Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

354 Fluid Mechanics, Thermodynamics of Turbomachinery
Blade planform
In all the preceding worked examples a constant value of chord size was used, mainly
to simplify proceedings. The actual planform used for the blades of most HAWTs is
tapered, the degree of taper is chosen for structural, economic and, to some degree, aesthetic
reasons. If the planform is known or one can be specified, the calculation procedure
developed previously, i.e. the BEM method, can be easily modified to include
the variation of blade chord as a function of radius.
In a following section, Glauert’s analysis is extended to determine the variation of
the rotor blade planform under optimum conditions.
Effect of varying the number of blades
A first estimate of overall performance (power output and axial force) based on actuator
disc theory was given earlier. The choice of the number of blades needed is one
of the first items to be considered. Wind turbines have been built with anything from
1 to 40 blades. The vast majority of HAWTs, with high tip–speed ratios, have either
two or three blades. For purposes such as water pumping, rotors with low tip–speed
ratios (giving high starting torques) employ a large number of blades. The chief considerations
to be made in deciding on the blade number, Z, are the design tip–speed
ratio, J, the effect on the power coefficient, CP, as well as other factors such as weight,
cost, structural dynamics and fatigue life, about which we cannot consider in this short
chapter.
Tangler (2000) has reviewed the evolution of the rotor and the design of blades for
HAWTs, commenting that for large commercial machines, the upwind, three-bladed
rotor is the industry accepted standard. Most large machines built since the mid-1990s
are of this configuration. The blade number choice appears to be guided mainly by
inviscid calculations presented by Rohrback and Worobel (1977) and Miller and
Dugundji (1978). Figure 10.16 shows the effect on the power coefficient CP of blade
number for a range of tip–speed ratio, J. It is clear, on the basis of these results, that
there is a significant increase in CP in going from one blade to two blades, rather less
gain in going from two to three blades and so on for higher numbers of blades. In reality,
the apparent gains in CP would be quickly cancelled when blade frictional losses are
included with more than two or three blades.
Tangler (2000) indicated that considerations of rotor noise and aesthetics strongly
support the choice of three blades rather than two or even one. Also, for a given rotor
diameter and solidity, a three-bladed rotor will have two thirds the blade loading of a
two-bladed rotor resulting in lower impulsive noise generation.
Effect of varying tip–speed ratio
The tip–speed ratio J is generally regarded as a parameter of some importance in the
design performance of a wind turbine. So far, all the examples have been determined
with one value of J and it is worth finding out how performance changes with other
values of the tip–speed ratio. Using the procedure outlined in Example 10.6, assuming
zero drag (e = 0) and ignoring the correction for a finite number of blades, the overall