The Effect of Strain Rate on Diffusion Flames

Several steady state and time-dependent solutions to the compressible conservation laws describing direct one-step near-equilibrium irreversible exothermic burning of initially unmixed gaseous reactants, with Lewis-Semenov number unity, are presented. The quantitative investigation first establishes the Burke-Schumann thin-flame solution using the Shvab-Zeldovich formulation. Real flames do not have the indefinitely thin reaction zone associated with the Burke-Schumann solution. Singular perturbation analysis is used to provide a modification of the thin-flame solution which includes a more realistic reaction zone of small but finite thickness. The particular geometry emphasized is the un bounded counterflow such that there exists a spatially constant rate of strain along the flame. While the solutions for diffusion flames under a finite tangential strain rate may be of interest in and of themselves for laminar flow, the problems are motivated by the authors' belief that they are pertinent to the study of diffusion-flame burning in transitional and turbulent shear flows.