CSP analysis of a transient flame-vortex interaction: Time scales and manifolds

The interaction of a two-dimensional counter-rotating vortex-pair with a premixed methane-air flame is analyzed with the Computational Singular Perturbation (CSP) method. It is shown that, as the fastest chemical time scales become exhausted, the solution is attracted towards a manifold, whose dimension decreases as the number of exhausted time scales increases. A necessary condition for a chemical time scale to become exhausted is that it must be much faster than the locally prevailing diffusion and convection time scales. Downstream of the flame, the hot products are in a regime of near-equilibrium, characterized by a large number of exhausted fast chemical time scales and the development of a low dimensional manifold, where the dynamics are locally controlled by slow transport processes and slow kinetics. In the flame region, where intense chemical and transport activity takes place, the number of exhausted chemical time scales is relatively small. The manifold has a large dimension and the driving time scale is set by chemical kinetics. In the cold flow region, where mostly reactants are present, the flow regime can be described as frozen, as the active chemical time scales are much slower than the diffusion and convection time scales; the driving scale set by diffusion. The algebraic relations among the elementary rates, which describe the manifold, are discussed along with a classification of the unknowns in three classes: i) CSP radicals; ii) trace; and, iii) major species. It is established that the optimal CSP radicals must be: i) strongly affected by the exhausted fast chemical time scales; and, ii) significant participants in the algebraic relations describing the manifold. The identification of CSP radicals, trace and major species, is a prerequisite for simplification or reduction of chemical kinetic mechanisms.