Parameterization of the turbulent Schmidt number in the numerical simulation of turbulent open channel flows

Computational Fluid Dynamics (CFD) is being increasingly used to study a wide variety of complex environmental phenomena. Oftentimes, the accuracy and reliability of CFD modelling and the correct interpretation of CFD results become under scrutiny because of implementation issues. One aspect that must be carefully addressed during the simulation process pertains to the proper selection of the input parameters. If the approach of the model is based on the Reynolds-Averaged Navier–Stokes equations (RANS), the turbulent scalar fluxes are generally estimated by assuming the gradient-diffusion hypothesis, which requires the definition of the turbulent Schmidt number, ScT. This parameter is defined as the ratio of momentum diffusivity to mass diffusivity in a turbulent flow. In spite of its widespread use, no universally-accepted values of this parameter have been established. It is sometimes assumed, by analogy between momentum and mass transport, that ScT is equal to one (Prandtl analogy); however, different values are suggested in commercial CFD codes and applications, and other empirical values have been used in different studies. This paper presents two case studies where the role of a correct parameterization of the turbulent Schmidt number for a reliable estimation of turbulent transport is assessed. They are: (1) modelling of contaminant dispersion due to transverse turbulent mixing in a shallow water flow, and (2) modelling of sediment-laden, open-channel flows. The comparison between numerical results and the available experimental data shows that the turbulent Schmidt number is a key parameter to obtain satisfactory predictions of both solute mixing and sediment transport in suspension.