Page 159 - Wind Energy Handbook

THE METHOD OF ACCELERATION POTENTIAL 133

The once per revolution term in Equation (3.167) will cause an angle of attack
variation and, hence, a lift variation that will cause a yawing moment on the disc.
However, the pressure distribution, being axi-symmetric, cannot cause a yawing
moment. The situation is much the same as for the vortex theory of Coleman,
Feingold and Stempin (1945).
Pitt and Peters (1981) use, or rather, impose Glauert’s assumption (Equation
(3.108)) for the variation of the axial induced flow factor:
a ¼ a 0 þ a S ì sin ł (3:170)

The value of a S is obtained by equating the first moment about the yaw axis of
Equation (3.170) with the first moment of Equation (3.167) using the Mangler and
Squire velocity distributions of Equations (3.168).
ð ð
2ð 1
ì sin ł(a 0 þ a S ì sin ł)2ðì dì dł
0 0
ð ð !
1
2ð 1 A 0 (ì, ª) X
¼ ì sin łC T þ A k ( ì, ª)sin kł ì dì dł (3:171)
0 0 2
k¼1
All terms, apart from that containing A 1 , vanish on integration, giving
15ð ª
a S ¼ tan C T (3:172)
128 2

Hence, using Equation (3.169), the axial induced velocity becomes

15ð ª
a ¼ a 0 1 þ ì tan sin ł (3:173)
32 2
Which, apart from the use of the yaw angle instead of the wake skew angle, has the
same form as Equations (3.108) and (3.118) and so there is some consistency in the
various methods for dealing with yawed flow.

3.11.4 The anti-symmetric pressure distributions

As has been determined in Section 3.10.11, there is a moment about the vertical
diameter of a yawed wind turbine rotor disc, the restoring yaw moment. An axi-
symmetric pressure distribution, however, is not capable of producing a yaw
moment and so more terms from the series solution of Equation (3.159) need to be
included.
The only terms in Equation (3.159) which will yield a yawing moment are those
1
1
for which m ¼ 1 and for which D 6¼ 0. Terms for which m ¼ 1 and C 6¼ 0 will
n
n
cause a tilting moment. Recalling that m þ n must be odd to achieve a pressure
discontinuity across the disc the values of n that may be combined with m ¼ 1 must
be even.