A consistent flamelet formulation for a reacting char particle considering curvature effects

In the present work, the combustion of a single char particle in quiescent and convective environments is investigated numerically. Fully resolved CFD calculations are carried out considering heterogeneous reactions at the particle surface and detailed homogeneous reactions in the gas phase. Unity and non-unity Lewis number diffusion modeling approaches are employed and compared to each other. The flame shape of the particle in a quiescent atmosphere shows full symmetry whereas the particle in the convective environment exhibits a stagnation region upstream of the particle and a wake region downstream of the particle. The detailed CFD results are used to analyze the flame structure around the char particle and corresponding flamelet simulations are carried out. For the presently investigated case, curvature effects of mixture fraction, species and temperature are found to be significant in almost all the cases. These curvature effects correspond to diffusion tangential to iso-surfaces of mixture fraction. To describe these processes, new extended flamelet equations are derived. The individual terms in the flamelet equations are analyzed for both the quiescent and the convective environment based on the CFD data and the results confirm the importance of tangential diffusion. Except for the quiescent environment and unity Lewis numbers, curvature cannot be neglected for the investigated char combustion case. For all other cases, significant differences between the standard flamelet model and the detailed CFD results are found. On the other hand, applying the extended flamelet equations yields very good agreement with the CFD results.