Blade Element Theory for Wind Turbines - Small Wind Turbines: Analysis, Design, and Application - page 41

Chapter 3
Blade Element Theory for Wind Turbines
3.1 Introduction
The conservation equations of fluid mechanics were used in the last chapter to
derive equations for the power output and thrust for a turbine modeled as an
actuator disk. When it is assumed that there is no radial dependence in the flow or
over the disk, these equations lead to the well-known Betz-Joukowsky limit on
wind turbine performance. However, they do not consider the forces acting on the
individual blades which give rise to the thrust and torque, and hence power. These
are obviously the main quantities required for analysis of wind turbine perfor-
mance and strength and are necessary for aerodynamic and structural design.
The traditional way to extend the analysis of Chap. 2 is to divide the flow
through the blades into a number of concentric annular streamtubes. In practice, the
number of streamtubes should be large enough to provide a good approximation to
the variations in velocity, chord, and twist along a blade. Experience shows that
typical performance analyses can be done accurately with between 10 and 20 blade
elements. The conservation equations for these streamtubes are easily-recognised
generalisations of those derived in Chap. 2 for mass, axial and angular momentum,
and energy. The velocity and pressure within each streamtube do not vary with
radius but may vary from one streamtube to the next. Each streamtube intersects a
blade element, generating a lift and drag. The next section makes explicit a number
of the fundamental assumptions of blade element theory, of which the most
important is that blade elements behave as aerofoils. It is, therefore, necessary to
review the important aspects of aerofoil theory with special reference to small wind
turbines; this is done in Chap. 4 . Section 3.3 develops the important conservation
equations in annular streamtube form, starting from the analysis of Chap. 2 . Sec-
tion 3.4 considers the forces acting on the blade elements. The implementation of
these equations in a Matlab computer program to predict wind turbine performance
is covered in Sect. 3.5 . Section 3.6 describes this program which allows the use of
any number of blade elements. The M-files of all listed programs are available in
the online materials ( http://extras.springer.com ).