Bifurcation and Asymptotic Analyses of Hydrogen  Diffusion Flames
Abstract
The objective of this study is to investigate the structure of the steady, counterflow, hydrogenair diffusion flame by bifurcation and asymptotic methods in two different regimes of interest. First, ignition for oxidizerstream temperatures T_infty larger than or of the order of the crossover temperature T_ {c} associated with the second explosion limit of hydrogen is considered. Two types of solutions are identified, a frozen solution that always exists because for hightemperature ignition all rates of relevant steps are proportional to concentrations of intermediate radicals, and an ignited solution, represented by a branch of the curve giving the maximum concentration of radicals in terms of the strain time. The form of this ignited branch is investigated for twostep reduced chemistry. It is found that for T_infty> T_{c } this branch bifurcates from the frozen solution if the strain time is increased to a critical value. For T_infty larger than a value T_{rm s}>T_{ rm c} the effects of chemical heat release are small and ignition is always gradual in the sense that the limiting ignitedbranch slope is positive. For T _infty in the range T_ {rm c}<T_infty < T_ {rm s} the heat release associated with the radicalconsumption step causes the limiting ignition branch slope to become negative producing abrupt ignition which leads to an S curve. For values of T_ infty below crossover the ignited branch appears as a Cshape curve unconnected to the frozen solution. Although the qualitative behavior that emerges agrees well with numerical results, it is shown that at least three overall steps, with O and H atoms as the chainbranching species and a detailed model adopted for the flow field, are necessary to provide accuracy. The second regime considered is that of a vigorously burning flame corresponding to strain times larger than the characteristic chemical time of threebody recombination reactions. Under these conditions, it is shown that the reactants can coexist only within a thin reaction zone separating two radicalfree equilibrium regions. Matching the solutions from the inner reaction region with those from the outer equilibrium regions, determined by introduction of appropriate conserved scalars, yields a firstorder asymptotic solution to the problem, which compares favorably with results of numerical integrations. The results help to improve understanding of flame structure and provide information needed in design of high speed airbreathing propulsion devices.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT.......105S
 Keywords:

 COUNTER FLOW;
 Engineering: Mechanical; Physics: Fluid and Plasma; Engineering: Aerospace