Strain rate flame extinction

It is expected that as the strain rate increases, the overall coupling between the surface and the gas-phase increases, since the flame is pushed toward the surface. Figure 26.6a shows the wall heat flux that can be extracted from the system, and the fuel mole fraction near the surface vs. the inverse of the strain rate for 28% inlet H2 in air, at two surface temperatures. The end points of the curves in Fig. 26.6, at high-strain rates, are the extinction points. The conductive heat flux exhibits a maximum as the strain rate increases from low values, which is at first counterintuitive. In addition, with increasing strain rate the fuel mole fraction increases monotonically, while the mole fractions of NOj, decrease, as seen in Fig. 26.66. The species mole fractions show sharper changes with strain rate near extinction, as the mole fractions of radicals decrease sharply near extinction. 

Comparison of static- and dynamic-extinction stretch rates for various hydrogen/air flames. When the equivalence ratio is sufficiently rich, the dynamic-extinction strain rate can be substantially lower than the corresponding static extinction limit. 

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... 

In this section we apply the adaptive boundary value solution procedure and the pseudo-arclength continuation method to a set of strained premixed hydrogen-air flames. Our goal is to predict accurately and efficiently the extinction behavior of these flames as a function of the strain rate and the equivalence ratio. Detailed transport and complex chemical kinetics are included in all of the calculations. The reaction mechanism for the hydrogen-air system is listed in Table... 

Strain Rate Extinction. We performed a sequence of strain rate calculations for an 8.4% and a 9.3% (mole fraction) hydrogen-air flame. The equivalence ratios of these flames are = 0.219 and = 0.245, respectively. In both cases the Lewis number of the deficient reactant (hydrogen) was significantly less than one. In particular, at the input jet, the Lewis numbers were equal to 0.29 for both the 8.4% flame and the 9.3% flame. We also found that these values did not change by more than 15% through the flame. 

Figure 7. Extinction curve illustrating the maximum temperature versus the equivalence ratio for hydrogen-air flames with a strain rate of a = 1000...

Let us reconsider the critical flame temperature criterion for extinction. Williams [25], in a review of flame extinction, reports the theoretical adiabatic flame temperatures for different fuels in counter-flow diffusion flame experiments. These temperatures decreased with the strain rate (ua0/x), and ranged from 1700 to 2300 K. However, experimental measured temperatures in the literature tended to be much lower (e.g. Williams [25] reports 1650 K for methane, 1880 K for iso-octane and 1500 K for methylmethracrylate and heptane). He concludes that 1500 50 K can represent an approximate extinction temperature for many carbon-hydrogen-oxygen fuels burning in oxygen-nitrogen mixtures without chemical inhibitors . 

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. 

The opposed-flow geometry has some important differences, as well as benefits, compared with the burner-stabilized flat flame (e.g., Fig. 1.1). One is that the strain field can be varied by controlling the flow rate, ranging from an essentially strain-free situation to a flame extinction. As discussed subsequently, this flow configuration can be used experimentally for the accurate measurement of laminar burning velocities [238,438,448]. 

Fig. 17.9 Selected species profiles in opposed-flow, premixed, twin flames [214]. The solution in the upper panel is at a high strain rate, which is very near extinction, and that in the lower panel is far from extinction. Both are for a mixture of 9% methane in air. The flow is from left to right, with the symmetry plane on the right.

In addition to the low-strain limit, which can be used to determine laminar burning velocities, the opposed-flow configuration can also be used to determine high-strain-rate extinction limits. As the inlet velocities increase, the flame is pushed closer to the symmetry plane and the maximum flame temperature decreases. There is a flow rate beyond which a flame can no longer be sustained (i.e., it is extinguished). Figure 17.11 illustrates extinction behavior for premixed methane-air flames of varying stoichiometries. 

Fig. 17.11 Extinction behavior of strained, opposed-flow, premixed, methane-air flames. The left-hand panel shows the dependence of the maximum temperature at the symmetry plane as a function of the semi-infinite strain-rate parameter a, for five different mixture stoichiometries. The right-hand panel compares measured extinction strain rates [238] with predictions for both the semi-infinite and finite-gap model formulations. The nozzle separation distance is 7 mm (i.e., 3.5 mm from nozzle to symmetry plane).

The general idea of arc-length continuation is illustrated in the upper panel of Fig. 17.13. The illustration is motivated by the premixed, opposed-flow, twin-flame extinction. The maximum flame temperature (at the symmetry plane) is shown as a function of the inlet velocity U. This is essentially the same situation as shown in Fig. 17.11, although in Fig. 17.11 the reciprocal strain rate 1 /a, and not the inlet velocity, is used as the parameter. 

As the strain rate increases (e.g., higher inlet velocities), the flame can be extinguished. Determine how process pressure, wafer temperature, and mixture stoichiometry affect the extinction limits. 

This experimental investigation was motivated by the requirements of lean-premixed methane-air flames in modern gas-turbine combustors and the periodic extinction and relight observed close to the lean limit [1]. The first involves low equivalence ratios with possible dynamic effects, and the second involves a strain rate mechanism that may imply oscillations in bluff-body stabilized flames at all equivalence ratios. Opposed flames are used here to examine the nature of extinction, and to a lesser extent ignition to quantify extinction velocities and times and to determine limitations of this comparatively simple arrangement. The same arrangement was used in investigations of the corresponding isothermal flow [2]. 

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