Ignition-Extinction Curve

For the adiabatic condition in which RHL is suppressed, the flame response exhibits the conventional upper and middle branches of the characteristic ignition-extinction curve, with the upper branch representing the physically realistic solutions. It can be noted that the effective Le of this lean methane/air mixture is sub-unity. It can be seen from Figure 6.3.1 that, with increasing stretch rate, first increases owing to the nonequidiffusion effects (S > 0), and then decreases as the extinction state is approached, owing to incomplete reaction. Furthermore, is also expected to degenerate to the adiabatic flame temperature, when v = 0. 

The values of kinetic parameters (pre-exponential factors k0j and activation energies Ej of rate constants k and inhibition constant Kg) can for a particular catalyst be determined by weighted least squares method, Eq. (35), from the light-off or complete ignition-extinction curves measured in experiments with slowly varying one inlet gas variable—temperature or concentration of one component (cf., e.g., Ansell et al., 1996 Dubien et al., 1997 Dvorak et al., 1994 Kryl et al, 2005 Koci et al., 2004c, 2007b Pinkas et al., 1995). 

In Fig. 7.6 the plots of integrated heat against Ru-content of the same libraries at 50 °C and at 150 °C show ignition-extinction curves typical of steady-state exothermic reactions. 

Figure 1 Typical S-shaptd ignition-extinction curve, showing a experimental temperature trace vs external power input for one fixed fueT.air ratio. In addition to surface ignition (a), extinction of the. surface reaction (b) is also indicated. The inset. shows the experimental. stagnation point set up.

Figure 26.2 Ignitions (solid curves), extinctions (dashed curves), HB (open circles), and HB temperatures with the heat of all reactions set to zero (open squares) as functions of inlet H2 concentration in air at 4 atm. The strain rate is 200 s ... 

The observed phenomenon is the so-called ignition-extinction-behaviour. A close examination of Figure 4-11 will explain this terminology. If one follows the curve of possible steady-state operating points, starting at low reference temperature values, a point is reached at which ... 

Figure 2 Experimental ignition and extinction curve for hydrogen oxidation on a platinum foil.

Figure 26.1 shows the mole fraction of H2 just above the surface vs. the surface temperature for a mixture of 10% H2 in air at various pressures. At atmospheric pressure (Fig. 26.1a), the mole fraction of H2 is almost insensitive to surface temperature until a turning point, called an ignition (/i), is reached, where the system jumps from an unreactive state to a reactive one. As the surface temperature decreases from high values, the H2 mole fraction increases, and a Hopf bifurcation (HB) point is first found at 980 K, outside the multiplicity regime. The solution branch between the HBi and the extinction is locally unstable (dashed curve). 

Surl iiec Icmpcraturc K Figure 26.1 The mole fraction of H2 just above the surface as a function of the surface temperature for 1 (a), 3 (6), and 4 atm (c), respectively. Gas-phase ignitions and extinctions are represented by arrows. The HB and VH points are indicated with circles and triangles, respectively. Stable and unstable branches are represented by solid and dashed curves, respectively. The mixture is 10% H2-air and the strain rate is 200 s ... 

We are again concerned with intersections of R and L on the flow diagram. The larger the value of k2, the steeper the minimum gradient of the flow line and hence L will not cut as far into R as tres varies. In particular we may lose the possibility of one or even both tangencies between the curves, and hence lose points of ignition and extinction. To illustrate the effect of the autocatalyst decay through if2 on the stationary-state response we can consider a CSTR which is fed only by the reactant A, so po = 0. 

Figure 6.14 shows these stationary-state solutions as a function of residence time for various small values of k2. The non-zero states exist over a limited range of ires they lie on the upper and lower shores of a closed curve, known as an isola . The size of the isola decreases as k2 increases. At each end of the isola there is a turning point in the locus, corresponding to extinction or washout. There are no ignition points in these curves. 

Fig. 7.2. Thermal or flow diagram for the first-order non-isothermal reaction (FON1) in a non-adiabatic CSTR the rate curve R and the flow line L both depend on the dimensionless residence time, but their intersections still correspond to stationary-state solutions—and tangen-cies to points of ignition or extinction. Note that R has a non-zero value at zero conversion. Exact numerical values correspond to 0ai = 10, t, = tn = A ...

The flow diagram technique works very well for this adiabatic case. This is because, as noted above, the reaction curve R does not vary with the residence time, whereas the gradient of the flow line L does. The condition for an ignition or an extinction point is that R and L should become tangential, as shown in Fig. 7.3. We should simultaneously satisfy... 

When the residence time is varied so that we approach an ignition or extinction point in the stationary-state locus, then the flow and reaction curves L and R become tangential. The condition for tangency is R = L and 8R/da = SL/da. Thus the difference between the slopes of R and L decreases to zero. From eqn (8.17) we see that the tangency condition also causes the value of the eigenvalue A to tend to zero. An alternative interpretation, in... 

The condition tr(J) = det(J) = 0 corresponds to a Hopf bifurcation point moving exactly onto the saddle-node turning point (ignition or extinction point) on the stationary-state locus. Above the curve A the system may have two Hopf bifurcations, or it may have none as we will see in the next subsection. Below A there are two points at which tr (J) = 0, but only one of... 

The theory of adiabatic reaction developed in the previous article is here generalized to the case when heat transfer is present. Consideration of the heat transfer leads to the appearance of new features in the consumptiontime kinetic curves, specifically, the possibility of extinction as the residence time is increased and of self-ignition when the reaction time is decreased (in the previous article, in the adiabatic case, extinction occurred only for a decrease in the reaction time, and self-ignition only for an increase). 

For an adiabatic reaction we found two kinds of features in the curves of the dependence of the percentage consumption on the chemical reaction time. In stable regimes an increase in the time facilitates an increase in the percentage of reacted substance and an increase in the temperature. With an increase in the residence time, for sufficient initial concentration, self-ignition of the mixture is possible in contrast, extinction occurs only when the reaction time is reduced. 

The corresponding features of the curves are portrayed graphically in Fig. la,b,c,d, where a and b are adiabatic ignition and extinction, respectively, and c and d are the new kinds of features just described (the abscissa plots time, the ordinate—the percentage of the reacting substance, which falls when consumption is increased). 

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