Towards a predictive combustion chemistry model

1. 7ISFS, July 11-15, 2011 Towards a predictive combustion chemistry model Hai Wang University of Southern California

2. Combustion Kinetics of Jet Fuels Applications Gas-turbine engines: CFD-based design Pollutant emission Hypersonics: Ignition Flame holding

3. Jet Fuels Composition (courtesy of Tim Edwards) 4658 3327 4734 4572 4765 3773 World survey Jet A composite blend JP-7 F-T Jet RP-1 Coal-based jet fuel DCL JP-8 Jet A, Jet A-1, JP-8, JP-5, TS-1 Paraffins (n- + i-) 55.2 67.9 99.7 57.6 0.6 57.2 58.8 Cycloparaffins 17.2 21.2 <0.2 24.8 46.4 17.4 10.9 Dicycloparaffins 7.8 9.4 0.3 12.4 47.0 6.1 9.3 Tricycloparaffins 0.6 0.6 <0.2 1.9 4.6 0.6 1.1 Alkylbenzenes 12.7 0.7 <0.2 2.1 0.3 13.5 13.4 Indanes/Tetralins 4.9 <0.2 <0.2 0.3 1.1 3.4 4.9 Indenes <0.2 <0.2 <0.2 <0.2 <0.2 <0.2 <0.2 Naphthalene <0.2 <0.2 <0.2 <0.2 <0.2 <0.2 0.13 Naphthalenes 1.3 <0.2 <0.2 0.3 <0.2 1.7 1.55 Acenaphthenes <0.2 <0.2 <0.2 <0.2 <0.2 <0.2 <0.2 Acenaphthylenes <0.2 <0.2 <0.2 0.4 <0.2 <0.2 <0.2 Tricyclic Aromatics <0.2 <0.2 <0.2 <0.2 <0.2 <0.2 <0.2

4. Surrogate Strategy • A mixture of 4 to 5 neat hydrocarbons as the surrogate to mimic the chemical and physical behaviors of real jet fuels: • boiling and evaporation characteristics • C/H ratio • A possible set of surrogate componentsStaight-chain alkane:n-dodecane Cyclo alkane: n-butylcyclohexane Brached-chain alkane: 2,7-dimethyl octane One-ring aromatics: n-propylbenzene Two ring compounds:tetralin/a-methyl naphthalene?

5. Model Hierarchy Aliphatics Aromatics CH4 CHxOy, C2-4Hx Oxidation CO-H2 Oxidation H2 Oxidation Products H2O, CO2 H2, CO C2H2, soot ……

6. Performance Requirements • Ignition (homogeneous vs. diffusive) • Steady burning • Extinction • Premixed vs. nonpremixed flames • Pressure and concentration variations • Global responses (flame speed, ignition, extinction) • Detailed flame structure (major, minor species, NO, soot precursors) Law, Sung, Wang, Lu, AIAA J, 2005.

7. Model Parameters • Reaction Pathways and Rate ConstantsT-dependenceP-dependence • Thermochemical properties Enthalpy of formation, specific heat, entropy • Transport Properties Lennard-Jones Parameters

8. Sample Reaction Model

10. Selected Fundamental Problems • Reaction kinetics of CO + HO2→ CO2 + OH • Quantum tunneling in H-shift of alkyl radicals • Kinetic model uncertainty prediction/ minimization

11. CO + HO2→ CO2 + OH • RCM results suggest k(CO + HO2) should be reduced by a factor of 3 from Mueller et al. Mittal, Sung, Yetter Int. J. Chem. Kinet. 2006

12. CO + HO2 → Products ±0.5 CCSD(T)/CBS Potential energy in kcal/mol

13. CO + HO2 → Products ±0.5 CCSD(T)/CBS Potential energy in kcal/mol Theoretical Treatment and Assumptions • Monte Carlo solution of master equation of collision energy transfer • Exponential down model for collision energy transfer • RRKM microcanonical rate constants • 1-D hindered internal rotation by inverse Laplace Transform of rotational partition function

14. CO + OH → Products Pressure Dependency – Overall Rate Coefficient HOCO CO2 + H HOCO CO2 + H Joshi, Wang, Int. J. Chem. Kinet. (2006)

15. CO + HO2 → CO2 + OH upperlimit lowerlimit

16. CO + HO2 → CO2 + OH Now we get the ignition delay times right

17. Role of Tunneling in n-alkyl Radical Isomerization/b-Scission + CH3 2C2H4 + C3H7 + C3H7 2C2H4 + C3H7 + C2H5 • Example: n-heptane + (H, O, OH, ..) → heptyls + (H2, OH, H2O) • Isomerization determines the C1-C6 fragment distribution, and hence the main flame chemistry.

18. Role of Tunneling in n-alkyl Radical Isomerization • Tunneling must be considered to reconcile low and high temperature data → tunneling affects the post-cracking kinetics W.Tsang, J.A. Walker, J.A. Manion Proc. Combust. Inst. 31 (2007) 141

19. Tunneling in Reaction Rate Theory • Transition State Theory: transmission coefficient κ(T) • Approximations: • One dimensional assumption: • Potential Energy Surface expressed as a function V(s) • Wigner (1932): parabola function • Eckart (1917) & Johnston and Heicklen (1966): « Eckart potential »

20. Various Approximations • One dimensional tunneling transmission coefficient κ(T): • Wigner, Skodje & Truhlar, and Eckart • Multi-dimensional tunneling transmission coefficient κ(T): • Small Curvature Tunneling (SCT) Hessian required for each points along the Minimum Energy Path Computationally expensive Truong et al., http://therate.hec.utah.edu/

21. PES: n-heptyl radicals H-shifts CBS-QB3 E (0K, ZPE corrected)

22. Multi- vs One-dimensional Tunneling Eckart  good approximation for 300 < T < 2000 K Wigner  good for T > 800 K

23. Sensitivity Analysis of Eckart κ(T): Variation of Imaginary Frequency It’s all about the accuracy of the potential energy!

24. JetSurF 1.0 Validation – Species Concentrations behind reflected shock waves H. Wang, E. Dames, B. Sirjean, D. A. Sheen, R. Tangko, A. Violi, J. Y. W. Lai, F. N. Egolfopoulos, D. F. Davidson, R. K. Hanson, C. T. Bowman, C. K. Law, W. Tsang, N. P. Cernansky, D. L. Miller, R. P. Lindstedt, A high-temperature chemical kinetic model of n-alkane (up to n-dodecane), cyclohexane, and methyl-, ethyl-, n-propyl and n-butyl-cyclohexane oxidation at high temperatures, JetSurF version 2.0, September 19, 2010 (http://melchior.usc.edu/JetSurF/JetSurF2.0). Plot stolen from Ron Hanson. Solid line: experiments; dashed line: JetSurF

25. Kinetic Parameter Uncertainties • H + O2 ↔ OH + O (R1) • Uncertainty factor ~1.25 • Logarithmic sensitivity coefficient • = 0.24 (ethylene-air, f = 1, p = 1 atm) • ±5% (±4 cm/s) uncertainty in predicted flame speed due to R1 alone • Key question (Sheen et al. 2009): How do we propagate uncertainties in rate constants in combustion simulations? ~50% Baulch, et al. (2005)

26. 1-atm C2H4-air mixtures Propagation of Uncertainty 2nd order coefficients 1st order coefficients basis random variable nominal value Data structure that describes a chemical model + associated uncertainty Represents some physics model, e.g. PREMIX Predictions of a chemical model (e.g. laminar flame speed) + associated uncertainty Sheen et al. (2009)

27. Prediction Uncertainties in As-Compiled Model Good nominal prediction with significant uncertainty!

28. Method of Uncertainty Minimization k2 Chemical model + associated uncertainty h1 k1 least-squares minimization Physics model Covariance matrix Predictions + associated uncertainty

29. Predictions of As-Compiled and Uncertainty-Minimized Models Unconstrained Constrained

30. Effect on predicted laminar flame speed Considering no experiments Model constrained by species profiles Model constrained by species profiles + flame speeds

31. Effect on predicted laminar flame speed

32. What did uncertainty minimization do?

33. Acknowledgements • Previous students/postdocs • Ameya Joshi • Xiaoqing You • Scott G. Davis • Alexander Laskin • Current students/postdocs • David Sheen • Enoch Dames • Baptiste Sirjean • Collaborators • Stephen Klippenstein (ANL) • Chung-King Law (Princeton) • Fokion Egolfopoulos (USC) • Elke Goos (DLR) The JetSurF team Ron Hanson (Stanford) Tom Bowman (Stanford) Heinz Pitsch (Stanford) Wing Tsang (NIST) Angela Violi (UMich) Peter Lindstedt (Imperial Col.) Nick Cernansky (Drexel) David Miller (Drexel) Financial Support AFOSR, AFRL, SERDP, DOE, NSF