Page 162 - Wind Energy Handbook

136 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

The tilting moment coefficient is given by
ð ð ð
1 2ð 1 1 1 3 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð
2
2
C my ¼ ì cos łp( ì, ł)ì dì dł ¼ 6iC ì 1 ì dì cos ł dł (3:184)
2
ð 0 0 ð 0
Therefore
5
1
iC ¼ ðC my (3:185)
2
4
The axial induced velocity distribution resulting from the pressure field of Equation
(3.183) is calculated by integration of Equations (3.145) and is then matched with
the linear velocity distribution of Equation (3.182) using the same method as for
Equation (3.171).
ð ð
2ð 1
ì cos ł(a 0 þ a c ì cos ł)2ðì dì dł
0 0
ð ð !
1
2ð 1 (ì, ª) X
¼ ì cos łC T A 0 þ A k ( ì, ª)cos kł ì dì dł (3:186)
0 0 2 k¼1
The functions A n ( ì, ª) being determined numerically. Again, using the Mangler
and Squire results as guidance, an expression for a c is found.
ª
a c ¼ sec 2 C my (3:187)
2

3.11.5 The Pitt and Peters model

Pitt and Peters (1981) have developed the linear theory that relates the axial induced
flow factors to the thrust and moment coefficients given in Equations (3.169),
(3.172), (3.180), (3.181) and (3.187) which collect together in matrix form

2 3
1 15 ª
0 ð tan
2 36 4 128 2 72 3
6
a 0 6 ª 7 C T
7
4 a c 56 0 sec 2 2 0 74 C my 5 (3:188a)
7
6
6
5
a S 4 7 C mz
15 ª 2 ª
ð tan 0 1 tan
128 2 2
(a) ¼ [L](C) (3:188b)
The procedure for using Equation (3.188) is to assume initial values for (a) from
which the values of (C) can be calculated from the blade element theory. New
values of (a) are then found from Equation (3.188) and an iteration proceeds.