Stagnation flames extinction

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. 

It is often important to predict and understand the flame extinction phenomenon in stagnation or opposed flows. As discussed briefly in Sect. 17.5 and illustrated in Fig. 17.11, the extinction point represents a bifurcation where the steady-state solutions are singular. Thus direct solution of the discrete steady problem by Newton s method necessarily cannot work because the Jacobian is singular and cannot be inverted or factored into its LU products. Moreover, in some neighborhood around the singular point, the numerical problem becomes sufficiently ill-conditioned as to make it singular for practical purposes. 

The subject of flame extinction at the forward stagnation point of the liquid sphere under forced-convection conditions has also been analyzed in some detail (56). Basing his conclusion on theoretical considerations of the chemical kinetics and the hydrodynamics at the forward stagnation point, Spalding stated that for specified physical conditions the flame extinction velocity is proportional to the sphere diameter. This relationship was confirmed by his experimental observations but not by work performed subsequently (1). 

When the flow of air past a burning liquid sphere is increased, the distance of the luminous portion of the flame from the forward stagnation point of the sphere decreases. Spalding (51) reports that at flame extinction the flame distance is a constant (0.9 mm.) for kerosine-wetted spheres (0.7 to 2.6 cm. in diameter). Recently the same constant value has been obtained with ethyl- and n-butyl alcohol-wetted porous spheres (1). 

Tsuji, Ft. and Yamaoka, 1., Structure and extinction of near-limit flames in a stagnation flow, Proc. Combust. Inst., 19,1533,1982. 

Beginning with the innovative work of Tsuji and Yamaoka [409,411], various counter-flow diffusion flames have been used experimentally both to determine extinction limits and flame structure [409]. In the Tsuji burner (see Fig. 17.5) fuel issues from a porous cylinder into an oncoming air stream. Along the stagnation streamline the flow may be modeled as a one-dimensional boundary-value problem with the strain rate specified as a parameter [104], In this formulation complex chemistry and transport is easily incorporated into the model. The chemistry largely takes place within a thin flame zone around the location of the stoichiometric mixture, within the boundary layer that forms around the cylinder. 

V. Giovangigli and M.D. Smooke. Calculation of Extinction Limits for Premixed Laminar Flames in a Stagnation Point Flow. J. Comp. Phys., 68 327-345,1987. 

Stream, is equivalent by symmetry to a one-stream problem in which one of the reactant streams is directed normally onto an infinite adiabatic flat plate at which the no-slip condition is replaced by a zero-stress condition a number of theoretical analyses of this problem have been published (for example, [101], [102], [103], [107], [112], [118]), and nonadiabatic problems also have been studied [112], [118]. The results of these analyses are qualitatively similar to those just discussed, but the multiple-valued dependence of upon k is now found to occur for J > 4 in the symmetric problem by removing the possibility of thermal adjustments occurring in the product stream, the introduction of symmetry strengthens the dependence of the flame temperature on the Lewis number and enables abrupt extinctions to be encountered for many real reactant mixtures that have Lej > 1. There are clear experimental confirmations of this qualitative prediction [114], [120]. As K is increased for reactants with Lcj > 1 to a sufficient extent, the two flames move closer together but experience abrupt extinction at a critical value of k before they reach the stagnation point for reactants with Lcj < 1, the two flames tend to merge at the plane of symmetry prior to abrupt extinction. 

H. Tsuji and I. Yamaoka, An Experimental Study of Extinction of Near-Limit Flames in a Stagnation Flow, Colloque International Berthe lot-Vieille-Mallard-le Chatelier, First Specialists Meeting International) of The Combustion Institute, Pittsburgh The Combustion Institute, 1981, 111-116. 

The images of the single-brush flame were complemented by profiles of temperature, velocity, and calculated strain rates at the stagnation plane (not shown here), and the effects of forcing amplitude and frequency on the reduction in the mean extinction strain rate close to the axis were quantified while previous results [15] were extended to include the effects of bulk velocity and separation on extinction times. The amplitude of imposed oscillations was quoted in terms of the rms of the axial velocity fluctuations at the nominal stagnation point normalized by the bulk velocity [14],... 

Sato, J. 1982. Effect of Lewis number on extinction behaviour of premixed flames in a stagnation flow. 19th Symposium (International) on Combustion Proceedings. Pittsburg, PA The Combustion Institute. 1.541-48. 

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