An improved machine learning method for thermochemistry tabulation, with application to LES-PDF simulations of piloted diffusion and swirl-bluff-body stabilised flames with NOx formation

Many turbulent combustion modelling approaches require real-time computation of reaction source terms, which is time-consuming and represents a bottleneck of turbulent combustion simulations. In order to speed up the reaction computation process, an artificial neural network (ANN) thermochemistry tabulation methodology has been proposed and developed in our previous work (Ding et al., 2021). In the present work, this methodology is further developed and applied to thermochemistry that includes NO x formation, which poses further challenges due to the small concentrations of the N-containing species. In particular, we build on the Multiple Multilayer Perceptrons (MMLP) concept, which aims to improve prediction accuracy by systematically combining multiple ANNs. A new method, MMLP-II, is proposed in this work, which trains different ANNs to predict states with different ranges of initial species concentration, in contrast to the previous MMLP-I method which trains several ANNs with different ranges of output magnitude. Both MMLP methods are applied to tabulate the complete GRI-3.0 mechanism and the resulting ANNs are tested on two different turbulent methane flames: Sandia flame D and Sydney flame SMA2. It is found that MMLP-II method can reduce the ANN error accumulation of minor species, and very accurate results are obtained in both turbulent flames. The successful application to two different turbulent combustion problems is indicative of the capacity for generalisation of the ANN tabulation approach. Finally, the reaction integration step is accelerated by a factor of about 15 with ANNs, thus rendering chemical kinetics no longer the bottleneck of the whole simulation. Novelty and significance A new ANN thermochemistry tabulation methodology is developed, aimed at providing the higher accuracy needed for predicting species with small concentrations, as encountered in NO x chemistry. The methodology is applied to two different turbulent flames with NO x formation: a piloted diffusion flame (Sandia D) and a swirl-bluff-body stabilised flame (Sydney SMA2). The results demonstrate that the method provides both high accuracy and capacity for generalisation. The LES-PDF method is employed here, but the method is applicable to any method that involves real-time calculation of thermochemistry.