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: louisdanao@gmail.com, louisdanao@coe.upd.edu.ph (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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124 L.A. Danao et al. / Applied Energy 116 (2014) 111124

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