Page 87 - Wind Energy Handbook

ROTOR BLADE THEORY 61

Ωr(1+a)
Lcos φ + D sin φ
β

φ U (1-a) φ L
α ∞
W
D
L sin φ − D cos φ

(a) Velocities (b) Forces
Figure 3.14 Blade Element Velocities and Forces

U 1 (1 a) Ùr(1 þ a9)
sin ö ¼ and cos ö ¼ (3:42)
W W

The angle of attack Æ is then given by
Æ ¼ ö â (3:43)

The lift force on a span-wise length är of each blade, normal to the direction of W,is
therefore
1 2
äL ¼ rW cCär (3:44)
2

and the drag force parallel to W is

1
2
äD ¼ rW cC d rär (3:45)
2
3.5.3 The blade element – momentum (BEM) theory

The basic assumption of the BEM theory is that the force of a blade element is solely
responsible for the change of momentum of the air which passes through the
annulus swept by the element. It is therefore to be assumed that there is no radial
interaction between the flows through contiguous annuli—a condition that is,
strictly, only true if the axial flow induction factor does not vary radially. In
practice, the axial flow induction factor is seldom uniform but experimental
examination of flow through propeller discs by Lock (1924) shows that the assump-
tion of radial independence is acceptable.
The component of aerodynamic force on N blade elements resolved in the axial
direction is

1 2
äL cos ö þ äD sin ö ¼ rW Nc(C L cos ö þ C d sin ö)är (3:46)
2