Closely spaced co-rotating helical vortices: General solutions

Abstract

In this work, we present general solutions for closely spaced co-rotating helical vortices using a filament approach. For these vortex structures, helical symmetry is broken, but solutions maintain a form of spatial periodicity. We show there exists a moving frame where vortex elements move along the structure without distorting it. These solutions can be used to characterize the evolution of the twin-tip vortices produced in the wake of a tip-splitting rotor blade. The resulting wake has a dual nature. Locally, the structure behaves much like an helical pair aligned with the locally tangent flow. However, as we move away from the vortex structure the induced flow is reminiscent of an ‘equivalent’ helical vortex with thicker core.