DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.