Detailed analysis and flamelet modeling of early-stage NO$_x$ formation in a turbulent pulverized coal/ammonia co-combustion flame with differential diffusion

In pulverized coal/ammonia co-combustion systems, differential diffusion is expected to be important due to the co-existence of large molecules in the volatile matter and small molecules such as NH$_3$ and H$_2$. To investigate the role of differential diffusion in early-stage pulverized coal/ammonia co-combustion, a state-of-the-art carrier-phase direct numerical simulation (CP-DNS) is conducted for a turbulent mixing layer with differential diffusion and NO$_x$ formation considered. A three-mixture-fraction flamelet model that was initially developed based on the unity Lewis number assumption is further extended to incorporate the effects of differential diffusion, which are expected to be important in pulverized coal/ammonia co-combustion. Based on the CP-DNS dataset, the suitability of the flamelet model with differential diffusion for predicting NO$_x$ formation is evaluated through an a priori analysis. The NO$_x$ formation mechanism and the assumptions used to build the flamelet model are investigated through a reaction pathway analysis, a chemical timescale analysis, a budget analysis, and a sensitivity analysis. The results show that the proposed model accurately predicts temperature and major species while NO$_x$ predictions show deviations with respect to the CP-DNS due to multi-dimensional diffusion effects.