A multi-fidelity framework for the estimation of the turbulent Schmidt number in the simulation of atmospheric dispersion

A multi-fidelity framework is presented to accurately predict the turbulent Schmidt number, Sct, with applications to atmospheric dispersion modelling. According to the literature and experimental evidence, different physical correlations can be traced for Sct, relating this quantity to various turbulent parameters. The objective is to derive a reliable formulation for Sct that can be used in various test cases and combined with several turbulence models in the context of Reynolds-averaged Navier-Stokes (RANS) simulations. To achieve that, high-fidelity data are obtained with a delayed Detached Eddy Simulation (dDES) and used in a correlation study to analyze the inter-dependencies of Sct with important turbulent variables. A first data-driven model for Sct is proposed by calibrating the data to the semi-empirical relation by Reynolds. A second model is presented using the results of a correlation study in combination with Principal Component Analysis (PCA). Both data-driven models were verified with the RANS simulation of the Cedval A1-5 case, and 2 additional dispersion cases: the Cedval B1-1 array of building, and the empty street canyon from the CODASC database. The resulting Sct formulation is able to significantly improve the accuracy of the concentration field compared to standard RANS approaches. Furthermore, the validity of the new formulation is demonstrated in combination with several turbulence models.