New small turbine technologies - Wind Power Generation and Wind Turbine Design - page 392

10,000,000

Re(100%RPM)
Re(75%RPM)
Re(50%RPM)
Re(25%RPM)

1,000,000

100,000

10,000

Potentially low Reynolds
number region

1,000

0.1 1 10 100 1000

Rotor Diameter (m)

Figure 3: Reynolds number at 75% radius of rotor blade vs. rotor diameter at
10 m/s of wind speed and different rotor speed (100%, 75%, 50% and
25% of rated value).

due to laminar fl ow separation. Then it will rapidly be accelerated with good wind,
however, the operation will very unstable when the wind is turbulent. One of the
worst cases, the brake system will soon shutdown the system to prevent the WT
from excessive rotation.
Figure 3 shows how SWTs suffer from low Reynolds number problem. Reynolds
number varies along blade axial location. However for simplicity, a representative
Reynolds number is defi ned here at 75% axial location of a blade from the rotor
centre as follows:

cW
n

75%

Re =

(2 )

where c 75% is chord length of a blade at r = 0.75 R , R is rotor radius, W is relative
fl ow speed to the blade aerofoil section in the cylindrical plane of rotor at r =
0.75 R , v is kinematic viscosity.
Having simply designed a non-dimensional rotor by blade element and
momentum theory (BEM theory) with tip speed 60 m/s and tip speed ratio is 6
as a typical case, one may evaluate what size of SWT shall be potentially affected
by the low Reynolds number problem by changing the rotor diameter and rota-
tional speed. In Fig. 3 the region where a low critical Reynolds number poten-
tially affect on rotor aerodynamic performance is shown below dotted line.
SWTs below several meters of diameter or rotors rotating at a low rotor speed
will tend to enter into the critical region.
Figure 4 shows some typical relations between rotor diameter and output power
for three kinds of rated wind speed: 7, 10, and 13 m/s assuming 35% of system