Computation of Complex Compressible Aerodynamic Flows with a Reynolds Stress Turbulence Model

Abstract

Aeronautical aerodynamics is characterized by compressible flow at high Reynolds numbers. Therefore turbulence modeling is an important issue for predicting the flow field in agreement with measurements. In industrial applications the state-of-the-art is defined by so-called eddy viscosity models based on the Boussinesq hypothesis. Standard models usually provide one or two convection-diffusion equations with additional source terms, from which the eddy viscosity is computed. Since the eddy viscosity increases the diffusion coefficient of momentum and heat, i.e. the dissipative terms of the mean flow equations, these models are numerically forgiving. Nevertheless their applicability is restricted, because the underlying Boussinesq assumption strictly does not hold. Despite eddy viscosity models have proven to reliably predict attached boundary layer flows, they have deficiencies concerning the prediction of shock locations, separation or free vortices. Improvements can be achieved, when using so-called Reynolds stress turbulence models. These models replace the Boussinesq hypothesis by providing altogether seven convection-diffusion equations with additional source terms, yielding directly the missing terms in the mean flow equations. Besides the increased effort for solving in total twelve instead of six or seven equations, these models cause additional numerical difficulties, which have prevented their application in industry in the past. With Reynolds stress models there is no additional dissipation in the mean flow equations, because there is no eddy viscosity. Instead, the turbulence equations are coupled to the mean flow equations via a divergence term, which potentially destabilizes the numerical solution. Finally the number of terms contributing to the source terms in the turbulence equations is much larger than with eddy viscosity models and therefore more difficult to analyze with respect to numerical stability. In the EU-project FLOMANIA these problems have been solved in principle. Considerations will be presented, that allow the robust and efficient numerical computation of complex compressible aerodynamic flows with the SSG/LRR-<greek>w</greek> Reynolds stress turbulence model also developed in FLOMANIA. Examples will be given for the simulation of flows around configurations as complex as aircraft and helicopters.