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A Nonlinear Theory of Cellular Flames
SIAM Journal on Applied Mathematics, 1980Experiments with laminar flames in gaseous combustible mixtures show that for certain mixtures a flame front will often break up into numerous cells. Cellular flames are periodic structures with pointed crests, pointing in the direction of the burned gas. The smoother sections (troughs) of the front are convex toward the fresh mixture.
Matkowsky, B. J. +2 more
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Nonlinear Dynamics of Cellular Flames
SIAM Journal on Applied Mathematics, 1992The problem of a flame stabilized by a line source of fuel in the cellular regime, i.e., $L < 1$,where L is the Lewis number, is solved numerically. It is found that as L is decreased, transitions from stationary axisymmetric to stationary cellular to nonstationary cellular flames occur.
Bayliss, Alvin, Matkowsky, Bernard J.
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Flame Propagation in Vertical Channels: Bifurcation to Bimodal Cellular Flames
SIAM Journal on Applied Mathematics, 1984We derive a nonlinear evolution equation and associated boundary conditions which, under certain circumstances, describe downward adiabatic flame propagation in long, vertical channels. We analyze this problem for the case of axial symmetry and show that there exist two critical parameters, the channel radius R and a gravitational acceleration ...
Margolis, Stephen B. +1 more
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A cellular automata model for expanding turbulent flames
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020Cellular automata models based on population dynamics, introduced by Von Neumann in the 1950s, has been successfully used to describe pattern development and front propagation in many applications, such as crystal growth, forest fires, fractal growth in biological media, etc.
Vishnu R. Unni +2 more
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Wrinkled flames and cellular patterns
ACM SIGGRAPH 2007 papers, 2007We model flames and fire using the Navier-Stokes equations combined with the level set method and jump conditions to model the reaction front. Previous works modeled the flame using a combination of propagation in the normal direction and a curvature term which leads to a level set equation that is parabolic in nature and thus overly dissipative and ...
Jeong-Mo Hong +2 more
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On Disintegration of Cellular Flames
2003A three-dimensional reaction-diffusion model for premixed flames with radiative heat losses is studied numerically. In accordance with previous analytical predictions and two-dimensional numerical simulations, it is shown that cellular flames occurring in low Lewis number premixtures can propagate at heat-loss rates greater than the maximum that ...
Leonid Kagan +2 more
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Analyzing the dynamics of cellular flames
Physica D: Nonlinear Phenomena, 1996Abstract Video data from experiments on the dynamics of two-dimensional flames are analyzed. The Karhumen-Loeve (KL) analysis is used to identify the dominant spatial structures and their temporal evolution fot several dynamical regimes of the flames. A data analysis procedure to extract and process the boundaries of flame cells is described.
Antonio Palacios +3 more
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On the hexagonal structure of cellular flames
Canadian Journal of Physics, 1990The effect of hexagonal pattern formation in steady spherical flames is studied both analytically and numerically. It is shown that the hexagonal cells emerge as a subcritical bifurcation from the basic state provided the flame radius exceeds a certain critical value.
Shtilman, L., Sivashinsky, G.
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On Spinning Propagation of Cellular Flames
Combustion Science and Technology, 1990Abstract The appearance of time-dependent cellular structures in premixed flame propagation is known to occur in a parameter regime usually associated with the onset of steady cellular flame formation. We consider this phenomenon in the context of a model for downward flame propagation in vertical channels.
STEPHEN B. MARGOLIS +1 more
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The characteristics of four ratcheting states in cellular flames
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009A premixed flat flame on a circular porous plug burner can form patterns of one or two concentric rings of cells in which brighter, hotter regions are separated by darker, cooler cusps and folds. Dynamic states are found at parameter values that are interleaved between those of the ordered states.
M, Gorman, M, el-Hamdi, B, Pearson
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