Wind Turbine Aerodynamics Part A: Basic Principles - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 310

Vortex Wake Models
A variety of vortex wake models have been employed for wind turbines in axial flow.
Coton and Wang [1999] extended the earlier work of Robinson et al. [1994, 1995] on the use
of a prescribed wake to treat yawed flow. As the name implies, prescribed wake methods
simplify the location of the wake and use the wake locations and the Biot-Savart relation to
determine the influence of each trailing vortex on each blade station. Currin et al. [2007a,
2007b] have extended the prescribed wake approach to create a dynamic wake model which
has been incorporated into a structural code. In this approach, the wake is divided into three
near-wake regions where wake expansion is occurring and a far-wake region where radial
expansion no longer occurs. Comparisons with test data have shown good agreement.
Rotor Coniguration Effects
A large number of variables exist in the design of a HAWT rotor, including taper , twist ,
solidity , and number of blades . As taper and twist are intimately associated with and often
controlled by manufacturing techniques, we will consider the aerodynamic effects on perfor-
mance of only solidity and blade number.
Rotor Solidity and Number of Blades
Solidity, defined as the total blade planform area divided by the swept area of the rotor
is typically less than 0.10 for modern wind turbines. The rotor solidities of the NASA/DOE
Mod-0, Mod-1, and Mod-2 two-bladed experimental HAWTs were 0.029, 0.042, and 0.036,
respectively, while typical three-bladed HAWTs have solidities between 0.070 and 0.080.
(See Chapters 3 and 4 for descriptions of these wind turbines.)
As the solidity of a wind turbine rotor is increased, the tip-speed ratio for maximum
power coefficient is reduced. This effect can be explained by considering a rotor of a given
solidity at its peak power coefficient and associated tip-speed ratio, producing its optimum
axial induction. If the solidity of this rotor is increased and all other parameters are held
constant, both lift and drag forces will increase and, as a result, the axial induction factor
will increase beyond its optimum value. To restore optimum axial induction, aerodynamic
forces on the blade must be decreased, which is accomplished by reducing the tip-speed ratio.
Additionally, the peak power of a fixed-pitch rotor increases as solidity is increased. These
effects of solidity on power and power coefficient occur regardless of whether the solidity is
changed by increasing the number of blades or by increasing the chord dimensions of each
blade or both.
A different situation occurs when solidity is held constant and the number of blades is
changed. In this case, performance changes are caused by two opposing effects, which are
the effect of blade Reynolds number and the effect of tip losses . As the number of blades is
increased, chord dimensions decrease (to keep solidity constant), which reduces the blade's
Reynolds number. Rotor power decreases, as a result, since modern wind turbines usually
have turbulent flow over their blades, which is a regime in which a lower Reynolds number
produces lower lift and higher drag. The effect of increasing the number of blades on tip
losses is the opposite: Reducing the tip chord dimensions decreases the total tip loss, and
rotor power is increased.
Empirical Equation for Maximum Power Coefficient
Because of the many configuration variables that must be considered in the design of
a wind turbine rotor, it is often useful to be able to quickly estimate the maximum or peak