On the structure of a hydrogen-oxygen diffusion flame

Abstract

A simplified scheme of four chemical reactions is chosen to represent the kinetics of the hydrogen-oxygen system; in particular, this scheme includes the influence of the hydroxyl radical. The diffusion flame supported by this set of reactions is assumed to form behind a (planar, two-dimensional) body of parabolic meridian profile with downstream-pointing vertex. The body initially separates the oxygen and hydrogen streams, which are assumed to have equal speeds and pressures far upstream. (The pressure is subsequently assumed to be constant everywhere.) For pressures of about one atmosphere it is found that nett reaction rates can be treated as infinitely fast; the four reactions then yield four chemical equilibrium equations whose behaviour is dominated by the largeness of the equilibrium constant for the (thermal) dissociation-recombination reaction of hydrogen. The flame-sheet model emerges as the limiting solution when the reciprocal of this large quantity is allowed to vanish. The method of matched asymptotic expansions is used to investigate the structure of the flame which results from a relaxation of this limit. The results bear a satisfactory resemblance to some experimental measurements which, although made in other gas mixtures, exemplify the behaviour of the type of diffusion flames considered.