The velocity field induced by a helical vortex filament

Abstract

An exact analytical solution for the velocity field, both interior and exterior, induced by an infinite right-handed helical vortex filament is derived. Due to the way the variables combine in this solution, the paper also shows that it is possible to derive a stream function for this nonaxisymmetric flow. Sample calculations of these expressions are included.

The rotor theories by Professor Joukowsky: Vortex theories

“…They compared their results with the disk theory only, i.e. with the first term of the same expansion and omitted any comparisons with other known solutions for the helicoidal vortex sheet [33] and a single helical vortex filament [36].…”

“…This approach was used in one radial direction along the blade, Lerbs [52], who tried to describe the radial dependence of the induction factor by considering the blade contribution only. The full trigonometric form of the Kapteyn's series was derived by Hardin [36] for the velocity field induced by a single, singly infinite helical vortex filament. In the notation of Ref.…”

Accumulation of heavy particles in N-vortex flow on a disk

“…The instantaneous three-dimensional potential velocity field induced by a helical vortex filament in an unbounded space follows from the Biot-Savart law and was studied in detail by Hardin. 3 The analysis was extended to a helical vortex filament in a cylindrical tube by Alekseenko et al 4 The calculation of this velocity field is far from trivial due to the torsion of the helical vortex filament.…”

The Relative Stream Function of the Uniformly Moving Helical Vortex Tube

“…Furthermore, if set V 0 =0, and R tends to infinite, the formula will degenerate into Hardin's formula [6].…”

“…By introducing a stream function, Adebiyi [5] had discussed the existence of steady helical tube with small cross-section. The works about the velocity field induced by the static single helical vortex filament (vortex core radius tends to zero) were carried out successfully by Hardin [6] and Okulov [7] . Hardin managed to acquire analytical formula of the velocity field in an unbound space with the help of the Biot-Savart law.…”