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Jun 11, 2018 - Abstract: The blade pitch angle has a significant influence on the aerodynamic characteristics of horizontal axis wind turbines. However, few ...
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Effect of Blade Pitch Angle on the Aerodynamic Characteristics of a Straight-bladed Vertical Axis Wind Turbine Based on Experiments and Simulations Yanzhao Yang 1,2 , Zhiping Guo 1 , Qing Song 3 , Yanfeng Zhang 1,2 and Qing’an Li 4,5, * 1 2 3 4 5

*

College of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China; [email protected] (Y.Y.); [email protected] (Z.G.); [email protected] (Y.Z.) Graduate School of Bioresources, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie 514-8507, Japan School of Electrical Engineering, University of Jinan, Jinan 250022, China; [email protected] CAS Laboratory of Wind Energy Utilization, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China Division of Mechanical Engineering, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie 514-8507, Japan Correspondence: [email protected]

Received: 22 April 2018; Accepted: 30 May 2018; Published: 11 June 2018

 

Abstract: The blade pitch angle has a significant influence on the aerodynamic characteristics of horizontal axis wind turbines. However, few research results have revealed its impact on the straight-bladed vertical axis wind turbine (Sb-VAWT). In this paper, wind tunnel experiments and CFD simulations were performed at the Sb-VAWT to investigate the effect of different blade pitch angles on the pressure distribution on the blade surface, the torque coefficient, and the power coefficient. In this study, the airfoil type was NACA0021 with two blades. The Sb-VAWT had a rotor radius of 1.0 m with a spanwise length of 1.2 m. The simulations were based on the k-ω Shear Stress Transport (SST) turbulence model and the wind tunnel experiments were carried out using a high-speed multiport pressure device. As a result, it was found that the maximum pressure difference on the blade surface was obtained at the blade pitch angle of β = 6◦ in the upstream region. However, the maximum pressure coefficient was shown at the blade pitch angle of β = 8◦ in the downstream region. The torque coefficient acting on a single blade reached its maximum value at the blade pitch angle of β = 6◦ . As the tip speed ratio increased, the power coefficient became higher and reached the optimum level. Subsequently, further increase of the tip speed ratio only led to a quick reversion of the power coefficient. In addition, the results from CFD simulations had also a good agreement with the results from the wind tunnel experiments. As a result, the blade pitch angle did not have a significant influence on the aerodynamic characteristics of the Sb-VAWT. Keywords: wind energy; Sb-VAWT; blade pitch angle; pressure coefficient; power coefficient

1. Introduction Wind power technology, which utilizes the renewable clean energy, has been regarded as an important way to alleviate the energy crisis and environmental pollution [1–5]. After hundreds of years, as shown in Figure 1, there are presently two main types of wind turbines: horizontal axis wind turbines (HAWTs) and vertical axis wind turbine (VAWTs) [6,7]. Currently, the large-type HAWT is very popular, but it is mainly installed in mountains, grasslands and oceans, where the infrastructure costs are very high. Moreover, there is an inevitable transmission loss of power because the wind turbines are far away from the power demand centers [8–10]. Straight-bladed vertical axis wind turbines (Sb-VAWTs) have been favored by global researchers due to their low production cost and insensitivity to high turbulence intensity in cities [11–13]. Energies 2018, 11, 1514; doi:10.3390/en11061514

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turbines (Sb-VAWTs) Energies 2018, 11, 1514

have been favored by global researchers due to their low production cost2 of and 15 insensitivity to high turbulence intensity in cities [11–13].

(a) Vertical Axis Wind Turbine

(b) Horizontal Axis Wind Turbine

Figure of wind wind turbine. turbine. Figure 1. 1. Types Types of

For HAWT, the International Electrotechnical Commission (IEC) has developed a set of uniform For HAWT, the International Electrotechnical Commission (IEC) has developed a set of uniform design standards [14]. However, the research progress on VAWTs is relatively slow compared with design standards [14]. However, the research progress on VAWTs is relatively slow compared with HAWTs. Up to now, uniform worldwide design standard has not been established. For the SbHAWTs. Up to now, uniform worldwide design standard has not been established. For the Sb-VAWT, VAWT, the blade pitch angle is one of the basic parameters [15]. It is also a factor with a direct impact the blade pitch angle is one of the basic parameters [15]. It is also a factor with a direct impact on on the flow field around the blade, which then affects the pressure distribution on the blade surface, the flow field around the blade, which then affects the pressure distribution on the blade surface, which may lead to a change in the lift-to-drag ratio of the blade and power coefficient of the wind which may lead to a change in the lift-to-drag ratio of the blade and power coefficient of the wind turbine [16]. turbine [16]. In the study of Sb-VAWT standardization, researchers have achieved remarkable results. In 2013 In the study of Sb-VAWT standardization, researchers have achieved remarkable results. In 2013 Conaill et al. characterized the relationship between the Sb-VAWT design parameters and the best Conaill et al. characterized the relationship between the Sb-VAWT design parameters and the best performance based on the averaged moment values [17]. It was found that the lift-to-drag ratio had performance based on the averaged moment values [17]. It was found that the lift-to-drag ratio an effect on the rotating rotor speed of the Sb-VAWT and the peak value of the power output had an effect on the rotating rotor speed of the Sb-VAWT and the peak value of the power output coefficient. As the rotating rotor speed of the Sb-VAWT gets faster, the lift-to-drag ratio increased. coefficient. As the rotating rotor speed of the Sb-VAWT gets faster, the lift-to-drag ratio increased. Maeda et al. [18] in 2013 studied the effect of the rotor angular frequency of the Sb-VAWT on the Maeda et al. [18] in 2013 studied the effect of the rotor angular frequency of the Sb-VAWT on the pressure distribution acting on the blade surface by using a high-speed multiport pressure device pressure distribution acting on the blade surface by using a high-speed multiport pressure device and a torque meter. This experiment revealed that the tip speed ratio increased with the increase of and a torque meter. This experiment revealed that the tip speed ratio increased with the increase of the pressure difference on the blade surface. Based on this experiment, Li et al. [19] in 2015 further the pressure difference on the blade surface. Based on this experiment, Li et al. [19] in 2015 further investigated the influence of the number of blades on the aerodynamic characteristics of the Sbinvestigated the influence of the number of blades on the aerodynamic characteristics of the Sb-VAWT VAWT via a torque meter. The results of this experiment showed that the peak value of the power via a torque meter. The results of this experiment showed that the peak value of the power coefficient coefficient of the Sb-VAWT decreased with the increase of the number of blades. Sun et al. [20] in of the Sb-VAWT decreased with the increase of the number of blades. Sun et al. [20] in 2016 and 2016 and Battisti et al. [21] in 2016 also obtained a similar conclusion by conducting wind tunnel Battisti et al. [21] in 2016 also obtained a similar conclusion by conducting wind tunnel experiments experiments and CFD simulations. Abu-El-Yazied et al. [22] performed in 2015 CFD simulations to and CFD simulations. Abu-El-Yazied et al. [22] performed in 2015 CFD simulations to verify the verify the conclusions, and analyzed the influence of various lengths of blade chords on the power conclusions, and analyzed the influence of various lengths of blade chords on the power coefficient of coefficient of the SB-VAWT. They found that the power coefficient decreased with the increase of the the SB-VAWT. They found that the power coefficient decreased with the increase of the chord length. chord length. In order to analyze the effect of blade solidity on the power coefficient of the Sb-VAWT, Roh and In order to analyze the effect of blade solidity on the power coefficient of the Sb-VAWT, Roh and Kang et al. [23] in 2013 investigated the aerodynamic characteristics of the NACA0015 airfoil at the Kang et al. [23] in 2013 investigated the aerodynamic characteristics of the NACA0015 airfoil at the Reynolds number of Re = 3.6 × 1055 in reference to the multiple streamtube model. When the blade Reynolds number of Re = 3.6 × 10 in reference to the multiple streamtube model. When the blade solidities were 0.251, 0.333, 0.417, and 0.500, the maximum values of the power coefficient of the wind solidities were 0.251, 0.333, 0.417, and 0.500, the maximum values of the power coefficient of the wind turbine were around 0.48, 0.47, 0.40, and 0.27, respectively. Li et al. also verified this conclusion via turbine were around 0.48, 0.47, 0.40, and 0.27, respectively. Li et al. also verified this conclusion via wind tunnel experiments [24] and the panel method [25], from which the maximum value of power wind tunnel experiments [24] and the panel method [25], from which the maximum value of power coefficient decreased with the increase of the blade solidity. coefficient decreased with the increase of the blade solidity. Islam et al. [26] in 2007 evaluated the effects of the NACA0012, NACA0022, NACA5522 and Islam et al. [26] in 2007 evaluated the effects of the NACA0012, NACA0022, NACA5522 and LS0421 airfoils on the power coefficient of the Sb-VAWT via CFD simulations. The results showed LS0421 airfoils on the power coefficient of the Sb-VAWT via CFD simulations. The results showed that the power coefficient of the high-thickness NACA00XX was higher than that of the low-thickness that the power coefficient of the high-thickness NACA00XX was higher than that of the low-thickness NACA00XX, and the total output power of the symmetrical airfoil was higher than that of the NACA00XX, and the total output power of the symmetrical airfoil was higher than that of the asymmetric airfoil. Danao et al. [27] in 2012, concluded that the NACA0012 was the optimal airfoil asymmetric airfoil. Danao et al. [27] in 2012, concluded that the NACA0012 was the optimal airfoil of of the Sb-VAWT [27]. Iida et al. [28] in 2003, Claessens et al. [29] in 2006, and Armstrong et al. [30] in 2011 used wind tunnel experiments and CFD simulations to analyze the influence of the Reynolds

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number on the energy conversion of the Sb-VAWT. Their studies found that with the increase of Reynolds number, the wind energy utilization of the Sb-VAWT increased and the optimal tip speed ratio decreased. In summary, the current research on design parameters such as rotor diameter, airfoil, the number of blade, blade solidity, etc. has achieved significant results. However, studies on the blade pitch angle of the Sb-VAWT by using CFD simulations and wind tunnel experiments are few. Therefore, the objectives of this research are to clarify the influence of the blade pitch angle on the aerodynamic characteristics of the Sb-VAWT and look for the optimal blade pitch angle by using CFD simulations and wind tunnel experiments. In order to investigate in detail the aerodynamic characteristics of the Sb-VAWT at different blade pitch angles, pressure distribution on blade surface, torque coefficient, and power coefficient will be analyzed. The outline of the following work is shown as follows: Firstly, the pressure distributions at the blade pitch angles of β = 4◦ , 6◦ , and 8◦ are compared and analyzed in order to investigate the effect of blade pitch angle on aerodynamic characteristics of the Sb-VAWT. Secondly, the torque coefficients acting on the single blade are discussed at the blade pitch angles of β = 4◦ , 6◦ , and 8◦ . Besides, the torque coefficients acting on the single blade calculated by CFD simulations are compared with high-speed multiport pressure device at the blade pitch angle of β = 6◦ . Finally, the optimal blade pitch angle is studied from the aspect of the power coefficient of wind turbine. The power coefficients of wind turbine are compared with torque meter in wind tunnel experiments and CFD simulations, respectively. 2. Theories and Methods 2.1. Theories In order to study the effect of the blade pitch angle of the Sb-VAWT on the power coefficient, the mathematical model of aerodynamics should be analyzed. As shown in Figure 2, the dotted circle is the rotating shaft of the rotor and θ is the azimuth angle. The direction of the mainstream wind velocity U0 flows from left to right and the rotating direction of the rotor is clockwise viewed from topside of wind turbine. V and W are the tangential velocity of the blade and the resultant flow velocity to blade, respectively. The resultant flow velocity to blade W is expressed with the tangential velocity V and the mainstream wind velocity U0 as: W = U0 + V

(1)

The blade angle of attack α is the angle between the resultant flow velocity to blade and the blade chord. The blade pitch angle β is the angle between the tangential velocity V of the blade and the blade chord. ϕ is the angle between the resultant flow velocity to blade W and the tangential velocity V, which can be expressed as: ϕ = α+β (2) P is the pressure acting on the blade surface and it is perpendicular to the blade surface. The pressure coefficient acting on the blade surface Cp is expressed as: Cp =

P 0.5ρU02

(3)

where, ρ represents the air density. Tangential force can be obtained from the following expression: FT = Fl sin ϕ − Fd cos ϕ

(4)

where, Fl is the lifting force of the blade and its direction is perpendicular to the blade chord. Fd is the drag force of the blade and its direction is parallel to the blade chord.

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The torque of the single blade Q is generated by the tangential force of the blade. Therefore, Q can Energies 2018, 11, the x FOR PEER REVIEW 4 of 15 be expressed with tangential force FT as: Z The torque of the single blade Q is generated R 2πby the tangential force of the blade. Therefore, Q Q = FT (θ )dθ (5) can be expressed with the tangential force F2π T as: 0

R 2π Hence, the torque coefficient CQ is defined as: FT (θ ) d θ Q = 2 π 0 NQ as: NQ Hence, the torque coefficient CQ is defined CQ = = 2 2R 0.5ρAU R 0.5ρDHU NQ0 0 NQ 0 0 C =

=

(5)

(6) (6)

Q 0.5 ρ AU 2 R0 0.5 ρ DHU 02 R0 where, N and R0 represent the number of blades0 and the rotor radius. D and H represent the rotor diameter andNthe length, respectively. According to the rotorDtorque, the power coefficient where, andSpanwise R0 represent the number of blades and the rotor radius. and H represent the rotor and the Spanwise respectively. According to the rotor torque, the power coefficient CPower diameter can be determined by thelength, following equation:

CPower can be determined by the following equation:

CPower == C Power

NQω NQω 3 0.5ρDHU 0.5 ρ DHU003

(7)

(7)

where,where, ω is the frequency of theofrotor. ωangular is the angular frequency the rotor.

Blade 2 Rotating trajectory

U0

p

FN

φ

Figure 2. Definitions of velocity and force.

Figure 2. Definitions of velocity and force.

2.2. Methods

2.2. Methods

In this paper, the influence of the blade pitch angle on the aerodynamic characteristics of the Sb-

is investigated by using simulations. aerodynamic characteristics of the Sb-VAWT InVAWT this paper, the influence ofCFD the blade pitch The angle on the aerodynamic characteristics of the include the pressurebydistribution, torque coefficient and the power coefficient. TheSb-VAWT CFD Sb-VAWT is investigated using CFD the simulations. The aerodynamic characteristics of the simulations aredistribution, performed in three-dimensional it adopts sliding mesh include the pressure thethe torque coefficient andnumerical the powermodel; coefficient. The CFD simulations technology, k-ω Shear Stress Transport (SST) turbulence model and the SAMPLE iterative algorithm are performed in the three-dimensional numerical model; it adopts sliding mesh technology, k-ω Shear for numerical calculation. The sliding mesh technique is commonly used in CFD simulations for Stress Transport (SST) turbulence model and the SAMPLE iterative algorithm for numerical calculation. simulating the aerodynamic characteristics of the Sb-VAWT. According to reference [31], the CFD The sliding mesh technique is commonly used in CFD simulations for simulating the aerodynamic simulations of the Sb-VAWT can obtain a high computational accuracy under the constant speed of characteristics of can the be Sb-VAWT. to the reference the CFD simulations of advantages the Sb-VAWT the rotor. As seen fromAccording reference [32], k-ω SST [31], turbulence model combines the can obtain high computational accuracy the constant speed of the rotor. As can be seen from of theastandard k-ω and the standard k-εunder turbulence models, and it includes the modified turbulent reference [32], formula, the k-ω SST model the combines advantages the standard and the viscosity whichturbulence takes into account effect ofthe turbulence shearof stress, being ablek-ω to more accurately simulatemodels, the size and of the separation and separation caused by the negative standard k-ε turbulence it includes thepoint modified turbulentzone viscosity formula, which takes pressurethe gradient. It also has the advantages of being adaptive filtering foraccurately the boundary layer and into account effect of turbulence shear stress, able to more simulate theless size of sensitivity to the quality of the mesh. the separation point and separation zone caused by the negative pressure gradient. It also has the advantages of adaptive filtering for the boundary layer and less sensitivity to the quality of the mesh.

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As 3, 3, the model of the turbine is double-blade Sb-VAWT. The rotorThe diameter As shown Figure model of the turbine is Sb-VAWT. rotor As shown showninin inFigure Figure 3, the the model ofwind the wind wind turbine is double-blade double-blade Sb-VAWT. The rotor is D = 2.0 m with the spanwise length of H = 1.2 m. The airfoil is the standard NACA0021 with the diameter diameter is is D D == 2.0 2.0 m m with with the the spanwise spanwise length length of of H H == 1.2 1.2 m. m. The The airfoil airfoil is is the the standard standard NACA0021 NACA0021 blade chord length oflength c = 0.265 with blade chord of with the the blade chord length of cm. c == 0.265 0.265 m. m. Due to the effect of the tip vortex on distribution on the blade surface the spanwise Due on the distribution on blade in Due to to the the effect effect of of the the tip tip vortex vortexthe onpressure the pressure pressure distribution on the the bladeinsurface surface in the the direction [33], the CFD simulations used the three-dimensional numerical model to increase the spanwise to spanwise direction direction [33], [33], the the CFD CFD simulations simulations used used the the three-dimensional three-dimensional numerical numerical model model to increase increase accuracy of theof as shown in Figure The length, andwidth heightand of the three-dimensional the the as in 4. length, height of the accuracy accuracy ofcalculation, the calculation, calculation, as shown shown in4.Figure Figure 4. The Thewidth length, width and height of the the threethreenumerical model are L = 20.0D, W = 10.0D and H = 1.0D, respectively. The rotor center of 0 dimensional are rotor center dimensional numerical numerical model model are LL00 ==020.0D, 20.0D, W W00 == 10.0D 10.0D0and and H H00 == 1.0D, 1.0D, respectively. respectively. The The rotor center the Sb-VAWT is located 5D5D away from the inlet surface. the of Sb-VAWT is away from the inlet surface. located at the center position of of the the Sb-VAWT is located located 5D away from the inlet surface.ItIt Itisis islocated locatedat atthe thecenter center position position of of the the three-dimensional numerical model in width and height. Since the CFD simulations are based on three-dimensional three-dimensional numerical numerical model model in in width width and and height. height. Since Since the the CFD CFD simulations simulations are are based based on on the the the sliding mesh technique, the computational domain is divided into a stationary domain and sliding sliding mesh mesh technique, technique, the the computational computational domain domain is is divided divided into into aa stationary stationary domain domain and and aa rotating rotating adomain. rotating domain. domain. The mesh of and the for are The the stationary domain rotating domain the CFD simulations The mesh mesh of of the the stationary stationary domain domain and and the the rotating rotating domain domain for for the the CFD CFD simulations simulations are are constructed using the topological meshing technique. As shown in Figure 5, the outer radius of constructed constructed using using the the topological topological meshing meshing technique. technique. As As shown shown in in Figure Figure 5, 5, the the outer outer radius radius of of the the the rotating domain is 0.6D the inner radius is 0.4D. The interfaces between the inner and walls outer rotating domain is and the radius is The between the and rotating domain is 0.6D 0.6D and and the inner inner radius is 0.4D. 0.4D. The interfaces interfaces between the inner inner and outer outer walls walls are Interface1 and Interface2, respectively. To obtain a higher calculation precision, the mesh of are are Interface1 Interface1 and and Interface2, Interface2, respectively. respectively. To To obtain obtain aa higher higher calculation calculation precision, precision, the the mesh mesh of of the the the rotating domain is encrypted. The mesh near theblades bladeswas wasgiven givenfurther further encryption, encryption, which which is is rotating domain is The mesh near the rotating domain is encrypted. encrypted. The mesh near the blades was given further encryption, which is depicted in Figure 6. depicted depicted in in Figure Figure 6. 6.

Figure Figure 3. A Three-dimensional model of Sb-VAWT. Figure 3. 3. A A Three-dimensional Three-dimensional model model of of Sb-VAWT. Sb-VAWT. 20D 20D

10D 10D

Figure Figure 4. 4. Computation Computation of of the the domain domain meshes. meshes.

D D

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Static Static

0.6D 0.6D 0.4D 0.4D Move Move

Static Static Interface1 Interface1 Blade Blade Interface2

Interface2

Figure 5. Rotating region mesh. Figure 5. Rotating region mesh. Figure 5. Rotating region mesh. 0.265m 0.265m

Figure 6. Mesh near blade.

Figure 6. Mesh near blade.

Figureof 6. the Mesh near From Table 1, the boundary condition inlet ofblade. numerical domain adopts the VELOCITYINLET and the mainstream wind velocity is defined as 8.0 m/s. The boundary condition of the outlet From Table 1, the boundary condition of the inlet of numerical domain adopts the VELOCITYTabledomain 1, the boundary of the inlet of numerical of From numerical employscondition the PRESSURE-OUTLET and the domain pressureadopts value the is 0 VELOCITY-INLET Pa. Other walls INLET and the mainstream wind velocity is defined as 8.0 m/s. The boundary condition of the outlet arethe setmainstream as non-sliding boundary condition as a as default setting. and wind velocity is defined 8.0 m/s. The boundary condition of the outlet of of numerical domain employs the PRESSURE-OUTLET and the pressure value is 0 Pa. Other walls numerical domain employs the PRESSURE-OUTLET and the pressure value is 0 Pa. Other walls are are set as non-sliding boundary condition as a defaultconditions. setting. Boundary set as non-sliding boundary conditionTable as a 1. default setting. Type 1. Boundary conditions. Boundary Conditions Table 1. surface Boundary conditions. BoundaryTable of inlet Velocity-inlet Boundary Conditions BoundaryType of outlet surface Pressure-outlet Boundary Conditions Boundaries ofType other outside surfaces Symmetry Boundary of inlet surface Velocity-inlet Boundaries ofinlet junction surface Interface Boundaryofof outlet surface Pressure-outlet Boundary surface Velocity-inlet Boundaries of blade surfaces Wall Boundaries ofof other outside surfaces Symmetry Boundary outlet surface Pressure-outlet Boundaries of other defaults Wall Boundaries of junction Interface Boundaries of other outside surface surfaces Symmetry

Boundaries of blade surfaces Boundaries of junction surface

Wall Interface

Since the flow field of the Sb-VAWT has a Reynolds number that is greater than the critical Boundaries ofof blade Wall Boundaries othersurfaces defaults Wall Boundaries of other defaults Wall Reynolds number, the turbulence model is used. The number of time steps of the CFD simulations is setSince as 540. (6) and the velocity of thethat blade, the timethan step the t can be theAccording flow fieldtoofFormula the Sb-VAWT hasangular a Reynolds number is greater critical expressed as: Reynolds turbulence model is used. number of timethat stepsisofgreater the CFD simulations is Sincenumber, the flowthe field of the Sb-VAWT has a The Reynolds number than the critical

set as 540.number, According Formula model (6) andisthe angular velocityofoftime the steps blade,ofthe t can be Reynolds the to turbulence used. The thetime CFDstep simulations π number t= (8) expressed as: is set as 540. According to Formula (6) and the angular 90ω velocity of the blade, the time step t can be expressed as: ππ In the wind tunnel experiments, the center (z = 0) along the blade span direction was t==surface (8) t considered to measure the pressure distribution by using the multiport pressure device during the(8) 90 ω 90ω one-cycle rotation of theexperiments, rotor. The torque and power the single blade In the wind tunnel the coefficient center surface (z = 0)coefficient along theacting bladeon span direction was are calculated by integrating the pressure distribution on the blade surface. The torque of the Sbconsidered to measure the pressure distribution by using the multiport pressure device during the one-cycle rotation of the rotor. The torque coefficient and power coefficient acting on the single blade are calculated by integrating the pressure distribution on the blade surface. The torque of the Sb-

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2018, 7 7ofof1515 Energies 2018,11, 11, FORPEER PEERREVIEW REVIEW areEnergies calculated byxxFOR integrating the pressure distribution on the blade surface. The torque of the Sb-VAWT was measured by a torque meter, and then the utilization rate of wind energy (power coefficient) was VAWT measured by aatorque meter, and then the rate (power VAWTwas wasThe measured torquepitch meter, andon then theutilization utilizationcharacteristics rateofofwind windenergy energy (power investigated. effect ofby the blade angle the aerodynamic of the Sb-VAWT coefficient) was investigated. The effect of the blade pitch angle on the aerodynamic characteristics coefficient) was investigated. The effect of the blade pitch angle on the aerodynamic characteristics could be verified scientifically via CFD simulations and wind tunnel experiments. ofofthe theSb-VAWT Sb-VAWTcould couldbe beverified verifiedscientifically scientificallyvia viaCFD CFDsimulations simulationsand andwind windtunnel tunnelexperiments. experiments. Figure 7 shows the the schematic diagram of the Sb-VAWT in wind tunnel experiments. The experiments Figure Figure 77 shows shows the schematic schematic diagram diagram ofof the the Sb-VAWT Sb-VAWT inin wind wind tunnel tunnel experiments. experiments. The The were carried out in an open test in section of circular type wind tunnel with an tunnel outlet diameter of 3.0 m experiments experimentswere werecarried carriedout out inan anopen opentest testsection sectionofofcircular circulartype typewind wind tunnelwith withan anoutlet outlet and the maximum windthe velocity was 40.0 m/s. Thewas torque meter of TS-2700 was chosen to measure diameter diameterofof3.0 3.0mmand and themaximum maximumwind windvelocity velocity was40.0 40.0m/s. m/s.The Thetorque torquemeter meterofofTS-2700 TS-2700was was the torque coefficients of the rotor. The mainstream wind velocity was 8.0velocity m/s and the bladeand pitch chosen chosentotomeasure measurethe thetorque torquecoefficients coefficientsofofthe therotor. rotor.The Themainstream mainstreamwind wind velocitywas was8.0 8.0m/s m/s and ◦ , 6◦ and 8◦ , respectively. The size ratio between the actual wind turbine and the angles were set at β = 4 the theblade bladepitch pitchangles angleswere wereset setatatββ==4°, 4°,6°6°and and8°, 8°,respectively. respectively.The Thesize sizeratio ratiobetween betweenthe theactual actual model ofturbine the wind turbine in CFD simulations wasinin 1:1. Figure 8 illustrates the correction system for wind and the ofofthe wind CFD simulations was the wind turbine and themodel model the windturbine turbine CFD simulations was1:1. 1:1.Figure Figure88illustrates illustrates thethe high-speed pressure device. More detailedpressure experimental parameters have been introduced correction system the multiport device. More experimental correctionmultiport system for for the high-speed high-speed multiport pressure device. More detailed detailed experimental inparameters the previous studies of Li et al. [10,19,24,34,35]. have been introduced in the previous studies of Li et al. [10,19,24,34,35]. parameters have been introduced in the previous studies of Li et al. [10,19,24,34,35].

Wind WindTunnel TunnelOutlet Outlet

Wind WindTunnel TunnelInlet Inlet

Pitot WirelessLAN LAN PitotTube TubeWireless Mutiport Mutiport Pressure Pressure Device Device Computer Computer Torque TorqueMeter Meter Thermometer Thermometer

Figure 7. A schematic diagram diagram of Sb-VAWTin in thewind wind tunnelmeasurement. measurement. Figure Figure7.7.AAschematic schematic diagramofofSb-VAWT Sb-VAWT inthe the windtunnel tunnel measurement.

Pressure Pressuredetector detector Pressurizer Pressurizer Tubes Tubes

Chamber Chamber

Reference ReferencePort Port Airfoil Airfoil

Figure 8.8.Calibration Calibration Figure of dynamic response inair airofof oftubing. tubing. Figure8. Calibrationof ofdynamic dynamicresponse responseinin air tubing.

Figure 99represents the distribution ofofpressure blade surface. As shown ininthis figure, Figure represents the distributionof pressuretaps tapson onthe the this figure, Figure 9 represents the distribution pressure taps on the blade bladesurface. surface.As Asshown shown in this figure, the circle represents the pressure taps on the blade surface. The pressure taps atatthe leading edge of the circle represents the pressure taps on the blade surface. The pressure taps the leading edge the circle represents the pressure taps on the blade surface. The pressure taps at the leading edge ofofthe the theblade bladewere werearranged arrangedwith withhigh highdensity. density.The Thereason reasonisisthat thatthe thepressure pressuregradient gradientofofthe theleading leading blade were arranged with high density. The reason is that the pressure gradient of the leading edge of edge edgeofofthe theblade bladewas wasgreater greaterthan thanthat thatofofthe thetrailing trailingedge edgeofofthe theblade. blade.The Thedistance distancebetween betweenthe the the blade was greater than that of the trailing edge of the blade. The distance between the pressure pressure taps is s i and the measured pressure value of each tap is P i . The value of the static pressure taps is si and the measured pressure value of each tap is Pi. The value of the staticpressure pressure taps is si and theeach measured pressure value of each tap isdirection Pi . The value of the static pressurethe point is P0 . point ofofthe pointis isPP0.0.At At eachpressure pressuretap, tap,the theangle anglebetween betweenthe the direction thepressure pressurevalue valueand and theblade blade Atchord each pressure tap, the angle between the direction of the pressure valueFand the blade chord is γi . chordisisγγi.i.The Thetangential tangentialforce forceand andthe thenormal normalforce forcefor forthe theblade bladeare are FT Tand andFFNN, ,respectively. respectively. The tangential force and the normal force for Fthe bladeexpressed are FT and F , respectively. According to the According as: Accordingtotothe thepressure pressureofofeach eachtap, tap,FFT Tand and FNNcan canbe be expressed as:N pressure of each tap, FT and FN can be expressed as: FFT == (9) (9) ( (ppi i−− pp0 0) )s is is sininγ γi i T FFTN = (9) =  ∑ ((ppii i−−−ppp000))s)sisiicsin (10) coos sγγγi ii (10) N =  ( p

FN = ∑ force (force pi −FpT0can )si cos γi (10) According be AccordingtotoEquation Equation(9), (9),the thetangential tangential FT can becalculated. calculated.And Andthen, then,the thetorque torqueofofthe the single singleblade bladecan canbe becalculated calculatedfrom fromEquation Equation(4). (4).Furthermore, Furthermore,the thepower powercoefficient coefficientofofthe therotor rotorcan can be obtained. be obtained.

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Thickness to blade Thickness to blade chordchord y/c y/c

According to Equation (9), the tangential force FT can be calculated. And then, the torque of the Energies 2018, can 11, x FOR PEER REVIEW 8 of 15can single blade be calculated from Equation (4). Furthermore, the power coefficient of the rotor be Energies obtained. 2018, 11, x FOR PEER REVIEW 8 of 15

si si γi γi

Chord length x/c Chord length x/c Figure ofpressure pressuretaps tapson onblade bladesurface. surface. Figure 9. 9. Distribution Distribution of

3. 3. Results Results

Figure 9. Distribution of pressure taps on blade surface.

3. Results Figure1010shows showsthe theresult result of of monitor monitor of pitch angle of βof=β6°. Figure of the the CFD CFDsimulation simulationatatthe theblade blade pitch angle = 6◦ . The monitored data the torque of monitor axis axis represent theβthe flow The monitored isisthe of the rotor.ofThe The horizontal axisand and vertical axis represent flow Figure 10data shows thetorque result of thehorizontal CFD simulation at vertical the blade pitch angle of = 6°. time and the rotor torque, respectively. When the time is 0 < t 0 < 0.3, the curve fluctuates irregularly. time the rotordata torque, the horizontal time is 0 the 0.8, the This shows the of computation of the CFD isWhen not convergent. time is is tphenomenon >t 0.3, thethe computation thethe CFD simulation is simulation convergent. thethe time isWhen tis> t0.8, theflow curve curve fluctuation becomes stabilized. time is t >becomes 0.3, the computation of the CFD simulation is convergent. When the time is t > 0.8, the fluctuation stabilized. As shown in Figure 11, the torque coefficients acting on the single blade computed by CFD curve fluctuation becomes As shown in Figure 11,stabilized. the torque coefficients acting on the single blade computed by CFD simulations are compared with those measured by high-speed multiport pressure device in As shown in Figure 11, the torque coefficients acting on the single blade computed bywind simulations are compared with those measured by high-speed multiport pressure device inCFD wind tunnel experiments. As shown in the figure, the fluctuation of torque coefficient acting on the single simulations are compared with those measured by high-speed multiport pressure device in tunnel experiments. As shown in the figure, the fluctuation of torque coefficient acting on thewind single blade computed by CFD simulations is in athe good agreement with the curve of the experimental tunnel experiments. As shown in the figure, fluctuation of torque the single blade computed by CFD simulations is in a good agreement with coefficient the curveacting of theon experimental measurements when the azimuth angles are . However, the curve measured by 60 ° < θ < 300 ° blade computed by the CFDazimuth simulations is in a 60 good the curve the experimental ◦ 6◦ > 4◦ 6°◦ > 4°◦ > 8° 6 > 8 > 4◦ ◦> ◦ > 44°◦ >> 88° 66° ◦>4 ◦ 4°◦ >> 88° 66° ◦> ◦ > 46°◦ >> 84° 68° ◦>6 ◦ 6°◦ >> 44° 88° ◦ > 6◦ > 4◦ 88° > 6° > 4° 8◦ > 6◦ > 4◦ 8°◦ > 6°◦ > 4° 8 > 6 > 4◦ > 66°◦ >> 88° ◦> ◦ 44°

Single blade torque coefficient CQ

4.2. 4.2.Torque TorqueCoefficient Coefficientfor forSingle SingleBlade Blade In this section, CFD simulations are are usedused to analyze the torque coefficients acting acting on the on single In this section, CFD simulations to analyze the torque coefficients the blade blade pitch angles β = 4°,are 6°,βand Then, the torque ◦ , and 8◦ , respectively. singlewhen bladethe when the blade pitchare angles = 4◦8°, , 6respectively. Then,coefficients the torque obtained by the CFD simulations the wind tunnel experiments areexperiments compared atare thecompared blade pitchat coefficients obtained by the CFDand simulations and the wind tunnel angle of β =pitch 6°. The torque actingcoefficients on the single bladeon are calculated by Equation (5). The the blade angle of β coefficients = 6◦ . The torque acting the single blade are calculated by tangential force F T in Equation (5) is obtained by the pressure value acting on the blade surface. As Equation (5). The tangential force FT in Equation (5) is obtained by the pressure value acting on the shown in Figure the in three curves have a little difference in difference the upstream region, while the blade surface. As 13, shown Figure 13, the three curves have a little in the upstream region, difference the downstream region is even fewer. Whenfewer. the azimuth angles are around = 30° and while the in difference in the downstream region is even When the azimuth anglesθare around 180°, the curves present two wave troughs and the values of which are both negative. When the ◦ ◦ θ = 30 and 180 , the curves present two wave troughs and the values of which are both negative. azimuth angle is around θ = 100°, the torque coefficient acting on the single blade achieves the When the azimuth angle is around θ = 100◦ , the torque coefficient acting on the single blade achieves maximum value at the pitchpitch angle of βof = 6° the minimum value at the pitch angle of the maximum value at blade the blade angle β =and 6◦ and the minimum value at blade the blade pitch angle βof= β8°.= When the azimuth angle is around θ = 260°, the blade has the maximum torque coefficient ◦ ◦ 8 . When the azimuth angle is around θ = 260 , the blade has the maximum torque coefficientatat the theblade bladepitch pitchangle angleof ofββ==8°8◦and andthe theminimum minimumtorque torquecoefficient coefficientatatthe theblade bladepitch pitchangle angleof ofββ==6°, 6◦ , which are consistent with the results of the pressure distribution on the blade surface. The torque which are consistent with the results of the pressure distribution on the blade surface. The torque coefficients acting on the single blade at the blade pitch angles of β = 4°,◦ 6°,◦ and 8° ◦reach the maximum coefficients acting on the single blade at the blade pitch angles of β = 4 , 6 , and 8 reach the maximum values at the upstream region of around θ = 100°◦and reach the minimum values in the downstream values at the upstream region of around θ = 100 and reach the minimum values in the downstream region of around θ = 200°.◦ region of around θ = 200 .

Azimuth angle θ (°) Figure obtained from CFD Figure13. 13.Torque Torquecoefficients coefficientsacting actingon onthe thesingle single blade blade obtained CFD simulations simulationsat atdifferent different pitchangles anglesof ofββ==4°, 4◦6°and , 6◦ and8°8,◦respectively. , respectively. pitch

4.3. Power Coefficient for the Wind Turbine Sb-VAWT is an energy conversion device, for which the power coefficient is the core of all design parameters. This section discusses the influence of the blade pitch angle on the power coefficient

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4.3. Power Coefficient for the Wind Turbine Energies 2018, 11, 1514

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Sb-VAWT is an energy conversion device, for which the power coefficient is the core of all design parameters. This section discusses the influence of the blade pitch angle on the power coefficient based on on the the torque torque meter meter measurements measurements and and the the CFD CFD simulations. simulations. In this paper, paper, because because both both wind wind based tunnel experiments experiments and CFD simulations only involve the energy conversion of the rotor, rotor, the the power power tunnel coefficient is is estimated estimated purely purely on on the the basis basis of of aerodynamics. aerodynamics. However, since since the the power power coefficients coefficients coefficient measured by by the the torque torque meter meter in in wind wind tunnel tunnel experiments experiments do do not not exclude exclude energy energy loss resulting resulting from from measured the mechanical mechanical structure, structure,the the results results are are smaller smaller than than those those calculated calculated by by CFD CFD simulations. simulations. The The power power the coefficientsobtained obtainedbyby CFD simulations are calculated by Equation (7), in the which theis torque is coefficients CFD simulations are calculated by Equation (7), in which torque obtained obtained from the Section previous Section 4.2. from the previous 4.2. As shown in coefficients calculated by by CFD simulations can agree well well with As inFigure Figure14, 14,the thepower power coefficients calculated CFD simulations can agree thosethose measured by thebywind tunneltunnel experiments at lowattip speed ratio (λ < 1.50), the power with measured the wind experiments low tip speed ratio (λ