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.

Automated summary

A machine learning-based model utilizing PCA and CNN was proposed to predict NO reaction rate in turbulent flames within the framework of LES. Evaluation using DNS showed good performance in predicting thermal, prompt, and N2O pathways, but larger errors were observed for the NO2 pathway.