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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
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/jweia
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
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(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
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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
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123114
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123 115
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123116
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123 117
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123118
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123 119
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123120
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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.
M. Elkhoury et al. / J. Wind Eng. Ind. Aerodyn. 139 (2015)
111123 121
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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