Design of Wind Turbines - Wind Energy: Renewable Energy and the Environment - page 106

FIGURE 6.6 Diagram of blade element.
There are a number of computer programs for predicting aerodynamic performance of wind
turbines [15]. These are based on momentum theory, also referred to as strip theory. The theory
assumes that each element of the blade (Figure 6.6) can be analyzed independently from the others,
and the two-dimensional data for lift and drag coefficients can be used at the center of the section.
Performance predictions of power, torque, force, and power coefficient can be obtained for a blade
(rotor) using a numerical technique. Values are calculated for sections of the blade and then summed
to obtain the total performance.
Drag and lift coefficients versus angle of attack and Reynolds number are available for lots of
airfoils. In general, the coefficients are given for attack angles from around zero to a few degrees
past stall. Stall is where the lift decreases and drag increases steeply. So the problem, in the calcula-
tion for performance prediction, is to use the correct inflow angle to the blade, as the angle depends
on the wind speed at the blade. So the relative wind speed has to be corrected for the actual speed
at the blade, which uses the axial interference factor, ] , and the rotational interference factor, ]' . At
each section of the blade, an iterative procedure is used to calculate the angle of the inflow to the
airfoil. Because sections of the blade may operate at high angles of attack, for those attack angles,
lift and drag data from a flap plate or other actual measured data from some airfoil are added to the
tabular values. Tip losses and hub losses can be included along with wind shear and yaw (off-axis
components). The main limitations with the programs are the treatment of unsteady aerodynamics
in the region of dynamic stall and the use of 2-D data for lift and drag.
Rotors for vertical-axis wind turbines present another problem since the blades go through attack
angles of 360° and the blades are curved for the Darrieus wind turbine. A number of performance
models for the Darrieus rotor have been formulated [3, 16-18]. In general, symmetrical airfoils are
used, so lift and drag data are needed from 0 to 180°. The operation of vertical-axis wind turbines
also means at an attack angle of 90°, there is no lift, so the torque and power are negative, a cyclic
variation on every revolution [19].
From observations of the flow field of a Savonius rotor, an analytical model was developed for the
analysis of performance [3]. Two major discernable features of the flow field are: vortices are shed
from the vane tips when the vane is approximately at right angles to the flow, and these vortices are
counterrotating, and the vortices move rearward at approximately the free stream speed. The model
was adequate in that it predicted a power coefficient around 0.30 at a tip speed ratio around 1, which
is in line with field data and wind tunnel tests for Savonius rotors.