Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine. The NN training process presents an extraordinary challenge. The multi-dimensional combustion instability problem involves multi-scale lengths and characteristic times in an unsteady flow problem with nonlinear acoustics, addressing both transient and dynamic-equilibrium behaviors, superimposed on a turbulent reacting flow with very narrow, moving flame regions. Accurate interpolation between the points of the training data becomes vital. The NNs proposed here are trained based on data processed from a few CFD simulations of a single-injector liquid-propellant rocket engine with different dynamical configurations to reproduce the information stored in a flamelet table. The training set is also enriched by data from the physical characteristics and considerations of the combustion model. Flame temperature is used as an extra input for other flame variables to improve the NN-based model accuracy and physical consistency. The trained NNs are first tested offline on the flamelet table. These physics-aware NN-based closure models are successfully implemented into CFD simulations and verified by being tested on various dynamical configurations. The results from those tests compare favorably with counterpart table-based CFD simulations.
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