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3 BLADE ELEMENT MOMENTUM THEORY<br />
Split the blade up along its length into elements.<br />
Use momentum theory to equate the momentum changes in the air<br />
flowing through the turbine with the forces acting upon the blades.<br />
Pressure distribution along curved streamlines enclosing the wake<br />
does not give an axial force component.<br />
(For proof see one-dimensional momentum theory, e.g. Hansen)<br />
3.1 Momentum changes<br />
V V ( 1−<br />
a)<br />
ϖ r a′<br />
0<br />
0<br />
r<br />
Fig. 14<br />
R<br />
ϖ<br />
V ( 1−<br />
2a)<br />
Thrust from the rotor plane on the annular control volume is δ N<br />
δ N = m&<br />
V − u ) = 2πrρu(<br />
V − u ) δr<br />
( 0 1<br />
0 1<br />
Torque from rotor plane on this control volume is δ T<br />
δT = m&<br />
ru = 2m & ϖr<br />
a′<br />
θ<br />
2<br />
0<br />
2 ϖr<br />
a′<br />
(7)<br />
(8)<br />
12
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