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Small Scale Features of Velocity and Scalar Fields in Turbulent Premixed Flames

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Abstract

Because the ultimate stages of turbulent mixing take place at the unresolved scales in either Reynolds Average Navier Stokes (RANS) or Large Eddy Simulation (LES) approaches of turbulent reactive flows, the closure of molecular dissipation rates still remains an essential problem in the field of turbulent combustion. In the present study, turbulent flames with premixed reactants are considered in the flamelet regime of turbulent premixed combustion: Damköhler and Karlovitz number’s values are such that Da > 1 and Ka < 1. In this situation, the mixing rate clearly depends upon the turbulence characteristics but is also strongly influenced by the laminar flamelet structures that drive the instantaneous gradients of the reactive species. In the present work, the analysis is focused on some among the different unclosed terms that arise in the transport equation of the mean reactive scalar dissipation rate. New closures relying on the fast chemistry assumptions are proposed for these production terms and similarities and differences with existing models are discussed. Previous works devoted to the modeling of the scalar dissipation rate have recently shown that both reactive features and expansion phenomena strongly influence the behavior of some terms with respect to the passive scalar situation of reference, and the present study confirms the relevance of these findings. Finally, Direct Numerical Simulation (DNS) databases are considered to assess the validity of the proposed models. These DNS correspond to the calculations of three-dimensional statistically steady planar turbulent premixed flames obtained for three distinct values of the gas expansion factor τ=(T b  − T u )/T u namely 1.5, 4 and 6.5, where subscripts u and b refer to unburned reactants and burned products respectively. With respect to previous studies, these data allow a detailed check of the validity of the different modeling proposals when the gas expansion factor is varied.

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References

  1. Bray, K.N.C.: The interaction between turbulence and combustion. Proc. Combust. Inst. 17, 223–233 (1979)

    Google Scholar 

  2. Bray, K.N.C.: Turbulent flows with premixed reactants. In: Libby, P.A., Williams, F.A. (eds.) Turbulent Reacting Flows, pp. 115–183. Springer, Berlin Heidelberg New York (1980)

    Google Scholar 

  3. Borghi, R.: Réactions chimiques en milieu turbulent. PhD Thesis, Pierre and Marie Curie University, Paris, France (1978)

  4. Borghi, R., Dutoya, D.: On the scales of fluctuations in turbulent combustion. Proc. Combust. Inst. 17, 235–244 (1979)

    Google Scholar 

  5. Peters, N.: Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 21, 1231–1256 (1986)

    ADS  Google Scholar 

  6. Borghi, R.: On the structure and morphology of turbulent premixed flames. In: Casci, C. (ed.) Recent Advances in the Aerospace Sciences, pp. 117–138. Plenum, New York (1985)

    Google Scholar 

  7. Borghi, R.: Turbulent premixed combustion: further discussions on the scales of fluctuations. Combust. Flame 80, 304–312 (1990)

    Article  Google Scholar 

  8. Pope, S.B.: The PDF method for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  9. Borghi, R.: Turbulent combustion modelling. Prog. Energy Combust. Sci. 14, 245–292 (1988)

    Article  Google Scholar 

  10. Anand, M.S., Pope, S.B.: Calculations of premixed turbulent flames by pdf methods. Combust. Flame 67, 127–142 (1987)

    Article  Google Scholar 

  11. Mura, A., Galzin, F., Borghi, R.: A unified PDF-flamelet model for turbulent premixed combustion. Combust. Sci. Technol. 175, 1573–1609 (2003)

    Article  Google Scholar 

  12. Dopazo, C.: Recent develoments in the PDF methods. In: Libby, P.A., Williams, F.A. (eds.) Turbulent Reacting Flows, pp. 375–474. Academic, London (1994)

    Google Scholar 

  13. Bilger, R.W.: Turbulent jet diffusion flames. Prog. Energy Combust. Sci. 1, 96–109 (1976)

    Article  Google Scholar 

  14. Bilger, R.W.: Effects of kinetics and mixing in turbulent combustion. Combust. Sci. Technol. 19, 89–93 (1979)

    Article  Google Scholar 

  15. Mura, A., Robin, V., Champion, M.: Modeling of scalar dissipation in partially premixed turbulent flames. Combust. Flame 149(1–2), 217–224 (2007)

    Article  Google Scholar 

  16. Robin, V., Mura, A., Champion, M., Degardin, O., Renou, B., Boukhalfa, M.: Experimental and numerical study of stratified turbulent V-shaped flames. Combust. Flame 153, 288–315 (2008)

    Google Scholar 

  17. Antonia, R.A., Browne, L.W.B.: The destruction of temperature fluctuations in a turbulent plane jet. J. Fluid Mech. 134, 67–83 (1983)

    Article  ADS  Google Scholar 

  18. Swaminathan, N., Bray, K.N.C.: Effect of dilatation on scalar dissipation in turbulent premixed flames. Combust. Flame 143(4), 549–565 (2005)

    Article  Google Scholar 

  19. Mura, A., Robin, V., Champion, M., Tsuboi, K., Hasegawa, T.: Small scale reactive scalar dynamics in turbulent premixed flames: mean reactive scalar dissipation. In: Proceedings of the XXIst ICDERS, Poitiers, July 2007

  20. Mura, A., Tsuboi, K., Hasegawa, T.: Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data. Combust. Theory Model. 12(4), 671–698 (2008)

    Article  MATH  ADS  Google Scholar 

  21. Lumley, J.L., Khajeh-Nouri, B.: Computational modeling of turbulent transport, Turbulent diffusion in environmental pollution. In: Frenkiel, R.N., Munn, R.E. (eds.) Advances in Geophysics, pp. 169–172. Academic 18A, London (1974)

    Google Scholar 

  22. Zeman, O., Lumley, J.L.: Modeling buoyancy driven mixed layers. J. Atmos. Sci. 33, 1974–1988 (1976)

    Article  ADS  Google Scholar 

  23. Mantel, T., Borghi, R.: A new model of premixed wrinkled flame based on a scalar dissipation equation. Combust. Flame 96, 443–457 (1994)

    Article  Google Scholar 

  24. Mura, A., Borghi, R.: Towards an extended scalar dissipation equation for turbulent premixed combustion. Combust. Flame 133, 193–196 (2003)

    Article  Google Scholar 

  25. Martin, J., Dopazo, C., Valiño, L.: Joint statistics of the scalar gradient and the velocity gradient in turbulence using linear diffusion models. Phys. Fluids 17, 028101.1–028101.4 (2005)

    Article  Google Scholar 

  26. Garcia, A., Gonzalez, M.: Analysis of passive scalar gradient alignment in a simplified three-dimensional case. Phys. Fluids 18, 058101.1–058101.4 (2006)

    Article  Google Scholar 

  27. Swaminathan, N., Grout, R.W.: Interaction of turbulence and scalar fields in premixed flames. Phys. Fluids 18, 045102.1–0.45102.9 (2006)

    Article  MathSciNet  Google Scholar 

  28. Chakraborty, N., Swaminathan, N.: Influence of the Damköhler number on turbulence scalar interaction in premixed flames. II. Model developement. Phys. Fluids 19, 045104.1–045104.11 (2007)

    Google Scholar 

  29. Jones, W.P., Musonge, P.: Closure of Reynolds stress and scalar flux equations. Phys. Fluids 31, 3589–3604 (1988)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  30. Newman, G.R., Launder, B.E., Lumley, J.L.: Modelling the behavior of homogeneous scalar turbulence. J. Fluid Mech. 111, 217–232 (1981)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. Elghobashi, S.E., Launder, B.E.: Turbulent time scale and the dissipation rate of temperature variance in the thermal mixing layer. Phys. Fluids 26, 2415–2419 (1983)

    Article  ADS  Google Scholar 

  32. Shih, T.H., Lumley, J.L.: Influence of time scale ratio on scalar flux relaxation. J. Fluid Mech. 162, 211–222 (1986)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. Libby, P.A., Bray, K.N.C.: Implications of the laminar flamelet model in premixed turbulent combustion. Combust. Flame 39, 33–41 (1980)

    Article  Google Scholar 

  34. Robin, V., Mura, A., Champion, M., Hasegawa, T.: A new analysis of the modeling of pressure fluctuations effects in premixed turbulent flames and its validation based on DNS data. Combust. Sci. Technol. 180, 996–1009 (2008)

    Google Scholar 

  35. Nishiki, S., Hasegawa, T., Borghi, R., Himeno, R.: Modeling of turbulent scalar flux in turbulent premixed flames based on DNS databases. Combust. Theory Model. 10(1), 39–55 (2006)

    Article  MATH  Google Scholar 

  36. Nishikki, S.: DNS and modelling ot turbulent premixed combustion. PhD Thesis, Nagoya Institute of Technology, Japan (2003)

  37. Trouvé, A., Poinsot, T.: The evolution equation for the flame surface density in turbulent premixed combustion. J. Fluid Mech. 278, 1–31 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  38. Said, R., Borghi, R.: A simulation with a cellular automaton for turbulent combustion modelling. Proc. Combust. Inst. 22, 569–577 (1988)

    Google Scholar 

  39. Veynante, D., Trouvé, A., Bray, K.N.C., Mantel, T.: Gradient and counter-gradient scalar transport in turbulent premixed flames. J. Fluid Mech. 332, 263–294 (1997)

    MATH  ADS  Google Scholar 

  40. Mura, A., Champion, M.: Relevance of the Bray number in the small scale modelling of turbulent premixed flames. Combust. Flame (2008, in press)

  41. Robin, V., Mura, A., Champion, M., Plion, P.: A multi-Dirac presumed PDF model for turbulent reactive flows with variable equivalence ratio. Combust. Sci. Technol. 178, 1–28 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. LCD UPR 9028 du CNRS ENSMA, Téléport 2, Futuroscope, 1 Avenue Clément Ader, BP 40109, 86961, Chasseneuil Cedex, France

    Arnaud Mura, Vincent Robin & Michel Champion

  2. EcoTopia Science Institute, F3-4 (670) Nagoya University, Nagoya, 464-8603, Japan

    Tatsuya Hasegawa

Authors
  1. Arnaud Mura
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  2. Vincent Robin
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  3. Michel Champion
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  4. Tatsuya Hasegawa
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Correspondence to Arnaud Mura.

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Mura, A., Robin, V., Champion, M. et al. Small Scale Features of Velocity and Scalar Fields in Turbulent Premixed Flames. Flow Turbulence Combust 82, 339–358 (2009). https://doi.org/10.1007/s10494-008-9180-0

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  • DOI: https://doi.org/10.1007/s10494-008-9180-0

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