Numerical simulation of tip vortices of wings in subsonic and transonic flows

A multi block zonal algorithm which solves the thin-layer Navier-Stokes and the Euler equations is used to numerically simulate the formation and roll-up of the tip vortex in both subsonic and transonic flows. Four test cases which used small and large aspect ratio wings have been considered to examine the influence of the tip-cap shape, the tip planform and the free-stream Mach number. It appears that both the tip-planform and the tip-cap shape have some influence on the formation of the tip vortex, but its subsequent roll-up seems to be more influenced by the tip-planform shape. In general, a good definition of the formation and the roll-up of the tip vortex has been observed for all the cases considered here. Comparions of the numerical results with the limited, available experimental data show good agreement with both the surface pressures and the tip-vortex strength.