Energy Conversion and Management 108 (2016) 275–286
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Numerical investigation on aerodynamic performance of a novel vertical axis wind turbine with adaptive blades Ying Wang a, Xiaojing Sun a, Xiaohua Dong b, Bing Zhu a, Diangui Huang a,⇑, Zhongquan Zheng c a
University of Shanghai for Science and Technology, Shanghai 200093, China Shanghai University, Shanghai 200072, China c Aerospace Engineering Department, University of Kansas, United States b
a r t i c l e
i n f o
Article history: Received 24 August 2015 Accepted 2 November 2015
Keywords: Adaptive blade Darrieus vertical axis wind turbines Computational Fluid Dynamics Numerical simulation Aerodynamic performance
a b s t r a c t In this paper, a novel Darrieus vertical axis wind turbine was designed whose blade can be deformed automatically into a desired geometry and thus achieve a better aerodynamic performance. A series of numerical simulations were conducted by utilizing the United Computational Fluid Dynamics code. Firstly, analysis and comparison of the performance of undeformed and deformed blades for the rotors having different blades were conducted. Then, the power characteristics of each simulated turbine were summarized and a universal tendency was found. Secondly, investigation on the effect of blade number and solidity on the power performance of Darrieus vertical axis wind turbine with deformable and undeformable blades was carried out. The results indicated that compared to conventional turbines with same solidity, the maximum percentage increase in power coefficient that the low solidity turbine with three deformable blades can achieve is about 14.56%. When solidity is high and also turbine operates at low tip speed ratio of less than the optimum value, the maximum power coefficient increase for the turbines with two and four deformable blades are 7.51% and 8.07%, respectively. However, beyond the optimal tip speed ratio, the power improvement of the turbine using the deformable blades seems not significant and even slightly worse than the conventional turbines. The last section studied the transient behavior of vortex and turbulent flow structures around the deformable rotor blade to explore the physical mechanism of improving aerodynamic performance. The adaptive blades could obviously suppress the separation of flow from the blade surfaces. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Background to the study Compared with conventional energy sources, wind energy is unexhausted and free of pollution [1]. Reasonable development and utilization of wind power is of strategic importance to economic development of China and the whole world [2]. As one of the most key components in a wind turbine, the rotor blades are responsible for converting the kinetic energy of the wind into mechanical energy first and then into electricity if needed [3]. Wind turbines can be classified into two categories based on the axis about which the turbine rotates: horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT) [4]. Recently there is a growing interest in vertical axis wind turbines as they are capable of catching the wind from all directions [5]. In addition, ⇑ Corresponding author. E-mail address:
[email protected] (D. Huang). http://dx.doi.org/10.1016/j.enconman.2015.11.003 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.
compared to HAWTs, the VAWTs are quieter, more bird and batfriendly and less expensive to maintain [6]. The lifting-type VAWTs (often referred to as Darrieus turbines) are powered by lift forces which helps it function effectively. Since Darrieus wind turbine with straight blades shows the advantages of lightweight, simple structure and good balance, it shows relatively high wind power coefficient and prosperous application. Therefore, the design research on straight-bladed Darrieus turbines to further improve their power coefficients became one of the hot spots of recent wind power technology development [7]. Intensive computational and experimental studies have made on the aerodynamic performance of novel vertical axis wind turbine concepts. Daynes [8] presented a morphing flap design with a highly anisotropic cellular structure. The experimental validation for morphing flap was conducted with a manufactured demonstrator. Compared with conventional hinged flap, the morphing flap can obviously reduce actuation requirements. Kerho [9] studied an adaptive airfoil design to reduce the negative influences of dynamic stall on rotorcraft blades. His results showed that a higher
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Clmax than that of the baseline section could be achieved for the proposed variable droop/camber compliant leading-edge system. Or else, while maintaining the baseline section’s high Mach number, the dynamic stall vortex at a Cl equivalent to the baseline section Clmax could be eliminate. Capuzzi [10] described a novel aeroelastic method to design the blades of large-scale wind turbines. While simultaneously alleviating extreme loading conditions due to gusts, it was found that the turbine’s Annual Energy Production increased through tailoring the blade’s elastic due to aerodynamic pressure suitably. Hoogedoorn [11] conducted a 2D numerical computation to study the aero-elastic behavior of a flexible blade used in HAWT. It was found that higher lift and lift to drag ratio can be achieved by applying flexible cambered airfoils in HAWT, and thereby this type of airfoils has great potential to improve the turbine performance. Lee [12] designed a novel flexible blade for HAWT. The aerodynamic performance and work capacity for this type of blade were investigated, and the power curve was also obtained. Liu [13] proposed a new design method for wind turbine blade which is based on the topology structure of central axis of leaf vein. By utilizing the similarity of structures and working environment between wind turbine blade and plant leaf, the performance for this bionic designed flexible blade was studied. This type of flexible blade not only widens the range of wind velocity, but it also raises the wind power coefficients. Hua [14] firstly investigated the fly posture and the feather construction for wind turbines. It was found that flow separation hardly occurs on wing surface due to the streamlined configuration on the gull wings surface and the unique feather construction on wings. Therefore, the configuration data of the convex shape and the bending shape of the gull wings were extracted and combined with the requirement of wind turbine blades. Two types of bionic blades with convex shape and front bending shape were designed. According to numerical results, the bionic blade shows better aerodynamic performance than conventional turbine blade. 1.2. A novel vertical axis wind turbine concept However, all the novel designs of wind turbine blade introduced above have common drawbacks, such as poor aerodynamics, structural stability and difficulty in manufacture. Therefore, a new type of VAWT whose blade shape can be automatically changed according to changes in blade surface pressure is proposed in this paper. According to Huang’s research [15], the adaptive reconfigurable airfoil can automatically change its shape according to the pressure distribution over its surface. Thus, this paper adopts Huang’s idea of balloon-type airfoil and applies it on the novel VAWT. In order to balance the aerodynamic performance of blades at different phases, most of the current Darrieus wind turbines adopt the symmetrical airfoil. However, based on the basic principle of aerodynamics, the shape of airfoil has great influence on its aerodynamic performance. Normally, if the pressure surface of an airfoil is more flat than the suction surface (like NACA2412 airfoil), this type of asymmetric airfoils then can achieve higher lift-to-drag ratio than that of symmetric airfoils (like NACA0012) at positive angles of attack greater than 0° where no flow separation occurs. In one revolution, the upper and lower surfaces of a Darrieus wind turbine blade become alternatively the blade suction surface and the pressure surface. In Fig. 1, for blade in the position of 0 < h < p, the outside of airfoil is the pressure surface and the inside of airfoil is the suction surface; when blade rotates to the position of p < h < 2p, the outside of airfoil turns to the suction surface and the inside of airfoil turns to the pressure surface. Therefore, a new type of airfoil whose shape varies with the surface pressure can be designed. For this type of airfoil, the airfoil surface
Wind direction
Fig. 1. Forces and velocities acting on a Darrieus turbine for various azimuthal positions.
turns inward due to high pressure, and its shape becomes relatively gentle (such as the pressure surface of NACA 2412). While the airfoil surface turns outward due to low pressure, and the shape of airfoil becomes relatively convex (such as the suction surface of NACA 2412). If the proposed airfoil can deform automatically according to a change of the pressure on its surface as described above, it is expected that incorporation of this new type of airfoil section on the Darrieus VAWT would contribute to high overall efficiency. Aerodynamic performance of this new type of wind turbine was numerically investigated in this paper and discussed in detail in the following sections. This paper proposes a new method that the shape of blade airfoil adapts with the surface pressure (VAWTDB). The numerical study for this new type of VAWT is conducted. First of all, the validation of simulation by using the United Computational Fluid Dynamics (UCFD) software was presented. Then, the simulation was carried out for both of the two, three and four bladed conventional VAWT and VAWTDB at different solidities and TSR. Besides, the wind power coefficients of the simulated turbines were summarized and analyzed. After that, three different solidities were chosen for two, three and four bladed VAWT and VAWTDB, and the wind power coefficients at different TSR were compared and analyzed. Finally, the whole flow field of VAWTDB and VAWT with three blades was analyzed from the aspect of vortex, and the tracking analysis of vortex at different positions for the first blade was conducted. In this way, the aerodynamic performance of threebladed wind turbine with deformable blade was analyzed.
2. Computational methods 2.1. Mathematical model The UCFD software [16] is adopted in this paper to conduct numerical simulation, and the corresponding control equation and pre-processing technique applied are as follows [17,18]: Governing equations of fluid mechanics can be expressed as the following general form:
@Q @ðF F v Þ @ðG Gv Þ @ðH Hv Þ þ þ ¼0 þ @t @n @g @f
ð1Þ
for p ¼ p0 þ pg , where p0 is the atmospheric pressure, pg is the gauge pressure.
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Wind direction
(a) Sketch for two-bladed wind turbine
(b) Sketch for three-bladed wind turbine
(c) Sketch for four-bladed wind turbine
(d) Mesh topology for 2D calculation around wind turbine rotor
Fig. 2. Schematic of the wind turbines with different number of blades (a–c) and mesh topology for 2D calculation around three-bladed wind turbine rotor (d).
In Eq. (1), the conservative variables and expressions of inviscid flux is as follows:
0
q
0
1
1
qU
1
0
0
LR
q_ xi ¼ 4
C
U ¼ U=jrnj
V ¼ gx u þ gy v þ gz w þ gt
V ¼ V=jrgj
W ¼ fx u þ fy v þ fz w þ ft
W ¼ W=jrfj
where e ¼ q h þ
1 ðu2 2
þ v þ w2 Þ ðp0 þ pg Þ 2
l 5 @h Ree Pr @xi LR
@q @Q @q @F @q @G @q @H @q þ þ þ þ @ s @q @t @q @n @q @ g @q @f @F v @q @Gv @q @Hv @q ¼ þ þ @q @n @q @ g @q @f
where q ¼ 1J ðpg ; u; v ; w; hÞ
1
H 0 0 6 q 0 6 uH 6 0 q C¼6 6 vH 6 0 0 4 wH HH 1 qu qv 2
qpg 6q u 6 pg @Q 6 6 ¼ 6 qp v @q 6 g 6q w 4 pg Hqpg 1 qh ¼
@q @h
qp ¼
ð2Þ
T
2
g;f;tÞ where J is the Jacobian matrix: J ¼ @ðn; . @ðx;y;z;tÞ
U ¼ nx u þ ny v þ nz w þ nt
@u @u @u 2 l i þ j þ k k dij k ¼ l 3 @xj @xi @xk
The pretreatment was conducted for Eq. (1), and then
0 0 Bn s þn s þn s C Bg s þg s þg s C B x xx B x xx y xy z xz C y xy z xz C C C 1B 1B gx syx þ gy syy þ gz syz C nx syx þ ny syy þ nz syz C Gv ¼ B Fv ¼ B C C B B JB J C Bg s þg s þg s C @ nx szx þ ny szy þ nz szz A @ x zx y zy z zz A gx bx þ gy by þ gz bz nx bx þ ny by þ nz bz 1 0 0 Bf s þf s þf s C B x xx y xy z xz C C 1B fx syx þ fy syy þ fz syz C Hv ¼ B C B JB C @ fx szx þ fy szy þ fz szz A fx bx þ fy by þ fz bz
The relation of velocity in the above equation is:
1 Ree
bxi ¼ uj sxi xj q_ xi 2 3
B quU þ n^ p C C B C B x g B qu C C B C B 1 ^ny p C C F ¼ jrnj B q v U þ Q¼ B q v C B g C B C JB J B C B qwU þ ^n p C @ qw A z g A @ e ðe þ pÞU ^nt pg 1 1 0 0 qW qV B B quW þ ^f p C ^ x pg C C C B quV þ g B x g C C B jrgj B j r fj C C B qv V þ g B ^ ^ G¼ C H¼ B B qv W þ fy pg C y pg C C J B J B B qwV þ g B qwW þ ^f p C ^ z pg C z g A A @ @ ^ t pg ðe þ pÞV g ðe þ pÞW ^ft pg The expression of viscous flux is as follows:
sxi xj ¼
3
qh 7 0 uqh 7 7 0 v qh 77 7 q wqh 5 qw Hqh þ q 0
3 qh 7 q 0 0 qh u 7 7 7 0 q 0 qh v 7 7 7 0 0 q qh w 5 qu qv qw q þ Hqh 0
@q @pg
0
H¼
0
1 U 2r
qh q
8 qffiffiffiffiffiffiffiffiffiffiffi 2 > > u2 þ v 2 þ w2 < eU 2ref < eU ref p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ur ¼ u2 þ v 2 þ w2 eU 2ref 6 u2 þ v 2 þ w2 6 a2 > > : a u2 þ v 2 þ w2 > a2
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Fig. 3. Close-up view of the grid at the leading and trailing edge.
This paper used the Spalart–Allmaras (S–A) turbulent model [19]. The Spalart–Allmaras model solves a single field equation for a variable v~ related to the eddy viscosity through,
lt ¼ qv~ f v 1 3
v where f v 1 ¼ v3 þC 3 v1
v¼
v~ v
The equation is
2 @ v~ @ v~ M1 1 v~ þ uj C b1 ½ð1 f t2 Þf v 2 þ f t2 2 C w1 f w ¼ C b1 ð1 f t2 ÞXv~ þ @t @xj Re j d M1 C b2 @ 2 v~ M 1 1 @ @ v~ v~ þ ðv þ ð1 þ C b2 Þv~ Þ Re r @x2j Re r @xj @xj
The trip function is not used, where
boundary on the computation results, the diameter of computational domain is 30 times the turbine diameter. Moreover, the mesh is refined in the vicinity of the blade surface and the regions where large changes in flow properties might occur. For the stationary region, the grid size is relatively large as the flow field is relatively simple. The other area shows homogeneous transition, and the growth rate is less than 1.1. Fig. 3 presents the mesh details of leading edge as well as the trailing edge of a blade, both of which satisfy the requirement of orthogonality. According to the analysis of mesh independence study, when the total number of grid cells for the computational domain is more than 110 thousand, a gridindependent solution can be obtained. For the wind turbine with adaptable blades, once the total number of grid cells used is more than 300 thousand, the solution does not change with further increase grid densities.
2.3. Turbulence modeling
f t2 ¼ C t3 expðC t4 v2 Þ d ¼ distance to closet wall ¼ minimum distance function " #16 g 6 þ C 6 w3 fw ¼ 1 þ C 6 w3 g ¼ r þ C w2 ðr6 rÞ v~ r¼ 2 e SðRe=M 1 Þj2 d e S ¼Xþ
v~ f v
2
ðRe=M 1 Þj2 d
2
X is the magnitude of the vorticity, term f v 3 is no longer used as it was employed as a smooth fix to prevent e S from going negative prior to 12/97, but was removed after an error was discovered. The constants are C b1 ¼ 0:1355; C b2 ¼ 0:622; j ¼ 0:41; r ¼ 2=3; C t3 ¼ 1:2; C t4 ¼ 0:5; C w2 ¼ 0:3; C w3 ¼ 2:0; C v 1 ¼ 7:1 and C w1 ¼ C b1 =j2 þ ð1 þ C b2 Þ=r .
The flow in wind turbine flow field is highly nonlinear turbulent flow. Therefore, for 2D wind turbine simulation, the dynamic RANS (Reynolds Averaged Navier-Stokes) combined with turbulent model is normally adopted [19]. For dynamic RANS simulation, different turbulent models have been developed, and their applications are introduced: Reynolds stress model was used to model engineering flows [20]; new two-equation eddy viscosity turbulence model was introduced where original k–x model of Wilcox was used in the inner region and standard k–x was used in the outer region and in the free shear flows [21]; k–x model of Wilcox performed remarkably well over a wide range of roughness values, while a modified two-layer k–e based model required further refinement [22]. For the advantages and disadvantages of different types of turbulent models, Davidson [23] conducted the comparison in detail. In the present work, the Spalart–Allmaras (S–A) turbulent model which solves directly a transport equation for the eddy viscosity is adopted because of its reasonable results for a wide range of flow problems and its numerical properties.
2.2. Geometry and mesh 2.4. Boundary conditions In the numerical simulation, NACA0015 airfoils are adopted, and all the blades revolve counterclockwise around center. The phase of the blade on Z axis is set to 0, and the number is set to 1. The other blades are numbered anticlockwise in turn. Fig. 2 illustrates the wind turbine with different number of blades as well as the mesh topology for 2D calculation around its three blades. An O-type grid has been employed to discretize the entire computational domain which consists of a rotating region around the turbine blades and an outer stationary flow region. The diameter of turbine rotor is 2.5 m. In order to reduce the influence of
In the simulation, the boundaries of computational domain are composed of velocity inlet, static pressure outlet, wall boundary and control domain boundary. As a circular computational domain is used, the wind direction is set along the X axis as shown in Fig. 2. The incoming wind speed is 10 m/s, the diameter of rotating rotor is 2.5 m, and the surface of turbine blades are set as the non-slip wall boundary condition. The properties of the flow at the interface between the stationary and rotating zones are obtained via interpolation.
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1.5
Cl_Exp Cd_Exp Cl_Num Cd_Num
1.2
Coefficient
279
0.9 0.6 0.3 0.0 0
4
8
12
16
20
24
Angle of attack (Degree) Fig. 8. The variation of wind power coefficients with TSR for a two-bladed VAWT. Fig. 4. Comparison between simulation and experimental results of lift and drag coefficients for NACA0012 at different angle of attacks.
0.44 0.42
Cp
0.40 0.38 0.36 0.34 0.32 0.30 0.0000
0.0004
0.0008
0.0012
0.0016
dmax
Fig. 9. The variation of wind power coefficients with TSR for a VAWTDB with two deformable blades.
Fig. 5. Influence of dmax on Cp for the wind turbine with two deformable blades.
0.44 0.42
Cp
0.40 0.38 0.36 0.34 0.0000
0.0004
0.0008
0.0012
dmax Fig. 6. Influence of dmax on Cp for the wind turbine with three deformable blades.
Fig. 10. The variation of wind power coefficients with TSR for a three-bladed VAWT.
0.30 0.28
3. Numerical model validation
0.26
Cp
0.24 0.22 0.20 0.18 0.16 0.14 0.0000
0.0004
0.0008
0.0012
0.0016
dmax Fig. 7. Influence of dmax on Cp for the wind turbine with four deformable blades.
In order to verify the reliability of the software used, simulation of 2D incompressible flow past a NACA0012 airfoil at Re = 5,000,000 has been undertaken. With the variation of angle of attack, the values of the lift and drag coefficients at different angle of attack are computed and compared with the published experimental results [24,25]. O-type mesh around the simulated airfoil with diameter 20c (c = chord length) was generated. According to the results of the mesh independence study, 121 mesh nodes are adopted along the airfoil chord, and 149 mesh nodes are employed along radial direction. A steady state two-dimensional RANS type calculation
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0.50 0.45
Cp
0.40
0.32 0.32_deform 0.52 0.52_deform 0.72 0.72_deform
0.35 0.30 0.25 0.20 0.15 0.8
Fig. 11. The variation of wind power coefficients with TSR for a VAWTDB with three deformable blades.
1.2
1.6
2.0
2.4
2.8
3.2
Fig. 14. The variation of power coefficient with TSR for VAWT and VAWTDB with two blades.
0.50 0.45
Cp
0.40
0.18 0.18_deform 0.28 0.28_deform 0.68 0.68_deform
0.35 0.30 0.25 0.20 0.15 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4
Fig. 12. The variation of wind power coefficient with TSR for a four-bladed VAWT. Fig. 15. The variation of power coefficient with TSR for VAWT and VAWTDB with three blades.
0.45 0.40
Cp
0.35 0.30
0.24 0.24_deform 0.34 0.34_deform 0.74 0.74_deform
0.25 0.20 Fig. 13. The variation of wind power coefficient with TSR for a VAWTDB with four deformable blades.
is performed at different angle of attack. The turbulence model selected for this study is the one-equation eddy viscosity model of S–A. While using S–A turbulence model in the UCFD software, y+ equals to 1–10 and the maximum value of y+ is 10. This software uses the finite volume method and adopts the velocity, pressure, and enthalpy as original variables. The fluid with low velocity is also preprocessed accordingly. The numerical simulation conducted in this paper adopted S–A turbulence model which can be irrelevant to solution of y+. Thus, this paper didn’t use wall function approach. The wall of airfoil is set as non-slip wall boundary condition. At the inlet boundary, a uniform velocity profile is given. The outlet is set as pressure boundary condition. The symmetrical boundary condition is used for the spanwise direction.
0.15 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
Fig. 16. The variation of power coefficient with TSR for VAWT and VAWTDB with four blades.
Fig. 4 shows the comparison between simulation and experimental results of lift and drag coefficients for NACA0012 airfoil over the range of angle of attack from 0° to 20°. In Fig. 4, when the angle of attack is less than 12°, the numerical results of lift and drag coefficients are in good agreement with experimental results. When the angle of attack is more than 14° and less than 20° in simulation, the lift coefficient is relatively large and the drag coefficient is relatively small. At a higher angle of attack, a large fraction of the flow over the upper surface of the airfoil may be sep-
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First blade
First blade
Third blade Third blade
Second blade
Second blade
(a) Position of 0
Position of 20
First blade
First blade
Third blade
Third blade
Second blade
Second blade
(b) Position of 30
Position of 40 Third blade
Third blade First blade
First blade
Second blade
Second blade
(c) Position of 60
Position of 60
Third blade
Third blade
First blade
First blade
Second blade Second blade
(d) Position of 90
Third blade
First blade
Position of 80
Third blade Second blade
Second blade
First blade
(e) Position of 120
Fig. 17. Comparison of vortex structures in the flow field around the wind turbine with three deformable blades (left) and conventional three-bladed wind turbine (right).
Position of 100
Fig. 18a. The vortex shedding at different positions for a single blade of three bladed VAWTDB (left) and VAWT (right).
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Position of 120
Position of 220
Position of 140
Position of 240
Position of 160
Position of 260
Position of 180
Position of 280
Position of 200 Fig. 18b. The vortex shedding at different positions for a single blade of three bladed VAWTDB (left) and VAWT (right).
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which presents both experimental and numerical results for an H-Darrieus wind turbine. The numerical method in Ref. [28] which is the same as this paper is believed to be accurate enough for simulating the flow field around an H-Darrieus wind turbine rotor. 4. Results and discussions 4.1. Influence of the degree of deformation on power coefficient of VAWTDB
Position of 300
Solidity, r, is the ratio of total rotor blade area to total swept area and is one of the most important parameters for wind turbine design.
r¼
nC 2R
ð3Þ
where n is the number of blades, C is the blade chord length, R is the wind turbine radius. In per unit time, the displacement increment vertical to the chord line of the airfoil is defined as:
dðlÞ ¼ 2bpf sin
Position of 320
p
l lfront edge ltrailing edge lfront edge
ð4Þ
where l is the coordinate of the position along the chord direction, and b is the maximum camber. Thus, the linear displacement of a point on the airfoil surface that is vertical distance to the chord line during rotation is defined as:
Z
Dðl; tÞ ¼
t
dðlÞ cosð2pftÞ dt
ð5Þ
0
Position of 340
Position of 360
Fig. 18c. The vortex shedding at different positions for a single blade of three blades VAWTDB (left) and VAWT (right).
arated and rather large differences exist between the experimental and numerical results. Nevertheless, the numerical model is believed to be accurate enough to provide reliable results. Moreover, as stated in Sun’s paper [26] done by our research group, a model validation has already been developed. Validation test is carried out with the model selected from the work of Castelli
The maximum degree of deformation is a key factor to influence the performance of the wind turbine equipped with deformable blades. Here, a control factor which is related with the maximum degree of deformation is defined as dmax and its effect on the performance of wind turbines with two, three and four blades is analyzed respectively in this section. In this way, the optimum value of dmax for which the maximum power is extracted can be obtained. At a TSR of 1.4, the influence of dmax on the Cp of the wind turbine with two deformable blades which yields a turbine solidity of 0.42 is shown in Fig. 5. It is found that when dmax is smaller than 0.0012, Cp of VAWTDB increases with the increase of dmax. When dmax equals to 0.0012, the maximum Cp increase compared to the conventional wind turbine is observed. Conversely, a decrease in Cp occurs when dmax is larger than 0.0012. As a result, the optimum value of dmax for the Darrieus wind turbine with two deformable blades is 0.0012. Fig. 6 shows the influence of dmax on Cp for the wind turbine with three deformable blades when its solidity is 0.48 and TSR is 1.6. When dmax is smaller than 0.0006, Cp increases with the increase of dmax. When dmax is 0.0006, the turbine has the highest value of Cp. When dmax is larger than 0.0006, Cp gradually decreases with the further increase of dmax. For the turbine with three deformable blades, 0.0006 is therefore the optimum value of degree of deformation. Fig. 7 illustrates the influence of dmax on Cp for the wind turbine with four deformable blades when its solidity is 0.64 and TSR is 1.6. As can be seen in Fig. 7, when dmax is smaller than 0.0014, Cp increases with the increase of dmax. When dmax is 0.0014, the turbine has the highest value of Cp. When dmax is larger 0.0014, Cp then gradually decreases with the further increase of dmax. Hence, the optimum value of dmax for four-bladed wind turbine is 0.0014.
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4.2. Influence of lade chord length and TSR on power coefficient of VAWTDB For a Darrieus wind turbine with straight blades, its maximum power coefficient normally is about 40%. According to Mohamed’s study [28], there exists an optimum turbine solidity for a given number of blades. At a given tip speed ratio, the power coefficient of a turbine initially increases with an increasing solidity until a maximum is reached; beyond this point, performance actually decreases with further increase in the solidity. Similarly, for a given solidity, it is well known that there is an optimum value of TSR that leads to maximum power coefficient [29]. Furthermore, the higher the solidity, the smaller the corresponding optimal TSR is. Figs. 8 and 9 present the variation of wind power coefficients with TSR for a conventional two-bladed wind turbine as well as for a wind turbine with two deformable blades. In some cases, it is found that the optimal TSR of the wind turbine with deformable blades is smaller than that of the conventional wind turbine. In addition, the optimal value of the solidity for both types of turbines is 0.32. Figs. 10 and 11 present the variation of wind power coefficients with TSR for a conventional three-bladed wind turbine as well as for a wind turbine with three deformable blades. Compared to the conventional wind turbine, the optimal TSR of a wind turbine with deformable blades earlier reaches the optimum TSR at solidity factors of 0.22 and 0.68. Moreover, the optimal value of solidity for both types of turbines is 0.38. Figs. 12 and 13 illustrate the variation of wind power coefficients with TSR for a conventional four-bladed wind turbine as well as for a wind turbine with four deformable blades. When solidity is 0.34 and 0.54, compare with, the optimal TSR of the wind turbine with deformable blades is smaller than that of a conventional wind turbine. In addition, the optimum solidity for the conventional four-bladed turbines is 0.44 but for wind turbine with deformable blades, the optimal value of solidity is 0.34. 4.3. Comparison of power coefficients for VAWT and VAWTDB Fig. 14 is the comparison of power coefficient for conventional two-bladed wind turbine and wind turbine with two deformable blades. For a given solidity, the power coefficients of the wind turbine with deformable blades are evidently higher than those of the conventional wind turbine when the TSR is smaller than the optimal value. However, beyond this optimal value of TSR, the power coefficients of the wind turbine with deformable blades drop rapidly and become lower than those of the conventional wind turbine. As can be seen in Fig. 14, the most dramatic improvement occurs at solidity of 0.32 and TSR of 1.4 and the maximum power coefficient of the wind turbine with deformable blades is up to 7.51% higher than that of the conventional wind turbine. Comparison of power coefficient for VAWT and VAWTDB with three blades is illustrated in Fig. 15. At relatively low solidities, the power coefficients of proposed wind turbine are generally higher than those of the conventional wind turbine. For high solidities, the power coefficients of VAWTDB are higher than those of conventional VAWT at TSRs that are lower than optimal value but start to decrease when the TSR continues to increase above the point of optimal function. For three bladed VAWTDB, the optimal combinations of operation parameters are the solidity of 0.18 and the TSR of 4.0 for which the maximum power coefficient of proposed turbine can be 14.56% higher than that of conventional VAWT. Fig. 16 demonstrates comparison of power coefficient for conventional VAWT and VAWTDB with four blades. The improvement of the power coefficient of VAWTDB shows similar features as the above two cases. As can be seen in Fig. 16, the highest Cp that is 8.07% higher than that of conventional VAWT occurs at the solidity
of 0.34 and TSR of 1.6. Part of the performance improvement at low (Fig. 16) and high (Fig. 15) k are might due to the coupling with electrical generator. 4.4. Aerodynamic performance of three bladed VAWTDB In this section, the flow field characteristics around the threebladed VAWTDB at the solidity of 0.18 and TSR of 4.0 were analyzed in an attempt to uncover the mechanisms underlying the improvement of power performance by deformable blade. Fig. 17 gives the comparison of vortex structures in flow field around the wind turbine with deformable blades (left image) and conventional wind turbine (right image) at different angle of rotation. When wind turbine is at position of 0, no large vortex separation on the deformable blades is observed. However, there is relatively large vortex separation and shedding on all the three blades of the conventional wind turbine. For the first blade, there exists vortex at the trailing edge of airfoil; for the second blade, there is a positive separation vortex A at the suction surface of the blade and a negative separated vortex B at the trailing edge of the blade; for the third blade, the vortex at the leading edge and trailing edge of the airfoil is about to separate from its suction surface. When blade spins to position of 30°, there are still two trailing vortexes on the blade. However, for the underformable blade, a new positive vortex C appears on the suction surface of the second airfoil. Besides, vortex A and B sheds from the blade surface completely. When wind blade turns from the position of 30–90°, there are still two trailing vortexes on the deformable blade. However for the conventional blade, the vortex grows to an unstable size and sheds, such as vortex C and D. Moreover, there is vortex on the third blade. The shed vortex continuously moves downstream as a pair. When the first blade turns to the position of 120°, the entire flow field then turns to the next cycle. Figs. 18a–18c show the comparison of vortexes on one underformed blade and deformable blade when they rotate to different azimuthal positions. By tracking a single blade from the position of 20°, as shown in Fig. 18a, both of the inside and outside of the undeformed and deformable blades show two back tracks. When blade turns from 40° to 80°, the deformable blade still shows two back tracks which fit well with the rotating c path. At the same time, a positive vortex on the inside of the undeformed blade gradually grows thicker, and the trailing vortex is slowly deflected from the rotating path. When the blade turns to 100°, there is large bulge of positive vorticity region at the inside of undeformed blade, and the back track from the trailing vortex has already seriously deviated from the rotary path. As can be seen in Fig. 18b, when the blade moves from position of 100–120°, no obvious change for the back track behind the deformable blade occurs. However, for undeformed blade, the large bulge of positive vorticity region at its inside surface has already developed into a large separation vortex A. Besides, a relatively large negative vortex at the inside and trailing edge of airfoil appears. When it turns to 120°, the trailing vortex remains almost the same for the deformable blade. The vortex A on the surface of deformable blade forms into the shape of a sickle, while the negative vortex B is surrounded by this sickle-shaped positive vorticity region and is about to be shed from the blade surface. Moreover, a new positive vortex C around the leading edge of the airfoil emerges. When the blade turns to 140°, 160° and 180°, the pair of positive and negative vortices on the undeformed blade grow and are shed alternatively. When it turns to 200°, a negative vortex E at the leading edge and the outside of underformed blade is observed, and additionally there is also a positive vortex F at the trailing edge of the airfoil. When the blade turns to 240° to 260°, the vortex on the inside of deformed blade separates from the blade, convects downstream, and ultimately dissipates. The size
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of vortexes E and F generating at the outside of blade continuously grow and become extended. When the blade turns to 280°, the vortex generating at the outside of undeformed blade has been completely shed, and a new vortex forms on the outside of blade. From 280° to 290°, there are still two long, thin, vortex-threads that trails downstream of the deformable blade. The vortex generating from the outside of the undeformed blade continuously grows, separates and sheds in turn. Eventually, the trailing vortices are systematically shed from the downstream side of the blade and have an effect on the trailing edge region of the blade. The intensity of shed vortex finally dissipates under the action of viscosity. As flow separation is a major contributing factor to the aerodynamic challenges associated with wind turbine operation, the ability to control or reduce the magnitude of regions of separated flow over an airfoil can play a significant role in improving the performance of the entire turbine in terms of power, loads and service life. Apart from thin trailing wake, no periodic vortex shedding phenomenon from the adaptive blade over the entire cycle of its rotation was observed. Therefore, the above results indicate that the adaptive blades can effectively act as a means of controlling flow separation.
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The numerical calculations in this study were performed on a single-precision grid and the double-precision grid will be used in the future work to evaluate the possible numerical errors that exist in the present work. The unsteady RANS method combined with a S–A turbulence model is adopted for simulation of wind turbine in this paper. This method is more accurate for calculation without large separating vortex, while it cannot provide satisfied accuracy of simulation of flows with large separated-flow region. Therefore, the (Detached Eddy Simulation) DES method based on S–A turbulence model or SST model could be considered in the future as it is capable of predicting the unsteady motions associated with separated flows. In this way, more accurate flow field would be obtained, and the mechanism that attributes to the power performance improvement of this new type wind turbine can be revealed. In the future work, scale-model wind tunnel experiments will be conducted in order to verify the actual effect of this new type wind turbine to increase the wind power absorption as well as to raise the wind power coefficient.
Acknowledgements 5. Conclusions A new type of VAWT whose blade can automatically deformed caused by the pressure distribution over its surface is proposed and studied in this paper. The numerical simulations were conducted for the conventional Darrieus wind turbine as well as for the new type wind turbine with two, three and four blades at different solidities and TSR, respectively. In addition, the vorticity field around the adaptive blade was analyzed in order to explore the mechanism responsible for its performance improvement. Based on the numerical results, the conclusions of this work are summarized in the following points: (1) Some common rules that apply to both the conventional VAWT and the proposed VAWTDB are identified: at a given number of blades, there is an optimum value of rotor solidity; an optimum TSR exists for a Darrieus rotor with a given number of blades and solidity; the higher the solidity, the smaller the value of the corresponding optimal TSR can be achieved. (2) At three different solidities and TSR, the power coefficients of the conventional VAWT and the new type VAWTDB which have two, three and four blades, respectively, were calculated and compared. It is found that compared to the conventional VAWT, the power coefficients of the VAWTDB are generally improved when the rotor solidity is relatively low. On the other hand, when the solidity is high, the power coefficients of the VAWDTB is found to be higher than that of the conventional VAWT at the tip speed ratios lower than the optimal value but opposite results are obtained beyond this optimal value of TSR. (3) The vorticity fields around a three-bladed VAWT and VAWTDB are analyzed and the vortex shedding phenomenon at a single turbine blade is studied in detail. Our results suggest that the adaptive blade is effective in controlling the vortex shedding as it is able to be automatically deformed during rotation to shape it into a desired geometry that exhibits better aerodynamic performance. (4) Among all the simulated turbines, the power improvement of the three-bladed VAWTDB is most obvious and its maximum power coefficient is about 14.56% higher than that of the conventional VAWT, whereas the maximum power coefficients of the four bladed and two-bladed VAWTD have increased by 8.07% and 7.51%, respectively.
This work was supported by National Natural Science Foundation of China (Grant Nos. 51406117, 51536006 and 11202123), and USST Key Laboratory of Flow Control and Simulation (D15013).
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