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5% - eTheses Repository - University of Birmingham

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will not enter the core from any starting location.<br />

Figure 8b-e. The diagrams show the similarity in trajectory plots for<br />

particles with various fall speeds near a 5mm Rankine core. The four cases<br />

correspond to the triangles in figure 8a.<br />

Figure 9a-c. The above plates show the effect <strong>of</strong> keeping the velocity at the<br />

core radius constant whilst increasing the core size. The graph on the right<br />

shows the fall time for each <strong>of</strong> the trajectories in the picture on the left.<br />

Figure 10. The pictures show a) a particle that is not captured by the core,<br />

b) a particle that is captured and c) a particle that is just captured. The<br />

value <strong>of</strong> AR/VT here is the criterion C below.<br />

Figure 11. Values <strong>of</strong> the capture criterion C for various values <strong>of</strong> (X,Y), the<br />

particle starting position at initial velocity (Vx/ VY ) = (0,0) .<br />

Figure 12. Variation <strong>of</strong> the critical vortex strength criterion C AR/VT with<br />

vortex radius R at constant vortex tip speed AR.<br />

Figure 13. Time-averaged horizontal velocity induced below the mid-plane <strong>of</strong><br />

a moving Rankine vortex over 100 time-steps.<br />

Figure 14. Time-averaged vertical velocity induced below the mid-plane <strong>of</strong> a<br />

moving Rankine vortex over 100 time-steps.<br />

Figure 15. Time-averaged horizontal velocity induced below the mid-plane <strong>of</strong><br />

a moving Rankine vortex over 10 time-steps.<br />

Figure 16. Time-averaged vertical velocity induced below the mid-plane <strong>of</strong> a<br />

moving Rankine vortex over 10 time-steps.<br />

Figure 17. Time-averaged and time-dependent trajectories <strong>of</strong> a particle in a<br />

moving Rankine vortex. The trajectories in the time-averaged flows are<br />

xvi

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