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Isolating strain and curvature effects in premixed flame/vortex interactions

  • F. Thiesset (a1), F. Halter (a1), C. Bariki (a1), C. Lapeyre (a2) (a3), C. Chauveau (a1), I. Gökalp (a1), L. Selle (a2) and T. Poinsot (a2)...


This study focuses on the response of premixed flames to a transient hydrodynamic perturbation in an intermediate situation between laminar stretched flames and turbulent flames: an axisymmetric vortex interacting with a flame. The reasons motivating this choice are discussed in the framework of turbulent combustion models and flame response to the stretch rate. We experimentally quantify the dependence of the flame kinematic properties (displacement and consumption speeds) to geometrical scalars (stretch rate and curvature) in flames characterized by different effective Lewis numbers. Whilst the displacement speed can be readily measured using particle image velocimetry and tomographic diagnostics, providing a reliable estimate of the consumption speed from experiments remains particularly challenging. In the present work, a method based on a budget of fuel on a well chosen domain is proposed and validated both experimentally and numerically using two-dimensional direct numerical simulations of flame/vortex interactions. It is demonstrated that the Lewis number impact neither the geometrical nor the kinematic features of the flames, these quantities being much more influenced by the vortex intensity. While interacting with the vortex, the flame displacement (at an isotherm close to the leading edge) and consumption speeds are found to increase almost independently of the type of fuel. We show that the total stretch rate is not the only scalar quantity impacting the flame displacement and consumption speeds and that curvature has a significant influence. Experimental data are interpreted in the light of asymptotic theories revealing the existence of two distinct Markstein numbers, one characterizing the dependence of flame speed to curvature, the other to the total stretch rate. This theory appears to be well suited for representing the evolution of the displacement speed with respect to either the total stretch rate, curvature or strain rate. It also explains the limited dependence of the flame displacement speed to Lewis number and the strong correlation with curvature observed in the experiments. An explicit relationship between displacement and consumption speeds is also given, indicating that the fuel consumption rate is likely to be altered by both the total stretch rate and curvature.


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Balusamy, S., Cessou, A. & Lecordier, B. 2011 Direct measurement of local instantaneous laminar burning velocity by a new PIV algorithm. Exp. Fluids 50 (4), 11091121.
Bechtold, J. K. & Matalon, M. 2001 The dependence of the markstein length on stoichiometry. Combust. Flame 127 (1), 19061913.
Bell, J. B., Cheng, R. K., Day, M. S. & Shepherd, I. G. 2007 Numerical simulation of lewis number effects on lean premixed turbulent flames. Proc. Combust. Inst. 31 (1), 13091317.
Bosschaart, K. J. & De Goey, L. P. H. 2004 The laminar burning velocity of flames propagating in mixtures of hydrocarbons and air measured with the heat flux method. Combust. Flame 136 (3), 261269.
Bougrine, S., Richard, S., Colin, O. & Veynante, D. 2014 Fuel composition effects on flame stretch in turbulent premixed combustion: Numerical analysis of flame-vortex interaction and formulation of a new efficiency function. Flow Turbul. Combust. 93 (2), 259281.
Bouvet, N.2009, Experimental and numerical studies of the fundamental flame speeds of methane/air and syngas ( $\text{H}_{2}/\text{CO}$ )/air mixtures. PhD thesis, University of Orléans.
Boyer, L. 1980 Laser tomographic method for flame front movement studies. Combust. Flame 39 (3), 321323.
Bradley, D., Gaskell, P. H. & Gu, X. J. 1996 Burning velocities, markstein lengths, and flame quenching for spherical methane-air flames: A computational study. Combust. Flame 104, 176198.
Candel, S. M. & Poinsot, T. 1990 Flame stretch and the balance equation for the flame area. Combust. Sci. Technol. 70 (1–3), 115.
Chao, B. H., Egolfopoulos, F. N. & Law, C. K. 1997 Structure and propagation of premixed flame in nozzle-generated counterflow. Combust. Flame 109 (4), 620638.
Charlette, F., Meneveau, C. & Veynante, D. 2002 A power-law flame wrinkling model for LES of premixed turbulent combustion part I: non-dynamic formulation and initial tests. Combust. Flame 131 (1), 159180.
Chen, Z., Burke, M. P. & Ju, Y. 2009 Effects of lewis number and ignition energy on the determination of laminar flame speed using propagating spherical flames. Proc. Combust. Inst. 32 (1), 12531260.
Chen, J. H. & Im, H. G. 1998 Correlation of flame speed with stretch in turbulent premixed methane/air flames. Sympos. Combust. 27 (1), 819826.
Chen, J. B. & Im, H. G. 2000 Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames. Proc. Combust. Inst. 28 (1), 211218.
Chen, Z. & Ju, Y. 2007 Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Combust. Theor. Model. 11 (3), 427453.
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. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11 (1), 159.
Clavin, P. & Garcia, P. J. 1983 The influence of the temperature dependence on the dynamics of flame fronts. J. Méc. 2, 245263.
Clavin, P. & Graña-Otero, J. C. 2011 Curved and stretched flames: the two Markstein numbers. J. Fluid Mech. 686, 187217.
Clavin, P. & Joulin, G. 1983 Premixed flames in large scale and high intensity turbulent flow. J. Phys. Lett. 44 (1), 112.
Clavin, P. & Joulin, G. 1989 Flamelet library for turbulent wrinkled flames. In Turbulent Reactive Flows, Lecture Notes in Engineering, vol. 40, pp. 213240. Springer.
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.
Clavin, P. & Williams, F. A. 1982 Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. J. Fluid Mech. 116, 251282.
Colin, O., Ducros, F., Veynante, D. & Poinsot, T. 2000 A thickened flame model for large eddy simulations of turbulent premixed combustion. Phys. Fluids 12 (7), 18431863.
Colin, O. & Rudgyard, M. 2000 Development of high-order Taylor–Galerkin schemes for unsteady calculations. J. Comput. Phys. 162 (2), 338371.
Dong, Y., Vagelopoulos, C. M., Spedding, G. R. & Egolfopoulos, F. N. 2002 Measurement of laminar flame speeds through digital particle image velocimetry: mixtures of methane and ethane with hydrogen, oxygen, nitrogen, and helium. Proc. Combust. Inst. 29 (2), 14191426.
Durox, D., Baillot, F., Searby, G. & Boyer, L. 1997 On the shape of flames under strong acoustic forcing: a mean flow controlled by an oscillating flow. J. Fluid Mech. 350, 295310.
Echekki, T. & Chen, J. H. 1996 Unsteady strain rate and curvature effects in turbulent premixed methane-air flames. Combust. Flame 106 (1), 184202.
Egolfopoulos, F. N., Zhang, H. & Zhang, Z. 1997 Wall effects on the propagation and extinction of steady, strained, laminar premixed flames. Combust. Flame 109 (1), 237252.
Fogla, N., Creta, F. & Matalon, M. 2015 Effect of folds and pockets on the topology and propagation of premixed turbulent flames. Combust. Flame 162 (7), 27582777.
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.
Giannakopoulos, G. K., Gatzoulis, A., Frouzakis, C. E., Matalon, M. & Tomboulides, A. G. 2015a Consistent definitions of flame displacement speed and markstein length for premixed flame propagation. Combust. Flame 162 (4), 12491264.
Giannakopoulos, G. K., Matalon, M., Frouzakis, C. E. & Tomboulides, A. G. 2015b The curvature markstein length and the definition of flame displacement speed for stationary spherical flames. Proc. Combust. Inst. 35 (1), 737743.
Halter, F., Tahtouh, T. & Mounaïm-Rousselle, C. 2010 Nonlinear effects of stretch on the flame front propagation. Combust. Flame 157 (10), 18251832.
Haworth, D. C. & Poinsot, T. J. 1992 Numerical simulations of Lewis number effects in turbulent premixed flames. J. Fluid Mech. 244, 405436.
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.
Joulin, G. 1994 On the response of premixed flames to time-dependent stretch and curvature. Combust. Sci. Technol. 97 (1–3), 219229.
Karlovitz, B., Denniston, D. W., Knapschaefer, D. H. & Wells, F. E. 1953 Studies on turbulent flames: A. flame propagation across velocity gradients b. turbulence measurement in flames. Sympos. Combust. 4 (1), 613620.
Kerl, J., Lawn, C. & Beyrau, F. 2013 Three-dimensional flame displacement speed and flame front curvature measurements using quad-plane PIV. Combust. Flame 160 (12), 27572769.
Kim, S. H. 2017 Leading points and heat release effects in turbulent premixed flames. Proc. Combust. Inst. 36 (2), 20172024.
Lefebvre, A., Larabi, H., Moureau, V., Lartigue, G., Varea, E., Modica, V. & Renou, B. 2016 Formalism for spatially averaged consumption speed considering spherically expanding flame configuration. Combust. Flame 173, 235244.
Lipatnikov, A. N. & Chomiak, J. 2005 Molecular transport effects on turbulent flame propagation and structure. Prog. Energ. Combust. 31 (1), 173.
Lu, T. & Law, C. K. 2008 A criterion based on computational singular perturbation for the identification of quasi steady state species: A reduced mechanism for methane oxidation with no chemistry. Combust. Flame 154 (4), 761774.
Mantel, T. & Samaniego, J. M. 1999 Fundamental mechanisms in premixed turbulent flame propagation via flame vortex interactions. Part 2: Numerical simulation. Combust. Flame 118, 557582.
Markstein, G. H. 1964 Nonsteady Flame Propagation, vol. 75. Elsevier.
Matalon, M. & Bechtold, J. K. 2009 A multi-scale approach to the propagation of non-adiabatic premixed flames. J. Engng Maths 63 (2–4), 309326.
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.
Moureau, V., Fiorina, B. & Pitsch, H. 2009 A level set formulation for premixed combustion LES considering the turbulent flame structure. Combust. Flame 156 (4), 801812.
Moureau, V., Lartigue, G., Sommerer, Y., Angelberger, C., Colin, O. & Poinsot, T. 2005 Numerical methods for unsteady compressible multi-component reacting flows on fixed and moving grids. J. Comput. Phys. 202 (2), 710736.
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. Sympos. Combust. 26, 347355.
Najm, H. N., Paul, P. H., Mueller, C. J. & Wyckoff, P. S. 1998 On the adequacy of certain experimental observables as measurements of flame burning rate. Combust. Flame 113 (3), 312332.
Oberlack, M., Wenzel, H. & Peters, N. 2001 On symmetries and averaging of the G-equation for premixed combustion. Combust. Theor. Model. 5, 363383.
Otsu, N. 1979 A threshold selection method from gray-level histogram. IEEE Trans. Syst. Man Cybern. 9, 6266.
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Sympos. Combust. 21 (1), 12311250.
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.
Peters, N. 2009 Multiscale combustion and turbulence. Proc. Combust. Inst. 32, 125.
Pitsch, H. 2005 A consistent level set formulation for large-eddy simulation of premixed turbulent combustion. Combust. Flame 143 (4), 587598.
Poinsot, T. 1998 Comments on flame stretch interactions of laminar premixed hydrogen air flames at normal temperature and pressure by Aung et al. Combust. Flame 113, 279284.
Poinsot, T. & Lele, S. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104129.
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion, 2nd edn. RT Edwards, Inc.
Poinsot, T. & Veynante, D. 2011 Theoretical and Numerical Combustion, 3rd edn;
Poinsot, T., Veynante, D. & Candel, S. 1991 Quenching processes and premixed turbulent combustion diagrams. J. Fluid Mech. 228, 561606.
Renard, P.-H., Thevenin, D., Rolon, J.-C. & Candel, S. 2000 Dynamics of flame/vortex interactions. Prog. Energy Combust. Sci. 26 (3), 225282.
Renou, B., Boukhalfa, A., Puechberty, D. & Trinité, M. 1998 Effects of stretch on the local structure of preely propagating premixed low-turbulent flames with various Lewis numbers. In Symposium (International) on Combustion, vol. 27, pp. 841847. Elsevier.
Renou, B., Boukhalfa, A., Puechberty, D. & Trinité, M. 2000 Local scalar flame properties of freely propagating premixed turbulent flames at various Lewis numbers. Combust. Flame 123 (4), 507521.
Roberts, W. L. & Driscoll, J. F. 1991 A laminar vortex interacting with a premixed flame: measured formation of pockets of reactants. Combust. Flame 87 (3), 245256.
Roberts, W. L., Driscoll, J. F., Drake, M. C. & Goss, L. P. 1993 Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion. Combust. Flame 94 (1), 5869.
Rutland, C. J. & Trouvé, A. 1993 Direct simulations of premixed turbulent flames with nonunity Lewis numbers. Combust. Flame 94 (1), 4157.
Samaniego, J. M. & Mantel, T. 1999 Fundamental mechanisms in premixed turbulent flame propagation via flame vortex interactions. Part I: Experiment. Combust. Flame 118, 537556.
Schønfeld, T. & Rudgyard, M. 1999 Steady and unsteady flows simulations using the hybrid flow solver AVBP. AIAA J. 37 (11), 13781385.
Shepherd, I. G. & Kostiuk, L. W. 1994 The burning rate of premixed turbulent flames in divergent flows. Combust. Flame 96 (4), 371380.
Sinibaldi, J. O., Driscoll, J. F., Mueller, C. J., Donbar, J. M. & Carter, C. D. 2003 Propagation speeds and stretch rates measured along wrinkled flames to assess the theory of flame stretch. Combust. Flame 133 (3), 323334.
Sinibaldi, J. O., Mueller, C. J. & Driscoll, J. F. 1998 Local flame propagation speeds along wrinkled, unsteady, stretched premixed flames. In Symposium (International) on Combustion, vol. 27, pp. 827832. Elsevier.
Steinberg, A. M. & Driscoll, J. F. 2010 Stretch-rate relationships for turbulent premixed combustion LES subgrid models measured using temporally resolved diagnostics. Combust. Flame 157 (7), 14221435.
Thielicke, W. & Stamhuis, E. J. 2014 PIVlab–towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Research Software 2 (1), 30.
Thiesset, F., Maurice, G., Halter, F., Mazellier, N., Chauveau, C. & Gökalp, I. 2017 Flame-vortex interaction: Effect of residence time and formulation of a new efficiency function. Proc. Combust. Inst. 36, 18431851.
Trouvé, A. & Poinsot, T. 1994 The evolution equation for the flame surface density in turbulent premixed combustion. J. Fluid Mech. 278, 131.
Vagelopoulos, C. M. & Egolfopoulos, F. N. 1998 Direct experimental determination of laminar flame speeds. Sympos. Combust. 27 (1), 513519.
Vagelopoulos, C. M., Egolfopoulos, F. N. & Law, C. K. 1994 Further considerations on the determination of laminar flame speeds with the counterflow twin-flame technique. Sympos. Combust. 25 (1), 13411347.
Varea, E.2013 Experimental analysis of laminar spherically expanding flames. PhD thesis, INSA Rouen.
Veynante, D. & Vervisch, L. 2002 Turbulent combustion modeling. Prog. Energ. Combust. 28 (3), 193266.
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2007 Vorticity and Vortex Dynamics. Springer.
Zhang, F., Zirwes, T., Habisreuther, P. & Bockhorn, H. 2017 Effect of unsteady stretching on the flame local dynamics. Combust. Flame 175, 170179.
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Isolating strain and curvature effects in premixed flame/vortex interactions

  • F. Thiesset (a1), F. Halter (a1), C. Bariki (a1), C. Lapeyre (a2) (a3), C. Chauveau (a1), I. Gökalp (a1), L. Selle (a2) and T. Poinsot (a2)...


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