3b. basic study of winglet effects on aerodynamics and aeroacoustics using large-eddy simulation
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8/14/2019 3B. Basic Study of Winglet Effects on Aerodynamics and Aeroacoustics Using Large-Eddy Simulation
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Basic Study of Winglet Effects on Aerodynamics and Aeroacoustics
Using Large-Eddy Simulation
Masakazu Shimooka, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656
E-mail: [email protected]
Makoto Iida, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656
E-mail: [email protected]
Chuichi Arakawa, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656
E-mail: [email protected]
Abstract
This paper describes detailed analysis of unsteady flow
around wind turbine blades, including the tip vortex effects.
We applied to the tip shapes winglets, which have been saidto improve the aerodynamic performance. First, Unsteady
flow was simulated using compressible LES (Large-Eddy
Simulation) with 300 million grid points around the blade.
This simulation was performed on Earth Simulator. We
captured winglet effects in detail that have been reported in
the past. Winglets can be said to diffuse and weaken tip
vortices, and reduce the downwash effects. Such detailed
information obtained from this simulation will be useful for
designing the tip shapes. Secondly, we have investigated
possibility of DES (Detached-Eddy Simulation) for the
whole blade design tools. In this paper, initial results of the
DES for NREL PhaseⅥ
blade are introduced.
1. Introduction
Detailed analysis of aerodynamic performances (loads and
noise) in horizontal axis wind turbine (HAWT) is important
for designing optimal shapes of the blade. Especially, the
effective flow velocity at the tip is 8 to 10 times as high as the
speed of the wind into the rotor plane. Thus, analysis of the
flow field around wind turbines, including the tip effects is
essential.
To date, as the numerical simulation focused on tip shapes,
Oliver et al. [1] performed a direct noise simulation with 300
million grid points, using LES (Large-Eddy simulation).
They have reported noise reduction in high frequency by
changing the tip shape. While, as the simulation focused on
macroscopic aerodynamic performance of the whole blade,
Kawame et al. [2] performed RANS (Reynolds-Averaged
Navier-Stokes Simulation) for less computational costs.
They simulated several cases of wind speeds, considering
atmospheric variations.
In this paper, first, high-resolution numerical simulations
focused on the tip shape using unsteady compressible LES
code are performed, in purpose of capturing tip vortices and
unsteady flow field near the blade in detail. We applied to the
tip shapes winglets which have been said to improve
aerodynamic performances, and investigated winglet effects
in detail comparing with the conventional tip shape.
Winglet was first developed by Whitcomb [3] as the small
wing for subsonic flows around aircraft. Winglets have been
said to diffuse tip vortices toward the tip, and reduce thedownwash effect and the induced drag. As examples of
winglets for the blade of rotation, there have been “Tip Vane”
(for wind turbine) by van Holten [4], “Mie Vane” (for wind
turbine) by Shimizu [5], “Bladelet” (for marine propeller) by
Ito [6]. The results of their experiments have shown reduction
of the tip vortices and spread of wake. As for numerical
analysis, van Bussel [7] and Hasegawa [8] have shown that
installation of winglets causes increase in rotor output, using
BEM (Blade Element Momentum method) and VLM (Vortex
Lattice Method) respectively.
However, these results of analysis do not derive from detailed
information about 3-dimensional and complex structure of tipvortices. Moreover, aerodynamic noise has never been
calculated to date. It is preferable to use directly Navier-Stokes
equation in order to resolve structure of vortices accurately. In
this paper, according to the knowledge by Oliver et al. [1],
large-scale numerical simulation with 300 million grid points
using compressible LES is implemented, and aeroacoustics as
well as aerodynamics is investigated.
Secondly, in purpose of application of CFD to the blade
design tools, the dependence in the LES on the number of grid
points is investigated, and finally DES (Detached-Eddy
simulation) [9] is introduced for less computational costs. DES
is a method for predicting turbulence in computational fluid
dynamic simulations by combining RANS methods in the
boundary layer with LES in the free shear flow. DES leads to
reduction of computational costs in the boundary layer that
would be required in LES in high Reynolds number flow. The
conventional RANS produces too much viscosity, which
causes a delay of separation leading to a region of attached
flow that is too large. This leads to over-prediction of the lift.
Johansen et al. [10] simulated the flow around the non-rotating
NREL Phase VI blade. They showed that DES predicts
considerably more three dimensional flow structures compared
to conventional two-equation RANS turbulence models.
In this work, calculations were performed on Earth Simulator.
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( ) ( )1/ 22
2SGS s ij ijC S S µ ρ = ∆
2. Numerical approach
2.1 LES
The governing equation for the flow is 3-dimensional
unsteady compressible Navier-stokes equation. The flow
solver was developed by Matsuo [11]. The numerical
method for the solution is based on the implicit
finite-difference approach proposed by Beam and Warming
[12]. The solution is advanced in time using a first-order
implicit approximate-factorization. The spatial derivatives
are discretized using a third-order finite-difference upwind
scheme. The effects of the subgrid-scale (SGS) eddies are
modeled using the Smagorinsky model [13] as shown Eq.
(1). Smagorinsky constant Cs is 0.15. The Van Driest wall
damping function [14] as shown Eq. (2) is used to correct the
excessive eddy viscosity predicted by the Smagorinsky
model near the wall.
(1)
(2)
2.2 DES
The governing equation and numerical method for the DES
are the same as for the LES. The DES formulation in this
work is based on a modification to the Spalart-Allmaras
(S-A) RANS model [15]. The DES formulation is obtained
by replacing in the conventional S-A model the distance to
the nearest wall, d , by d , where d is defined as Eq. (3). In
Eq. (3), Δ is the largest grid size under consideration. The
wall-parallel grid spacings are at least on the order of the
boundary layer thickness and the S-A RANS model is
retained throughout the boundary layer, i.e., d d = .
Consequently, prediction of the boundary layer separation is
determined in the ‘RANS mode’ of DES. Away from the
wall, the closure is a one equation model for the SGS eddy
viscosity. The additional model constant C DES is 0.65 for
homogeneous turbulence.
(3)
2.3 Acoustic method
Hydrodynamic pressure fluctuations in the flow cause
acoustic waves. The propagation of the acoustic waves from
the near field to the far field can be predicted with the
compressible Navier-Stokes equations. They contain the
equations governing wave propagation and are thus able to
model the acoustic field directly and simultaneously in
addition to the noise generating flow field. However, the grid
spacing has to be smaller than the smallest acoustic
wavelength of interest. Thus, direct simulation of the
propagation of acoustic waves from the noise source all the
way to the far field observer position is computationally very
expensive due the extremely fine grids required over a long
distance. Since turbulent fluctuations are dissipative, the far
field is constituted only of acoustic fluctuations. In this case
acoustic analogy methods can be used to predict the far field
sound efficiently.
In this work, the compressible LES computes the flow and
acoustic wave propagation simultaneously in the non-linear
flow region in close proximity to the blade, i.e., 1-2 chord
length away from the blade surface, taking into account
refraction effects through the inhomogeneous unsteady flow
and reflection and scattering effects on the blade surface.
This region is called the near field. The grid spacing and time
step are determined by the smallest wavelength of interest.
The far field flow is computed by LES, whereas the far field
sound is computed using acoustic analogy. The Ffowcs
Williams-Hawkings (FW-H) equation [16] is the most
general form of the Lighthill acoustic analogy and can be
used to predict the noise generated by the complex arbitrary
motion of the wind turbine blade. It is based on an analytical
formula which relates the far field pressure to integrals over a
closed surface that surrounds all or most of the acoustic
sources. Since it is based on the conservation laws of fluid
mechanics, the FW-H approach can include non-linear flow
effects in the surface integration and does not need to
completely surround the non-linear flow region. The acoustic
field obtained by LES is fed into the FW-H equation for
integration on a specific surface for prediction of the far field
sound. The approach developed by Brentner and Farassat
[17] is applied. They developed the permeable surface FW-H
method on a fictitious permeable integration surface which
does not necessarily correspond with the body surface. This
allows the accurate simulation of the most intense
quadrupole sources in close proximity to the blade while
neglecting the computationally expensive quadrupole
volume integration. By simulating the propagation of
acoustic waves in the near field directly, the restrictions of the
compact body assumption posed by the acoustic analogy
methods are relaxed. The acoustic analogy method applied
on a surface away from the blade surface is expected to yield
more accurate results for the far field noise in the high
frequency domain than would be obtained by integrating the
blade surface pressure fluctuations directly. When the
smallest wavelength of interest is smaller than the body
reference length, such as is the case with trailing edge or tip
vortex related noise in high Reynolds number flow, the far
field noise cannot be predicted accurately just by integrating
the surface pressure fluctuations. Configuration of the noise
simulation method in this work is shown in Fig.1.
min( , )
max( , , )
DES d d C
x y z
= ∆
∆ = ∆ ∆ ∆
1 exp26.0
g
y+ ∆ = ∆ − −
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50deg
0deg
0.98R
z
x
R
U eff
U eff
Fig.1 Method of noise simulation
3. WINDMELⅢ simulation
3.1 Simulation parameters
In this section, flow simulations around a rotating
WINDMELⅢ blade with a winglet are performed.
Simulations are performed for 2-type tip shapes whose
installation angle is 0deg and 50deg as illustrated in Fig.2.
0deg corresponds to the conventional tip shape, but its shape
is a little modified adequately to compare with the shape of
50deg. The radius of the rotor in 0deg is the same as that of
actual WINDMELⅢ and the span length of the winglet is
2 % of the radius of the rotor.
The simulated wind turbine is a 2-bladed wind turbine of
upwind type which has a diameter of 15 m and operates at a
wind speed of 8 m/s with a constant speed of 67.9 rpm. The
tip speed ratio is 7.5 and the tip speed is 53.3 m/s,
corresponding to a Mach number of 0.16. The chord length
corresponding to the dotted line in Fig.1 will be referred to as
the reference chord length c which equals 0.23 m. The
effective flow velocity U eff at the reference chord length is the
reference velocity. The Reynolds number based on the
reference chord length c and the reference velocity U eff is
1.0×106.
The computational domain for the wind turbine blade is
illustrated in Fig.3. A single block grid is used. Since the
wind turbine has 2 blades, the domain is chosen to consist of
half a sphere. Only one of the blades is explicitly modeled in
the simulation. The remaining blade is accounted for using
periodic boundary conditions, exploiting the 180 degrees
symmetry of the two-bladed rotor.
Fig.2 Tip shapes (top: 50deg, bottom: 0deg)
Uniform flow, U ∞, corresponding to the wind speed is
prescribed in the -x-direction. The blade rotates about the
x-axis. The outer boundary of the computational domain is
located 2 rotor radii away from the center of rotation. The
detailed geometry of the hub and the wind turbine tower are
not taken into account in the simulation.
Two types of grid spacings around the airfoil section, what
are called Grid1 and Grid2, are used as illustrated in Fig.4.
Grid1 is consisting of 765 grid points along the airfoil
surface (ξ-direction), 193 grid points perpendicular to the
airfoil surface (η-direction), and 2209 grid points along the
span direction (ζ-direction). The total number of grid points
is 300 million. The grid spacings in the near field, i.e. 1-2
chord lengths away from the rotor blade are set sufficiently
fine and equally distributed in order to perform a direct noise
simulation. Since the main interest is the tip shapes, the
computational grid is made extremely fine in the blade tip
region. Grid2 is consisting of 383 grid points inξ-direction,
97 grid points inη-direction, and 553 grid points in ζ
-direction. The total number of grid points is 20 million. This
number of the grid points corresponding to 1/16 of that of
Grid1 is computationally more practical. In Grid2, only
aerodynamic simulation is implemented without
aeroacoustic simulation. In both Grid1 and Grid2, Δy+ is
set to take a value of approximately 1.0 along the entire blade
surface. No wall model is used.
Concerning the boundary conditions, no-slip conditions are
applied at the wall, and pressure and density are extrapolated.
Uniform flow conditions are implemented at the inlet.
Convective boundary conditions are implemented at the
outlet. As for Grid1, Outer boundaries are made coarse
enough to allow for non-reflecting acoustic boundary
conditions. The computational domain extends extremely far
away from the blade, while direct noise simulation is
performed only in the near field. Due to the large rate of
stretching and the extreme distance between the blade and
the outer boundaries, high frequency fluctuations and even
Near field:
Direct noise simulation
By compressible LES
Far field:
Modeled
By Ffowcs Williams-Hawkings
(FW-H) equation
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low frequency fluctuations can be considered to be filtered
out before reaching the outer boundary. It must also be noted
that numerical dissipation with the third-order upwind
scheme is high in the outer regions due to the coarse grid.
Acoustic waves will be dissipated.
Fig.3 Computational domain
Fig.4 Grid spacing of airfoil section
(top: Grid1 , bottom: Grid2)
3.2 Simulation results: flow field
Computations in Grid1 using LES were performed and the
effects of winglets have been investigated by comparing
50deg with 0deg in detail.
Fig.5 shows the contours of the spanwise velocity
components w at y/c = 0.7 which is located at the center of
the blade chord length. The left region to the blade is suction
side, while the right one is pressure side. The region colored
black (w > 0) is where the flow goes to the outside of the
blade, while the region colored white (w < 0) is where the
flow goes to the inside of the blade. In both 0deg and 50deg,
there can be seen the flow is drifting up from the pressure
side to the suction side at the very tip. Especially at the
suction side, the region colored white is smaller for 50deg
than for 0deg. This means that a winglet prohibits tip vortices
from drifting up to the suction side of the blade and reduces
downwash effects. As for at the pressure side, the region
colored black is larger for 50deg than for 0deg. This means
that a winglet can spread the wake in spanwise direction.
Fig.5 Spanwise velocity components contours
(top: 50deg, bottom: 0deg)
ξ
η ζ
ξ
η
ζ
Grid1
765 x 193 x 2209
Grid2
383 x 97 x 553
Rotation axis
U ∞
z
x
y
(a)
(b)
(c)
z
y
x
z
y
x
Direct noise simulation
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Fig.6 shows the pressure contours near the trailing edge at
y/c = 1.0. As for 50deg, there can be seen smaller but more
complex structure of tip vortices. A winglet diffuses tip
vortices and causes large-scale structure of vortices into
small scale.
Fig.7 shows the vorticity magnitude contours at the near
wake of the tip region with vorticity magnitude iso-surfaces
(|ω| = 4.0). Each contoured section corresponds to y/c = 1.0,
1.2, 1.4, 1.6, 1.8, 2.0. As for 50deg, there can be seen the
reduction of the strength of tip vortices at any section, and the
tip vortices dissipate nearer the wall than for 0deg. Winglets
can be said to weaken tip vortices.
Fig.6 Pressure contours at the trailing edge ( y/c = 1.0)
(top: 50deg, bottom: 0deg)
Fig.7 Vorticity magnitude contours at the near wake
( y/c = 1.0, 1.2, 1.4, 1.6, 1.8, 2.0)
with iso-surface (|ω| = 4.0)
(top: 50deg, bottom: 0deg)
3.3 Simulation results: loadsLoads caused by time-averaged pressure on the blade
surface are investigated.
Fig.8 and Fig.9 shows rotational torque and flap
momentum distribution in the tip region respectively.
Horizontal axis in these figures means the spanwise position
non-dimensioned by the reference chord length c. 0 < z/c <
36.0 corresponds to the region of the main rotor blade, while
36.0 < z/c corresponds to the region of a winglet. As for the
rotational torque, at the center of the winglet, z/c = 36.5, and
in the region of the main blade near the tip, 31.0 < z/c < 35.0,
50deg produces higher torque than 0deg. On the other hand,
at the joint between a winglet and the main blade, 50deg is
1.01.2
1.41.6
1.82.0
1.01.2
1.41.6
1.8
z y
x
y z
x
2.0
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30 32 34 36 38
0
0.01
0.02
Spanwise position (z/c)
R o t a t i o n a l t o r q u e ( n o n - d i m e n s i o n )
0deg50deg
30 32 34 36 38
0
0.1
0.2
Spanwise position (z/c)
F l a p m o m e n t ( n o n - d i m e n s i o n )
0deg50deg
0 0.2 0.4 0.6 0.8 1
-5
-4
-3
-2
-1
0
y/chord
C p
0deg50deg
losing torque as compared with 0deg. This would be
improved by smoother connection between the main blade
and winglet. As for the flap momentum, reduction of the flap
momentum is identified at the winglet region for 50deg,
while increase can be found in the region of the main blade
near the winglet.
Fig.10 shows time- averaged pressure distribution on the
suction side in the tip region. There can be seen differences in
the pressure distribution between 0deg and 50deg. Regarding
50deg, sharper suction peak and more sufficient recovery of
the pressure can be identified at the leading edge and the
trailing edge respectively. Fig.11 shows the pressure
coefficient at the center of the winglet, z/c = 36.5, where the
most remarkable difference in the rotational torque is found.
In Fig.11, larger and sharper suction peak at the leading edge
and more sufficient recovery of the pressure is identified for
50deg than for 0deg. As for 50deg, at the suction side of the
winglet, the spanwise flow is reduced as investigated in Fig.5,
and this leads to more 2-dimentional flow in streamwise
direction, and enables to obtain higher rotational torque.
Fig.8 Rotational torque distribution
Fig.9 Flap momentum distribution
Finally, the overall aerodynamic performance is
investigated. Power coefficient C P and thrust coefficient C T are calculated. As for 50deg, C P = 0.310, and C T = 0.610,
while as for 0deg, C P = 0.305, and C T = 0.602. Both C P and
C T are found to be slightly higher for 50deg than for 0deg.
Fig.10 Pressure contours on the suction side
(top: 50deg, bottom: 0deg)
Fig.11 Pressure coefficient at z/c = 36.5
3.4 Simulation results: acoustic field
The acoustic field is simulated using the method as
mentioned in 2.3. To evaluate the effect of the difference in
the structure of the vortices in the blade tip region on the
acoustic field, the pressure fluctuations in the near blade
region are analyzed and compared between 0deg and 50deg.
The pressure fluctuations are the difference between
instantaneous pressure values and time-averaged pressure
values. The sound pressure level spectra are obtained by a
FFT analysis. The sampling time of the time-dependent
z/c = 36.5
Main blade Winglet
WingletMain blade
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Point B
Point A
1000 5000 10000100
120
140
160
180
50deg
0deg
Frequency (Hz)
S P L ( d B ) , r e f : 2 × 1 0 - 5 P
a
Point A
1000 5000 10000100
120
140
160
180
50deg
0deg Point B
Frequency (Hz)
S P L ( d B ) , r e f : 2 × 1 0 - 5
P a
pressure fluctuations is 4.0×10-5 s meaning a frequency
resolution of 12.5 kHz .
As shown in Fig.12, the pressure fluctuations are taken at
the two points, Point A and Point B, which are located
slightly downstream of the blade trailing edge, i.e., 50 grid
points away from the blade surface. Point A is where the tip
vortices are exactly developed, while Point B is in the region
of the main blade near the winglet. At Point A, 50deg shows
increase in sound pressure level for frequency especially
above 4 kHz . This is attributed to the small-scale structure of
tip vortices caused by the winglet as investigated in Fig.6. On
the other hand, at Point B, 50deg and 0deg are the same
order in sound pressure level. Smaller but more complex
structure of tip vortices caused by a winglet can be thought to
emit strong noise especially in high frequency.
Fig.12 Near field sound pressure level
(top: Point A, bottom: Point B)
Fig.13 Integration surface for FW-H equation
Fig.14 Far field overall sound pressure level (OASPL)
(2.3 m downstream from rotor)
(top: 50deg, bottom: 0deg)
Then, the far field noise level is investigated. In Fig.13, the
integration surface for FW-H equation as mentioned in 2.3 is
colored yellow. This surface is located 100 grid points away
from the blade surface, and is within the region where the
direct noise simulation is performed. Pressure fluctuations
obtained from the LES solver are fed into the FW-H
equation.
As shown in Fig.14, the overall sound pressure level
(OASPL) is analyzed on the plane of 20 m square located 10
chord lengths, i.e., 2.3 m downstream from the rotor plane.
The value of OASPL is calculated integrating the sound
pressure level in frequencies from 1 kHz to 12.5 kHz . For the
sake of convenience, projection of the blade is shown at the
same time. In both cases of 0deg and 50deg, noise sources
can be identified especially in the tip region. However, some
differences in distribution of OASPL between 0deg and
50deg can be found. As for 50deg, most of the sound sources
(dB)
(dB)
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0 0.5 1-2
0
2
4
6
y/chord
- C p
calc.r/R=0.95
Fig. 17 Pressure distribution at each spanwise position
(U ∞ = 7.0 m/s)
5. Conclusions
First, large-scale numerical simulation using 300 million
grid points was implemented to predict winglet effects for
rotating WINDMELⅢ wind turbine blade. The effects of
winglets on aerodynamic performance and acoustic noise
were investigated in detail using compressible LES
(Large-Eddy Simulation). Winglets can be found to perform
as follows.
1. Winglet can diffuse and weaken tip vortex.
2. Winglet can prohibit spanwise flow on the suction side,
and reduce downwash effect as well as spread wake.
3. Winglet causes increased rotational torque, and reduced
flap momentum.
4. Both C P and C T as the overall aerodynamic performance
are higher for 50deg than for 0deg.
5. Smaller but more complex vortices caused by winglet
emit strong noise in high frequency.
This knowledge will be very useful for designing the future
optimal tip shape of wind turbine blades.
Secondly, simulations focused on the whole blade design
tools were performed with less computational costs. LES
with 20 million grid points as computationally more practical
was implemented to predict the macroscopic aerodynamic
performance. In this simulation, C P was less estimated than in
case of 300 million grid points. In the LES, the effect of the
numerical dissipation related to computational grid resolution
is significant for predicting aerodynamic performances. Thus,
DES (Detached-Eddy Simulation) has been implemented
instead of LES. In this paper, initial results of simulation of
the flow around rotating NREL PhaseⅥ blade were
introduced. In the future, several cases of wind speed will be
simulated and grid refinement will be implemented in the
DES, focused on application of CFD to the blade design
tools.
Acknowledgements
The Earth Simulator Center is gratefully acknowledged for
providing the computational resources for this work. We
would like to thank Dr. Masami Suzuki, who contributed
many valuable comments and suggestions throughout this
work.
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0 0.5 1-2
0
2
4
6
y/chord
- C p
calc.exp.
r/R=0.30
0 0.5 1-2
0
2
4
6
calc.exp.
y/chord
- C p
r/R=0.47
0 0.5 1-2
0
2
4
6
y/chord
- C p
calc.exp.
r/R=0.63
0 0.5 1-2
0
2
4
6
y/chord
- C p
calc.exp.
r/R=0.80