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

Abstract

The present work reports on the further development of the Hanjalić--Jakirlić (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 $λ$ and its exact relationship to the dissipation rate $ε$ 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-$ω$ 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.