Modelling and validation of covariance transport equations for large-eddy-simulation of ternary, turbulent mixing

Large-Eddy-Simulation (LES) of turbulent reactive flows have an unclosed term for the filtered reaction rate. In order to obtain this rate, the subgrid-scale mixing state needs to be modelled. For the present case of ternary mixing, like it appears in a coannular jet-in-crossflow configuration, multi-variate Filtered Density Functions (FDFs) are used to model this mixing state. These FDFs are parameterized by the first and second order statistical moments, which include the covariance. It has been shown in literature that the covariance can have a noticable impact on the filtered reaction rate. This work develops and test transport equations for these moments, which include a non-equilibrium model for the subgrid scale scalar dissipation and the subgrad scale scalar cross-dissipation rates. Mixing models are then used to particle ensembles which represent the FDFs with the required moments.