0
Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Optimization of Reduced Kinetic Models for Reactive Flow Simulations

[+] Author and Article Information
R. Joklik

e-mail: rgjoklik@csefire.com

M. Klassen

Combustion Science & Engineering, Inc.,
8940 Old Annapolis Road,
Suite L,
Columbia, MD 21045

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 8, 2013; final manuscript received August 6, 2013; published online October 21, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(1), 011503 (Oct 21, 2013) (12 pages) Paper No: GTP-13-1244; doi: 10.1115/1.4025265 History: Received July 08, 2013; Revised August 06, 2013

A robust optimization scheme, known as rkmGen, for reaction rate parameter estimation has been developed for the generation of reduced kinetics models of practical interest for reactive flow simulations. It employs a stochastic optimization algorithm known as simulated annealing (SA), and is implemented in C++ and coupled with Cantera, a chemical kinetics software package, to automate the reduced kinetic mechanism generation process. Reaction rate parameters in reduced order models can be estimated by optimizing against target data generated from a detailed model or by experiment. Target data may be of several different kinds: ignition delay time, blow-out time, laminar flame speed, species time-history profiles, and species reactivity profiles. The software allows for simultaneous optimization against multiple target data sets over a wide range of temperatures, pressures, and equivalence ratios. In this paper, a detailed description of the optimization strategy used for the reaction parameter estimation is provided. To illustrate the performance of the software for reduced kinetic mechanism development, a number of test cases for various fuels were used: one-step, three-step, and four-step global reduced kinetic models for ethylene, Jet-A and methane, respectively, and a 50 step semiglobal reduced kinetic model for methane. The 50 step semiglobal reduced kinetic model was implemented in the Star*CCM+ commercial CFD code to simulate Sandia Flame D using laminar flamelet libraries and compared with the experimental data. Simulations were also performed with the GRI3.0 mechanism for comparisons.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hilbert, R., Tap, F., El-Rabii, H., and Thévenin, D., 2004, “Impact of Detailed Chemistry and Transport Models on Turbulent Combustion Simulations,” Prog. Energy Combust. Sci., 30(1), pp. 61–117. [CrossRef]
Peters, N., 2000, Turbulent Combustion, Cambridge University Press, New York.
Gokulakrishnan, P., Foli, K., Klassen, M., Roby, R., Soteriou, M., Kiel, B., and Sekar, B., 2009, “LES-PDF Modeling of Flame Instability and Blow-Out in Bluff-Body Stabilized Flames,” Proceedings of the 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Denver, CO, August 2–5, AIAA Paper No. 2009-5409. [CrossRef]
Gokulakrishnan, P., Bikkani, R., Klassen, M., Roby, R., and Kiel, B., 2009, “Influence of Turbulence–Chemistry Interaction in Blow-Out Predictions of Bluff-Body Stabilized Flames,” Proceedings of the 47th AIAA Aerospace Sciences Meeting, Orlando, FL, January 5–8, AIAA Paper No. 2009-1179. [CrossRef]
Tomlin, A., Turányi, T., and Pilling, M., 1997, “Mathematical Tools for the Construction Investigation and Reduction of Combustion Mechanisms,” Low-Temperature Combustion and Auto Ignition, (Comprehensive Chemical Kinetics, Vol. 35), M.Pilling ed., Elsevier, Amsterdam, pp. 293–437.
Vajda, S., Valko, P., and Turanyi, T., 1985, “Principal Component Analysis of Kinetics Models,” Int. J. Chem. Kinet., 17, pp. 55–81. [CrossRef]
Gokulakrishnan, P., McLellan, P., Lawrence, A., and Grandmaison, E., 2005, “Kinetic Analysis of NO-Sensitized Methane Oxidation,” Chem. Eng. Sci., 60, pp. 3683–3692. [CrossRef]
Gokulakrishnan, P., Lawrence, A., McLellan, P., and Grandmaison, E., 2006, “A Functional-PCA Approach for Analyzing and Reducing Complex Chemical Mechanisms,” Comput. Chem. Eng., 30, pp. 1093–1101. [CrossRef]
Lam, S., and Goussis, D., 1994, “The CSP Method for Simplifying Kinetics,” Int. J. Chem. Kinet., 26, pp. 461–486. [CrossRef]
Maas, U., and Pope, S., 1992, “Simplifying Chemical Kinetics: Intrinsic Low-Dimensional Manifolds in Composition Space,” Combust. Flame, 88, pp. 239–264. [CrossRef]
Law, C., and Lu, T., 2008, “Towards Accommodating Realistic Fuel Chemistry in Large-Scale Computations,” Proceedings of the 46th AIAA Aerospace Sciences Meeting, Reno, NV, January 7–10, AIAA Paper No. 2008-969. [CrossRef]
Kuo, K., 1986, Principles of Combustion, Wiley, New York.
Westbrook, C., and Dryer, F., 1981, “Simplified Reaction Mechanism for the Oxidation of Hydrocarbon Fuels in Flames,” Combust. Sci. Technol., 27, pp. 31–43. [CrossRef]
Jones, W., and Lindstedt, R., 1988, “Global Reaction Schemes for Hydrocarbon Combustion,” Combust. Flame, 73, pp. 233–249. [CrossRef]
Gokulakrishnan, P., Kwon, S., Hamer, A., Klassen, M., and Roby, R., 2006, “Reduced Kinetic Mechanism for Reactive Flow Simulation of Syngas/Methane Combustion at Gas Turbine Conditions,” Proceedings of the ASME Turbo Expo 2006: Power for Land, Sea and Air, Barcelona, Spain, May 8–11, ASME Paper No. GT2006-90573. [CrossRef]
Gokulakrishnan, P., Pal, S., Klassen, M., Hamer, A., Roby, R., Kozaka, O., and Menon, S., 2006, “Supersonic Combustion Simulation of Cavity-Stabilized Hydrocarbon Flames Using Ethylene Reduced Kinetic Mechanism,” Proceedings of the AIAA/ASME/SAE 42nd Joint Propulsion Conference, Sacramento, CA, July 9–12, AIAA Paper No. 2006-5092. [CrossRef]
Polifke, W., Geng, W., and Dobbeling, K., 1998, “Optimization of Rate Coefficients for Simplified Reaction Mechanisms With Genetic Algorithms,” Combust. Flame, 113, pp. 119–135. [CrossRef]
Heinz, C., Brandt, M., and Polifke, W., 2005, “Optimization of Rate Coefficients for Global Reaction Mechanisms Using a Nested Genetic Algorithm,” Proceedings of the European Combustion Meeting (ECM2005), Louvain-la-Neuve, Belgium, April 3–6.
Elliott, L., Ingham, D., Kyne, A., Mera, N., Pourkashanian, M., and Wilson, C., 2004, “Genetic Algorithms for Optimisation of Chemical Kinetics Reaction Mechanisms,” Prog. Energy Combust. Sci., 30, pp. 297–328. [CrossRef]
Kirkpatrick, S., 1983, “Optimization by Simulated Annealing,” Science, 220, pp. 671–681. [CrossRef] [PubMed]
Szu, H., and Hartley, R., 1987, “Fast Simulated Annealing,” Phys. Lett. A, 122(3), pp. 157–162. [CrossRef]
Horchner, U., and Kalivas, J., 1995, “Further Investigation on a Comparative Study of Simulated Annealing and Genetic Algorithm for Wavelength Selection,” Anal. Chim. Acta, 311, pp. 1–13. [CrossRef]
Goodwin., D. G., 2003, “An Open-Source, Extensible Software Suite for CVD Process Simulation,” Chemical Vapor Deposition XVI and EUROCVD 14, ECS Proceedings Volume 2003–08, M.Allendorf, F.Maury, and F.Teyssandier, eds., The Electrochemical Society, Pennington, NJ, pp. 155–162.
Ingber, L., 1989, “Very Fast Simulated Re-Annealing,” Math. Comput. Model., 12(8), pp. 967–973. [CrossRef]
Ingber, L., and Rosen, B., 1992, “Genetic Algorithms and Very Fast Simulated Re-Annealing—A Comparison,” Math. Comput. Model., 16(11), pp. 87–100. [CrossRef]
Ehrgott, M., 2005, Multicriteria Optimization, Springer, Berlin.
Cohen, S., and Hindmarsh, A., 1994, “CVODE User Guide,” Lawrence Livermore National Laboratory, Livermore, CA, Report No. UCRL-MA-118618.
Burcat, A., 2006, “Burcat's Thermodynamic Data,” http://garfield.chem.elte.hu/Burcat/burcat.html
Nishiie, T., Singh, D., and Qiao, L., 2009, “Laminar Burning Velocity and Markstein Length of n-Decane-Air, Jet-A-Air and S-8-Air Flames,” Proceedings of the 6th U.S. National Combustion Meeting, Ann Arbor, MI, May 17–20.
Smith, G., Golden, D., Frenklach, M., Moriarty, N., Eiteneer, B., Goldenberg, M., Bowman, C. T., Hanson, R., Song, S., Gardiner, W., Jr., Lissianski, V., and Qin, Z., 2013, “GRI-Mech 3.0,” http://www.me.berkeley.edu/gri_mech/
Petersen, E., Hall, J., Smith, S., de Vries, J., Amadio, A., and Crofton, M., 2007, “Ignition of Lean Methane-Based Fuel Blends at Gas Turbine Pressures,” ASME J. Eng. Gas Turbines Power, 129, pp. 937–944. [CrossRef]
Li, J., Zhao, Z., Kazakov, A., Chaos, M., Dryer, F., and Scire, J., 2007, “A Comprehensive Kinetic Mechanism for CO, CH2O, CH2OH Combustion,” Int. J. Chem. Kinet, 39, pp. 109–136. [CrossRef]
Barlow, R., and Frank, J., 1998, “Effects of Turbulence on Species Mass Fractions in Methane/Air Jet Flames,” Sym. (Int.) Combust., 27(1), pp. 1087–1095. [CrossRef]
Jaishree, J., 2011, “Lagrangian and Eulerian Probability Density Function Methods for Turbulent Reacting Flows,” Ph.D. thesis, Penn State University, University Park, PA.

Figures

Grahic Jump Location
Fig. 1

Growth in the size of detailed chemical kinetic models for various fuels (adopted from Law and Lu [11])

Grahic Jump Location
Fig. 2

Schematic of the main components of the rkmGen optimization software

Grahic Jump Location
Fig. 3

Visual representation of the search domain of simulated annealing path for global optimum for ignition delay time generated by rkmGen for one-step ethylene reduced model

Grahic Jump Location
Fig. 4

Ignition delay time predictions for one-step ethylene model compared with detailed mechanism

Grahic Jump Location
Fig. 5

Laminar flame speed data of Nishiie et al. [29] for Jet-A and n-decane compared with 3-step reduced model predictions

Grahic Jump Location
Fig. 6

Simultaneous optimization of ignition delay time and lean blow-out time with current 4-step reduced model. Key: symbols, target data (GRI3.0); solid lines, current optimized model; dashed lines, Jones and Lindstedt model [14].

Grahic Jump Location
Fig. 7

Current four-step reduced model predictions for CO and H2 concentrations at blow-out. Key: symbols, target data (GRI3.0); solid lines, current optimized model; dashed lines, Jones and Lindstedt model [14].

Grahic Jump Location
Fig. 8

Current four-step model predictions for blow-out temperature at 600 K and 1 atm compared with the model predictions from GRI3.0. Key: symbols, GRI3.0; solid lines, current four-step optimized model; dashed lines, Jones and Lindstedt model [14].

Grahic Jump Location
Fig. 9

Ignition delay time predictions for off-design conditions using the four-step reduced model. The model predictions are compared with the shock tube experimental data of Petersen et al. [31] for methane/air (equivalence ratio = 0.5) at 0.7 and 20 atm. Design condition is stoichiometric at 1 atm. Key: symbols, experimental data [31]; lines, current four-step model predictions.

Grahic Jump Location
Fig. 10

Current four-step model predictions for laminar flame speed at 300 K and 600 K at 1 atm compared with the model predictions from GRI3.0. Key: symbols, GRI3.0; solid lines, current optimized model; dashed lines, Jones and Lindstedt model [14].

Grahic Jump Location
Fig. 11

Schematic of 50 step reduced kinetic model for a generic hydrocarbon fuel, CxHy

Grahic Jump Location
Fig. 12

GRI3.0 model predictions compared with 50 step methane reduced kinetic model predictions obtained from simultaneous optimization of ignition delay time and lean blow-out time in rkmGen

Grahic Jump Location
Fig. 13

Species time-history profile obtained from 50 step methane semiglobal reduced kinetic model compared with GRI3.0. Key: symbols, GRI3.0; lines, 50 step model.

Grahic Jump Location
Fig. 14

Axial profiles of different centerline quantities of Sandia Flame D experimental data [33] compared with current model predictions: experiments (symbols), GRI 3.0 (black line), CSE's 50 step mechanism (red line)

Grahic Jump Location
Fig. 15

Radial profiles for velocity, temperature, mixture fraction, and mixture fraction variance at different distances downstream (x) from the exit plane of the jet. Key: same as in Fig. 14.

Grahic Jump Location
Fig. 16

Radial profiles for chemical species at different distances downstream (x) from the exit plane of the jet. Key: same as in Fig. 14.

Grahic Jump Location
Fig. 17

Isotherms for λ as function of probability (u) at different annealing temperatures (Tj) in Eq. (10)

Grahic Jump Location
Fig. 18

Number of iterations needed to reach the final annealing temperature, Tf, as a function of T0/Tf for various quench factors, and constants m and n. k(Tf) is the number of iterations needed to reach the final annealing temperature.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In