  Neural networks (NN) are implemented as sub-grid flame models in a large-eddy
simulation of a single-injector liquid-propellant rocket engine with the aim to
replace a look-up table approach. 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. A major novel aspect of the proposed NNs is
that they are trained to reproduce relevant portions of the information stored
in a flamelet table by using only limited data from a few CFD simulations of a
single-injector liquid-propellant rocket engine under different dynamical
configurations. This is made possible by enriching the training set with
contrived data resulting from the physical characteristics of the combustion
model and also by including the flame temperature as an extra input to the NNs
that are trained to model other flame variables of interest. These
physics-aware NN-based closure models are first tested offline by comparing
them directly with the flamelet table and then are successfully implemented
into CFD simulations in place of the flamelet table and verified on various
dynamical configurations. The results from those tests compare favorably with
counterpart table-based CFD simulations. Computational advantages of the
approach are discussed.
