Effects of Turbulence Modeling on RANS Simulations of Tip Vortices

Abstract

The primary purpose of this thesis is to quantify the effects of RANS turbulence modeling on the resolution of free shear vortical flows. The simulation of aerodynamic wing-tip vortices is used as a test bed. The primary configuration is flow over an isolated finite wing with aspect ratio, , and Reynolds number, . Tip-vortex velocity profiles, vortex core and wake turbulence levels, and Reynolds stresses are compared with wind tunnel measurements. Three turbulence models for RANS closure are tested: the Lumley, Reece, and Rodi full Reynolds stress transport model and the Sparlart-Allmaras model with and without a proposed modification. The main finding is that simulations with the full Reynolds stress transport model show remarkable mean flow agreement in the vortex and wake due to the proper prediction of a laminar vortex core. Simulations with the Spalart-Allmaras model did not indicate a laminar core and predicted over-diffusion of the tip-vortex. Secondary investigations in this work include the study of wall boundary layer treatment and simulating the wake-age of an isolated rotorcraft in hover using a steady-state RANS solver. By comparing skin friction plots over the NACA 0012 airfoil, it is shown that wall functions are most effective in the trailing edge half of the airfoil, while high velocity gradient and curvature of the leading edge make them more vulnerable to discrepancies. The rotorcraft simulation uses the modified Spalart-Allmaras turbulence model and shows proper, qualitative, resolution of the interaction between the vortex sheet and the tip vortex.