Aerodynamics and aeroelastics of wind turbines - Wind Power Generation and Wind Turbine Design - page 92

= = =
. This shows that a wind turbine is heavily loaded at the optimum condition.
The following limitations apply to the theory:

ca

T () 4(1

= a − a ) a 1 / 3 c ( a 1 / 3) 8 / 9 ~ 0.9.

is seen to be at Betz' value of

Betz T

• it is implicitly assumed that there is no slipstream as there are no radial components

calculation of the full details of the slipstream expansion cannot be performed •

as the theory does not consider the radial velocity component
the axisymmetric disk is assumed to be infi nitesimally thin. •

As already discussed by Betz [9] and further by Loth McCoy [70] in the context
of a double AD for vertical axis wind turbines there is a possibility to beat Betz to
some extent (roughly to 0.64 for a double AD). A recent discussion for beating
Betz with general devices was given by Jamieson [34].
Wind turbines are rotating machines, and a very important dimensionless number
is the tip speed ratio (TSR) defi ned as

Ω R

l : = ,

( 6 )

v

wind

where is the angular velocity of the turbine.

Figure 3 gives a graph of various c P against l . Apart from its own data, data
from the classical literature, for example [14,18], was also included. Two items are

Ω

Figure 3 : c P as function of TSR, various types of wind turbines.