Helical vortices in swirl flow are studied theoretically and experimentally.A theory of helical vortices has been developed. It includes the following
results:
an analytical solution describing an elementary helical vortex structure
– an infinitely
thin filament; a solution for axisymmetrical vortices accounting for the
helical shape
of vortex lines and different laws of vorticity distribution; a formula
for calculation
of the self-induced velocity of helical vortex rotation (precession) in
a cylindrical
tube; an explanation of the zone with reverse flow (recirculation zone)
arising in swirl
flows; and the classification of vortex structures.The experimental study of helical vortices was carried out in a vertical
hydrodynamical
vortex chamber with a tangential supply of liquid through turning nozzles.
Various vortex structures were formed owing to changing boundary conditions
on the
bottom and at the exit section of the chamber. The hypothesis of helical
symmetry
is confirmed for various types of swirl flow. The stationary helical vortex
structures
are described (most of them for the first time) the features of which agree
with the
results and predictions of the theoretical model developed. They are the
following:
a rectilinear vortex; a composite columnar vortex; helical vortices screwed
on the
right or on the left; a vortex with changing helical symmetry; a double
helix – two
entangled vortex filaments of the same sign.
A derivation of an expression for the self-induced velocity of a helical vortex filament with moderate and small pitch is presented for the cases of an infinite space as well as a space bounded by a cylindrical tube. This result supplements the known Kelvin’s formula for helix with large pitch in an infinite space.
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