Abstracts - KTH Mechanics

138
Dynamics of heavy particles near a helical vortex lament
R. H.A. IJzermans ∗ , R. Hagmeijer ∗ and P.J. van Langen ∗
The motion of small heavy particles near a helical vortex filament is investigated
both numerically and analytically. We study the case of a helical vortex filament
in unbounded space and the case of a helical vortex filament which is placed in a
concentric cylindrical pipe. Potential flow is assumed which is not influenced by the
presence of the heavy particles (one-way coupling). For both cases, the velocity field
in a helical coordinate frame is described by a stream function 1 , 2 . In the equation
of motion of the heavy particles, Stokes drag is taken into account.
Numerical results show that heavy particles may accumulate in a fixed point in
the helical coordinate frame, near an elliptic region in the stream function. In physical
space this corresponds to a helically shaped equilibrium trajectory. The relation
between the topology of the carrier flow field and the phenomenon of particle accumulation
becomes clear from figure 1, where the positions of a group of initially uniformly
distributed particles are plotted after a long time. The particle accumulation is proven
analytically by a linear stability analysis. In addition, a full classification of possible
flow field topologies is presented.
These results can be useful in the design of gas-liquid separators, in which a helical
vortex filament is used for the separation of small dust particles and/or very small
droplets 3 .
η
∗ University of Twente, P/O box 217, 7500 AE, Enschede, Netherlands.
1 Hardin, Phys. of Fluids 25(11), (1982).
2 Alekseenko et al., J. Fluid Mech. 382, 185 (1999).
3 Hagmeijer et al., Phys. Fluids 17, 056101 (2005).
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2 -1.5 -1 -0.5 0
ξ
0.5 1 1.5 2
a) ɛ/a = 10 −3 , l/a = 0.5.
η
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2 -1.5 -1 -0.5 0
ξ
0.5 1 1.5 2
b) ɛ/a = 10 −2 , l/a = 1.
η
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2 -1.5 -1 -0.5 0
ξ
0.5 1 1.5 2
c) ɛ/a = 10 −2 , l/a =5.
Figure 1: Positions of heavy particles (blue dots) after time tΓ/a 2 = 100, for three
different values of the thickness of the vortex filament ɛ/a and the helix pitch 2πl/a;
the tube radius R/a = 2 and the particle relaxation time τpΓ/a 2 = 0.4, whereΓ
is the vortex strength and a the radius of the helix geometry. For comparison, the
streamlines of passive tracers are plotted in the background (red lines).