19th Australasian Fluid Mechanics ConferenceMelbourne, Australia8-11 December 2014

Scaling of Vertical Axis Wind Turbine Dynamic Stall

A-J. Buchner1,2, A. J. Smits1,2, and J. Soria2,3

1Department of Mechanical and Aerospace EngineeringPrinceton University, Princeton NJ 08540, USA

2Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC)Department of Mechanical and Aerospace EngineeringMonash University, Melbourne, Victoria 3800, Australia

3Department of Aeronautical EngineeringKing Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

Nomenclature

c Chord length of turbine bladesKc Dimensionless pitch rateR Radius of vertical axis turbineRe Reynolds numberU∞ Freestream velocityα Angle of attackΓ Circulationθ Azimuthal blade angleλ Tip speed ratioν Kinematic viscosityΩ Rotation speed of vertical axis turbine

Abstract

Vertical axis wind turbines (VAWT) are an alternative to hor-izontal axis wind turbines (HAWT) for wind and tidal energyharvesting applications. Studies of vertical axis wind turbineshave heavily invested in understanding the behaviour of thecomplete turbine, but often with only cursory assessment of thecontributions of unsteady aerodynamics of individual blades.This paper experimentally explores the process of unsteady flowseparation, or dynamic stall, of the flow around the blades of agyromill-style vertical axis wind turbine, and the factors uponwhich its appearance and evolution rely.

Introduction

Wind and tidal energy harvesting have long been mainstays of agrowing renewable energy generation industry. Horizontal axiswind turbines (HAWT) have been the dominant turbine formfor decades, but there has at times been an interest in alterna-tive configurations. Amongst these, the vertical axis wind tur-bine (VAWT) presents a number of potential advantages, butalso significant technical challenges. Chief amongst the aero-dynamic challenges posed by vertical axis wind turbines is thedynamic stall phenomenon. This unsteady flow separation isthought to induce undesirable structural vibrations, contributeto the production of noise, and have a deleterious effect on theefficiency of the turbine, and is a crucial problem to understandand address for more widespread adoption of vertical axis windturbine technology.

The history of dynamic stall research is rich, but the highly non-linear nature of the phenomenon, and the large parameter spacewithin which the experimentalist must work, mean that previ-ous results must be considered with caution when approachingthe question of dynamic stall in a new application or context.Much previous work has been published on dynamic stall of he-licopter blades, and of flapping wings or oscillating fins [1, 2, 3],

but the combination of rotation and rapid blade incidence an-gle changes particular to vertical axis wind turbines warrantsgreater attention. Insufficient study of the relative importance ofthe kinematic parameters involved has been performed. Buch-ner and Soria [4] addresses the dynamic stall’s dependence onReynolds number, while Ferreira et al [5] studies the effect oftip speed ratio, and also touches on the dependence of the flowon Reynolds number, but the dimensionless pitching rate, andits relevance to the onset and evolution of the dynamic stall arenot addressed.

Dynamic Stall and its Governing Parameters

The bulk of the literature regarding the aerodynamics of verticalaxis wind turbine blades considers the effect of tip speed ratio λ,

λ =RΩ

U∞

(1)

but without regard for the pitch rate of the blade itself. Theseare two distinct properties of the turbine and it is possible tovary the dimensionless pitch rate Kc, defined by

Kc =cΩ

2U∞

=c

2R(2)

independently of the tip speed ratio. The definition of pitch rate,as used by Ferreira et al [5], reduces to a purely geometric form(equation 2), independent of the tip speed ratio if the tangen-tial blade velocity is used as the reference velocity. It must berecognized therefore that the tip speed ratio is primarily a mod-ulator of effective velocity relative to the turbine blade, whilstthe dimensionless pitch rate is independent and separate. Thishas not been made clear in the available literature.

Of interest is the relatively low dimensionless pitch rate of theblades in the operational range for a vertical axis wind turbine,typically on the order of 0.1 ≤ Kc ≤ 0.2. Airfoils pitchingat such low dimensionless rates typically undergo stall (if theangle of attack excursion is great enough), but it is debatablewhether such pitch rates are sufficiently high for the stall tobe considered “dynamic” stall. At these pitch rates, the flowseparation from the upper surface of the airfoil is likely to be-gin near the trailing edge, with the point of separation movingrapidly forward as the stall progresses. Dynamic stall on theother hand is characterised by a strong separation of the bound-ary layer near the leading edge and subsequent roll-up into aleading edge vortex [1].

This reasoning holds for an airfoil undergoing a pure pitchingmotion. The situation which presents itself currently however,has an important complicating factor. The existence of a ve-locity modulation relative to each turbine blade, as a result of

θ

α rela

tive

0 60 120 180 240 300 360-45

-30

-15

0

15

30

45

λ=5

λ=1

λ=2

λ=3

θ

Ure

lativ

e

0 60 120 180 240 300 360

λU

-U

+U

λ=5

λ=1

λ=2

λ=3

Figure 1: Azimuthal variation of the local angle of attack (top),and local relative velocity (bottom), experienced by each tur-bine blade, and variation with tip speed ratio indicated. Angularunits expressed in degrees.

the rotation of the turbine, means that expectations based onthe behaviour of purely pitching airfoils no longer strictly hold.It remains to be seen what the effect of this λ-related velocitymodulation is, and how it interplays with the effect of the localangle of attack variation.

It must be recognised that the angle of attack variation and az-imuthal phase change are not synonymous, but that the localangle of attack of each blade is a function of both azimuthal an-gle and tip speed ratio. This variation is illustrated for one cyclein figure 1(top). The relationship between angle of attack, tipspeed ratio, and azimuthal angle can be derived as

αrelative = arctan[

sinθ

λ+ cosθ

](3)

Of note is that the pitch-up and pitch-down parts of the cycleare not symmetric. The kinematic asymmetry, coupled with thealready low dimensionless pitching rate of the blades, suggeststhat the stall during the pitch-up phase will be less severe andmore likely to exhibit more “quasi-steady” behaviour. It is thispart of the cycle which has been measured in the present study.

The mean velocity experienced by each blade is equal to thetangential velocity, RΩ, with the cyclic variations being due tothe change in orientation relative to the freestream, as

Urelative/U∞ =√

1+2λcosθ+λ2 (4)

This is illustrated in figure 1(bottom). With increasing tip speedratio, the relative contribution of the tangential blade velocitygrows, thus reducing the size of the excursions from the mean ofboth relative velocity and angle of attack. The blade tangentialvelocity is an appropriate choice for the reference velocity whenconcerned with blade aerodynamics and is used to define the

1.5c

2.0c

x y

U

R

c

θ=0° θ=30°

θ=60°

θ=90°

representative domain

Figure 2: Vertical axis wind turbine apparatus mounted in windtunnel test facility (top), and representation of the vertical axisturbine (as viewed from above), indicating representative mea-surement domain, coordinate system, and geometric parameters(bottom). Data are taken for 30 ≤ θ ≤ 135.

Reynolds number in this experiment as

Re =RΩc

ν(5)

Experiment

Apparatus

A giromill H-type wind turbine with NACA0015 blade sectionis placed in the three by two foot wind tunnel at Princeton Uni-versity (figure 2(top)). The turbine blades are of span 450mm,have chord lengths ranging from c = 50mm to c = 100mm andare constructed of aluminium and carbon fibre. Rotor induc-tion, and blade-wake interaction, are minimised by restrictingthe turbine configuration to two blades only and low solidity.

Measurements on and above the suction surface of the turbineblades are conducted by stereoscopic particle image velocime-try (SPIV), with mineral oil seeding particle size of approxi-mately 1 µm provided by an MDG brand clean nitrogen fedfog machine. Phase-locked measurements are conducted us-ing two 2560×2160 pixel sCMOS double shutter cameras, fit-ted with 50mm focal length lenses, over a region of interestof approximately two blade chord lengths by 1.5. The cam-eras are mounted suspended above the tunnel on a turntable ax-isymmetric with the turbine to allow for measurements to betaken in blade-coordinates at arbitrary azimuthal angles. Fig-ure 2(bottom) represents a schematic view from above the tur-bine, marking some relevant parameters and the coordinate sys-tem. An approximate representative PIV measurement domainis also shown.

Parametric Conditions

The Reynolds number is set equal to 70,000, matching data pre-sented by Ferreira et al [5], but by varying the chord length theeffect of dimensionless pitching rate can be isolated from that ofthe tip speed ratio. Tip speed ratios between λ= 1 and λ= 5 areconsidered, with blade chord lengths of c= 50, 75, and 100mm,relating to a dimensionless pitching rate of Kc = 0.10, 0.15, and0.20, respectively. The turbine is rotated at an angular velocity,Ω, of 43, 60, and 90 radians per second, depending on chordlength, and the tip speed ratio is set by varying the freestreamvelocity, U∞, between approximately 4.5 and 16m/s. Measure-ments of the dynamic stall process are taken at between θ = 30

and θ= 165, in 15 increments, encompassing angles of attackbetween α = 5.83 and α = 52.5 (figure 3). The parametersexplored are listed in table 1.

θ

α rela

tive

0 60 120 1800

15

30

45

60

λ=1

λ=5

Figure 3: Conditions for which PIV measurements were taken.Angular units expressed in degrees.

Parameter ValueRe 70,000λ 1, 2, 3, 3.5, 4, 4.5, 5c 50, 75, 100 mm

Kc 0.10, 0.15, 0.20θ 30–165

Table 1: Experimental parameters.

PIV Analysis

Image pairs are pretreated via a high-pass filter and the mini-mum intensity across the ensemble is subtracted. Residual re-flections from the blade surface are removed via a masking fil-ter. Cross-correlation PIV is performed on a multi-resolutiongrid, with initial and final resolution of 64 × 64 pixels and24×24 pixels, respectively, yielding a spatial resolution of ap-proximately 0.7mm per vector, or between 0.7% and 1.4% ofchord, with 1000 velocity fields acquired at each parametriccondition and azimuthal phase.

Vectors are validated against a maximum particle displacementconstraint, and a normalised local median filter is applied. Onaverage approximately 1% of vectors are rejected, and these arereplaced via mean vector interpolation with nearest neighbours.

Results and Discussion

Strong dynamic stall vortex shedding is observed across a rangeof conditions. Figure 4 illustrates the flow separation structureat a single phase (θ= 90) via contours of phase-averaged span-wise vorticity and velocity vectors in the frame of the movingblade. The three figures relate to tip speed ratios of λ = 1, 2,

and 3 from left to right, respectively. It is observed that flowseparation from the leading edge occurs significantly earlier ineach cycle at lower tip speed ratios, consistent with the morerapid increase in the effective angle of attack of the blade, whileat higher tip speed ratios the onset of stall is delayed. Figure 4thus depicts three quite distinct phases of the dynamic stall.

Due to the earlier flow separation, the velocity field at λ = 1 iscirculatory over a large region, with a large leading edge vor-tex present. At this stage of the stall’s progression the flow hasalso separated around the trailing edge, forming a trailing edgevortex. Both of these structures continue to be fed circulationfrom their points of origin via strong shear layers. Of note isthe small region of positive vorticity between the airfoil’s uppersurface and the leading edge vortex. This is a result of the inter-action of the leading edge vortex with the no-slip condition atthe airfoil’s surface. This secondary vorticity has been observedexperimentally in pitching and impulsively started airfoil stud-ies [3, 6] but never noted in the literature, to the authors’ knowl-edge, in measurements of vertical axis wind turbine blades.

Conversely, at λ = 3, no clear leading edge separation has oc-curred and the flow over the airfoil looks much like an incipientsteady or quasi-steady stall, with marginal separation and thick-ening of the boundary layer occuring along the length of the up-per surface. The λ = 2 flow presents an intermediate case witha tight leading edge vortex, and only some sign of separation ofthe boundary layer further downstream. Based on these resultsit appears that the progression of the dynamic stall at these lowpitch rates consists of an initially quasi-steady-like separationfrom near the trailing edge, followed soon thereafter by suddenseparation of the boundary layer at the leading edge and subse-quent roll up of the boundary layer into a coherent leading edgevortex, thus forcing reattachment of the boundary layer down-stream of this vortex until separation at the trailing edge and theformation of a trailing edge vortex.

Figure 5(top) shows the evolution of the average circulation inthe leading edge vortex as a function of blade azimuthal an-gle, for several pitching rates and tip speed ratios. At this stagethe data processing is not sufficiently advanced to observe cleartrends for Kc = 0.10 and 0.20 cases, but delayed onset and de-velopment of stall with increased tip speed ratio is evident inthe Kc = 0.15 data. The usual scaling of circulation, with chordlength and freestream velocity,

Γ =Γ

cU∞

(6)

collapses the Kc = 0.15 data well (figure 5(bottom)) if alsophase-shifted to account for variation in dynamic stall onset an-gle.

x (m)

y (m

)

0 0.05 0.1 0.15-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 -40 -30 -20 -10 0 10 20 30 40

c z/U

x (m)

y (m

)

0 0.05 0.1 0.15-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 -40 -30 -20 -10 0 10 20 30 40

c z/U

x (m)

y (m

)

0 0.05 0.1 0.15-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 -40 -30 -20 -10 0 10 20 30 40

c z/U

Figure 4: Phase-averaged vorticity contours and vector fields in the vicinity of a NACA0015 vertical axis wind turbine blade, at aRe = 70,000, θ = 90, and dimensionless pitch rate Kc = 0.15. Left: λ = 1, Middle: λ = 2, Right: λ = 3.

The effect of dimensionless pitch rate, Kc, is more nuanced.Figure 6 illustrates selected vorticity fields, all relating to atip speed ratio of λ = 2 and azimuthal angle of θ = 105, butwith increasing dimensionless pitch rate from left to right. Withgreater pitch rate, the leading edge vortex system is seen to in-habit a smaller spatial extent, relative to the chord length. Atlow pitch rate, Kc = 0.10, a significant difference in stall topol-ogy is observed. The dynamic stall vortex pinches off from theleading edge earlier at the lower pitch rates, due to the closermutual proximity and enhanced interaction between the leadingand trailing edge vortices.

Concluding Remarks

The distinction between the roles of tip speed ratio and dimen-sionless pitching rate in governing the aerodynamics of windturbines has been explored. There exist some notable distinc-tions between the behaviour induced by variation of each. Thetip speed ratio is a measure of the relative importance of theblade tangential velocity to the freestream velocity, and has asignificant effect on the azimuthal position at which a leadingedge dynamic stall vortex first forms on the turbine blade. Therate at which circulation is added to the leading edge vortexonce dynamic stall has begun scales with the chord and thefreestream velocity for any given dimensionless pitching rate,but the data available at the time of publication are insufficientto draw conclusions as to the scaling behaviour of circulationproduction across a range of dimensionless pitching rates. Theresults do suggest however that the primary effect of variationin dimensionless pitching rate is in the spatial extent of the dy-namic stall vortex system relative to the blade chord, thus sig-nificantly affecting the late-stage leading edge vortex pinch-offbehaviour. A lower dimensionless pitching rate increases theinteraction strength between leading and trailing edge vorticesand induces an earlier pinch-off. This is expected to have sig-nificant implications for the force-generation behaviour of theturbine blades, and in turn the turbine efficiency.

Acknowledgements

This research is supported by the Australian-American Ful-bright Commission.

References

[1] McCroskey, W. J., “Unsteady airfoils,” Ann. Rev. FluidMech., 12, 1982, 285–311.

[2] Mulleners, K., and Raffel, M., “The onset of dynamic stallrevisited,” Exp. Fluids, 52(1), 2012, 779–793.

θ

Γ,m

2 /s

0 20 40 60 80 100 120 140-8

-6

-4

-2

0

2

4

6

8Kc=0.10, λ=2Kc=0.10, λ=3Kc=0.10, λ=3.5Kc=0.10, λ=4Kc=0.15, λ=1Kc=0.15, λ=2Kc=0.15, λ=3Kc=0.20, λ=1Kc=0.20, λ=2

θ−θstall

Γ/cU

0 20 40 60 80

-8

-6

-4

-2

0

2

4 Kc=0.15, λ=1Kc=0.15, λ=2Kc=0.15, λ=3

8

Figure 5: Average circulation in the shed vortex structures (top),and normalisation of the evolution of leading edge vortex circu-lation (bottom).

[3] Buchner, A-J., Buchmann, N., Kilany, K., Atkinson, C.,and Soria, J., “Stereoscopic and tomographic PIV of apitching plate,” Exp. Fluids, 52, 2012, 299–314.

[4] Buchner, A-J., and Soria, J., “Measurements of the three-dimensional topological evolution of a dynamic stall eventusing wavelet methods,” 43rd AIAA Fluid Dynamics Con-ference, San Diego, California, 2013, AIAA-2013-2818.

[5] Ferreira, C. S., van Kuik, G., van Bussel, G., and Scarano,F., “Visualization by PIV of dynamic stall on a vertical axiswind turbine,” Exp. Fluids, 46(1), 2009, 97–108.

[6] Soria, J., New, T. H., Lim, T. T., and Parker, K., “MultigridCCDPIV measurements of accelerated flow past an airfoilat an angle of attack of 30,” Exp. Therm. Fluid Sci., 27(5),2003, 667–676.

x (m)

y (m

)

0 0.05 0.1 0.15-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 -40 -30 -20 -10 0 10 20 30 40

c z/U

x (m)

y (m

)

0 0.05 0.1 0.15-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 -40 -30 -20 -10 0 10 20 30 40

c z/U

x (m)

y (m

)

0 0.05 0.1 0.15-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 -40 -30 -20 -10 0 10 20 30 40

c z/U

Figure 6: Phase-averaged vorticity contours and vector fields in the vicinity of a NACA0015 vertical axis wind turbine blade, at aRe = 70,000, θ = 105, and tip speed ratio λ = 2. Left: Kc = 0.10, Middle: Kc = 0.15, Right: Kc = 0.20.