Composition-Space Behavior of Diffusion-Reaction Systems

Species concentrations in homogeneous well-stirred reacting (WSR) systems with multiple time scales mostly access only a small portion (slow manifold) of the permitted composition space. This offers a mathematically sound basis for reducing complex kinetics. Computational investigation of such slow manifolds in inhomogeneous reaction systems undergoing diffusion in addition to chemical reaction is the subject of this paper. We perform simulations of a one-dimensional diffusion–reaction system from random non-premixed initial conditions to study the accessed composition space for a variety of diffusion to reaction time scale ratios. A detailed hydrogen–oxygen chemical kinetic set (6 species, 14 reactions) is used. Our results show that, to first order, the effect of random advection and diffusion is merely to increase the accessed state-space dimensionality over that of the WSR by the number of relevant mixture fractions. Circumstances under which the above simplification is not accurate are also identified.