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A practical approach for selecting optimum wind rotors
Article in Renewable Energy · April 2003
DOI: 10.1016/S0960-1481(02)00028-9
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Renewable Energy 28 (2003) 803–822
www.elsevier.com/locate/renene
A practical approach for selecting optimum
wind rotors
K.Y. Maalawi, M.A Badr
Mechanical Engineering Department, National Research Center, Dokki, Cairo, Egypt
Received 20 October 2001; accepted 5 February 2002
Abstract
The main objective of this paper is to categorize practical families of horizontal-axis wind
turbine rotors, which are optimized to produce the largest possible power output. Refined blade
geometry is obtained from the best approximation of the calculated theoretical optimum chord
and twist distributions of the rotating blade. The mathematical formulation is based on dimensionless quantities so as to make the aerodynamic analysis valid for any arbitrary turbine
models having different rotor sizes and operating at different wind regimes. The selected
design parameters include the number of blades, type of airfoil section and the blade root
offset from hub center. The effects of wind shear as well as tower shadow are also examined.
A computer program has been developed to automate the overall analysis procedures, and
several numerical examples are given showing the variation of the power and thrust coefficients
with the design tip speed ratio for various rotor configurations.
 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction
Wind turbines having high power output are increasingly developed as potential
candidates for clean energy substitution. The applications are diverse, ranging from
domestic usage to large-scale wind farm and utility operation. There has been a large
and active research interest in this field, with an extensive literature. Glauert [1]
initiated the calculation of the optimum windmill by making the power integral equation stationary. The resulting implicit relations between the velocity induction factors were solved by an iterative procedure [refer to eqs. (2.10), (2.11) and (2.14), p.
328 of Ref. [1] ]. Rohrbach and Worobel [2] used the constant wake displacement
method of propeller theory to predict the peak performance where the local power
coefficient was only maximized at 75% of the rotor radius. The wake displacement
0960-1481/03/$ - see front matter.  2002 Elsevier Science Ltd. All rights reserved.
PII: S 0 9 6 0 - 1 4 8 1 ( 0 2 ) 0 0 0 2 8 - 9
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Nomenclature
a
a’
az
As
C
Cn
Ct
CD
CDO
CL
CLα
CL∗
CP
CQ
CT
F
Ho
NB
r
rH
ro
R
Re
Ts
Vo
Vr
Vw
Ws
Z
a
ao
a∗
qB
qo
qs
l
lr
s
f
y
yo
Axial induction factor
Angular induction factor
Wind shear exponent
Wind velocity reduction factor
Blade chord
Normal force coefficient
Tangential force coefficient
Drag coefficient
Drag coefficient at zero lift
Lift coefficient
Lift curve slope
Lift coefficient at optimum angle of attack, a∗
Power coefficient
Torque coefficien
Thrust coefficient
Tip-loss factor
Hub height
Number of blades
Local blade radius
Blade-root offset from hub center
Rotor radius-to-hub height ratio ( ⫽ R / Ho)
Rotor radius
Reynold’s number
Tower shadow coefficient
Mean wind velocity at hub height
Resultant wind velocity
Net wind velocity
Wind shear coefficient
Height above the ground
Angle of attack
Zero-lift angle of attack
Angle of attack for minimum (CD/CL)
Airfoil setting angle
Initial built-in twist
Setting angle at blade root (blade pitch)
Tip-speed ratio (TSR)
Local speed ratio
Local solidity
Inflow angle
Azimuth angle
Shadow-half angle
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
805
velocity was assumed to be the same at all radial stations along the blade. Wilson
et al. [3] extended Glauert’s work and performed a local optimization analysis by
maximizing the power output at each radial station. The axial induction factors were
varied until the power contribution became stationary (see p. 59 of Ref. [3]). A more
analytical approach was given by Pandey et al. [4], where the effects of drag and
tip losses were taken into consideration in calculating the axial and rotational induction factors. Pandey’s results were in complete agreement with the optimum design
values obtained from Wilson’s method.
A recent study [5] has indicated that the theoretical optimum distribution of the
inflow angle can be adequately determined from an exact trigonometric function
method, which is based on Glauert’s optimum condition [1]. The developed approach
eliminated much of the numerical efforts as required by the other iterative procedures, and a unique relation in the angle of attack was developed, ensuring convergence of the attained solutions [refer to eq. (15) of Ref. [5] ].
In all the above methods, the obtained theoretical optimum configuration of the
rotor blades may be too difficult to fabricate and produce economically. It is a major
aim of the present study to generate practical families of optimum blade shapes,
which can conform to manufacturing and production requirements. The analysis also
accounts for the influence of the earth boundary layer and tower shadow (for downwind machines) on the calculated maximum power output, two important factors
that were missed in previous publications. Another feature of this work is the independence of the developed mathematical model on either the rotor size or mean wind
velocity of a specific site. The present formulation deals with dimensionless quantities in order to make the model valid for any arbitrary configuration. The actual
dimensional values can be determined for a given mean wind velocity and an estimated rotor size from known energy needs. Numerical solutions are presented and
discussed, covering wide range of tip speed ratios, airfoil sections and number of
blades.
2. Optimum rotor configuration
The main aerodynamic design aspects of a wind turbine rotor include the determination of blade platform and twist distribution, choice of airfoil section, number of
blades and the design tip speed ratio (TSR). The determination of the rotor size
depends basically on the needed energy and average mean wind speed for a specific site.
The theoretical optimum chord and twist at any radial station along the blade,
shown in Fig. 1, can be determined from the relations [3–5]:
Chord: C ⫽
pr
s
NB r
Twist: qB ⫽ f⫺a.
(1a)
(1b)
The solidity ratio sr can be calculated from eq. (5) for optimum conditions. The
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 1.
Wind rotor velocity components.
optimum angle of attack a corresponds to the value at which the airfoil produces
the maximum lift-to-drag ratio. It is to be noticed that, all parameters are expressed
in dimensionless form in order to make the mathematical formulation valid for any
arbitrary turbine model. For example, the chord c is defined by the notation
c←c / 2R, which means that the dimensionless airfoil chord is equal to its dimensional
value divided by twice the rotor radius (more details are given in Table 1).
Extensive computer analysis of performance-optimized turbine models has indicated that the practical blade configuration producing a power coefficient close to
the optimum theoretical one can have a linear chord variation and an exponential
twist distribution. The chord has been found to be best represented by the tangent
line to the theoretical distribution at 75% radial station. Such refined blade geometry
can be mathematically expressed by:
Blade chord: C ⫽ ac ⫹ bcx
(2a)
Built-in twist: qo ⫽ aq(1⫺e ).
bqx
(2b)
The total twist, qB, is the difference between the setting angle at blade root, qs,
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
807
Fig. 2. General program flowchart. (a) Module 1: generation of optimum rotor configurations. (b) Module 2: calculation of optimum aerodynamic coefficients.
and qo. The b’s coefficients are always negative provided that both chord and twist
are decreasing towards blade tip.
3. Aerodynamic performance analysis
Performance analysis of a horizontal axis wind turbine rotor combines both
momentum and blade element theories [1,3–5]. Several effects exist in calculating
the resultant velocity of the incident wind. The most important ones are the atmospheric winds, induced velocities and blade velocity (see Fig. 1). Thresher et al. [6]
considered the atmospheric winds to be composed of the mean (gradient) wind super-
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Table 2
Aerodynamic characteristics of airfoil sections (Re ⫽ 3.0 × 106)
NACA
series
0012
1412
2412
4412
23012
23015
23018
23021
ao (°)
0.0
–1.2
–2.0
–3.8
–1.2
–1.15
–1.1
–1.1
Fig. 3.
a∗ (°)
9.6264
7.7404
4.8804
5.46
8.1919
9.0736
9.4369
9.6109
CLα (per
radian)
6.16
5.73
7.162
6.0311
5.73
5..73
5.73
5.73
CL∗ (per
radian)
1.04730
0.93404
0.7882
0.9589
0.9792
1.0649
1.0487
1.0161
CD coefficients×10⫺3
CDO
K1
K2
5.79125
5.65154
6.09675
6.32025
6.2582
6.5785
6.7985
7.52157
0.441075
–0.87185
–2.82939
–3.49366
–2.16741
–2.13732
–1.05613
–1.8112
5.853473
6.030301
7.938405
7.502153
6.81380
7.61093
6.83437
7.05985
Optimum chord coefficients for NACA-4 digit airfoils (rH ⫽ 0.05).
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 4.
809
Optimum chord coefficients for NACA five-digit airfoils (rH ⫽ 0.05).
imposed by unsteady turbulence components. The latter is essential when dealing
with structural dynamics, and is out of the scope of the present analysis. The gradient
wind includes the earth boundary layer (wind shear) and tower shadow effects.
3.1. Wind shear
The wind shear is modeled by the simple power law [6]
Vz ⫽ (z)az
(3a)
where Vz and z are the dimensionless wind speed and height above the ground,
respectively (Vz←Vz / Vo, z←z / Ho ). Vo is the wind speed at hub height Ho, and az
is the wind shear exponent varying between 0.15 and 0.5 depending on local topological conditions. Substituting for z⬇1 ⫹ rrocosy, and expanding into a Taylor series about z ⫽ 1, one obtains:
Vz⬇1 ⫹ Ws
Ws is termed as the wind shear coefficient defined by
(3b)
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 5.
Effect of root offset on the optimum chord distribution (NACA 4412).
Ws ⫽ azrrocosy ⫹ 0.25az(az⫺1)(rro)2(1 ⫹ cos2y) ⫹ …
(3c)
where y is the azimuth angle of the rotating blade.
3.2. Tower shadow effects
For downwind machines, the decrease in the wind velocity when the blade is
hidden by the tower may be represented by a function B(⌿) called the tower shadow
blockage factor defined as [6,7]
B(y)
⫽ 1⫺Ts(y) for (p⫺yo)ⱕyⱕ(p ⫹ yo)
⫽1
otherwise
.
(4a)
Ts(y) is called the tower shadow coefficient which, for a single-pole configuration,
is given by
Ts(y) ⫽
冋
册
As
p
1 ⫹ cos (y⫺p) .
2
yo
(4b)
In the above derivations, the tower shadow is represented by a 2yo-sector of the
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 6.
811
Optimum pitch for different types of airfoils (rH ⫽ 0.05) (NB ⫽ 1, 2, 3, and 4).
rotor plane centered aty ⫽ p with the rotor blade straight down at the 6 o’clock
position for the maximum decrease in the velocity, which is represented by the factor As.
Therefore, combining both effects, the dimensionless net wind velocity is given
by the linearized form:
Vw(r,y)⬇1 ⫹ Ws⫺Ts.
The average net velocity at any radial station is given by the integral
(4c)
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Table 1
Definition of dimensionless quantities
Quantity
Blade chord
Blade length
Radial distance from hub
center
Blade root offset from hub
center
Radial distance from blade
root
Wind velocity
Height above ground
a
Notation
Non-dimensionalizationa
C
L
r
C←C / 2R
L←L / R
r←r / R
rH
rH←rH / R
x
x←x / L
(Vr, Vw, Vz)
z
V←V / Vo
z←z / Ho
Reference parameters: Ho, hub height; r, rotor radius; Vo, wind velocity at Ho.
冕
2p
1
V̄w(r) ⫽
V (r,y)dy.
2p w
(4d)
0
3.3. Aerodynamic thrust and power coefficients
The variation of the inflow angle, f, along the blade span can be determined by
solving the transcendental equation [see eq. (15) of Ref.[5]]:
4Fsinf(cosf⫺lrsinf)⫺sr(lrCn ⫹ Ct) ⫽ 0.
(5)
where F denotes Prandtle’s tip-loss factor [1–5], and Cn and Ct are known as the
normal and tangential aerodynamic coefficients, respectively. They are determined
from the relations (see Fig. 1)
Cn ⫽ CLcosf ⫹ CDsinf
(6a)
Ct ⫽ CLsinf ⫹ CDcosf.
(6b)
The thrust, torque and power coefficients developed by the NB-bladed rotor can
be computed by summing up the contributions of the individual blades and integrating over one complete revolution. First, the dimensionless velocity of the relative
wind is calculated from the relation:
V2r ⫽ V̄2w[(1⫺a)2 ⫹ l2r(1 ⫹ a’)2]
where lr ⫽ l∗r / V̄w , a’ ⫽ 1 / {[(2Fsin2f) / (srCt)]⫺1} and a ⫽ a⬘lr(Cn / Ct).
Therefore, the thrust, torque and power coefficients are determined from [5]
(7)
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
813
冕
1
2NBL V2rCCndx
Thrust ⫺ coefficient: CT ⫽
0
p(1⫺r2H)
(8a)
冕
1
2NBL V2rCCtrdx
Torque ⫺ coefficient: CQ ⫽
0
p(1⫺r2H)
Power ⫺ coefficient: CP ⫽ lCQ
(8b)
(8c)
where l ⫽ ⍀r / V0 is the design TSR.
4. Description of the computer program
A computer program has been prepared in Fortran-77 for the implementation
of the developed model on the computer. The general flowchart structures of the
established modules are shown in Fig. 2. The first module, shown in Fig. 2a, generates the refined blade geometry by best approximating the calculated theoretical optimum chord and twist distributions defined in eq. (1). The input data comprises the
number of radial stations along the blade, the dimensionless root offset rH and the
maximum number of airfoil sections employed (Nmax). The necessary airfoil data,
such as those given in [8], are stored in a special subroutine, which has the flexibility
to include variety of airfoil types and shapes. The program also allows for the airfoil
type to vary along the blade, with each type given a specific index number. The lift
and drag coefficients can be determined at any desired value of the angle of attack
for a specified Reynold’s number. The dimensionless chord and twist are calculated
at equidistant stations along the blade for different values of blade number and TSR.
The corresponding values of the a and b coefficients, defined in eq. (2), are determined and stored in a special file, which is used afterwards as an input data file for
the second module. The second module, depicted in Fig. 2b, performs the complete
performance analysis for the specified input data. The main tasks include, the analysis
of wind shear and tower shadow, root-finding problem for the determination of the
angle of attack [see Eq. (5)], and computation of the thrust and power coefficients
by integrating eq. (8) numerically.
5. Applications and computational results
For a specified TSR, the main parameters that have a bearing on the aerodynamic
design of a wind rotor include the geometry and number of the rotating blades, type
of airfoil sections and hub size. The distribution of wind velocity in the earth boundary layer as well as in the tower shadow region can also have significant effects on
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
the overall rotor design. In the examples that follow, the range of the TSR is taken
between 4 and 16, and blade number between 1 and 4. These are typical values for
large machines utilized for electricity generation. Operating the wind turbine at a
constant TSR corresponding to the maximum power point at all times may generate
20–30% more electricity per year. This requires, however, a control scheme to operate with variable speed. Concerning blade number (NB), a rotor with one blade can
be cheaper and easier to erect but it is not popular and too noisy. The two-bladed
rotor is also simpler to assemble and erect but produces less power than that
developed by the three-bladed one. The latter produces smoother power output with
balanced gyroscopic loads, and is more aesthetic.
Perhaps, the choice of a specific type of airfoil section is the key point in designing
an efficient rotor [9,10]. Griffiths [9] showed that the output power is greatly affected
by the airfoil lift-to-drag ratio, while the study of [10] recommended that the airfoil
be selected according to its location along the blade to ensure its highest contribution
to the overall performance. In the present study, two NACA-airfoil families are
implemented: the four-digit and five-digit series, which are commonly used in the
design of rotary wings and wind turbines. The classification of the NACA four-digit
range of airfoils is very simple where the maximum thickness occurs at 30% chord
position from leading edge. The NACA-0012, 1412, 2412 and 4412 series have
maximum thickness of 12% and camber of 0, 1, 2 and 4% at 40% chord, respectively.
The effect of camber is merely to reduce the incidence at which a given lift coefficient is produced. The NACA five-digit has been chosen to have a mean line of
230-series with 1.8% camber at 15% of the chord from leading edge. The maximum
thickness takes the values of 12, 15, 18 and 21% of chord. The aerodynamic characteristics of these airfoils were extracted from the data given in [8], and the relations
between the drag and lift coefficients have been approximated by the following
second degree polynomial
CD ⫽ CDO ⫹ K1CL ⫹ K2C2L
Fig. 7.
Effect of root offset on optimum pitch (NACA 4412).
(9)
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 8.
815
Optimum twist coefficients for different root offsets.
Fig. 9. Variation of power coefficient with TSR for NACA five-digit airfoils (rH ⫽ 0.05, no shear, no
shadow).
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 10. Variation of thrust coefficient with TSR for NACA five-digit airfoils (rH ⫽ 0.05, no shear, no
shadow).
which can be valid only for unstalled conditions. The various aerodynamic data that
are used in the generation of the numerical results are given in Table 2. Other airfoil
types with different Reynold’s number can be easily considered by adding the corresponding data to the specific computer routines.
Several cases of study, showing the developed optimal blade shapes, are presented
in Figs. 3–8. Variation of the optimum chord coefficients (ac, bc) with TSR is
depicted in Fig. 3, for different blade number. Blades with the selected NACA-4
digit airfoils have been investigated in detail. It is remarked that the calculated distributions are of a hyperbolic functional type, which may look like the streamlines of
a fluid flow emitting from a jet and striking normal to a flat plate. As a general
observation, the chord at blade root (ac) and the tapering rate (–bc) decrease with
TSR for all airfoil types and blade number. However, for a specified TSR, they
decrease with blade number and increase with increasing airfoil camber up to a value
of 2%, after which they show slight decrease for further increase in camber. Good
one or two-bladed rotors shall have a nearly triangular blade configuration, while
optimum three or four-bladed rotors shall have thinner trapezoidal blades with a
smaller chord at root and slower rate of tapering. Fig. 4 shows the optimal distributions for NACA five-digit airfoils. The same design trends obtained for the NACA-
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
817
Fig. 11. Power coefficient for different blade number (NACA four-digit airfoils, rH ⫽ 0.05).
4 digits are repeated, except that the root chord and the tapering rate show gradual
decrease as the airfoil thickness increases. As a noticeable result, the optimal blades
with NACA-4 digit airfoils shall have wider chord distributions than those with fivedigit series. It must be mentioned here that, additional modifications shall be necessary to the final optimized blade geometry in order not to violate structural design
requirements.
To investigate the effect of hub size on the resulting optimum chord distribution,
four values of the dimensionless blade root offset, rH, were examined; 0.025, 0.05,
0.075 and 0.1. Fig. 5 shows the variation of the coefficients ac and bc with the design
TSR for different number of blades having NACA-4412 airfoil section.
Optimum variation of the pitch angle, qs, with TSR for all of the selected airfoil
types is shown in Fig. 6. The root-offset, rH, was kept constant at 0.05, and the
number of blades can take any desired value. It is seen that good blades ought to
have smaller pitch as the TSR increases. It is also noticed that qs increases with
camber up to a specified value, after which a slight decrease can be observed (Fig.
6a). The opposite trend occurs with airfoil thickness, where, as shown in Fig. 6b,
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 12.
Thrust coefficient for different NACA four-digit airfoils (rH ⫽ 0.05).
θs decreases with increasing thickness. Fig. 7 illustrates variation of the pitch angle
for different root offsets. For a prescribed airfoil type, the pitch decreases for increasing offset, which is an expected result. The same values of rH were reconsidered to
examine their effect on the optimal variation of the twist coefficients (aq, bq) with
the design TSR, as indicated in Fig. 8. The optimization process produces smaller
aq and ⫺bq for increasing values of rH, independently on the airfoil type or blade
number.
Concerning performance of the developed optimal configurations, several cases
of study have been considered to examine the variation of the power and thrust
coefficients with TSR, for different blade number, NACA airfoils, wind shear and
tower shadow coefficients. Referring to Fig. 9, it is seen that Cp increases rapidly
with TSR up to its optimum value after which it decreases gradually with a slower
rate. The optimum range of the TSR is observed to lie between 6 and 11, depending
on the number of blades. The NACA 23012 series excels all other five-digit families
at producing extra power output. Rotors with smaller number of blades are recommended to operate at higher TSR to compensate for the loss in the power, which
would be produced if more blades were used. Fig. 10 shows variation of CT with
TSR for the same families. It is remarked that CT increases rapidly with TSR until
it reaches a constant level at its maximum attainable value. Thinner airfoils produce
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 13.
819
Effect of tower shadow on power (Cp) and thrust (CT) coefficients (rH ⫽ 0.05, ro ⫽ 0.7).
the smallest thrust loading among all of the five-digit airfoils. The same behavior is
repeated for wind rotors with NACA four-digit series depicted in Figs. 11 and 12.
Two cases were considered: the basic case without wind shear and tower shadow,
and the case with 100% shadow and 20% shear exponent. The average reduction in
the power and thrust coefficients was found to be 16 and 11%, respectively. The
design TSR at which Cpmax occurs is also reduced by about 9%. The NACA 1412
produces higher power output and lower level of the thrust loading. More results
are given in Figs. 13 and 14 for several types of airfoils and blade number, showing
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K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
Fig. 14.
Effect of wind shear on Cp and CT for different NACA airfoils (ro ⫽ 0.7, As ⫽ 0).
the effect of including tower shadow and wind shear on the power and thrust coefficients.
6. Conclusions
A practical methodology has been presented for generating optimized wind rotor
configurations, which produce the largest possible power output. The approach uses
a direct formulation based on blade-element strip theory, and the developed mathematical model deals with dimensionless quantities so that it can be applied to variety
of wind turbines having different rotor sizes and operating at different wind regimes.
The selected design parameters include the chord and twist distributions, number of
blades, type of airfoil section, hub size and TSR. The model also incorporates both
of the tower shadow and wind shear effects. A general computer program, composed
of two main modules, has been developed for automating the overall performance
analysis and design procedures. Several illustrating examples are given, showing the
influences of the various parameters on the resulting optimum designs. Two families
K.Y. Maalawi, M.A. Badr / Renewable Energy 28 (2003) 803–822
821
of NACA airfoils have been demonstrated: the four-digit series having constant thickness and the five series with constant camber. Other types of airfoils working at
different values of Reynold’s number could be readily covered in the developed
computer program. Important results have indicated that rotor blades with thinner
airfoils and higher camber are recommended for increasing the power output, and
lowering the level of thrust loading. For most of the selected airfoil types and blade
number the chord and rate of taper decrease with TSR. Suitable blade designs with
NACA five-digit airfoils shall have thinner platforms than those with four-digit series. It has been shown that for a prescribed value of TSR, the blade pitch is a direct
function in the type of airfoil and blade root offset, independently on the number of
blades. The variation of the optimal twist distribution with TSR is merely the same
for all airfoil types and blade number. More results have indicated that a substantial
reduction in the power output occurs when the tower shadow or wind shear is taken
into consideration.
For known airfoil type, blade number and hub size the design TSR at which the
maximum power occurs can be directly determined, and hence, the optimum blade
geometry. The actual dimensions of the blade can be obtained by estimating the
rotor size from known energy needs and average wind speed of a specific site.
Finally, intended future studies will consider the effect of changing the airfoil shape
along the blade span with the use of special types other than those from the NACA
families. The optimal chord, twist, and power coefficients shall hopefully be calculated directly from a generated set of surface functions, which best fit the obtained
results at the different values of the selected design parameters. Wind velocity analysis shall contain additional components due to turbulence, which needs large statistical data collection of wind fluctuations at the specific site.
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