Page 163 - Wind Energy Handbook

THE METHOD OF ACCELERATION POTENTIAL 137

For the wind turbine the value of a 0 may not be small compared with 1 and so the
above procedure will converge on values of a 0 which are too small compared with
what the momentum theory would deliver.
To produce more realistic results that is, results in line with Glauert’s momentum
theory where
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C T ¼ 4a 1 a(2 cos ª a) ¼ 4aA G (a) (3:105)

or the Coleman theory, where

÷ ÷
C T ¼ 4a cos ª þ tan sin ª a sec 2 ¼ 4aA C (a) (3:111)
2 2

Also, the wake skew angle should be used in matrix [L] instead of the yaw angle.
The matrix [L] should then be modified to become
2 3
1 15 ÷
6 4A(a 0 ) 0 128 ð tan 2 7
6 7
6 ÷ 7
6
7
[L] ¼ 6 0 sec 2 0 7 (3:189)
6 2 7
6 7
4 15 ÷ ÷ 5
ð tan 0 1 tan 2
128A(a 0 ) 2 2
where A(a 0 ) is chosen according to which momentum theory is to be used.
The Pitt and Peters method does not include any determination of induced
velocities in the plane of the rotor disc and as a consequence it is not possible to
m
account for wake rotation. However, it is possible that the Kinner solutions Q (í)
n
2
that were excluded from the analysis because they give infinite pressure at í ¼ 1,
which lies along the axis of rotation, may give velocity distributions which provide
for wake rotation; the momentum theory of Section 3.3 also predicts an infinite
pressure at the axis of rotation because of wake rotation. In practice, of course, the
rotor disc would not extend to the axis of rotation and the singularity would not
occur.
With or without wake rotation a flow angle ö can be determined from which a
torque can be found. If the normal force on an element of the rotor disc is equal to
äL cos ö then the tangential force will be äL sin ö.

3.11.6 The general acceleration potential method

Peters with a number of associates has developed the theory further and a reading
of these references (Pitt and Peters, 1981, Goanker and Peters, 1988, HaQuang and
Peters, 1988) is recommended. The acceleration potential method has been devel-
oped specifically for wind turbines by van Bussell (1995) where a much more
comprehensive account of the theory is given.