Aerofoils: Lift, Drag, and Circulation - Small Wind Turbines: Analysis, Design, and Application - page 73

Cummings [ 19 ]. Lift and drag of aerofoils can be found in Althaus [ 23 ], Althaus
and Wortmann [ 24 ], and Miley [ 25 ] and from the web site maintained by Professor
Michael Selig's group at the University of Illinois, Urbana-Champaign http://
www.ae.illinois.edu/m-selig/ (accessed 1 Oct 2010). Hard copies of their data can
be found in Selig et al. [ 26 , 27 ] and Lyon et al. [ 28 ]. The small wind turbine
community owes a great debt to NASA and Professor Selig for making available
so much valuable information.
4.6.2 Exercises
1. If Figs. 4.1 and 4.2 are thought of as sections through typical wind turbine
blades, will the wind direction be up or down the page? What is the direction of
rotation?
2. The three blades of a vertical axis wind turbine are attached to the hub by
horizontal support arms, one for each blade. The turbine is 4 m in diameter and
the chord length of the non-lifting supports is 7 cm. To determine the effect of
the supports' drag on performance, the blades were removed and the main shaft
was instrumented to measure the torque, Q, necessary to drive the supports at
an angular velocity X (in rad/s) in still air. The data were fitted by the curve
Q (Nm) = 0.504 X 2 . Show that this is consistent with the drag coefficient C d
being independent of radius and determine its value.
3. Show that the pressure coefficient, C P , has the value of unity at the stagnation
point of an aerofoil in incompressible flow.
4. Why can C P never exceed this value?
5. Show that Eqs. 4.6 and 4.7 with A = B = C = 1 imply that the fluid force on a
thin flat plate is due entirely to the pressure at high a.
6. Show that ( 4.6 ) and ( 4.7 ) are consistent with C l /C d = 1/tan a in general only
when A = B = C.
7. Using your fluid dynamics textbook, review the discussion on the origin of lift
in fluid flow in terms of Bernoulli's equation and circulation and the rela-
tionship to the material in this chapter.
8. Go the web site of a large wind turbine manufacturer to see if you can find
enough data to include the operational range of Reynolds number on Fig. 4.10 .
Note that blade mass has no direct operational consequences and is used mainly
to separate the data.
9. The Lock number is used in helicopter aerodynamics to measure the ratio of
aerodynamic to inertial blade loads. At high lift, the Lock number can be
approximated as
qC l ; a cR 4 J
where q is the air density, C l,a is the slope of the lift coefficient (assumed
constant for the linear range), and J is the inertia. For a 5 kW, 2.5 m long blade,