A numerical and experimental investigation of the mean and turbulent characteristics of a wing-tip vortex in the near-field

Turbulent wing-tip vortices are an extremely important fluid dynamics phenomena for their negative impact in several applications. Despite the many numerical and experimental studies conducted on this particular flow, there are still parameters that require further research to advance the current understanding and provide a benchmark for future prediction methods and computational studies. In this study, the near-field (up to three chord lengths) development of a wing-tip vortex is investigated at two angles of attack (five and ten degrees) using experimental and numerical methods. The experimental study was conducted a priori to the numerical simulations to provide a base case and inlet boundary conditions for the numerical models. The vortex shed from a straight rectangular wing with squared tips was investigated to identify the main mechanisms involved in the near-field roll up of the vortex. The combination of experimental measurement techniques, such as hot-wire anemometry and a five-hole pressure probe, gave great insight into the behaviour of the mean and turbulent characteristics of the vortex during roll up and near-field formation. The experimental measurements revealed both wake-like and jet-like axial velocity profiles depending on the angle of attack and the presence of a secondary counter rotating vortex just behind the wing (x/c = 0) for both angles of attack. The vortex was also characterized by high levels of vorticity in the core and a circulation parameter that increased with downstream distance. Turbulence levels in the vortex were found to be highest on the core periphery just behind the wing (x/c = 0) but decayed with downstream distance in the core of the vortex due to the relaminarizing effect of the core solid body rotation. The numerical investigation utilised finite volume flow solver Star- CCM+ and consisted of Steady and Unsteady Reynolds Averaged Navier-Stokes (RANS/URANS) modelling using a Reynolds stress model, Large Eddy Simulation (LES) and the application of a vorticity confinement model (VC) to the URANS and LES equations. The RANS and URANS with VC models predicted the mean flow reasonably well for an angle of attack of five degrees, whereas the mean flow for an angle of attack of ten degrees and the turbulence magnitudes for both angles of attack were greatly under-predicted. The LES with VC model had the best agreement with experiment, reproducing the principal features observed in the experimental measurements. The LES with VC model correctly predicted the wake-like and jet-like axial velocity profiles, the presence of a secondary counter rotating vortex and turbulent quantities in close agreement with those of experiment. The LES with VC model predicted the axial velocity and the root mean square (rms) of the streamwise turbulent fluctuations to within 3% and 15% of the experimental results and the core radius to be the same size as experiment at the last measurement location of x/c = 3 for an angle of attack of five degrees.