Direct and Large-Eddy Simulation of the Compressible Turbulent Mixing Layer

The Large-Eddy Simulation technique of compressible flows and the effect of compressibility on mixing layers are the main subjects of this thesis. Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) of the temporal compressible mixing layer at various Mach and Reynolds numbers have been conducted to investigate these subjects. With respect to the LES technique, Large-Eddy Simulations have been performed at convective Mach numbers 0.2, 0.6 and 1.2 and the results have been compared with filtered DNS-data. It appeared that the dynamic subgrid-models lead to relatively accurate results compared to the other models tested. The dynamic approach turned out to yield acceptable results too in LES of a mixing layer that currently cannot be simulated using DNS. Care has to be taken to ensure that the numerical errors in LES are sufficiently small. It was found that these errors are usually sufficiently small if the filter width equals twice the grid-spacing. In addition to modelling the turbulent stress tensor, compressible LES formally requires the modelling of the subgrid-terms in the energy equation, which do not occur in incompressible LES. However, the compressible Large- Eddy Simulations demonstrated that the turbulent stress tensor is the dominant subgrid-term, even at convective Mach number 1.2. This important subgrid-term was also investigated from a theoretical point of view and realizability conditions for this tensor were derived. Regarding compressibility effects in the mixing layer, shock-waves were found in the three-dimensional DNS at convective Mach number 1.2. Furthermore, we have investigated the cause of the mixing layer growth rate reduction with increasing compressibility, using four DNS-databases covering the range of convective Mach numbers from 0.2 to 1.2. It was found that the growth rate reduction cannot be explained by the dilatational terms, but rather by the reduced pressure fluctuations, leading to reduced pressure strain and turbulent production terms