Wind Turbine Aerodynamics Part A: Basic Principles - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 305

(1 - a ) x
(1 + 2 a )

D f = arctan - arctan [ ( 1 - a ) x ]

This change in flow angle occurs in a time period of Dt = c / V r , so there is an effective pitch
rate of the blades, d b/ dt . Airfoil pitching is assumed to occur about an axis through the
1/4-chord point , so the effective change in angle of attack from a finite blade width is
Da 2 = arc sin Dt
4

d b
dt

» Df
4

(5-38c)

Note that for the conditions illustrated in Figure 5-14, Da 1 > 0 and Da 2 < 0. The cascade
corrections are most significant near the blade roots where they influence yaw loads.

Gap Correction

Another modification of the strip theory approach is the gap correction required to ac-
count for the effects of a space along the span of a HAWT blade. Such spaces occur, for ex-
ample, on blades with partial-span pitch control , to accommodate the actuating mechanism.
Gaps can affect both lift and drag forces, so corrections are expressed as

D C P , G = D C P , GL + D C P , GD (5-39a)

where D C P , G = total reduction in power coefficient caused by a gap in the airfoil

D C P , GL = reduction in power coefficient caused by the loss of lift in the gap
D C P , GD = reduction in power coefficient caused by the increased drag in the gap

Gap Lift Correction

A gap in the span of the blade causes the circulation to drop to zero locally. As a result,
vorticity is shed in the wake, with vorticities of opposite sign being present. That is, the
vorticity shed outboard of the gap is of the opposite sign of the vorticity shed inboard of the
gap. The effect of this shed vorticity can be modeled as a semi-infinite vortex doublet extend-
ing downwind of the gap. A linear doublet is employed in lieu of a helical vortex because
the extent of the velocity field of a doublet is smaller. The influence of the doublet falls off
inversely as the square of the downwind distance, while the extent of the velocity field of a
vortex diminishes inversely with distance.
The local circulation deficit from such a doublet can be calculated by considering its
local downwash and employing linear aerodynamics. We find that the effect of the gap is
approximated by deleting the lift contribution to the power coefficient for a distance along
the span of the rotor of

s g
c

s g , e = 2 c

where s g , e = effective spanwise width of the gap (m)

s g = actual spanwise width of the gap (m)

We can approximate the effect of lost lift by assuming that no power is extracted from the
streamtube enclosing the effective width of the gap, which gives

r
R

c
R

2

s g
c

l V r
U C L (1 - a )

D C P , GL = 2 B cos 2 q

(5-39b)

p

where r and c are the radius and airfoil chord, respectively, at the gap.