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Conditional Moment Closure for Large Eddy Simulations

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Abstract

A conditional moment closure (CMC) based combustion model for large-eddy simulations (LES) of turbulent reacting flow is proposed and evaluated. Transport equations for the conditionally filtered species are derived that are consistent with the LES formulation and closures are suggested for the modelling of the conditional velocity, conditional scalar dissipation and the fluctuations around the conditional mean. A conventional β-probability density distribution of the scalar is used together with dynamic modelling for the sub-grid fluxes. The model is validated by comparison of simulations with measurements of a piloted, turbulent methane-air jet diffusion flame.

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References

  1. Colucci, P.J., Jaberi, F.A., Givi, P. and Pope, S.B., Filtered density function for large eddy simulation of non-premixed turbulent reacting flows. Phys. Fluids 10 (1998) 499.

    Google Scholar 

  2. Branley, N. and Jones, W.P., Large eddy simulation of a turbulent non-premixed flame. Combust. Flame 127 (2001) 1914–1934.

    Article  Google Scholar 

  3. DiMare, F., Jones, W.P. and Menzies, K.R., Large eddy simulation of a model gas turbine combustor. Combust. Flame 137 (2004) 278–294.

    Google Scholar 

  4. Kempf, A., Lindstedt, R.P. and Janicka, J., Large eddy simulations of a bluff-body stabilized non-premixed flame. Combust. Flame (submitted for publication).

  5. Pitsch, H. and Steiner, H., Large-eddy simulation of a turbulent piloted methane/air. Phys. Fluids 12(10) (2000) 2542–2554.

    Article  ADS  Google Scholar 

  6. Pitsch, H., Improved pollutant predictions in large-eddy simulations of turbulent non-premixed combustion by considering scalar dissipation rate fluctuations. In: 29th International Symposium on Combustion (2002).

  7. Bushe, W.K. and Steiner, H., Conditional moment closure for large eddy simulation of nonpremixed turbulent reacting flows. Phys. Fluids A 11 (1999) 1896–1906.

    ADS  MATH  Google Scholar 

  8. Klimenko, A.Y. and Bilger, R.W., Conditional moment closure for turbulent combustion. Prog. Energy Combust. Sci. 25 (1999) 595–687.

    Article  Google Scholar 

  9. Kuo, K.K., Principles of Combustion. Wiley, New York (1986).

    Google Scholar 

  10. Poinsot, T. and Veynante, D., Theoretical and Numerical Combustion. R.T. Edwards, Inc. (2001).

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

    MATH  Google Scholar 

  12. Gao, F. and O'Brien, E.E., A large eddy simulation for turbulent reacting flows. Phys. Fluids A 5(6) (1993) 1282–1284.

    Article  ADS  MATH  Google Scholar 

  13. Lighthill, M.J., Introduction to Fourier Analysis. Cambridge University Press, Cambridge (1958).

    MATH  Google Scholar 

  14. Steiner, H. and Bushe, W.K., Large-eddy simulation of a turbulent reacting jet with conditional source estimation. Phys. Fluids 25 (2001) 595–687.

    Google Scholar 

  15. Bilger, R.W., Conditional moment closure for turbulent reacting flow. Phys. Fluids A 5 (1993) 436–444.

    Article  ADS  MATH  Google Scholar 

  16. Pitsch, H. and Steiner, H., Scalar mixing and dissipation rate in large-eddy simulations of non-premixed turbulent combustion. In: 28th International Symposium on Combustion (2000).

  17. Press, W.H., Teukolsky, S.A., Vettering, W.T. and Flannery, B.P., Numerical Recipes in C. Cambridge University Press, Cambridge (1997).

    Google Scholar 

  18. Pitsch, H., Chen, M. and Peters, N., Unsteady flamelet modeling of turbulent hydrogen/air diffusion flames. Proc. Combust. Inst. 1057–1064 (1998).

  19. Cleary, M.J. and Kent, J.H., A numerical method for conditional moment closure. In: Australian Symposium on Combustion (2003).

  20. Kim, S.H. and Huh, K.Y., Second-order conditional moment closure modelling of turbulent piloted jet diffusion flames. Combust. Flame 138(4) (2004) 336–352.

    Article  Google Scholar 

  21. Kronenburg, A., Double conditioning of turbulent scalar transport equations in turbulent non-premixed flames. Phys. Fluids 16(7) (2004) 2640–2648.

    Article  ADS  Google Scholar 

  22. Smagorinsky, J., General circulation experiments with the primitive equations, Part I: The basic experiment. Month. Weather Rev. 91 (1963) 99–164.

    ADS  Google Scholar 

  23. Pope, S.B., Turbulent Flows. Cambridge University Press, Cambridge (2001).

    Google Scholar 

  24. Germano, M., Piomelli, U., Moin, P. and Cabot, W.H., A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7) (1991) 1760–1765.

    Article  ADS  MATH  Google Scholar 

  25. Piomelli, U. and Liu, J., Large-eddy simulation of rotating channel flows using a localized dynamic model. Phys. Fluids 7(4) (1995) 839–848.

    Article  ADS  MATH  Google Scholar 

  26. Ghosal, S., Lund, T.S., Moin, P. and Akselvoll, K., A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286 (1995) 229–255.

    ADS  MathSciNet  MATH  Google Scholar 

  27. Schmidt, H. and Schumann, U., Coherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech. 511–562 (1989).

  28. Pierce, C.D. and Moin, P., A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar. Phys. Fluids 10(12) (1998) 3041–3044.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Cook, A.W. and Riley. J.J., A subgrid model for equilibrium chemistry in turbulent flows. Phys. Fluids 6(8) (1994) 2868–2870.

    Article  ADS  Google Scholar 

  30. Kops, S.M.D., Riley, J.J., Kosaly, G. and Cook, A.W., Investigation of modeling for non-premixed turbulent combustion. Flow Turbulence Combust. 60 (1998) 105–122.

    MATH  Google Scholar 

  31. Girimaji, S.S. and Zhou, Y., Analysis and modeling of subgrid scalar mixing using numerical data. Phys. Fluids 8(5) (1996) 1224–1236.

    Article  ADS  MATH  Google Scholar 

  32. DiMare, F., Large eddy simulation of reacting and non-reacting turbulent flows. Ph.D. Thesis, Imperial College, University of London (2002).

  33. Rhie, C.M. and Chow, W.L., Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21(11) (1983) 1525–1532.

    Article  MATH  ADS  Google Scholar 

  34. Jones, W.P. and Lindstedt, R.P., Global reaction schemes for hydrocarbon combustion. Comput. Fluids 73 (1988) 233–249.

    Google Scholar 

  35. Brizuela, E.A., A contribution towards the mathematical modelling of intermittent PDFS. Combust. Flame 132 (2003) 275–279.

    Article  Google Scholar 

  36. Jimenez, J., Linan, A., Rogers, M.M. and Higuera, F.J., A priori testing of sub-grid models for chemically reacting nonpremixed turbulent shear flows. J. Fluid Mech. 349 (1997) 149–171.

    ADS  MATH  Google Scholar 

  37. Wall, C., Boersma, B.J. and Moin, P., An evaluation of the assumed beta probability density function subgrid-scale model for large eddy simulation of nonpremixed turbulent combustion with heat release. Phys. Fluids 12(10) (2000) 2522–2529.

    Article  ADS  Google Scholar 

  38. Barlow, R.S. and Frank, J., Effects of turbulence on species mass fractions in methane-air jet flames. Proc. Combust. Inst. 27 (1998) 1087.

    Google Scholar 

  39. Schneider, C., Dreizler, A., Janicka, J. and Hassel, E.P., Flow field measurements of stable and locally extinguishing hydrocarbon-fuelled jet flames. Combust. Flame 135 (2003) 185–190.

    Article  Google Scholar 

  40. Roomina, M.R. and Bilger, R., Conditional moment closure (CMC) predictions of a turbulent methane-air jet flame. Combust. Flame 125 (2001) 1176–1195.

    Article  Google Scholar 

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

    Article  Google Scholar 

  42. Karpetis, A.N. and Barlow, R.S., Measurements of flame orientation and scalar dissipation in turbulent partially premixed methane flames. Proc. Combust. Inst. 30 (2004) 665–672.

    Google Scholar 

  43. Klimenko, A.Y., Note on the conditional moment closure in turbulent shear flows. Phys. Fluids 7(2) (1995) 446–448.

    Article  ADS  MATH  Google Scholar 

  44. Yoshizawa, A., Statistical theory for compressible turbulent shear flows, with the application to subgrid modelling. Phys. Fluids 29(7) (1986) 2152–2164.

    Article  ADS  MATH  Google Scholar 

  45. Navarro-Martinez, S. and Kronenburg, A., Conditional moment closure in large eddy simulation. In: 2nd International Workshop on trends in Numerical and Physical Modelling of Turbulent Process in Gas Turbine Combustors, Heidelberg, Germany, pp. 29–36 (2004).

  46. Kempf, A., Flemming, A.F. and Janicka, J., Investigation of length scales, scalar dissipation and flame orientation in a piloted diffusion flame by LES. Proc. Combust. Inst. 30 (2005) 557–565.

    Google Scholar 

  47. Meyer, M., The application of detailed and systematically reduced chemistry to transient laminar flames. Ph.D. Thesis, Imperial College, University of London (2001).

  48. Barlow, R.S., Karpetis, A.N., Frank, J.H. and Chen, J.Y., Scalar profile and no formation in laminar opposed-flow partially premixed methane/air flames. Combust. Flame 127 (2001) 2101–2118.

    Article  Google Scholar 

  49. Danaila, I. and Boersma, B.J., Direct numerical simulation of bifurcating jets. Phys. Fluids 12(5) (2000).

  50. Klein, M., Sadiki, A. and Janicka, J., A digital filter based generation of inflow data for apatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186 (2003) 652–665.

    Article  ADS  MATH  Google Scholar 

  51. Barlow, R.S. and Karpetis, A.N., Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames. Proc. Combust. Inst. 30 (2004) 673–680.

    Google Scholar 

  52. Barlow, R.S. and Karpetis, A.N., Measurements of scalar variance, scalar dissipation and length scales in turbulent piloted methane/air jet flames. Flow Turbulence Combust. 72 (2004) 427–448.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Imperial College, London, U.K.

    S. Navarro-Martinez, A. Kronenburg & F. Di Mare

Authors
  1. S. Navarro-Martinez
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  2. A. Kronenburg
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  3. F. Di Mare
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Correspondence to A. Kronenburg.

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Navarro-Martinez, S., Kronenburg, A. & Mare, F.D. Conditional Moment Closure for Large Eddy Simulations. Flow Turbulence Combust 75, 245–274 (2005). https://doi.org/10.1007/s10494-005-8580-7

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  • DOI: https://doi.org/10.1007/s10494-005-8580-7

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