Closely spaced co-rotating helical vortices: General solutions

TL;DR

This paper derives general solutions for closely spaced co-rotating helical vortices, revealing their complex wake behavior and providing insights into vortex evolution behind rotor blades.

Contribution

It introduces a filament-based approach to model co-rotating helical vortices with broken symmetry but maintained periodicity, applicable to rotor wake analysis.

Findings

Vortex elements move without distortion in a special moving frame.

The wake exhibits dual behavior: local helical pair and distant thicker-core vortex.

Solutions help characterize twin-tip vortex evolution in rotor wakes.

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.