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Renewable Energy 35 (2010) 1043–1051

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Renewable Energy

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Effects of stator vanes on power coefficients of a zephyr vertical axis wind turbine

K. Pope a,*, V. Rodrigues a, R. Doyle a,b, A. Tsopelas a, R. Gravelsins a, G.F. Naterer a, E. Tsang c

a University of Ontario Institute of Technology, Faculty of Engineering and Applied Science, 2000 Simcoe Street, Oshawa, Ontario, L1H 7K4, Canadab Dalhousie University, 1360 Barrington Street, Halifax, Nova Scotia, B3J 1Z1, Canadac Zephyr Alternate Power Inc., 80 East Humber Drive, King City, Ontario, L7B 1B6, Canada

a r t i c l e i n f o

Article history:Received 21 February 2009Accepted 11 October 2009Available online 5 November 2009

Keywords:Wind energyVertical axis wind turbine

* Corresponding author.E-mail addresses: kevin.pope@mycampus.uoit.ca

mycampus.uoit.ca (V. Rodrigues), rob.doyle@dal.camycampus.uoit.ca (A. Tsopelas), rob.gravelsins@uonaterer@uoit.ca (G.F. Naterer), etsang@zephyrpower.c

0960-1481/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.renene.2009.10.012

a b s t r a c t

In this paper, numerical and experimental studies are presented to determine the operating performanceand power output from a vertical axis wind turbine (VAWT). A k-3 turbulence model is used to perform thetransient simulations. The 3-D numerical predictions are based on the time averaged Spalart-Allmarasequations. A case study is performed for varying VAWT stator vane (tab) geometries of a Zephyr verticalaxis wind turbine. The mean velocity is used to predict the time averaged variations of the power coeffi-cient and power output. Power coefficients predicted by the numerical models are compared for differentturbine geometries. The predictive capabilities of the numerical model are verified by past experimentaldata, as well as wind tunnel experiments in the current paper, to compare two particular geometricdesigns. The numerical results examine the turbine’s performance at constant and variable rotor velocities.The effects of stator vanes on the turbine’s power output are presented and discussed.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the adverse environmental impact and non-renewablesupplies of fossil fuels, worldwide efforts have turned towardsrenewable energy sources, particularly wind power, to meet thegrowing demand for electricity. Today, renewables (includingnuclear power) supply about 18% of the global energy needs [1].Through government incentives such as Ontario’s Standard OfferProgram, the expansion of wind power by many private industriesis growing rapidly. Although wind power dates back to ancienttimes, numerous technological advances over the past few decadeshave significantly reduced the costs of extracting energy from thewind.

Although wind power has been predominantly derived fromlarge centralized installations, there is a significant opportunity toincrease capacity by smaller scale, distributed generation.Producing power where it will be used can reduce installation andland costs, with little or no transmission expense. Currently, mostwind power systems consist of horizontal axis wind turbines(HAWTs), in mid to large-scale wind farms. These conventionalturbines are often favored due to higher efficiency, but they are notnecessarily suitable for all purposes. Horizontal axis turbines

(K. Pope), viren.rodrigues@(R. Doyle), alex.tsopelas@

it.ca (R. Gravelsins), greg.om (E. Tsang).

All rights reserved.

require sustained wind velocities to efficiently generate power. Inan urban setting, the wind is always changing speed, and thedirection is rarely uniform. In these conditions, vertical axis windturbines (VAWTs) can be more effectively harnessed withincomplex urban terrains to significantly increase the capacity ofsmall-scale wind power generation. Mertens [2] recommendedthree urban locations for VAWT placement. Locating it betweendiffuser shaped buildings can improve the aerodynamic efficiencyof the turbine. Placing a wind turbine in a duct through a buildingcan use the pressure difference between the windward andleeward sides of the building for power generation. Also, a turbineon top or alongside a building will be exposed to higher windspeed areas close to the building.

Placing a wind turbine in an urban setting exposes it to signif-icant turbulence in its operating conditions. Rohatgi et al. [3]investigated the effects of wind turbulence and atmosphericinstabilities on wind turbine performance. Densely populatedurban centers have unstable conditions because cities act like heatsources for the atmospheric air above. Decreased shear over therotor diameter can be achieved by placing the turbine in lowturbulence conditions. However it is generally not helpful to powergeneration since a stable atmospheric condition normally coin-cides with lower wind speeds. For complex terrain, Botta et al. [4]reported that fatigue loads on HAWTs can be increased by up to75%, when placed in regions of high turbulence and changing winddirection. Similarly, small wind turbine loading increases by about25% when placed in complex terrains, compared with stable windconditions [5].

Nomenclature

A vertical area of VAWT (m2)Cp power coefficientD diameter (m)F force (N)H height (m)_m mass flow rate (kg/s)

Qevs equi-size skewr!0 distance to origin of rotating system (m)

�sr viscous stress (N/m2)R rotor radius (m)S area of mesh element (m2)u!r whirl velocity (m/s)v!r relative velocity (m/s)

v! absolute velocity (m/s)V wind velocity (m/s)W turbine width (m)

Greek3 surface roughness (m)h efficiencyq stator angle (degrees)l tip speed ratiom dynamic viscosity (Ns/m2)r air density (kg/m3)s stator vane spacing (m)u! angular velocity relative to a stationary frame (rad/s)U rotary speed (rad/s)

K. Pope et al. / Renewable Energy 35 (2010) 1043–10511044

When the change of wind direction is not considered in theoverall operating conditions, the performance of wind turbinesunder turbulent conditions does not necessarily decrease. Theeffects of different levels of inlet turbulence intensity were exper-imentally investigated by Zhang et al. [6]. Changing the turbulenceintensity from 0.9% to 5.5% or 16.2% had little effect on the turbineperformance. In icing conditions, turbulence affects the heattransfer and input power needed for de-icing. Wang et al. [7]reported that the average Nusselt number for a wind turbine bladeis smaller than a flat plate and cylinder at the same Reynoldsnumber. This occurs due to differences between the turbulentboundary layer behaviour after the transition point. The authorsobserved that no systematic trend, relating the Nusselt and Rey-nolds numbers, occurred with varying liquid water content [8].

Computational fluid dynamics (CFD) is a useful design tool forwind power analysis. A large number of simulations can be per-formed, analyzed and optimized without investing in physicalconstruction of many turbines with different geometrical configu-rations. Using CFD simulations, the torque and pressure on the rotorcan be predicted. These can then be used to predict the turbine’spower coefficient. There are several CFD methods in the literatureto predict wind turbine performance. One method is the MultipleReference Frame model (MRF), which uses a time averaged solutionto determine the turbine performance. It has been used frequentlyin wind power simulations to determine the power curves andperformance of horizontal axis wind turbines [9].

Past studies have shown that numerically predicted results fora 2-D rotating rotor compare better to experimental data thanpredictions with a stationary rotor [10], due to the assumption offlow separation at the blade tips [10]. The Navier-Stokes equationswere used with a rotating reference frame to simulate the airmotion. Additional studies also found this technique gave accuratepredictions of the blade forces [11]. Three-dimensional effects canlead to discrepancy with 2-D predictions [12]. Cochran et al. [13]used a 2-D sliding mesh formulation to examine Savonius turbineperformance with a stator cage. A Reynolds stress 5-equationturbulence model was used and the optimal tip speed ratio (TSR)was predicted, with the use of a sliding mesh formulation torepresent the rotor rotation [13]. The sliding mesh model iscomputationally intensive, particularly for complex geometriesand it is generally limited to 2-D predictions. For a VAWT,particularly those with a stator cage, the power output can behighly erratic throughout each rotation. The sliding mesh model istime-dependent and it represents the rotor-stator interaction,thereby proving useful when predicting the turbine performancein 2-D simulations.

VAWTs could expand wind energy generation by utilizing anurban resource, where traditional horizontal axis wind turbinescannot operate well. Because of the attractive aesthetics of thisturbine, it can be integrated into the design of buildings ina commercial, industrial or dense urban area, to produce power foronsite use. This would reduce demands on the electrical grid andenvironmental impact of the building design. VAWTs are omni-directional, which negates the need for a yawing mechanism. Thispaper investigates the aerodynamic performance of a new type ofVAWT for urban applications (see Fig. 1), called a Zephyr verticalaxis wind turbine (ZVWT). This turbine has a unique design thatincludes stator vanes with reverse winglets (also called stator tabs).The design has a high degree of solidity, which can limit the tur-bine’s peak performance in strong winds. However, VAWTs witha higher degree of solidity have other performance advantageswhen operating at a lower TSR [14]. In particular, the effect of thetabs on turbine performance will be explored in this paper. Vali-dation of the numerical predictions will be performed throughcomparisons against wind tunnel measurements. Wind tunnelexperiments are presented in this paper to further examine thenumerical model’s predictions of turbine performance with/without the stator vanes.

2. Numerical formulation of air flow

In this section, two fluid flow formulations will be presented: (1)a Multiple Reference Frame (MRF) model, whereby the rotorreference frame rotates with respect to the inertial frame, and (2)a moving grid transient formulation. For the second model, theoverall domain is divided into two sub-domains; a stationary statordomain and a rotor sub-domain that rotates. Commercial softwareFLUENT 6.3.26 [15] is used for the CFD simulations. The solutiondomain and mesh discretizations are generated with GAMBIT 2.4.6[16]. The governing equations, boundary conditions and solutionformulations will be discussed in this section.

The governing equations are given by the incompressible formof the Navier-Stokes equations. A time averaged turbulence solu-tion is developed. This introduces several turbulent stresses intothe solution. Due to the approximations needed to solve theturbulent stress equations, many different models have beendeveloped in the past. Each method offers different advantages forthe operating conditions under which it was developed [17]. Thenumerical predictions solve a rotating frame adaptation of thegoverning Navier-Stokes equations. The governing equations forfluid flow include the following conservation of mass (1) andmomentum equations (2).

Fig. 1. Zephyr vertical axis wind turbine prototype – (a) illustration and (b) geomet-rical variables.

K. Pope et al. / Renewable Energy 35 (2010) 1043–1051 1045

vr

vtþ V$r v!r ¼ 0 (1)

v

vtðr v!rÞ þ V$ðr v!r v!rÞ þ rð2 u!� v!r þ u!� u!� r!Þ

¼ �Vpþ Vsr þ F!

(2)

The conservation of momentum contains two accelerationterms that represent the rotation. These include the Coriolisacceleration, defined as 2 u!� v!r , and the centripetal accelerationdescribed by u!� u!� r!. In these equations, r!is the radial positionfrom the origin of the rotating domain, u! is the angular velocity ofthe rotor domain, v!r is the relative velocity, p is the static pressure,�s is the stress tensor and F

!refers to external body forces [15]. A

mixed formulation of cylindrical and Cartesian coordinates is usedto simulate the two separate regions of the domain, i.e., rotatingrotor-stator section and external incoming flow, respectively. Thevelocity at the inlet of the domain is specified as a constant and the

pressure at the exit is estimated at standard atmospheric pressure.Standard wall functions are used to represent the stator walls, rotorblades, and outer boundary walls in the solution.

The 3-D Multiple Reference Frame model is utilized for compar-isons against the experimental results. To account for the highsolidity and wind tunnel blockage, the numerical model is scaled tothe same size (1/5 scale) as the experimental setup, and placed ina domain with boundaries at the same distance from the VAWT asthe wind tunnel. The formulation uses 3 sub-domains, includinga wind tunnel domain, stator domain, and the rotor domain. Aboveand below the rotor and stator are walls, while the other cylindricalfaces in contact with the other domains are defined as interfaces.This simulates flow through the turbine. The wind tunnel domainand stator domain are kept stationary, while the reference frame ofthe rotor domain rotates at variable rotational speeds to representthe rotor motion. A setback with this formulation is it does notaccount for the rotor-stator interaction, because all calculations arebased on one rotor position. The model uses an absolute velocityformulation around the interfaces between the sub-domains toprovide approximate values of velocity throughout the domains.

A Spalart-Allmaras model is used for turbulence effects on theMRF predictions. The Spalart-Allmaras model is a one-equationmodel for the eddy viscosity. The transport variable, ~v, is identical tothe turbulent kinematic viscosity, except in the viscous-affectedregions near the boundary walls:

v

vtðr~vÞ þ v

vxiðr~vuiÞ ¼ Gv þ

1s~v

24 v

vxj

(�mþ r~v

� v~v

vxj

)þ Cb2r

v~v

vxj

!235

� Yv þ S~v

(3)

where Gv is the turbulent viscosity production and Yv is theturbulent viscosity destruction that occurs in the near-wall region,s~v and Cb2 are constants and v is the molecular kinematic viscosity.The turbulence viscosity ratio is defined as the ratio of turbulentviscosity ðmtÞ to molecular viscosity ðmÞ as follows,

Turbulent viscosity ratiohmt

m(4)

The hydraulic diameter relates to the size of large eddies presentin the turbulent flow. Turbulent eddies are restricted by the size ofthe wind tunnel, since they cannot be larger than the tunnel whenthe flow is fully developed [15].

The 3-D MRF numerical formulation uses the following modelsand parameters: finite volume method with a segregated solver,steady state, standard wall functions for near-wall treatment, wallroughness height of 0, pressure-velocity coupling by PRESTO [14].In the next section, a comparison of CFD results with experimentaldata will be outlined. To allow this comparison, the majority ofwind speeds simulated are obtained from the experimental testconditions. Since the experimental model uses freely movingturbine blades, as opposed to a constant rotational speed, a changein the specification of parameters is necessary. The wind speedsand rotational speeds in the CFD models correspond to thoseobtained in the wind tunnel.

Another formulation in this paper is a 2-D transient, sliding meshformulation. For this model, the overall domain is divided into twosub-domains (see Fig. 2 for sample mesh discretization). The rotorsub-domain rotates with respect to the stationary stator sub-domain.This formulation allows cells adjacent to the boundary between thesub-domains to slide relative to one another, thus allowing for tran-sient predictions of the rotor interaction with the flow field, createdby the stationary stator blades. To provide the appropriate values of

Fig. 2. Sample 2-D mesh discretization of the VAWT - a) rotor, b) stator and surroundingsub-domain.

K. Pope et al. / Renewable Energy 35 (2010) 1043–10511046

velocity for each sub-domain, a continuity of absolute velocity isenforced at the boundary. This formulation requires that the fluxacross the boundary between sub-domains is computed with the cellfaces at the boundary misaligned. Thus, new interface zones aredetermined at each timestep. Each cell face is converted to an interiorzone. The resulting overlap between opposing interior faces producesa single interior zone. Therefore, the number of faces at the boundarywill vary with each timestep [15].

A standard k-3 model is used to predict turbulence effects in thetransient predictions. This model can achieve better accuracy thanthe 1-equation Spalart-Allmaras model. The k-3 model is widelyused and able to simulate many different flow regimes. Its twoequations below are written in terms of the turbulent kineticenergy, k, and dissipation rate, 3, as follows,

v

vtðrkÞþ v

vxiðrkuiÞ¼

v

vxj

"�mþmt

sk

�vkvxj

#þGkþGb�r3�YMþSk (5)

v

vtðr3Þ þ v

vxiðr3uiÞ ¼

v

vxj

"�mþ mt

s3

�v3

vxj

#þ C13

3

kðGk þ C33GbÞ

� C23r32

kþ S3 (6)

In this model, Gk represents the generation of turbulent kineticenergy due to mean velocity gradients, Gb is the generation ofturbulent kinetic energy due to buoyancy, and Ym represents thecontribution of the fluctuating dilatation to the overall dissipationrate. The variables sk and s3 are the turbulent Prandtl numbers for kand 3, with values of 1.0 and 1.3, respectively. The constants C13 and

C23 are C1e¼ 1.44 and C23¼ 1.92. The turbulent eddy viscosity, mt, iscalculated by combining k and 3 such that mt ¼ rCmk2=3, where Cm isa constant 0.09 [15].

The model requires values of turbulence intensity and turbu-lence viscosity ratio. The turbulence intensity (I) is defined as theratio of the root-mean-square of the velocity fluctuation (u) to themean freestream velocity (uavg), described as follows,

Ihu0

uavg: (7)

A turbulence intensity of 10% is assumed at the velocity inlet [18]and the turbulent viscosity ratio is assumed to be 1 [19]. At thepressure outlet, a backflow turbulence intensity of 12% is assumed toaccount for the increased turbulence created by the turbine inter-action [17]. The backflow turbulence viscosity ratio is also assumedto be 1. Other features of the solution parameters include a SIMPLEpressure-velocity coupling, second order implicit unsteady formu-lation, and a second order upwind scheme for turbulent kineticenergy and turbulence dissipation rate predictions. This numericalformulation will be used to predict air flow through the turbine andsubsequently improve its performance.

3. Experimental wind tunnel study

An experimental prototype of a Zephyr vertical axis windturbine (ZVWT) was altered to construct a 1/5th scale model withtwo particular design modifications, on a rapid prototype machine.The drive shaft protrudes through the anchor point and it isattached to a DC generator. This generator is connected to a variableload and a set of multi-meters for measurement. The wind speed isvaried by adjusting the rotary speed of the wind tunnel fan. Themeasurement method is an adaptation of a previous systemdescribed by the Automatic System for Wind Turbine Testing [20].A data acquisition method is used, with an electric motor togenerate power. The system includes two multi-meters, variableresistor, and a DC electric alternator. The rotating turbine is coupledwith an elastic belt to the motor to generate electricity, poweringa resistor of 0.8 Ohms. Two multi-meters are connected to thecircuit to measure the voltage across the resistor and current flow,thereby allowing for the calculation of the turbine power coeffi-cient. Voltage and current readings have a resolution within�0.005 V and �0.005 mA, respectively. At any wind speed, thevoltage and current vary over a small range. However, the multi-meters average the values over a short time and display the resultsin addition to the real-time measurement. An optical tachometermeasures the rotational frequency of the turbine rotor blades.

The wind tunnel apparatus is a Flotek 1440 [21]. The unit hasa testing area of dimensions 12 inches wide by 12 inches high by 36inches long. The fan is located at the downstream end to generatethe air flow. Control of the wind tunnel allows repeatability towithin�0.25 m/s. This causes a variation of tip speed ratio between0.02 and 0.05. The power output is determined with multi-metersto measure the voltage and current from the generator, after whichpower in the circuit is calculated. The TSR is measured by an opticaltachometer to measure the rotary speed of the turbine.

Testing was also performed to determine losses in the motorand pulley drive train. To calculate the losses in the setup, the drivetrain was doubled using two motors/generators, 4 pulleys and 2belts. One motor drives the system and the second generatespower. By measuring the power drawn by the first motor and thepower produced by the second, the efficiency of the system wascalculated. A set of batteries supplied power to the system. Thepower drawn by the motor was calculated by measuring thevoltage across the leads of the motor and the current flowing

K. Pope et al. / Renewable Energy 35 (2010) 1043–1051 1047

through the circuit. The motor was coupled to a 5/16th inch shaft,the same diameter as the turbine rotor shaft, by two pulleys anda belt. The shaft was then attached to a second identical motor inthe same way. The power output was again measured. The inputvoltage was varied using two and then three batteries. This appa-ratus effectively doubles the drive train used in the turbine tests,therefore the losses were approximately double that of the turbinetests. Using this information, the efficiency of the motor drive traincould be determined.

Since the apparatus is double the actual power train, the effi-ciency of one half of the system is the square root of the totalefficiency. This can be understood by considering each half, withthe drive motor to the shaft and the shaft to the generator asseparate systems, where the efficiency of both systems connectedin series is the product of the efficiencies of the individual systems,ht ¼ h1$h2. Since each system is the same, their efficiencies shouldbe equal and the product is h2

1 ¼ h22 ¼ ht . The efficiency of the

drive train was found to be 45%. The power input made a significantdifference in the calculated efficiency. When the input voltage isincreased from 1.2 V to 2.0 V, the efficiency decreases by 3%. Theoutput voltage and current for both supply voltages are within therange of values measured during the turbine tests, so the averageefficiency is a reasonable estimate of the conditions in the turbinetests. The test setup efficiency is determined to be 38.5%. Thesystem is more efficient at lower power levels, which suggests thatthe operating efficiency of each motor/generator unit differsslightly when the generator is operating at a reduced input power.There are additional sources of experimental error.

The effects of scaling on the experiments are formulated by theBuckingham Pi theorem [22]. The overall problem can be repre-sented by 8 variables, described by 3 dimensional units, so 5 pifactors are required (see Table 1). The dimensionless coefficients arethe relative roughness (3/D), geometric scaling (H/D), ReynoldsNumber (rVD/m), TSR (UD/V), and a non-dimensional force coeffi-cient (F/D2V2r).

Re ¼ rVDm

(8)

Matching the Reynolds number between simulations andexperiments ensures that the ratio of inertial and viscous forcesremain the same. Also, the 3-D MRF formulation is scaled to matchthe dimensions of the experimental prototype. This set of simula-tions was validated by reproducing the experimental conditions,such as matching the wind velocities and tunnel dimensions, torepresent the wall blockage effect.

4. Results and discussion

In this section, results from the numerical and experimentalstudies will be presented. For the 3-D mesh, the space above andbelow the rotor is neglected, to allow larger elements to be created.Two geometries are represented, one with the stator tabs and

Table 1Variables in dimensional analysis.

Variable Actual value Model value Units

Force – Measured NDensity 1.225 1.225 kg/m3

Dynamic viscosity 1.82� 10�5 1.82� 10�5 Ns/m2

Velocity 12 Calculated m/sDiameter 1 1/5 mHeight 1 1/5 mSurface roughness – – mRotary speed 1 Measured rad/s

another with tabs removed. The full-scale turbine height (H) anddiameter (W) are both 0.762 m, with a rotor radius (R) of 0.302 m.The stator spacing (s) and angle (q) are 0.266 m and 45�, respec-tively. The rotor and wind tunnel grids are used in all simulations,while two stator meshes are developed for comparison purposes.Two 3-D discretizations are created for each geometry: a full scalemodel and a 1/5th scale model. The domain is discretized with anunstructured tetrahedral mesh [23]. The quality of the mesh will becharacterized by the Equi-Size Skew (Qevs), defined as

Qevs ¼�Seq � S

�Seq

(9)

where S is the area of the mesh element, and Seq is the maximumarea of an equilateral cell of identical circumscribing radius to thatof the mesh element. A null Qevs describes an equilateral element,while a Qevs value of 1 describes an element that is completelydegenerate [16]. A large number of skewed elements would resultin a highly inaccurate model. The number of elements and skew-ness of each sub-domain is presented in Table 2. At this resolution,the results showed grid independence of the results [24].

Predictions are made using both constant and varying rotationalspeeds of the turbine to examine the change in performance of theturbine. One of the main practical objectives of the simulations is todetermine the significance of the stator tabs. A comparison ofconstant and variable speeds could yield insight into the turbine’sperformance with different operational characteristics. Deter-mining the performance of the turbines at constant speed is valu-able, as any power generation device connected to the electricitygrid needs to operate at constant speed. The predicted optimalrotational speed is used for the simulations of the full size models.Five times the rotational speed is required for simulations of the 1/5th scale models. The increased rotational speed maintainsa constant TSR between the full size and 1/5th scale models. Eachmodel is operated at a variety of wind speeds to investigate how thechange in velocity affects power generation.

A rotational speed of 17 rad/s is maintained for the full scalemodels, while the rotational speed for the 1/5th scale model is85 rad/s. To determine the power generation, the moment (M) isrecorded at the bottom of the rotor where the shaft is connected andmultiplied by the rotor speed (U). The power coefficient is calculatedby CP ¼ MU=0:5rAV3, where r and A are estimated to be 1.225 kg/m3 and 0.581 m2, respectively. Comparing the coefficient ofperformance with TSR, the peak for the tabular design occurs ata TSR of about 0.39. With the constant operational speed, thiscorresponds to a wind speed of 12.5 m/s. However, the no-tab designhad a peak at TSR of 0.45, corresponding to a wind speed of 10.8 m/s.Both characteristic curves can be correlated by the followingquadratic curve fits (predicted by the 3-D MRF formulation):

Tabs : Cp ¼ �0:5285l2 þ 0:4422lþ 0:0059 (10)

No tabs : Cp ¼ �0:5674l2 þ 0:5225lþ 0:002 (11)

Table 23-D mesh discretizations.

Sub-domain Total number ofelements

Most skewedelement

Skewed range:0.9–0.97

Skewed range:0.8–0.9

Tunnel 448,690 0.7708 0 0Rotor 387,960 0.9320 6 33Stator

(tabular)419,965 0.9424 27 911

Stator(withouttab)

606,244 0.9458 21 859

0

0.03

0.06

0.09

0.12

0 0.2 0.4 0.6 0.8

λ

CpWith tabs full size (constant load)

With tabs 1/5th scale (constant load)

With tabs 1/5th scale (variable load)

No tab full size (constant load)

No tab 1/5th scale (constant load)

No tab 1/5th scale (variable load)

Fig. 3. MRF power curves with variable scaling, loading and geometry.

Table 32-D mesh discretizations.

Sub-domain Total number ofelements

Most skewedelement

Skewedrange: 0–0.1

Skewed range:0.1–0.2

Rotor 13,617 0.5971 13,191 330Stator

(tabular)92,378 0.5665 90,214 1,758

Stator(withouttab)

92,056 0.5469 90,278 1,508

0.12

With tabs

K. Pope et al. / Renewable Energy 35 (2010) 1043–10511048

A peak in efficiency at a lower wind speed is useful information,since locations of lower speeds may become more suitable. Whencomparing the 1/5th scale model with the full size model, thecurves are almost identical, which supports the notion that verticalaxis wind turbines are highly scalable. When comparing the 3-DMRF tabular design with the results of the 2-D sliding mesh tabulardesign, the peak occurs at about the same point. The general curveis slightly lower due to the end effects that are represented by the3-D model.

Variable rotational speed operation is investigated with the 3-D1/5th scale models. One of the limitations of the multiple referenceframe model is a free spinning turbine cannot be fully simulated.Although the simulation measures the forces acting upon it, it doesnot react to the forces. Therefore, the rotational speed is deter-mined by the measured rotational speed from the experimentalmodel. With a variable rotational speed, the no-tab modeloutperforms the tabular model. The coefficient of performance ofthe turbine under these conditions is illustrated in Fig. 3. Thetabular design has a predicted maximum power coefficient of 0.098at a TSR of 0.43, which corresponds to a wind velocity of 12.9 m/s.This compares well with the constant rotational speed results.

For the 2-D transient predictions, the simulation is initially con-ducted for 2000 timesteps with a timestep size of 0.008776 s. The

Fig. 4. Time varying plot of the moment coefficient.

resulting 1.76 s allows four complete rotor revolutions to becompleted. This ensures that a time periodic state is achieved (seeFig. 4). The moment coefficient is defined as the moment divided by1=2rV2AL, where r, V, A, and L are the wind density, wind velocity,effective area of the turbine, and the length, respectively. These valueswere explicitly specified from the inlet conditions, with a density of1.225 kg/m3, velocity of 12.5 m/s, area of 1 m2, and a length of 1 m.The results show a clearly defined time periodic trend. Next, themodel is advanced for 500 more timesteps. This allows one morecomplete rotor revolution with data saved every 10 timesteps. Fromthe results, the transient predictions of performance are obtained.

For each 2-D simulation, the rotor starting position is maintainedconstant. The blade (identified as rotor 1 in Fig. 2) is used for allsingle blade comparisons. Fig. 2 shows the initial angular position ofthe rotor blade mesh relative to the stator sub-domain. The rotorsub-domain is removed and enlarged for clarity. For these simula-tions, the overall domain is discretized into triangular elements. Theskewness and number of elements of each sub-domain is presentedin Table 3. Grid sensitivity studies indicated that the solutionconverges to a power coefficient of 0.09. The selected mesh has anaverage discretization area of 2.191 cm2, resulting in 105,995 totalcells. Comparing this grid to one with an average discretization areaof 2.754 cm2 reveals a percent error of 1.9%.

The results of the 2-D sliding mesh formulation show transientplots of the turbine performance. These plots are useful for deter-mining the maximum cutoff limits, fatigue stresses and averagepower output of the turbine. The transient formulation providedcomparable results to the 2-D MRF formulation. The predicted Cp withthe sliding mesh formulation was 0.111 (a 13.3% error compared to the2-D MRF prediction). Similar to the 3-D time averaged predictions, the

-0.12

-0.06

0

0.06

0 120 240 360

Angular position (degrees)

Pow

er (

kW)

No tabs

Fig. 5. Comparison of transient power output for a single rotor blade.

K. Pope et al. / Renewable Energy 35 (2010) 1043–1051 1049

results from the 2-D transient numerical model predict a decreasedperformance with the tabular length design. Fig. 5 illustrates that thepower output of the geometry with no stator tabs has a higher poweroutput throughout the majority of each rotor blade revolution. Thus,the presence of the stator tabs does not offer an aerodynamicadvantage and does not change the shape of the transient curves ina significant way. Although the tabular geometry exhibits the bestpower through the first 120� of the rotation, the following 240� ofrotation has lower performance than the no-tab design.

Fig. 6. VAWT a) tabular contour plot shaded by the static pressure (Pa) and b)

The predictions of the transient analysis provide useful results ofvelocity vectors and pressure contours in the flow domain. Plotsgenerated from 50 data points were assembled to give a transientanimation of the turbine and surrounding flow field. Theseanimations can provide useful insight into the aerodynamicperformance of the turbine. They can also give predictions formultiple turbine interactions. A sample of the tabular geometry ispresented in Fig. 6a. From these animations, the stator tab effectson fluid flow can be visualized. The velocity vectors in the air flow

no-tab velocity vector diagram shaded by the velocity magnitude (m/s).

0

0.2

0.4

0.6

0 5 10 15 20

Wind velocity (m/s)

λ

With tabs (run 1)

With tabs (run 2)

With tabs (run 3)

With tabs (run 4)

With tabs (run 5)

No tabs (run 1)

No tabs (run 2)

No tabs (run 3)

No tabs (run 4)

No tabs (run 5)

Fig. 8. Experimental comparison of turbine performance with varying geometric design.

K. Pope et al. / Renewable Energy 35 (2010) 1043–10511050

through the turbine illustrate areas of both high and low velocities(see Fig. 6b). Also, the high torque acting on the blades, as theyrotate around to the backside of the turbine, can be explained bythe high pressure acting on the rotor blades in this region. The areaof low velocity behind the turbine is an important consideration ifmultiple turbines are placed in close proximity to one another.From the contour plots of static pressure, the adverse pressure onthe back of the rotor blades, as they rotate into the flow stream, canbe identified. This high static pressure on the backside of the rotorhas a significant drain on the overall power output of the turbine.This region of the rotation explains the area of negative power onthe plot of power output for one blade.

Fig. 7 shows the turbine’s performance throughout onecomplete cycle with all five rotor blades. The plot compares thepredicted transient effects for various tab angles. The base case hasa tab angle of 45�. The increased tab angle geometry has a tab angleof 65� and a tab length of 1’’. The decreased tab angle geometry hasa tab angle of 25�. For the three geometries, the decreased tab anglehas the best performance with Cp¼ 0.113. The base case andincreased tab angle have comparable performance predictions at0.111 and 0.109, respectively. However, the decreased tab anglegeometry has the largest range of Cp values. This coincides witha sizeable range of torque forces. The increased tab angle geometryproduces the smallest range in aerodynamic torque forces. Thisgeometry would limit the degradation of electrical equipment andmechanical systems, thereby increasing the turbine longevity andpower output. The predicted power output is nearly identical to thebase case, while maintaining lower torque forces. If the angle of thetabs is reduced, the rotor assembly of the turbine could be sub-jected to destructive forces and risks of creep.

During the wind tunnel experiment, data is collected for bothturbine variations with 5 separate runs. A minimum constant load isused for all turbine tests. The TSR for each turbine is measured fora given wind speed. With constant loading, an increased wind speedwill naturally result in an increased TSR. The curve generated bythese numbers (Fig. 8) was used for a comparison of the turbineloading. The presence of loading at a given wind speed will have aneffect of reducing the TSR normally observed at that wind speed, byrepresenting a form of inertial load. With the electrical and trans-mission loading constant, as well as surface roughness, the variationof the curve between turbines and tests will indicate the relativeamount of loading due to effects such as bearing friction, vibration

0

0.05

0.1

0.15

0.2

0 120 240 360

Angular position (degrees)

Cp

Base case

Increased tab angle

Decreased tab angle

Fig. 7. Transient comparison of coefficient of performance with variable tab angle.

and shaft alignment. The variability of the curve will also indicate therepeatability of acquired data.

The range of TSR shows repeatability to within �0.02 for bothmodels. This information is further augmented with the startupand safe maximum wind speeds for the different models. Themodel with tabs achieved startup at a wind velocity of 8.5 m/s, anda cutout velocity of 18 m/s. The no-tab model achieved startup ata wind velocity of 7.5 m/s, and a cutout velocity of 15 m/s. A startupTSR (between 0.0 and 0.3) typically follows a linear trend. Bothmodels displayed a tendency towards a linear decrease. For therequired startup velocities, it was not possible to obtain the effi-ciency values for a TSR below 0.3 without the use of a breakingmechanism. The maximum measured TSR for both turbinesoccurred at the maximum safe wind speed, which is limited by thestrength of the model. The conditions associated with higher windspeeds were mode difficult to replicate with the available labora-tory equipment. The data range between 0.3 and 0.6 was typical ofstudies of similar turbines.

Both turbines displayed a linear increase in efficiency up to a TSRof 0.5. The efficiency then peaked and began to decline again, leadingto a correlated quadratic curve fit as follows (based on experiments):

Tabs : Cp ¼ �0:0159l2 þ 0:0344l (12)

No Tabs : Cp ¼ �0:0126l2 þ 0:037l (13)

Due to a lack of data for TSR values beyond 0.6, these curves areskewed so they do not fully represent data when forecast beyondthe turbine peaks. Both curves should have a steep decline aftermoving through the efficiency peak. For the no-tab design, theexperimental results found the peak to occur at a TSR slightlyhigher than that predicted by the simulation, but significantlycloser to that of the tabular model. The no-tab results suggesta peak of 0.12 at a TSR of 0.48, which corresponds to a wind speed of14 m/s. The 2-D transient simulations predict a performanceimprovement of 13.5% with the no-tab geometry.

5. Conclusions

In this paper, two independent fluid flow formulations wereused to investigate the aerodynamic performance of a Zephyr

K. Pope et al. / Renewable Energy 35 (2010) 1043–1051 1051

VAWT. The change of 2-D transient and 3-D time averagednumerical predictions of the power coefficient exhibit a compa-rable change in magnitude to the experimental results. This indi-cated that both numerical formulations provide correct trends forthe changes of flow dynamics and power coefficients for changes inthe VAWT geometry. The simulations indicate the scalability forboth configurations. The constant speed model predicts the optimalTSR at lower wind speeds that are more likely to be found wherethe Zephyr turbine would be located. The simulations also exhibita high degree of scalability for both configurations. This paper hasprovided useful new data and empirical correlations that charac-terize the operating performance of a Zephyr VAWT.

Acknowledgements

The authors express their grateful appreciation to the NaturalSciences and Engineering Research Council of Canada (NSERC),Zephyr Alternative Power Inc., and the Ontario Graduate Scholar-ship program (OGS) for their financial support.

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