Turbulent Combustion: Concepts, Governing Equations and Modeling Strategies

  • Tarek Echekki
  • Epaminondas Mastorakos
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 95)


The numerical modeling of turbulent combustion problems is based on the solution of a set of conservation equations for momentum and scalars, plus additional auxiliary equations. These equations have very well-defined foundations in their instantaneous and spatially-resolved forms and they represent a myriad of problems that are encountered in a very broad range of applications. However, their practical solution poses important problems. First, models of turbulent combustion problems form an important subset of models for turbulent flows. Second, the reacting nature of turbulent combustion flows imposes additional challenges of resolution of all relevant scales that govern turbulent combustion and closure for scalars. This chapter attempts to review the governing equations from the perspective of modern solution techniques, which take root in some of the classical strategies adopted to address turbulent combustion modeling. We also attempt to outline common themes and to provide an outlook where present efforts are heading.


Probability Density Function Direct Numerical Simulation Mixture Fraction Turbulent Combustion Conditional Moment Closure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bell, J.B., Day, M.S., Shepherd, I.G., Johnson, M.R., Cheng, R.K., Grcar, J.F., Beckner, V.E., Lijewski, M.J.: Numerical simulation of a laboratory-scale turbulent V-flame. Proc. Nat. Acad. Sci. 102, 10006–10011 (2005) CrossRefGoogle Scholar
  2. 2.
    Bell, J.B., Day, M.S., Grcar, J.F., Lijewski, M.J., Driscoll, J.F., Filatyev, S.A.: Numerical simulation of laboratory-scale turbulent slot flame. Proc. Combust. Inst. 31, 1299–1307 (2009) CrossRefGoogle Scholar
  3. 3.
    Bilger, R.W.: The structure of turbulent nonpremixed flames. Proc. Combust. Inst. 22, 475–488 (1988) Google Scholar
  4. 4.
    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) CrossRefGoogle Scholar
  5. 5.
    Brown, P.N., Byrne, G.D., Hindmarsh, A.C.: VODE: A variable coefficient ODE solver. SIAM J. Sci. Stat. Comput. 10, 1038–1051 (1989) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chen, J.-Y.: A General procedure for constructing reduced reaction mechanisms with given independent relations, Combust. Sci. Technol. 57, 89–94 (1988) CrossRefGoogle Scholar
  7. 7.
    Chen, J.H., Choudhary A., de Supinski, B., DeVries, M., Hawkes, E.R., Klasky, S., Liao, W.K., Ma, K.L., Mellor-Crummey, J., Podhrszki, N., Sankaran, R., Shende, S., and Yoo, C.S.: Terascale direct numerical simulations of turbulent combustion using S3D. Comput. Sci. Discovery 2, 015001 (2009) CrossRefGoogle Scholar
  8. 8.
    Dixon-Lewis, G.: A FORTRAN computer code for the evaluation of gas-phase multicomponent transport properties. Proc. Royal Soc. A304, 111–134 (1968) CrossRefGoogle Scholar
  9. 9.
    Dixon-Lewis, G.: Structure of laminar flames Proc. Combust. Inst. 23, 305–324 (1990) Google Scholar
  10. 10.
    Dubois, T., Jauberteau, F., Temam, R.: Dynamic multilevel methods and the numerical simulation of turbulence, Cambridge University Press (1999) Google Scholar
  11. 11.
    Echekki, T., Chen, J.H.: Unsteady strain rate and curvature effects in turbulent premixed methane-air flames. Combust. Flame 106, 184–202 (1996) CrossRefGoogle Scholar
  12. 12.
    Eggenspieler, G., Menon, S.: Combustion and emission modelling near lean blow-out in a gas turbine engine. Prog. Comput. Fluid Dyn. 5 281–297 (2005) zbMATHCrossRefGoogle Scholar
  13. 13.
    Ern, A., Giovangigli, V.: EGLIB: A general purpose FORTRAN library for multicomponent transport property evaluations, Software Manual (1986) Google Scholar
  14. 14.
    Favre, A.: Equations des gas turbulents compressible. J. Mec. 4, 361–390 (1965) Google Scholar
  15. 15.
    Gao, F., O’Brien, E.E.: A large-eddy simulation scheme for turbulent reacting flows. Phys. Fluids 5, 1282–1284 (1993) zbMATHCrossRefGoogle Scholar
  16. 16.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765 (1991) zbMATHCrossRefGoogle Scholar
  17. 17.
    Hawkes, E.R., Sankaran, R., Sutherland, J.C. and Chen, J.H.: Structure of a spatially developing turbulent lean methane-air Bunsen flame. Proc. Combust. Inst. 31,1291–1298 (2007) CrossRefGoogle Scholar
  18. 18.
    Jones, W.P.: Models for turbulent flows with variable density and combustion. In Prediction Methods for Turbulent Flows, Kollman, W. ed., pp. 379–421. Hemisphere (1980) Google Scholar
  19. 19.
    Kee, R.J., Dixon-Lewis, G., Warnatz, J., Coltrin, M.E., Miller, J.A.: A FORTRAN computer code package for the evaluation of gas-phase multicomponent transport properties, SAND86-8246, Sandia National Laboratories (1986) Google Scholar
  20. 20.
    Kee, R.J., Rupley, F.M., and Miller, J.A.: Chemkin-II: A FORTRAN Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics. Sandia National Laboratories Report No. SAND 89–8009 (1989) Google Scholar
  21. 21.
    Kee, R.J., Coltrin, M.E., Glarborg, P.: Chemically Reacting Flow: Theory and Practice, Wiley-Interscience, New Jersey (2003) CrossRefGoogle Scholar
  22. 22.
    Kim, S.H., Pitsch, H.: Mixing characteristics and structure of a turbulent jet diffusion flame stabilized on a bluff-body. Phys. Fluids 18, 075103 (2006) CrossRefGoogle Scholar
  23. 23.
    Lam, S.H., Goussis, D.A.: Understanding complex chemical kinetics with the computational singular perturbations. Proc. Combust. Inst. 22, 931–941 (1988) Google Scholar
  24. 24.
    Law, C.K.: On the applicability of direct relation graph to the reduction of of reaction mechanisms. Combust. Flame 146, 472–483 (2006) CrossRefGoogle Scholar
  25. 25.
    Law, C.K.: Combustion Physics, Cambridge University Press, New York (2006) CrossRefGoogle Scholar
  26. 26.
    Law, C.K.: Combustion at a crossroads: Status and prospects. Proc. Combust. Inst. 31, 1–29 (2006) CrossRefGoogle Scholar
  27. 27.
    Libby, P.A., Williams, F.A.: Turbulent Reacting Flows, Springer-Verlag, Heidelberg (1980) zbMATHGoogle Scholar
  28. 28.
    Libby, P.A., Williams, F.A.: Turbulent Reacting Flows, Academic Press, London (1994) zbMATHGoogle Scholar
  29. 29.
    Lu, T.F., Law, C.K.: Toward accommmodating realistic chemistry in large-scale computations. Prog. Energy Combust. Sci. 35, 192–215 (2009) CrossRefGoogle Scholar
  30. 30.
    Lundgren, T.S.: Distribution of functions in the statistical theory of turbulence. Phys. Fluids 10, 969 (1967) CrossRefGoogle Scholar
  31. 31.
    Magnussen, B.F., Hjertager, B.H.: On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Proc. Combust. Inst. 16, 719–729 (1976) Google Scholar
  32. 32.
    Mizobuchi, Y., Sinjo, J., Ogawa, S., Takeno, T.: A numerical study of the formation of diffusion flame islands in a turbulent hydrogen jet lifted flame. Proc. Combust. Inst. 30, 611–619 (2005) CrossRefGoogle Scholar
  33. 33.
    Mizobuchi, Y., Tachibana, S., Shinjo, J., Ogawa, S., Takeno, T.: A numerical analysis of the structure of a turbulent hydrogen jet lifted flame. Proc. Combust. Inst. 29, 2009–2015 (2002) CrossRefGoogle Scholar
  34. 34.
    Moin, P., Squires, K., Cabot, W., Lee, S.: A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757 (1991) zbMATHCrossRefGoogle Scholar
  35. 35.
    Navarrao-Martinez, S., Kronenburg, A., Di Mare, F., Conditional moment closure for large-eddy simulations. Flow Turbul. Combust. 75, 245–274 (2005) CrossRefGoogle Scholar
  36. 36.
    McIlroy, A., McRae, G., Sick, V., Siebers, D.L., Westbrook, C.K., Smith, P.J., Taatjes, C., Trouve, A., Wagner, A.E., Rohlfing, E., Manley, D., Tully, F., Hilderbrandt, R., Green, W., Marceau, D., O’Neal, J., Lyday, M., Cebulski, F., Garcia, T.R., Strong, D., Basic research needs for clean and efficient combustion of 21st century transportation fuels. Department of Energy Office of Science Report (2006) Google Scholar
  37. 37.
    Patel, N., Kirtas, M., Sankaran, V., Menon, S.: Simulation of spray combustion in a lean-direct injection combustor. Proc. Combust. Inst. 31, 2327–2334 (2007) CrossRefGoogle Scholar
  38. 38.
    Paul, P.H.: DFRM: A new package for the evaluation of gas-phase transport properties, SAND98-8203, Sandia National Laboratories (1997) Google Scholar
  39. 39.
    Peters, N.: Local quenching due to flame stretch and non-premixed turbulent combustion. Combust. Sci. Techol. 30, 1–17 (1983) CrossRefGoogle Scholar
  40. 40.
    Peters, N.: Turbulent Combustion, Cambridge University Press, UK (2000) zbMATHCrossRefGoogle Scholar
  41. 41.
    Petzold, L.R., A description of dassl: A differential/algebraic system solver, SAND82-8637, Sandia National Laboratories (1982) Google Scholar
  42. 42.
    Pitsch, H., Large-eddy simulation of turbulent combustion. Ann. Rev. Fluid Mech. 38, 453–482 (2006) CrossRefMathSciNetGoogle Scholar
  43. 43.
    Poinsot, T., Candel, S., Trouve A.: Applications of direct numerical simulation to premixed turbulent combustion. Prog. Energy Combust. Sci. 21, 531–576 (1995) CrossRefGoogle Scholar
  44. 44.
    Poinsot, T., Veynante, D., Theoretical and Numerical Combustion, Second Ed., RT Edwards (2005) Google Scholar
  45. 45.
    Pope, S.B.: The statistical theory of turbulent flames. Philos. Trans., Roy. Soc. London Ser. A 291, 529–568 (1979) zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    Pope, S.B.: Computations of turbulent combustion: Progress and challenges. Proc. Combust. Inst. 23, 591–612 (1990) Google Scholar
  47. 47.
    Pope, S.B., Maas, U.: Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space. Combust. Flame 88, 239–264 (1992) CrossRefGoogle Scholar
  48. 48.
    Pope, S.B., Ren, Z.: Efficient implementation of chemistry in computational combustion. Flow Turbul. Combust. 82, 437–453 (2009) zbMATHCrossRefGoogle Scholar
  49. 49.
    Selle, L, Lartigue, G., Poinsot, T., Koch, R., Schildmacher, K.: Compressible large eddy simulation of turbulent combustion in complex geometry on unstructured meshes. Combust. Flame 137, 489–505 (2004) CrossRefGoogle Scholar
  50. 50.
    Smooke, M.D., Giovangigli, V.: Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames. Lecture Notes in Physics, Springer-Verlag, Berlin 384 (1991) CrossRefGoogle Scholar
  51. 51.
    Spalding, D.B.: Mixing and chemical reaction in steady confined turbulent flames Proc. Combust. Inst. 13, 649–657 (1971) Google Scholar
  52. 52.
    Triantafyllidis, A., Mastorakos, E., Eggels, R.L.G.M.: Large eddy simulations of forced ignition of a non-premixed bluff-body methane flame with conditional moment closure. Combust. Flame 156, 2328–2345 (2009) CrossRefGoogle Scholar
  53. 53.
    Valorani, M., Paolucci, S.: The G-scheme: A framework for multi-scale adaptive model reduction. J. Comput. Phys. 228, 4665–4701 (2009) zbMATHCrossRefMathSciNetGoogle Scholar
  54. 54.
    Vervisch, L., Poinsot, T.: Direct numerical simulation of non-premixed turbulent flames. Ann. Rev. Fluid Mech. 30, 655–691 (1998) CrossRefMathSciNetGoogle Scholar
  55. 55.
    Veynante, D., Vervisch, L.: Turbulent combustion modeling. Prog. Energy Combust. Sci. 28, 193–266 (2002) CrossRefGoogle Scholar
  56. 56.
    Warnatz, J.: Calculation of structure of laminar flat flames. 1. Flame velocity of freely propagating ozone decomposition flames. Ber. Bunsenges. Phys. Chem. Phys. 82, 193–200 (1978) Google Scholar
  57. 57.
    Williams, F.A., Combustion Theory: The Fundamental Theory of Chemically Reacting Flow Systems, Second Ed., Benjamin-Cummings (1985) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.North Carolina State UniversityRaleighUSA

Personalised recommendations