Extinction premixed-flame

Strehlow R.A., Noe K.A., and Wherley B.L., The effect of gravity on premixed flame propagation and extinction in a vertical standard flammability tube, Proc. Combust. Inst., 21 1899-1908,1986. 

Sung C.J. and Law C.K., Extinction mechanisms of nearlimit premixed flames and extended limits of flammability, Proc. Combust. Inst., 26 865-873,1996. 

Laminar flame speed is one of the fundamental properties characterizing the global combustion rate of a fuel/ oxidizer mixture. Therefore, it frequently serves as the reference quantity in the study of the phenomena involving premixed flames, such as flammability limits, flame stabilization, blowoff, blowout, extinction, and turbulent combustion. Furthermore, it contains the information on the reaction mechanism in the high-temperature regime, in the presence of diffusive transport. Hence, at the global level, laminar flame-speed data have been widely used to validate a proposed chemical reaction mechanism. 

Egolfopoulos, F.N., Zhang, H., and Zhang, Z., Wall effects on the propagation and extinction of steady, strained, laminar premixed flames. Combust. Flame, 109,237,1997. 

Kobayashi, H. and Kitano, M., Extinction characteristics of a stretched cylindrical premixed flame. Combust. Flame, 76,285,1989. 

Ishizuka, S. and Law, C.K., An experimental study on extinction and stability of stretched premixed flames, Proc. Combust. Inst., 19,327,1982. 

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,... 

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. 

Similarly, Figure 6.3.9b depicts the situation in which partial quenching of the flame results from unequal composition of the reactant mixtures issued from the inner and outer tubes, while keeping the mean velocities constant. If the equivalence ratio in the inner tube is excessively leaner or richer to exceed a typically flammable range, it would result in local extinction, thereby exhibiting a hole in the center of the premixed flame. 

The creation of a steady flame hole was previously carried out by Fiou et al. [36]. In their experiments, a steady-annular premixed edge flame was formed by diluting the inner mixture below the flammability limit, for both methane/air and propane/air mixtures. They found that a stable flame hole was established when the outer mixture composition was near stoichiometry. Their focus, however, was on the premixed flame interaction, rather than on the edge-flame formation, extinction, or propagation. 

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... 

A number of theoretical (5), (19-23). experimental (24-28) and computational (2), (23), (29-32). studies of premixed flames in a stagnation point flow have appeared recently in the literature. In many of these papers it was found that the Lewis number of the deficient reactant played an important role in the behavior of the flames near extinction. In particular, in the absence of downstream heat loss, it was shown that extinction of strained premixed laminar flames can be accomplished via one of the following two mechanisms. If the Lewis number (the ratio of the thermal diffusivity to the mass diffusivity) of the deficient reactant is greater than a critical value, Lee > 1 then extinction can be achieved by flame stretch alone. In such flames (e.g., rich methane-air and lean propane-air flames) extinction occurs at a finite distance from the plane of symmetry. However, if the Lewis number of the deficient reactant is less than this value (e.g., lean hydrogen-air and lean methane-air flames), then extinction occurs from a combination of flame stretch and incomplete chemical reaction. Based upon these results we anticipate that the Lewis number of hydrogen will play an important role in the extinction process. 

The control volume analysis of the premixed flame of Section 4.5.4 can be used together with the analysis here in Section 9.9 for the diffusion flame to relate the two processes. We assume the kinetics is the same for each and given as in Equation (9.102). Since we are interested in extinction, it is reasonable to assume the heat loss from the flame to be by radiation from an optically thin flame of absorption coefficient, k ... 

The right-hand side (RHS) of Equations (9.116) and (9.119) represent the net heat loss and the left-hand side (LHS) represents the energy gain. The gain and the loss terms can be plotted as a function of the flame temperature for both the diffusion and premixed flames as Semenov combustion diagrams. Intersection of the gain and loss curves indicates a steady solution, while a tangency indicates extinction. 

The tendency of premixed flames to detach from the flame holder to stabilize further downstream has also been reported close to the flammability limit in a two-dimensional sudden expansion flow [27]. The change in flame position in the present annular flow arrangement was a consequence of flow oscillations associated with rough combustion, and the flame can be particularly susceptible to detachment and possible extinction, especially at values of equivalence ratio close to the lean flammability limit. Measurements of extinction in opposed jet flames subject to pressure oscillations [28] show that a number of cycles of local flame extinction and relight were required before the flame finally blew off. The number of cycles over which the extinction process occurred depended on the frequency and amplitude of the oscillated input and the equivalence ratios in the opposed jets. Thus the onset of large amplitudes of oscillations in the lean combustor is not likely to lead to instantaneous blow-off, and the availability of a control mechanism to respond to the naturally occurring oscillations at their onset can slow down the progress towards total extinction and restore a stable flame. 

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