Direct Numerical Simulation and Large-Eddy Simulation of wake vortices: Going from laboratory conditions to flight conditions

This paper aims at presenting DNS and LES as applied to the simulation of vortex wakes: in laboratory conditions (moderate to medium Reynolds numbers) and up to real aircraft conditions (high to very high Reynolds numbers). Only incompressible flows are considered. DNS and LES are able to capture complex 3-D physics provided one uses high quality numerical methods: methods with negligible numerical dissipation (i.e., methods that conserve energy in absence of viscosity and/or subgrid modelling) and with low dispersion errors (to properly transport complex vortical structures). Methods that can do that are: spectral methods, high order finite difference methods, and vortex-in-cell (VIC) methods. As the problems of interest are of large spatial extent and contain vortices with small cores, it is also essential that the methods be efficiently parallelized. As to LES of wake vortex flows, this require subgrid scale (SGS) models that are essentially inactive during the gentle, well-resolved, phases of the flow and within the vortex cores, and that become active only during the complex turbulent phases of the flow. The recent multiscale models, that act solely on the high wavenumbers modes of the LES, are seen to be most appropriate. We present some illustrative examples of DNS and LES results that were obtained within our group