Computational Modelling of Transonic Aerodynamic Flows Using Near-Wall, Reynolds Stress Transport Models

Abstract

The present work reports on the further development of the Hanjalic-Jakirlic (1998) near-wall, second-moment closure (SMC) model in the RANS (Reynolds-Averaged Navier-Stokes) framework, updated to account for a wall-normal free, non-linear version of the pressure-strain term model, its implementation into the DLR-FLOWer code and its validation in computing some (compressible) transonic flow configurations. Furthermore, the wall boundary condition is based on the asymptotic behaviour of the Taylor microscale lambda and its exact relationship to the dissipation rate epsilon in the immediate wall vicinity. In addition, the calculations were performed using the DLR-FLOWer's default Reynolds stress transport model (Eisfeld, 2006), representing a numerically robust combination of the Launder-Reece-Rodi (1975) model resolving the near-wall layer with the Speziale-Sarkar-Gatski (1991) model being employed in the outer region. The flow geometries considered in this work include the transonic RAE 2822 profiles (cases 9 and 10), the ONERA M6 wing and the DLR-ALVAST wing-body configuration. The model results are analysed and discussed in conjunction with available experimental databases and the results of two widely used eddy-viscosity-based models, the one-equation Spalart-Allmaras model (1994) and the two-equation k-omega model of Wilcox (1988). The SMC predictions show encouraging results with respect to the shock position, shock-affected flow structure and the strength of the wing-tip vortex.