Scalar mass conservation in LES of soot formation using mixture fraction-based combustion models

Mixture fraction-based models, such as non-premixed flamelet or Conditional Moment Closure (CMC) models, find widespread application in the investigation of turbulent combustion and pollutant formation. These models solve for the mixing field in physical space, while the chemistry solution is obtained in mixture fraction space. The coupling between the two fields is accomplished by two flow-dependent parameters governing the transport in mixture fraction space. These parameters must be computed consistently with the mixture fraction field evolution in order to preserve scalar mass conservation. Analytic expressions can be derived for obtaining these flow parameters consistently to the widely applied presumed Filtered Density Function (FDF) approach. Two approaches are considered in this paper: the local model formulates the local flow parameters consistently with the local FDF evolution before determining the global flow parameters through volume averaging. The global model integrates the FDF in physical space first and then determines the global flow parameter directly from the global mixture distribution evolution. These two models are employed in Large Eddy Simulations (LES) of an auto-igniting -dodecane spray. The simulation results are compared with each other and to a conventional flow parameters model, with a specific focus on scalar mass conservation. Both new models outperform the conventional model in terms of scalar mass conservation, with the most pronounced effect observed for soot. Furthermore, it is demonstrated that, although both new models are analytically equal, numerical errors arising from scalar convection terms in the LES solver impact mass conservation properties differently. The local model accurately predicts conditional flow parameters but suffers from numerical inconsistencies within discretized equations, resulting in scalar mass conservation errors, particularly for highly-diffusive numerical schemes. In contrast, the global model incorporates numerical errors from the flow solver within the flow parameters, thus yielding small conservation errors for all considered scalar convection schemes.