Optimal Mixing Assumptions for Manifold-Based Modeling of Turbulent Nonpremixed Combustion of Many Streams

Abstract

Many-stream, turbulent nonpremixed combustion simulations often leverage manifold-based modeling strategies to reduce computational expense by making a priori assumptions about the nature of the combustion. In general, the manifold equations for n-stream nonpremixed combustion can be formulated in terms of n-1 independent mixture fractions. However, certain types of multi-stream mixing facilitate the approximation of the full manifold equation solutions with the solutions to lower-dimensional manifold equations, yielding further gains in computational efficiency. For example, if the first stream mixes relatively slowly with the other n-1 streams, then it suffices to solve one-dimensional manifold equations in the first mixture fraction, parameterized by the (locally-constant) ratios between pairs of the other mixture fractions. Depending on the relative mixing rates of the streams (as encoded in the mixture fraction dissipation rate ratios), there are an infinite number of similar one-dimensional manifold formulations that can be derived. Prior simulations of many-stream nonpremixed combustion tended to only employ a subset of these formulations (corresponding to asymptotic assumptions about mixing) and tended to choose a formulation based on user expertise. In the current work, a general Large Eddy Simulation (LES) modeling strategy is developed for identifying and using the optimal one-dimensional manifold formulation on-the-fly. This strategy is applicable to the combustion of an arbitrary number of streams and is not restricted to asymptotic models of mixing. Traditionally, the manifold equations are solved a priori and tabulated, requiring the computation of all possible candidate models. Due to the large number of possible one-dimensional manifold formulations, this approach is clearly intractable here, motivating the adoption of the In-Situ Adaptive Manifold (ISAM) framework for efficiently reusing manifold solutions with In-Situ Adaptive Tabulation (ISAT). The potential of the approach is demonstrated using a three-stream, piloted jet flame with a central inhomogeneous mixture of two fuels and a coflow of air. For this configuration, the on-the-fly modeling strategy developed here achieves orders of magnitude improved descriptions of mixing in many parts of the flame.