The Physics of Scalar Gradients in Turbulent Premixed Combustion and Its Relevance to Modeling

Abstract

ABSTRACTEquations for the absolute value of the scalar gradient and for the infinitesimal distance, between two adjacent iso-scalar non-material surfaces are obtained. ‘Effective’ strain rate normal to the iso-surfaces, which includes flow and physicochemically ‘added’ contributions, is shown to be an essential variable, causing either enhancement or destruction of scalar gradients and reduction or growth of distances between surfaces. Two DNS datasets for turbulent premixed flames, one simulating a statistically planar propagating front in an inflow-outflow configuration and the other computing a jet of a methane-air mixture, surrounded by a coflow of hot products, have been examined. DNS are used to estimate the relative importance of different processes determining the gradients fate. The flow normal strain rate apparently scales with the inverse of the Kolmogorov time microscale. Using as characteristic time, , and length, , where and are the laminar flame thickness and propagating velocity, a dimensionless equation for the time rate of change of depends on five dimensionless parameters, among them the Karlovitz number, ; the contribution of every term in the rate equation depends on the magnitude of compared to the other dimensionless groups. The chemically ‘added’ normal strain rate dominates the time evolution of in the burning and a good share of the preheat regions of the statistically planar flame, whereas ‘added’ and flow normal strain rates are comparable in the turbulent jet flame. Large values of some of these dimensionless parameters hint at the likely importance of accounting for Reynolds and/or Damhöhler numbers dependencies in future work. A consistent definition of an average premixed turbulent flame thickness is presented and its computed values are compared to a previous proposal. Some suggestions to model the molecular mixing term in the context of the scalar PDF transport methodology are discussed. It is hypothesized that the characteristic mixing time should be proportional to the inverse of the ‘effective’ normal strain rate.