Propagation speed

The balanced equation for turbulent kinetic energy in a reacting turbulent flow contains the terms that represent production as a result of mean flow shear, which can be influenced by combustion, and the terms that represent mean flow dilations, which can remove turbulent energy as a result of combustion. Some of the discrepancies between turbulent flame propagation speeds might be explained in terms of the balance between these competing effects. 

The most recent model of de Gennes and coworkers [100,101], the threshold toughness is related to the extra surface and elastic energy of the individual chains as they are pulled out. The threshold toughness and the critical crack propagation speed are given by... 

Recognizing that the information transmission is often both nonuniform (since the left and right fronts do not always propagate outward from the perturbation with a single well-defined velocity), and dependent on choice of initial states, one can instead define maximal and minimal average propagation speeds, and A " " ... 

If the strain rate exerted on an edge flame becomes very small, especially for weak intensity flames, the radiative heat loss could influence the edge behavior significantly. Consequently, the propagation speed could decrease appreciably in low-strained flames [29], as marked in fhe dash-dot line. 

Behavior of edge propagation speed with concentration gradient (A transition, B tribrachial, C bibrachial, D monobrachial and near extinction regimes). (From Chung, S.H., Proc. Combust. Inst., 31, 877,2007.)... 

Effect of strain rate on edge propagation speed with N2 dilution in CH4/O2/N2 mixtures. (From Cha, M.S. and Ronney, P.D., Combust. Flame, 146,312, 2006. With permission.)... 

The existence of tribrachial structure at the base of lifted flame implies that the stabilization of liftoff flames is controlled by the characteristics of tribrachial edge flames. The coexistence of three different types of flames dictates that the edge is located along the stoichiometric contour [52] and the premixed wings have the propagation characteristics, whose speed should balance with the local flow velocity for the edge to be stationary. In the first approximation, the propagation speed was assumed to be constant [10]. 

J. Lee, S. H. Won, S. H. Jin, S. H. Chung, O. Fujita, and K. Ito, Propagation speed of tribrachial (triple) flame of propane in laminar jets under normal and micro gravity conditions. Combust. Flame 134 411M20,2003. 

M. K. Kim, S. H. Won, and S. H. Chung, Effect of velocity gradient on propagation speed of tribrachial flames in laminar coflow jets, Proc. Combust. Inst. 31 901-908,2007. 

The mechanism is based on strong cooling of the products adjacent to the walls and injection of the cooled products in the form of an annular jet behind the flame, reducing its width as soon as the speed of the annular jet, proportional to the circumferential speed of the gas at the flame location becomes larger than the propagation speed of the edge flame. 

If the step is only equilibrium controlled, a lumped analysis of both fluid and solid phase is possible and the corresponding nonlinear wavefront analysis is straight forward too. Analysis of propagation speed data yield information about the relevant equilibrium sorption mechanism (7). The different form of the transients when a reaction step has been stimulated, is discussed in the Appendix. 

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