Studies in Tip Vortex Formation, Evolution and Control

Abstract

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 fixed wings and rotary blades. The numerical error is reduced by using high order accurate schemes on appropriately refined meshes. For vortex evolution problems, the equations are solved on multiple {\em overset} grids that ensure adequate resolution in an efficient 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 effects 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 fixed wing vortex formation studies to far-field vortex evolution on a two bladed hovering rotor. Comparisons include surface pressure distributions, vortex trajectory and wake velocity profiles. During the course of these validations, numerical issues such as mesh spacing, order of accuracy and fidelity of the turbulence model are addressed. These findings can be used as guidelines for future simulations of the tip vortex flow field. A detailed investigation is conducted on the generation of tip vortices from fixed wings. Streamwise vorticity is seen to originate from the cross-flow boundary layer on the wing tip. The separation and subsequent roll-up of this boundary layer forms the trailing vortex system. The initial development of the vortex structure is observed to be sensitive to tip shape, airfoil section and Reynolds number. While experimental comparison of the computed vortex structure beyond a few chord lengths downstream of the trailing edge is lacking in the literature, for a single bladed hovering rotor, good validations of the vortex velocity profiles are achieved upto a distance of 50 chord lengths of evolution behind the trailing edge. For the two bladed rotor case, the tip vortex could be tracked upto 4 revolutions with minimal diffusion. The accuracy of the computed blade pressures and vortex trajectories confirm that the inflow distribution and blade-vortex interaction are represented correctly. Finally, utilizing a surface boundary condition to represent a spanwise jet, the effect of tip blowing on the vortex structure is investigated. The interaction of the jet with the cross-flow boundary layer is shown to reduce the vortex strength with a marginal loss in performance. Overall, this level of consistent performance has not been demonstrated previously over such a wide range of test cases. The accuracy achieved in the validation studies establishes the viability of the methodology as a reliable tool that can be used to predict the performance of lift generating devices and to better understand the underlying flow physics.