Oscillatory ignition

Figure A3.14.4. P-T ignition limit diagram for H2 + O2 system showing first, second and third limits as appropriate to a closed reactor. The first and second limits have similar positions in a typical flow reactor, for which there is also a region of oscillatory ignition as indicated.

Johnson B R and Scott S K 1990 Period doubling and chaos during the oscillatory ignition of the CO + O2 reaction J. Chem. Soc. Faraday Trans. 86 3701-5... 

Even though the bifurcation behavior exhibits a Z-shaped curve, it is more complicated due to the existence of the HB. For example, upon ignition, the system is expected to oscillate because no locally stable stationary solutions are found (an oscillatory ignition). Time-dependent simulations confirm the existence of self-sustained oscillations [7, 12]. The envelope of the oscillations (amplitude of H2 mole fraction) is shown in circles (a so-called continuation in periodic orbits). 

K. Chinnick, C. Gibson and J.F. Griffiths, Isothermal Interpretations of Oscillatory Ignition During Hydrogen Oxidation in an Open System, 2 Numerical-Analysis, Proc. Roy. Soc. 405 (1986) 129-142. 

Fig. 5.19. Thep-Ta ignition diagram for an equimolar H2 + O2 mixture with mean residence time tres = 5.2 0.7 s showing region of slow reaction separated by second limit from regions of oscillatory ignition and steady-ignited state. (Reprinted with permission from reference [33], Royal Society of Chemistry.)...

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... 

Fig. 5.32. The p-T regions for steady dark reaction, steady glow, oscillatory glow and oscillatory ignition, and the influence of added H2 for the CO + O2 reaction in a flow reactor with = 8 S , (a) no added H2 (b) 150 ppm added H2 (c) 1500 ppm added H2 (d) 7500 ppm added H2 (e) 10% H2 in final mixture. (Reprinted with permission from reference [64], Royal Society of London.)...

Fig. 6 16. p-Ta) ignition diagram obtained for the combustion of n-butane + oxygen in a well-stirred flow reactor at a mean residence time of 9.4 0.4 s. Different phenomena are identified as follows L, low-temperature stationary states H, high-temperature stationary states CF, oscillatory cool-flames I, oscillatory ignitions. A hysteresis of the boundaries was measured as a result of increasing (solid lines) and reducing (broken lines) the vessel temperature. (After Proudler et al. [58].)... 

Gray, R Griffiths, J. F. Hasko, S. M. Lignola, P. G. Oscillatory ignitions and cool flames accompanying the non-isothermal oxidation of acetaldehyde in a well stirred, flow reactor. Proc. Roy. Soc. Lond. A 1981, 374, 313-339. 

Fig. 7.13 Comparison between model simulations based on ordinary differential equations describing the reduced scheme (solid) and fitted polynomial repro-model (dashed) for oscillatory ignition of CO-H2 mixtures alp = 25 Torr and 0.5 % H2 and initial temperatures (a) 720 K, (b) 735 K, (c) 750 K, (d) 770 K. Reprinted from Brad et al. (2007) with permission from Elsevier...

---