On the incorporation of conservation laws in machine learning tabulation of kinetics for reacting flow simulation

Abstract

Tabulation of chemical mechanisms with artificial neural networks (ANNs) offers significant speed benefits when computing the real-time integration of reaction source terms in turbulent reacting flow simulations. In such approaches, the ANNs should be physically consistent with the reaction mechanism by conserving mass and chemical elements, as well as obey the bounds of species mass fractions. In the present paper, a method is developed for satisfying these constraints to machine precision. The method can be readily applied to any reacting system and appended to the existing ANN architectures. To satisfy the conservation laws, certain species in a reaction mechanism are selected as residual species and recalculated after ANN predictions of all of the species have been made. Predicted species mass fractions are set to be bounded. While the residual species mass fractions are not guaranteed to be non-negative, it is shown that negative predictions can be avoided in almost all cases and easily rectified if necessary. The ANN method with conservation is applied to one-dimensional laminar premixed flame simulations, and comparisons are made with simulations performed with direct integration (DI) of chemical kinetics. The ANNs with conservation are shown to satisfy the conservation laws for every reacting point to machine precision and, furthermore, to provide results in better agreement with DI than ANNs without conservation. It is, thus, shown that the proposed method reduces accumulation of errors and positively impacts the overall accuracy of the ANN prediction at negligible additional computational cost.