Page 142 - Wind Energy Handbook

116 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

U 1 (cos ª a(1 þ F( ì)K(÷)sin ł))
þ Ùra9cos ł sin ÷(1 þ sin ł sin ÷)
tan ö ¼ (3:131)
(Ùr(1 þ a9 cos ÷(1 þ sin ł sin ÷)))

÷
þ U 1 cos(ł) a tan (1 þ F( ì)K(÷)sin ł) sin ª
2
where r is measured radially from the axis of rotor rotation.
The angle of attack Æ is found from

Æ ¼ ö â (3:132)

Lift and drag coefficients taken from two-dimensional experimental data, just as for
the non-yawed case, are determined from the angle of attack calculation for each
blade element (each combination of ì and ł).

3.10.8 The blade element–momentum theory for a rotor in steady
yaw

The forces on a blade element can be determined via Equations (3.131) and (3.132)
for given values of the flow induction factors.
The thrust force will be calculated using Equation (3.46) in Section 3.5.3, which is
for a complete annular ring of radius r and radial thickness är.
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

For an elemental area of the annular ring swept out as the rotor turns through an
angle äł the proportion of the force is

1 2 äł
äF b ¼ rW Nc(C l cos ö þ C d sin ö)är
2 2ð
putting C x ¼ C l cos ö þ C d sin ö and

Nc
ó r ¼
2ðr
then

1
äF b ¼ rW ó r C x räräł (3:133)
2
2
The values of C l and C d should really include unsteady effects because of the ever
changing blade circulation with azimuth angle which will depend upon the level of
the reduced frequency of the circulation fluctuation.
If it is chosen to ignore drag, or use only that part of the drag attributable to
pressure, then Equation (3.133) should be modified accordingly.