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Transport-chemistry coupling in the reduced description of reactive flows

The reduced description of inhomogeneous reactive flows by chemistry-based low-dimensional manifolds is complicated by the transport processes present and the consequent transport-chemistry coupling. In this study, we focus on the use of intrinsic low-dimensional manifolds (ILDMs) to describe inhomogeneous reactive flows. In particular we investigate three different approaches which can be used with ILDMs to incorporate the transport-chemistry coupling in the reduced description, namely, the Maas–Pope approach, the ‘close-parallel’ approach, and the approximate slow invariant manifold (ASIM) approach. For the Maas–Pope approach, we validate its fundamental assumption: that there is a balance between the transport processes and chemical reactions in the fast subspace. We show that even though the Maas–Pope approach makes no attempt to represent the departure of composition from the ILDM, it does adequately incorporate the transport-chemistry coupling in the dynamics of the reduced system. For the ‘close-parallel’ approach, we demonstrate its use with the ILDM to incorporate the transport-chemistry coupling. This approach is based on the ‘close-parallel’ assumption that the compositions are on a low-dimensional manifold which is close to and parallel to the ILDM. We show that this assumption implies a balance between the transport processes and chemical reaction in the normal subspace of the ILDM. The application of the ASIM approach in general reactive flows is investigated. We clarify its underlying assumptions and applicability. Also in the regime where the fast chemical time scales are much smaller than the transport time scales, we reformulate the ASIM approach so that explicit governing PDEs are given for the reduced composition. For the reaction–diffusion systems considered, we show that all the three approaches predict the same dynamics of the reduced compositions, i.e. each results in the same evolution equations for the reduced composition variables (to leading order). We also show that all the three approaches are valid only when the fast chemical time scales are much smaller than the transport time scales. Moreover, a simplified ASIM approach is proposed.