Flame propagation dynamics

The kinematics of moving fronts and interfaces has been studied in different physical contexts for over two hundred years. Most notable are the studies of free surfaces in ocean hydrodynamics and vortex sheets in free space (e.g., see Lamb, 1945), and more recently, flame propagation dynamics in combustion analyses. The following derivation, which applies to fluid fronts in porous media, is given in Chin (1993a). Let us consider a moving front or interface located anywhere within a three-dimensional Darcy flow (e.g., any surface marked by red dye), and let (()(x,y,z) denote the porosity. Furthermore, denote by u, v, and w the Eulerian speed components, and describe our interface by the surface locus of points... 

Influence of Governing Parameters on Flame Propagation and Ignition Dynamics... 

The problem of front propagation has been extensively studied in many different fields [11,12] such as chemical reaction fronts [7], flames propagation in gases [8], and population dynamics of biological communities [11,12]. In many of these systems the reaction takes place in moving media (i.e., fluids), so that it is important to understand how the flow affects the front propagation. 

Lewis number based on the limiting reactant is sufficiently large [3]. Therefore, the Darrieus-Landau instability is expected to result in enhanced flame-surface wrinkling only when it is able to overcome stabilizing influences of buoyancy and thermal diffusion. Additionally, a flame under confinement may be influenced by acoustic waves, and coupling between the flame and acoustic-wave dynamics may result in unstable flame propagation as well. 

A. P. Aldushin, A. Bayliss, B. J. Matkowsky, Dynamics of Layer Models of Solid Flame Propagation, Physica D, 143 (2000), 109. 

Aldusihn, A.P., Bayliss, A., and Matkowsky, B.J. (2000) Dynamics in layer models of solid flame propagation. Physica D, 143, 109-137. 

J.A. Syage, E.W. Fournier, R. Rianda, R.B. Cohen, Dynamics of flame propagation using laser-induced spark initiation Ignition energy measurements. J. Appl. Phys. 64, 1499-1507 (1988)... 

The rarefaction phase is a characteristic of slow combustion in unconfined and ventilated volumes. The rarefaction phase amplitude may be comparable with the compression phase amplitude. When the flame propagation velocity and the sound speed in the mixture are comparable, pressure waves are generated. The pressure wave amplitude depends on the mixture composition, initial conditions, the geometry and the combustion regime. Gas dynamics of the process must be taken into... 

The third and most interesting mode of the process occurs at C < C < C - This mode is characterized by powerful shock (detonation) waves generated in the system. Intensive chemical energy release supported by gas dynamic surges results in the formation of non-stationary detonation-like complexes with extreme temperature and pressure values. Many investigations into spontaneous modes of flame propagation have been devoted to critical conditions for their generation and the process of their amplification. 

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