Number: Mech 116/94
Author(s): BEREZOVSKI, A., KAPLANSKI, F.
Title: Simulation of vortex rings interaction by the method of liquid particles. 14 p.
Language: English
Keywords: Inviscid fluids; vortex flows; numerical calculations;
Lagrangian code.
Availability:
ftp://ftp.ioc.ee/pub/reports/mech/me116_94.ps.Z
ABSTRACT. The inviscid interaction of two identical vortex rings
is studied numerically. At the initial moment, the two rings are
inclined symmetrically to the horizontal plane for an angle, and
they are located sufficiently far apart, so that the effect of
their initial mutual influence was reduced at a minimum.
Particles are marked uniformly along the central vortex lines of
rings and their motion is described according to the Lagrangian
approach. Velocities of particles are calculated by using the
modified Biot-Savart law. A five-point filtration procedure is
used to prevent a calculation instability. When particles
belonging to different filaments overlapped, the topology of
filaments was redefined to continue the simulation. Positions of
particles were calculated at each moment of their motion, which
displayed the evolution of the vortex contours with time. A
correlation between the initial angle and the collision angle
was found. For example, when the initial distance between vortex
rings was equal to 4 of their radii, the smallest obtained value
for the collision angle was 43 , and it corresponded to the zero
value of the initial angle. Even in the case of such a small
initial angle two vortex rings would join into a single filament,
and after some time this resulting filament would split back into
two other vortex rings.