Complexity in the oscillatory ignition region

With different mixture compositions, however, the range of behaviour supported becomes richer. The variation of the oscillatory period with the ambient temperature for a stoichiometric mixture (2H.2 -i- O2) at an operating pressure of 16 Torr and a residence time of 4 s is compared with 

The p-T. ignition diagram for a stoichiometric 2H2 + O2 mixture with mean residence time fres = 2.0 0.2 s showing additional region of complex oscillatory ignition. (Reprinted with permission from reference [33], Royal Society of Chemistry.) 

The ignition limit lies in the region of the p-T plane, corresponding to the second limit in classical closed vessels, and so we may surmise that the dominant features of the mechanism will be the competition between the branching cycle (1-3) and the gas-phase termination step producing HO2, step (5). A full steady-state analysis on the intermediates OH and O would introduce (out)flow terms for each species and a fairly complex polynomial in terms of fres- The full analysis appears in Chapter 4 of this volume. For now, we can note that the typical residence times of interest, 1 to 10 s, 

The loss of oscillatory ignition can also be rationalized on the above 

In order to model the oscillatory waveform and to predict the p-T locus for the (Hopf) bifurcation from oscillatory ignition to steady flame accurately, it is in fact necessary to include more reaction steps. Johnson et al. [45] examined the 35 reaction Baldwin-Walker scheme and obtained a number of reduced mechanisms from this in order to identify a minimal model capable of semi-quantitative p-T limit prediction and also of producing the complex, mixed-mode waveforms observed experimentally. The minimal scheme depends on the rate coefficient data used, with an updated set beyond that used by Chinnick et al. allowing reduction to a 10-step scheme. It is of particular interest, however, that not even the 35 reaction mechanism can predict complex oscillations unless the non-isothermal character of the reaction is included explicitly. (In computer integrations it is easy to examine the isothermal system by setting the reaction enthalpies equal to zero this allows us, in effect, to examine the behaviour supported by the chemical feedback processes in this system in isolation 

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