ADM-modelling approach for SEMI-Direct Numerical Simulation of turbulent mixing and mass transport

This paper presents a model for calculating turbulent mixing and mass transport in high Schmidt number flows based on a Direct Numerical Simulation of the flow field and a solution of the filtered transport equation of the scalar field. We call this approach SEMI-DNS. It is shown that, in this strategy, the only term that needs to be modelled is the cross stress term C _i = u _ic′, which eases modelling of the unresolved scales of the scalar field considerably. An a-priori analysis of the DNS data of turbulent channel flow at Re _τ = 180 and Sc = 3 and Sc = 10 shows that this term is small. Because of the quasi linearity of the scalar transport equation, the ADM model is applied for this term, and SEMI-DNS calculations are performed up to Sc = 1000. Comparisons with full DNS results up to Sc = 10 and global quantities from the literature up to Sc = 1000 show excellent agreement.