In-Situ Adaptive Manifolds for soot evolution in non-adiabatic turbulent reacting flows

To reduce the computational cost of simulations of turbulent reacting flows, manifold-based combustion models are often employed. In these models, the thermochemical state is projected onto a low-dimensional manifold, which can be computed separately from the flow solver. Traditionally, the model involves the pretabulation of solutions to a set of manifold equations, which are obtained a priori. The inclusion of soot and emissions introduces additional physics due to the importance of radiation heat losses. To account for the effects of heat loss, the number of table dimensions necessarily increases. Consequently, these tables can become very memory intensive and include many thermochemical states that may not even be accessed during the simulation. To reduce this memory burden, the concept of In-Situ Adaptive Manifolds (ISAM) has recently been proposed. Within this framework, necessary manifold solutions are computed on-the-fly and stored for lookup using In-Situ Adaptive Tabulation (ISAT). In this work, ISAM is coupled to a soot model based on the Hybrid Method of Moments (HMOM) model. To incorporate heat losses, the manifold equations are augmented with an equation for the heat loss parameter $H$, which is also evolved in the LES flow solver. The manifold equations are formulated based on a quasi-steady assumption, and a model heat loss source term is multiplied by a constant $\Omega$ to account for varying magnitudes of radiation heat losses from the gas-phase and soot. During runtime, the $H$ field from the LES must be matched by ISAM to produce the correct thermochemical state. An iterative procedure is developed to obtain the correct value of $\Omega$ to ensure consistency of the heat loss parameter between LES and ISAM. The model is demonstrated on the Sandia Sooting Flame. Compared to traditional precomputed tables, ISAM is shown to provide significant memory savings at a minor increase in the computational cost, which is sensitive to the initial guesses for the iterative approach for matching $H$.