Blade Element Calculations - Small Wind Turbines: Analysis, Design, and Application - page 79

Fig. 5.1 Lift:drag ratio for
the NACA 4412 aerofoil

80

Re = 4.2x10 4
Re = 8.3x10 4
Re = 1.6x10 5
Re = 3.3x10 5
Re = 6.4x10 6

70

60

50

40

30

20

10

0

-10

-5 0 5 10 15

Angle of attack (degrees)

it achieved a high maximum C P with an old aerofoil section, so it forms a good
basis for investigating the practical optimisation of blade design. Secondly, the
measurements are still among the most detailed available; presumably for that
reason they are considered extensively in Chap. 5 of Spera [ 6 ]. The main drawback
in the current context is that the only lift and drag data for the NACA 4412 section
were obtained in 1937 in a wind tunnel with high free-stream turbulence (about
2%), so their accuracy is questionable. On the other hand, the lift and drag were
measured for 42,000 B Re B 640,000, which is a very appropriate range for this
wind turbine. The lift and drag data were taken from Miley [ 7 ]. The lift:drag
ratio is shown in Fig. 5.1 as function of a and Re. The data, as are all data and
programs mentioned in this chapter, are available from the online materials
( http://extras.springer.com ).
The tabulation of lift and drag data in terms of a is much more common than the
data fits that were used for the NACA 0012 section in the file LandD_0012.m
described in Chap. 3 . To make interpolation easy, the lift and drag should be mea-
sured at the same angles for each Re value, but this does not commonly occur. For
example, the drag for the NACA 4412 was not measured at 11 and 12 at the lowest
Re. This is the typical situation in using aerofoil data for wind turbine calculations.
The missing values were assumed to be equal to those at the nearest Re.
It is noted in passing that the lift and drag show the general trend of Reynolds
number dependence that is to be expected from knowledge of Chap. 4 ; C l tends to
decrease and C d increases as Re decreases, so the lift:drag ratio is strongly
Re-dependent as shown in Fig. 5.1 .
Linear interpolation is used to determine lift and drag as a function of a and
linear interpolation in log(Re). To do this LandD_0012.m from Chap. 3 is replaced
by ReadIn_4412.m and LandD.m. The first of these functions must be rewritten for
every new aerofoil used but the second is general. ReadIn_4412.m reads the data
from the data file naca4412.in .