-
ncf a
aDepartment of Mechanical Engineering, University of
tbDepartment of Civil and Structural Engineering, UnivercDepartment
of Mechanical Engineering, University of S
T werewere tet traceean k iuctuati
tions at U1 = 7 m/s were conducted and results have shown a
typical perfor-r this particular VAWT scale.
decade and will continue to do so in the future, because wind
tur-bines offer the potential for low carbon power generation.
Windturbines can be subjected to highly unsteady winds with high
lev-els of turbulence for signicant proportions of the time,
resulting inair ows characterised by rapid changes in speed and
direction.Vertical axis wind turbines (VAWT) may be more
appropriate forurban applications where unsteady winds are
prevalent because
over the conven-4]. The pinclude a
mechanism to adjust the rotor direction to the
changingdirection, but also potentially better performance in unand
skewed wind conditions [57].
The vast majority of research published (both numerical
andexperimental) has been with steady wind ows and very littlework
has been published into the effects of VAWT performancein unsteady
wind conditions. However, there have been a handfulof numerical
studies (usually using vortex methods) that have at-tempted to
provide initial understanding of the VAWT perfor-mance in unsteady
wind. McIntosh et al. [8,9] attempted tounderstand the performance
of VAWTs in unsteady wind. A uctu-
Corresponding author. Tel.: +63 9491847572.E-mail addresses:
[email protected], [email protected] (L.A.
Applied Energy 116 (2014) 111124
Contents lists availab
lseDanao).1. Introduction
The use of wind power has increased massively over the last
of a number of distinct advantages they presenttional horizontal
axis wind turbines (HAWT) [1advantage is probably that there is no
need to0306-2619/$ - see front matter 2013 Elsevier Ltd. All rights
reserved.http://dx.doi.org/10.1016/j.apenergy.2013.11.045rimaryyawingwind
steadyAvailable online 11 December 2013
Keywords:VAWTUnsteady windCFDVisualisationsPerformance
Very detailed understandings of the ow physics are discussed
showing the importance of stall andow re-attachment on the
performance of the turbine with unsteady winds. The three blades of
theVAWT experience very different ow regimes as they rotate during
a single periodic oscillation of thewind speed. When the VAWT
operates in periodically uctuating wind conditions, overall
performanceslightly improves if the following are satised: the mean
tip speed ratio is just above the k of the steadyperformance
maximum, the amplitude of uctuation is small (1 Hz). Operation at a
mean k that is lower than k for peak performance coefcient causes
theVAWT to run in the k band with deep stall and vortex shedding,
to the detriment of the VAWT perfor-mance coefcient. Large
uctuations in wind speed causes the VAWT to run in k conditions
that are dragdominated, thus reducing the performance of the wind
turbine. Within realistic conditions, higher fre-quencies of
uctuation marginally improve the performance of the VAWT.
2013 Elsevier Ltd. All rights reserved.Received in revised form
14 October 2013Accepted 17 November 2013
model, steady wind simulamance curve prediction foh i g h l i g
h t s
CFD simulations on a small scale VAW Varying k, amplitudes and
frequencies The unsteady CP of the VAWT does no Overall performance
improves when m CP also improves when amplitude of
a r t i c l e i n f o
Article history:Received 4 May 2013he Philippines, Quezon City,
Philippinessity of Shefeld, Shefeld, UKhefeld, Shefeld, UK
conducted in unsteady wind conditions.sted and results
presented.the steady CP curves.s just above steady CP maximum.on is
1 Hz.
a b s t r a c t
Numerical simulations using RANS-based CFD have been utilised to
carry out investigations on the effectsof steady and unsteady wind
on the performance of a wind tunnel scale VAWT. Using a validated
CFDLouis Angelo Danao a,, Jonathan Edwards b, Okeoghene Eboibi c,
Robert Howell cA numerical investigation into the inueon the
performance and aerodynamics o
Applied
journal homepage: www.ee of unsteady windvertical axis wind
turbine
le at ScienceDirect
Energy
vier .com/locate /apenergy
-
Eneating free stream wind, of sinusoidal nature, was created
whilerunning the VAWT at a constant rotational speed. An increase
inenergy extraction was obtained using a turbine rotational
speedgreater than the calculated steady state maximum. The
so-calledover-speed control technique resulted to a 245% increase
in energyextracted. Further improvements in the performance was
obtainedby using a tip speed ratio feedback controller
incorporating timedependent effects of gust frequency and turbine
inertia giving afurther 42% increase in energy extraction. At low
frequencies ofuctuation (0.05 Hz) away from stall, the unsteady CP
closelytracks the steady CP curve. However at higher
frequencies(0.5 Hz), the unsteady CP is seen to form hysteresis
loops withaverages greater than steady predictions.
In 2010, Kooiman and Tullis [10] experimentally tested a
VAWTwithin the urban environment to assess the effects of
unsteadywind on aerodynamic performance. Variations in wind speed
anddirection was quantied and compared to a reference case wind
Nomenclature
c blade chordCm moment coefcientCP power coefcientdo pressure
outlet boundary distance from VAWT axisds side wall boundary
distance from VAWT axisfc characteristic frequency of unsteady
windgr ination growth rate of meshkx SST variant of kx turbulence
model by Menter (1993)PB blade power (three blades)Pw wind powerR
rotor radiusTb blade torque (single blade)TB blade torque (three
blades)Tu turbulence intensityU1 free stream wind speedUamp
amplitude of uctuation of unsteady windUmean mean speed of unsteady
windy+ dimensionless wall distance
112 L.A. Danao et al. / Appliedtunnel performance. The
performance of the turbine was indepen-dent to the directional
uctuations, while amplitude-based windspeed uctuation decreased the
performance linearly.
Hayashi et al. [11] examined the effects of gusts on a VAWT
bysubjecting a wind tunnel scale rotor to a step change in wind
veloc-ity. Two types of control were implemented: constant rpm
andconstant load torque. When subjected to a step change in
windspeed from 10 m/s to 11 m/s under constant rpm control, theVAWT
torque was observed to respond almost instantaneouslyand attained a
steady state in less than 3 s. However when con-stant load torque
control was employed, the initial response is sim-ilar to the
constant rpm control where the torque instantly jumpsto a higher
level. The subsequent behaviour is a combination of agradual
increase in rpmwith a slow decrease in torque until steadystate is
again attained. The VAWT behaviour will thus follow a qua-si-static
condition during the gust.
Danao and Howell [12] conducted CFD simulations on a windtunnel
scale VAWT in unsteady wind inow and have shown thatthe VAWT
performance generally decreased in any of the testedwind
uctuations. The amplitude of uctuation studied was 50%of the mean
wind speed and three sinusoidal frequencies weretested: 1.16 Hz,
2.91 Hz, and 11.6 Hz where the fastest rate is equalto the VAWT
rotational frequency. The two slower frequencies ofuctuation showed
a 75% decrease in the wind cycle mean perfor-mance while the
fastest rate caused a 50% reduction. Closer inves-tigation revealed
that for a 2.91 Hz uctuation rate a largehysteresis is seen in the
unsteady CP of the VAWT within one windcycle. This hysteresis
occurs in the positive amplitude portion ofthe wind uctuation where
the blades passing the upwind progres-sively stall at earlier
azimuths and experience very deep stall dueto signicant reduction
in the effective k. Negative amplitude inwind uctuation does not
produce signicant hysteresis. However,the unsteady CP traces a
curve that does not follow the steady CPcurve but somehow crosses
it down to a lower level performancecurve.
The effects of pulsating winds on the performance of a
windtunnel based VAWT and the dependence of the performance
tochanges in the rotors moment of inertia were investigated by
Haraet al. [13]. The energy efciency of the VAWT was observed to
beconstant with changing rotor moment of inertia and
uctuationfrequency but a decrease is seen when uctuations have
largeamplitudes.
In 2012, Scheurich and Brown [14] published results from a
a angle of attackDCP change in CPDt in CFD, time step sizeh
azimuth positionk tip speed ratio, Rx/U1k tip speed ratio at peak
CPkmean tip speed ratio corresponding to xmeanl laminar viscositylt
turbulent viscosityx rotor angular speedxmean in unsteady wind,
mean of xCFD computational uid dynamicsFOV eld of viewPIV particle
image velocimetryRANS Reynolds Averaged NavierStokesURANS unsteady
RANSVAWT vertical axis wind turbine
rgy 116 (2014) 111124numerical model of VAWT aerodynamics in
unsteady wind condi-tions with a uctuating mean wind speed of 5.4
m/s and a uctu-ating frequency of 1 Hz. Different uctuation
amplitudes wereinvestigated for three blade congurations: straight,
curved, andhelical. Straight and curved blades exhibited
considerable variationin blade loading which is also observed in
steady wind results withthe variations in CP over one revolution
being more signicantthan those induced by the unsteadiness of the
wind. Helical bladesperform much better with the unsteady CP
tracing the steady per-formance curve quite well. Most importantly
a drop in perfor-mance was observed when the uctuation amplitudes
are high(as found by Danao and Howell [12]) while the effect of
frequencyis minor for practical urban wind conditions.
Danao et al. [15] carried out the rst experimental measure-ments
of wind turbine performance with unsteady sinusoidal vari-ations in
wind power. The time average of the unsteady CP with a7% uctuation
in wind velocity was very close to that with steadywind conditions
while 12% uctuations in wind speed resulted in adrop in the mean
CP, meaning unsteady winds of such amplitudesare detrimental to the
energy yields from these wind turbines. Atmean rotational speeds
corresponding to tip speed ratios (k) be-yond peak CP, no signicant
hysteresis was observed for both 7%and 12% uctuations. However,
substantial hysteresis is seen forconditions where mean k is below
peak CP.
The conicting conclusions from previous published
researchsuggest that very little is still understood about the
performance
-
and aerodynamics of VAWTs in unsteady winds. Any
generalisa-tions made about VAWT performance in the urban
environmentmay well be completely erroneous. The research presented
in thispaper show a signicant step forward in the understanding
ofVAWT performance in unsteady wind conditions. Fundamentalow
physics is shown as a VAWT is subjected to uctuating windspeeds to
further explain the performance predictions.
2. Development of the numerical model
The commercial CFD package Ansys Fluent 13.0 was used for allthe
simulations performed in this study. The code uses the nitevolume
method to solve the governing equations for uids. In thisstudy the
incompressible, unsteady Reynolds Averaged NavierStokes (URANS)
equations are solved for the entire ow domain.
el is sufcient in revealing the factors that inuence the
perfor-
surrounding geometry was dened based on studies of the extentsof
the boundaries that are detailed in later sections. There is an
in-ner circular rotating domain connected to a stationary
rectangulardomain via a sliding interface boundary condition that
conservesboth mass and momentum. No-slip boundaries are set to
representthe wind tunnel walls while a velocity inlet and a
pressure outletare used for the test section inlet and outlet,
respectively. The rota-tion of the inner domain relative to the
outer domain is prescribedwithin the solver that implements the
algorithm for the slidingmesh technique. Care is taken such that
tolerance between meshesin the interface region is kept low to
avoid excessive numericaldiffusion.
Fig. 2. An illustration of the 2D numerical domain.
L.A. Danao et al. / Applied Energy 116 (2014) 111124 113mance
and majority of ow physics that surround the VAWT.The contributions
of blade end effects and blade-support arm junc-tion effects are
neglected but deemed acceptable since these can beconsidered as
secondary. Two dimensional VAWT models areessentially VAWTs with
innite aspect ratio blades. The effect ofblade aspect ratio (AR)
comes in the form of shifting the CP curveupwards and to the right
as AR increases [27], but the generalshape is maintained. Full 3D
models were tested using coarsemeshes but, due to their immense
computational time require-ments, were considered impractical for
this study.
The domain mesh was created where the aerofoil coordinates ofa
NACA022 prole were imported to dene the blade shape. TheThe coupled
pressure-based solver was selected with a second or-der implicit
transient formulation for improved accuracy. All solu-tion
variables were solved via second order upwind discretisationscheme
since most of the ow can be assumed to be not in linewith the mesh
[16].
The entire domain was initialised using the inlet conditions
thatwere pre-determined to provide a matching turbulence
intensitydecay that was observed in VAWT experiments conducted in
theUniversity of Shefeld wind tunnel facility [15]. The inlet
turbu-lence intensity was set to Tu = 8% with a turbulence
viscosity ratioof lt/l = 14. The turbulence decay in the numerical
model is veryclose to the observed decay in the experiment as shown
in Fig. 1.
2.1. Meshing topology
A two-dimensional CFD model was used to represent the VAWTand
the wind tunnel domain (Fig. 2). This was based on the reviewof
relevant literature [3,4,12,1726] that has shown that a 2D mod-Fig.
1. Comparison of turbulent intensity decay between CFD and
experiments(x = 0: test section inlet). Fig. 3. Blade torque for
node density study: (a) k = 2, and (b) k = 4.
-
2.2. Mesh independence study
Each blade surface was meshed with 300 nodes and clusteringin
the leading and trailing edges was implemented to provide
therequired renement in regions where high gradients in pressureand
ow were expected. A node density study was performed todetermine
the appropriate number of surface nodes (Fig. 3). TheO-type mesh
was adapted for the model, where a boundary layerwas inated from
the blade surface (Fig. 4a). The motivation be-hind using the
O-type mesh instead of the conventional C-typeused in aerofoil
studies was primarily because the expected wakeis not xed on a
specic path relative to the blade but rather vary-ing greatly in
direction swaying from one side to another side due
to the high angles of attack experienced at low tip speed ratio
andthe dynamic stalling phenomenon.
The rst cell height used was such that the y+ values from theow
solutions did not exceed 1, the limit of the turbulence modelthat
was chosen for the simulations. To ensure sufcient boundarylayer
modelling, the growth rate of the ination was set to 1.1 togive a
minimum of 30 layers within the boundary layer, afterwhich a larger
growth rate of 1.15 was implemented. Beyond theblade surface of
about a chord width, the rotating inner domainmesh was generated
such that the maximum edge length of thecells did not exceed 0.5c
within the VAWT domain (Fig. 4b). Thiswas adapted to minimise the
dissipation of the turbulent struc-tures generated by the blades in
the upwind region that may inter-act with the other blades in
downwind region. A smoothingalgorithm in the meshing software was
used to reduce the angleskewness of the cells such that the maximum
was observed to beless than 0.6.
To reduce computation time, the outer domain was coarselymeshed
with a rough maximum edge length of the cells set to c(Fig. 4c).
This dissipated the high gradients in the wake, such asshed
vortices, but the general velocity decit was still captured.The
distance of the velocity inlet boundary from the VAWT axiswas set
to 1.5 m, 0.3 m short of the actual 1.8 m in the experimentsetup
[15]. This was not considered an issue since the modelledturbulence
intensity decay in the simulations matched that ofthe experiments
and is thought to be much more important.
2.3. Boundary location study
An outlet distance study was conducted to investigate the
ef-fects of wake development on the performance of the VAWT
114 L.A. Danao et al. / Applied Energy 116 (2014) 111124Fig. 4.
Images of the adopted mesh of the numerical model: (a) near blade
mesh, (b)rotating inner domain mesh, and (c) stationary outer
domain mesh.Fig. 5. Domain size study results for the 2D numerical
model: (a) domain length,and (b) side wall distance.
-
(Fig. 5a). The pressure outlet boundary was set to do = 2 m from
theVAWT axis. This has been selected as a distance between
theexperimental test section outlet of 1.2 m and the position of
thewind tunnel fan of about 3 m. In the actual wind tunnel
setup[15], the test section outlet was tted with a steel matting
gridof the same wire thickness and mesh size as the turbulence
gridin the inlet. This will have had a denite effect on the
developed
tions is required for this study, the chosen time step size
wasDt = 0.5x1 so that the vortex shedding at k = 2 is correctly
mod-elled and was adopted for the remaining runs.
3. Validation of CFD model
The numerical model developed was checked against experi-mental
data to assess its capability of correctly simulating VAWTow
physics. The validation is not considered exact, since theCFD model
is 2D, while the actual problem is 3D. Nevertheless, agood 2D CFD
model will provide substantial insight into the factorsdriving the
performance of the VAWT and a means of checking themodels accuracy
in capturing the details of the problem is pre-sented below.
3.1. Power coefcient
The rst aspect of the model validation is the comparison of
thepredicted VAWT performance over a wide range of operatingspeeds.
Both the fully turbulent kx SST and the Transition SST
Fig. 7. Time step size study results: (a) k = 2, and (b) k =
4.
L.A. Danao et al. / Applied Energy 116 (2014) 111124 1152.4.
Time step independence study
Sufcient temporal resolution is necessary to ensure proper
un-steady simulation of the VAWT. Different time step sizes Dt
thatare equivalent to specic rotational displacements along the
azi-muth were tested. The largest Dt used was equal to a Dt =
1x1
(time for one degree equivalent rotation) and was
subsequentlyhalved twice over to get Dt = 0.5x1 and Dt = 0.25x1.
All threeDts were tested at k = 2 and k = 4. Results for both k are
presentedin Fig. 7. It is clear that there is a delay in the torque
ripple for thecoarsest Dt = 1x1 at k = 2 while the two ner Dts are
in goodagreement especially in the upwind. A small difference in
pre-dicted magnitude of Tb between Dt = 0.5x1 and 0.25x1 is
seenfrom h = 280 to h = 330 but the peaks and troughs are still in
sync.There is negligible difference in CP between the three Dts
with amaximum DCP of only 0.003.
A similar agreement between the three Dts is observed at k =
4with the maximum DCP of 0.003 as well. There is very little
varia-tion between the three cases with the only noticeable
difference inthe torque ripple from h = 260 to h = 290. The upwind
is accu-rately predicted by the three Dts with all capturing the
maximumTb around h = 80. The maximum Tb in the downwind is also
prop-erly predicted by all Dts at h = 240. Since time accurate
simula-wake of the VAWT, breaking up the large vortex structures
gener-ated from the blades. There is also the presence of the
shuttermechanism, which is considered to inuence the destruction
ofthe shed vortices. As such, a long uid domain behind the VAWTwas
deemed unnecessary from a numerical standpoint since fullwake
development was not one of the objectives of the study.
A wall distance study was carried out to examine the effects
ofblockage in the 2D simulations (Fig. 5b). The side wall distance
wasset to ds = 1.2 m from the VAWT axis. This is double the actual
windtunnel wall distance of 0.6 m. The area blockage of the 2D
numer-ical model matches that of the 3D wind tunnel model and is
equalto 0.29. Since the study is mainly focused on the aerodynamics
ofthe VAWT in unsteady wind conditions within a wind tunnel
do-main, blockage was not a primary consideration in the
simulationssince no reference to actual eld test data is made.
Time step convergence was monitored for all conserved vari-ables
and it was observed that acceptable levels of residuals (lessthan 1
106) were attained after 6 rotations of the VAWT. Thismeant that
periodic convergence was also achieved. The blade tor-que Tb
monitored all though 10 rotations is shown in Fig. 6. Afterthe
sixth rotation, the peaks of the upwind torque for cycles 7through
10 are level and the downwind ripple match closely. Thedifference
in average torque between cycle 7 and cycle 10 isaround 0.5%, and
hence the simulation is considered converged.Fig. 6. Blade torque
ripple of one blade for 10 full rotations.
-
accuracy of the predicted stalling and reattachment of the owon
the blades as they go around the VAWT. Close analysis of
thevisualisations for the condition k = 4 were also carried out,
butare not presented for reasons of brevity. The data at k = 4
doesnot change any of the conclusions presented for k = 2.
Fig. 9 shows the vorticity plots for the upwind at k = 2. At
thestart of the rotation, both turbulence models clearly predict
fullyattached ow. There is an observed wake (green contour) seenon
the lower left portion of each CFD image at h = 10 that is
alsovisible in the PIV image. This is the wake of the preceding
blade al-ready at h = 130. Flow continues to be attached until h =
60whereboth the Transition SST model and PIV reveal a bubble that
is form-
Fig. 9. Flow visualisations of vorticity in the upwind for k =
2.
Eneturbulence models were tested against the experimentally
derivedCP. The steady wind speed chosen was 7 m/s and the
simulationswere run at different tip speed ratios from k = 1.5 up
to k = 5 inincrements of 0.5. It can be seen from Fig. 8 that both
2D modelsover-predict CP starting from k = 2 all the way up to k =
5. Maxi-mum CP for the fully turbulent model is 0.35 at k = 4 while
theTransition SST model predicts maximum CP = 0.33 at k = 4.5.
Themaximum CP for the fully turbulent model occurs at the same kas
that of the experiments. There is a gap in the predicted CPs
be-tween the two CFD models from k = 3 to k = 4.5 where the fully
tur-bulent model over-predicts the CP much more than the
TransitionSST model. A convergence of the curves is seen from k =
1.5 to k = 3and also from k = 4.5 to k = 5. Higher ks show the
greatest over-prediction of the CFD models from experiments. This
may be dueto the effects of nite blade span where the reduction in
aspect ra-tio as seen by McIntosh [27] cause a substantial drop in
CP at high kvs. the small drop in CP at low k.
The gap in predicted CP was expected since the 2D model doesnot
account for nite blade span as well as for blade-support
armjunction effects and support arm drag that are present in the
actualsetup. The results are consistent to published data by Raciti
Castelliet al. [23], Howell et al. [21] and Edwards et al. [3]
where 2D CP isover-predicted over the entire range of k. Raciti
Castelli et al. com-pared their 2D simulations to wind tunnel
experiments and arguedthat the difference is due to blockage
effects that increase the owvelocities near the blades to much
higher values than the unper-turbed ow at the inlet. Howell et al.
show an improved match be-tween 3D CFD and experiments. Edwards et
al. attribute the
Fig. 8. Steady CP curves at 7 m/s.116 L.A. Danao et al. /
Applieddifference in predicted CP to nite blade span and
blade-supportarm junction effects.
Overall, the general behaviour of the predicted CP matches
wellwith the experimental data. There is an observed negative
troughat the low k which rapidly rises and reaches maximum values
nearthe experiment maximum at k = 4 after which a rapid drop in CP
isseen. The fully turbulent model results show a smoother curve
andbetter shape agreement to experiments. On the other hand,
theTransition SST model results do not form a smooth curve and
pre-dict maximum CP at a higher k but calculates CP values closer
toexperiments.
3.2. Flow visualisation
The second aspect of validation is the comparison of ow
visu-alisations between CFD and PIV to examine the dynamic
behaviourof the ow around the VAWT blades adding signicant insight
asto why the CP varies as it does at different operating
conditions.The ow physics at k = 2 is inspected and an assessment
of themost appropriate turbulence model is performed based on
thergy 116 (2014) 111124ing on the suction surface of the blade.
The fully turbulent kx SSTpredicts the same formation of a
separation bubble 10 later ath = 70. This delay has a signicant
effect on the blade torque sincethis can mean extended generation
of lift that may positively affectthe predicted performance of the
VAWT.
As seen in the PIV at h = 70 the separation bubble has
formedinto a dynamic stall vortex and has already been detached
fromthe blade surface. This is properly captured by the Transition
SSTmodel. However, the fully turbulent model still predicts the
vortexto be on the blade surface. This delay in the formation and
detach-ment of the dynamic stall vortex affects the shedding of the
subse-quent pairs of leading edge and trailing edge vortices and is
evidentin the presence of a trailing edge vortex in the FOV of the
fully tur-bulent model at h = 140 but is not seen on both the
Transition SSTmodel and PIV.
The downwind (not shown for brevity) shows better
agreementbetween the two CFD models when it comes to the scale and
tim-ing of the shed vortices although slightly smaller when
comparedto the PIV. The ow reattachment is seen to have started
earlierin the Transition SST model as the stall is signicantly
shallower
-
at h = 280 as compared to the fully turbulent model and PIV.
Thismay, in part, explain the higher predicted CP at this k.
Overall, thetiming and depth of stall in the upwind for the
Transition SST mod-el matches the PIV quite well while the
reattachment of the ow inthe downwind is better captured by the
fully turbulent model.
Based on the results obtained from both force and ow
valida-tion, the Transition SST model was selected as the better
modelthat most accurately captures the ow physics of the VAWT.
Fromthe correct prediction of start of stall and the rate and scale
of shedvortices at k = 2 to the stalling and reattachment of ow at
k = 4(not shown), the Transition SST model better calculates the
owphysics vs. the kx SST model. The predicted positive
performanceof the Transition SST model is closer to experiments
with lowervalues of CP vs. the kx SST model. All simulations
conductedfor the unsteady wind study will use the Transition SST
model.
4. Unsteady wind performance
Numerical modelling of the unsteady wind inow through thetunnel
was carried out by specifying the velocity inlet magnitudeas a
time-dependent variable and running the simulation forapproximately
1.5 wind cycles. This is necessary so as to attain
incompressible solver is used for all runs. As such, a change
inthe inlet velocity results in the entire domain changing in
owvelocity. A test was conducted to verify this assumption by
runninga simulation with an empty wind tunnel domain under
uctuatingvelocity inlet condition. Seven monitor points were placed
be-tween the two wall boundaries along the length of the domain.
Re-sults conrm that velocities downwind are in sync with
theuctuating inlet velocity and are shown in Fig. 10.
4.1. The reference case
A reference case is selected to act as the baseline model
towhich parametric variations can be compared. The mean windspeed
is Umean = 7 m/s with a uctuating amplitude of Uamp = 12%(0.84 m/s)
and uctuation frequency of fc = 0.5 Hz. The rotorangular speed is a
constant x = 88 rad/s (840 rpm) resulting in amean tip speed ratio
of kmean = 4.4. The steady CP curve shows thiscondition is just
before peak performance at k = 4.5.
A total of 28 rotor rotations completes one periodic wind
cycle.As shown in Fig. 11, the k changes with the uctuating U1.
Increas-ing U1 causes the k to fall owing to their inverse
relationship and aconstant turbine rotational speed x. Maximum U1
is 7.84 m/s and
L.A. Danao et al. / Applied Energy 116 (2014) 111124 117not just
periodic convergence in the simulations, but also to gener-ate a
contiguous set of converged data that covers the entire cycleof the
wind uctuation. It has been determined that in order tomatch the
experimental wind cycle with a uctuation frequencyof 0.5 Hz, the
simulations had to be run for 40 full rotations ofthe VAWT. For
each run, a total of about 5400 processor hourswas required to
complete 40 rotations in the University of Shef-elds Intel-based
Linux cluster using 16 cores of Intel XeonX5650 2.66 GHz
processors. Full convergence per time step wasachieved after 6
rotations when residuals of all conserved variablesfell below 1
106.
One major assumption in the computation of unsteady CP is
thefree stream velocity in the wind power term. Since the inlet
veloc-ity is the specied parameter in all simulations, one may
assumethat there is a delay in the uctuating wind that the VAWT
seesas a consequence of its position downstream. However, the
modelis constrained within the wind tunnel and conditions are
wellwithin the limits of incompressible ow regime. Additionally,
anFig. 10. Study of U1 variation in an empty tunnel domain with
uctuating inlet conditioshowing velocities are in sync.occurs at
the end of the 7th rotation with k dropping to its mini-mum of
3.93. The maximum a of the blade per rotation can be seento
increase with the increasing U1 reaching a peak value ofa = 14.74
between the 6th and 8th rotation. Following the maxi-mum U1 is the
gradual drop of U1 back towards the mean windspeed. It continues to
fall until it reaches the minimum value ofU1 = 6.16 m/s at the end
of the 21st rotation. At this U1, the k risesto its maximum value
of 5.0. Within this part of the wind cycle, themaximum a per
rotation falls to 11.55 between the 20th and 22ndrotation depending
on the blade in question. The subsequent in-crease of U1 back to
the mean value causes the k to drop in mag-nitude and the peak a
per rotation to increase.
The peak Tb of each rotor cycle increases together with
increas-ing U1 with maximum Tb value of roughly 1.28 N m
generatedwithin the 8th rotation (Fig. 12). The maximum combined
bladetorque TB is 1.59 N m, also within the 8th rotation. In the
secondhalf of the wind cycle, the peak Tb of each rotor cycle drops
to0.79 N m within the 22nd rotation. It is observed that TB is
mostlyn: (a) position of monitor points along tunnel length, and
(b) results of simulation
-
Ene118 L.A. Danao et al. / Appliedpositive, which suggests
positive overall performance. Also, thelarge uctuations in the TB
with characteristic frequency equal tothree times the rotor
frequency would result in large uctuationsin the rotor power PB.
The variation of PB is shown in Fig. 13 to-gether with the
uctuating wind power Pw. As expected, the peaksof PB follow the
wind variation much like the TB does. Maximum PBis 140 W generated
as Pw reaches its peak at the end of the 7throtation, with
magnitude of 207 W. Also presented are the unstea-
Fig. 11. Variation o
Fig. 12. Variation
Fig. 13. Variation ofrgy 116 (2014) 111124dy CP and quasi-steady
CP using moving average smoothing.Smoothing the unsteady CP
provides a useful comparative plot tothe experimental data [15],
where the unsteadiness of the experi-mental CP over one rotor cycle
is not captured. In addition, this isshown to be consistent with
the cycle averaged method of comput-ing for the rotor CP in steady
wind conditions, that lters out theuctuating nature of the blade
torque to give a single value predic-tion of VAWT performance.
f U1, k, and a.
of Tb and TB.
power and CP.
-
In Fig. 14, the plots of the unsteady CP and quasi-steady CP vs.
kare shown relative to the steady wind performance at 7 m/s.
Theuctuations in the unsteady CP over the band of operating k showa
massively varying VAWT performance that greatly exceeds thelimits
of the steady wind CP. The maximum CP is recorded at0.69 and occurs
just after the 15th rotation (k = 4.55). The mini-mum CP is seen to
take place after the 21st rotation with a valueof 0.15 (k = 5). The
wind cycle-averaged CP is computed to be0.33 (kmean = 4.4) and is
equal to the maximum steady wind CPof 0.33 at k = 4.5. It is clear
from the gure that the quasi-steady
brevity, since a complete set of visualisations for an entire
wind cy-cle will compose of 3024 images from three blades that see
com-pletely different free stream conditions at a conservative
36azimuth positions per rotor cycle. The rst half of the wind
cyclehas been selected since most of the interesting ow features
occurat k lower than kmean, whereas higher k would only show
mostlyattached ow with little or no separation at all. Presented
are visu-alisations using vorticity at azimuth positions with the
deepeststall for each blade in the upwind region of the rotor cycle
shown.
It is clear that as the wind speed increases, the stall on blade
1becomes deeper and occurs at a later azimuth (Fig. 15a and d)
dueto decreasing k. Also, the separation point moves from
mid-chordto the leading edge. As the wind speed falls back to
Umean, k in-creases, the depth of stall reduces, deepest stall
occurs at an earlier
The reference case x was a constant 840 rpm giving akmean = 4.4.
To investigate the effects of different kmean, two simula-
Fig. 14. Performance of the VAWT in 12% uctuating free
stream.
L.A. Danao et al. / Applied Energy 116 (2014) 111124 119CP
crosses the steady CP curve. Increasing wind speeds cause theCP to
deviate from the steady CP curve and rise to higher levelsas the k
falls to lower values. On the other hand, decreasing windspeeds
cause the CP to drop below the steady CP curve as the krises.
Floweld visualisations of the reference case are shown inFig.
15. Only selected cycles and azimuth positions are shown forFig.
15. Flow visualisations of vorticity from selected rotor cycles in
the rst half ofthe wind cycle of the reference case: (ac) h = 130;
(df) h = 140; (gi) h = 130.tions were run at x = 78 rad/s (745 rpm)
and x = 95 rad/s(907 rpm) resulting in kmean = 3.9 and kmean =
4.75, respectively.The variation of k with time for the three kmean
cases is shown inFig. 16a. Looking at the reference case of kmean =
4.4, the maximumk is recorded at 5.0, while the minimum is at 3.93.
The peak-to-peak value for this case is 1.07. The case with the
highest kmeanat 4.75 shows the maximum k has moved up to 5.4, while
the min-imum is now at 4.24 resulting in a peak-to-peak value of
1.16. Theopposite behaviour is observed when kmean is lower at 3.9.
Themaximum k is seen to be 4.43 while the minimum is 3.48, givinga
peak-to-peak value of 0.95. With the same uctuation amplitudeof
Uamp = 12%, the peak-to-peak value increases as the kmean
in-creases; an expected consequence of the direct relationship of
xand k. The trends of the CP curves do not follow the simple
andazimuth, and the separation point moves back to mid-chord
posi-tion (Fig. 15d and g). A similar observation is seen for
blades 2(Fig. 15b, e and h) and 3 (Fig. 15c, f and i). One thing to
point outis there is no visible difference between the three blades
at thesame h. The reason behind this is the low frequency of the
windspeed cycle compared to the rotor cycle causing a
quasi-steadycondition relative to the VAWT. As blades pass a specic
h withinone rotation, the free stream wind speeds between blades
differby only 0.04 m/s. Furthermore, the stalling mechanism at
cycle14, where the wind speed has dropped back to Umean is very
similarto the stalling in cycle 1. For the full +12% change in the
windspeed, the azimuth of the deepest stall in the upwind
regionchanges by only 10 from 130 in cycle 1 to 140 in cycle 7 and
goesback again to 130 in cycle 14.
4.2. Effect of varying the mean kFig. 16. Quasi-steady
performance of the VAWT for the different kmean cases: (a) kvs.
time, and (b) CP vs. time.
-
straightforward trend of k. It can be seen in Fig. 16b that the
behav-iour of CP as U uctuates depends on the k at the start of the
cycle.The reference case, which starts at k = 4.4, is closest to
the steadyCP maximum k at 4.5. As a result, the starting CP = 0.33
is highestof the three cases. The kmean = 4.75 case comes next with
a starting
4.3. Effect of varying the uctuation amplitude
The effects of variations in amplitude Uamp was investigated
byrunning two simulations at Uamp = 7% (0.49 m/s) andUamp = 30%
(2.1 m/s). These conditions were compared to thereference case of
Uamp = 12% (0.84 m/s). The variation of k withtime for the three
different kmean cases is shown in Fig. 20a. Fromthe previous
section, the maximum k of the reference case(Uamp = 12%) occurs at
k = 5.0 while the minimum is at 3.93 witha peak-to-peak variation
of 1.07. The case with the highestUamp = 30% shows the maximum k
has jumped to 6.28 while theminimum is now at 3.38 resulting in a
peak-to-peak value of 2.9.Less extreme behaviour is observed when
Uamp = 7%. The maxi-mum k is seen to be 4.73 while the minimum is
4.11 giving a
Fig. 17. Study on the effect of varying kmean.
Fig. 18. Flow visualisations of vorticity of selected rotor
cycles in the rst quarter ofthe wind cycle showing effects of
varying kmean at h = 130.
120 L.A. Danao et al. / Applied EneCP of 0.31 and the kmean =
3.9 case is last with a starting CP of 0.27.Both kmean = 4.4 and
4.75 cases see their CP rise as the wind speedincreases while the
kmean = 3.9 case CP falls with increasing windspeed. The position
of the starting k of the kmean = 3.9 case is muchlower than k and
is within the drop-off part of the steady CP curve.Low ks mean
higher angle of attack and greater occurrence ofstalled ow that
lead to poorer performance. Maximum CP forthe kmean = 4.75 case is
0.37 and coincides with the point of maxi-mumwind speed and minimum
k. The other two cases do not havetheir maximum CP at the extreme
values of U1 but rather betweenthe Umean and a U1. Minimum CP for
the kmean = 3.9 case is 0.2 andoccurs at the point of maximum wind
speed and minimum kwhilethe other two cases have their minimum CP
at the point of mini-mum wind speed and maximum k. A summary of the
cycle-aver-aged CP is presented in Table 1.
As can be seen from Fig. 17, all quasi-steady CP curves cross
thesteady CP curve as the wind uctuates. For the kmean = 4.75
case,maximum CP is 0.37 at k = 4.24 while minimum CP is 0.16 atk =
5.4. These two points are essentially the points of maximumand
minimum wind speeds in the wind cycle. At this kmean, an in-crease
in wind speed induces an improvement in the performanceof the VAWT
while falling wind speeds cause the VAWT perfor-mance to drop. The
cycle-averaged CP, dened as the ratio of themean blade power PB to
the mean wind power Pw over one windcycle, is 0.35 which is higher
than the maximum steady wind CPof 0.33 at k = 4.5 and also higher
than the cycle-averaged CP ofthe reference case equal to 0.33. The
case when kmean = 3.9 showsa contrasting behaviour; as the wind
speed increases, the quasi-steady CP falls together with the
decreasing k. At the minimumk = 3.48, the CP is at its lowest with
a value of 0.2. Maximum CPis attained in the second half of the
wind cycle with a value of0.29 at k = 4.24. At maximum k = 4.43
when the wind speed is atits lowest, the computed CP is 0.28. The
cycle-averaged CP for thiscase is 0.24.
Fig. 18 shows the stalling of one blade at different rotor
cycleswithin the rst quarter of the wind cycle as U1 rises from 7
m/sto 7.84 m/s. All images shown are for one azimuth position,h =
130. A most obvious observation of the images is the very deepstall
on the blade for the kmean = 3.9 case (Fig. 18a, d and g). Thereare
also large vortex structures shed from the blade leaving a
verythick trailing wake. Tb values at this h are negative and lower
than0.2 N m (Fig. 19a). The reference case of kmean = 4.4 shows
signif-icantly shallower stall than the kmean = 3.9 case, with no
shed vor-tices, stall induced by trailing edge separation and a
much thinnerwake (Fig. 18b, e and h). All Tb values are positive,
though the Tb forcycle 7 is very low at 0.05 N m (Fig. 19b). The
third case, wherekmean = 4.75 shows the shallowest stall of the
three with all cyclesexperiencing trailing edge separation
extending only up to the midchord (Fig. 18c, f and i). The wake
produced is also thin, with neg-ligible ripple in the tail. All Tb
values are positive and greater than0.4 N m (Fig. 19c). Negative Tb
generated by the blades is not due todeep stall inducing high drag,
but rather the limited a that theblades see affecting the lift
generated.
Table 1Wind cycle-averaged CP at different kmean.kmean 3.9 4.4
4.75Cycle-averaged CP 0.24 0.33 0.35rgy 116 (2014)
111124peak-to-peak value of 0.62. With a common x = 88 rad/s(840
rpm), the peak-to-peak value increases as the Uamp increasesdue to
the expanding limits of U1.
-
Table 2Wind cycle-averaged CP at different Uamp.
Energy 116 (2014) 111124 121L.A. Danao et al. / AppliedEach half
of the wind cycle shows a trough in the CP curve at thepoint of an
extreme value of U1 specically at the quarter cycle(t = 0.5 s) and
three quarter cycle (t = 1.5 s). From Fig. 20b, the CPat quarter
cycle falls from 0.34 to 0.32 then to 0.23 with increasingUamp from
7% to 12% then to 30%. A more severe drop in CP is seen
at the three quarters cycle where the increasingly negative
Uampfrom 7% to 12% then to 30% cause the CP to plummet from0.29 to
0.24 down to 0.19. The CP at the start, middle and endof the wind
cycle is common for all Uamp cases. A summary ofthe cycle-averaged
CP is presented in Table 2.
The quasi-steady CP curves of all three cases are shown inFig.
21. It can be seen from the gure that the curves are overlap-ping
and practically coincident, over their ranges of k. Both theUamp =
7% and Uamp = 12% cases trace the quasi-steady CP curve
Fig. 19. Blade torque Tb plots from three rotor cycles of the
different kmean cases(markers are Tb at h = 130): (a) kmean = 3.9,
(b) kmean = 4.4, and (c) kmean = 4.75.
Fig. 20. Quasi-steady performance of the VAWT for the different
Uamp cases: (a) kvs. time, and (b) CP vs. time.
Uamp 7% 12% 30%Cycle-averaged CP 0.35 0.33 0.25of the Uamp = 30%
case. Maximum instantaneous CP is 0.34 forall three cases close to
k = 4.2. The cycle-averaged CP for Uamp = 7%is 0.35 while that of
Uamp = 30% is 0.25. When compared to thereference case
cycle-averaged CP of 0.33, a signicant drop (24%reduction) in
performance is observed for the largest uctuationamplitude of Uamp
= 30% while a marginal improvement (6% in-crease) is seen for the
smallest uctuation amplitude at Uamp = 7%.At the highest
instantaneous k, the CP registers at 0.19 (k = 6.29)for the Uamp =
30% case, while it is 0.29 (k = 4.73) for theUamp = 7% case. The
extent of the quasi-steady CP curve is longerrelative to the kmean
point as the wind cycle goes through the sec-ond half causing the k
to rise to much higher values vs. the rsthalf. The non-linear
inverse relationship of U1 to k is the primaryfactor behind the
asymmetric behaviour of the quasi-steady CP.
The stalling of one blade at different rotor cycles within the
rstquarter of the wind cycle is shown in Fig. 22. Again, all
imagesshown are for the azimuth position h = 130. Starting with
thesmallest uctuation amplitude of Uamp = 7%, the deepest stall
thatthe blades see is only partial stall from the trailing edge to
mid-chord of the blade (Fig. 22a, d and g). The wake is thin and
thereare no visible structures shed from the blade, as well as
pro-nounced oscillation of the wake tail, likely due to the
stagnationpoint staying near or at the trailing edge.
The Tb for the three cycles do not differ very much, as shown
inFig. 23a where it is 0.36 N m for cycle 1, 0.30 N m for cycle 4,
and0.27 N m for cycle 7. The reference case of Uamp = 12% shows
aprogressively deepening stall but with no shed vortices and
slightoscillation of the trailing edge wake (Fig. 22b, e and h).
The Tb val-ues at h = 130 range from a high 0.36 N m at cycle 1 to
a low of0.05 N m at cycle 7 (Fig. 23b). The last case with the
largest uctu-ation amplitude at Uamp = 30% shows a drastic change
in stallingbehaviour from shallow stalling at cycle 1 to very deep
stalling atFig. 21. Study on the effect of varying Uamp.
-
Energy 116 (2014) 111124cycle 4 and cycle 7 (Fig. 22c, f and i).
The wake of the blade changesfrom a thin strip at cycle 1 to a
thick and complex wake at cycle 7that involves alternating pairs of
almost chord-sized shed vortices.These huge differences in stalling
affect the Tb generated by the
Fig. 22. Flow visualisations of vorticity of selected rotor
cycles in the rst quarter ofthe wind cycle showing effects of
varying Uamp at h = 130.
122 L.A. Danao et al. / Appliedblades as Fig. 23c shows. Cycle 1
Tb is positive 0.36 N mwhile cycle4 and cycle 7 Tb are 0.38 N m and
0.39 N m, respectively.
Scheurich and Brown [14] conducted a study to investigate
theinuence of uctuation amplitude on the overall performance of a5
kW VAWT. Their results show that the behaviour of the unsteadyCP
almost follows the steady prole as a result of the low reducedgust
frequency of kg = 0.08, which requires 14 rotor cycles to com-plete
one wind cycle. The width of the k range is wider for theUamp = 30%
case than the Uamp = 10% case. What they foundwas that the
cycle-averaged CP of the straight-bladed VAWT wasgreatly affected
by the magnitude of the Uamp and when comparedto an ideal case VAWT
in steady wind, the cycle-averaged CPdropped to 92% of the ideal CP
when Uamp = 30% while the cy-cle-averaged CP fell only slightly to
99% of the ideal CP whenUamp = 10%. Kooiman and Tullis [10]
determined in their eldtests that uctuation amplitude has a linear
effect on the perfor-mance of the VAWT and that a 15% uctuation
only reduced per-formance by 3.6% from ideal wind conditions.
4.4. Effect of varying the uctuation frequency
The effects of the varying uctuation frequencies fc was
investi-gated by running two simulations at fc = 1 Hz and fc = 2 Hz
andcompared to the reference case of fc = 0.5 Hz. The variation of
kin time for the three fc cases is shown in Fig. 24a. It is evident
thatthe k variations of the two higher fc cases have the same
maximumof 5 and minimum of 3.93 as the reference case. The k plots
areseen to be compressed laterally as fc increases resulting in
shorterperiods (tc = 1 s for fc = 1 Hz, tc = 0.5 s for fc = 2 Hz).
A summary ofthe cycle-averaged CP is presented in Table 3.
The CP variations between fc cases show some slight
contractionin the peaks and troughs as fc increases. From Fig. 24b,
the
Fig. 23. Blade torque Tb plots from three rotor cycles of the
different Uamp cases(markers are Tb at h = 130): (a) Uamp = 7%, (b)
Uamp = 12%, and (c) Uamp = 30%.
Fig. 24. Quasi-steady performance of the VAWT for the different
fc cases: (a) k vs.time, and (b) CP vs. time.
Table 3Wind cycle-averaged CP at different fc.
fc 0.5 Hz 1 Hz 2 HzCycle-averaged CP 0.33 0.33 0.34
-
fects of varying conditions of VAWT operation on the overall
CP.The case with the highest kmean = 4.75 predict a
cycle-averaged
Eneminimum CP of the reference case is 0.236 while the case
withfc = 1 Hz shows a small rise of the minimum to 0.24 and withfc
= 2 Hz to 0.25. The maximum CP also changes in decreasing val-ues
of 0.343, 0.342, and 0.338 for fc = 0.5 Hz, 1 Hz, and 2 Hz,
respec-tively. At points within the wind cycle where U1 = 7 m/s
(start,midway, and end), the predicted CP for all fc cases are
within the0.320.33 range. These changes are considered to be
negligible asthe cycle-averaged CP marginally changes from 0.33 for
the refer-ence case and the fc = 1 Hz case to 0.34 for the fc = 2
Hz case. This isshown more clearly in the CPk plot in Fig. 25. The
CP curves of thethree fc cases are practically on top of each other
with very littledeviation of the highest fc case in the high k
region. As far as thisstudy is concerned, these differences are
insignicant and can beconsidered negligible within the test
parameters that have beeninvestigated.
A study on the effects of uctuation frequency was conductedby
Scheurich and Brown [14] for uctuation amplitudes of 10%and 30%.
For each uctuation amplitude, two fcs were tested, alow fc of 0.1
Hz and a high fc of 1 Hz. Their results show that theunsteady CP of
both fc cases generally fall within the limits of thesteady CP
performance band. As the higher fc entails fewer rotorcycles per
wind cycle, the resulting plot is less condensed withsparsely
crisscrossing unsteady CP lines. Cycle-averaged CP in-creases by
less than 2% when fc changes from 0.1 Hz to 1 Hz. At alower Uamp of
10%, the cycle-averaged CP change is even smaller
Fig. 25. Study on the effect of varying fc.L.A. Danao et al. /
Appliedat less than 1% for the same fc change from 0.1 Hz to 1 Hz.
In con-trast, McIntosh et al. [9] present increased performance as
fc risesfrom 0.05 Hz to 0.5 Hz, especially at operating conditions
near peakperformance. Danao and Howell [12] studied the effects of
differ-ent uctuating frequencies on a VAWT subjected to unsteady
windwith Umean = 6.64 m/s, Uamp = 50% and kmean = 4. All of the
casespredict performance degradation under any uctuation
frequency.While the present work shows a 25% drop in cycle-averaged
CP forconditions of fc = 0.5 Hz and Uamp = 30%, their data show a
75%drop in cycle-averaged CP when conditions are fc = 1.16 Hz
andUamp = 50%. An even higher and unrealistic fc = 2.91 Hz showsthe
cycle-averaged CP to be very close to the slower case, thusagreeing
to the results of the present work. The case with the high-est fc
at 11.6 Hz is equal to the rotational frequency of the VAWTand is
likely not observable in actual conditions, but results stillshow a
drop in performance by about 50%.
5. Conclusions
Unsteady wind simulations revealed a fundamental relation-ship
between instantaneous VAWT performance and wind speed.CP = 0.35
that is marginally higher than the peak steady wind CPof 0.33. In
both the reference case with kmean = 4.4 and the higherkmean case,
the quasi-steady CP is seen to increase as the windspeed rises. On
the other hand, the case with the lower kmean = 3.9behaves
differently with falling quasi-steady CP as the wind
speedincreases. All three cases predict cycle-averaged CPs that are
closeto steady wind performance at ks corresponding to the kmean
ofeach case. Maximum quasi-steady CP is observed to occur atk = 4.2
for all cases.
The effects of varying amplitudes of uctuation were studiedby
conducting unsteady wind simulations at Uamp of 7%, 12%and 30%. As
the magnitude of Uamp is increased, a detrimentaleffect is seen in
the quasi-steady CP due to the non-linear in-verse relationship
between U1 and k. Within the second halfof the wind cycle where the
U1 falls below the mean windspeed, the case with Uamp = 30% shows
the quasi-steady CPdrop to 0.19 as k peaks to above a value of 6.
The Uamp = 30%case is the worst performing with a cycle-averaged CP
of 0.25while the Uamp = 7% case sees an improvement in
cycle-aver-aged CP at 0.35.
Different uctuation frequencies were also tested and com-pared
to the reference case of fc = 0.5 Hz. Results show perfor-mance
invariance with respect to uctuation frequency withcycle-averaged
CP changes not exceeding 0.01. The case with thehighest fc of 2 Hz
has a quasi-steady CP curve that almost tracesthe CP curve of the
reference case, despite it being 4 times faster.Cycle-averaged CP
predictions are near the steady wind CP maxi-mum of 0.33.
The following conclusions can be derived from theresults:
When a VAWT operates in periodically uctuating wind condi-tions,
overall performance slightly improves if the following aresatised:o
the mean tip speed ratio is just above the k of the steady CP
maximum,o the amplitude of uctuation is small (1 Hz).
Operation at a kmean that is lower than k causes the VAWT torun
in the k band with deep stall and vortex shedding, to thedetriment
of the VAWT CP.
Large uctuations in wind speed causes the VAWT to run in
kconditions that are drag dominated, thus reducing the
positiveperformance of the wind turbine.
Within realistic conditions, higher frequencies of
uctuationmarginally improve the performance of the VAWT.
Acknowledgements
For the funding provided for this research, Mr. Eboibi wouldlike
to thank the Tertiary Education Trust Funds (TETF) ofNigeria
through the Delta State Polytechnic, Ozoro and Dr. Da-nao would
like to thank the Engineering Research and Devel-The data shows a
CP variation in unsteady wind that cuts acrossthe steady CP curve
as wind speed uctuates. A reference case withUmean = 7 m/s, Uamp =
12%, fc = 0.5 Hz and kmean = 4.4 has shown awind cycle mean CP of
0.33 that equals the maximum steady windCP at k = 4.5.
Three cases of different kmean were simulated to study the
ef-
rgy 116 (2014) 111124 123opment for Technology Program of the
Department of Scienceand Technology through the University of the
Philippines Col-lege of Engineering.
-
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A numerical investigation into the influence of unsteady wind on
the performance and aerodynamics of a vertical axis wind turbine1
Introduction2 Development of the numerical model2.1 Meshing
topology2.2 Mesh independence study2.3 Boundary location study2.4
Time step independence study
3 Validation of CFD model3.1 Power coefficient3.2 Flow
visualisation
4 Unsteady wind performance4.1 The reference case4.2 Effect of
varying the mean 4.3 Effect of varying the fluctuation amplitude4.4
Effect of varying the fluctuation frequency
5 ConclusionsAcknowledgementsReferences