Wind Turbine Aerodynamics Part A: Basic Principles - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 307

The circulation developed by the blade is a key item associated with the flow field.
Figure 5-15 illustrates the circulation distributions along the span of the blade as calculated
according to the strip theory and the free-wake methods for Cases 1 and 4. These two cases
had similar thrust coefficients but different power coefficients. The graphs show good agree-
ment, with both methods predicting a fairly uniform circulation distribution in both cases.
The two methods agree on the circulation in the stalled inboard region in Case 1.
Figure 5-15. Circulation distributions calculated by two different analytical methods.
[Wilson and Walker 1984, and Gohard 1978]
Comparison of Strip Theory with Test Results
Anderson et al. [1982] conducted wind tunnel tests of a 3-m diameter HAWT at a variety
of wind speeds over a wide range of rotor speeds, with tip-speed ratios from 8 to 14. The
rotor had two tapered and twisted blades with an NACA 4412 airfoil section and a solidity of
4.58percent. Test data included local axial and tangential velocities near the rotor, measured
using hot-film anemometry , and rotor power and thrust. Angles of attack experienced by the
blades where below those for stall, so linear aerodynamics ( i.e. , lift coefficient directly pro-
portional to angle of attack) could be employed. Reynolds numbers , N R for the tests of this
turbine at a free-stream wind speed of 10 m/s ranged from 240,000 at a tip-speed ratio of 8
to 420,000 at a tip-speed ratio of 14. (Because of the taper in the blade planform, Reynolds
number is almost constant over the outer 70percent of these blades.) Lift and drag test data
for the NACA 4412 airfoil below stall over this Reynolds-number range have been reported
by Jacobs and Sherman [1936].
The turbine tests were performed in a wind tunnel with a blockage ratio of 0.12. Correc-
tions were made to the test data to account for blockage due to wake expansion. At higher
tip speeds, blockage corrections were very sensitive to the induction ratio used. This was
not the case, however, at lower tip speeds. Since the blockage correction has a very large
effect at the higher tip-speed ratios, comparison of experimental and theoretical results will
be limited to those obtained at a tip-speed ratio of 8. The slope of the lift curve ( dC L / d a) was
modified by the Prandtl-Glauert rule to account for local Mach number , which reached 0.26
at this tip-speed ratio.