Optimal model assumptions for manifold-based modeling of many-stream turbulent nonpremixed combustion

Practical simulations of many-stream turbulent nonpremixed combustion often leverage a priori mixing assumptions to derive manifold-based models that alleviate computational cost. Generally, the governing manifold equations for n-stream combustion can be formulated in terms of n-1 mixture fractions, but, for more than three streams, the dimensionality of the manifold equations would become unwieldy. Therefore, local mixing conditions can be used to locally further simplify these n-1-dimensional equations to one-dimensional equations in a mixture fraction-like variable that is some function of the original n-1 mixture fractions. For instance, if the first stream mixes relatively slowly with the other streams, then it is sufficient to solve 1D manifold equations in the first mixture fraction, parameterized by the (locally constant) values of the other n-2 mixture fractions. There are an infinite number of similar potential one-dimensional manifold formulations that depend on the relative mixing rates (mixture fraction dissipation rates) between the streams, with the optimal candidate model potentially varying throughout the flame. In this work, a general Large Eddy Simulation (LES) modeling strategy is derived for identifying the optimal one-dimensional manifold formulation on-the-fly. In traditional implementations of manifold-based models, the manifold equations are solved a priori and tabulated. However, this would require computation of all possible candidate models, which is clearly intractable. Therefore, the In-Situ Adaptive Manifold (ISAM) framework is adopted in which manifold solutions are computed on-the-fly and stored for efficient reuse with In-Situ Adaptive Tabulation (ISAT). The optimal model depends on the relative magnitudes of the mixture fraction dissipation rates, which become inputs to ISAM. The approach is demonstrated using a three-stream, piloted jet flame with a central inhomogeneous mixture of two fuels.