3B. Basic Study of Winglet Effects on Aerodynamics and Aeroacoustics Using Large-Eddy Simulation

8/14/2019 3B. Basic Study of Winglet Effects on Aerodynamics and Aeroacoustics Using Large-Eddy Simulation

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1

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


Chuichi Arakawa, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656


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.



2

( ) ( )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+ ∆ = ∆ − −



3

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



4

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



5

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)


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)


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



6

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


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



7

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)


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)





9

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.

References

[1] Fleig, O., Arakawa, C., 23rd ASME Wind Energy

Symposium, January 5-8, 2004, Reno, Nevada.

[2] Kawame, H., Master’s Thesis, the Univ. of Tokyo, 2005.

[3] Whitcomb, R. T., NASA TN D-8260, 1976.

[4] van Holten, Th., Proc. 2nd Int. Symp. Wind Energy Syst.,

F2-13-24, 1978.

[5] Shimizu, Y., Yosikawa, T., Matumura, S., JSME, Series B,

56-522, pp. 495-501, 1990.

[6] Ito, S., Doctoral Thesis, the Univ. of Tokyo, 1986.

[7] van Bussel, G. J. W., Proc. 4th IEA Symp. Aerodynamics

of Wind Turbines, Rome, 1-18, 1990.

[8] Hasegawa, Y., Kikuyama, K., Imamura, H., JSME,

Series B, 62-600, pp. 3088-3094, 1996.

[9] Spalart, P. R., Jou, W. H., Strelets, M., Allmaras, S. R., In

Advances in DNS/LES, 1st AFOSR Int. Conference on

DNS / LES, Greyden Press, 1997.

[10] Johansen, J., Sorensen, N. N., Michelsen, J. A., Schreck,

S., Wind Energ, John Wiley & Sons Ltd, pp. 185-197, 2002.

[11] Matsuo, Y., Doctoral Thesis, the Univ. of Tokyo, 1988.

[12] Beam, R. M. and Warming, R. F., AIAA Journal, Vol.

16, No. 4, pp.393-402, 1978.

[13] Smagorinsky, J., Monthly Weather Review, Vol. 91, No. 3,

pp. 99-164, 1963.

[14] Van Driest, E. R., Journal of Aeronautical Science, Vol. 23,

p. 1007, 1956.

[15] Spalart, P. R., Allmaras, S. R., Recherche Aerospatiale,

Vol. 1, pp. 5-21, 1994. [16] Ffowcs Williams, J. E., Hawkings, D. L., Phil. Trans. of

the Royal Soc. Of London, A: Mathematical and Physical

Sciences, Vol. 264, No. 1151, pp. 321-342, 1969.

[17] Brentner, K. S. and Farassat F., AIAA Journal, Vol. 36,

No. 8, pp. 1379-1386, 1998.

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

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3B. Basic Study of Winglet Effects on Aerodynamics and Aeroacoustics Using Large-Eddy Simulation