Skip to main content Accessibility help
×
Home

Evolution of local flame displacement speeds in turbulence

  • Himanshu L. Dave (a1) and Swetaprovo Chaudhuri (a1)

Abstract

In this study, we assess the veracity of models for density-weighted local flame displacement speed of turbulent premixed flames. It will be shown that a combination of two models, one for the weakly stretched laminar flame state and another derived for a configuration where a curved laminar flame interacts with itself to annihilate, can describe most local realizations of a turbulent premixed flame. To that end, we have performed direct numerical simulations of a reactive mixture of hydrogen–air at atmospheric pressure using a detailed chemical reaction mechanism and analysed the dataset with recently developed flame particle tracking techniques. Forward tracking a large number of flame particles from the generating locations of the corresponding flame surfaces (given by backward tracking) to the corresponding annihilating locations, creates a manifold of local states that can represent nearly all possible states realizable for the turbulent premixed flame under consideration. With all the states of the flame accessible over time, we first assess the applicability of the two-parameter Markstein length based flame speed model. It is found that the model prediction is reasonably accurate for a significant part of the flame particles’ lifetime, for turbulent premixed flames with Karlovitz number $O(10)$ . However, during the final stage of annihilation of the flame particles in the negatively curved trailing regions, the local structure of the flame no longer resembles a standard premixed flame, even qualitatively. A new interaction model for the flame displacement speed, during these final stages of annihilation of the flame elements, has been derived.

Copyright

Corresponding author

Present address: Institute for Aerospace Studies, University of Toronto, ON M3H 5T6, Canada. Email address for correspondence: schaudhuri@utias.utoronto.ca

References

Hide All
Amato, A. & Lieuwen, T. C. 2014 Analysis of flamelet leading point dynamics in an inhomogeneous flow. Combust. Flame 161 (5), 13371347.
Babkovskaia, N., Haugen, N. E. L. & Brandenburg, A. 2011 A high-order public domain code for direct numerical simulations of turbulent combustion. J. Comput. Phys. 230 (1), 112.
Bechtold, J. K. & Matalon, M. 2001 The dependence of the Markstein length on stoichiometry. Combust. Flame 127 (1–2), 19061913.
Bledjian, L. 1973 Computation of time-dependent laminar flame structure. Combust. Flame 20 (1), 517.
Candel, S. M. & Poinsot, T. J. 1990 Flame stretch and the balance equation for the flame area. Combust. Sci. Technol. 70 (1–3), 115.
Chakraborty, N., Klein, M. & Cant, R. S. 2007 Stretch rate effects on displacement speed in turbulent premixed flame kernels in the thin reaction zones regime. Proc. Combust. Inst. 31 (1), 13851392.
Chaudhuri, S. 2015 Life of flame particles embedded in premixed flames interacting with near isotropic turbulence. Proc. Combust. Inst. 35 (2), 13051312.
Chen, C. L. & Sohrab, S. H. 1995 Upstream interactions between planar symmetric laminar methane premixed flames. Combust. Flame 101 (3), 360370.
Chen, J. H., Echekki, T. & Kollmann, W. 1999 The mechanism of two-dimensional pocket formation in lean premixed methane-air flames with implications to turbulent combustion. Combust. Flame 116 (1–2), 1548.
Chen, J. H. & Im, H. G. 1998 Correlation of flame speed with stretch in turbulent premixed methane/air flames. In Symposium (International) on Combustion, vol. 27, pp. 819826. Elsevier.
Chen, J. H. & Im, H. G. 2000 Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames. Proc. Combust. Inst. 28 (1), 211218.
Chung, S. H. & Law, C. K. 1984 An invariant derivation of flame stretch. Combust. Flame 55 (1), 123125.
Chung, S. H. & Law, C. K. 1988 An integral analysis of the structure and propagation of stretched premixed flames. Combust. Flame 72 (3), 325336.
Clavin, P. & Graña-Otero, J. C. 2011 Curved and stretched flames: the two Markstein numbers. J. Fluid Mech. 686, 187217.
Clavin, P. & Joulin, G. 1997 High-frequency response of premixed flames to weak stretch and curvature: A variable-density analysis. Combust. Theor. Model. 1, 429446.
Creta, F. & Matalon, M. 2011 Propagation of wrinkled turbulent flames in the context of hydrodynamic theory. J. Fluid Mech. 680, 225264.
Darrieus, G.1938 Propagation d’un front de flamme. Unpublished work; presented at la Technique Moderne (Paris) and in 1945 at Congrès de Méchanique Appliquée.
Dave, H. L., Abinesh, M. & Chaudhuri, S. 2018 Genesis and evolution of premixed flames in turbulence. Combust. Flame 196, 386399.
Day, M., Tachibana, S., Bell, J., Lijewski, M., Beckner, V. & Cheng, R. K. 2012 A combined computational and experimental characterization of lean premixed turbulent low swirl laboratory flames: I. Methane flames. Combust. Flame 159 (1), 275290.
Day, M., Tachibana, S., Bell, J., Lijewski, M., Beckner, V. & Cheng, R. K. 2015 A combined computational and experimental characterization of lean premixed turbulent low swirl laboratory flames: II. Hydrogen flames. Combust. Flame 162 (5), 21482165.
Driscoll, J. F. 2008 Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities. Prog. Energy Combust. Sci. 34 (1), 91134.
Echekki, T. & Chen, J. H. 1996 Unsteady strain rate and curvature effects in turbulent premixed methane-air flames. Combust. Flame 106 (1–2), 184190.
Echekki, T., Chen, J. H. & Gran, I. 1996 The mechanism of mutual annihilation of stoichiometric premixed methane-air flames. In Symposium (International) on Combustion, pp. 855863. Elsevier.
Fogla, N., Creta, F. & Matalon, M. 2017 The turbulent flame speed for low-to-moderate turbulence intensities: Hydrodynamic theory versus experiments. Combust. Flame 175, 155169.
Frankel, M. L. & Sivashinsky, G. I. 1983 On effects due to thermal expansion and Lewis number in spherical flame propagation. Combust. Sci. Technol. 31 (3–4), 131138.
Frankel, M. L. & Sivashinsky, G. I. 1984 On quenching of curved flames. Combust. Sci. Technol. 40 (5–6), 257268.
Giannakopoulos, G. K., Gatzoulis, A., Frouzakis, C. E., Matalon, M. & Tomboulides, A. G. 2015 Consistent definitions of flame displacement speed and Markstein length for premixed flame propagation. Combust. Flame 162 (4), 12491264.
de Goey, L. P. H. & ten Thije Boonkkamp, J. H. M. 2008 Mass burning rate of premixed stretched flames: integral analysis versus large-activation-energy asymptotics. J. Engng Maths 62 (1), 6784.
Haghiri, A., Talei, M., Brear, M. J. & Hawkes, E. R. 2018 Sound generation by turbulent premixed flames. J. Fluid Mech. 843, 2952.
Hamlington, P. E., Darragh, R., Briner, C. A., Towery, C. A. Z., Taylor, B. D. & Poludnenko, A. Y. 2017 Lagrangian analysis of high-speed turbulent premixed reacting flows: Thermochemical trajectories in hydrogen-air flames. Combust. Flame 186, 193207.
Hawkes, E. R. & Chen, J. H. 2005 Evaluation of models for flame stretch due to curvature in the thin reaction zones regime. Proc. Combust. Inst. 30 (1), 647655.
Im, H. G., Arias, P. G., Chaudhuri, S. & Uranakara, H. A. 2016 Direct numerical simulations of statistically stationary turbulent premixed flames. Combust. Sci. Technol. 188 (8), 11821198.
Im, H. G. & Chen, J. H. 2000 Effects of flow transients on the burning velocity of laminar hydrogen/air premixed flames. Proc. Combust. Inst. 28 (2), 18331840.
Kee, R. J., Grcar, J. F., Smooke, M. D., Miller, J. A. & Meeks, E.1985 PREMIX: A Fortran program for modeling steady laminar one-dimensional premixed flames. Sandia National Laboratories Report (SAND85-8249).
Kerstein, A. R., Ashurst, W. T. & Williams, F. A. 1988 Field equation for interface propagation in an unsteady homogeneous flow field. Phys. Rev. A 37 (7), 27282731.
Landau, L. D. 1944 On the theory of slow combustion. Acta Physicochim. USSR 77, 7785.
Law, C. K. 2006 Combustion Physics. Cambridge University Press.
Li, J., Zhao, Z., Kazakov, A. & Dryer, F. L. 2004 An updated comprehensive kinetic model of hydrogen combustion. Intl J. Chem. Kinet. 36 (10), 566575.
Liang, W., Wu, F. & Law, C. K. 2017 Extrapolation of laminar flame speeds from stretched flames: Role of finite flame thickness. Proc. Combust. Inst. 36 (1), 11371143.
Lipatnikov, A. N. & Chomiak, J. 2005 Molecular transport effects on turbulent flame propagation and structure. Prog. Energy Combust. Sci. 31 (1), 173.
Lu, Z. & Ghosal, S. 2003 A similarity solution describing the collision of two planar premixed flames. Combust. Theor. Model. 7 (4), 645652.
Markstein, G. H. 1964 Nonsteady Flame Propagation: AGARDograph. Macmillan.
Matalon, M. 1983 On flame stretch. Combust. Sci. Technol. 31 (3–4), 169181.
Matalon, M., Cui, C. & Bechtold, J. K. 2003 Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders. J. Fluid Mech. 487, 179210.
Matalon, M. & Matkowsky, B. J. 1982 Flames as gasdynamic discontinuities. J. Fluid Mech. 124, 239259.
Mikolaitis, D. W. 1984a The interaction of flame curvature and stretch, part 1: the concave premixed flame. Combust. Flame 57 (1), 2531.
Mikolaitis, D. W. 1984b The interaction of flame curvature and stretch, part 2: the convex premixed flame. Combust. Flame 58 (1), 2329.
Minamoto, Y., Yenerdag, B. & Tanahashi, M. 2018 Morphology and structure of hydrogen–air turbulent premixed flames. Combust. Flame 192, 369383.
Möller, T. & Trumbore, B. 2005 Fast, minimum storage ray/triangle intersection. In ACM SIGGRAPH 2005 Courses, p. 7. ACM.
Mueller, C. J., Driscoll, J. F., Reuss, D. L. & Drake, M. C. 1996 Effects of unsteady stretch on the strength of a freely-propagating flame wrinkled by a vortex. In Symposium (International) on Combustion, vol. 26, pp. 347355. Elsevier.
Nilsson, T., Carlsson, H., Yu, R. & Bai, X. S. 2018 Structures of turbulent premixed flames in the high Karlovitz number regime – DNS analysis. Fuel 216, 627638.
Osborne, J. R., Ramji, S. A., Carter, C. D. & Steinberg, A. M. 2017 Relationship between local reaction rate and flame structure in turbulent premixed flames from simultaneous 10 kHz TPIV, OH PLIF, and CH2O PLIF. Proc. Combust. Inst. 36 (2), 18351841.
Pelce, P. & Clavin, P. 1982 Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech. 124, 219237.
Peters, N. 1999 The turbulent burning velocity for large-scale and small-scale turbulence. J. Fluid Mech. 384, 107132.
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.
Poinsot, T. J., Echekki, T. & Mungal, M. G. 1992 A study of the laminar flame tip and implications for premixed turbulent combustion. Combust. Sci. Technol. 81 (1–3), 4573.
Poinsot, T. J. & Veynante, D. 2005 Theoretical and Numerical Combustion. RT Edwards, Inc.
Pope, S. B. 1988 The evolution of surfaces in turbulence. Intl J. Engng Sci. 26 (5), 445469.
Pope, S. B., Yeung, P. K. & Girimaji, S. S. 1989 The curvature of material surfaces in isotropic turbulence. Phys. Fluids A 1 (12), 20102018.
Rutland, C. J. & Trouvé, A. 1993 Direct simulations of premixed turbulent flames with nonunity Lewis numbers. Combust. Flame 94 (1–2), 4157.
Spalding, D. B. 1956 The theory of flame phenomena with a chain reaction. Phil. Trans. R. Soc. Lond. A 249 (957), 125.
Steinberg, A. M. & Driscoll, J. F. 2009 Straining and wrinkling processes during turbulence–premixed flame interaction measured using temporally-resolved diagnostics. Combust. Flame 156 (12), 22852306.
Sun, C. J. & Law, C. K. 2000 On the nonlinear response of stretched premixed flames. Combust. Flame 121 (1–2), 236248.
Sun, C. J., Sung, C. J., He, L. & Law, C. K. 1999 Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters. Combust. Flame 118 (1–2), 108128.
Thiesset, F., Halter, F., Bariki, C., Lapeyre, C., Chauveau, C., Gökalp, I., Selle, L. & Poinsot, T. J. 2017 Isolating strain and curvature effects in premixed flame/vortex interactions. J. Fluid Mech. 831, 618654.
Trivedi, S., Griffiths, R., Kolla, H., Chen, J. H. & Cant, R. S. 2019a Topology of pocket formation in turbulent premixed flames. Proc. Combust. Inst. 37 (2), 26192626.
Trivedi, S., Nivarti, G. V. & Cant, R. S. 2019b Flame self-interactions with increasing turbulence intensity. Proc. Combust. Inst. 37 (2), 24432449.
Trouvé, A. & Poinsot, T. J. 1994 The evolution equation for the flame surface density in turbulent premixed combustion. J. Fluid Mech. 278, 131.
Uranakara, H. A., Chaudhuri, S., Dave, H. L., Arias, P. G. & Im, H. G. 2016 A flame particle tracking analysis of turbulence–chemistry interaction in hydrogen–air premixed flames. Combust. Flame 163, 220240.
Uranakara, H. A., Chaudhuri, S. & Lakshmisha, K. N. 2017 On the extinction of igniting kernels in near-isotropic turbulence. Proc. Combust. Inst. 36 (2), 17931800.
Veynante, D. & Vervisch, L. 2002 Turbulent combustion modeling. Prog. Energy Combust. Sci. 28 (3), 193266.
Wichman, I. S. & Vance, R. 1997 A study of one-dimensional laminar premixed flame annihilation. Combust. Flame 110 (4), 508523.
Williams, F. A. 1985 Combustion Theory. Benjamin Cummings.
Wu, C. K. & Law, C. K. 1985 On the determination of laminar flame speeds from stretched flames. In Symposium (International) on Combustion, vol. 20, pp. 19411949. Elsevier.
Wu, F., Liang, W., Chen, Z., Ju, Y. & Law, C. K. 2015 Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames. Proc. Combust. Inst. 35 (1), 663670.
Yeung, P. K., Girimaji, S. S. & Pope, S. B. 1990 Straining and scalar dissipation on material surfaces in turbulence: Implications for flamelets. Combust. Flame 79 (3–4), 340365.
Yeung, P. K. & Pope, S. B. 1988 An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phy. 79 (2), 373416.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Evolution of local flame displacement speeds in turbulence

  • Himanshu L. Dave (a1) and Swetaprovo Chaudhuri (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.