-
Journal of Mechanical Science and Technology 26 (1) (2012)
81~92
www.springerlink.com/content/1738-494x DOI
10.1007/s12206-011-1014-7
CFD Investigation on the aerodynamic characteristics of a
small-sized wind
turbine of NREL PHASE VI operating with a stall-regulated method
Jang-Oh MO1 and Young-Ho LEE2,*
1School of Mechanical Engineering, The University of Adelaide,
South Australia 5005, Austrailia 2Division of Mechanical and
Energy-System Engineering, Korea Maritime University, Busan,
606-791, Korea
(Manuscript Received January 24, 2011; Revised August 30, 2011;
Accepted October 12, 2011)
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Abstract The objective of this investigation is to clearly
understand the aerodynamic characteristics of a small-sized wind
turbine of NREL
Phase VI, operating with a stall-regulated method using CFD
code. Based on this, it is possible to provide turbine designers
with the aerodynamic design data to increase efficiency and improve
performance in the design phase of future small-sized wind turbine
blades. Moreover, a comparison was made between experimental
datasets, in order to verify the reliability and validity of the
analysis results. The first height in the normal direction from the
surface of a rotor blade is about 0.2 mm, and the average value of
y+ is about 7 at 7 m/s. The domain is chosen to consist of only two
hexahedral mesh regions, namely the interior region, including the
wind turbine blade, and the external region excluding the
rectangle. The total cell number of the numerical grid is about Ng
= 3.0 106. Five different inflow velocities, in the range Vin =
7.0-25.1 m/s, are used for the rotor blade calculations. The
calculated power coefficient is about 0.35 at a TSR of 5.41,
corresponding to 7 m/s, and showed considerably good agreement with
the experimental measurements, to within 0.08%. It was observed
that the 3-D stall begins to generate near the blade root at a wind
speed of 7 m/s. Therefore, root design approaches consid-ering the
appropriate selection of the angle of attack and the thickness are
very important in order to generate the stall on the blade root.
Through a clear understanding of aerodynamic characteristics of a
small-sized NREL Phase VI wind turbine, it is expected that this
use-ful aerodynamic data will be made available to designers as
guidance in designing stall-regulated wind turbine blades in the
development phase of small-sized wind turbine systems in the
future.
Keywords: CFD; A small-sized wind turbine; Aerodynamic
characteristics; Stall-regulated method; Blade element momentum
theory; Power coefficient;
Pressure coefficient; 3-D stall; Separated flow; Stall angle;
Surface streamlines; Tip speed ratio
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1. Introduction
Owing to the potential severity of climate change as a result of
global warming, every country in the world is taking an active
interest in the development of renewable energy. In particular, the
installation of wind power generation systems, which are
economically feasible and environmentally friendly, has shown a
sharp increase since the 1990s, with an annual average increase of
28% over the past five years. By 2020, wind power will generate
about 1,200 GW, approximately 12% of the worldwide total energy
production, and it is ex-pected that capacity of 2,270 MW,
corresponding to about 3% of the total capacity, will be introduced
to the domestic market by 2012 [1].
The fundamental technological field in wind power system
development is the blade. Once the basic design, including the
capacity of the wind turbine and its operating wind speed, is
finished, the blade development is the next stage. Develop-ment of
a control system for the generator and gear box will then follow.
For this reason, the major commercial wind power development
companies and research institutes have made great efforts to
develop unique blades; through this, the large scale-up and high
efficiency of wind power generators has been realized. However, as
there is no opportunity for independent blade development, this
becomes an obstacle to the further activity in the wind power
generation industry.
Most blades for wind power generation require an opti-mized
aerodynamic design, and new rotor blade designs must clearly
understand the characteristics of the flow field in order to
increase efficiency and improve performance. To obtain the optimum
design parameters, it is necessary to study the char-acteristic
results of the huge flow field and aerodynamic per-formance from
reliable experiments. This is often difficult, owing to problems of
cost and time. Moreover, full-scale measurements are often
contaminated by varying wind speeds, changes in wind direction,
etc. Therefore, various numerical
This paper was recommended for publication in revised form by
Associate Editor Jun Sang Park
*Corresponding author. Tel.: +82 51 410 4293, Fax.: +82 51 403
0381 E-mail address: [email protected]
KSME & Springer 2012
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82 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92
analytic studies using the wake code, aero-elastic code, and CFD
code have been attempted in order to understand the flow around the
blade and the characteristics of efficient aero-dynamic
performance.
Studies on full Navier-Stokes simulations of wind turbine rotors
have been performed by Duque [2], Xu and Sankar [3, 4], Srensen and
Hansen [5], and Srensen and Michelsen [6]. Additionally, a large
number of rotor simulations have been performed by the helicopter
community.
The objective of this investigation is to clearly understand the
aerodynamic characteristics of a small-sized wind turbine of NREL
Phase VI, operating with a stall-regulated method using CFD code.
Based on this, it is possible to provide tur-bine designers with
the aerodynamic design data to increase efficiency and improve
performance in the design phase of future small-sized wind turbine
blades. Moreover, a compari-son was made between experimental
datasets, in order to ver-ify the reliability and validity of the
analysis results.
2. Computational methodologies
2.1 Specification of NREL Phase VI wind turbine
NREL successfully completed an experimental test for a Phase VI
wind turbine in a wind tunnel (24.4 36.6 m) at NASAs Ames Research
Center in May 2000. After this test, NREL revealed the experimental
results and information on the shape of the test blade on their
website, in order to verify the performance of commercial
analytical codes developed around the world. Therefore, the present
study adopts the blade shape used in the Phase VI tests as an
analysis target for CFD simulation, because the NREL Phase VI blade
shape can be accurately modeled using the released information, and
reliable test results for the turbine can be easily obtained. The
shape model of the Phase VI wind turbine blade (shown in Fig. 1) is
controlled by a stall-regulated method, and produces a rated output
power of 19.8 kW. The turbine blade diameter, rotational speed, and
blade number is D = 10.058 m, N = 71 rpm, and Z = 2, respectively.
Detailed specifications of the turbine model are shown in Table 1.
For the cases considered in the present study, the rotor cone angle
is set at 0, and the blade pitch angle is set at 5. This rotates
the blade tip chord line 5 towards feather, relative to the rotor
plane, thus point-
ing the leading edge into the oncoming wind. The distribution of
rotor blade twist angle from hub to tip is shown in Fig. 2. The
twist angles are relative values to zero twist at the 0.75 span,
and show negative values from 0.75 to 1 span. The blade shape of
the Phase VI wind turbine consists of airfoil S809 from root to
tip. This airfoil has a thickness of 21% of its chord length, and
is designed to be less sensitive to the surface roughness at the
leading edge of the wind turbine blade, in order to improve the
turbine output power [7, 8].
2.2 k- SST turbulence model
In the present work, the turbulence in the boundary layer is
modeled by the SST k- model. This model is chosen because of its
very promising results for 2-D separated flows [9, 10]. The
shear-stress transport (SST) k- model was developed by Menter [11,
12] to effectively blend the robust and accurate formation of the
k- model in the near-wall region with the free-stream independence
of the k- model in the far field. To achieve this, the k- model is
converted into a k- for-mulation [12]. The equations for the
turbulence model are solved after the momentum and pressure
correction equations in every sub-iteration. All computations are
performed assum-ing fully turbulent flow, excluding any laminar and
transi-tional effects at the leading edge region of the rotor.
Fig. 1. Shape model of the NREL Phase VI wind turbine blade.
Table 1. Specification of the NREL Phase VI wind turbine.
Number of blade Z 2
Rotor radius R 5.029 m
Rotational speed N 71.9 rpm
Cut-in wind speed Vc 6 m/s
Rated power Pr 19.8 kW
Power regulation Stall
Rotational direction CCW
Global pitch angle 5
Fig. 2. Twist angle of the NREL Phase VI wind turbine blade.
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J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92 83
( ) ( ) ( )i k k k ki j j
kk ku G Y St x x x + = + +
%
(1)
( ) ( ) ( )ii j j
u G Y D St x x x
+ = + + + (2) In these equations, kG% represents the generation
of turbu-
lent kinetic energy attributed to mean velocity gradients, G
represents the generation of , k and represent the effective
diffusivity of k and , respectively, kY and Y represent the
dissipation of k and attributed to tur-bulence, D represents the
cross-diffusion term, and kS and S are user-defined source terms.
The equations to which these symbols relate can be confirmed in
more detail in Ref. [13].
The wall boundary conditions for the k equation in the k- models
are treated in the same way as when enhanced wall treatments are
used with k- models. This means that all boundary conditions for
wall-function meshes will correspond to the wall function approach,
while for fine meshes the ap-propriate low Reynolds number boundary
conditions will be applied.
In the ANSYS FLUENT solver, the value of at the wall is
specified as
. (3)
The asymptotic value of + in the laminar sublayer is giv-
en by
(4)
where
(5)
and
(6)
where Sk is the roughness height. In the logarithmic region, the
value of + is
(7)
which leads to the value of in the wall cell as
. (8)
In the case of a wall cell being placed in the buffer region,
ANSYS FLUENT will blend + between the logarithmic and laminar
sublayer values. The meaning of these symbols can be confirmed in
Ref. [13]. Numerous experiments have shown that the near-wall
region can be largely subdivided into three layers, namely the
viscous layer (to y+ = 5), the buffer layer (to y+ = 60), and the
fully turbulent layer [14]. In this study, the first height in the
normal direction from the surface of a rotor blade is about 0.2 mm,
and the average value of y+ is about 7 at 7 m/s, which is between
the viscous and buffer lay-ers. If y+ exists within this range, it
is possible to perform the rotor blade calculations.
2.3 Numerical method
The geometrical model of the NREL Phase VI rotor blade was
constructed using GAMBIT software, based on the shape data
information [7, 8]. The twist angle is a maximum of 20.04 at the
root, and reduces to a minimum of -2.15 at the tip in order to
maximize aerodynamic performance. Each air-foil begins to attach
from r/R = 0.267 to the tip (Fig. 3).
The original NREL S809 airfoil contains a sharp trailing edge,
which is clearly not the case for the real blade. This feature also
unnecessarily complicates the construction of the hexahedral grids.
For this reason, it was replaced with a blunt trailing edge by
cutting at 0.99c. The computational domain for the wind turbine
blade is illustrated in Fig. 4. The domain is chosen to consist of
only two hexahedral mesh regions, namely the interior region,
including the wind turbine blade, and the external region excluding
the rectangle, whose line is expressed in detail in Fig. 4. Only
one of the two blades is explicitly modeled in the computations.
The remaining blade is accounted for using periodic boundary
conditions, exploit-ing the 180 symmetry of the two-bladed rotor.
In the compu-tational domain, a cylindrical cross-section with an
area less than the actual tunnel cross-section (24.4 36.6 m) is
used, corresponding to a radius of 15.1 m. The calculation domain
is defined by the reference length of the blade radius R, as shown
in Fig. 5. A spatial resolution of 2.5R to the calculation
Fig. 3. Shape Configuration of the NREL Phase VI blade using
GAMBT software.
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84 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92
domain inlet, 3.5R to the downstream region, and 3.0R to the
radial direction of the wind turbine model is applied. The sur-face
grid is comprised solely of quad meshes. The 100 nodes on the upper
and lower edges of each airfoil section were meshed in the
chordwise direction and concentrated in the leading and trailing
edge regions, and the 200 nodes in the spanwise direction, as shown
in Fig. 6. In order to create boundary layers on the blade surface,
20 nodes were meshed in the O type block surrounding the rotor
blade, with a spacing ratio of 1.1 in the normal direction and a
first height of 0.2 mm. The total cell number of the numerical grid
is about Ng = 3.0 106, consisting of hexahedral grids over the
total domain.
For the boundary conditions, a velocity condition with a
turbulent intensity of 3% is applied at the upstream boundary where
the flow enters the cylindrical domain, and an ambient pressure
condition is applied at the downstream point at which the flow
leaves the cylindrical domain. Six different inflow velocities, in
the range Vin = 7.0-25.1 m/s, are used for the rotor blade
calculations. The analysis conditions are summa-rized in Table
2.
2.4 Flow patterns around rotor blade
The 3-D flow generated from a rotor blade on the actual wind
turbine is quite complex. The flow that is branched out by
separation at the root moves towards the tip, because of the
influence of the centrifugal acceleration and the pressure
gra-dient in the radial direction. The centrifugal acceleration can
be expressed as r.+ The pressure gradient in the radial di-rection
changes according to the variation of the angle of at-tack on the
airfoil in a given position, and according to the variation of the
local velocity ratio (Tip speed ratio,
in
R V = ). The wind that is separated at the root and flows
in the radial direction of the blade passes the wind ( ) that
flows on the surface of the blade, thus forcibly generating a 3-D
separation on the surface of the blade, as shown in Fig. 7. At a
certain point, the wind separates out in the direction. This
airflow is also generated across the entire blade in both the
leading and trailing edges of the airfoil [15, 16]. Although it is
difficult to quantify the related data, the effect of this
phe-nomenon is thought to be significant.
3. Results and discussion
Fig. 8 represents the airfoil cross-section at radius r, having
a local blade twist angle of to the rotors plane of rotation. The
inflow wind speed Vin in the rotor plane, and the tangen-
Fig. 4. Computational domain.
Fig. 5. Surface grid on a rotor blade.
Fig. 6. Grid section at r/R=0.35 on a rotor blade.
Table 2. Analysis conditions.
Wind speed(Vin), m/s RPM , kg/m3 Case 1 7 71.9 1.246
Case 2 10 72.1 1.246
Case 3 13 72.1 1.227
Case 4 15.1 72.1 1.224
Case 5 20.1 72.0 1.221
Case 6 25.1 72.1 1.220
Fig. 7. sketch on the stream of separated flow around rotor
blade.
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J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92 85
tial speed r at the radius of the blade cross-section, combine
to give the local relative flow velocity, Vr. Together with the
airfoil chord line, this forms the aerodynamic angle of attack, .
The angle of attack is an aerodynamic parameter referring to the
relative flow velocity. The blade pitch angle is a geo-metrical
parameter referring to the plane of rotation. Blade element
momentum theory is used to derive the axial and circumferential
inflow factors, with the introduction of a tip loss factor to take
into account the finite number of rotor blades. Therefore, the wind
speed Vin can be expressed as Vin(1-a), owing to the aerodynamic
interference among blades, where a is the axial inflow factor with
a value of 1/3. This value is used in order to maximize the power
coefficient at 0.593, called the Betz limit. The angle of attack
can be calcu-lated using Eq. (9) according to the axial and
tangential veloci-ties when the axial inflow factor is assumed to
be 0. Owing to the global pitch angle, the axial inflow factor
becomes much lower than 1/3; however, we cannot ascertain its exact
value.
(9)
where 5 is a global pitch angle.
In the process of the blade design, the rotor blade should be
twisted in order to produce a maximum output power at an optimal
angle of attack. This corresponds to a maximum lift-to-drag ratio
for the rated wind speed at each location, because the rotational
speed linearly increases from root to tip. There-fore, it is
important to confirm the performance characteristics of airfoils
applied to a wind turbine blade.
Fig. 9 shows experimental lift-to-drag ratios, according to
different Reynolds numbers, of a S809 airfoil [8]. The lift-to-drag
ratio corresponding to 6.11 is approximately 55.4 at Re = 3 105. As
the Reynolds number rises to 3 105, the lift-to-drag ratio
increases up to a maximum of 89.58, corresponding to 6.16. The
important point is that the angle of attack corre-sponding to the
maximum lift-to-drag ratio is in the vicinity of 6 regardless of
the Reynolds number. The design angle of attack is generally at the
point of maximum lift-to-drag ratio. Therefore, this fact will
assist designers in performing the pitched-controlled or
stall-regulated design of a rotor blade. In this study, the
Reynolds number ranges from approximately
3.7-9.2 105 from root to tip for a wind speed of 7 m/s. Fig. 10
represents the streamline distributions on the suction
side of the rotor blade at six different wind speeds (7 m/s, 10
m/s, 13.1 m/s, 15.1 m/s, 20.1 m/s, and 25.1 m/s) from top to
bottom. It is observed that the stall phenomenon is initially
generated on the blade root, because the effective angle of attack
at the blade region for a wind speed of 7 m/s can be calculated
from Eq. (9) as approximately 11.6. This is higher than the stall
angle of 9 mentioned in the 2-D S809 airfoil experiments [8], as
shown in Fig. 11. However, near r/R = 0.6, corresponding to an
angle of attack of approximately 10, an unseparated flow exists,
unlike in the results of the 10 m/s wind speed. This is known as
the stall delay phenomenon due to the rotation effect [17]. In a 7
m/s wind speed, the flow is
Fig. 8. Flow velocities and aerodynamic forces at a blade
element.
Fig. 9. Experimental lift-to-drag ratios according to different
Reynolds numbers of a S809 airfoil.
Fig. 10. Surface streamlines on suction side (7 m/s, 10 m/s, 13
m/s, 15.1 m/s, 20.1 m/s and 25.1 ms from top to bottom).
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86 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92
separated near the blade root, and then the radial flow is
gen-erated and moves to the spanwise section of approximately 0.35
because of the influence of the centrifugal acceleration and
pressure gradient in the radial direction. Beyond that sec-tion,
however, the attached flow is formed and stably passes along the
blade surface. As the wind speed is increased, the streamlines on
the blade surface develop very complicated flow patterns owing to
the increasing angles of attack and radial flow in the direction It
is confirmed that a 3-D stall separated from the blade root slowly
generates and spreads toward the tip with the increasing wind
speeds to keep the output power constant. The control of wind
turbine systems with this flow phenomenon is called the
stall-regulated method. In this study, the Phase VI wind turbine
blade has a maximum thickness of 47% of chord length at r/R = 0.2
on the blade root, which is almost the shape of an ellipse. Thus,
it is found that the root design on a blade is very important in
al-lowing 3-D stall to slowly generate at a rated wind speed in
wind turbines operating with a stall-controlled method. How-ever,
the root design with a pitch-controlled method should performed in
such a way that the region of separated flow is decreased and the
target output is increased.
Figs. 12, 13, and 14 show a comparison of measured and
calculated pressure coefficients on the spanwise sections r/R =
0.3, 0.47, 0.63, 0.80, and 0.95 for wind speeds of 7 m/s, 15.1 m/s,
and 25 m/s, respectively [7, 8]. The pressure coefficient is
defined by Eq. (10)
. (10)
For the 7 m/s wind speed, a good agreement is found with the
experimental data in Fig. 12 for all five spanwise sections, even
though weak separated flow exists from r/R = 0 to r/R = 0.5, as
shown in Fig. 10. It is widely known that the thickness around the
blade root should be thick approximately to r/R = 0.25, from the
viewpoint of the structural safety of the rotor
blade, whereas, from an aerodynamic viewpoint, the thickness at
r/R = 0.251.0 (at the blade tip) should be thin for produc-ing of
the required output power. In the case of a 15.1 m/s wind speed
(Fig. 13), it can be observed that the computation results are in
comparatively good condition. At the point r/R = 0.3, the computed
pressure distribution agrees well with the experimental results
only on the pressure side. The agreement is not so good in the
regions of the upper surface including the leading edge and
trailing edge, where the pressure is over- or under-predicted over
the forward and backward half at X/c = 0.5. The calculated pressure
distributions at r/R = 0.47, 0.63, 0.80, and 0.95 show a little
difference from the experimental results on the upper surface. For
the highest wind speed of 25.1 m/s, the calculated results show
comparatively good agreement with the measured results at r/R =
0.47, 0.63, and 0.95, but this is not the case for r/R = 0.3 and
0.8, as shown in Fig. 14. Although it is known that the SST k-
model pro-vides reasonable results for separated flows, in these
cases, beyond expectation, the calculated results show
comparatively good agreement with experiments even at the highest
wind speed conditions, except for the regions of greatly separated
flow on the blade root at r/R = 0.3 and the upper surface at r/R =
0.8. Generally, it is true that the SST k- turbulence model has an
excellent prediction ability for wall characteristics, but there is
a limitation to the accurate prediction of aerodynamic
characteristics at extremely high angles of attack using the
applied turbulence model. However, in this study, even at the two
higher wind speed conditions, the calculated results agree
wonderfully well with the experiments. Later, in regard to this
matter, it is judged that additional investigation will be needed
using the transition model developed by Ref. [18].
Fig. 15 shows the distribution of computed unit span torque
divided into 10 sections for various wind speeds. At a wind speed
of 7 m/s, the unit span torque at each location shows a linearly
increasing tendency up to the point r/R = 0.85, and then suddenly
drops off. It is known that the torque of a rotor blade is directly
proportional to distance from the center of an object when the
rotor blade is designed to be optimal. This phenomenon is related
to tip vortices with very complex 3-D flow structures in the local
cross flow along the trailing edge of the blade tip [19, 20]. Owing
to these tip vortices, the pres-sure around the tip is decreased
and the airflow changes its direction toward the optimal angle of
attack, contrary to our initial design. It is also known that the
shape of the blade tip has a strong influence on mechanical power.
With increasing wind speeds, the partial torque at each location
shows uneven distributions owing to the stall phenomenon with
complex flow over the blade, and a negative partial torque is
confirmed at the blade tip in conditions of 20.1 m/s and 25.1 m/s
winds. Therefore, it is expected that this flow phenomenon will be
able to keep the output power constant even in extreme
situa-tions.
Table 3 shows the percentage ratio of partial torque to total
torque. At 7 m/s, the partial torque from r/R = 0.35 to r/R = 0.85
is around 85.0% of all the torque generated from the rotor
Fig. 11. Angle of attack distribution for various wind
speeds.
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Technology 26 (1) (2012) 81~92 87
(a) r/R = 0.3
(b) r/R = 0.47 (c) r/R = 0.63
(d) r/R = 0.8 (e) r/R = 0.95 Fig. 12. Comparison of measured and
calculated pressure coefficient on the spanwise sections r/R=0.3,
0.47, 0.63, 0.80 and 0.95 for a wind speed of 7 m/s .
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Technology 26 (1) (2012) 81~92
(a) r/R = 0.3
(b) r/R = 0.47 (c) r/R = 0.63
(d) r/R = 0.8 (e) r/R = 0.95 Fig. 13. Comparison of measured and
calculated pressure coefficient on the spanwise sections r/R=0.3,
0.47, 0.63, 0.80 and 0.95 for a wind speed of 15.1 m/s.
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Technology 26 (1) (2012) 81~92 89
(a) r/R = 0.3
(b) r/R = 0.47 (c) r/R = 0.63
(d) r/R = 0.8 (e) r/R = 0.95 Fig. 14. Comparison of measured and
calculated pressure coefficient on the spanwise sections r/R=0.3,
0.47, 0.63, 0.80 and 0.95 for a wind speed of 25.1 m/s.
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Technology 26 (1) (2012) 81~92
blade, while that from r/R = 0 to r/R = 0.35 accounts for just
3.7% of the total. This confirms that the partial torque gener-ated
in this region of the blade root has a weak effect on aero-dynamic
performance. With increasing wind speed, the pro-portion of the
torque between r/R = 0.35 and r/R = 0.85 de-creases up to the 15.1
m/s wind speed, and then begins to in-crease. The torque between
r/R = 0.85 and 1.0 shows a nega-tive value at wind speeds of 20.1
m/s and 25.1 m/s because of the strong separated flow limiting
local power output. Gener-ally, there are two methods of
controlling the output power under stall control. The first
approach is passive stall control, in which the fixed-blade pitch
is chosen so that the turbine reaches its maximum or rated power at
the desired wind speed. A wind turbine with this control suffers
from the disadvantage of uncertainties in its post-stall
aerodynamic behavior, which can result in inaccurate predictions of
the power level and blade loading at the rated wind speed and
above. The other approach is active stall control, which achieves
power limita-tion above the rated wind speed by changing the blade
pitch angle to a larger, so-called critical aerodynamic angle of
attack. A significant advantage of this control is that the blade
re-mains essentially stalled above the rated wind speed, so that
gust slicing results in much smaller cyclic fluctuations in blade
loads and output power [21]. Because the increasing wind
speeds have the same effect as increasing the pitch angle in the
negative direction, an appropriate angle of attack corre-sponding
to the rated wind speed is very important in design-ing a
small-sized wind turbine blade operating in the stall-regulated
method.
Fig. 16 shows the distribution of lift force to drag force ratio
per unit span at each r/R location for various wind speeds. This
value is acquired by solving the simultaneous equations of Eqs.
(11) and (12). The Q and T can be easily calcu-lated, rather than
obtaining L and D due to the blade twist angle in the orthogonal
coordinates system, as already ex-plained in Fig. 8. For the 7 m/s
wind speed, the ratio is 0.17 and 19.23 at r/R = 0.05 and 0.85,
respectively, corresponding to Reynolds numbers 3.7 105 and 8.8
105. The calculated values for a given Reynolds number and angle of
attack are somewhat low compared with the 2-D experimental data.
This is attributed to a limitation of the present fully turbulent
mod-els without transition effects, which have considerable
diffi-culty in exactly predicting a drag force [22]. Therefore,
these amplification errors in drag and lift forces cause the value
to be inaccurately calculated. In addition, it is confirmed that
the ratio decreases with increasing wind speeds over the entire
region. This means that the D increment is much larger than L when
the wind speed increases, owing to the stall phe-nomenon at wind
speeds above 7 m/s.
(11) (12)
Fig. 17 compares the measured and computed shaft torques
[7, 8]. The rotor blade used in this study adopts the
stall-regulated method, whose torque is regulated by stall
genera-tion throughout its range at wind speeds above 10 m/s. As
shown by the comparison of these results, the torque does not
increase from its value at a wind speed of 10 m/s, and is
con-trolled in the range between 10 m/s and 25.1 m/s, thus
gener-
Table 3. Percentage ratio of partial torque to total torque.
Percentage ratio of partial torque to total torque wind speed
(Vin), m/s
0 - 0.35 0.35 - 0.85 0.85 - 1 0 - 1
7 3.7% 85.0% 11.3% 100.0%
10 4.6% 81.1% 14.3% 100.0%
13 7.2% 68.8% 24.0% 100.0%
15.1 20.0% 56.9% 23.1% 100.0%
20.1 27.8% 76.5% -4.3% 100.0%
25.1 21.9% 81.2% -3.1% 100.0%
Fig. 15. Distribution of computed torque per unit span for
various wind speeds.
Fig. 16. Distribution of lift force to drag force ratio per unit
span at r/R locations for various wind speeds.
-
J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92 91
ating the constant torque required for the output power. The
computed and measured torques show a similar tendency, with an
error range between a minimum of 0.08% and a maximum of 24.7%.
Fig. 18 shows a comparison of the measured and computed power
coefficients for various wind speeds [7, 8]. The power coefficient
is defined by Eq. (13). The maximum achievable value of the power
coefficient is 0.593, which is known as the Betz limit. To date, no
wind turbine has been designed which is capable of exceeding this
limit. The power coefficient of wind turbines currently in
operation is lower than 0.593, and that of the recently
commercialized small- or middle-sized wind turbine is around 0.45.
In the NREL Phase VI wind tur-bine, the calculated power
coefficient is about 0.35 at a TSR of 5.41, corresponding to 7 m/s,
and this agrees with the ex-perimental results to within 0.08%.
(13)
4. Conclusions
(1) It was observed that the 3-D stall begins to generate near
the blade root at a wind speed of 7 m/s. This is attributed to
having a higher angle of attack than the stall angle of attack, and
a maximum thickness of 47% of the chord length. There-fore, in the
case of a stall-regulated method, it is judged that root design
approaches considering the appropriate selection of the angle of
attack and the thickness are very important in order to generate
the stall on the blade root.
(2) Through analysis of existing experimental data, the an-gle
of attack corresponding to the maximum lift-to-drag ratio was found
to be in the vicinity of 6, regardless of the Rey-nolds number.
This fact will assist designers in performing the
pitched-controlled or stall-regulated design of a rotor blade. The
calculated lift force to drag force ratio for a given Rey-nolds
number and angle of attack were somewhat low com-pared with the 2-D
experimental data. This is attributed to a limitation of the
present fully turbulent models without transi-tion effect.
(3) It was confirmed that 3-D stall that has separated from the
blade root slowly generates and, as the wind increases, spreads
toward the tip. This allows the rated output power to remain
constant. This wind turbine system is controlled by a flow
phenomenon called a stall-regulated method
(4) The computed torque and power coefficients showed
considerably good agreement with the experimental meas-urements, to
within 0.08% at a TSR of 5.41, which corre-sponds to 7 m/s.
(5) Through a clear understanding of aerodynamic
charac-teristics of a small-sized NREL Phase VI wind turbine, it is
expected that this useful aerodynamic data will be made avail-able
to designers as guidance in designing stall-regulated wind turbine
blades in the development phase of small-sized wind turbine systems
in the future.
Acknowledgments
This work is the outcome of a Manpower Development Program for
Marine Energy by the Ministry of Land, Trans-port and Maritime
Affairs (MLTM).
Nomenclature------------------------------------------------------------------------
: Twist angle : Angle of attack : Flow angle c : Local chord
length Ng : Grid number Vin : Inflow wind speed : Tip speed ratio
(TSR) : Rotational speed r : Radial position R : Radius of blade CP
: Pressure coefficient
Fig. 17. Comparison of measured and computed shaft torques.
Fig. 18. Comparison of measured and computed power
coefficient.
-
92 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and
Technology 26 (1) (2012) 81~92
P0 : Absolute pressure P : Ambient pressure Vr : Local Relative
flow velocity : Dimensionless length X : Length in chordwise
direction
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Jang-Oh Mo is currently a visiting researcher at the University
of Adelaide in Australia. He received his B.E, M.E degrees and Ph.D
in Mechanical Engineering from the Korea Maritime University in
2001, 2003 and 2009, Korea. He worked as a CFD consulting engineer
for 6 years from 2004 to 2009
in ANSYS KOREA branch (ATES Inc., Seoul, Korea). His research
interests include wind farm optimal layout, design and aerodynamic
noise of a wind turbine blade for an on and off-shore wind turbine
blade.
Young-Ho Lee received his B.E. and M.E. degrees from Korea
Maritime University, Korea. He received his Ph.D in Engineering
from the University of Tokyo, Japan. Dr. Lee is currently a
Professor at the Division of Mechanical and Energy System, Korea
Maritime University. His research interests
include ocean energy, wind energy, small hydro power, fluid
machinery, PIV, and CFD.
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