Mixing of Fuel Jet in Supersonic Crossflow: Estimation of Subgrid-Scale Scalar Fluctuations
Résumé
Non-reactive large-eddy simulations (LES) of a hydrogen jet injected into a transverse supersonic flow of vitiated air at Mach 2 are conducted. The present investigation is focused on the intertwinement of first- and second-order subgrid-scale (SGS) moments, such as the filtered value of a normalized reference scalar and its associated SGS variance level. Such a reference scalar is often settled to follow the mixing between the jet of hydrogen and the vitiated airflow. The discussion covers the influence of numerical errors, including commutation and discretization errors, as well as the possible effects of the closures retained to represent the unresolved SGS scalar dynamics. The sensitivity of the SGS scalar description, on the former, i.e., numerical errors, is enlightened with a special focus placed on the SGS variance evaluation, which is of practical importance for applications to turbulent reactive flow simulations. The SGS scalar variance is presently calculated by using three distinct procedures, which are at least formally, i.e., mathematically, equivalent. However, the results obtained by using the various procedures display some remarkable differences, which are the subject of the present analysis and discussion. It is finally demonstrated that the different results can be reconcilied together. The present results may thus provide some useful guidance for SGS variance estimation in the context of LES of turbulent scalar mixing and combustion.