Effects of trailing-edge movable flap on aerodynamic performance and noise characteristics of VAWT

Energy xxx (xxxx) xxx

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Effects of trailing-edge movable flap on aerodynamic performance and noise characteristics of VAWT Qingsong Liu a, Weipao Miao a, Chun Li a, b, *, Winxing Hao a, Haitian Zhu a, Yunhe Deng c a

School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai, 200093, China c Shenzhen Yatu New Energy Technology, Co., Ltd. Shenzhen, 518000, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 March 2019 Received in revised form 8 September 2019 Accepted 1 October 2019 Available online xxx

Efficiency enhancement and noise reduction are the two critical factors in the wind turbine design. In this paper, the effects of trailing-edge flap on the aerodynamic performance and noise characteristics of NACA0018 airfoil and vertical axis wind turbine (VAWT) were investigated, and the geometric parameters including flap angle, flap position and flap length were considered. The aerodynamic performance was simulated with the Detached-Eddy Simulation (DES) based on Spalart-Allmaras turbulence model and noise characteristics is calculated by CFD combined with Ffowcs-Williams and Hawkings (FW-H) acoustic analogy method. The research results indicate that the trailing-edge flap could effectively suppress flow separation and reduce the airfoil noise at high angle of attack (AOA). The optimum flap parameters obtained by orthogonal experimental design (OED) method were applied in VAWT, and it was observed that the trailing-edge flap could significantly improve the power coefficient at high tipspeed ratio (TSR) and reduce the VAWT noise. The research in this paper provided a comprehensive reference for improving the dynamic stall characteristics and reducing the noise of VAWT in practical engineering applications. © 2019 Elsevier Ltd. All rights reserved.

Keywords: CFD Trailing-edge flap Flow separation Aerodynamic performance Noise VAWT

1. Introduction Flow separation is an important factor affecting aerodynamic performance of airfoils [1]. Presence of flow separation on the blade surface of wind turbine will firstly lead to rapid reduction of lift, the sudden increase of drag, and fatigue loads [2]. In addition, it will lead to the change of pressure distribution on the surface of the airfoil and the destroy of pitch balance in the process of flow. Moreover, the fluid field in flow separation has strong instability and will periodically generate separation vortices, which will lead to the vibration of rotating machinery and noise generation. For a long time, various flow control techniques have been explored to control flow separation. The flow control techniques can be divided into the passive flow control and active flow control [3]. Common active flow control techniques include moving wall flow control technology, such as adding rotating cross-flow fan [4], blowing and suction air flow control technology [5], synthetic jet

* Corresponding author. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 200093. China. E-mail address: [email protected] (C. Li).

flow control technology [6]. Active flow control will increase too many mechanical devices, which will not only bring inconvenience to installation and maintenance, but also make it more difficult to realize engineering application [7]. The control mode without external energy input is called passive flow control. This control method is simple and easy to implement, such as adding flap on airfoil to improve lift [8], suppressing separation by vortex generator [9,10], and reducing drag by wingtip control device [11]. Although passive flow control is relatively simple to implement, its disadvantage is that it cannot be adjusted to the change of environmental conditions, but if the installation location and other parameters are appropriate, it can also play a very satisfactory flow control effect. Adaptive flap is a relatively advantageous passive flow control method [12]. By installing aerodynamic flap similar to bird feathers at the tailing edge of the airfoil, it not only has the advantages of simple structure, no need for control system and energy input, but also can adhere to the surface of the blade at a low AOA through relevant measures to maintain the optimal flow state of the airfoil. Patone [13] et al. took the lead in arranging the adaptive flap on the trailing edge of the suction surface of the blade to study their

https://doi.org/10.1016/j.energy.2019.116271 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

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control effect on flow separation. The results show that when flow separation occurs, the flap can self-adaptively lift and prevent further development of flow separation. Bramesfeld [14] et al. placed adaptive flap on the upper surface of S824 airfoil to study its flow control effect. The experimental results show that the maximum lift coefficient is increased by 20% compared with the airfoil without flap. Schlurter [15] studied the effect of adaptive flap on SD8020 and NACA4412 airfoils. The maximum lift of airfoils with adaptive flap increased to a certain extent. Meyer [16] et al. used experimental and numerical simulation methods to investigate the motion mechanism of adaptive flap, and arranged the adaptive flap on the aircraft blades for flight experiments. Wang [17] and Arivoli [18] studied the effect of adaptive flap on low aspect ratio blades. Compared with high aspect ratio blades, the effect of adaptive flap on aerodynamic performance of blades was slightly reduced. Rosti [19] et al. investigated the effect of rigid flap on airfoil in the process of pitching up by means of experiments. It was found that the flap can increase the mean lift fluctuation and affect the vortex shedding frequency at high AOA. However, the above-mentioned researches mostly focus on the study of flow control effect of flap under specific conditions. There is little analysis on geometric parameters of flap and the noise of airfoil with flap is not considered. Furthermore, there is little research on the application of trailing-edge flap to VAWT. Adding flap to the trailing edge of airfoil will inevitably change the shape of trailing edge and affecting the flow field distribution. The trailing edge shape of airfoil has a great influence on noise, and it is the main noise source of large wind turbines at present [20]. At low AOA, laminar flow will turn into turbulence at some position on airfoil surface. Turbulence will produce fluctuating pressure on pressure and suction surface of trailing edge, resulting in noise generation [21,22]. As the AOA increases continuously, large-scale vortices occur on the suction surface. When the deep stall happens, the scale of turbulent vortices becomes extremely large, and the whole suction surface turns into unsteady flow [23,24]. At this time, stall noise becomes the main noise. In this paper, the effects of three parameters of trailing-edge flap on aerodynamic performance and noise characteristics of NACA0018 airfoil were studied by numerical simulation. Orthogonal design method was used to optimize the combination of the three parameters in order to find the flap form which minimizes noise characteristics and maximizes aerodynamic performance. Eventually, the curves of power coefficient, torque coefficient, tangential force and the noise spectrum are illustrated comparatively to explore the control effect of trailing edge flap on VAWT.

2. Method and verification 2.1. Computational method of noise The numerical calculation of wind turbine aerodynamic noise can be divided into direct method and hybrid method [25]. The main idea of hybrid method is to solve the flow and sound field separately. Firstly, CFD method is used to solve the flow field to obtain the most important pressure fluctuation information for calculating aerodynamic noise. Then the propagation law of aerodynamic noise is obtained by solving the selected noise source parameters. Hybrid method eliminates more model assumptions and is more practical. It is often used to solve the far-field noise characteristics. In 1969, Ffowcs Willianms and Hawkings [26] extended Curle equation to the problem of sound generation in the interaction between solid and fluid boundary. The FW-H equation [27] named after them is obtained, which can be expressed as:

"

# # " 1 v2 v2 v 2
V p’ðx; tÞ ¼ T Hðf Þ
vxi vxi vxj ij c0 2 vt 2 nh i o v b j þ rui ðun
vn Þ dðf Þ þ f½r0 vn þ rðun
vn Þdðf Þg pij n vt (1)

where c0 is the sound velocity, p’ðx; tÞ is the SPL of received point, Tij is the Lighthill stress tensor,Hðf Þis the Heaviside performance b j is the unit vector outward function, For inviscid flowpij ¼ p’dij, n bi. r from vertical surface, ui is the fluid velocity component, un ¼ ui n and r0 is the fluid density and density at rest, dðf Þ is the Dirac function. Aerodynamic noise calculation requires better capture of small pressure fluctuations in unsteady flow field. Therefore, the DES turbulence model is used in transient simulation in this paper. The source correction length scale is 5c, the noise source is written out every two time steps, the data is extracted every 200 time steps, the time step Dt is 5  10
5, and the rough factor n of the source data is 2. The cut-off frequency f is obtained from:

f¼

1 2nDt

(2)

In order to study the effects of trailing-edge flap on noise characteristics of the airfoil, receiving points (A and B) and (D and E) are arranged in the horizontal and vertical directions respectively at the end of the flap, as shown in Fig. 1a, where c is the chord length. The additional 36 points are used to analyze the directivity of sound, as shown in Fig. 1b. 2.2. The DES (Detached-Eddy simulation) turbulence model The Detached-Eddy simulation method developed by Spalart [28] in 1997 makes it feasible to simulate large-scale separated flows in practical engineering problems. DES combines the advantages of LES and RANS, which is a three-dimensional unsteady numerical solution method using a single turbulence model. The turbulence model where the mesh is dense enough is equivalent to the Subgrid-Scale Stress Model in LES, and to the RANS model in other places [29]. The S-A turbulence one-equation model [30] solves a transport equation for the modified diffusivity ~v in order to determine the turbulent eddy viscosity. The nearest distance to the wall is used in this equation, and the strain of S-A model varies linearly with the distance far from the wall. Therefore, when using S-A one-equation turbulence model, there is no need for a more refined grid near the wall, but only a grid equivalent to the algebraic turbulence model. Therefore, it has the advantage of easy calculation and good convergence speed for simple flow. The turbulent eddy viscous expression is assumed to be vt ¼ ~vfv1 , the basic transported equation of ~v defined by:

ð ð ð   d 1 r~v v
vg , da ¼ ðm þ r~vÞV~v,da þ ½Cb2 rðV~v , V~vÞ þ G~v dt s~v V

A

V


Yv þ Sv dV (3)    2 ~v C f Yv ¼ r Cw1 fw
b1 k2 t2 d~

(4)

where Sv is the user-specified source term, and the transported variable ~v is a modified diffusivity. The terms on the right-hand side represent diffusion, production, and dissipation.

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3

Fig. 1. The distribution of noise receiving point.

cb1 ð1 þ cb2 Þ þ s k2

cw1 ¼

fw ¼ g

1 þ c6w3 g6 þ c6w3

(6)

~2 ¼ ~ We can conclude that~vf~ Sd SðCdse DÞ2 , the eddy viscosity coefficient is proportional to the magnitude of deformation rate and the square of filtration scale. This is exactly what Smagorinsky’s eddy viscous model requires.

(7)

2.3. Computational domain and mesh strategy

6

~v

(8)

~ Sk2 d2

~ S ¼ fv3 S þ

h~v i2 cb1 r~ S~vzcw1 fw r ~ d

!1

  g ¼ r þ cw2 r 6
r r¼

(5)

~v fv2 k2 d2

(9)

The damping functionsfv2 and fv3 are defined as:

fv2 ¼ 1


fv3 ¼

c 1 þ cfv1

ð1 þ cfv1 Þð1
fv2 Þ c3 þ c3v1

(10)

(11)

The additional damping function fv1 is:

fv1 ¼

c3 c3

þ C 3v1

(12)

The model coefficients have the following values: b2 Þ cb1 ¼ 0.1335, cb2 ¼ 0.622, sv ¼ 2/3, cw1 ¼ ckb12 þ ð1þc ¼ 0:3; ¼ sv ; 2:0; ¼ 7:1; ¼ 0:41cw2 ¼ 0.3, cw3 ¼ 2.0, cv1 ¼ 7.1, k ¼ 0.41

S¼

qffiffiffiffiffiffiffiffiffiffiffiffiffi ~v 2Sij Sij ; cdesD ; CLdes ¼ 0:65; c ¼ v

~ ¼ minðd; C d desD Þ; C ¼ d ¼ minÞC; don tan sundecall; 0:65 ~ is a function of the distance to the nearest The length scale d wall. For the DES model, Cdes is a coefficient and D is the largest distance between the cell center under consideration and the cell centers of the neighboring cells. ~ ¼ d, DES is Nearby the object surface satisfiesd < Cdes Dd consistent with S-A turbulence model. With the increase of d, ~ ¼ C D, at this time, the attenuation of turbulent whend > Cdes Dd des eddy viscosity coefficient is determined by the local grid scale. From basic transport equation (3), when the first item on the right side and the last item reached equilibrium:

Fig. 2a is the topology structure of computational domain, which consists of three parts. Overset mesh area (S1), overset refine area (S2), background area (S3), and two-dimensional polygonal mesh with overset mesh generated by STAR-CCMþ12.06 Polyhedral Mesh Generator. The AOA of airfoil is changed by rotating overset mesh region to avoid repeated modeling process. Fig. 2b, c and d show the overall mesh distribution and local mesh details of the flow field. The boundary layer mesh is set on the airfoil wall and flap wall. In this research, the pressure-velocity coupling method is used to solve the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations, and the second-order upwind scheme is used for the discretization accuracy of time and space. The inlet condition of the computational domain is the velocity inlet, the free stream velocity V∞ ¼ 30 m/s, and the Reynolds number Re based on the chord length c is about 5.0  105, the outlet boundary condition is the pressure outlet, the relative pressure is 0 Pa, and the other boundary conditions are the no-slip wall. Fig. 3 shows the lift coefficient at the AOA of 10 and 20 , it can be observed that the mesh number of 80000 provides mesh independence [31] for the airfoil with flap. In order to improve the calculation accuracy, the first layer thickness of mesh distribution on the airfoil surface is 1  10
4 m, corresponding to yþz1. 2.4. Validation of numerical simulation method The DES method was introduced in section 2.2. To verify the reliability of the numerical result in this paper, different turbulence model are selected to calculate the lift and drag coefficient compared with the experimental value [32]. The calculation results shown in Fig. 4. As can be seen from Fig. 4, the results of the three turbulence models are in a good agreement with the experimental data. With the increase of the AOA, the lift coefficient of the experiment gradually tends to be moderate at the AOA of 12 , while the lift coefficient in simulation continues to increase. It is suggested that the turbulence models fail to accurately capture the separation

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(a) Mesh topology of airfoil with trailing-edge flap

(b) The whole mesh distribution

Flap

(c) The mesh distribution around airfoil

(d) The mesh distribution around flap

Fig. 2. Computational domain and computational mesh.

0.78

AOA=10°

AOA=20°

0.77

Cl

0.76 0.75 0.74

1.8

1

SST k-omega (Cl) DES (Cl) LES (Cl) Experiment (Cl) SST k-omega (Cd) DES (Cd) LES (Cd) Experiment (Cd)

1.6 1.4 1.2 1

0.8 0.6

Cd

Cl

position, and the laminar-to-turbulent transition is neglected, which leads to the lift coefficient significantly larger than the experimental value. Generally speaking, all of the three turbulence models can reflect the trend of lift and drag coefficient of NACA0018 airfoil. On the basis of flow field calculation, DES turbulence model are selected to verify the accuracy of noise calculations. Receiving points (0.024 m, 0.095 m) are adopted to monitor the noise signals, the free stream velocity V∞ ¼ 30 m/s. In order to ensure the consistency with the experimental conditions [33], the chord length of NACA0018 airfoil for 0.08 m is obtained by scaling the mesh model (shown in Fig. 2) with equal ratio. Fig. 5 shows the spectrum of aerodynamic noise generated from the airfoil surface at different AOA, which was calculated by Fast Fourier Transform (FFT) analysis in the commercial CFD software STAR-CCMþ12.06. By comparison with the experiment noise spectrum [33], the trend of the SPL curves calculated by the DES turbulence model is basically the same as experiment data. Both of the two curves show high peaks at low frequency at the AOA of 0 and 6 , followed by the gradual decrease of SPL with the increase of frequency. As the AOA increases to 9 , the high frequency noise gradually disappears and the magnitude of the noise spectrum

0.8

0.4

0.6 0.4

0.2

0.2 0

0 0

2

4

6

8

10 12 14 16 18 20 22 AOA (e)

Fig. 4. Comparison of lift-drag coefficient between experiment and numerical simulation (NACA0018, Reynold number Re ¼ 5  105).

increases. At the AOA of 15 , the airfoil noise shows broadband characteristics. The reason for this phenomenon may be that the flow field around the airfoil is highly unstable at high AOA, which results in the formation of multi-scale vortices at the trailing edge of the airfoil. The merging and splitting of these vortices at different scales makes the noise show broadband characteristics. Considering comprehensively, due to the RANS model is adopted in the near wall area, it does not need too fine mesh resolution, which greatly reduces the computational complexity. At the same time, the results of DES turbulence model are comparable to LES model [34]. Therefore, the simulation results of aerodynamic performance and noise characteristics using DES turbulence model are relatively optimal. 2.5. Feasibility research

0.73 0.72 3

4

5

6 7 8 Cell number (10k)

Fig. 3. Mesh independence verification.

9

10

11

The lift drag coefficient and lift-to-drag ratio of original airfoil and airfoil with flap at various angles of attack ranging from a ¼ 6 to 24 are calculated, as shown in Fig. 6. When the AOA was less than 14 , the lift coefficient of the airfoil with flap is obviously smaller than that of the original airfoil and

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100

Experiment value

5

Calculated in this paper

AOA=15°

50

Sound Pressure Level (dB)

100

Experiment value

Calculated in this paper

AOA=9°

50 100

Experiment value

AOA=6°

Calculated in this paper

50

100

Experiment value

Calculated in this paper

AOA=0°

50

0

1000

2000

3000 Frequency (Hz)

4000

5000

Fig. 5. Comparison of SPL distribution between the experiment and numerical simulation (NACA0018, Reynold number Re ¼ 1.6  105).

the lift-to-drag ratio decreases greatly. This is because the flap destroyed the attachment flow at low AOA. When the AOA was larger than 14 , the trailing-edge flap could have a positive effect on the aerodynamic performance of the airfoil, and the stall AOA is delayed from about 14 to 16 . We can conclude that the trailingedge flap could play a good role at high AOA. Similarly, in order to obtain the effect of flap on airfoil noise, points A, B, D and E (shown in Fig. 1a) are selected as noise analysis. Fig. 7 shows the total SPL of receiving points for original airfoil and airfoil with flap at different AOA. As can be seen from Fig. 7, the total SPL of receiving points A and D are generally larger than that of receiving points B and E. This is mainly because the receiving point A and D are seriously affected by the vortex shedding from the trailing edge of the airfoil. When the AOA was less than 14 , the flap did not produce the desired effect, and the total SPL of the receiving point B was increased by 11.12% at the AOA of 6 . After the stall AOA, the total SPL of the airfoil with flap is lower than that of the original airfoil. The SPL of receiving point A was decreased from 131.03 dB to 125.48 dB and the SPL decreased by 4.23% at the AOA of 22 . Fig. 8 shows the scaled directivity of the sound for original airfoil and the airfoil with flap before and after the stall AOA. It can be observed that the scaled directivity of the sound shows obvious dipole characteristics for whole cases, which mainly due to the dipole sources works in the sound field. Before the stall AOA, the SPL of the 36 receiving points for airfoil with flap is larger than original airfoil. After stall AOA, flow separation point was delayed backward by flap, which effectively decreases the noise level. Through the above research, we can conclude that the trailingedge flap only works at high AOA. After the stall AOA, the trailingedge flap could effectively delay flow separation and reduce the

pressure fluctuation on the airfoil surface induced by vortex shedding. In a word, when the aerodynamic performance of airfoil improves, the noise level decreases accordingly. 3. Result and discussion In this section, the effect of different geometric parameters of trailing-edge flap on the aerodynamic performance and noise characteristics of the airfoil are performed in three different subsections. 3.1. Investigation of the effect of flap angle In this subsection, the influence of flap angle on aerodynamic performance and noise characteristics of the airfoil was investigated. The range of flap angle b was 0 e90 , the flap length was 0.2c, and the flap position was located on the upper surface of the trailing edge of the airfoil and intersects the vertical line upward at 0.75c from leading edge, as shown in Fig. 9. 3.1.1. Aerodynamic performance Fig. 10 shows the variation of lift drag coefficient of airfoil followed by flap angle before and after stall AOA (about 14 ) respectively. In Fig. 10a and c, it can be seen that before the stall AOA, no matter how much the flap angle is, the flap always has the negative effect, resulting in the lift coefficient decreases and the drag coefficient increases with an increase of AOA. After the stall AOA, the flap angle begins to produce the desired effect. The lift coefficient increases first and then decreases with the increase of flap angle, while the variation of drag coefficient is opposite. Therefore, the lift

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1.6

Original airfoil-Cl

Airfoil with falp-Cl

Original airfoil-Cd

Airfoil with flap-Cd

1.6 1.2

0.8

0.8

0.4

0.4

Cl

Cd

1.2

0

35

Cl/Cd

6

30

Original airfoil

25

Airfoil with flap

20 15 10 5 0

0 6

6

8 10 12 14 16 18 20 22 24 AOA (e)

(a) Lift drag coefficient

8 10 12 14 16 18 20 22 24 AOA (e)

(b) Lift-to-drag ratio

140 135 130 125 120 115 110 105 100

Original airfoil Airfoil with flap

SPL (dB)

SPL (dB)

Fig. 6. The lift drag coefficient and lift-to-drag ratio for original airfoil and airfoil with flap at different AOA.

6

8

140 135 130 125 120 115 110 105 100

10 12 14 16 18 20 22 24 AOA (e)

Original airfoil Airfoil with flap

6

8

10 12 14 16 18 20 22 24 AOA (e)

140 135 130 125 120 115 110 105 100

(b) Point B

Original airfoil Airfoil with flap

SPL (dB)

SPL (dB)

(a) Point A

6

8

10 12 14 16 18 20 22 24 AOA (e)

(c) Point D

140 135 130 125 120 115 110 105 100

Original airfoil Airfoil with flap

6

8

10 12 14 16 18 20 22 24 AOA (e)

(d) Point E

Fig. 7. The total SPL of the receiving points for original airfoil and airfoil with flap at different AOA.

coefficient has a maximum value and the drag coefficient has a minimum value at a certain AOA. As shown in Fig. 10b and d, the optimum flap angles b ¼ 13 , 40 , 48 , 52 and 61 respectively at the AOA of 15 , 18 , 20 , 25 and 30 . The optimum flap angle increases with an increase of AOA, but it does not show a linear relationship. The flow field was analyzed by choosing the AOA before and after the stall attack angle (a ¼ 5 and 12 ) and (a ¼ 18 and 30 ) respectively. The instantaneous z-vorticity contours of airfoil with different flap angle were shown in Fig. 11. In Fig. 11, with the increase of AOA, the position of separation vortices formed on the upper surface of the airfoil gradually moves

toward the leading edge. Before the stall AOA, the flow pattern was relatively simple and there are no evident large-scale vortices at the trailing edge. When the AOA is 18 , the increase of the flap angle results in periodic shedding vortices occurs on the trailing edge of airfoil when flap angle b ¼ 70 . But when the AOA increases to 30 , the scale and distance of vortices increase significantly. The flap length is shorter than the size of large separated vortices, changing the flap angle cannot achieve the desired control effect.

3.1.2. Noise characteristic In the previous subsection, it was observed that the trailingedge flap could effectively increase the lift coefficient and control

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Original airfoil

Airfoil with flap

120

SPL (dB)

80

110 SPL (dB)

90

Airfoil with flap

115

110 100

Original airfoil

105 100

7

stall AOA, the SPL increases first and then decreases with an increase of the flap angle, which is the smallest at the optimum flap angle. Because of the difference between the upper and lower surface of airfoil and the different propagation rules of noise in different directions, the directional distribution of sound for airfoil with different flap angle will overlap partially. 3.2. Investigation of the effect of flap position

Airfoil with flap

120

SPL (dB)

115 110

(c) AOA=18°

(b) AOA=12° Original airfoil

Airfoil with flap

122 118 SPL (dB)

(a) AOA=6° Original airfoil

114

In this subsection, the influence of flap position on aerodynamic performance and noise characteristics of the airfoil was investigated. For this purpose, simulations were conducted on NACA0018 airfoil with trailing-edge flap of three different positions. Due to the existence of flap will cause forced flow separation at low AOA. Therefore, the flap position close to the leading edge is not necessarily able to achieve better results. Based on this, the flap positions of 0.5c, 0.625c and 0.75c were selected, flap angle was fixed at 20 , and flap length of 0.2c was adopted, as shown in Fig. 14.

110

(d) AOA=24°

Fig. 8. Directional distributions of the sound for original airfoil and airfoil with flap before and after the stall AOA.

Fig. 9. Schematic diagram of airfoil with different flap angle.

flow separation at high AOA when the flap angle was in optimum. Therefore, in order to investigate the effect of flap angle on noise characteristics, receiving point A and D (shown in Fig. 1a) are adopted in this numerical simulation. Fig. 12 shows the SPL distribution of the receiving points when the frequency varies from 0 Hz to 5000 Hz. In Fig. 12, comparing the SPL curves of the two receiving points, it can be seen that the SPL of receiving point A is slightly larger than that of point D at the same AOA due to the generation of trailing edge shedding vortices. Before the stall AOA, the SPL of the two receiving points increases with an increase of flap angle. At this time, the SPL curves have obvious peak value at a low frequency, while the high frequency shows broadband characteristics. When AOA is 25 , The SPL of receiving point A is the smallest at the optimum flap angle of 50 . But the receiving point D was less affected by the separation vortices. Its law is different from that of the receiving point A. Fig. 13 shows the scaled directivity of the sound for airfoil with different flap angle before and after the stall attack angle. As we can see from this figure, the directional SPL increases with the increase of flap angle at the AOA of 5 and 10 . After the

3.2.1. Aerodynamic performance Fig. 15 shows the effect of the flap position on the lift drag coefficient, before the stall AOA, the lift coefficient of the airfoil with flap is smaller than that of the original airfoil. This is because the flow attached to the upper surface of the airfoil, and the trailingedge flap play a negative effect. After the stall AOA, the lift coefficient of the airfoil with flap exceeds the original airfoil and the drag coefficient of the airfoil decreases significantly, with a maximum reduction of 67.04% when the flap position is 0.5c and the AOA is 20 . We can conclude that the closer the flap is to the leading edge, the better the effect will be. In order to understand the influence of flap length on fluid structure deeply, the Instantaneous z-vorticity contours of airfoil with different flap position before and after the stall AOA are shown in Fig. 16. As can be seen from Fig. 16, the closer the flap position is to the trailing edge, the smaller the scale and distance of the shedding vortices will be, so that the shedding vortices almost disappear at the AOA of 12 , flap position of 0.75c, and at the AOA of 16 , flap position of 0.625c. Therefore, the closer the flap position is to the trailing edge at low AOA, the better the effect will be. As the AOA increases to 20 , the flow separation is serious, and the flap position has little influence on vortex structure. 3.2.2. Noise characteristic Similarly, receiving points D and A are selected to evaluate the acoustic performance, which are present in Fig. 1 a. Fig. 17 shows the curves of SPL in frequency varies from 0 Hz to 5000 Hz of NACA0018 airfoil with different flap position. As can be seen from Fig. 17, the closer the flap position is to the trailing edge, the smaller the SPL will be at the AOA of 8 . When the AOA increases to 20 , the SPL of airfoil with flap position of 0.75c is still the lowest. Combining with the analysis of vorticity field (shown in Fig. 16), the closer the flap position is to the trailing edge, the lower the frequency of vortex shedding, the smaller the core size and the distance of the vortices. Eventually, the pressure fluctuations on the airfoil surface are much less than other cases, which is the main reason for the noise reduction. The scaled directivity of the sound is shown in Fig. 18. In Fig. 18, the SPL of the receiving points around the airfoil increases with an increase of AOA and shows dipole characteristics. At low AOA (a ¼ 8 and 12 ), we can observed that the SPL of flap position at 0.75c is the lowest, followed by 0.65c and 0.5c. It shows that the closer the flap position is to the trailing edge, the higher the noise level will be. This is because the flap position near the leading edge may be in front of the point of flow separation, which destroys

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1.2

1.5

1

1.4 1.3

0.8

1.2

0.6

1.1

Cl

Cl

AOA=15° AOA=18° AOA=20° AOA=25° AOA=30°

AOA=2° AOA=5° AOA=10° AOA=12° AOA=13° AOA=14°

0.4 0.2

1 0.9 0.8

0 0

5

10 15 20 Flap angle (e)

25

30

0.7 0

10

(a) Before the stall AOA

20

30 40 50 60 Flap angle (e)

70

80

(b) After the stall AOA

0.05

0.7 0.6

0.04

0.5

AOA=15° AOA=18° AOA=20° AOA=25° AOA=30°

Cd

0.4 Cd

0.03

0.3

AOA=2° AOA=5° AOA=10° AOA=12° AOA=13° AOA=14°

0.02

0.2 0.1 0

0.01 0

5

10 15 Flap angle (e)

20

25

(c) Before the stall AOA

0

10

20

30 40 50 Flap angle (e)

60

70

80

(d) After the stall AOA

Fig. 10. The lift drag coefficient of airfoil with different flap angle at different AOA.

Vorticity (/s) Flap angle =2e

Flap angle =5e

Flap angle =10e

Flap angle =20e

Flap angle =4e

Flap angle =8e

Flap angle =30e

Flap angle =40e

Flap angle =6e

Flap angle =12e

Flap angle =8e

Flap angle =15e

AOA=5°

AOA=12°

Flap angle =50e

Flap angle =70e

AOA=18°

Flap angle =60e

Flap angle =80e

AOA=30°

Fig. 11. Instantaneous z-vorticity contours of airfoil with different flap angle at different AOA.

the initial attached flow. However, the law is different at high AOA. Fig. 18c and d shows that the noise level of flap position at 0.75c is still the lowest, but the difference between flap position at 0.5c and 0.625c is not significant.

3.3. Investigation of the effect of flap length In this subsection, the influence of flap length on aerodynamic performance and noise characteristics of airfoil was investigated. In the previous subsections, we can conclude that the trailing-edge flap only works at a certain condition. If the flap is too long, it

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Flap angle=3° Flap angle=6° Flap angle=9° Flap angle=12° Flap angle=15°

100

SPL (dB)

80 60 40

120 Flap angle=3° Flap angle=6° Flap angle=9° Flap angle=12° Flap angle=15°

100 SPL (dB)

120

80 60 40 20

20

0

0

0

1000

2000 3000 f (Hz)

4000

5000

0

(a) AOA=10°, Point D Flap angle=20° Flap angle=40° Flap angle=50° Flap angle=60° Flap angle=80°

120 100

1000

2000 3000 f (Hz)

4000

5000

(b) AOA=10°, Point A

80 60

140

100 80 60

40

40

20

20

0

Flap angle=20° Flap angle=40° Flap angle=50° Flap angle=60° Flap angle=80°

120

SPL (dB)

140

SPL (dB)

9

0 0

1000

2000

3000

f (Hz)

(c) AOA=25°, Point D

4000

5000

0

1000

2000

3000

f (Hz)

4000

5000

(d) AOA=25°, Point A

Fig. 12. The effect of flap angle on SPL distribution of the receiving points A and D.

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=2° =8°

=4° =10° 110

=3° =12°

=6°

=6° =15° 110 100 SPL (dB)

SPL (dB)

100 90

90

80

80

(a) AOA=5° =20° =60° 120 118 116 114 112 110

(b) AOA=10° =20° =60°

=30°

SPL (dB)

=10° =40°

will become a device that can dominate fluid motion, which makes the control of flow separation meaningless. Therefore, the flap lengths of 0.05c, 0.1c, 0.15c and 0.2c were selected, the flap position was mounted on the upper surface of the trailing edge of the airfoil, and intersects the vertical line upward at 0.75c from leading edge, and the flap angle b ¼ 20 , as shown in Fig. 19.

=9°

(c) AOA=20°

=40° =80° 122 120 118 116 114 112 110

=50°

(d) AOA=30°

Fig. 13. Directional distribution of sound for airfoil with different flap angle before and after the stall AOA.

3.3.2. Noise characteristic The effect of flap length on SPL distribution of receiving points A and D are shown in Fig. 22. The SPL curves of the two receiving points has obvious peak value at the low frequency band at the AOA of 8 , showing obvious low frequency characteristic, while the high frequency band still shows broadband characteristic. At this time,

Fig. 14. Schematic diagram of airfoil with different flap position.

1.5

0.8

Flap position=0.5c

1.2

0.7

Flap position=0.625c

0.9

0.6

Flap position=0.75c Original airfoil

0.5

0.6

Cl

Cl

3.3.1. Aerodynamic performance Fig. 20 shows the effect of flap length on the lift drag coefficients of NACA0018 airfoil at different AOA. In Fig. 20, before stall AOA, the lift coefficient decreases with an increase of flap length, while this phenomenon is opposite after the stall AOA. It is suggest that the shedding of vortices becomes more intense with an increase of AOA, which makes the longer flap have the strong ability to divide the vortices. In Fig. 20b, the drag coefficient of the original airfoil and the airfoil with flap are basically the same before the stall AOA. After the stall AOA, the drag coefficients increase substantially. By comparison, a maximum deviation of 40% is obtained at the AOA of 18 , but the drag coefficient curves of airfoil with different flap length coincide very well. Therefore, we can conclude that the flap length has a little effect on aerodynamic performance of airfoil at high AOA. Fig. 21 shows the Instantaneous z-vorticity contours of airfoil with different flap length before and after the stall AOA. As can be seen from this figure, the vortices shed continually from the upper surface of trailing edge of airfoil at the AOA of 8 , flap length of 0.2c. This is because the longer flap will affect the attachment flow on the airfoil surface at low AOA. As the AOA increases further, the separation point continuously move to the leading edge, and the stall range of the airfoil is affected substantially by the flap, so that no separated vortices are generated for whole cases at the AOA of 12 and 16 . When the AOA increases to 20 , the deep stall happens, and the effect of the flap length on the separation vortices becomes more and more insignificant.

0.3 0

-0.3

Flap position=0.5c

0.3

Flap position=0.625c

0.2

Flap position=0.75c

0.1

Original airfoil

-0.6 0

4

8

0.4

12 16 AOA (e)

(a) The lift coefficient (Cl)

20

0 24

0

4

8

12 16 AOA (e)

20

24

(b) The drag coefficient (Cd)

Fig. 15. The lift and drag coefficient of airfoil with different flap positon at different AOA.

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Vorticity (/s) Flap position=0.5c

Flap position=0.5c

Flap position=0.5c

Flap position=0.5c

Flap position=0.625c

Flap position=0.625c

Flap position=0.625c

Flap position=0.625c

Flap position=0.75c

Flap position=0.75c

Flap position=0.75c

Flap position=0.75c

AOA=8°

AOA=12°

AOA=16°

AOA=20°

Fig. 16. Instantaneous z-vorticity contours of airfoil with different flap position at different AOA.

120

Flap position=0.5c Flap position=0.625c

100

Flap position=0.75c

120

Flap position=0.625c

100

80

Flap position=0.75c

80

SPL (dB)

SPL (dB)

Flap position=0.5c

60 40 20

60 40 20

0

0

0

1000

2000 3000 f (Hz)

4000

5000

0

(a) AOA=8°, Point D 140

Flap position=0.625c Flap position=0.75c

140

4000

5000

80

80

SPL (dB)

100

60 40 20

Flap position=0.5c Flap position=0.625c

120

100 SPL (dB)

2000 3000 f (Hz)

(b) AOA=8°, Point A

Flap position=0.5c

120

1000

Flap position=0.75c

60 40 20

0

0 0

1000

2000 3000 f (Hz)

(c) AOA=20°

Point D

4000

5000

0

1000

2000 3000 f (Hz)

4000

5000

(d) AOA=20° Point A

Fig. 17. The effect of flap position on SPL distribution of receiving points A and D.

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0.625c

0.5c

(b) AOA=12°

0.625c

0.75c

0.5c

0.625c

0.75c

120 116 112 108 104 100

SPL (dB)

SPL (dB)

120 116 112 108 104 100 96

0.75c

112 109 106 103 100 97 94

(a) AOA=8° 0.5c

0.625c

SPL (dB)

112 109 106 103 100 97 94

0.75c

SPL (dB)

0.5c

(c)AOA=16°

the increase of the flap length leads to the increase of the SPL at the two receiving points. As the AOA increases to 20 , the SPL curves of both low frequency and high frequency band have no obvious peak value, showing the characteristic of broadband, which is caused by the dominance of airfoil self-noise. The scaled directivity of the sound was calculated using the receiving points discussed above, which placed around airfoil in a 5c radius as shown in Fig. 23. Before the stall AOA, the directional SPL of the receiving points increases with the increase of flap length, which is especially prominent on the upper surface of airfoil. It is shown that the shorter the flap length at low AOA, the smaller the impact of the increased noise level. When the AOA increases to stall AOA, the directivity curves of airfoil noise no longer increases with the increase of the flap length, as shown in Fig. 23c and d. When the flap length is 0.15c and 0.2c, the area of the directivity curve on the upper surface of the airfoil coincides, but the flap length of 0.05c is still the lowest. 4. The OED method in simulation design

(d)AOA=20°

Fig. 18. Directional distribution of sound for airfoil with different flap position before and after the stall AOA.

In this paper, the OED method [35] was selected to optimize the flap geometric parameters. There are three factors that affect the aerodynamic performance and noise characteristics of the airfoil with trailing-edge flap. Three levels were selected for each factor, so it belongs to 3 influential parameters (factors) and 3 levels. The selected array (L9 (34)) matches well the number of the factors (3 factors) and levels (3 levels). The influence factors and level values selected in this study shown in Table 1. The orthogonal experimental design aims to obtain the optimal

1.5

0.8

1.2

0.7

0.9

0.6

Flap length=0.05c Flap length=0.1c Flap length=0.15c Flap length=0.2c Original airfoil

0.5

0.6

Cl

Cl

Fig. 19. Schematic diagram of airfoil with different flap length.

0.3

Flap length=0.05c Flap length=0.1c Flap length=0.15c Flap length=0.2c Original airfoil

0 -0.3

0.4 0.3 0.2 0.1

-0.6

0 0

4

8

12 16 AOA (e)

(a) The lift coefficient

20

24

0

4

8

12 16 AOA (e)

20

24

(b) The drag coefficient

Fig. 20. The lift and drag coefficient of airfoil with different flap length at different AOA.

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Vorticity (/s) Flap length=0.05c

Flap length=0.05c

Flap length=0.05c

Flap length=0.05c

Flap length=0.1c

Flap length=0.1c

Flap length=0.1c

Flap length=0.1c

Flap length=0.15c

Flap length=0.15c

Flap length=0.15c

Flap length=0.15c

Flap length=0.2c

Flap length=0.2c

Flap length=0.2c

Flap length=0.2c

AOA=8°

AOA=12°

AOA=16°

AOA=20°

Fig. 21. Instantaneous z-vorticity contours of airfoil with different flap length at different AOA.

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120

Flap length=0.05c Flap length=0.1c Flap length=0.15c Flap length=0.2c

100

120 100

80

80 SPL (dB)

SPL (dB)

Flap length=0.05c Flap length=0.1c Flap length=0.15c Flap length=0.2c

60 40 20

60 40 20

0

0

0

1000

2000 3000 f (Hz)

4000

5000

0

(a) AOA=8°, Point D 120

120

4000

5000

Flap length=0.05c Flap length=0.1c Flap length=0.15c Flap length=0.2c

100 80

SPL (dB)

80 SPL (dB)

2000 3000 f (Hz)

(b) AOA=8°, Point A

Flap length=0.05c Flap length=0.1c Flap length=0.15c Flap length=0.2c

100

1000

60 40 20

60 40 20

0 0

1000

2000 3000 f (Hz)

(c) AOA=20°, Point D

4000

5000

0 0

1000

(d)

2000 3000 f (Hz)

4000

5000

AOA=20°, Point A

Fig. 22. The effect of flap length on SPL distribution of receiving points A and D.

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0.1c 0.2c

0.05c 0.15c

0.1c 0.2c

110

104

106

100 96

SPL (dB)

108

102 98

SPL (dB)

0.05c 0.15c

combination of flap parameters. The experimental indexes include lift-to-drag ratio (Cl/Cd) and SPL. The SPL is the average SPL of receiving points A and D. The purpose of the trailing-edge flap is to improve the aerodynamic performance and reduce the noise level. Therefore, the ratio of Cl/Cd and SPL is proposed as a comprehensive test index g to measure the quality of results, as the following expression:

g¼

AOA=8°

0.05c 0.15c

b AOA=12° 0.05c 0.15c

0.1c 0.2c

0.1c 0.2c

114

108

110

104

106

100 96

SPL (dB)

112

102 98

SPL (dB)

a

Cl =Cd SPL

d AOA=20°

Fig. 23. Directional distribution of sound for airfoil with different flap length before and after the stall AOA.

Table 1 Influence factors and level values. Parameters 1 2 3

Factor A Angle ( ) 

10 20 30

Factor B Position (m)

Factor C Length (m)

0.5c 0.625c 0.75c

0.1c 0.15c 0.2c

(13)

The simulation experiments were carried out at angles of attack of 10 and 20 by numerical simulation. The orthogonal experimental data are shown in Table 2 and Table 3. The results of the OED calculations are summarized in Tables 2 and 3 for the selected 9 experiments. The right side of the experimental matrix is the corresponding measured Cl/Cd and SPLvalues for the 9 experiments. The matrix of ki data is obtained by averaging g data. For example, the k1 ¼ 0.2119 value for Factor A (shown grey in Table 2) is obtained by adding all g values for which Factor A ¼ 1, divided by the total number of values 3: k1 ¼ (0.1483 þ 0.1989þ0.2885)/3 ¼ K1/3 ¼ 0.2119

c AOA=16°

15

(14)

The R value of each factor is obtained by calculating the maximum and minimum of ki. For example, for Factor A: R1 ¼ 0.2119e0.0510 ¼ 0.1609. Obviously, the R value of factor A in the first column is the largest compared to other factors. We can conclude that the change of factor A has the greatest influence on the comprehensive test index g at the AOA of 10 , so factor A should be the main factor under this condition. According to R values, the other two factors were ordered by significance (from most to least), and the order is shown in Table 2. The larger the R value, the greater the impact on the results [36]. The order of influence for R is RA > RB > RC. The factors A, B, and C for g correspond to the physical parameters of flap angle > flap position > flap length, and is ranked by their influence level. From Table 2, it can be concluded that for factor A, k1 > k3 > k2, factor B, k3 > k2 > k1, factor C, k1 > k3 > k2, therefore, the best combination of

Table 2 The orthogonal test design data (AOA ¼ 10 , before stall angle).

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Table 3 The orthogonal test design data (AOA ¼ 20 , after stall angle).

Fig. 24. Computational domain and boundary conditions.

Fig. 25. Three flap motion law in two rotational cycles.

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Background B1

Refine

Rotation region B2

B3

Flap

Fig. 26. Illustration of the computational domain mesh, local sections and magnifications.

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0.4

and flap3 are mounted on the inner side of blade1 (B1), blade2 (B2) and blade3 (B3) respectively. The parameters of the flap are obtained by OED method in chapter 4, which shows the combination of B1A3C2 could achieve the best result at high AOA. Therefore, the flap position of 0.5c and flap length of 0.15c are selected. Flap angle varies periodically. When the azimuth angle is 90e135 , the flap is raised by velocity -Vf, and falls by velocity Vf when the azimuth angle is 135e180 . In other azimuths, the flap attaches to the airfoil surface, and its motion law is shown in Fig. 25. The maximum rotation angle of flap is 30 , so the velocity Vf can be calculated by:

Airfoil with flap Original airfoil Paper1-without connecting rod Paper1-with connecting rod Paper2-Exp

0.3 0.2 0.1 0 0.25

Vf ¼

0.5

0.75

1

1.25

30p=180 T=8

(15)

1.5

Fig. 27. Comparison of calculated values of Cp with experimental data.

factors will be A1B3C1. In summary, the best g will be achieved at flap angle of10 , flap position of 0.75c, and flap length of 0.2c. Similarly, when the AOA is 20 , we can draw the following conclusions from Table 3. The order of influence for R is RB > RA > RC, the R value of factor C is smaller than other factors, and followed by flap angle, flap length. We can conclude that the change of factor C has the least effect on the experimental results, which is the same as the AOA of 10 . Therefore, we can conclude that the best combination of factors is B1A3C2, and the best g will be achieved at flap angle of 30 , flap position of 0.5c, and flap length of 0.15c. 5. Effects of the trailing-edge flap on the VAWT 5.1. Aerodynamic performance The trailing-edge flap was applied to the straight blade VAWT in this paper. In Fig. 29, it can be seen that the tangential force of VAWT blades at different TSR decreased dramatically when the azimuth angle is between 90 and 180 , the reason is large flow separation occurs in this azimuth range and the vortex shedding is intense [37]. By adding trailing-edge flap in the inner side of the VAWT blades can delay the flow separation, which lead to the improvement of aerodynamic performance. The computational domain and boundary conditions are shown in Fig. 24. Flap1, flap2

T¼

2p

(16)

u

where T is the time required for the wind turbine to rotate a cycle, u is the rotating angular velocity. The SIMPLE algorithm is adopted to deal with the pressurevelocity coupling and the DES turbulence model was chosen in the present study. Fig. 26 shows the computational domain mesh. The VAWT blades and trailing-edge flap was given as the no-slip wall. The polyhedral mesh was generated by STAR-CCMþ12.06, which provides a complete set of capabilities for both surface and volume meshing operations [38]. The total mesh number of the flow field domain was approximately 1.86  105 (without trailingedge flap) and 5.37  105 (with the trailing-edge flap). The prism layer near wall thickness is 1.0e-5m and the total thickness of the boundary layer is 0.024 m.For further details of the operational conditions and size of computational domain, see Ref. [39]. In order to confirm the reliability of the calculation results in this paper, the variation of power coefficient (Cp) of VAWT blades without and with trailing-edge flap are compared to the experiment data [39] (paper2) and 3D CFD numerical result [40] (papaer1), as shown in Fig. 27. By comparison, the 2D CFD results (original airfoil) in this paper and 3D CFD results (without connecting rod) calculated by Elkhoury [40] can replicate the shape of Cp curve at low TSR, but quantitative differences with experiment are observed at high TSR. The discrepancy between both numerical results is mostly due to shaft interference and strut drag, while the connecting rods are considered in experiment. In addition,

Original airfoil

(a) =90°

(b) =110°

(c) =130°

(d) =150°

Airfoil with flap

Fig. 28. Instantaneous z-vorticity contours at TSR ¼ 1.3 for the VAWT blades.

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(a) TSR=1.2

(b) TSR=1.3

(c) TSR=1.4

(d) TSR=1.5 Fig. 29. Variation of torque coefficient and tangential force of single blade at different TSR.

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Fig. 30. The distribution of receiving points in VAWT.

although present results (original airfoil) show good agreement with 3D CFD results, the Cp is much higher for high TSR. This may be due to the fact that 2D CFD does not take account of tip losses, compared with real time 3D CFD simulation, 2D simulation can over predict the performance up to 32%, and this is also mentioned in Ref. [41]. In Fig. 27, when at high TSR, the flow separation region will cover the whole range of flap action, and the flap length is shorter than the size of large separation vortices. Changing the flap angle within the allowable range of geometric conditions cannot achieve the desired control effect. At this time, the control effect of flap is not obvious, and the power coefficient (Cp) is slightly smaller than the case of without trailing-edge flap. While with the increase of TSR, the flow separation range of VAWT blades at the maximum AOA can be greatly affected by trailing-edge flap. Therefore, the flap can significantly increase the Cp at high TSR. It is observed that the flap can enhance the Cp by 24.2% (0.344) and 23.7% (0.365) respectively at TSR ¼ 1.3 and TSR ¼ 1.4, compared to the Cp of VAWT blades without trailing-edge flap. The instantaneous z-vorticity contours of VAWT blades with trailing-edge flap are presented in Fig. 28. As can be seen from this figure, the flow separation occurs on the inner side of the B1 with the increase of azimuthal angle. When the trailing-edge flap was added, the flow separation point was delayed backward to the trailing edge, and this phenomenon is most obvious at azimuth angle of 110 and 130 . Fig. 29 shows azimuth changes in torque coefficient and tangential force of the VAWT blades in five complete rotations following the steady state at TSR ¼ 1.2, 1.3, 1.4 and 1.5. It can be observed that the trailing-edge flap has a positive effect on the torque and thrust force for four cases. As can be seen from Fig. 28, when the flow separation points were delayed, the torque and tangential force of the VAWT blades were increased basically. 5.2. Noise characteristic The noise characteristics of VAWT were calculated based on the above flow computation results. Fig. 30 shows the positions of 4 receiver points in the downward direction of VAWT, the distance

between each monitoring point is 2R. Fig. 31 shows the noise spectrum of clean VAWT and VAWT with flap at the TSR of 1.3 and 1.4. As can be observed in this figure, the VAWT noise was reduced at all receiving points, particularly at low frequencies band. In addition, the SPL at high frequency is much lower than that at low frequency for all receiving points which can be explained that the low-frequency noise is the main component in the flow filed. By comparison of the noise spectrum at different TSR, the calculation results indicate that the increase of TSR would increase the VAWT noise, this phenomenon was also verified in Ref. [42]. In order to deeply explore the detailed physical mechanism that reduces the VAWT noise. The time fluctuations of max pressure of 4 receiving points at the TSR of 1.4 were analyzed, shown in Fig. 32. As can be seen from Fig. 31, when the trailing-edge flap was added, the pressure pattern of receiving points of VAWT with flap is more regular than that of clean VAWT and the pressure fluctuations can be significantly reduced. In conjunction with Fig. 28, we can conclude that the trailing-edge flap reduces the VAWT noise by moderating pressure pulsation, stabilizing the flow field and influencing the vortex shedding. Therefore, suppressing the flow separation and improve the vortex structure is the predominant technological approaches to improve the aerodynamic performance and reduce the noise of VAWT.

6. Conclusion In this paper, the control mechanism of the trailing-edge flap on aerodynamic performance and noise characteristics of the airfoil were investigated, and the optimum geometric parameters of trailing-edge flap were obtained by using the orthogonal experimental design method. The power coefficient, torque coefficient, tangential force, and the SPL distribution were analyzed quantitatively to explore the influence of trailing-edge flap on the aerodynamic performance and noise reduction of VAWT. The main results observed in this study are summarized as follows: 1) The trailing-edge flap could increase the lift coefficient and improve the aerodynamic performance of the airfoil after stall AOA. By comparison with original airfoil, the stall AOA can be delayed from about 14 to about 16 , and the maximum lift coefficient increases from 0.85 to 1.16, and increases by 37.12% at the AOA of 18 . 2) After stall AOA, the total SPL of the airfoil with trailing edge flap is lower than that of the original airfoil, and the maximum decrease is about 4.23% at the receiving point A. The noise characteristics of airfoil with trailing-edge flap are in agreement with the aerodynamic performance, the expected effects can be achieved when the AOA is more than 16 , while the effect is opposite when the AOA is less than 16 . 3) The results of orthogonal experimental design optimization of flap parameters at the AOA of 10 and 20 show that the flap angle has the greatest influence on the flow control effect, followed by position and length before stall AOA (AOA ¼ 10 ), and the best combination is A1B3C1, while the flap position has the greatest influence, followed by flap angle and length after the stall AOA (AOA ¼ 20 ), and the best combination is B1A3C2. 4) A motion control strategy of trailing-edge flap for VAWT blades is proposed to improve the aerodynamic performance of VAWT, and the flow separation can be effectively suppressed at azimuth angle of 90e180 . The flap can enhance the Cp by 24.2% and 23.7% respectively at TSR ¼ 1.3 and 1.4, compared to clean VAWT.

Please cite this article as: Liu Q et al., Effects of trailing-edge movable flap on aerodynamic performance and noise characteristics of VAWT, Energy, https://doi.org/10.1016/j.energy.2019.116271

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Fig. 31. The effect of trailing-edge flap on SPL distribution of VAWT at different TSR.

Please cite this article as: Liu Q et al., Effects of trailing-edge movable flap on aerodynamic performance and noise characteristics of VAWT, Energy, https://doi.org/10.1016/j.energy.2019.116271

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Fig. 32. Pressure fluctuations of the receiving points at the TSR of 1.4.

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Please cite this article as: Liu Q et al., Effects of trailing-edge movable flap on aerodynamic performance and noise characteristics of VAWT, Energy, https://doi.org/10.1016/j.energy.2019.116271