Below we list the various aerodynamic constraints identified in the literature.
2.3.2.1 SHELL AND AIRFOIL THICKNESS
A feasibility condition is forced on the shell thickness and the surface of the airfoil of the
wind turbine blade in the following references (Benini & Toffolo, 2002; Bizzarrini et al., 2011; F.
Grasso, 2011; Francesco Grasso, 2012; Ju & Zhang, 2012; Maki et al., 2012; Petrone et al.,
2011). For example, Benini and Toffolo restricted the shell thickness to half of the blade profile
thickness at any radius.
In addition, Grazzo (F. Grasso, 2011) also imposes a minimum trailing edge thickness of 0.25 and a minimum leading edge radius of 0.015c to ensure airfoil’s feasibility and ensure a proper trailing edge separation. In (Francesco Grasso, 2012), a minimum airfoil thickness of
35% of the chord and a minimum shell thickness at the trailing edge of 1% (to take into account
manufacturing requirements) of the chord were chosen.
Bizzarrini et al. (Bizzarrini et al., 2011) and Grasso (F. Grasso, 2011) impose a minimum
airfoil thickness of 18 % of the chord at the tip a trailing edge thickness of 0.25% of the chord to ensure airfoil’s practicability and feasibility from manufacturing point of view.
Maki et al. (Maki et al., 2012) ensured that the thickness of the shell ts and web tw are
decreasing along the span. Two additional inequality constraints on their thicknesses in terms
of the maximum sectional thickness t were added as follows (refer to Figure 7):
𝑡𝑠≤
1
Figure 7 : Blade section diagram (source (Maki et al., 2012)).
Petrone et al. (Petrone et al., 2011) inserted a geometrical constraint to avoid the
intersections of the upper and lower airfoil surfaces. In addition, the curvature change of the
upper and lower surfaces of the airfoil is restricted (Bak, 2013; Petrone et al., 2011). For
instance, the inner part of the blade is designed with thicker airfoil to withstand loads whereas
the outer part can be made with a thinner airfoil (Bak, 2013).
2.3.2.2 AIRFOIL CHARACTERISTICS
Two different aerodynamic constraints are imposed to control the airfoil behavior near
stall in (Bizzarrini et al., 2011). The first is achieved by imposing a separation point, guarantying
the robustness of the airfoil performance in case of gust. Second, in order to control the nature
of the stall, the absolute value of the slope beyond the stall angle is limited to a certain threshold
value. Similarly, Grasso (F. Grasso, 2011) imposes a minimum value of -0.08 for the moment
coefficient Cmc as to limit the blade torsion based on a comparative analysis made in (Timmer
& Van Rooij, 2003; Van Rooij, 1996). Likewise, a maximum value of Cmc -0.15 was assigned
at the design condition (6 degrees of angle attack) in (Francesco Grasso, 2012).
Grasso (F. Grasso, 2011) also imposes -a minimum range of 7 degrees between the
start of a significant separation and the AoA by forcing the position of the separation point on
the suction side to be at minimum 90 % of the chord at 14 degrees AoA. Finally, to avoid abrupt
side and 0.1c on the pressure side are taken for the occurrence of flow separation (stall) on the
airfoil. In the airfoil design for the inner part of the blade, Grasso (Francesco Grasso, 2012)
adds a upper limit of 1.8 for the lift coefficient at 15 degrees AoA and a maximum drop in CL
less than 0.3 between 15 and 16 degrees (based on (Hoerner, 2012; Hoerner & Borst, 1985;
Timmer & Van Rooij, 2003)) all of this to avoid excessive lift performance that may lead to an
abrupt stall. Ju et al. (Ju & Zhang, 2012) limit the drag coefficient value in the airfoil geometry
optimization to prevent it from undesirably becoming higher during the optimization of the CL/CD
and CL of the airfoil.
2.3.2.3 MAXIMUM CHORD
The maximum chord is a geometric dimension that should be set to ensure proper
transportation of the blade across difficult landmarks such as tunnels and bridges (Bottasso et
al., 2010; Petrone et al., 2011). As stated in (Bak, 2013; Petrone et al., 2011), this constraint is
vital to consider if the wind turbine is to be installed on offshore sites.
2.3.2.4 NOISE LEVELS
Noise levels constraints were employed in the following references (T Diveux et al.,
2001; P Fuglsang & Aagaard Madsen, 1994; Peter Fuglsang et al., 2002; P. Fuglsang &
Madsen, 1999; Giguere & Selig, 2000; Lee et al., 2007; A. Ning et al., 2013; Xuan et al., 2008).
Fuglsang and Madsen (P. Fuglsang & Madsen, 1999) constrain the noise level emitted by the
wind turbine blades using semi-empirical aerodynamic noise models proposed by Brooks
(Brooks, Pope, & Marcolini, 1989) and Lowson (Lowson, 1994) that are mainly function of: the
stream flow, angle of attack and the turbulent inflow.
Giguère et Selig (Giguere & Selig, 2000) identify that the main sources of aerodynamic
tip speed of the rotor rather than incorporating a noise model, to save computational time. In
order to limit the noise level and sound pollution, Diveux et al. (T Diveux et al., 2001) fixed the
maximum rotor tip speed to be 80 m/s. Similarly, different limits for the blade tip velocity are
used in references (Bottasso et al., 2010) to contain noise emissions.
𝑉𝑡𝑖𝑝=
𝜋𝑁𝐷𝑅
60 ≤ 𝑉𝑡𝑖𝑝.𝑚𝑎𝑥 [2.11]
Lee et al. (Lee et al., 2007) considered the compressibility effect as a limitation of noise
level and proposed a constraint based on the upper limit of the Mach number at the blade tip:
𝑀𝑁𝑡𝑖𝑝= √𝑀𝑁2+ (
𝜋𝑛𝐷 𝑎𝑠 )
2≤ 0.3
[2.12]
where, MN is the Mach number, as is the speed of sound, and n is the blade revolution
per second (rps).
Xuan et al. (Xuan et al., 2008) conducted an airfoil optimization to minimize the noise
level by constraining the lift to drag ratio and the maximum lift coefficient. Ning et al. (A. Ning
et al., 2013) imposed a constraint on the maximum tip speed as an equivalent for noise
limitation and implemented it directly into the analysis.