Direct Simulation and RANS Modelling of a Vortex Generator Flow

Abstract

An array of co-rotating vortex generators (VG) is placed in a supersonic boundary layer, similar to that on an airliner wing. Direct numerical simulations (DNS) are conducted, with unsteady turbulent content in the incoming boundary layer obtained from the synthetic-turbulence approach of Shur et al. (Flow Turbul. Combust. 93, 63–92, 2014). The RANS models are tested in two ways: with a straightforward application to the problem, but also by solving the turbulence equations in the “frozen” average flow field of the DNS and therefore in “passive” mode, which appears to be a powerful procedure, similar to that of Parneix et al. (J. Fluids Eng. 120(1), 40–47, 1998). Side-by-side comparisons become clearer. The model Reynolds stresses are compared with the Reynolds stresses of the DNS. A plausible definition of an effective scalar eddy viscosity extracted from the DNS is also used for comparison, providing a target value. The models are the k- ω Shear Stress Transport model of Menter (1993) (SST) and the curvature-corrected version of Smirnov and Menter (J. Turbomach. 131(4), 041010, 2009) which we will denote by SST-RC, the eddy-viscosity transport model of Spalart and Allmaras (1992) (SA), and the SA model with Rotation and Curvature correction of Spalart and Shur (Aerosp. Sci. Technol. 1(5), 297–302, 1997) (SARC). As expected, SST and especially SA return an excessive decay of the peak vorticity, and both SST-RC and SARC perform better, but the flow is too complex for RANS to near perfection. This decay is very detrimental in practice, since their persistence is the key property of vortices used for separation control.