1-s2.0-S0167610515000136-main

Experimental and numerical investigation of a three-dimensionalvertical-axis wind turbine with variable-pitch

M. Elkhoury a,n, T. Kiwata b, E. Aoun a

a Mechanical Engineering, Lebanese American University, PO Box 36, Byblos, Lebanonb Mechanical Engineering, Kanazawa University, Kakuma-machi, Kanazawa-shi 920-1192, Ishikawa, Japan

a r t i c l e i n f o

Article history:Received 10 September 2014Received in revised form11 January 2015Accepted 11 January 2015Available online 14 February 2015

Keywords:Vertical-axis wind turbineLarge eddy simulationVariable-pitchWind tunnel experiments

a b s t r a c t

A combined experimental and numerical investigation is carried out to study the performance of a microvertical-axis wind turbine (VAWT) with variable-pitch. Three-dimensional numerical simulations areessentially employed, for the VAWT involves a low aspect ratio (AR) three straight blades with struts. Theperformance of the VAWT is experimentally measured using a wind tunnel, while large eddy simulation(LES) with dynamic smagorinsky subgrid scale (SGS) model is employed to help understand theassociated flow structure. The effects of wind speed, turbulence intensity, airfoil shape, and strutmechanism with and without variable-pitch on the performance of the turbine are carefully assessed,both experimentally and numerically. The accuracy of the SGS model in predicting the laminarturbulent transition is also examined.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Wind turbines have been historically known to be mounted inopen rural areas. However, in recent years, there has been anincreasing interest in the deploying these turbine in urban areas.The chief objective is to generate energy on site thereby cuttingcables cost and reducing transmission loses (Mertens, 2006).Horizontal axis wind turbines (HAWTs) have long been utilizedin large-scale wind farms, for they are known to be more efficientthan VAWTs in steady winds. Small scales HAWTs have also beenincreasingly implemented in built environments. However, variousrecent studies have shown that VAWTs perform better in urbanareas when compare to HAWTs (Mertens, 2006; Ferreira et al.,2007; Hofemann et al., 2008; Stankovic et al., 2009). Theseadvantages are mainly due to various reasons, the most importantof which is the VAWTs ability to function in a multidirectionalflow of wind that could continuously change in residential areas.Unlike HAWTs, VAWTs do not need a yaw control mechanism andrespond instantly to change in wind speed and direction, which inturn makes them more efficient in turbulent flow regions.

In recent decades there has been a substantial increase in theuse of computational fluid dynamics (CFD) to depict performanceof VAWTs. This has been mainly driven not only by the increase inavailability of user-friendly CFD software and relatively affordable

computational cost, but also by the complexity of flow structuresassociated with VAWTs. Performance of a three-blade windturbine has been recently investigated using 2-D CFD by Dai andLam (2009) who compared results against experimental data at asingle TSR value. 2-D CFD simulations were also performed for astraight-bladed Darrieus-type cross flow marine turbine by Lain(2010) and favorably assessed their findings against experimentsof Dai and Lams (2009) however, at a single TSR value. Danao et al.(2014) studied the influence of unsteady incoming wind on theperformance of a 2-D VAWT. Mesh independent solution by meansof Richardson Extrapolation method, Grid Convergence Indexmethod, and the fitting method, was recently investigated for a2-D VAWT by Almohammadi et al. (2013). Nobile et al. (2014)carried out a 2-D CFD investigation of an augmented VAWT thatinvolved omnidirectional stator located around the VAWT. Theyreported an increase of around 30 to 35% in torque and powercoefficients.

Elkhoury et al. (2013) assessed the influence of various turbu-lence models on the performance of a straight-blade VAWTutilizing a 2-D CFD analysis. With similar experimental andcomputational setup to the currently considered test cases, over-estimations of power coefficients were predicted by fully turbulentmodels, a scenario that was deemed to be due to laminarturbulent transition. Lanzafame et al. (2014) compared predictionsof classical fully turbulence models to those of the SST transitionmodel (Menter et al., 2006) for a VAWT utilizing a 2D CFD solver.McLaren et al. (2012) successfully performed a 2D UnsteadyReynolds-Averaged Navier-Stokes (URANS) CFD simulation of asmall-scale high solidity wind turbine. Scheurich and Brown

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Journal of Wind Engineeringand Industrial Aerodynamics

http://dx.doi.org/10.1016/j.jweia.2015.01.0040167-6105/& 2015 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: 961547262.E-mail addresses: [email protected] (M. Elkhoury),

[email protected] (T. Kiwata), [email protected] (E. Aoun).

J. Wind Eng. Ind. Aerodyn. 139 (2015) 111123

www.sciencedirect.com/science/journal/01676105www.elsevier.com/locate/jweiahttp://dx.doi.org/10.1016/j.jweia.2015.01.004http://dx.doi.org/10.1016/j.jweia.2015.01.004http://dx.doi.org/10.1016/j.jweia.2015.01.004http://crossmark.crossref.org/dialog/?doi=10.1016/j.jweia.2015.01.004&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.jweia.2015.01.004&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.jweia.2015.01.004&domain=pdfmailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.jweia.2015.01.004

(2013) used the vorticity transport model to investigate perfor-mance and wake dynamics of different VAWT configurations insteady and unsteady wind conditions.

Studies considered previously were all bounded by 2D simula-tions utilizing 2D flow models, many of which were performed at aspecific TSR with scarce experimental data that are essential tovalidate the models. These recently accomplished studies do notaccount for connecting rods that tend to have considerableinfluence on the performance of a VAWT. This important featurecannot be neglected at high TSR (Elkhoury et al., 2013), not tomention blade-rod interference that arises at low TSR. Further-more, flow over turbines with low AR blades departs from the 2Dbehavior as blade tip effects become significant, rendering theflow three-dimensional.

To address these limitations, this work capitalizes on suchaspects and aims at building a credible 3D CFD model that closelypredicts the experimental results. Within this framework, theeffects of incoming freestream velocity, turbulence intensity, fixed-and variable-pitch mechanism, and airfoil shape on the powercoefficient of the turbine are carefully assessed. LES is employed asthe complexity of the flowfield represented by high solidity andlow AR. In addition, the interference among the three blades issubstantial and would be affected further by the presence of thecentral shaft and the connecting four-bar linkage mechanism,necessitating a 3-D modeling approach. Furthermore, the abilityof LES with dynamic SGS model to predict separation inducedtransition associated with dynamic stall at relatively low TSRs isexamined. It is worth noting that any future attempt to improvethis novel design of VAWTs should be facilitated by the use of 3DCFD simulations.

2. Variable-pitch mechanism and experimental system

A 3-D overview of the wind turbine with a variable-pitch anglemechanism is depicted in Fig. 1. The turbine had a diameter of0.8 m and a height (blade span) of 0.8 m. The turbine had threestraight blades each was connected to the rotors center by threemain circular rods with a diameter of 0.02 m each. The pitch of thethree straight-blade rotor varies by means of a four-bar linkagemechanism, the top view of which is shown in Fig. 1b.

The pitching axis for the variable-pitch mechanism was locatedapproximately at 15% of the chord from the leading edge. Thismechanism has an eccentric rotational center which is differentfrom the main rotational point as shown in Fig. 2. Thus, thismechanism is able to vary blade pitch angle p, which is the angle

between the blade chord line (i.e., blade-link lc) and a perpendicularline to the main-link, without actuators. This mechanism is able tomake an arbitrary selection of the blade offset pitch angle c (i.e., anaverage of the change of blade pitch angle) and the blade pitch angleamplitude w by combinations of the link length. The blade offsetpitch angle c decreases with increasing length of the second link ls.The blade pitch angle amplitude w increases with increasing lengthof the eccentric-link le. The angle between the main link lm and theeccentric link le is the blade azimuth angle , and p is the anglebetween the eccentric-link and the wind direction. The averageamplitude of the blade angle of attack for p1201 is larger thanthat of the wind turbine of fixed-pitch blade while the variation ofblade angle of attack for p01 is smaller than that for p1201.Therefore, an optimum blade angle of attack could be maintained atall azimuthal angles, improving the performance of the VAWT.

The equations governing the motion of the pitch-angle in eachquadrant are given as follows

p =2

for 0oo, and p =2

foroo2, where

cos 1 d2 lm2 le2

2dlm

!; cos 1 d

2 lc2 ls22dlc

!1

Fig. 1. A 3-D overview of the modeled wind turbine (a) isometric view of the rotor (b) top view of the rotor.

Fig. 2. Schematic diagram of the variable-pitch angle mechanism.

M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015) 111123112

For p =2 for 0, and p =2 for where

cos 1 lc2 lm le 2 ls2

2lc lm le

!; cos 1 lc

2 lm le 2 ls22lc lm le

!

2

Experiments were performed in a large-scale open-circuit typewind tunnel, with a square test section of 1.2 m1.2 m and a1.4 m long working section. A schematic diagram of the apparatusis depicted in Fig. 3. The turbulence intensity level and flow non-uniformity at a wind speed of 6 m/s in the working section wereless than 0.8% and 71.8%, respectively. Two freestream velocityvalues of 6 and 8 m/s were employed corresponding to Reynoldsnumbers of Re8.002103 and Re1.067104, respectively. Theperformance of the wind turbine with three different airfoilsections, namely, NACA 0018, NACA634-221, and NACA 0012 wasmeasured in the present experiments. All utilized blades had achord of C0.2 m and were made of aluminum monocoque withthin wall thickness of 0.5 mm. Table 1 summarizes the consideredVAWT specifications.

A three-phase induction motor (Mitsubishi Electric, SB-JR2.2 kW 4 P) accompanied by a variable-frequency inverter (Hita-chi, SJ200) was used to drive the turbine. Thus the behavior of thepower coefficient, Cp, could be easily observed at different TSRs by

varying the frequency of the motor. In order to calculate the powercoefficient, the torque and rotation speed of the turbine weremeasured in each case using a torque transducer (TEAC TQ-AR5Nwith a rated capacity of 5 N m) and a digital tachometer (ONOSOKKI HT-5500). The wind speed in the working section wasmeasured using a Pitot tube and a thermal anemometer (KANO-MAX, Climomaster model 6531).

3. Computational set-up and numerical approach

3.1. Components of simulated VAWT

Effects of connecting rods cannot be neglected especially forTSRs 41 (Elkhoury et al., 2013). Thus, to account for theirinfluence, it was necessary to undertake a 3-D approach. However,the modeled rotor had simpler mechanisms/connections than thatused in the experimental setup. This in turn will substantiallyimprove the mesh quality and as a result accelerate convergencewith minimal influence on the accuracy of the results. Themodeled rotor had 3 straight blades with matching dimensionsto the experimental setup, resulting in an AR of 4. 3-D effectsmanifested at the blade tip cannot be neglected for such a low AR,creating another incentive for the 3-D approach. The blades werelinked to the shaft through 9 straight cylindrical rods; 2 of whichsupport every blade. The rotors shaft had a diameter of 5 cm. Therods on another hand had diameters ranging from 1.0 to 1.5 cm.Finally, the blade was connected to the main crank at 0.25c as wasthe case in the experiment.

3.2. Computational domain

The 3-D investigation of the VAWT necessitates the partition-ing of the computational domain into three regions: blade domain,rotor domain, and wind tunnel domain. The blade domain is amoving domain, engulfed by the rotor domain which is alsorotating. The rotor domain is encapsulated inside the wind tunneldomain as depicted in Fig. 4.

Fig. 3. Schematic diagram of the experimental apparatus.

Table 1Turbine specifications.

Turbine diameter D 800 mmBlade span h 800 mmBlade chord length c 200 mmAirfoil section NACA 634-221

NACA 0018NACA 0021

Number of blades N 3Main-link lm 373 mmSecond-link ls 365 mmEccentric-link le 16 mmBlade-link lc 85 mmSolidity 0.75Aspect ratio AR 4

M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015) 111123 113

3.3. Outer domain

This fixed domain represents the bulk of the fluid surroundingthe VAWT. The dimensions of this domain were carefully con-sidered, in order to allow for sufficient clearances around theVAWT, making sure that there was no interference caused by theboundaries. Thus, the width was chosen to be 11 times the

diameter of the rotor. The inlet boundary was placed 3 rotordiameters upstream of the rotor, and the pressure outlet boundarywas situated 16 rotor diameters downstream of the rotor. Thelatter considerations are necessary to provide enough space for thegeneration of the wake behind the rotor. As for the height of thedomain, it was chosen to be more than twice that of the wingspan. This again is due to the fact that we need to provide enoughclearance for the produced vortices at the blades tips, whichcontribute to the induced drag. Dimensions of the domain that areshown in Fig. 5 however, are not drawn to scale.

As for the boundary conditions, the inlet boundary was assignedan inlet velocity according to the simulated case (6 m/s or 8 m/s) andthe turbulence intensity was set equal to the experimental value of0.8%. Turbulence intensity is set at the inlet boundary and is definedas I u0=V1 which is a ratio of the root mean square of the turbulentvelocity fluctuations and the mean Reynolds averaged velocity. Thepressure outlet was assigned a value of 0 Pa, which stands for thevalue of the pressure of air at the exit of the outer domain. The otherfour boundaries surrounding the VAWT were assigned a symmetryboundary condition. A Boolean operation was carried out to removecylindrical shape, which represents the rotor domain, from the outerdomain. An interface boundary conditionwas set at these surfaces, toensure the continuity of fluid flow into the rotor domain. Anunstructured tetrahedral relatively coarse mesh was used in thisdomain as there is no intricate fluid interaction that needs to bemonitored. A conformal mapping was necessary at the interface, forthe sizing of elements in that region should match the sizing of the

Fig. 4. Outer, rotor, and blade domains of the VAWT with the specified boundaryconditions.

Fig. 5. Plane views of all three domains with the specified dimensions.


elements in the adjacent rotor domain. Otherwise, the convergenceof the solution was adversely affected.

3.4. Rotor and blade domains

As mentioned earlier, the rotor and blade domains were movingdomains. This was necessary in order to simulate the rotation of theVAWT embedded within these two domains. The cylindrical rotordomain contained the shaft and the rods of the turbine. A rotationalspeed was specified around the z-axis for this domain and variedaccording to the tip speed ratio being studied. An unstructured meshwas chosen as it suits fluid applications with irregular geometries.The mesh was made finer in this region as the influential elements ofthe VAWT were being approached. The rods and shaft were treatedwith fine face sizing and inflation layers to accurately capture flowvariations within the boundary layer. Furthermore, a no-slip bound-ary condition was set for all rods and shafts. An interface is assignedat the contact surfaces with the wind tunnel and the blade domains.The blade domains consisted of three cylindrical domains thatengulfed the blades. Blade domains were created through Booleanoperations by subtracting the three cylinders from the main cylind-rical rotor domain. The variable pitch mechanism, in which theblades tend to rotate around two axes, was the main motive behindchoosing to separate the blade domains from the rotor domain. Thefirst rotation was set around the z-axis with a specified rotationalspeed , while the other took place around an axis passing through25% of its chord length with a pitching angle related to the azimuthalangle as given by Eqs. (1) and (2). These equations were fed into thesolver and were necessary in guiding the bladesmotion. Thus, it wasextremely important to center the blade at 0.25c inside this domainfor any error in the placement would yield different angle of attacksthan those intended throughout the rotation. In addition, having thethree blade domains provided a simpler method to control the griddensity and quality in the most important region of the field studied.

The finest unstructured mesh amongst all regions was in thisdomain. The blades were treated with special sizing functions andinflation layers to accurately resolve near-wall flow structures. How-ever, the airfoils trailing edge provided a more complex geometry andthe inflation function adversely affected the quality of the mesh. Toremedy this problem, fine sizing functions were used at the edges andfaces of the blade. In such a situation, a trade-off problem arisesbetween the quality of the grid and the number of elements that canbe conceded without reaching an unrealistic computational time lateron. Another interface boundary condition was set at the interfacebetween surfaces of the outer and the rotating domains. Finally, a wallboundary condition was assigned to the faces of the blades.

3.5. Flow solver

ANSYS Fluent, a commercial CFD solver, was utilized to solve theequations of motion. An unsteady implicit coupled pressure baseddouble precision solver was employed. A second order upwind-baseddiscretization scheme was selected for all flow variables whereasbounded central difference discretization scheme was employed forLES simulations with variable Smagorinsky coefficient. The filteredincompressible NavierStokes equations can be summarized by

uixi

0uit xj uiuj

1 pxi2ui Sijxj 3The subgrid scale stress term, Sij is written in terms of eddy

viscosity, t as

Sij 2tSij13kkij 4

where Sij is the strain rate and t is evaluated using dynamicSmagorinsky model (Germano et al., 1991). The second-orderinterpolation scheme was used to calculate cell-face pressures.

The modified Menter turbulence model (Elkhoury, 2011) wasused initially at the beginning of each simulation for the first twoblade rotations, after which LES was set to take over. Acquisition ofdata started after the elapse of the first three full blade rotations,which was necessary to eliminate any transient effects. Time-averaged solution of flow fields was obtained by averaging flowvariables at a sampling interval that is equal to the chosen timestep. A maximum of 60 iterations per time step was allowedbefore the solver proceeded to the next time step; however, about15 to 20 iterations on average were necessary to converge. Aconvergence criterion of 1103 of scaled residuals of all flowvariables was obtained before proceeding to the next time step.

4. Validation of CFD model

4.1. Grid dependency study

Mesh density/quality may have a substantial influence on theCFD results. Thus, to ensure grid independent results and yet avoidprohibitive computational cost, simulations were carried out usingthree different mesh resolutions: coarse, medium, and fine. Solu-tions were deemed grid independent when negligible differencewas achieved in the average power coefficients of at least twoconsecutive meshes. Comparisons among the forgoing threemeshes were made for the NACA 0018 fixed-pitch mechanism ata wind speed of 8 m/s and TSR of 1. This case was selected becauseit relatively requires tolerable computational cost as lower TSRsinvolve massive flow separation and thus require more iterationsper time step to converge. Fig. 6 depicts the instantaneous powercoefficient vs azimuthal angle for a complete rotation post thetransient startup of the turbine.

10 and 16 layers of inflation prisms were placed in theboundary-layer with the first grid node set at y of 3106 mand 2.1106 m off the surface for the medium and the highdensity meshes, respectively, resulting in values of y that close toone on all three blades and connecting mechanisms. These valuesare further reduced over the first two consecutive rotations usinggrid adaptation techniques.

Fig. 6. Effect of grid size on the accuracy of the solution at TSR1.


A geometric expansion ratio of 1.2 was employed, resulting inprisms that contributed to about 18 and 22% of the total number ofcells for the fixed and variable pitch mechanisms, respectively. Therest of the domain was composed of a combination of pyramidsand tetrahedron elements. Table 2 details the grid-resolutionstudy along with corresponding values of y for the consideredNACA 0018 test case. For all forthcoming cases, assessments aremade based on the results of the finest employed mesh. A top viewof the coarse size mesh in which a cut is taken at a chordwiselocation near mid plane, showing mesh layout and concentrationof nodes, is depicted in Fig. 7. All values of y reported in Table 2belong to the NACA 0018 test case at a TSR of 1.0.

4.2. Time dependency study

Two simulations were carried out in order to determine howthe time step affects the turbine power coefficient. The objective isto use a large time step that guarantees the lowest computationaltime without compromising the accuracy of the results. The studywas run for the NACA 0018 with wind speed of 8 m/s at a TSR of1 at two different time steps corresponding to t0.00157079and t0.00078535. These values correspond to the time neededto rotate 2/300 and 2/600, respectively. The results of theinstantaneous power coefficients are plotted in Fig. 8 for both ofthese time steps post the transient startup of the turbine. It can beseen that the results are extremely close and thus utilizing thelarger t does not decrease the accuracy of the predicted results.Hence, a time step based on 2/300 degree is adopted for all tipspeed ratios throughout the present work.

5. Results

The inflow angle of the tail vane (eccentric angle p) was set tozero in both the experiments and the numerical simulations. Themodeling of p along with Eqs. (1) and (2) were employed inFluent utilizing the user defined scalars/functions (UDS/UDF). It isworth mentioning that the power coefficient as measured in theexperiment includes the power loss due to pitching motion ofblades (inertia moment of blades), and excludes the bearings lossof the main shaft. On the contrary, the numerical study accountsonly for the losses of the main and the second links.

It should be noted that solidity plays a major role in dictating theTSR at which the turbine reaches its maximum power coefficient.Turbines attaining their maximum efficiency at TSR between 2 and3 showed maximum power coefficients of less than 30%. Given thehigh solidity of the present turbine, as well as its low AR, it isexpected that its maximum Cp values to be even lower. Low solidityturbines are conventionally used for low torque, low speed opera-tions whereas high solidity turbines are used for high torque, low

Table 2Considered grids for the NACA0018 fixed-pitch mechanism at TSR1 and incomingwind speed of 8 m/s.

Grid Name Number of cells (106) Model y

1 Coarse 5.647 LES 0.87682 Medium 11.960 LES 0.95403 Fine 15.371 LES 0.6478

Fig. 7. A plane view of the overall domains showing the rotating core of the three-straight blades along with near surface grid clustering.

Fig. 8. Effect of time step on the accuracy of the solution at TSR1.


speed operations. The later scenario is of interest in the presentdesign as relatively low velocities minimize vibration response dueto turbine imbalance. This in turn maximizes the turbine longevitywhile producing acceptable power output.

In the following subsections the effects of wind speed, airfoilshape, connecting rods, and incoming turbulent intensity on theperformance of the VAWT are assessed. It is worthwhile tomention that only five points at TSRs of 0.25, 0.5, 0.75, 1.0, 1.25,and 1.5 were numerically simulated for each of the considered testcases as the computational cost was substantially excessive. Forinstance, it took about 38 h for the medium density mesh tocomplete one full rotation using parallel computing of 6 cores onIntel Xeon E5 2.6 GHz processors. In the best case scenario, aminimum of five full rotations were necessary to confidentlypredict a single averaged power coefficient value. These six valuesare designated by symbols, whereas the experimental data pointsare connected together via a third order spline function.

5.1. Effect of wind speed

The power coefficient of a VAWT increases with an increase inthe tip speed ratio and reaches a peak, after which it takes a dip aslarger tip speed ratios are attained. To shed some light on thisbehavior, the angle of attack is assessed for tip speed ratios of0.5 and 1.5 as depicted in Fig. 9. It can be clearly evident that theblade throughout its motion concedes much smaller angles ofattack at higher tip speed ratios. This in turn causes the blades togenerate more lift as they operate for a longer period in theenvelope that produces higher lift. On the contrary, at lower tipspeed ratios, the blades operate for a longer period at very highangles of attack. Thus stalling occurs, which eventually leads to flowseparations and vortices formation that are convected downstream.These vortices interact with the blades downstream and hampertheir lift generation. At high tip speed ratios, the role played by therods becomes more imminent as drag builds up. Consequently, thisresult in an adverse effect on the power coefficient since lift createdin by the blade is desired while the drag of the connecting rodstends to slow down the motion of the turbine.

The effect of freestream velocity on the power coefficient for afixed-pitch NACA 0018 is shown for a wind speed range of 610m/s in Fig. 10. The predictions of LES compare very favorably withcorresponding experimental findings for wind speeds of 6 m/s and8 m/s. This close agreement clearly indicates that connecting rods

are appropriately accounted for in the numerical model. Further-more, it is evident that for wind speeds Z8 m/s results of theexperimental data fall very close to each other. It is worth notingthat the discrepancy between numerical and experimental datawas computed using the normalized mean square error (NMSE).The maximum error took place at a TSR of 0.5 with values of1.562% and 9.387% for the 6 m/s and 8 m/s, respectively.

The lift generation of the blades depends on the Reynoldsnumber which in turn depends on the speed. To a certain extent,lift generation increases with the increase in Reynolds number.However, the highest power coefficient curve, with a maximumvalue of 0.21 at a TSR of 1.3, was noticed at the smallest windspeed of 6 m/s. This could be related to the Reynolds numberassociated with complex flow physics that may well involvelaminar separation transition, a scenario encountered byElkhoury et al. (2013) on a similar test case. URANS models arenot capable of capturing this flow feature as they are verydissipative in nature and usually results in over predicting theperformance of the turbine. Therefore, as a result of this laminarseparation transition it could be deduced that the increase in dragoutweighs the increase in lift for NACA0018 airfoil for wind speedsbetween 8 and 10 m/s, a phenomenon that does not occur at alower velocity of 6 m/s for this airfoil. A similar behavior however,to a lesser extent is also noticed by the experimental data asdepicted in Fig. 11. The largest Cp distribution for the fixed-pitch

Fig. 9. Variation of angle of attack vs azimuthal angle for two tip speed ratios of0.5 and 1.5 at p01.

Fig. 10. Average power coefficient vs tip speed ratio for a fixed-pitch, NACA 0018, atthree different freestream velocities.

Fig. 11. Average power coefficient vs tip speed ratio for a fixed-pitch, NACA 634-221, at three different freestream velocities.


NACA 634-221 blade occurs for the freestreamwind speed of 4 m/safter which experimental values collapse very well at 8 m/s and10 m/s. Given these similarities in Cp distribution at 8 and 10 m/sfor the NACA0018 and the NACA 634-221 blades, it was deemednumerically cheaper to carry out the simulations at the lowerwind speed of 8 m/s. In addition, this wind turbine is intended forurban use and therefore, wind speeds of 10 m/s or above would berarely encountered.

5.2. Effect of airfoil shape

Thickness and camber of the airfoil were altered in order toassess the influence of these characteristics on the performance ofthe VAWT. The effect of the former on the power coefficient isdepicted in Fig. 12 for the NACA 0018 and the NACA 0021 airfoilsections. The comparison was made on a fixed-pitch mechanism ata wind speed of 8 m/s. Aside from the thickness all variables wereheld the same for both cases. Conventionally, the third and fourthdigits of a four digit NACA airfoil resemble the maximum thicknessas a percentage of the chord, located at 30% of the chord lengthmeasured from the leading edge. Hence, NACA 0021 is 3% thickerthan NACA0018. When thickness is increased, the radius ofcurvature at the leading edge is also increased. This in turn allowsfor milder changes in pressure leading to better stall character-istics. This is clearly verified by both the experimental and thenumerical results as the power coefficient of the NACA 0021 isconsistently higher than that of the NACA 0018 for all tip speedratios. Thinner airfoils tend to perform better when used withlower solidity turbines at high TSRs (43.0) (Dai and Lam, 2009).Increasing the thickness is usually beneficial for strengthening theblades structure which is subject to fatigue as the forces acting onit fluctuate during a complete revolution of the turbine. Accordingto the NMSE, the maximum discrepancy between the computa-tional and the experimental data was found to be 9.22% for theNACA 0018 and 2.04% for the NACA 0021 airfoil at a TSR of 0.5 forboth cases.

The camber effect is assessed through the comparison of thesymmetric 4-digit NACA 0021 and the laminar cambered 6-digitNACA 634-221 airfoils. Both airfoils have a thickness ratio of 21%and were compared with variable-pitch mechanism at an incom-ing wind speed of 8 m/s. The experimental results of the powercoefficient show little difference between the two airfoils asdepicted in Fig. 13. The NACA 0021 exhibits a slightly higher Cpvalues at tip speed ratios between 1.0 and 1.25. The results of theLES are in good agreement with the experiments as they clearlyshow lower Cp values for the NACA 634-221. It is worth noting that

the effect of camber did not show any improvement on the self-start of the turbine. The maximum NMSE between the computa-tional and the experimental data was found to be 10.15% for theNACA 0021 and 7.81% for the NACA 634-221 airfoil, both of whichoccurred at a TSR of 1.5.

5.3. Blade vortex interaction

Complex flow structures evolve around the blades of a VAWTundergoing dynamic stall at high angles of attack and low TSR.Dynamic stall is characterized by large recirculation separatedflow regions with the formation of vorticies that are shed down-stream and may impinge on other rotating blades in the down-wind half as will be depicted shortly. As a result of this bladevortex interaction, this turbine produces power at low TSR, a traitthat is missing in turbines with low solidity. This serves as anothermotive behind the selection of present turbine.

To shed some light on the complex flow structures associatedwith low TSRs, consider the vorticity contours on a plane that cutsmid through the turbine blades of a variable-pitch with NACA634-221 at TSR 0:5 as shown in Fig. 14. Not only interaction offlow structures can be notice at this low TSR but also the variousstages involved through dynamic stall at different azimuth angles.Attached flow is observed between an azimuthal angle of 901 and1601. Leading edge vortex begins to roll up around 1701 andcontinues to grow while remaining intact until 2401. For this rangeof azimuthal angles, the trailing edge vortex gets detached at firstand convected downstream. Afterwards, an elongated vortexforms and rolls towards the surface of the blade as can beobserved at 2251 in Fig. 14. Then the leading edge vortexbreaks up into small patches as a result of the leading/trailing edgevortex interaction which can be clearly noticed at 2701 inFig. 14. At 2901 the formation of a new leading and trailingedge vorticies are observed. The trailing edge vortex detachesaround 01 and gets convected downstream. Again, an elon-gated vortex forms at the leading edge and rolls up towards thesurface of the blade as can be observed at 3451 in Fig. 14. Theinteraction between these two vorticies takes place around 201and starts to form negative and positive concentrated patches thatare well noticed at 301. At 651 the trailing edge vortex getsshed downstream and a new vortex begins to develop and expandalong with the leading edge vortex. A large scale vortex interactionis observed between an azimuthal angle of 601 and 901. Finally, theflow reattaches to the blade surface and the same vortex dynamicsstarts over in a new cycle.

Fig. 12. Average power coefficient vs tip speed ratio for a fixed-pitch-angle, NACA0018, and NACA 0021, at a freestream velocity of 8 m/s.

Fig. 13. Average power coefficient vs tip speed ratio for a variable-pitch-angle,NACA 0021, and NACA 634-221, at a freestream velocity of 8 m/s.


Considering the selected instantaneous vorticity fields depictedin Fig. 14, it is evident that all wakes generated by the bladeslocated upwind (901oo2701) are convected towards the topright quarter. These flow structures not only interact with theblades but also with the shaft (as seen to the right of the figure) todegenerate into unsteady vortices.

5.4. Effect of variable-pitch

The effect of variable-pitch on the performance of the VAWT isassessed against that of the fixed-pitch mechanism. The variation inthe angle of attack with azimuthal position for fixed- and variable-pitch turbine as well as the adjustment made by the variable-pitchmechanism is depicted in Fig. 15. Moreover, the adjustment made bythe variable-pitch mechanism modifies the angle of attack in order tofit into an envelope that enhances the lift, and thus the generatedpower. A comparison of power coefficient vs TSR between fixed-and variable-pitch is depicted in Fig. 16. The utilized airfoil ofthe considered VAWT is the NACA 0018 at a wind speed of 8 m/s.The power coefficient at all TSRs below 1.5 shows significant increasewith variable-pitch mechanism. However, the peak in the powercoefficient takes place at a lower TSR than that of the fixed-pitch,suggesting that the losses due to the moving mechanism is larger thanthat of the fixed, and is evident by the steep decrease in Cp values forTSRs 41.1. LES predicts the same remarkable increase in the powercoefficients and matches to a large extent the experimental data witha slightly under predicted value at TSR 1:0, inferring that slidingmesh approach is sufficiently accurate to model a high solidity VAWTwith variable-pitch mechanism. Thus, the maximum NMSE was8.856% for the fixed-pitch and 9.61%for the variable-pitch at TSRs of0.5 and 0.75, respectively.

Instantaneous contours of pressure coefficient on a plane thatcuts midway through the VAWT are shown in Fig.17. Thesecontours are compared for fixed- and variable-pitch NACA 0018turbine at TSR 1:0. This TSR was chosen for it belongs to alocation at which large difference in power coefficient betweenfixed- and variable-pitch is observed. A comparison betweenfixed- and variable-pitch blade orientations is shown in the leftside of Fig. 17. This slight orientation difference is sufficient tocause larger areas of negative pressure coefficient around theblades as opposed to those observed with the fixed-pitch shown inthe right side of Fig. 17. The increase in the power coefficient of the

Fig. 14. Instantaneous vorticity field on a mid-plane of a variable-pitch-angle VAWT, with NACA 634-221, at TSR 0:5, showing different azimuthal angles .

Fig. 15. Variation of angle of attack vs azimuthal angle for a tip speed ratio of 1.5,c121, w 7101, and p01.

Fig. 16. Average power coefficient vs tip speed ratio for a fixed- and a variable-pitch-angle, NACA 0018, at a freestream velocity of 8 m/s.


variable-pitch VAWT is, to a large extent, due to this rise innegative pressure coefficient.

Another test case of a fixed- vs variable-pitch mechanism,however, for a thicker NACA 0021 airfoil is shown in Fig. 18. Againas was the case with the NACA 0018, the power coefficient of thevariable-pitch is higher than that of the fixed-pitch with a peakthat occurred slightly earlier, however, drops to a lower value thanthat of the fixed-pitch at TSR 41:35. A quick comparison betweenboth considered variable-pitch airfoils reveals that the VAWT withthe thinner airfoil achieves a higher CPMAX value and continues tohave a higher aerodynamic performance at high TSRs past CPMAX.Thinner airfoils tend to perform better because the proposedvariable-pitch mechanism improves flow characteristics by redu-cing the time during which the blade stalls. It is worth noting thatthe effect of variable-pitch mechanism had a positive influence onthe self-start of the turbine, where the self-start velocity droppedfrom 3 m/s for the fixed- to 2.5 m/s for the variable-pitch mechan-ism. Comparisons between experimental and computational datareveal a maximum NMSE of 8.81% for the fixed-pitch and1.05% forthe variable-pitch at TSRs of 0.25 and 1.5, respectively.

5.5. Effect of connecting rods

The NACA 0018 airfoil at a wind speed of 8 m/s was used toassess the impact of connecting rods on the performance of theVAWT. The power coefficient of a fixed-pitch mechanism withnine connecting rods along vs a rod-free three-blade turbine isdepicted in Fig. 19. The effect of strut drag and shaft interferencehas a great influence on Cp with increasing TSR, and becomes moreimportant at TSRs41.0. The influence of the rods on the powercoefficient as a function of TSR could be better understood byplotting the difference of the two Cp curves of Fig. 19. Anotheranalytical/empirical solution to quantify the contribution of rodscould be approximated utilizing the following drag coefficientequation for cylinders (White, 1991), which is valid up to the dragcrisis ReD 250;000

Cdrod 110Re2=3D

5

The velocity at which the ReD is evaluated is the normalvelocity relative to a rod, which is based on the average rigidbody rotation of a rod R=2

and upstream velocity component

Vrod R=2V1 sin . The contribution of Eq. (5) is directlyadded to or subtracted from the power coefficient based on the

sign of R=2V1 sin . The loss due to connecting rods, here-after referred to as Cploss, is depicted in Fig. 20 for both ofapproaches. The discrepancy between both solutions is mostlydue to strut interference that the analytical/empirical approachdoes not account for. It is obvious that any attempt at modeling the

Fig. 17. Instantaneous pressure coefficient through mid-plane of a fixed- and variable-pitch angle VAWT, with NACA 0018, at TSR 1:0.

Fig. 18. Average power coefficient vs tip speed ratio for a fixed- and a variable-pitch-angle, NACA 0021, at a freestream velocity of 8 m/s.

Fig. 19. Average power coefficient vs tip speed ratio for a fixed-pitch-angle, NACA0018, with and without connecting rods, at a freestream velocity of 8 m/s.


present VAWT without accounting for rods renders the solutioninaccurate.

Contours of vorticity field on a plane that cuts through theupper connecting rods for fixed-pitch NACA 0018 are shown in theleft side of Fig. 21, while the right side is for a rod-free simulationat TSR 1:5. By close inspection of Fig. 21, it is clearly evident thatstrut blade interference is not substantial as vorticity field adjacentto turbine blades is minimally affected by the presence of the rods.Therefore, 3-D numerical simulations with variable-pitch mechan-ism could be carried out without physically modeling the con-necting mechanisms that could be accounted for analytically usingEq. (5). It is worth noting that strut blade interference is present atlow TSR however, this effect could be neglected as shown inFig. 19. At this high TSR, static stall is apparent by the presence ofamplified vorticity contours adjacent to the surface of the blades.These vortices are shed behind forming a wake structure that iscaught by the following blade, an interaction that is clearly seen inboth vorticity fields of Fig. 21.

5.6. Effect of incoming turbulence

As the experiments were carried out at a low turbulenceintensity level of 0.8%, velocity fluctuations at the inlet boundarycondition were neglected, and thus it was assumed that instanta-neous velocity components are set equal to their mean velocity

equivalents. In order to rule out the effect of time-dependent inletvelocity fluctuations on the solution, the vortex method (Matheyet al., 2003) was used where turbulence is imposed via 2-Dperturbations that are added to the inlet mean velocity profile.The previously solved fixed-pitch VAWT with NACA 0018 airfoiland incoming wind speed of 8 m/s was chosen to carry out thiscomparison.

A turbulence intensity level of 0.8% as specified in the experi-ment was set at the inlet with 190 specified vorticies. Thesevorticies are formed through particle discretization and convectedrandomly downstream. Turbulent length scale of 0.0028 m wasspecified according to l 0:07Dh, where Dh is the hydraulicdiameter of the honeycomb openings of the settling chamber inthe wind tunnel. As depicted in Fig. 22, LES results showed almostno difference in the power coefficients between the two simula-tions. This is due to the fact that the vortices created at the inletwould have died out by the time they reach the turbine. Therefore,such a low level of turbulence at the inlet with or without imposedperturbations has not effect on the predicted LES results.

6. Concluding remarks

Wind tunnel experiments accompanied by LES were success-fully carried out for a VAWT with variable-pitch straight blades to

Fig. 20. Losses in power coefficient due to connecting rods for the fixed-pitchNACA 0018 airfoil at a freestream velocity of 8 m/s.

Fig. 21. Instantaneous vorticity field on a plane that cuts through the upper rods of a fixed-pitch-angle VAWT, with NACA 0018, at TSR 1:0, showing the effect ofconnecting mechanisms.

Fig. 22. Average power coefficient vs tip speed ratio for a fixed-pitch-angle, NACA0018, at a freestream velocity of 8 m/s, and various inlet boundary conditions.


assess the effect of wind speed, airfoil shape, and variable-pitchmechanism on the performance of turbine. Understanding theimpact of these parameters is crucial and should be employed infutures ventures to improve the functionality of VAWTs. Majorfindings emerging from the study may be summarized as follows:

(a) LES with dynamic Smagorinski coefficient was able to accu-rately predict the performance of VAWT with fixed- andvariable-pitch mechanism. The sliding mesh technique wasused in the modeling of the variable-pitch mechanism.Although some eccentric links lc and le were not modeled alongwith the inertial effect of the blades, the approach deemed to besufficiently accurate with a maximum NMSE of 10.15%. In themajority of the cases, the maximum NMSE was noticed either ata low TSR or at a high TSR. This in turn reflects the challenges ofaccurately capturing complex flow physics associated withdynamic stall at low TSRs as well as correctly accounting forthe connecting mechanism at high TSRs.

(b) Experimental and numerical findings revealed that thicker airfoilstend to perform better for the considered fixed-pitch VAWT withhigh solidity ratio. This is mainly due to the better stall character-istics thicker airfoils inherit. The NACA 0021 and NACA 634-221airfoils were compared to assess the effect of camber on theperformance of the turbine. It was found that the symmetric airfoilhad a slightly better performance at TSRs corresponding to highestCp values without a noticeable effect on the self-start of the VAWT.

(c) The considered four-bar-linkage variable-pitch mechanismshowed superior performance compared to its counterpartfixed-pitch VAWT. Unlike with the fixed-pitch mechanism, thethinner airfoil, NACA 0018, resulted in better performance thanthat obtained with the NACA 0021 at high TSR 41.0. This wasattributed to the benign envelope of angles of attack withinwhich the variable-pitch mechanism operates. The self-start ofthe VAWT with variable-pitch mechanism exhibited a lowerstart-up speed compare to that of the fixed-pitch turbine.

(d) It was found that the contribution of the connecting rods can onlybe neglected at low TSRs as their impact on the power coefficientincreases exponentially with increasing TSR. Furthermore, bladestrut interactionwas found to be minimal at high TSRs. This in turnalleviates the necessity to model complex strut mechanisms byaccounting for their contribution using analytical approaches. Theeffect on incoming turbulence manifested by imposed velocityfluctuations on the mean velocity components at the inlet wasassessed. Results were insensitive to inlet velocity perturbationsprovided that experimental turbulence intensity and length scalevalues were not altered.

(e) Highest power coefficient distribution curves were noticed inthe experiments at low wind speeds of 6 m/s and 4 m/s for thefixed-pitch NACA0018 and NACA 634-221 airfoils, respectively,after which experimental values collapse very well for higherwind speeds. This is thought to be related to the complex flowphysics that may involve laminar separation transition atrelevant Reynolds numbers, a point that deserves furtherinvestigation in future studies. LES with dynamic Smagorinskiwas capable of capturing this variation in the power coefficient.

Nomenclature

AR aspect ratio of blade (h/c)Cd drag coefficientCp turbine power coefficient (T/RhV3)CPMAX maximum pressure coefficientc blade chord lengthD turbine diameter

Dh hydraulic diameterh blade span lengthI turbulence intensity (u0/V1)l turbulent length scalelc blade link lengthle eccentric link lengthlm main link lengthls second link lengthN turbine rotational speedn number of bladesp filtered pressureR turbine radiusRe Reynolds numberSij strain rate tensorT turbine torqueTSR tip speed ratio (R/V1)u0 root mean square of the turbulent velocity fluctuationui filtered velocity componentV1 wind speedy dimensionless wall distance geometrical angle of attackc blade offset pitch anglep blade pitch anglew blade pitch angle amplitude azimuth angle (angle between the main-link and x-axis)p eccentric angle (angle between the eccentric link and x-

axis) air density turbine solidity (nc/2R) laminar kinematic viscosity subgrid turbulent viscositySij subgrid scale stress tensor turbine angular velocity (2N/60)

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Experimental and numerical investigation of a three-dimensional vertical-axis wind turbine with variable-pitchIntroductionVariable-pitch mechanism and experimental systemComputational set-up and numerical approachComponents of simulated VAWTComputational domainOuter domainRotor and blade domainsFlow solver

Validation of CFD modelGrid dependency studyTime dependency study

ResultsEffect of wind speedEffect of airfoil shapeBlade vortex interactionEffect of variable-pitchEffect of connecting rodsEffect of incoming turbulence

Concluding remarksNomenclatureReferences

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