A generalized Burke-Schumann formulation for hydrogen-oxygen diffusion flames maintaining partial equilibrium of the shuffle reactions

Under a wide range of conditions of ambient pressures, temperatures, dilutions and strain rates, nonpremixed combustion in hydrogen-oxygen systems maintains partial equilibrium of the four two-body chain-carrying reactions while experiencing finite rates of the three-body radical-recombination reactions H + O-2 + M --> HO2 + M and H + H + M --> H-2 + M. There then exists a three-step reduced mechanism, with H as the only intermediate species and concentrations of the radicals O, OH and HO2 related to that of H through steady states. The conservation equations corresponding to this chemical description are formulated here in terms of generalized coupling Functions that account For species diffusivities that differ from the thermal diffusivity, providing a set of equations that describe the flame structure for strain conditions ranging from near extinction to weakly strained flames. As a model example, the formulation is applied to the analysis of flame development in the hydrogen-air laminar mixing layer with free-stream temperatures above the crossover temperature corresponding to the second explosion limit. The formulation can be used for many other model problems as well as for computational studies of nonpremixed combustion in complex configurations involving both laminar and turbulent flows.