Page 180 - Wind Energy Handbook

154 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

helical and the wakes of other blades will also be present. Loewy (1957) developed
a theory for a rotor blade that accounts for the repeated wake in a similar manner to
Prandtl (see Section 3.8.3). As did Theodorsen, Loewy used two-dimensional, thin
aerofoil theory and produced a modification to Theodorsen’s function. In Equation
(3.216) the Bessel function of the first kind, J n (k), is multiplied by (1 þ W(k)) where
W(k) is called the Loewy wake-spacing function.

1
W(k) ¼ (3:219)
e (2[d=c]kþi2ð) 1

d is the wake spacing defined in Equation (3.75) and c is the chord of the aerofoil.
Miller (1964) arrived at a very similar result to Loewy by using a discrete vortex
wake model.
Loewy’s and Miller’s theories apply only to the non-yawed rotor but Peters, Boyd
and He (1989) have developed a much more extensive theory based upon the
method of acceleration potential. A sufficient number of Kinner pressure distribu-
tions are required to model both the radial and azimuthal pressure distribution on a
helicopter rotor such that the pressure spikes of individual blades are present. The
theory obviates the use of blade element theory and includes automatically un-
steady effects and tip losses; modelling of the blade geometry by this method does
present some problems, however. Suzuki and Hansen (1999) have applied the
theory of Peters, Boyd and He to wind turbine rotors and make comparisons with
the blade-element/momentum theory. Van Bussel’s theory (1995) is very similar to
that of Peters, Boyd and He but is intended for application to wind turbines.

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