Calculation of rotor blade-vortex interaction noise using parallel super computer

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CALCULATION OF ROTOR BLADE-VORTEX INTERACTION

NOISE USING PARALLEL SUPER COMPUTER

Takashi AOYAMA, National Aerospace Laboratory

7-44-1, Jindaijihigashi-machi, Chofu, Tokyo 182, Japan

Natsuki KONDO, Makoto AOKI, Hideaki NAKAMURA, Advanced Technology Institute of Commuter-helicopter, Ltd.

2 I<awasaki-cho, Kagamigahara City, Gifu-Pref. 504, Japan

Shigeru SAITO

National Aerospace Laboratory

7-44-1, Jindaijihigashi-machi, Chofu, Tokyo 182, Japan

Abstract

A prediction method for blade- vortex interaction (BVI) noise of a helicopter rotor is developed. This method consists of following four steps: 1) trim analysis using CAMRAD II based on a lifting-line theory, 2) interpolation of the blade motion and the wake geometry, 3) aerodynamic analysis using a finite difference solver for the three-dimensional unsteady Euler equations, and 4) noise analysis using an aeroacoustic code based on the Ffowcs Williams and Hawkings (FW-H) formulation with-out the quadrupole term. The predicted acoustic waveform for the OLS model rotor is compared with experimental data and reasonable correlation is ob-tained. This method is applied to investigate the effect of the tip shape on the intensity of the BVI noise. For the first step, the effects of anhedral, dihedral) tapered, and swept tip shapes are dis-cussed. The most time-consuming step of our pre-diction method is the unsteady Euler calculation. In this study) the calculation is performed using Nu-merical Wind Tunnel (NWT) in National Aerospace Laboratory (NAL). The NWT is a parallel super computer which consists of 166 processing elements (PEs). The total peak performance of the NWT is about 280GFLOPS and the total capacity of the main memory is as much as 45GB. The NWT makes it possible to conduct our parametric study for the effect of the blade-tip shape on the intensity of the BVI noise.

!ntrodu~~ion

:Main rotor of a helicopter generates two types of impulsive noise. One is the high-speed impulsive (HSI) noise which is caused by the shock wave gen-erated on the blade surface of the advancing side in

high-speed forward flight. The other is the blade-vortex interaction (BVI) noise which is caused by the sudden change of the blade loads during the interactions of the blade with previously shed tip vortices. Ref.[1] helps us to understand the mecha-nism of the occurrence of the BVI noise. In general, the interactions occur in descent flight conditions, especially during approach to a landing. The noise generated by the interactions radiates mostly be-low the helicopter's tip-path plane in the direction of forward flight. The acoustic signal is generally in the frequency range most sensitive to human subjec-tive response (500 to 5000Hz) [2]. The BVI noise, therefore, prevents that the commuter helicopter is widely used in the densely populated area. In 1994, Advanced Technology Institute of Commuter-helicopter (ATIC) is established in Japan in order to investigate the noise and safety problems of heli-copters. This paper reports the results of the collab-orative research between National Aerospace Labo-ratory (NAL) and ATIC. The main objectives of the collaborative research are to develop prediction methods of rotor noise and to investigate reduction methods for the noise.

Many efforts have been made in both experi-mental and theoretical researches about the BVI noise. Ref.[3] presents a review of the recent re-searches about the BVI aerodynamics. It cov-ers both analytical and experimental studies of two-dimensional parallel airfoil-vortex interactions) three-dimensional BV!s and helicopter rotor BVIs. A procedure was developed for the prediction of the BVI noise by coupling a lifting-line model) a three-dimensional unsteady full potential solver1 and a linearized acoustic formulation [4]. It is reported that several methods which couple aerodynamic and aeroacoustic codes have been developed to predict the BVI noise by the Aeroflight-dynamics Direc-torate (AFDD) of the U.S. Army, DLR of Germany,

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and ONERA of France, respectively [5]. One of the two objectives of this study is to develop a predic-tion method of the BVI noise. A method which couples a trim code, an aerodynamic code, and an aeroacoustic code is developed.

The intensity of the BVI noise is strongly affected by the factors, 1) the local strength of the tip vortex, 2) the core size of the tip vortex, 3) the local inter-action angle between the blade and the vortex line, and 4) the miss-distance between the vortex and the blade [1]. It is known that some kinds of tip shapes may reduce the intensity of the BVI noise. Time histories of the BVI noise were measured by using a in-flight technique for the UH-lH helicopter with its standard NACA0012 airfoil rotor and the AH-18 he-licopter configured with its standard 540 rotor, the Kaman K747 rotor, and the OGEE tip rotor [6]. A cooperative research was performed between AFDD, the NASA Ames and Langley Research Centers, the United Technologies Research Center (UTRC), and the Sikorsky Aircraft Division of United Technolo-gies in order to improve understanding of rotor aero-dynamics, acoustics, and dynamics including the ef-fect of blade- tip shape [7]. An experimental research was conducted in order to characterize the BVI noise created by various blade geometries as a function of rotor operating parameters [2] . The tip-vortex structure of several tip shapes were examined ex-perimentally in non-rotational conditions to investi-gate tip shapes for reduced BVI [8][9]. However, the comprehensive understanding of the effect of the tip shape on the intensity of the BVI noise has not been obtained yet. Therefore, the second objective of this study is to investigate its effect. For the first step, the effects of anhedral, dihedral1 swept1 and tapered tip shapes are discussed. The anhedral and dihedral tip shapes are selected in order to investigate the ef-fect of the miss-distance between the vortex and the blade on the intensity of the BVI noise. The swept and tapered tip shapes a.re also selected in order to investigate the effect of the local interaction angle between the blade and the vortex line and the effect of the local strength and the core size of the tip vor-tex on the intensity of the BVI noise1 respectively.

The most time-consuming step of our prediction method is the unsteady Euler calculation. In this study, the calculation is performed using· N umeri-cal Wind Tunnel (NWT) in NAL. The NWT is a parallel super computer which consists of 166 pro-cessing elements (PEs). The performance of an in-dividual PE is equivalent to that of a super com-puter, 1. 7GFLOPS. Each FE has a main memory of 256N1B. High-speed cross-bar network connects 166PEs. The total peak performance of the NWT is about 280GFLOPS and the total capacity of the main memory is as much as 45GB. In the case of our calculation to predict the BVI noise1 the typi-cal dividing number along the azimuthal direction

is about 2000/rev. It takes less than 1 hour to ob-tain a fully converged solution for about 150,000 grid points by using 36 PEs. The NWT makes it possible to conduct our parametric study for the effect of the blade-tip shape on the intensity of the BVI noise.

Calculation Method

The method used in this study consists of follow-ing four steps as shown in Fig.1: 1) trim analy-sis using CAMRAD II based on a liftingcline the-ory, 2) interpolation of the blade motion and the wake geometry, 3) aerodynamic analysis using a fi-nite difference solver [10] for the three-dimensional unsteady Euler equations, and 4) noise analysis us-ing an aeroacoustic code [11] based on the Ffowcs Williams and Hawkings (FW-H) formulation.

In the first step, the blade motion and the wake geometry are obtained as the result of the free-wake analysis of CA!v!RAD II owned by ATIC. The code is run in 10-deg azimuthal increments. However, it is too coarse to capture the instantaneous BVI events. Therefore, the azimuthal resolution is improved to 1 deg in the second step by using the method similar to that in ref.[12]. The core radius is a user specified parameter in CAMRAD II. It is set 0.3C except for the tapered blade case in which it is set 0.5C for the blade with the taper ratio of 0.3 according to ref.[8]. The quantity Cis the chord length of the blade here.

In the third step, the governing equations are the three-dimensional unsteady Euler equations in the blade fixed rotating Cartesian coordinate sys-tem. In order to conduct the calculation with arbi-trary curved grid, these equations are transformed from the Cartesian coordinate system to the arbi-trary curvilinear coordinate system. The numerical method to solve the governing equations is an im-plicit finite-difference scheme. A higher-order up-wind scheme based on TVD is applied for the invis-cid terms of the explicit right-hand side. To obtain the unsteady solution in the forward flight condition of a helicopter rotor, the Newton iterative method is added. In the beginning of the calculation1 the

steady calculation is conducted at 1/J = 90° using the implicit time-marching method. Then, the un-steady calculation is started from this initial condi-tion. Periodic converged solutions are obtained at about 1jJ = 360°. Four iterations are sufficient to reduce the residual at each time step. The effect of the wake is modeled by using the angle-of-attack ap-proach in which the effect of the disturbance caused by the blade-vortex interaction is only felt through the surface boundary condition. The effective angle of attack obtained in the second step is used in this boundary condition.

In the fourth step, the aeroacoustic code utilizes the FW-H formulation without the quadrupole term

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because strong shock waves are not generated in the flight condition considered here. The acoustic pres-sure at an observer position is calculated by using the pressure distributions on the blade surface ob-tained in the third step.

Results and Discussions

In this section, the comparison between measured and calculated time histories of the BVI noise is shown first. Then, the effects of anhedral, dihedral, swept, and tapered tip shapes on the intensity of the BVI noise are discussed.

Comparison between measured and calculated results

Calculations are performed to predict the BVI noise of the 1 /7-scale model AH-1 Operational Loads Survey (OLS) blades obtained in the German-Dutch Wind Tunnel (DNW) [13]. The blade geom-etry and the condition are shown in Table 1 and Ta-ble 2, respectively. The observer position is shown in Fig.2. The quantity R is the rotor radius in this fig-ure. The predicted acoustic waveform for the OLS model rotor is compared with experimental data ob-tained by Splettstoesser et al. [13] in Fig.3. Two pos-itive peaks of the sound pressure, A and B, are ob-served both in the measured and calculated time his-tories. Therefore, the calculated result adequately predicts the number of the BVI events. The am-plitude of the peak A is underpredicted but that of the peak B is accurately predicted. A top view of the predicted BVI location is shown in Fig.4. The open and filled circle respectively represent the in-teraction above and below the rotor disk. The miss-distance is indicated by the size of the circle. The larger circle means the close interaction. The BVI noise is usually radiated from the outer 20-30 % of the blade in the advancing side. In Fig.4, the inter-actions A and B indicate the interinter-actions between the outer blade and the vortex in the advancing side. Each interaction causes the peak A and B in Fig.3, respectively. Figure 5 shows the miss-distance be-tween the vortex and the blade during the blade-vortex interactions. The quantity dz is the vertical distance between the vortex and the blade. The open and filled circle respectively represent the in-teraction of the blade with the vortex shed from the own blade and the vortex shed from the previous blade. The interactions A and B in Fig.5 correspond to the interactions A and B in Fig.4, respectively. According to the time history in Fig.3(a) the miss-distance of the interaction A should be smaller than that of the interaction B. However, the miss-distance of the interaction A is larger than that of the inter-action B in Fig.5. It seems that the underprediction for the peak A is caused by the reason why the miss-distance between the blade and the vortex shed from

the own blade, which travels longer than the vortex shed from the previous blade before the blade-vortex interaction, is not so accurate in the first step of our prediction method. Our additional calculation con-firms that to artificially reduce the miss-distance of the interaction A makes a larger amplitude of the peak A as mentioned in ref. [4].

Effect of Anhedral and Dihedral

The anhedral and dihedral tip shapes are selected in order to investigate the effect of the miss-distance between the vortex and the blade on the intensity of the BVI noise. Figure 6 shows the time histo-ries of the BVI noise for the blades with anhedral, rectangular, and dihedral tip shapes. Both the an-hedral and dian-hedral angles are 20° as illustrated in Figs.6(a) and (c). The modifications start from 0.9R

radial station as also illustrated in Figs.6(a) and (c). Figure 7 shows the strength of the tip vortex dur-ing the blade-vortex interactions for the blades with anhedral, rectangular, and dihedral tip shapes. The quantity

r

is the tip-vortex circulation and \!tip is

the rotor rotational speed at the tip. The open and filled circle respectively represent the interaction of the blade with the vortex shed from the own blade and the vortex shed from the previous blade. It is observed that the strength is almost same among the three types of the tip shapes. Figure 8 shows the miss-distance between the vortex and the blade dur-ing the blade-vortex interactions for the blades with anhedral, rectangular, and dihedral tip shapes. The miss-distances of the interaction A and B are larger in Fig.8(a) than in Fig.8(b). Therefore, the ampli-tudes of the peak A and B are smaller in Fig.6(a) than in Fig.6(b ). The miss-distance of the interac-tion A is smaller in Fig.8(c) than in Fig.S(b) and the miss-distance of the interaction B is larger in Fig.8(c) than in Fig.8(b). Therefore, the ampli-tude of the peak A is larger in Fig.6(c) than in Fig.6(b) and the amplitude of the peak B is smaller in Fig.6(c) than in Fig.6(b). It is concluded that in this case the anhedral tip shape decreases the BVI noise because it increases both the miss-distances of the interaction A and B. It is also concluded that in this case the dihedral tip shape doesn't al-ways increase the BVI noise because it decreases the miss-distance of the interaction A but increases that of the interaction B. lvluch more calculations are needed to obtain the comprehensive understanding of the effect of the anhedral and dihedral tip shapes. Effect of Sweep

The swept tip shapes are selected in order to in-vestigate the effect of the local interaction angle be-tween the blade and the vortex line on the inten-sity of the BVI noise. Figure 9 shows the time his-tories of the BVI noise for the blades with swept-forward, rectangular, and swept-back tip shapes.

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Both the sweepback and sweepforward angles are 40° as illustrated in Figs.9(a) and (c). The mod-ifications start from 0.9R, radial station as also il-lustrated in Figs.9(a) and (c). Figure 10 shows the strength of the tip vortex during the blade-vortex interactions for the blades with swept-forward, rect-angular, and swept-back tip shapes. It is ob-served that the strength is almost same among the three types of the tip shapes. Figure 11 shows the miss-distance between the vortex and the blade during the blade-vortex interactions for the blades with swept-forward, rectangular, and swept-back tip shapes. The miss-distance is not so different among the three types of the tip shapes. Figure 12 shows the calculated trajectories of the tip vortex for the blades with forward, rectangular, and swept-back tip shapes. The azimuth angles of the blade location are 72° and 252° in Figs.l2(a), (b), and (c). In the tip region of the advancing side, the local in-teraction angle between blade and vortex line is dif-ferent among the three types of the tip shapes. The angle is nearly 90° in the case of the swept-forward tip shape. This type of perpendicular interaction doesn't cause strong BVI noise. Therefore, the am-plitudes of the peak A and B are much smaller in Fig.9(a) than in Fig.9(b). On the other hand, the angle is almost 0° in the case of the swept-back tip shape. This type of parallel interaction generates strong BVI noise. It doesn't seem that the result of the interaction angle is reflected in the amplitude of the peak A in Fig.9(c). The reason is ·shown in Fig.13. In this figure, the effect of swept tip shapes on the directivity of the BVI noise is indicated. Fig-ures 1~(a)-(c), (d)-(f), and (g)-(i) respectively show the results at the observer positions 2, 1, and 3 as

il-lustrated in Fig.13. In comparison of Figs.13(b), (e), and (h), the intensity of the BVI noise is strongest at the observer position 1. However, in comparison of Figs.l3(c), (f), and (i), the intensity is strongest at the obscrvPr position 2. The directivity of the ra-diatu. n) therefore, is shifted toward the right hand side of the forward flight direction by the swept- back tip shape. The amplitudes of the peak A and B in Fig.13( c) are much larger than those in Fig.13( e) be-cause the local interaction angle between the blade and the vortex line is almost 0° in the swept- back tip region. Such kind of shift in the directivity is not clear in the case of swept-forward tip shape because the strong interaction doesn't occur in the swept re-gion, It is concluded that in this case the blade with the swept-forward tip shape reduces the BVI noise because it causes the perpendicular BVI in the tip reginn in the advancing side. On the other hand, the blade ·.':ith the swept-back tip shape intensifies the BVI noise because it causes the parallel BVI in the tip region in the advancing side. The directivity of the radiation shifts toward the right hand side of the forward flight direction in the case of the swept-back

tip shape. Effect of Taper

The tapered tip shape is selected in order to in-vestigate the effect of the the local strength and the core size of the tip vortex on the intensity of the BVI noise. Figure 14 shows the time histories of the BVI noise for the blades with tapered and rectangular tip shapes. The taper ratio is 0.3 as illustrated in Fig.14(a). The modification starts from 0.9R, radial station as also illustrated in Fig.l4(a). It is observed that the amplitudes of A and B are reduced by the tapered tip shape. Figure 15 shows the strength of the tip vortex during the blade-vortex interac-tions for the blades with tapered and rectangular tip shapes. The strength is almost same between the two types of the tip shapes. Figure 16 shows the miss-distance between the vortex and the blade during the blade-vortex interactions for the blades with tapered and rectangular tip shapes. The miss-distance is not so different between the two types of the tip shapes. The core radius of the tip vor-tex is a user specified parameter in the first step of our calculation method. The effect of tapered tip shape on the core radius is not so clear at present. In this research, a larger core radius is used for the tapered tip shape than for the rectangular one. The core radii for the blades with tapered and rectan-gular tip shapes are 0.5C' and 0.3C', respectively. Figure 17 shows the time histories of the effective angle of attack for the rectangular and tapered tip shapes. The calculated effective angle of attack is directly affected by the core radius. The amplitudes of the peak in the advancing and retreating side are remarkably reduced by the tapered tip shape com-pared with the rectangular one. The effective angle of attack has a strong correlation with the blade load. Therefore, it is concluded that the intensity of the BVI noise is reduced by the tapered tip shape for which a core radius larger than that for the rect-angular tip shape is applied. More detailed exper-imental result about the strength and the core size of the tip vortex is needed to obtain the comprehen-sive understanding of the effect of the tapered tip shape.

Conclusions

A calculation method which couples a trim code) an aerodynamic code, and an aeroacoustic code is applied to predict the BVI noise of the OLS model rotor. The following conclusion is obtained.

• The calculated result adequately predicts the number of the BVI events. The amplitude of the peak A is underpredicted but that of the peal< B is accurately predicted.

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The calculation method is applied to investigate the effect of the tip shape on the intensity of the BVI noise. For the first step, the effects of anhedral, di-hedral, tapered, and swept tip shapes are discussed. The following major conclusions are obtained.

• The anhedral tip shape decreases the BVI noise because it increases both the miss-distances of the interaction A and B. The dihedral tip shape doesn't always increase the BVI noise because it decreases the miss-distance of the interaction A but increases that of the interaction B. • The swept-forward tip shape reduces the BVI

noise becaUse it causes the perpendicular BVI in the tip region in the advancing side. On the other han·d, the swept-back tip intensifies the BVI noise because it causes the parallel BVI in the tip rE;gion in t~~ advancing side. The direc-tivity of the radiation shifts toward the right hand side of the forward flight direction in the case of the swept-back tip shape.

• The intensity of the BVI noise is reduced by the tapered tip shape for which a core radius larger than that for the rectangular tip shape is applied.

References

1. Schmitz,F.H. and Yu,Y.H., Helicopter Impul-sive Noise: Theoretical and Experimental Sta-tus, Journal of Sound and Vibration, 109(3), 1986, pp.361-422.

2. lvlartin,R.lvl. and Connor,A.B., Wind- Tunnel Acoustic Results of Two Rotor Models with Several Designs, NASA-TM 87698, 1986. 3. Tung,C., Yu,Y.H., and Low,S.L., Aerodynamic

Aspects of Blade-Vortex Interaction (BVI), AIAA Paper 96-2010, June 1996.

4. Tadghighi,H.,Hassan,A.A.,and Charles,B., Pre-diction of Blade-Vortex Interaction Noise Us-ing Airloads Generated by a Finite-Difference Technique, Journal of the American Helicopter Society, Vol.37, No.4, October 1992, pp.38-4 7. 5. Yu,Y.H., Tung, C., Gallman,J., Klaus,K.J., Van

der Wall,B., Spiegel,P., and Michea,B., Aero-dynamics and Acoustics of Rotor Blade- Vortex Interactions, Journal of Aircraft, Vol.32, No.5, Sep.-Oct. 1995, pp.970-977.

6. Boxwell,D.A. and Schmitz,F.H., Full-Scale Measurements of Blade-Vortex Interaction Noise, Journal of the American Helicopter So-ciety, Vo!.27, (4), October 1982, pp.ll-27. 7. Yu,Y.H.,Liu,S.R.,Jordan,D.E.,Landgrebe,A.J.,

Lorber,P.F., Pollack,NI.J., and Martin,R.M.,

Aerodynamic and Acoustic Test of a United Technologies Model Seale Rotor at DNW, 46th Annual Forum of the American Helicopter So-ciety, May 1990.

8. Wagner,W.J., Comparative Measurements of the Unsteady Pressures and the Tip-Vortex Pa-rameters on four Oscillating Wing Tip Models, lOth European Rotorcraft Forum, Nr.9, August 1984.

9. Mullins,B.R.Jr, Smith,D.E., Rath,C.B., and Thomas,S.L., Helicopter Rotor Tip Shapes for Reduced Blade-Vortex Interaction - An Exper-imental Investigation, Part II, AIAA Paper 96-0149, 1996.

10. Aoyama,T., Kawachi,K., and Saito,S., Effect of Blade-Tip Planform on Shock Wave of Ad-vancing Helicopter Blade, Journal of Aircraft, Vol.32, No.5, Sep.-Oct. 1995, pp.955-961. 11. Nakamura,Y. and Azuma,A., Rotational Noise

of Helicopter Rotors, Vertica, vol.3, no.3/4, 1979, pp.293-316.

12. Hassan,A.A., Tung,C, and Sankar,L.N., An As-sessment of Full Potential and Euler Solutions for Self-Generated Rotor Blade-Vortex Interac-tions, 46th Annual Forum of the American He·· licopter Society, May 1990.

13. Splettstoesser, W.R.,Schultz,K. J.,

Boxwell,D.A., and Schmitz,F.H., Helicopter Model Rotor Blade Vortex Interaction Impul-sive Noise: Scalability and Parametric Varia-tions, lOth European Rotorcraft Forum, Paper Nr.18, 1984.

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Compute CAMRAD II • Compute blade motion

• Compute wake geometry

J,

Interpolation code

• Interpolation of blade and tip-vortex position • Compute effective angle of attack of blade

elements

J,

Unsteady Euler code • Modify surface boundary conditions • Compute pressure distributions

J,

FW·H code

• Compute acoustic wavefonns

Fig.l Flow chart illustrating the

calculation method.

3.44 R

\

Observer

Table 1 Main rotor characteristics.

AH-1/0LS model rotor

Radius 0.958 m Chord length 0.104 m Solidity 0.056 Number of blade 2 Airfoil modified BHT 540 (1/e = 9.71 %)

Hinge teeter type

Tip planform rectangular

Table 2 Operating condition.

Hover tip Mach number 0.664 Forward speed

Advance ratio

Rotor thrust coefficient Shaft inclination angle

72.0 kts 0.164 0.0054 2.0 deg (+ aft.)

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60

I

Measured

Calculated

(by W.R.Splettstoesser et al.)

,...--.. ,.--.,

ro

40 A

ro

40 -P-<

_~

'--" <!) <!) 1-< 1-< ;::j ;::j

A

r.n

₂₀

_B

r.n

₂₀

B

<!)

~

1-<

P-<

'"d

1:::

"

;::j

0

;::j

_{0 ~}

0

0 vv

C/.l

-20

. .I

1/2 REV.

Fig.3 Comparison between measured and calculated time histories of BVI noise.

o: interaction above rotor disk

•=

interaction below rotor disk

I

____ j __ _

270°

Fig.4 Top view of predicted BVI locations.

o: vortex shed from own blade e: vortex shed from previous blade

1

0 ~

~

_··<

-

_0'

"0

_~

.

-1

0

0 -2

0

180

360 Azimuth Angle (deg.)

Fig.S Miss- distance between vortex

and blade during BVIs.

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60 r-;:::::;:;:;:;~;:;===;--1

(a) Anhedra

~ t rJR=0.9 Top •""'

-r---t

w· Frootview L

*"!

A

60

40

20

0 (b)Kectangu 1 ar

Top view '-1---) Front view t.

A

B

N

_Vv

-20

' - - - ' - - - _ _ J

20 <0---1/2

REV.----c,. -

<0---1/2

REV.-_,.

60 r;=:;;::;;:;:::::;=;===;~

(c

Di

edral

Topv--40

Front view

A

20 B

-2o

_<E-

~~IRFv=~

_1/2

_{REV.-_,.}

Fig.6 Time histories of BVI noise for blades with anhedral, rectangular,

and dihedral tip shapes.

0.4 . - - - ,

(a)Anhedral

(b)Rectangular

_(c)Dihedral

a.

·=

>

02 ro··

"""·---u .

d?i ..

foe••

cP ••••••• . .

•••••••

0 coo •••

10oo··~

_{... •••}

~

--..

.

••

t:....

u

---

N "Cl

o: vortex shed from own blade

•=

vottcx shed from previous blade

0.0

'----~--__J

0

180 360 0

180

360 Azimuth Angle (deg.)

Azimuth Angle (deg.)

Fig.7 Strength of tip vortex during BVIs for blades with anhedral, rectangular,

and dihedral tip shapes.

1

0 -I

0 0 0 0

-2

0 (a)Anhedral

0

•

• B _-..::;

• o#""'

•, A

• ...

e: vottcx shed from previous blade

180

360 Azimuth Angle (deg.)

ro

₀ 0

0 (b)Rectangular

8

(c)Dihedral

~

-..,!3

""

.._

.

...-

--

•• <.Y A

0~

0 •, A 0 0 0 0 .

180 360 0

180 Azimuth Angle (deg.)

Azimuth Angle (deg.)

Fig.8 Miss- distance between vortex and blade during BVIs for blades with

anhedral, rectangular, and dihedral tip shapes.

0

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,...._

~ 0...

.._,

~ ::I

"'

~ 0... "0

c::

::I 0 (I)

60

60 (b)Rectangu 1 ar

'-r

I

(c)Swept-bacJ<.

t r~.9

Top view Topview I ~

Front vkw t_ I 4{}'

40

Fron1view '- -

40 B

20

20 AB

A

B

f-A

20

0

0 _1---v\

ltV

~

0 -20 '---'---' -20

-20

'

<1---1/2

REV-~

«---1/2

REV---?

.,___ 1/2

REV-~

Fig.9 Time histories of BVI noise for blades with swept-forward, rectangular,

and swept- back tip shapes.

0.4 ,---~---,

(a)Swept-forward

(b)Rectangular

(c)Swept-back

e: vortex shed from previous blade

o.o o!c----.-:18:-ro,---;;-;J360

o!c---,-18!:-::o:---~360 o~--·1"*'8o~-_____,3;-;!6o

Azimuth Angle (deg.) Azimuth Angle (deg.) Azimuth Angle (deg.)

Fig.IO Strength of tip vortex during BVIs for blades with swept-forward,

rectangular, and swept- back tip shapes.

I

,----,----~--,---,---,

( a)Swept -forward

~

0 ~---~---1

.~ • A

•

0

-1

~-0 •

0 o: vortex shed from own blade

(b)Rectangular

~

-·.~

'% •

0 0

-2

Lo~---~---~

0

180 360 0

180

Azimuth Angle (deg.) AZimuth Angle (deg.)

(c)Swept-back

._B 0 8 0

360 0

180

Azimuth Angle (deg.)

Fig.ll Miss- distance between vortex and blade during BVIs for blades with

swept-forward, rectangular, and swept-back tip shapes.

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(a)Swept-f01ward

(b)Rectangular

(c)Swept-back

Fig.12 Trajectories of tip vortices for blades with swept-forward, rectangular,

and swept- back tip shapes.

60

~

40 ~ ~ ~ 20 ~

""

"Q

"

g

0

"'

-20 60

E;

40 -20 60

~

40 ~ ~ ~ 20 ~ ~

""

"Q

"

~ ₀ 0

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-20

Swept-forward

Rectangular

Swept-back

(a)

(b)

(c)

H

~

N

~

F-v

l r

(d)

(e)

(f)

~"'

~v-

~

_'rJ

L-~--~---(g)

(h)

(i)

[\,

j

_/liv-~

~

_"I

l__ _{L...__._~-'----~}

< -1/2 REV-> <---- 1/2 REV.----> <----1/2 REV.->

(11)

,-., til

c..

' - ' <1)

....

::l Cll Cll

~

c..

"0 t:: ::l 0 <Zl

60 ₆₀

(a)1

a

per

r/R=0.9 Top vlcw

'-1---p---I 4::0.33

40

Front v\ew

40

20

20 A

B

0 ₀

-20

' - - - ' - - - - _ j

-20

<i---1/2

REV..-_,.

(b) Rectangu I ar

Top view

•

Front view t

A

1-

_B

rv----.

~

_vv

'

-E----1/2

REV.-_,.

Fig.14 Time histories of BVI noise for blades with tapered and rectangular

tip shapes.

0.4 1 , - - - ,

(a)1/3 Tapered

0.

>

~

...

~

0.2

F-""o•• ~·•••• ...

t:-.

o: vortex shed from own blade •: vortex shed from previous blade

0.0

c__--~~---_j 0.4,----~---,

(b)Rectangular

.g->o2'0A

U · --~o•• oo0 ••••••••

••••••••

~ ao ••• •

t:-.

• 0.0 ::---;-;;-~----,=-o!

0

180

360

Azimuth Angle (deg.)

Fig.15 Strength of tip vortex during

BVIs for blades with tapered and

rectangular tip shapes.

]

Br,======]---~

r

/R=O. 92

~ 0 Rectangular 1/3 lopored ... ·· ... ··· ... ··

w

·

2

oL-~4oso,2o~t~60~2~oo~24~o~za~o-7.32~o-!J6o

Azioulh (dog)

(a)1/3 Tapered

0 '-.B

~

.. '"f"'

~

"C)

\

.

-1

₀

0 o: vottex shed &.urn own blade

-2

1 (b)Rectangular

0 '-.'3

~

.~

-0 ' "C) •. A

-1

:1!, 0 0

-2

0

180

360

Azimuth Angle (degc)

Fig.16 Miss-distance between vortex

and blade during BVIs for blades with

tapered and rectangular tip shapes .

Fig.17 Time histories of effective angle of attack for

blades with tapered and rectangular tip shapes.