The use of slow manifolds in reactive flows

In calculations of chemically reactive flows, dimension reduction of reactive systems via the use of slow attracting manifolds is an effective approach to reducing the computational burden. In the reduced description, the reactive system is described in terms of a smaller number of reduced composition variables (e.g., some major species) instead of the full composition (i.e., the full set of chemical species), and the evolution equations for the reduced composition variables are solved. In this work, we address the issues arising from the use of chemistry-based slow manifolds in inhomogeneous reactive flows. Chemistry-based slow manifolds are identified (or constructed) based solely on chemical kinetics (i.e., based on homogeneous reactive systems) without accounting for transport processes such as convection and molecular diffusion. For a class of reaction–diffusion systems, by perturbation analysis, it is shown that three different mechanisms contribute to pulling compositions off the chemistry-based slow manifolds, namely, noninvariance, dissipation–curvature, and differential diffusion effects. As the names indicate, these mechanisms contribute, respectively, if the manifold is not invariant; if the manifold is curved (and there is nonzero molecular diffusion); and if the diffusivities of the species differ. In the regime where the fast chemical time scales are smaller than the physical time scales, the composition perturbations off the slow manifold by these three mechanisms are small. However, these three seemingly small perturbations introduce three generally nontrivial terms into the governing equations for the reduced compositions, which in general are of leading order. Moreover, for the convection–reaction–diffusion systems, we validate the close-parallel assumption [Z. Ren, S.B. Pope, A. Vladimirsky, J.M. Guckenheimer, Proc. Combust. Inst. (2007), doi:10.1016/j.proci.2006.07.106] to account for these effects in the reduced description. It is shown that with the use of the close-parallel assumption, the reduced description agrees well with the full reactive system. Different scenarios where these three effects could be neglected are also discussed.