Modelling high Schmidt number turbulent mass transfer

We perform Direct Numerical Simulation (DNS) and Reynolds-Averaged Navier-Stokes (RANS) simulations of a plane turbulent channel flow with high Schmidt number mass transfer. The DNS, which considers passive scalars with Schmidt numbers between 1 and 50, is used to analyse the mass transfer coefficient K and the near-wall behaviour of various turbulence quantities. A parameterisation for the turbulent Schmidt number, which varies sharply very close to the wall, is proposed. The RANS simulations, which consider Schmidt numbers between 1 and 500, are performed with the Launder-Sharma low-Reynolds number k-ε model, the ζ-f model and the elliptic blending model. We show that the values of K predicted by the ζ-f and elliptic blending model are in reasonably good agreement with the available numerical and experimental correlations, even without the new parameterisation for the turbulent Schmidt number. The Launder-Sharma model significantly underpredicts K, which is due to incorrect values of the eddy viscosity near the wall. A simple modification of the damping function fμ for the Launder-Sharma model is proposed which significantly improves the prediction of K. The good predictions of the three RANS models studied here are a bit fortuitous as errors in the near-wall profile of the eddy viscosity and the turbulent Schmidt number cancel each other out.