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Efficient Implementation of Chemistry in Computational Combustion

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Abstract

For hydrocarbon fuels, detailed chemical kinetics typically involve a large number of chemical species and reactions. In a high-fidelity combustion calculation, it is essential, though challenging, to incorporate sufficiently detailed chemical kinetics to enable reliable predictions of thermo-chemical quantities, especially for pollutants such as NO x and CO. In this paper, we review the recent work on efficient implementation of chemistry at Cornell, specifically: the invariant constrained equilibrium-edge pre-image curve dimension-reduction method for the reduced description of reactive flows; the transport-chemistry coupling in the reduced description; the computationally efficient operator-splitting schemes for reactive flows; and, recent developments in the storage/retrieval algorithm in situ adaptive tabulation.

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References

  1. Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion, 1st edn. R.T. Edwards Inc., Philadelphia (2001)

    Google Scholar 

  2. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  3. Bilger, R.W., Pope, S.B., Bray, K.N.C., Driscoll, J.F.: Paradigms in turbulent combustion research. Proc. Combust. Inst. 30, 21–42 (2005)

    Article  Google Scholar 

  4. Law, C.K.: Combustion Physics. Cambridge University Press, Cambridge (2006)

    Google Scholar 

  5. Peters, N.: Turbulent Combustion. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  6. Tomlin, A.S., Turányi, T., Pilling, M.J.: Mathematical Tools for the Construction, Investigation and Reduction of Combustion Mechanisms. Comprehensive Chemical Kinetics 35: Low-temperature Combustion and Autoignition. Elsevier, Amsterdam (1997)

    Google Scholar 

  7. Warnatz, J., Maas, U., Dibble, R.W.: Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation, 3rd edn. Springer, Berlin Heidelberg New York (2001)

    MATH  Google Scholar 

  8. Cao, R., Pope, S.B.: The influence of chemical mechanisms on PDF calculations of nonpremixed piloted jet flames. Combust. Flame 143, 450–470 (2005)

    Article  Google Scholar 

  9. Cao, R., Wang, H., Pope, S.B.: The effect of mixing models in PDF calculations of piloted jet flames. Proc. Combust. Inst. 31, 1543–1550 (2007)

    Article  Google Scholar 

  10. Wang, H., Pope, S.B.: Comparison of detailed reaction mechanisms in non-premixed combustion. Combust. Flame (2008, submitted)

  11. Hawkes, E.R., Sankaran, R., Sutherland, J.C., Chen, J.H.: Scalar mixing in direct numerical simulations of temporally evolving plane jet flames with skeletal CO/H 2 kinetics. Proc. Combust. Inst. 31, 1633–1640 (2007)

    Article  Google Scholar 

  12. Curran, H.J., Gaffuri, P., Pitz, W.J., Westbrook, C.K.: A comprehensive modeling study of iso-octane oxidation. Combust. Flame 129, 253–280 (2002)

    Article  Google Scholar 

  13. Lu, T., Law, C.K.: A directed relation graph method for mechanism reduction. Proc. Combust. Inst. 30, 1333–1341 (2005)

    Article  Google Scholar 

  14. Pepiot, P., Pitsch, H.: Systematic reduction of large chemical mechanisms. Paper presented at the 4th joint meeting of the U. S. Sections of the Combustion Institute, Philadelphia, PA, 21–23 March 2005

  15. Bodenstein, M., Lind, S.C.: Geschwindigkeit der Bildung des Bromwasserstoffs aus seinen Elementen. Z. Phys. Chem. 57, 168–175 (1906)

    Google Scholar 

  16. Smooke, M.D. (ed.): Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, vol. 384. Springer, Berlin (1991)

    Google Scholar 

  17. Keck, J.C., Gillespie, D.: Rate-controlled partial equilibrium method for treating reacting gas-mixtures. Combust. Flame 17, 237–241 (1971)

    Article  Google Scholar 

  18. Keck, J.C.: Rate-controlled constrained equilibrium theory of chemical reactions in complex systems. Prog. Energy Combust. Sci. 16, 125–154 (1990)

    Article  Google Scholar 

  19. Lam, S.H.: Using CSP to understand complex chemical kinetics. Combust. Sci. Technol. 89, 375–404 (1993)

    Article  Google Scholar 

  20. Lam, S.H., Goussis, D.A.: The CSP method of simplifying kinetics. Int. J. Chem. Kinet. 26, 461–486 (1994)

    Article  Google Scholar 

  21. Maas, U., Pope, S.B.: Simplifying chemical-kinetics: intrinsic low-dimensional manifolds in composition space. Combust. Flame 88, 239–264 (1992)

    Article  Google Scholar 

  22. Pope, S.B., Mass, U.: Simplifying chemical kinetics: trajectory-generated low-dimensional manifolds. FDA 93-11. Cornell University, Ithaca (1993)

  23. Roussel, M.R., Fraser, S.J.: Global analysis of enzyme inhibition kinetics. J. Phys. Chem. 97, 8316–8327 (1993)

    Article  Google Scholar 

  24. van Oijen, J.A., de Goey, L.P.H.: Modelling of premixed laminar flames using flamelet-generated manifolds. Combust. Sci. Technol. 161, 113–137 (2000)

    Article  Google Scholar 

  25. Bongers, H., van Oijen, J.A., de Goey, L.P.H.: Intrinsic low-dimensional manifold method extended with diffusion. Proc. Combust. Inst. 29, 1371–1378 (2002)

    Article  Google Scholar 

  26. Gorban, A.N., Karlin, I.V.: Method of invariant manifold for chemical kinetics. Chem. Eng. Sci. 58, 4751–4768 (2003)

    Article  Google Scholar 

  27. Singh, S., Powers, J.M., Paolucci, S.: On slow manifolds of chemically reactive systems. J. Chem. Phys. 117, 1482–1496 (2002)

    Article  ADS  Google Scholar 

  28. Gear, C.W., Kaper, T.J., Kevrekidis, I.G., Zagaris, A.: Projecting to a slow manifold: singularly perturbed systems and legacy codes. SIAM J. Appl. Dyn. Syst. 4, 711–732 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Bykov, V., Maas, U.: The extension of the ILDM concept to reaction-diffusion manifolds. Combust. Theory Model. 11, 839–862 (2007)

    Article  MATH  Google Scholar 

  30. Ren, Z., Pope, S.B., Vladimirsky, A., Guckenheimer, J.M.: The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics. J. Chem. Phys. 124, Art. No. 114111 (2006)

    Google Scholar 

  31. Chen, J-Y., Kollmann, W., Dibble, R.W.: PDF modelling of turbulent nonpremixed methane jet flames. Combust. Sci. Technol. 64, 315–346 (1989)

    Article  Google Scholar 

  32. Turányi, T.: Parameterization of reaction mechanisms using orthogonal polynomials. Comput. Chem. 18, 45–54 (1994)

    Article  Google Scholar 

  33. Christo, F.C., Masri, A.R., Nebot, E.M.: An integrated PDF/neural network approach for simulating turbulent reacting systems. Proc. Combust. Inst. 26, 43–48 (1996)

    Google Scholar 

  34. Pope, S.B.: Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theory Model. 1, 41–63 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Tonse, S.R., Moriary, N.W., Brown, N.J., Frenklach., M.: PRISM: Piecewise Reusable Implementation of Solution Mapping. An economical strategy for chemical kinetics. Isr. J. Chem. 39, 97–106 (1999)

    Google Scholar 

  36. Yang, B., Pope, S.B.: An investigation of the accuracy of manifold methods and splitting schemes in the computational implementation of combustion chemistry. Combust. Flame 112, 16–32 (1998)

    Article  Google Scholar 

  37. Xu, J., Pope, S.B.: PDF calculations of turbulent nonpremixed flames with local extinction. Combust. Flame 123, 281–307 (2000)

    Article  Google Scholar 

  38. Tang, Q., Xu, J., Pope, S.B.: PDF calculations of local extinction and NO production in piloted-jet turbulent methane/air flames. Proc. Combust. Inst. 28, 133–139 (2000)

    Article  Google Scholar 

  39. Lu, L., Ren, Z., Raman, V., Pope, S.B., Pitsch, H.: LES/FDF/ISAT computations of turbulent flames. In: Proceedings of CTR Summer Program 2004, Center For Turbulence Research, pp. 283–294, CTR, December 2004

  40. Lu, L., Ren, Z., Lantz, S.R., Raman, V., Pope, S.B., Pitsch, H.: Investigation of strategies for the parallel implementation of ISAT in LES/FDF/ISAT computations. Paper presented at the 4th joint meeting of the U. S. Sections of the Combustion Institute, Philadelphia, PA, 21–23 March 2005

  41. Singer, M.A., Pope, S.B.: Exploiting ISAT to solve the reaction-diffusion equation. Combust. Theory Model. 8, 361–383 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Singer, M.A., Pope, S.B., Najm, H.N.: Operator-splitting with ISAT to model reacting flow with detailed chemistry. Combust. Theory Model. 10, 199–217 (2006)

    Article  MathSciNet  Google Scholar 

  43. Gordon, R.L., Masri, A.R., Pope, S.B., Goldin, G.M.: A numerical study of auto-ignition in turbulent lifted flames issuing into a vitiated co-flow. Combust. Theory Model. 11, 351–376 (2007)

    Article  MATH  Google Scholar 

  44. Gordon, R.L., Masri, A.R., Pope, S.B., Goldin, G.M.: Transport budgets in turbulent lifted flames of methane autoigniting in a vitiated co-flow. Combust. Flame 151, 495–511 (2007)

    Article  Google Scholar 

  45. Schwer, D.A., Lu, P., Green, W.H. Jr.: An adaptive chemistry approach to modeling complex kinetics in reacting flows. Combust. Flame 133, 451–465 (2003)

    Article  Google Scholar 

  46. Ren, Z., Pope, S.B.: Species reconstruction using pre-image curves. Proc. Combust. Inst. 30, 1293–1300 (2005)

    Article  Google Scholar 

  47. Ren, Z., Pope, S.B., Vladimirsky, A., Guckenheimer, J.M.: Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport. Proc. Combust. Inst. 31, 473–481 (2007)

    Article  Google Scholar 

  48. Ren, Z., Pope, S.B.: Reduced description of complex dynamics in reactive systems. J. Phys. Chem. A 111, 8464–8474 (2007).

    Article  Google Scholar 

  49. Strang, G.: On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5, 506–517 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  50. Ren, Z., Pope, S.B.: Second-order splitting schemes for a class of reactive systems. J. Comput. Phys. (2008, submitted)

  51. Davis, M.J., Skodje, R.T.: Geometric investigation of low-dimensional manifolds in systems approaching equilibrium. J. Chem. Phys. 111, 859–874 (1999)

    Article  ADS  Google Scholar 

  52. Ren, Z., Pope, S.B.: The use of slow manifolds in reactive flows. Combust. Flame 147, 243–261 (2006)

    Article  Google Scholar 

  53. Kaper, H.G., Kaper, T.J.: Asymptotic analysis of two reduction methods for systems of chemical reactions. Physica D 165, 66–93 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. Goussis, D.A., Valorani, M., Creta, F., Najm, H.N.: Reactive and reactive-diffusive time scales in stiff reaction-diffusion systems. Prog. Comput. Fluid Dyn. 5, 316–326 (2005)

    Article  MathSciNet  Google Scholar 

  55. Yannacopoulos, A.N., Tomlin, A.S., Brindley, J., Merkin, J.H., Pilling., M.J.: The use of algebraic sets in the approximation of inertial manifolds and lumping in chemical kinetic systems. Physica D 83, 421–449 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  56. Maas, U., Pope, S.B.: Implementation of simplified chemical kinetics based on intrinsic low-dimensional manifolds. Proc. Combust. Inst. 24, 103–112 (1992)

    Google Scholar 

  57. Pope, S.B.: Accessed compositions in turbulent reactive flows. Flow Turbul. Combust. 72, 219–243 (2004)

    Article  MATH  Google Scholar 

  58. Lam, S.H.: Reduced chemistry-diffusion coupling. Combust. Sci. Tech. 179, 767–786 (2007)

    Article  Google Scholar 

  59. Ren, Z., Pope, S.B.: Transport-chemistry coupling in the reduced description of reactive flows. Combust. Theory Model. 11, 715–739 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Stephen B. Pope.

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The paper is from the 2nd ECCOMAS Thematic Conference on Computational Combustion.

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Pope, S.B., Ren, Z. Efficient Implementation of Chemistry in Computational Combustion. Flow Turbulence Combust 82, 437–453 (2009). https://doi.org/10.1007/s10494-008-9145-3

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