Introduction to Wind Turbine Technology - Small Wind Turbines: Analysis, Design, and Application - page 8

1.4 Turbine Operating Parameters

As with any fluid machine, it is often useful to discuss wind turbine operation in
terms of parameter groupings that can be obtained from dimensional analysis.
Here the important parameters are introduced by taking advantage of Eq. 1.1 ,
which strongly suggests that the most important parameter, the power coefficient,
C P , should be defined as

P

C P ¼ ð 1 : 7 Þ

1

2 qU 0 pR 2

C P the ratio of the actual power produced to the power in the wind that would
otherwise pass the blade disk. Note that:

• C P is dimensionless
• By convention, it includes the factor of to relate power to the kinetic energy
flux through the blade disk as determined in Sect. 1.1 .
• For later use, note that C P is not strictly an efficiency, even though it is often
treated as one. As will be evident from the next chapter, it is possible to increase
C P by increasing the velocity of the wind through the blades by, for example,
surrounding the blades by a diffuser. However, C P can be interpreted as an
efficiency when comparing turbines of the same type, such as the diffuser-less
ones considered in this topic.

The form of ( 1.3 ) helps the dimensional analysis. By making the very general
statement that the turbine power should depend on wind speed, air density, turbine
radius, X, and the kinematic viscosity of the air, m, then

fP ; U 0 ; q ; R ; X ; m ð Þ ¼ 0 ð 1 : 8 Þ

where f denotes (the as yet unknown) functional dependence. m is the actual
viscosity divided by the density, and has units of m 2 /s. For sea level conditions,
m = 1.5 9 10 -5 m 2 /s at 20C. There are many ways of proceeding with the
dimensional analysis, all of which should produce the same results. If the fol-
lowing is not familiar, the reader is referred to standard fluid mechanics texts such
as White [ 10 ].
Equation 1.8 contains six parameters or variables and three dimensions, so
there should be three non-dimensional groups resulting from the dimensional
analysis. To ensure that C P as defined by ( 1.7 ), is one of these groups, the
''repeating variables'' must be U 0 , q, and R. These repeating variables can, in
principle, appear in all the non-dimensional groups. Forming these groups then
allows ( 1.8 ) to be rewritten as

fC P ; XR = U 0 ; U 0 R = m ð Þ ¼ 0 ð 1 : 9 Þ