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3.12.3 The effect of solidity on performance

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At this stage, the other principal parameter to consider is the solidity, defined as total blade area divided by the swept area. For the three blade machine, above, the solidity is 0.0345, but this can be altered readily by varying the number of blades, as shown in Figure 3.52.

The solidity could also have been changed by changing the blade chord.

The main effects to observe of changing solidity are:

1 Low solidity produces a broad, flat curve, which means that the CP will change very little over a wide tip speed ratio range, but the maximum CP is low because the drag losses are high (drag losses are roughly proportional to the cube of the tip speed ratio).

2 High solidity produces a narrow performance curve with a sharp peak, making the turbine very sensitive to tip speed ratio changes and, if the solidity is too high, has a relatively low maximum CP. The reduction in CP max is caused by stall losses.

3 An optimum solidity appears to be achieved with three blades, but two blades might be an acceptable alternative because although the maximum CP is a little lower, the spread of the peak is wider, and that might result in a larger energy capture.

It might be argued that a good solution would be to have a large number of blades of small individual solidity, but this greatly increases production costs and results in blades that are structurally weak and very flexible.

There are applications that require turbines of relatively high solidity; one is the directly driven water pump, and the other is the very small turbine used for battery charging. In both cases it is the high starting torque (high torque at very low tip speed ratios) that is of importance, and this also allows small amounts of power to be developed at very low wind speeds, ideal for trickle charging batteries.


Figure 3.52 Effect of changing solidity.

Wind Energy Handbook

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