Page 107 - Wind Energy Handbook

THE EFFECTS OF A DISCRETE NUMBER OF BLADES 81

1

RdCp/dr

0.5

0
0 0.2 0.4 0.6 0.8 1
r/R
With tip-loss
Without tip-loss
Figure 3.30 Span-wise Variation of Power Extraction in the Presence of Tip-loss for a Blade
with Uniform Circulation on a Three-blade Turbine Operating at a Tip Speed Ratio of 6

If the circulation varies along the blade span vorticity is shed into the wake in a
continuous fashion from the trailing edge. Therefore, each blade sheds a helicoidal
sheet of vorticity, as shown in Figure 3.31, rather than a single helical vortex as
shown in Figure 3.27. The helicoidal sheets convect with the wake velocity and so
there can be no flow across the sheets which can therefore be regarded as imperme-
able. The intensity of the vortex sheets is equal to the rate of change of bound
circulation along the blade span and so increases rapidly towards the blade tips.
There is flow around the blade tips because of the pressure difference between the
blade surfaces which means that on the upwind surface of the blades the flow
moves towards the tips and on the downwind surface the flow moves towards the
root. The flows from either surface leaving the trailing edge of a blade will not be

Figure 3.31 A Helicoidal Vortex Sheet Wake for a Two-blade Rotor