Premixed Counterflow Flames

This section emphasizes on flame quenching by stretch, as well as highlights and separately discusses the four aspects of counterflow premixed flame extinction limits, including (1) effect of nonequidiffusion, (2) influence of different boundary conditions, (3) effect of pulsating instability, and (4) relahonship of the fundamental limit of flammability. 

Ju, Y, Guo, H., Maruta, K., and Niioka, T., Flame bifurcations and flammable regions of radiative counterflow premixed flames with general Lewis numbers. Combust. Flame, 113, 603, 1998. 

In Chapter 6.3, C-J. Sung examines extinction of counterflow premixed flames. He emphasizes flame quenching by stretch and highlights four aspects of counterflow premixed flame extinction limits effect of nonequidiffusion, parf played by differences in boundary conditions, effect of pulsating insfabilify, and relation to the fundamental limit of flammability. 

In flame extinction studies the maximum temperature is used often as the ordinate in bifurcation curves. In the counterflowing premixed flames we consider here, the maximum temperature is attained at the symmetry plane y = 0. Hence, it is natural to introduce the temperature at the first grid point along with the reciprocal of the strain rate or the equivalence ratio as the dependent variables in the normalization condition. In this way the block tridiagonal structure of the Jacobian can be maintained. The flnal form of the governing equations we solve is given by (2.8)-(2.18), (4.6) and the normalization condition... 

Chao, B.H., Egolfopoulos, F.N., and Law, C.K., Structure and propagation of premixed flame in nozzle-generated counterflow. Combust. Flame, 109,620,1997. 

Observed premixed edge flames (a) Bunsen flame-tip opening, (b) propagating premixed flame in tube (From Jarosinski, J., Strehlow, R.A., and Azarbarzin, A., Proc. Combust. Inst., 19, 1549, 1982. With permission.), (c) slanted counterflow flame (From Liu, J.-B. and Ronney, P.D., Combust. Sci. Tech., 144,21,1999. With permission.), and (d) spinning premixed flames in sudden expansion tube [7]. 

One significant result from the studies of stretched premixed flames is that the flame temperature and the consequent burning intensity are critically affected by the combined effects of nonequidiffusion and aerodynamic stretch of the mixture (e.g.. Refs. [1-7]). These influences can be collectively quantified by a lumped parameter S (Le i-l)x, where Le is the mixture Lewis number and K the stretch rate experienced by the flame. Specifically, the flame temperature is increased if S > 0, and decreased otherwise. Since Le can be greater or smaller than unity, while K can be positive or negative, the flame response can reverse its trend when either Le or v crosses its respective critical value. For instance, in the case of the positively stretched, counterflow flame, with k>0, the burning intensity is increased over the corresponding unstretched, planar, one-dimensional flame for Le < 1 mixtures, but is decreased for Le > 1 mixtures. 

It is also well known that there exist different extinction modes in the presence of radiative heat loss (RHL) from the stretched premixed flame (e.g.. Refs. [8-13]). When RHL is included, the radiative flames can behave differently from the adiabatic ones, both qualitatively and quantitatively. Figure 6.3.1 shows the computed maximum flame temperature as a function of the stretch rate xfor lean counterflow methane/air flames of equivalence ratio (j) = 0.455, with and without RHL. The stretch rate in this case is defined as the negative maximum of the local axial-velocity gradient ahead of the thermal mixing layer. For the lean methane/air flames,... 

The modeling of steady-state problems in combustion and heat and mass transfer can often be reduced to the solution of a system of ordinary or partial differential equations. In many of these systems the governing equations are highly nonlinear and one must employ numerical methods to obtain approximate solutions. The solutions of these problems can also depend upon one or more physical/chemical parameters. For example, the parameters may include the strain rate or the equivalence ratio in a counterflow premixed laminar flame (1-2). In some cases the combustion scientist is interested in knowing how the system mil behave if one or more of these parameters is varied. This information can be obtained by applying a first-order sensitivity analysis to the physical system (3). In other cases, the researcher may want to know how the system actually behaves as the parameters are adjusted. As an example, in the counterflow premixed laminar flame problem, a solution could be obtained for a specified value of the strain... 

SMOOKE GIOVANGIGLI Counterflow Premixed Laminar Flames 405... 

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