5% - eTheses Repository - University of Birmingham

particle velocity Vx=0. The initial Eulerian vertical component
particle relative velocity is then VY=Uy -VT (eg -0.2m/s in figure
2a) , where UY is the flow velocity component at the initial
particle position. To illustrate the sensitivity to initial slip
velocity we show cases a) , b) , c) and d) in which Vy is initially
-0.20m/s, O.Om/s, 0.05m/s and 0.3m/s.
Now consider figure 3 showing eight particle trajectories from
initial positions varying from two radii horizontally to the
right of the vortex axes to three radii directly above the axis.
VY and Vx initially assigned equal to the local fluid velocity
values and the resultant trajectories were non-chaotic. The
essential point is that system parameters and initial conditions
serve to define uniquely subsequent behaviour which, in figure
2 is chaotic and figure 3 is ordered. Careful selection of
initial conditions (if arbitrarily chosen) is advised.
3 RESULTS
We survey various values of VT with core parameter AR fixed
(section 3.1), assess the forces on particles falling from
starting points below and above a vortex (section 3.2 and 3.3)
and describe a vortex-particle capture criterion (section 3.4).
3.1 Varying VT at fixed R and A
We chose parameter values A=100 rad/s and R=0.006m for the vortex
and varied VT to assess the sensitivity of particle trajectories.
5-6