Airfoil Dynamic Stall and Aeroelastic Analysis Based on Multi-frequency Excitation Using CFD Method

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 99 (2015) 686 – 695

“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology, APISAT2014

Airfoil Dynamic Stall and Aeroelastic Analysis Based on MultiFrequency Excitation Using CFD method Daobo HUANG, Jiandong LI, Yong LIU* National Key Laboratory of Rotorcraft Aeromechanics, Nanjing University of Aeronautics and Astronautics, 29 YudaoStreet, Nanjing 210016, P.R.C

Abstract

This paper conduct a comprehensive research on time varying pitching, plunging (flapping) motion and Periodic alternating oncoming flow for NACA0012 airfoil in order to accurately capture the real aerodynamic characteristics and airfoil responses of the rotor blades in complex unsteady flow field. When simulating the pitch motions, the excitation of the second and third harmonic were got into consideration. The result shows that: (1) the aerodynamic coefficient generated for the steady stall and pitching motion are compared well with the experimental data; (2) when the second and third harmonic were got into consideration for the pitching motion, the aerodynamic loads and response show significant difference which would be used for active control of helicopter. ©2015 2014The The Authors. Published by Elsevier Ltd. © Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA) Keywords: 2-D airfoil, dynamic stall, couple motion, K-¹SST turbulence model, helicopter

1. Introduction It is well known that helicopter blades operate in strongly unsteady airflow environment when in forward flight; it shows complex aerodynamics and vibration characteristics. As the superposition of rotation speed and forward speed, transonic shock stall may occur at the preceding blade, flow separation and dynamic stall at a high angle of attack (AOA) may occur at the retreating blade. The aerodynamic properties and dynamic characteristics of 2-D airfoil are the basis for the analysis of the helicopter rotor. But most of the experimental studies on dynamic stall

* Corresponding author. Tel.: +86-025-8489-5167 E-mail address: [email protected]

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA)

doi:10.1016/j.proeng.2014.12.590

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Daobo Huang et al. / Procedia Engineering 99 (2015) 686 – 695

phenomenon have focused on airfoil oscillating only in pitching motion [1, 3]. There is few study available in the open literature on the combined effects of pitching, plunging and oncoming flow velocity variations on the aerodynamic characteristics of a 2-D airfoil [1, 3]. Carta[4] and Ericsson[5] had conducted an experiment on comparatively studying the effects of pitching and plunging motions of an oscillating airfoil in 1979 and 1983. Their experimental data show that pitching and plunging motions have similar effects on the aerodynamic characteristics of the airfoil for low angle of attack (about 2 degrees). But for high angels of attack (about 8 degrees), considerable were observed. In 1988, the combined effects of time varying oncoming velocity and pitching motion on the aerodynamic behaviour of a NACA0012 airfoil was investigated by D.favier[6]. This paper conduct a comprehensive research on time varying pitching, plunging (flapping) motion and Periodic alternating oncoming flow for NACA0012 airfoil in order to accurately capture the real aerodynamic characteristics and airfoil responses of the rotor blades in complex unsteady flow field. When simulating the pitch and plunge motions, the excitation of the airfoil elastic vibration were got into consideration. Under couple motions and oncoming flow, the response of a 2-D airfoil possesses some significant highfrequency components, which come from high-frequency airloads of dynamic stall airfoil. At the same time, the high-frequency response will feed back to the flow motion, and affect the lift and moment coefficient of the 2-D airfoil. The results of the investigation show that this CFD-CSD couple model provides a well correlation with experimental stall data; the model selection and discrete grid were proved to be reliable. 2. The 2-D airfoil unsteady model 2.1. Aerodynamic model As in forward flying, the AOA of a blade element is the resultant of a combination of forcing from collective and cyclic blade pitch, twist angle, elastic torsion, blade flapping velocity, and elastic bending. So based on the forward flight blade element theory, an unsteady aerodynamic model would be established to analysis the pitch, plunge and time-varying over flow effects for the 2-D airfoil. Assuming the blade element is located at the r radial position of the blade, so its relative flow velocity component is:

wx ZrcosE  PZRsin\

˄1˅

P cos\ cos E  (v1  O0 )sin E

˄2˅

wy =(Q 1  O0 ) cos E  VE  P cos\ sin E

˄3˅

wz

The AOA of the blade element is:

D

M  E*

˄4˅

Where M is cross-section installation angle, E * is oncoming flow angle

E* =arctan( wy / wx )

˄5˅

By calculating, the angle of attack varying along the azimuth can be obtained. In order to simplify the problem, just retain the manipulate input excitation and remove other components of the excitation. The sectional angle of attack Oscillation law at the r radial of the blade is show as:

D =M  M sin(Z ˜ t ) And the flapping speed (plunging) is:

˄6˅

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Daobo Huang et al. / Procedia Engineering 99 (2015) 686 – 695

h VE

rd E / dt

r(d E / d\ )(d\ / dt ) rZ(a1 sin\  b1 cos\ )

In the equation, a1 is rotor anteversion, b1 is rotor side chamfer, azimuth.

˄7˅

Z is rotational angular velocity, and \ is blade

2.1. Pitching  and plunging coupled dynamic model Figure 1 shows a coupled dynamic model of pitching and plunging motions. At the fig, position Q represents the center of aerodynamic pressure, C represents center of gravity and P represents the elastic center, θ represents the input pitch angle and V represents the oncoming flow velocity. By solving and analyzing the response of these two motions in a time-varying oncoming flow, simulating the condition of a typical blade element of a helicopter rotor blade in forward flight.

Fig.1. The two dimensional coupled dynamic model

Fig.2.The structure and unstructured mix grid

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The equations of these two coupled motions can be written as:

Where SI is the inertia coupling terms,

mh  SII  K h h

L

III  SI h  KII

Mf

I

˄8˅

is elastic torsion angle, h is plunging (flapping) displacement,

 L and M f is the lift and moment of the airfoil which were obtained by CFD method. The symbol M f is defined as the moment around the a quarter chords, M f =2b ˜ xa ˜ L / c The coupled equations given in matrix form is show as:

Mx  Gx  Kx Where M

§m ¨S © I

SI · ,G II ¸¹

§ 0 0· ¨ 0 0¸ , K © ¹

r(t )

˄9˅

0 · § L · , r (t ) ¨ ¸ ¸, x KI ¹ ©Mf ¹

§ Kh ¨ 0 ©

§h· ¨I ¸ © ¹

Response was calculated by symplectic numerical integration with high precision algorithm. Converted equation (9) into a first-order equation as: v

Hv  f ,

where H

§ A B· ¨C D¸ © ¹

˄10˅

Using Hamilton approach:

v

^x, p`

T

,

P

Mx  Gx / 2,

f

^0, r`

˄11˅

T

A  M 1G / 2, B GM 1G / 4  K , C

GM 1 / 2ˈD

M 1

Solution of equation (10) is: t

e Ht v0  ³ e H (1t ) f (W )dW

v (t )

Discrete the load on the time domain and let time step size as 't , tk

v(tk 1 )

˄12˅

0

Tv0  ³

tk 1

tk

k 't (k

0,1,2 )

e H ( tk 1 W ) f (W )dW

˄13˅

Where T eH 't (e HW )2 N ˈ W ='t / 2N Taylor series expansion for T:

T (W ) e HW T0

I  T0

˄14˅

HW  ( HW )2 / 2!

˄15˅

And then calculate by the following formula:

Ti

2Ti 1  Ti 1Ti 1 ,(i 1,2,

N)

˄16˅

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Finally, the matrix T was given as: T I  TN Assuming the inhomogeneous term in one time step is linear, so the solution of equation (8) is: vk 1

T ª¬vk  H 1 (r0  H 1r1 )º¼  H 1 ª¬ r0  H 1r1  r1W º¼

˄17˅

3. Grid Discrete and Turbulence Model Compared to structured grid, the unstructured grid does not consider the orthogonal and connectivity restrictions, it can be more easily controlled with the mesh shape, grid node positions and cell size [7]. During dynamic mesh computing, unstructured grid have a better geometric flexibility. It can also effectively preventing large cell skewness, ensuring mesh quality at an idea value. However, the structured grid has a better accuracy. Thus, in order to satisfy the boundary movement and accuracy requirements, grid discrete uses the form of structure grid combining with unstructured grid, as shown in Fig 2. The total height of the structure grid is 2 times the thickness of the airfoil. Far-field boundary wall is 15 times distance of the airfoil chord which would meet the far-field pressure condition. Due to the dynamic stall, the blades operate at a strongly unsteady flow field environment. So the K-¹SST(shear stress transport) turbulence model was selected for this paper, which was developed by Menter F R based on the Kω turbulence model. The turbulent viscosity coefficient of this model had considered the effects of non-equilibrium flow, so it was more suitable for the calculation of unsteady flow. The specific form of turbulent kinetic energy equation and turbulent frequency equation is [8, 9]:

DU k Dt DUZ Dt

w wx j

w wx j

ª wui wk º  E * UZk «( P  V k Pt ) »  W ij wx j »¼ wx j «¬

(W ij =  U u 'i u ' j )

ª wZ º J wui 1 wk wZ  EUZ 2 +2(1- F1 ) UV Z 2 «( P  V Z Pt ) »  W ij x v x w w Z wx j wx j » j j ¼ ¬«

˄18˅

˄19˅

Turbulent viscosity coefficient is:

Xt

a1k ; max(a1Z, :F2 )

a1

0.31

˄20˅

4. Results and Analysis The results of this paper consist of two parts: (a) Generation and validation of unsteady aerodynamic coefficients using CFD method, and (b) aeroelastic response of a 2-D airfoil undergoing pitching and plunging motion in timevariation oncoming flow. A. Validation of the CFD model Using the CFD method, the aerodynamic coefficients of the 2-D airfoil are generated and compared with experimental data for four conditions: (1) NACA0012 airfoil static stall characteristics, (2) pure pitching motion of an airfoil under the Light Stall and deep stall conditions, (3) combined pitching and plunging motion in a timevariation oncoming flow, (4) Consider the impact of multi-frequency excitation for airfoil aerodynamic coefficients and its spectral distribution. (1) NACA0012 airfoil static stall characteristics

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In order to verify the reliability of the grid discrete and turbulence model used in this study, First study the static stall characteristics of NACA0012 airfoil at Mach number M∞=0.301 and Reynolds Re=3.95h106. Airfoil chord is taken as c=0.61 and the speed of sound used for calculating Mach number is 340 m/s. The results shown in Fig.3 are in good agreement with the experimental data taken from Ref.2 which were conducted by McAlister and McCroske. Proving the grid model and turbulence model are effective and reliable. a

1.4

b

10

1.2

8 6

Calculated value

0.8

experimental data Ref.2

-cp

Lift Coefficient /CL

1

4

0.6 2

0.4 calculated value max-lift =1.32,D =13.5 experimental data max-lift =1.35, D =13.5

0.2



0 0

5

10 15 20 Angle of AttackD (degree)

0 -2 -0.2

25

0

0.2 0.4 0.6 0.8 Chordwise position x/c

1



Fig.3. (a)NACA0012 steady stall characteristics;(b)pressure distribution at max lift condition

(2) Only pitching motion For light stall condition, the airfoil is assumed to undergo a pitching motion D 5.0  5sin(Zt ) . The Mach number is M ∞=0.301, Reynolds is Re=3.93h106 and the reduced frequency k is equal to 0.1. The Calculated lift coefficient and moment coefficients hysteresis loop are as shown in Fig.4 (a). For deep stall condition, the airfoil’s pitching motion is assumed as D 14.84  9.87sin(Zt) . The Mach number is M∞=0.28, Reynolds is Re=3.52h106 and the reduced frequency k is equal to 0.0975. The Calculated lift coefficient and moment coefficients hysteresis loop are as shown in Fig.4 (b). It shows that whether in light stall at small angle of attack or deep stall at high angle of attack, the overall trend of lift coefficient and moment coefficient of the 2-D airfoil are compared very well with the experimental data. Figure 5 shows the pressure contours of a few typical moments of deep stall situation. In the rising phase, when the AOA of the airfoil rise to around 16.2 degrees, slightly flow separation occurred in the leading edge of the airfoil, and formed a low-pressure detached vortex. With the increasing of the AOA, the low-pressure detached vortex expands and moves backward to trailing edge gradually. Causing a suddenly increase of the pressure difference between the upper and lower surface of the airfoil. When the AOA increases to 22 degrees, the low-pressure detached vortex separate from the trailing edge, pressure on the upper surface of the airfoil rebound sharply, and lift coefficient drop sharply too, stall occurs. The stall process is reasonable and compared very well with the experimental data. a b Variation of lift coefficient

variation of lift coefficient

2.2

1.2

2

Lift coefficient /CL

lift coefficient/ CL

1.8

calculated value experimental data

1

calculated value experimental data

0.8

0.6

0.4

1.6 1.4 1.2 1 0.8 0.6

0.2 0.4 0 -2

0

2

4 6 8 angle of attack D (deg.)

10

12

0.2

5

10

15 20 angle of attack D˄deg.˅

25

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Daobo Huang et al. / Procedia Engineering 99 (2015) 686 – 695 The valiation of moment coefficient

variation of moment coefficient

0.05

0.1 0.05 0

moment coefficient /cm

Moment coefficient/ CM

0

-0.05

calculated value expeimental data

-0.1

-0.05 -0.1 -0.15 calculated value experimental data

-0.2 -0.25

-0.15

-0.3 -0.35

-0.2 -2

0

2

4 6 8 angle of attack D (deg.)

10

-0.4

12

5

10

15 20 angle of attack D˄deg.˅

Fig.4 Lift and moment coefficients generated for only pitching motion: (a) Light stall condition D stall condition D 14.84q  9.87qsin(Zt ) M∞=0.280

25

5.0q  5qsin(Zt ) ion, M∞=0.301; (b) Deep

Fig.5. The pressure contours of a few typical moments of deep stall situation

(3) Combined pitching and plunging motion in a time-variation oncoming flow For simulating the condition of a helicopter rotor blade cross-section in forward flight, aerodynamic coefficient and its spectral distribution were calculated out for NACA0012 airfoil undergoing combined pitching and plunging motion in time varying oncoming flow. Assuming the helicopter forward flight speed is V0 , Rotor angular velocity is

Z , so the relative oncoming flow speed to the r radial cross-section can be simplified as: Vf Z ˜ r  V0 sin(Zt ) . Plunging (flapping) speed is VE rd E / dt r ˜ Z ˜ (a1 sin\  b1 cos\ ) , the pitching motion is D (t) D0  'D sin( Zt) . The airfoil chord is 0.61m.the detail data used for this calculation are as the following table: Table 1. Detail data of plunging motion condition Case

Rotational speed (rad/s)

Forward speed(m/s)

Periodic pitching manipulation

Flapping motion coefficient

Light Stall

33.2185

69.5

D (t )

a1

69.5

D (t ) 14.84  9.87 sin(Zt )

Deep stall

30.4328

4.94  5 sin(Zt ) q

q

q

q

a1

2qˈb1 q

4 ˈb1

Radial position

2q 4

4m 3.13 m

q

The results are shown in Fig.6: variation of lift coefficient

variation of moment coefficient

1.4

0.4 0.2 0

-0.02 -0.04 -0.06

pitching and plunging motion in a time-variating oncoming flow Only pitching motion

-0.08

0

Moment Coefficient \CM

0.6

2

0 Lift Coefficient /CL

Lift coefficient /cl

1

0.05

Only pitching motion Pitching and Plunging motion in a pulsating flow

0.02

0.8

Variation of the Moment Coefficient

Variation of the Lift Coefficient 2.5

0.04

pitching and plunging motion in a time-variating oncoming flow Only pitching motion moment coefficient /cm

1.2

1.5

1

-0.1

-0.05 -0.1 -0.15 -0.2

Only pitching motion pitching and plunging motion in a pulsating flow

-0.25

0.5

-0.12

-0.2

-0.3

-0.14

-0.4 -2

0

2 4 6 angle of attack D (deg.)

8

10

-2

0

2

4 6 8 angle of attack D (deg.)

10

12

0

0

5

10 15 Angl e of Attack D (deg.)

20

25

-0.35

0

5

10 15 Angle of Attack D (deg.)

20

25

693

0.015

1

0.01

0.8 0.6 0.4 0.2

-0.01

-0.02 45

90

135

180 225 \ (deg.)

270

315

-0.025

360

(a)

1.5

0

-0.015

0

0

-0.005

0

0.05

2

0.005

-0.2 -0.4

2.5

Moment coefficient /CM

0.02

1.2

Lift coefficient /CL

1.4

Moment coefficient \CM

Lift coefficient

Daobo Huang et al. / Procedia Engineering 99 (2015) 686 – 695

1

0.5

0

45

90

135

180 225 \ (deg.)

270

315

0

360 400

-0.05 -0.1 -0.15 -0.2 -0.25 -0.3

0

45

90 135 180 225 270 315 360 400

\ (deg.)

Light stall

(b)

0

45

90

135

180 225 \ (deg.)

270

315

360

400

deep stall

Fig.6. the aerodynamic coefficient generated for combined pitching and plunging motion in a pulsating oncoming flow

(4) Multi-frequency excitation In the process of rotor rotating, changes of the blade AOA in addition to manipulating inputs as well have other incentives of harmonic components. This study take the second and third harmonic into account as well as the fundamental frequency which is mainly reflected the Pitching manipulating. So the total excitation for the angle of attack is D (t) D 0  D1 sin( Z t)  A1sin( Z1t M1)  A2sin( Z2 t M2) . Detail values are shown in the following table: Table 2. Detail values of the multi-frequency excitation conditions

Light Stall

Rotational speed/rad/s

Periodic pitching manipulation

33.2185

D (t )

a

Second harmonic

4.94  5 sin(Zt ) q

q

Amplitude

66.4

0.0175

b

1.4 only one frequency multi-fre-0-deg. phase multi-fre-30-deg. phase multi-fre-45-deg. phase multi-fre-60-deg. phase multi-fre-90-deg. phase multi-fre-120-deg. phase

1.2

Lift coefficient /CL

1 0.8

Phase 0,30,45,60, 90,120

0.02

0.4

Frequency

Amplitude

99.6

0.00875

Phase 0,30,45,60, 90,120

only one frequency multi-fre,0-deg.phase multi-fre,30-deg.phase multi-fre,45-deg.phase multi-fre,60-deg.phase multi-fre,90-deg.phase multi-fre,120-deg.phase

0.015

0.6

0.01

0.005

0

-0.005

0.2 0 -4

Third harmonic

Frequency

Moment coefficient /CM

Case

-2

0

2 4 6 angle of attack D (deg.)

8

10

12

-0.01 -4

-2

0

2 4 6 angle of attack D (deg.)

8

10

12

Fig.7. Aerodynamic coefficient generated for Multi-frequency excitation: (a) lift coefficient; (b) moment coefficient

As can be seen from the Fig.7, multi-frequency excitations have a significant effect on the airfoil aerodynamic coefficients. The hysteresis rings of lift coefficient will offset at different Phase. The moment coefficient also show different shape at different phases angles, for example, the moment hysteresis loop has two peaks at both ends when the phase angle is 30 degree. And its area will be smaller when the phase angle is 120 degree. From this phenomenon, there is a good reason to believe that an ideal curve of aerodynamic coefficient would be obtained by using multi-frequency excitation for helicopter and then achieve active control goals. B. 2-D airfoil response In this paper, the method of symplectic numerical integration was used to solve the motion equation (8), and the time step size was set as the CFD used. Frequency spectrums of the responses of the pitching and plunging motion were obtained using Fast Fourier Transform (FFT). Detailed parameters for the calculation are: m=7.95 kg;

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Daobo Huang et al. / Procedia Engineering 99 (2015) 686 – 695

K h =4396.0 N/m; KI =734.2 N/m; I I =0.115 kg/m2; airfoil chord is c=061. Case (1), for the light stall condition, the input excitation frequency is Z = 33.2185 rad/s (5.288Hz), Periodic pitching excitation and oncoming flow are: D 5.0  5sin(Zt ) deg. and Vf 132.874  69.5sin(Zt ) ; Case (2), for the deep stall, the input excitation frequency is Z = 30.4328 rad/s (4.84Hz), Periodic pitching excitation and oncoming flow are: D 14.84  9.87sin(Zt) deg. and Vf 95.26  69.5sin(Zt ) ; In the uncoupled analysis, the aerodynamic center was located at the quarter chord of the 2-D airfoil, and the mass center and elastic axis were assumed to be at the same location where 1% chord distance from the aerodynamic center was. As shown in Fig.8. 2.5

0.1

2

0.08

2

0.3

0.2

1 1.5

0.06

0.1

0.02 0

-1

0

-0.1

-2

-0.02

-1

Torsion˄ rad˅

0 -0.5

Heave(m)

0.5

-0.2 -0.04

-1.5

-3

-0.3

-0.06

-2 -2.5

0

0.04

Torsion˄ rad˅

Heave(m)

1

0

0.1

0.2

0.3 0.4 Time(s)

0.5

0.6

-0.08

0.7

0

0.1

0.2

0.3 0.4 Time˄ s˅

0.5

0.6

-4

0.7

0

0.1

0.2

0.3

0.4

0.5 Time(s)

0.6

0.7

0.8

0.9

-0.4

1

0

0.1

0.2

0.3

0.4 0.5 0.6 Time˄ s˅

0.7

0.8

0.9

1

-3

1.2

0.03

x 10

-3

0.08 7

x 10

0.07 1

0.025

6

0.06

0.6

0.05 Amplitude(m)

0.015

Amplitude(m)

Amplitude(m)

Amplitude(m)

5

0.8

0.02

0.04 0.03

4

3

0.4

0.01

2

0.02 0.2

0.005

0

1

0.01

0

5

10

15

20 25 Frequency(Hz)

30

35

0

40

(a)

0

5

10

15

20 25 Frequency(Hz)

30

35

0

40

0

5

10

15

20 25 Frequency(Hz)

30

35

Light stall

0

40

0

5

10

15

20 25 Frequency(Hz)

30

35

40

(b) deep stall

Fig.8. Airfoil response and its frequency contents for uncoupled condition

In the coupled analysis, the aerodynamic center was still located at the quarter chord of the 2-D airfoil, but elastic axis was located at the position of 5% chord after the aerodynamic center, and the mass center was between them and 3% after the elastic axis. The results of this calculation were shown in the Fig.9. 4

2

1

0.5

3

0.4

1 2

0.3

-1 -2

Heave(m)

Torsion˄ rad˅

0

Heave(m)

0

0.5

-1

-2

0

-3

0.2 Torsion˄ rad˅

1

0 -0.1 -0.2

-4

-3 -0.3

-5 -6

0.1

0

0.1

0.2

0.3 0.4 Time(s)

0.5

0.6

-0.5

0.7

0

0.1

0.2

0.3 0.4 Time˄ s˅

0.5

0.6

-4

0.7

0

0.1

0.2

0.3

0.4

0.5 Time(s)

0.6

0.7

0.8

0.9

-0.4

1

0

0.1

0.2

0.3

0.4 0.5 0.6 Time˄ s˅

0.7

0.8

0.9

1

-3

0.01

0.08

9

0.07

8

x 10

0.08

0.009 0.07

7

0.06

0.006

0.04

6

0.005 0.004

0.03

0.05

Amplitude(m)

0.05

Amplitude(m)

0.007

Amplitude(m)

Amplitude(m)

0.008 0.06

0.04 0.03 0.02

2

0.002 0.001

0

0 0

5

10

15

20 25 Frequency(Hz)

30

(a)

35

40

4 3

0.003 0.02 0.01

5

0.01

0

Light stall

5

10

15

20 25 Frequency(Hz)

30

35

40

0

1

0

5

10

15

20 25 Frequency(Hz)

30

35

0

40

0

5

10

(b) deep stall

Fig.9. Airfoil response and its frequency contents for coupled condition

15

20 25 Frequency(Hz)

30

35

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Daobo Huang et al. / Procedia Engineering 99 (2015) 686 – 695

5. Conclusions This paper studies the aerodynamic coefficients of NACA0012 airfoil at the condition of combined pitching and plunging motion in a pulsating oncoming flow, and the impact of multi-frequency excitation for dynamic stall. Draw some conclusions: The k-¹SST turbulence model is a more effective model for the calculation of airfoil dynamic stall; the plunging motion and pulsating oncoming flow have a significant effect on the airfoil aerodynamic characteristics, especially on the lift coefficient; when the second and third harmonic were got into consideration for the pitching motion, the Aerodynamic loads and response shows a significant difference which would be used for active control for helicopter. References [1] V. Laxman and C. Venkatesan, “Rotor Blade Dynamic Stall Model and Its Influence on Airfoil Response”, 47th AIAA, 2006. [2] McCroskey, W. J., Carr,K .w., and McAlister K.W, ”Dynamic stall Experiments on Oscilating airfoils ", Journal of Airc raft, Vol. 14 , No.1 Jan. 1976, pp.57-63 [3] McCroskey, W.J., McAlister, K.W., Carr, L.W. and Pucci , S. L. "An Experimental Study of dynamic Stall on Advanced Airfoil Sections" Vol.2, "Pressure and Force Data";Vol. 3, "Hot-Wire and Hot-film Measurements." NASA TM-84245,1982. [4] Carta, F.O. "A Comparison of Pitching /Plunging Response of an Oscillating Airfoil", NASA CR-317, Oct. 1979. [5] Ericsson, L. E. and Reding, J. P., “The Difference Between the Effects of Pitch and Plunge on Dynamic Airfoil Stal l", 9th European Rotorcraft Forum, Stresa, Italy, Sept.13-15, 1983 [6] Favier, D., Agnes, A., Barbi, C. and Maresca, C. "Combined translation/Pitch Motion: A New Airfoil Dynamic Stall Simulation", Journal of Aircraft, Vol. 25, No. 9, 1988, pp. 805-814. [7] Zhang Wei, Liu Yong, “Research of Unsteady Aerodynamic Model’s Multi-frequency Characteristics”, 25th CIAA, 2009. [8] QIAN Wei-qi, Fu Shong, CAI Jin-shi, “Numerical study of airfoil dynamic stall”, ACTA Aerodynamic Sinica, Vol. 19, No. 4, Dec. 2001 [9] Lei Yansheng, Zhou Zhenggui, “CFD Investigation on Wind Turbine Oscillating Airfoil Dynamic Stall”, ACTA Energiae Solaris Sinica”, Vol. 31, No.3, Mar.2010

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