A Priori Modeling of NO Formation with Principal Component Analysis and the Convolutional Neural Network in the Context of Large Eddy Simulation

Large
eddy simulation (LES) plays a significant role in turbulent
flame modeling. However, accurate prediction of nitrogen oxide (NOx) formation in turbulent combustion is challenging
in LES as the characteristic timescale of the NO reaction is much
larger than that of fuel oxidation. In the present work, a machine
learning-based model using principal component analysis (PCA) and
the convolutional neural network (CNN) was proposed to predict the
NO reaction rate in the framework of LES. Direct numerical simulation
(DNS) of CH4/air freely propagating premixed flames with
various turbulent intensities was employed to assess the model performance
a priori. The input features of the CNN model include the filtered
temperature and species mass fraction related to NO formation. PCA
was used to reduce the data dimensions and to remove the noise of
the input features. The presented model was trained using samples
from a single case and was tested using samples from cases with various
turbulent intensities and filter sizes. Various NO pathways, that
is, thermal, prompt, N2O, and NO2 pathways,
were examined. The distributions of the modeled NO pathways were compared
with those of the DNS. It was shown that the model performs well in
predicting the thermal, prompt, and N2O pathways, with
relative errors being smaller than 0.4 for these pathways. As for
the NO2 pathway, non-negligible errors were observed, and
the relative errors can be larger than 0.6. The correlations of the
actual and modeled total NO reaction rate are evident, with correlation
coefficients being higher than 0.98 generally. The conditional means
from the CNN model are in good agreement with those from the DNS.
Overall, the CNN model performs well for NO prediction in turbulent
flames with various turbulent intensities.