Development of a DNS-FDF Approach to Inhomogeneous Non-Equilibrium Mixing for High Schmidt Number Flows

Abstract

Turbulent mixing is of great importance in a wide range of engineering applications. In process engineering it is the rate determining step when the chemical time scales are small compared to the turbulent ones, and thus has a large impact on the product properties. As processes like precipitation take place in aqueous environments, such processes are challenging for numerical simulation. This is due to the wide range of involved scales, starting from the integral scale of the mixing apparatus L _Φ down to the Batchelor scale $\eta B = \eta K/\sqrt{Sc}$ [1], which can be much smaller than the Kolmogorov scale ηK due to the high Schmidt numbers encountered in aqueous solutions. To correctly predict the reaction rates both, the large scale inhomogeneities as well as the molecular mixing on the Batchelor scale have to be predicted correctly. In the last two decades two useful trends could be observed. With the advent of increasing computer power Direct-Numerical Simulation (DNS) became available for the simulation of low Reynolds number flows and was used intensively for analysis of such flows. Nevertheless a DNS of very high Sc flows is still out of reach.