parameters ...
2007 Fall Technical Meeting Eastern States Section of the Combustion Institute University of Virginia October 21-24, 2007
Assessment of RANS-Based Turbulent Combustion Models for Prediction of Gas Turbine Emissions: Turbulence Model and Reaction Mechanism Effects J. R. Nanduri1, 2, I. B. Celik2, 1, P. A. Strakey1 and D. R. Parsons1, 2 1
National Energy Technology Laboratory, Morgantown, WV 26507 Department of Mechanical and Aerospace Engineering, West Virginia University Morgantown, WV 26505-6106
The goal of this study is to assess current, commonly applied turbulence and combustion models with respect to their performance in gas-turbine combustion (GTC). Reynolds Averaged NavierStokes (RANS)-based turbulence and chemistry models are two primary factors influencing the uncertainty in predicting turbulent combustion characteristics, especially for GTC. RANS-based methods are the design tools of choice in the gas turbine industry due to the high computational costs of LES (Large Eddy Simulation). In this study, lean premixed combustion of methane was simulated using two different reduced mechanisms (ARM9 and ARM19) along with the Eddy Dissipation Concept (EDC) turbulent chemistry interaction model to calculate the CO and NOx emissions. The effect of turbulence models was assessed by considering two different models. Both of the models tested performed well in the prediction of temperature and major species profiles. Predicted values of NO emission profiles showed an average difference of ±5 ppm compared to experimental values. Computed intermediate species profiles showed large qualitative and quantitative errors when compared with the experimental data. These discrepancies, especially the intermediate species hydrogen, indicate the challenges these reduced mechanisms and turbulence models can present when modeling pollutant emissions from gas turbine combustors.
Research into optimization of power generation systems for advanced energy and emissions performance has become increasingly popular in the last two decades largely due to the increasing regulation of permitted NOx and SOx emissions along with other greenhouse gases such as CO2. Microturbine generation systems are on the forefront of this research due to the promise of “high-efficiency, ultra-clean” systems that can be used to produce electrical energy as well as thermal energy in co-generation applications . Specific objectives of optimizing microturbines include fuel flexibility with the ability to use multiple fuels such as diesel, ethanol, landfill gas and biofuels along with natural gas, and a total NOx emission typically less than 7 ppm for natural gas . The efficiency and emissions of microturbines rely on the use of lean premixed combustion techniques with performance issues that are widely known to be a function of the fuel composition. Even the seasonal variability in the composition of natural gas, which is the primary fuel of choice, may alter the emission characteristics of the combustor by changing the combustion process and chemical kinetics . Reliable prediction of emissions for various fuel blends using computational fluid dynamics (CFD) would allow microturbine developers to design and operate the combustor with various fuels and fuel blends without having to perform
as many costly field validation studies. Some recent experimental studies [3, 4] have shown the effects of fuel variability on gas turbine combustion. While these experimental studies tabulate the emissions for a variety of fuel compositions, there is a lack of well documented CFD studies predicting the effects of various fuels and fuel blends on gas turbine emissions. Utilization of CFD for combustor design could lower the design costs significantly. In fact, RANS and PDF (Probability Density Function) based turbulent combustion models are already used in the industry as a combustor design tool. However the cost of computing and the reliability of the emissions predictions prevent most developers from using detailed reaction mechanisms and NOx formation mechanisms in the design process. In this study, the basic objective is to assess some of the current commercial RANS methods for modeling turbulent reacting flows. This assessment will also aid in determining the capabilities and limitations of select RANS models for hybrid RANS/LES applications. A comprehensive literature review was performed to assess the available emissions data that has been generated in various model combustor experiments. These experiments are generally performed either to characterize the emissions or to optimize the design for various dynamic aspects such as acoustic stability, flame stability and flammability limits. The swirl-stabilized dump combustor design  is widely used (see Williams et al.,  for a more complete listing) in characterizing the flame structure, stability (including extinction and blow-off characteristics) and acoustics. Since the primary focus of this study is emissions characterization, only the studies measuring emissions are considered. Table 1 gives a short summary of the various model combustors considered and the available experimental data for each combustor. Table 1 - List of model gas turbine combustors measuring emissions and relevant experimental settings and references Combustor Name Research Group SimVAL National Energy Technology Laboratory (NETL)
NG NG + H2
UCI Combustor University of California at Irvine
Prof. Agrawal's Group University of Oklahoma University of Alabama
Swirl Stabilized Combustor
Prof. Malte's Group University of Washington
Jet Stirred Reactor
Prof. Pitz Group Vanderbilt University / Wright Laboratories
Bluff-Body Stabilized Combustor
CO, CO2, NOx (global emissions) Detailed Thermal BC
Sidwell et al., (2006)  Strakey et al., (2006)  Strakey and Yip, (2006)  Strakey et al., (2007) 
NG NG + Ethane NG + Propane CH4 CH4 + H2 C2H6 C2H6 + H2 C3H8 C3H8 + H2 Various Liquid and Gaseous Fuels
CO, CO2, HC, O2 (global emissions) NOx
Flores et al., 2000  Hack and McDonell, 2005 
CO, NOx (axial and radial profiles)
Schefer et al., 2002  Wicksall et al., 2005  Agrawal, 2006 
CO and NOx (global emissions)
Capehart et al., 1997  Lee et al., 2001 
CH4, CO, CO2, H2, OH, H2O, NO, O2 (axial and radial profiles) Inlet Turbulence
Pan, 1991  Nandula et al., 1996 
Based on a qualitative analysis of the available modeling variables, the SimVal combustor (optically accessible and designed for CFD model validation studies ) provided the most complete boundary condition characterization (with heat loss measured for every combustor surface ). However, the currently available data lack the measurement of species profiles inside the combustor with the emissions being measured as bulk emissions at the exit of the combustor. With efforts underway to include measurement of detailed species and turbulence profiles (see Strakey et al., 2006  and Strakey et al., 2007 ), the SimVal combustor is expected to play a major role in future CFD validation study using LES (Large Eddy Simulation) techniques. For this preliminary RANS based study the bluff-body combustor experiments (Pan, 1991  and Nandula et al., 1996 ) provided the necessary data on velocity, temperature and species profiles along with the inlet turbulence and boundary conditions to justify the testing of various turbulence combustion models on this simple geometry. COMBUSTOR GEOMETRY Combustor Length 342 mm Bluff-Body Length 52.25 mm Bluff Body Diameter 45.45 mm Bluff-Body Angle 450 Blockage Ratio 25 % INLET CONDITIONS Velocity 15 m/s Turbulence Intensity 24 % Fuel Mixture CH4 + Air Equivalence Ratio 0.586 Temperature 400 BOUNDARY CONDITIONS Water Cooled Outer Walls maintained at 500 K Outlet Outflow EXPERIMENTAL CONDITIONS Pressure 1 atm Figure 1 – Schematic of the Bluff-Body combustor experiment by Nandula et al., 1996 , the corresponding experimental conditions (center column) and the 2D axisymmetric grid (zoomed to show near wall grid) used in this study
Combustor and Geometry Figure 1 shows the schematic of the bluff-body combustor geometry and the 2D axisymmetric grid used here, along with a table containing the major parameters of the experiment. The combustor consists of a 79 mm diameter test section of 342 mm length with a stainless steel bluff body (base diameter 44.45 mm and apex angle 45o) mounted coaxially to serve as the flame holder. A methane and air mixture (at an equivalence ratio Φ = 0.586) are injected at the base of the combustor at a reference velocity of 15 m/s and a free stream turbulence intensity of 24%. The flame is stabilized by the bluff body, with a recirculation zone which extends approximately one diameter downstream, a shear layer or an annular flame zone, and a post flame zone . The experiments  provide data in the form of radial profiles at selected axial locations above the bluff body (see Figure 1).
CFD Code In the current study the focus is on commercial CFD codes. The wide use of the FLUENT (Ansys Inc., Lebanon, NH) code in the gas turbine research community both at national research centers and industry makes it an ideal candidate for the current study. FLUENT holds an approximate 40% market share making it the most widely used CFD package in the world . FLUENT provides  a variety of turbulence and combustion models, two reduced chemistry mechanisms (hard coded, ability to add other chemistry mechanisms available) along with an InSitu Adaptive Tabulation (ISAT) algorithm  based integrator for reducing the computational cost of the reacting flow calculations. Turbulence Models The Reynolds-averaged Navier-Stokes (RANS) equations are used to calculate the transport of the averaged flow quantities, with the entire range of turbulent time and length scales being modeled. The RANS approach greatly reduces the required computational effort and resources (relative to DNS or LES), and is widely adopted for practical engineering applications . The Boussinesq hypothesis is used to formulate the commonly used 2-equation turbulence models such as the Spalart-Allmaras model, the k-ε models, and the k-ω models. The disadvantage of the Boussinesq hypothesis is that it inherently assumes locally isotropic turbulence, which is usually not true for most practical flows . One of the RANS based turbulence models chosen for this study is the RNG (Renormalized Group Theory) variant of the k-ε model, a detailed description of which is available elsewhere . A description of the FLUENT implementation of the RNG k-ε model is also available . An alternative approach to the Boussinesq hypothesis, the Reynolds Stress Model (RSM) solves transport equations for each of the terms in the Reynolds stress tensor along with an additional scale-determining equation (usually for ε). This means that five additional transport equations are required in 2D flows and seven additional transport equations must be solved in 3D thus making it more computationally expensive. The RSM is usually superior for situations in which the anisotropy of turbulence has a dominant effect on the mean flows, such as in highly swirling flows and stress-driven secondary flows . A detailed description of the RSM model is available in references [23, 24 and 25] and a description of the FLUENT implementation of the RSM model is available in reference . Turbulence-Combustion Interaction Models Using the Eddy-Dissipation-Concept (EDC) model in FLUENT, multiple simultaneous chemical reactions can be modeled thus enabling the incorporation of detailed Arrhenius chemical kinetics in turbulent flames. The EDC model is an extension of the eddy-dissipation model to include detailed chemical mechanisms in turbulent flows [26, 27]. The EDC model assumes that reactions occurs in small turbulent structures, called the fine scales, with initial conditions taken from the current species concentrations and temperature in the cell. Reactions proceed over the time scale, governed by the Arrhenius rates of reaction and are integrated numerically using the ISAT algorithm  for tabulation. The equations for the size of the fine scale structure and time scale of reaction (along with the corresponding FLUENT implementation of the EDC model) can be found in references [26, 27, and 18]. The PDF method, where the transport equations for the single-point, joint probability density function (PDF) of species and energy are solved, is an alternative turbulent combustion model
where the primary advantage is a closed form of reaction terms which then need no modeling. The trade-off is that the use of Monte Carlo algorithms to solve the PDF equations increases the computational cost and introduces statistical errors. Also, the molecular mixing of species and energy must be modeled and is usually the largest source of modeling error in the PDF transport approach . More information on the PDF model can be found in references  and . Current work is in progress in applying PDF based combustion models for the same conditions reported here. All of the results presented in this paper use the EDC combustion model. Reaction Mechanisms A number of reduced mechanisms for methane combustion have been developed from detailed mechanisms (GRI 2.1  and GRI 3.0 ) and are available in the literature. While the differences in the prediction of major species among the mechanisms are minimal, the discrepancies in prediction of NO can be substantial. Table 2 gives a brief list of the available reduced mechanisms (with number of species < 20) that are suitable for this study. The MFC9 mechanism by Mallampalli et al., 1996  can be invoked in FLUENT and is called ARM9. Similarly the ARM2 mechanism by Sung et al., 1998  can be invoked as the ARM19 mechanism in FLUENT. In the current study these two mechanisms will be studied in conjunction with the turbulence and combustion models listed above. Table 2 – List of reduced mechanisms (with species < 20) available in the literature Mechanism MFC5 MFC9 = ARM9 (FLUENT) ARM2 = ARM19 (FLUENT) 12step GRI 211 13step GRI 3 10step. GRI 211 8step GRI 12 6step GRI 12
Species 9 9 19 16 17 14 12 10
Reactions 5-step, GRI2.11 9-steps, GRI 2.11 15-steps, GRI 3.0 12-steps, GRI 2.11 13-steps, GRI 3.0 10-steps, GRI 2.11 8 steps, GRI 1.2 6 steps, GRI 1.2
Reference      ,   
Grid and Numerics With the assumption of an axially symmetric flame, a hybrid (hexahedral and tetrahedral volumes) 2D axisymmetric grid consisting of 31,210 cells was constructed (see Figure 1). A 3D grid consisting 1,143,314 volumetric cells was also generated. While the grid densities used seem to be adequate for the current study, a more detailed grid dependence study is underway. Turbulent combustion calculations were carried out for methane-air mixtures at an equivalence ratio of 0.586 using various combinations of turbulence models and reaction mechanisms as listed in Table 3 below. FLUENT incorporates the In-Situ Adaptive Tabulation (ISAT) method to accelerate the chemistry calculations in multi-dimensional flow problems . The ISAT algorithm greatly reduces (~100-fold reduction ) the computational time of chemistry calculations by building and querying a table of accessed composition space with error control . More information on ISAT and the FLUENT ISAT implementation can be found in references  and . The numerical error in the ISAT table is controlled by the ISAT error tolerance . A larger error tolerance value implies greater error but faster run times. In order to accurately predict the minor species and emissions an ISAT error tolerance value of 5×10-6 is used in the current study (see Table 3). This value was determined by reducing the tolerance until levels of NO concentration at the outlet of the computational domain ceased to change.
The boundary conditions at the inlet of the combustor matched the experiments with a 15 m/s axial velocity and a free stream turbulent intensity of 24%. The turbulent length scale parameter is chosen to be 5% of the gap between the edge of the bluff body and the combustor walls at 1.72 mm. The experiments suggest that the outer walls of the combustor are maintained at 500 K using water cooling. Hence the thermal boundary condition at the walls is set to a temperature of 500 K. The mixture at the inlet of the combustor is considered to be fully premixed at an equivalence ratio of 0.586 and a temperature of 400 K. The use of higher order discretization schemes greatly improved the stability of the flame solution of the 2D axisymmetric cases (See Section 3). Table 3 tabulates the detailed computational specifications including the discretization schemes and the convergence criterion for all the models studied. Table 3 – Computational conditions for the five bluff-body cases modeled Model ID / Model Parameters Grid
RSM Linear Pressure-Strain SWF
RSM Linear Pressure-Strain SWF
Combustion Model ISAT Tolerance Reaction Mechanism Discretization
5×10-6 ARM9 2nd order
2nd Order UW
2nd Order UW
2nd Order UW
Residuals for Absolute Convergence Criterion
Results and Discussion
A series of cold flow simulations were first performed on 2D axisymmetric and 3D grids to determine the performance of the turbulence models in characterizing the recirculation zone in the flow field. Cold flow velocity calculations were conducted on the 2D mesh using the RNG kε and the RSM models and on the 3D grid using the RNG k-ε model. A comparison of the results of the simulations with measured axial and radial velocity profiles of cold case are shown in Figure 2. It can be seen that there is good agreement between the data and the simulations for axial velocity profiles close to the bluff body (x/d = 0.10). The agreement between the
experimental data and the simulations is much worse (about 20% variation) away from the stagnation plane. Radial velocity profiles also show good agreement with the experiments only in the recirculation zone close to the bluff body The radial velocity in the recirculation zone is well captured for the x/d = 0.30 slice. However, away from the stagnation plane and in the shear layer, there is substantial difference between the experiments and calculation in the values of the radial velocity profiles, though the general shape of the curve is similar.
Figure 2 – Comparison of axial velocity profiles (left) and Radial velocity profiles (right) for cold flow simulations obtained using 2D-RNG (••••), 2D-RSM (– –) and 3D-RNG (▬) with experiments (□) by Nandula et al., 1996 
Combustion calculations were carried out for the five cases listed in Table 3. A stable flame at the target equivalence ratio (Φ = 0.586) was obtained by igniting at a much higher equivalence ratio (usually Φ = 0.65 to 0.70), obtaining a steady flame and then slowly changing the inlet mass fractions until the target equivalence ration was reached. Initial studies with first order discretization of equations (FLUENT defaults; SIMPLE for P-V Coupling, Standard discretization for pressure and 1st order upwind scheme for all other variables) failed to produce a stable flame for equivalence ratios less than 0.62 to 0.63 for all of the cases studied. For the same conditions the use of higher order discretization schemes (as shown in Table 3) produced stable flames. For the 3D-ARM9-RNG case, use of first order discretization, produced oscillations in the flame height along with asymmetric flame shape. Higher order discretization schemes produced symmetric flames with no oscillations. These results show the significance of discretization errors in obtaining and maintaining a stable flame for this geometry. Even with the use of higher order discretization schemes, the 2D-ARM19-RNG case showed extinction at an equivalence ratio of 0.62. Application of various numerical ignition strategies to stabilize the flame ultimately led to extinction. Using the RNG k-ε turbulence model, a stable flame at the target equivalence ratio of Φ=0.586 was obtained using the ARM9 mechanism. Using the RSM turbulence model resulted in stable flames at the target equivalence ratio using
both the ARM9 and ARM19 mechanisms. It is postulated that the more robust RSM turbulence model can help to sustain the flame while using a robust reaction mechanism with a more dissipative turbulence model might lead to extinction. Figure 3 shows the temperature contours of the four flames obtained at the target equivalence ratio. Comparing Figures 3a and 3b, which have the same reaction mechanism (ARM9) but different turbulence models, a distinct change in the flame shape, can be attributed to better reproduction of the recirculation zone by the RSM model. Comparing Figures 3b and 3c, which have the same turbulence models (RSM) but different reaction mechanisms, the significant change in flame shape can be attributed to the more robust kinetics (presence of more intermediate species) of the ARM19 mechanism compared to the ARM9 mechanism. The validity of the axisymmetric flame assumption can be verified by comparing flame shape in the 2D axisymmetric simulation (Figures 3a) and the 3D simulation (Figure 3d) both of which use the same turbulence model and reaction mechanism.
Figure 3 – Temperature profiles (filled contours) and NO mass fraction (ppm) contours (white line) for the methane air flame at Φ = 0.586 obtained using the computational cases (a) 2D-ARM9-RNG, (b) 2D-ARM9-RSM, (c) 2D-ARM19-RSM and (d) 3D-ARM9-RNG. (e) Comparison of species profiles obtained using the computational cases, 2D-ARM9-RNG (– • –), 2D-ARM9-RSM (– –), 2D-ARM19RSM (••••) and 3D-ARM9-RNG (▬) with the experimental data (□) of Nandula et al., 1996 .
Figure 3e shows the temperature profiles obtained using all four cases compared to the experimental values at the respective axial and radial locations near the bluff body. On an average all the models tested in this work, overpredict the temperature by about 5%. Temperature profiles at the exit (at x/d = 6.0) do not match the experiments, especially in the shear layer and close to the outer wall, most probably due to ill defined boundary conditions. It is to be noted that the radial profiles of the variables were measured from the axis of the burner to approximately 10 mm into the shear layer (r/d = 0.60). There was no data available in the shear layer and close to the burner wall. Figure 4 gives a comparison of the species profiles from the current simulations against the corresponding experimental values. It can be seen that the resolution of the major species, CH4 (Figure 4a), O2 (Figure 4b), CO2 (Figure 4c) and H2O
(Figure 4d), is independent of the turbulence model and the reaction mechanism with all tested models giving acceptable agreement with the experimental values for all axial locations except x/d = 0.60 and x/d = 6.00.
Figure 4 – Comparison of species profiles obtained using the computational cases, 2D-ARM9-RNG (– • –), 2D-ARM9-RSM (– –), 2D-ARM19-RSM (••••) and 3D-ARM9-RNG (▬) with the experimental data (□) of Nandula et al., 1996 .
The differences in the profiles at locations close to the burner exit could be attributed to the lack of well defined boundary conditions as well as some differences in the turbulence models. The experiments suggest a ‘pinch’ in the flame at x/d = 0.60 which is not captured by any of the
models tested. While the CO radial profiles (Figure 4f) matched the experiments close to the stagnation plane (x/d = 0.10 and 0.30), all of the models tested consistently over-predicted the CO emissions. Since CO emissions are highly temperature dependent, the over prediction of CO can be attributed to the ill prescribed thermal boundary conditions along the wall (i.e. heat losses). Figure 4h shows the performance of the tested reaction mechanisms for the prediction of NO emissions. The difference between measured and calculated NO values is about ±5 ppm. These large variations (about ±50 % difference between the experiments and the computations in some cases) indicate that the tested reduced mechanisms are useful only for an engineering level or ‘ballpark’ estimation and trend calculation (not shown here) of NO emissions. Moreover, the ±5 ppm difference might present problems in calculation of emissions from fuel blends where the overall NO emissions are in this range. The mole-fraction profiles of OH (Figure 4g) and H2 (Figure 4e) show large differences, both qualitatively and quantitatively, when compared to the experiments. The prediction of H2, is particularly poor for both mechanisms and may indicate that these mechanisms are not appropriate for simulations using fuel blends, especially hydrogen enriched lean methane flames. Special attention needs to be paid in matching the turbulence time scales associated with the diffusion of H2 relative to the reaction time scales. 4.
Conclusions and Future Work
A detailed analysis of the emission prediction capabilities of several RANS-based turbulence combustion models was performed using two reduced methane chemistry mechanisms. An examination of the cold flow velocity profiles shows good reproduction of the recirculation zone at axial location close to the bluff body surface, with the RSM turbulence model producing the best agreement with the experimental data. All of the computational models studied here show good agreement with the experimentally measured temperature and major species mole fraction profiles near the bluff body. Significant differences were found in the axial and radial velocity and concentration profiles at higher axial locations (x/d ≥ 0.60) when compared to the experiments. The use of a chemical mechanism with more species did not necessarily improve the prediction of the intermediate species. This is evident in the fact that the computed profiles for the intermediate species (OH and H2) and emission species (CO and NO) using both the ARM19 and ARM9 mechanisms showed significant differences with the experiments. While the computed CO emissions matched the experimental profiles for axial locations x/d < 0.6, an average difference of 5 to 10 ppm was found for axial locations x/d ≥ 0.60. Similarly an average difference of ± 5 ppm between the computed and the experimental NO profile was observed. The qualitative and quantitative mismatch between the computed H2 profiles and the experimental H2 profiles suggests that the current reduced mechanisms might not be suitable for calculation of hydrogen enriched lean premixed combustion. A similar study is underway to test the accuracy of various reaction mechanisms in predicting emissions using Large Eddy Simulation (LES) and PDF models. Acknowledgements This technical effort was performed in support of the National Energy Technology Laboratory’s on-going research on the assessment of Turbo-Chemistry Models for Prediction of Fuel Composition Effects on GTC Emissions, under the RDS contract DE-AC26-04NT4181. The authors would like to thank Kent Castleton and Geo Richards at NETL for their invaluable support and insight.
References . http://www.eere.energy.gov/de/microturbines/, US Department of Energy, Distributed Energy Program . Richards, G. A., McMillian, M. M., Gemmen, R. S., Rogers, W. A., Cully, S. R., Progress in Energy and Combustion Science, 27, pp 141-169, (2001) . Hack, R. L., and McDonell, V. G., Paper GT2005-68777, presented at the 50th ASME International Gas Turbine and Aeroengine Congress and Exposition, Reno, June, (2005) . Sidwell, T. Richards, G., Caslteton, K., Straub, D., Maloney, D., Strakey, P.,Ferguson, D., Beer, S., Woodruff, S., AIAAJ 27510, (2006) . Strakey, P. A., Woodruff, S. D., Williams, T. C., and Schefer, R. W., AIAA-2007-0980, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 8-11, (2007) . Strakey, P. A., and Yip, M. J., FE-06-1087, NETL, (2006) . Starkey, P., Sidwell, T., and Ontko, J., Proceedings of the Combustion Institute, Vol. 31, pp xxx-xxx (2006) . Flores, R.M., McDonell, V.G., and Samuelsen, G. S., ASME Paper 2000-GT-0141, presented at the 45th ASME International Gas Turbine and Aeroengine Congress and Exposition, Munich, (2000) . Schefer, R. W., Wicksall, D. M., and. Agrawal, A. K, Proceedings of the Combustion Institute, Vol. 29, pp 843-851, (2002) . Wicksall, D. M., Agrawal, A. K., Schefer, R. W., and Keller, J. O., Proceedings of the Combustion Institute, (2005), Vol. 30, pp 2875-2883, (2005) . Agrawal, A. K., University of Alabama Presentation, (Obtained through personal correspondence), 2006 . Capehart, S. A., Lee, J. C. Y., Williams, J. T., and Malte, P. C., 97-GT-336, Proceedings of The International Gas Turbine and Aeroengine Congress and Exhibition, Orlando, FL, (1997) . Lee, J. C. Y., Malte, P. C., and Benjamin, M. A., 2001-GT-0081, Proceedings of: ASME Turbo Expo 2001, June 4-7, New Orleans, LA, USA, (2001) . J.C. Pan., PhD thesis, The University of Dayton, (1991). . Nandula, S. P., Pitz, R. W., Barlow, R. S., and Fiechtner., G. J., 34th Aerospace Sciences Meeting Exhibit, Reno, NV, January, pp 15–18, January (1996) . Williams, T. C., Schefer, R. W., Oefelein, J. C., and Shaddix, C. R., Review of Scientific Instruments, Vol. 783, pp. 035114-035114-9, (2007). . "ANSYS Completes Acquisition of Fluent", http://www.fluent.com/news/pr/pr131.htm . FLUENT Users Guide, Fluent Inc., September 2006 . C. T., Bowman, R. K., Hanson, D. F., Davidson, W. C., Gardiner, Jr., V. Lissianski, G. P., Smith, D. M., Golden, M. Frenklach and M., Goldenberg, http://www.me.berkeley.edu/gri_mech/ . Gregory P. Smith, David M. Golden, Michael Frenklach, Nigel W. Moriarty, Boris Eiteneer, Mikhail Goldenberg, C. Thomas Bowman, Ronald K. Hanson, Soonho Song, William C. Gardiner, Jr., Vitali V. Lissianski, and Zhiwei Q in http://www.me.berkeley.edu/gri_mech/ . Pope., S. B., Combustion Theory and Modeling, Vol. 1, pp 41-63, (1997) . Yakhot, V., and Orszag, S. A., Journal of Scientifc Computing, Vol. 1(1), pp 1-51, (1986) . Gibson, M. M., and Launder, B. E., Journal of Fluid Mechanics, Vol. 86, 491-511, (1978) . Launder, B. E., International. Journal of Heat Fluid Flow, Vol. 10(4), pp 282-300, (1989) . Launder, B. E., Reece, G. J., and Rodi., W., Journal of Fluid Mechanics, Vol. 68(3), pp 537-566, April (1975) . Magnussen, B. F., 19th AIAA Meeting, St. Louis, (1981) . Gran, I. R., and Magnussen, B. F., Combustion Science and Technology, Vol. 119, pp 191, (1996) . Pope, S. B., Progress Energy Combustion Science, Vol. 11, pp 119, (1985) . Available online at http://www.ca.sandia.gov/TNF/chemistry.html (Last accessed August 2007) . Available online at http://firebrand.me.berkeley.edu/ (Last accessed August 2007) . Chen, J-Y., Workshop on ‘Numerical Aspects of Reduction in Chemical Kinetics’, CERMICS-ENPC Cite Descartes - Champus sur Marne, France, September 2nd, (1997) . W.-C. Chang and J.-Y. Chen, http://firebrand.me.berkeley.edu/griredu.html (Last accessed August 2007) . Mallampalli, H. P., Fletcher, T. H., and Chen, J-Y., Paper 96F-098, Presented at the Fall Meeting of the Western States Section of the Combustion Institute, University of Southern California, Los Angeles, CA, October 28-29, 1996 . Sung, C. J., Law, C. K., and Chen, J. Y., Proceedings of the Combustion Institute, Vol. 27, pp 295-304, (1998)