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Combustion Science and Technology Volume 62, 1988 - Issue 1-3
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Original Articles

Cascade-Renormalization Theory of Turbulent Flame Speed

GREGORY I. SIVASHINSKY Program in Applied & Computational Mathematics. Princeton University, Princeton, NJ, 08544, U.S.A
Pages 77-96 | Received 02 Jun 1988, Accepted 19 Sep 1988, Published online: 30 Mar 2007

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Derek Bradley. (2002) Problems of predicting turbulent burning rates. Combustion Theory and Modelling 6:2, pages 361-382.
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Vitaliy Bychkov & Bruno Denet. (2002) Effect of temporal pulsations of a turbulent flow on the flame velocity. Combustion Theory and Modelling 6:2, pages 209-222.
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J Daou, J Dold & M Matalon. (2002) The thick flame asymptotic limit and Damköhler's hypothesis. Combustion Theory and Modelling 6:1, pages 141-153.
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VITALIY BYCHKOV, MICHAELA. LIBERMAN & RAYMOND REINMANN. (2001) VELOCITY OF TURBULENT FLAMELETS OF FINITE THICKNESS. Combustion Science and Technology 168:1, pages 113-129.
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Mark Ulitsky, Chaouki Ghenaï, Iskender Gökalp, Lian-Ping Wang & Lance R Collins. (2000) Comparison of a spectral model for premixed turbulent flame propagation to DNS and experiments. Combustion Theory and Modelling 4:3, pages 241-264.
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Wm T Ashurst. (2000) Flow-frequency effect upon Huygens front propagation. Combustion Theory and Modelling 4:2, pages 99-105.
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Bruno Denet. (1999) Possible role of temporal correlations in the bending of turbulent flame velocity. Combustion Theory and Modelling 3:3, pages 585-589.
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A.Y. KLIMENKO. (1998) Examining the Cascade Hypothesis for Turbulent Premixed Combustion. Combustion Science and Technology 139:1, pages 15-40.
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Bruno Denet. (1998) Are small scales of turbulence able to wrinkle a premixed flame at large scale?. Combustion Theory and Modelling 2:2, pages 167-178.
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RichardM. Mclaughlin & Jingyi zhu. (1997) The Effect of Finite Front Thickness on the Enhanced Speed of Propagation. Combustion Science and Technology 129:1-6, pages 89-112.
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B. Denet. (1997) A Lagrangian Method to Simulate Turbulent Flames with Reconnections. Combustion Science and Technology 123:1-6, pages 247-260.
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P. F. EMBID, A. J. MAJDA & P. E. SOUGANIDIS. (1994) Effective Geometric F-ront Dynamics for Premixed Turbulent Combustion With Separated Velocity Scales. Combustion Science and Technology 103:1-6, pages 85-115.
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CAMBRAY PIERRE & JOULIN GUY. (1994) Length-Scales of Wrinkling of Weakly-Forced, Unstable Premixed Flames. Combustion Science and Technology 97:4-6, pages 405-428.
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WM. T. ASHURST. (1993) Flame Propagation Through Swirling Eddies, A Recursive Pattern. Combustion Science and Technology 92:1-3, pages 87-103.
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J. C. VASSILICOS & J. C. R. HUNT. (1993) Turbulent Flamelet Propagation. Combustion Science and Technology 87:1-6, pages 291-327.
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JOHN MANTZARAS. (1992) Geometrical Properties of Turbulent Premixed Flames: Comparison Between Computed and Measured Quantities. Combustion Science and Technology 86:1-6, pages 135-162.
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PAULD. RONNEY & VICTOR YAKHOT. (1992) Flame Broadening Effects on Premixed Turbulent Flame Speed. Combustion Science and Technology 86:1-6, pages 31-43.
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WILLIAMT. ASHURST & GREGORYI. SIVASHINSKY. (1991) SHORT COMMUNICATION On Flame Propagation Through Periodic Flow Fields. Combustion Science and Technology 80:1-3, pages 159-164.
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PAUL CLAVIN & ERICD. SIGGIA. (1991) Turbulent Premixed Flames and Sound Generation. Combustion Science and Technology 78:1-3, pages 147-155.
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GUY JOULIN. (1989) On a Variational Principle for Thin Premixed Flames. Combustion Science and Technology 65:4-6, pages 313-316.
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WM. T. ASHURST, GREGORYI. SIVASHINSKY & VICTOR YAKHOT. (1988) Flame Front Propagation in Nonsteady Hydrodynamic Fields. Combustion Science and Technology 62:4-6, pages 273-284.
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VICTOR YAKHOT. (1988) Scale Invariant Solutions of the Theory of Thin Turbulent Flame Propagation. Combustion Science and Technology 62:4-6, pages 127-129.
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A. Y. Klimenko. (2021) The convergence of combustion models and compliance with the Kolmogorov scaling of turbulence. Physics of Fluids 33:2.
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Xiao Cai, Jinhua Wang, Zhijian Bian, Haoran Zhao, Meng Zhang & Zuohua Huang. (2020) Self-similar propagation and turbulent burning velocity of CH4/H2/air expanding flames: Effect of Lewis number. Combustion and Flame 212, pages 1-12.
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Sheng Yang, Abhishek Saha, Zirui Liu & Chung K. Law. (2018) Role of Darrieus–Landau instability in propagation of expanding turbulent flames. Journal of Fluid Mechanics 850, pages 784-802.
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Sheng Yang, Abhishek Saha, Wenkai Liang, Fujia Wu & Chung K. Law. (2018) Extreme role of preferential diffusion in turbulent flame propagation. Combustion and Flame 188, pages 498-504.
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E. Beauvier, S. Bodea & A. Pocheau. (2017) Front propagation in a regular vortex lattice: Dependence on the vortex structure. Physical Review E 96:5.
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B. Sundaram & A.Y. Klimenko. (2017) A PDF approach to thin premixed flamelets using multiple mapping conditioning. Proceedings of the Combustion Institute 36:2, pages 1937-1945.
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P. Pearce & J. Daou. (2014) Taylor dispersion and thermal expansion effects on flame propagation in a narrow channel. Journal of Fluid Mechanics 754, pages 161-183.
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Jack Xin & Yifeng Yu. (2014) Asymptotic Growth Rates and Strong Bending of Turbulent Flame Speeds of G-Equation in Steady Two-Dimensional Incompressible Periodic Flows. SIAM Journal on Mathematical Analysis 46:4, pages 2444-2467.
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Jack Xin & Yifeng Yu. (2013) Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton–Jacobi models. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 30:6, pages 1049-1068.
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S. Daniele, J. Mantzaras, P. Jansohn, A. Denisov & K. Boulouchos. (2013) Flame front/turbulence interaction for syngas fuels in the thin reaction zones regime: turbulent and stretched laminar flame speeds at elevated pressures and temperatures. Journal of Fluid Mechanics 724, pages 36-68.
Crossref
Lihua Shen, Jack Xin & Aihui Zhou. (2012) Finite Element Computation of KPP Front Speeds in Cellular and Cat’s Eye Flows. Journal of Scientific Computing 55:2, pages 455-470.
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L. Shen, J. Xin & A. Zhou. (2013) Finite Element Computation of KPP Front Speeds in 3D Cellular and ABC Flows. Mathematical Modelling of Natural Phenomena 8:3, pages 182-197.
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Yu-Yu Liu, Jack Xin & Yifeng Yu. (2013) A numerical study of turbulent flame speeds of curvature and strain G-equations in cellular flows. Physica D: Nonlinear Phenomena 243:1, pages 20-31.
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Tim C. Lieuwen. 2012. Unsteady Combustor Physics. Unsteady Combustor Physics 364 400 .
. 2012. Lees' Loss Prevention in the Process Industries. Lees' Loss Prevention in the Process Industries 3129 3580 .
Yu-Yu Liu, Jack Xin & Yifeng Yu. (2011) Asymptotics for Turbulent Flame Speeds of the Viscous G-Equation Enhanced by Cellular and Shear Flows. Archive for Rational Mechanics and Analysis 202:2, pages 461-492.
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Bruno Denet & Guy Joulin. (2011) Wrinkled flames and geometrical stretch. Physical Review E 84:1.
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Yu-Yu Liu, Jack Xin & Yifeng Yu. (2010) Periodic homogenization of G-equations and viscosity effects. Nonlinearity 23:10, pages 2351-2367.
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Toni Pujol, Joaquim Fort, Lino Montoro & Joan J. Suñol. (2009) Generalized analytical expressions for the burning velocity in a combustion model with non-constant transport coefficients and several specific heats. Physica A: Statistical Mechanics and its Applications 388:24, pages 4959-4972.
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S. KHOSID & Y. TAMBOUR. (2008) Analytic study of developing flows in a tube laden with non-evaporating and evaporating drops via a modified linearization of the two-phase momentum equations. Journal of Fluid Mechanics 603, pages 245-270.
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Ch. Proust. (2006) A few fundamental aspects about ignition and flame propagation in dust clouds. Journal of Loss Prevention in the Process Industries 19:2-3, pages 104-120.
Crossref
. 2005. Lees' Loss Prevention in the Process Industries. Lees' Loss Prevention in the Process Industries 401 449 .
M. Cencini, A. Torcini, D. Vergni & A. Vulpiani. (2003) Thin front propagation in steady and unsteady cellular flows. Physics of Fluids 15:3, pages 679-688.
Crossref
A.N. Lipatnikov & J. Chomiak. (2002) Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Progress in Energy and Combustion Science 28:1, pages 1-74.
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D. VOLCHENKOV. (2012) THE BENDING INSTABILITY IN THE VORTICITY TRANSPORT THROUGH A TURBULENT FLOW: FEEDBACK CHAOS CONTROLLING AND DYNAMICAL SYMMETRY BREAKING. International Journal of Modern Physics B 15:08, pages 1147-1164.
Crossref
F. A. Williams. 2001. Smart Control of Turbulent Combustion. Smart Control of Turbulent Combustion 1 11 .
Jack Xin. (2000) Front Propagation in Heterogeneous Media. SIAM Review 42:2, pages 161-230.
Crossref
Sergei Fedotov. (1997) Combustion Theory and Modelling 1:1, pages L1-L6.
Crossref
A. Pocheau. 1997. Scale Invariance and Beyond. Scale Invariance and Beyond 209 223 .
Ralph C. Aldredge. (1996) A novel flow reactor for the study of heat-loss effects on turbulent flame propagation. International Communications in Heat and Mass Transfer 23:8, pages 1173-1179.
Crossref
R.C. Aldredge. (1996) Premixed flame propagation in a high-intensity, large-scale vortical flow. Combustion and Flame 106:1-2, pages 29-40.
Crossref
Andrew J. Majda & Panagiotis E. Souganidis. (1996) Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields. Journal of Statistical Physics 83:5-6, pages 933-954.
Crossref
N. Peters. 1996. IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers. IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers 173 186 .
Sergei P. Fedotov. (1995) Renormalization for reaction-front propagation in a fully developed turbulent shear flow. Physical Review E 52:4, pages 3835-3839.
Crossref
S P Fedotov. (1995) Reaction front propagation in a turbulent flow. Journal of Physics A: Mathematical and General 28:17, pages L461-L468.
Crossref
Pedro F. Embid, Andrew J. Majda & Panagiotis E. Souganidis. (1995) Comparison of turbulent flame speeds from complete averaging and the G-equation. Physics of Fluids 7:8, pages 2052-2060.
Crossref
S P Fedotov. (1995) The problem of flame propagation in a random velocity field: weak turbulence limit. Journal of Physics A: Mathematical and General 28:7, pages 2057-2064.
Crossref
Jack X. Xin & Jingyi Zhu. (1995) Quenching and propagation of bistable reaction-diffusion fronts in multidimensional periodic media. Physica D: Nonlinear Phenomena 81:1-2, pages 94-110.
Crossref
K.M. Yu, C.J. Sung & C.K. Law. (1994) Some aspects of the freely propagating premixed flame in a spatially periodic flow field. Combustion and Flame 97:3-4, pages 375-383.
Crossref
L. Filyand, G.I. Sivashinsky & M.L. Frankel. (1994) On self-acceleration of outward propagating wrinkled flames. Physica D: Nonlinear Phenomena 72:1-2, pages 110-118.
Crossref
A. Pocheau. (1994) Scale invariance in turbulent front propagation. Physical Review E 49:2, pages 1109-1122.
Crossref
Jack X. Xin. (1993) Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media. Journal of Statistical Physics 73:5-6, pages 893-926.
Crossref
F.A. Williams. 1993. Turbulence and Molecular Processes in Combustion. Turbulence and Molecular Processes in Combustion 1 12 .
Ken Naitoh & Kunio Kuwahara. (1992) Large eddy simulation and direct simulation of compressible turbulence and combusting flows in engines based on the BI-SCALES method. Fluid Dynamics Research 10:4-6, pages 299-325.
Crossref
A Pocheau. (1992) Front Propagation in a Turbulent Medium. Europhysics Letters (EPL) 20:5, pages 401-406.
Crossref
N. Peters. (2006) A spectral closure for premixed turbulent combustion in the flamelet regime. Journal of Fluid Mechanics 242, pages 611-629.
Crossref
Pierre Cambray & Guy Joulin. (1992) On moderately-forced premixed flames. Symposium (International) on Combustion 24:1, pages 61-67.
Crossref
F.A. Williams. (1992) The role of theory in combustion science. Symposium (International) on Combustion 24:1, pages 1-17.
Crossref
George Papanicolaou & Xue Xin. (1991) Reaction-diffusion fronts in periodically layered media. Journal of Statistical Physics 63:5-6, pages 915-931.
Crossref
Henri Berestycki & Gregory I. Sivashinsky. (1991) Flame Extinction by Periodic Flow Field. SIAM Journal on Applied Mathematics 51:2, pages 344-350.
Crossref
J. Buckmaster. (1991) Mathematical topics in combustion. Chemometrics and Intelligent Laboratory Systems 10:1-2, pages 189-198.
Crossref
. (1997) Studies of the turbulent burning velocity. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 431:1882, pages 315-335.
Crossref
G. I. Sivashinsky. 1990. Dissipative Structures in Transport Processes and Combustion. Dissipative Structures in Transport Processes and Combustion 30 39 .
Gregory I. Sivashinsky. 1989. Numerical Combustion. Numerical Combustion 131 148 .

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