Wingtip vortices are unavoidable in a three dimensional lift producing wing. The vortices are a result of the pressure difference that causes the lift. The only ways to eliminate the vortices are,
- Make the wing two dimensional- i.e. make its span infinite, like an airfoil.
- Don't produce lift.
Unfortunately, neither of these help us much.
Some points to note are:
- Winglets and other wingtip devices reduce the intensity of the vortices, not eliminate them.
- 'Closing' the wing or wing tip does not eliminate the trailing vortex wake or induced drag. From aero.stanford.edu:
Wings that form closed loops ... do not eliminate the "tip vortices" or trailing vortex wakes even though the wing has no tips.
The figure below shows the CFD simulation of wings with different wingtip devices.
Image from Aerodynamic Efficiency Study of Modern Spiroid Winglets, by Tung Wan Hung-Chu Chou Kuei-Wen Lien, Figure numbers removed for proper fit.