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A local integral moment (LIM) model is described for numerical calculations of flow structure, molecular mixing, and chemical reactions in complex flows. This physically-based formulation is based on the experimental, numerical, and theoretical observation that gradients of advected and diffused quantities concentrate into universal, self-similar, small-scale structures for large Peclet numbers ReSc. The model incorporates this self-similar structure at the diffusive scales directly through a local parabolization of the governing transport equations on a time-evolving material surface on which the gradients in the velocity and scalar fields are originally centered. These lead to equations governing local integral moments computed along the layer-normal direction at each point on the surface. This procedure effectively transforms the original set of partial differential equations that must be solved throughout a three-dimensional volume to a set of ordinary differential equations that can be solved on a two-dimensional surface. No closure approximations are required. The scalar and scalar dissipation fields are subsequently constructed from the integral moments on this surface, giving the local chemical species concentration fields via a strained diffusion and reaction layer formulation. The model is applied to three different test cases: molecular mixing in a laminar vortex pair, a one-step chemical reaction in a temporally developing shear layer, and inixing and complex chemical reaction by fuel injection into an enclosure. Results obtained in all three cases indicate that the model correctly retains the essential physics underlying such problems while bringing practical calculations of complex flows with complex chemistry within computational reach. W’

LIM modeling of chemical reactions in spatially and temporally developing shear flows