Formula omitted]-[formula omitted] and [formula omitted]-[formula omitted] studies of filtered probability density function models and NO formation prediction in turbulent stratified premixed combustion using machine learning

Abstract

Accurate prediction of NO formation in turbulent stratified premixed combustion using large eddy simulation (LES) is challenging. In the present work, a reaction rate method for NO source modeling in the context of LES was proposed with the focus being placed on accurate modeling of the filtered probability density functions (FPDFs) and joint FPDFs. The NO source and various NO pathways from a direct numerical simulation (DNS) database of turbulent stratified premixed flames were conditionally averaged the progress variable and mixture fraction to provide the lookup table. A random forest (RF) model was developed for the FPDFs/joint FPDFs of the mixture fraction and progress variable. The β-PDF model was also analyzed for comparison. First, the FPDFs and joint FPDFs predicted by the β-PDF and RF models for the progress variable and mixture fraction were compared with those from the DNS data. It was found that the FPDFs and joint FPDFs by the RF model agree well with those from the DNS. In contrast, the β-PDF model failed to accurately capture the joint FPDFs as the correlations of the mixture fraction and progress variable are neglected. Then, the filtered NO source and various NO pathways were modeled a-priori using the lookup table and the joint FPDFs for turbulent stratified premixed flames. The results showed that the RF model reproduces the filtered NO source and NO pathways very well, and performs much better than the β-PDF model. Finally, a-posterior validation of the model performance was carried out in the context of LES. Various quantities from the LES were compared with the DNS filtered quantities. The results showed that the LES/RF model outperforms the LES/β-PDF model in the a-posterior simulation. Overall, the LES/RF model is promising for NO formation modeling using the reaction rate method a-priori and a-posterior in LES of turbulent stratified premixed combustion.