Modelling high Schmidt number turbulent mass transfer

Abstract

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.