ABSTRACT Title of Dissertation: Studies in Tip Vortex Formation, Evolution and Control

A high resolution computational methodology is developed for the solution of the Compressible Reynolds Averaged Navier Stokes (RANS) equations. This methodology is used to study the formation and evolution of tip vortices from xed wings and rotary blades. The numerical error is reduced by using high order accurate schemes on appropriately rened meshes. For vortex evolution problems, the equations are solved on multiple overset grids that ensure adequate resolution in an ecient manner. For the RANS closure, a one equation wall-based turbulence model is used with a correction to the production term in order to account for the stabilizing eects of rotation in the core of the tip vortex. A theoretical analysis of the accuracy of high resolution schemes on stretched meshes is performed as a precursor to the numerical simulations. The developed methodology is validated with an extensive set of experimental measurements ranging from xed wing vortex formation studies to far-eld vortex evolution on a two bladed hovering rotor. Comparisons include surface pressure distributions, vortex trajectory and wake velocity proles. During the course of these valida