Large Eddy Simulations of Separated Compressible Flows around Wing Sections

This thesis concerns numerical calculations of compressible separated flows, with and without shocks, around wing sections using Large Eddy Simulations (LES). The considered geometries are the NACA 0012 wing section and the ONERA AT15A wing section. Compressible separated flows around wing sections are of considerable interest, for engineering and scientific reasons, since they involve transition, near-wall turbulence and separation. At transonic speed the interaction between shock and the viscous boundary layer is of interest. If the shock is strong enough shock induced separation occurs. Using Reynolds Averaged Navier-Stokes Simulations (RANS) one has to know in advance where transition to turbulence occurs. The RANS turbulence models also include a set of model parameters which have to be set a priori. This is not the case for dynamic LES-formulation since the model parameters are computed during the simulation utilising the information in the resolved flow field. An explicit filter is used to extract this information. A filter derived on a mathematical basis is presented as well as a new dynamic model where the divergence of the subgrid-scale (SGS) terms are modelled rather than the SGS-terms themselves. In this way only three model parameters are needed for the momentum equations and still anisotropy effects can be accounted for. A novel idea how to treat filtering close to a shock is presented. In LES the large scale flow field is resolved both in time and space and the computational time is significant. To obtain results in acceptable time computations using Parallel Virtual Machine (PVM) have been conducted. The important role of the numerical viscosity as an implicit model in LES is demonstrated. The development of streamwise vortices is shown to be strongly dependent of the spanwise distance of the computational domain