HAWT Dynamic Stall ResponseAsymmetries Under YawedFlow Conditions

February 2000 � NREL/CP-500-27898

S. Schreck, M. Robinson, M. Hand, and D. Simms

Presented at the 2000 ASME/AIAA Wind EnergySymposiumReno, NevadaJanuary 10-13, 2000

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HAWT DYNAMIC STALL RESPONSE ASYMMETRIESUNDER YAWED FLOW CONDITIONS

S. Schreck, M. Robinson, M. Hand, and D. SimmsApplied Research Division

National Wind Technology CenterNational Renewable Energy Laboratory

Golden, CO 80401

ABSTRACT

Horizontal axis wind turbines can experiencesignificant time varying aerodynamic loads, potentiallycausing adverse effects on structures, mechanicalcomponents, and power production. As designersattempt lighter and more flexible wind energymachines, greater accuracy and robustness will becomeeven more critical in future aerodynamics models.Aerodynamics modeling advances, in turn, will rely onmore thorough comprehension of the three-dimensional, unsteady, vortical flows that dominatewind turbine blade aerodynamics under high loadconditions. To experimentally characterize these flows,turbine blade surface pressures were acquired atmultiple span locations via the NREL Phase IVUnsteady Aerodynamics Experiment. Surfacepressures and associated normal force histories wereused to characterize dynamic stall vortex kinematicsand normal force amplification. Dynamic stall vorticesand normal force amplification were confirmed to occurin response to angle of attack excursions above thestatic stall threshold. Stall vortices occupiedapproximately one-half of the blade span and persistedfor nearly one-fourth of the blade rotation cycle. Stallvortex convection varied along the blade, resulting indramatic deformation of the vortex. Presence anddeformation of the dynamic stall vortex producedcorresponding amplification of normal forces.Analyses revealed consistent alterations to vortexkinematics in response to changes in reducedfrequency, span location, and yaw error. Finally, vortexstructures and kinematics not previously documentedfor wind turbine blades were isolated.

NOMENCLATURE

AOA angle of attack (deg) Cn normal force coefficient c chord length (m) cp pressure coefficient ((p-p∞)/q) DSV dynamic stall vortex

This material is declared a work of the U.S.Government, and is not subject to copyright protectionin the United States.

ft feet Hz Hertz K reduced frequency (cω/2ULOC) m meter mm millimeter N Newton q dynamic pressure (N/m2) p static pressure (N/m2) p∞ freestream static pressure (N/m2) r span location (m) R span length (m) s second t time (s) ULOC cycle averaged local velocity (m/s) U∞ freestream velocity (m/s) VDSV DSV convection velocity (m/s) x chord location (m)α angle of attack (deg)αm mean angle of attack (deg)αω oscillation amplitude (deg)α+ nondimensional pitch rate (c(dα/dt)/U) γ yaw error (deg)ψ instrumented blade azimuth angle (deg)ω blade rotation rate (rad/s)

INTRODUCTION

Horizontal axis wind turbines (HAWT�s) routinelyexperience significant time varying aerodynamic loads.Extreme aerodynamic loads impose correspondinglyhigh structural loads on turbine blades andtransmissions, thus appreciably shortening machineservice life. In addition, extreme aerodynamic loadselicit power fluctuations that adversely impact powerquality. These and other factors arising from unsteadyaerodynamic loading conspire to drive up the overallcost of energy. Such problems are not unique to stallcontrolled HAWT�s, since pitch controlled turbinesfrequently experience extreme aerodynamic loads inresponse to wind variations, inflow anomalies, andmachine dynamics.

Though accompanied by multiple adverse effects,unsteady aerodynamic loads have stubbornly resistedmitigation via existing design strategies or devices.The lack of reliable methods for dealing with unsteady

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aerodynamic loads is due largely to the constraints onaccuracy and reliability that currently limit predictionmethods for HAWT aerodynamics. This situation, inturn, derives strongly from the lack of fundamentalcomprehension of the unsteady flow fields generated byHAWT�s.

Current modeling approaches have been deemedadequate for predicting HAWT force and momentlevels, subject to qualitative guidelines regardingregimes of validity. However, uncertainty remains as towhether these models accurately portray the physics ofthree-dimensional, unsteady, vortical flow fields thatroutinely occur in HAWT aerodynamics. To establish amore substantial basis for making these judgments, thecurrent effort seeks to quantify vortex kinematics forthree-dimensional, unsteady, vortex dominated flowfields observed on HAWT blades operating in yawedflow.

Multiple influences conspire to render dynamicallystalled flows physically complex and challenging tocomprehend. Viewed simplistically as a two-dimensional process, these flows initiate when liftingsurface angle of attack dynamically exceeds the staticstall threshold. Soon thereafter, unsteady boundarylayer separation gives rise to a small but energeticdynamic stall vortex. This vortex quickly grows,convects rapidly downstream, and soon sheds from thelifting surface. During this process, the vortexgenerates a region of low pressure on the lifting surface,causing dramatic lift amplification beyond static levels,followed by abrupt deep stall at vortex shedding. [1,2]Surface pressure signatures confirm that this sequenceof events occurs on HAWT blades [3-7], andconstitutes a significant contribution to HAWT loadsand yaw dynamics. [8]

The complexity of this situation is further compoundedby the influence of three-dimensionality. Allexperimental work of this nature appears to have beencarried out in wind tunnels, ensuring steady, uniforminflow. Still, complex spatial and temporal variationswere observed in the resulting vortex dynamics.Freymuth [9] visualized the unsteady, three-dimensional vortex structures elicited by various three-dimensional lifting surfaces driven through diversemotion histories. Using surface pressuremeasurements, Robinson, et al. [10] documented the liftenhancement and prolongation due to vortex pinningand straining near the tip of a rapidly pitching wing.Also using surface pressure measurements, Lorber,Carta, and Covino [11] characterized dynamic stall atelevated Reynolds numbers over a broad parameterrange, using a wing oscillating in pitch. Theseexperiments showed significant three-dimensionality in

stall vortex development and propagation, as well asmodifications to these processes in response tounsteady parameter alterations.

Schreck, Addington, and Luttges [12] employed surfacepressure data to characterize the vortex dynamics in theroot region of a rapidly pitching wing. They notedvortex straining and pinning analogous to that at the tip,as well as similarly enhanced and prolonged liftgeneration. Unified comprehension of the vortexdynamics governing the root, midspan, and tip regionswas provided by Schreck and Helin [13], by combiningflow visualization with surface pressure topologies. Inaddition to vortex pinning near the wing tip and root,these experiments revealed radical vortex deformationnear the wing midspan associated with dramatic spatialand temporal lift fluctuations. Subsequently, Piziali[14] confirmed the existence of these structures andinteractions for higher aspect ratio geometries.

Superimposing rotation on a lifting surface, as occurswith HAWT blades, adds still other physicalmechanisms and greater complexity. The widely citedexperiments of Himmelskamp [15] indicate that stalldelay and lift enhancement due to rotation were firstnoted for aircraft propellers. To explain these results,radial thinning and chordwise acceleration of the steadyboundary layer, due to centrifugal forces and Corioliseffect, respectively, were postulated. A complementarytheoretical analysis was performed by Banks and Gadd[16] for steady laminar boundary layers on a rotatingblade at small incidence. They concluded that the zeroshear stress separation criterion was avoided due tostabilization arising from a linear adverse externalvelocity gradient.

Later experimental and analytical research was carriedout in the rotorcraft field. McCroskey and Yaggy [17]carried out a theoretical analysis for quasi-steady rotorblade flows with small crossflows. For zero orfavorable chordwise pressure gradient, the effects ofcrossflow due to rotor rotation were judged beneficial,especially in regions of incipient separation, but ofsmaller magnitude than crossflows due to rotortranslation. It was also speculated that, in strongadverse pressure gradients, the rotationally inducedcrossflows played a more influential role. Subsequentrotor experiments [18] showed that centrifugal forcesmove the fluid significantly outward in separatedregions, but are relatively unimportant regardingaerodynamic force augmentation.

More recent HAWT experiments, all employing surfacepressure measurements, reached diverse conclusionsregarding the impact of blade crossflows. Using fieldtest data, Madsen and Christensen [19] concluded

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rotational effects to be of minor importance comparedto the influences of aspect ratio and spanwise pressuregradient. Two other experiments were carried out inwind tunnels and arrived at different conclusions.Using two-dimensional airfoil performance as abaseline, Barnsley and Wellicome [20] stated that thecombination of rotational and three-dimensional effectsappeared to suppress the loss of leading edge suctionacross the entire span, compared to two-dimensionalbehavior. Alternatively, Ronsten [21] used rotatingblade data as a baseline, and noted that rotationgenerated significant differences in lift behavior only atthe pressure measurement station farthest inboard onthe blade.

The current experimental investigation employs full-scale field test data in an attempt to isolate andcharacterize the fluid dynamic mechanisms responsiblefor pronounced aerodynamic loads under yawed rotorconditions. Unsteady blade surface pressure dataacquired via the NREL Unsteady AerodynamicsExperiment have been exploited to quantify bladenormal force generation as well as dynamic stall vortexkinematics. Analysis methodologies have been appliedto these data to better understand the fluid dynamicmechanisms responsible for unsteady, separated, vortexdominated, three-dimensional, rotational bladeaerodynamics generated by HAWT�s.

EXPERIMENTAL PROCEDURE

The Unsteady Aerodynamics Experiment HAWT iswell documented [22-24]. The downwind turbineemploys a three-bladed rotor that is 10.1 m in diameterand coned 3.4° downwind. The rotor turns clockwise(viewed from downwind) at a constant 71.6 rpm, is stallregulated, and has a maximum rated power of 19.8 kW.A cylindrical tower 0.4 m in diameter supports theturbine at a hub height of 17.03 m, with a rotoroverhang of 1.32 m. This generic configuration hasbeen employed for Phases I through V of the UnsteadyAerodynamics Experiment.

Data from Phase IV were used for the investigationdocumented herein. The Phase IV rotor employed threerectangular planform blades of 5.03 m radius. Between0.14 span and the tip, blade chord was constant (0.457m), and cross-section was uniform (NREL S809).Blade twist distribution, shown graphically in Figure 1,was optimized to yield α = 15° along the entire blade ata pitch angle of 3° and a wind speed of 8 m/s.

For Phase IV, one of the three blades was instrumentedas shown in Figure 2 to acquire detailed surfacepressure data. Data used in the current work wereobtained from the full pressure tap distributions located

at 0.30, 0.47, 0.63, 0.80, and 0.95 span (Figure 2,lower). A full pressure tap distribution consisted of 22taps distributed as shown in the upper portion of Figure2. Taps were more densely distributed near the bladeleading edge to better resolve the small structures andfleeting events typically observed in this region duringdynamic stall events.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

0.00 0.20 0.40 0.60 0.80 1.00r/R

SEC

TIO

N T

WIS

T (d

eg)

Figure 1. Twist distribution for Phase IV blades.

100

90

80

70

60

50

40

30

20

10

0

% R

a diu

s (5.023

m R

a diu

s)

1009080706050403020100

% Chor d (0.457m Chor d)

S809 Air foi l

Pr essur e T ap

Full Pr essur eT ap Dist r ibut ion

Pr essur e T apsat 4% and 36%Chor d Only

Optional ift r ai l ing edge

tap is blocked

Figure 2. Pressure tap locations on Phase IV blades.

t ip

root pr essur e

suct

ion

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Pressure taps were flush mounted at the blade surface,and had inside diameters of 0.69 mm. From the taps,stainless steel hypodermic tubes having insidediameters of 0.69 mm transmitted the surface pressuresto the pressure transducers. Hypodermic tubing lengthswere kept less than 0.45 m to mitigate pressure delayand dispersion effects. Pressures were measured byfive Pressure Systems Incorporated ESP-32electronically scanned pressure transducers locatedinside the blade near the five full pressure tapdistributions. Each of the transducer pressure inputswas scanned at 520.8 Hz. In conjunction with thetubing frequency response, this provided antialiaseddigitization and minimal gain variation out to 55 Hz.[22]

During Phase IV, dynamic pressures and inflow angleswere measured near these five pressure tap distributionsusing five hole probes. Probes were mounted oncylindrical stalks at 0.34, 0.51, 0.67, 0.84, and 0.91span, with the probe tip 0.37 m upstream of the bladeleading edge. Probes were angled 20° downwardrelative to the local chordline, allowing measurement oflocal flow angles between �15° and 55°. Five holeprobe pressures were measured using the ESP-32transducers described above. Local inflow anglesmeasured by the five hole probes were converted tosection angles of attack using an experimentally derivedupwash correction. [22] Wind speed was measured 15m upwind of the turbine using cup and sonicanemometers, and wind direction was measured at thesame location using bi-vane indicators.

It is important to note that the blade geometries used forthe Unsteady Aerodynamics Experiment are atypical.Multiple Unsteady Aerodynamics Experiment programphases were designed to provide a common data set forcomparing three-dimensional blade geometry effects onaerodynamic performance. Hence, the blade geometryhas been altered parametrically, and all other variableshave been held as constant as physical designconstraints would allow. The blade that will be testednext in the Unsteady Aerodynamics Experimentprogram will be a tapered and twisted blade resemblingthose currently used by industry. This blade will betested in both a field (National Wind TechnologyCenter) and wind tunnel (NASA Ames 80 ft x 120 ft)environment, providing a comprehensive data set fordeveloping and validating new aerodynamics codes.

RESULTS AND DISCUSSION

The entirety of Phase IV data comprises 75 campaigns,each of 10 minutes duration. For each campaign, theprocessed data file consists of 262 channels digitized at520.8 Hz. Overwhelming data volume combined with

labor intensive data analysis procedures preventedconsideration of the majority of Phase IV data. Torender data analysis tractable, one Phase IV datacampaign was selected for detailed examination on thebasis of coarse level statistics. Coarse level statisticsfor all 75 Phase IV campaigns are summarized in Table1. Campaign d403022 was judged to be typical ofPhase IV data in terms of mean hub height wind speed(10.1 m/s), mean wind direction (303° true), and meanyaw error (-11.5°). The results documented herein werederived entirely from campaign d403022. Duringd403022, average blade pitch angle was +2.3°.

Mean SDWind Speed (m/s) 11.4 3.9Wind Direction (deg) 286.9 15.8Yaw Error (deg) -8.9 13.6

Table 1. Aggregate statistics for all Phase IVcampaigns.

Stall α and Stall Cn

Normal force amplification beyond static stall levels isknown to be a reliable indicator of dynamic stalloccurrence under two-dimensional conditions. [1,2]Two-dimensional wind tunnel test data show that staticstall Cn for the NREL S809 airfoil lies between 0.93and 1.05, depending on the test facility. Accordingly,to isolate those cycles in d403022 during which a stallvortex developed, stall Cn (maximum Cn during thecycle) at 0.30 span was examined for each of the 720cycles in d403022. Those cycles wherein stall Cnreached or exceeded 1.3 at the 0.30 span station wereidentified as containing a dynamic stall event. Thiscriterion was subsequently validated by examiningsurface pressure histories for cycles thus identified.

The histogram in Figure 3 shows the frequency of stallCn magnitudes at 0.30 span for d403022. Of the 720original cycles, 284 met the criterion for dynamic stalloccurrence, attesting to the prevalence of dynamic stalloccurrence during HAWT operation. Cycles were thenselected from this subset of 284 according to cycleaverage yaw error, to uniformly characterize the yawerror range between �45° and +45°. This selectionprocedure identified 21 cycles that were subsequentlyanalyzed and the results presented herein.

Clearly, the cycle selection threshold of 1.30 identifiedstall Cn�s at 0.30 span that substantially exceeded staticlevels. However, this ensured that selected cyclescontained similarly amplified Cn�s at span locationsfarther outboard, as well. Figure 4 plots stall Cn versus

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stall α for all five blade span locations, for all 21cycles. To highlight the normal force amplification dueto dynamic effects, the static Cn-α curve for the NRELS809 airfoil, tested in the Colorado State University(CSU) wind tunnel, is included. The 0.30 span locationshowed the greatest degree of stall delay beyond staticstall and associated Cn amplification, with the highest0.30 span stall Cn reaching 2.81 at α = 25.4°. Similar to0.30 span, Cn amplification was significant at 0.47 and0.63 span, with several Cn values between 1.5 and 2.0,and accompanied by stall postponement to α beyondstatic stall. At 0.80, Cn amplification remains evident,though small, as is stall delay. At 0.95 span, neither Cnamplification nor stall delay is consistently observed forall 21 cycles. Similar trends in Cn amplification andstall delay have been shown by Acker [25] for Phase IVzero yaw error conditions.

0

10

20

30

40

50

-1.00 0.00 1.00 2.00 3.00 4.00STALL Cn

NU

MB

ER O

F O

CC

UR

REN

CES

0.30 SPAN

Figure 3. Stall Cn frequency distribution at 0.30span for campaign d403022.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.0 5.0 10.0 15.0 20.0 25.0 30.0STALL ANGLE OF ATTACK (deg)

STA

LL C

n

0.30 SPAN0.47 SPAN0.63 SPAN0.80 SPAN0.95 SPANCSU, 2-D

Figure 4. Stall Cn vs. stall αααα for 21 selected cycles.

During operation at nonzero yaw, wind turbine bladesexperience significant α variation in response to bladerotation. Even in the presence of stochastic inflow and

tower wake contributions, these α variations retain adistinctly repeatable oscillatory character. These cyclicvariations can be compactly, although approximately,represented using the sinusoidal waveform parametersαω (oscillation amplitude) and αm (mean angle ofattack). Accordingly, αω and αm were defined asfollows:

αm = (αmax + αmin)/2 (1)αω = (αmax - αmin)/2 (2)

where: αmin = minimum α during cycleαmax = maximum α during cycle

These two parameters were computed for all 21 cyclesat all five span stations. The results are plotted inFigure 5. Also plotted in Figure 5 are two points ((αm,αω) = (14.0, 10.0) and (αm, αω) = (20.0, 10.0))indicating pure sinusoidal α oscillations of a two-dimensional S809 airfoil in the Ohio State Universitywind tunnel [26]. Finally, the line marked �STATICSTALL THRESHOLD� corresponds to combinationsof αm and αω that drive α up to the S809 two-dimensional static stall threshold of 15.2° just onceduring the cycle, but do not exceed it. Points below thisline indicate α histories that never exceed the static stallthreshold. Alternatively, points above this linecorrespond to α histories that exceed the static stallthreshold, passing through the threshold twice percycle.

0.0

5.0

10.0

15.0

20.0

25.0

0.0 5.0 10.0 15.0 20.0MEAN ANGLE OF ATTACK (deg)

OSC

ILLA

TIO

N A

MPL

ITU

DE

(deg

) 0.30 SPAN0.47 SPAN0.63 SPAN0.80 SPAN0.95 SPANOSU, 2-D

STATICSTALLTHRESHOLD

Figure 5. Oscillation amplitude vs. mean angle ofattack for 21 selected cycles.

Figure 5 indicates that 0.30 span reaches the highestangles of attack and exceeds the static stall thresholdfor all 21 cycles. Angle of attack at 0.47 span alsoattains high α, and all but one cycle exceeds the staticstall threshold. Span locations 0.63 and 0.80 displaysimilar trends, in that both experience moderately

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elevated α, and approximately one third of cycles atthese span locations do not exceed the static stallthreshold. Finally, the 0.95 span location is distinctfrom the other four since α exceeds the static stallthreshold in only three cycles at this span.

The trends shown in Figures 4 and 5 are consistent,attesting to the presence and influence of dynamic stallon the turbine blades. Penetrating the static stallthreshold elicited dynamic stall and generated adynamic stall vortex responsible for amplifying Cn[1,2]. Generally, dynamic amplification of Cn and stalldelay (Figure 4) correlated well with combinations ofαm and αω that penetrated the static stall threshold(Figure 5). However, some points in Figure 5 belowthe static stall threshold corresponded to points inFigure 4 that showed dynamic amplification and stalldelay. This can be attributed to the instantaneous angleof attack increments due to induced angle of attackeffects arising from blade leading edge velocity [27,28].

In addition to α variations driven by blade rotation atnonzero yaw, equally prominent α fluctuations can beprompted by blade passage through the tower wake.Passage of the blade through the tower wake resemblesa rapid ramp pitch up, and elicits a bifurcated response[29] likely to be distinct from the physics reportedherein. The 21 cycles used in this study were chosensuch that tower wake impingement on the blade did notimpact the aerodynamics of interest. This isdocumented in Figure 6, where blade interaction withthe tower wake was restricted to the gray cross hatchedarea marked �TOWER WAKE�. The individual pointsrepresent stall Cn for the five blade span locations ineach of the 21 cycles. Importantly, for the 21 cyclesemployed herein, the events of interest either precededblade passage through the tower wake, or followed it bya delay sufficient to allow tower wake impingementeffects to dissipate prior to the onset of the events ofinterest.

-50.0

-25.0

0.0

25.0

50.0

0.0 90.0 180.0 270.0 360.0STALL BLADE AZIMUTH (deg)

STA

LL Y

AW

ER

RO

R (d

eg)

0.30 SPAN0.47 SPAN0.63 SPAN0.80 SPAN0.95 SPAN

TOWERWAKE

Figure 6. Stall yaw error vs. stall blade azimuth for21 selected cycles.

α, Cn, and cp Time Series

In addition to stall α and stall Cn, time series data for α,Cn, and blade suction surface cp distributions also wereexamined to clarify the physics of the vortex dominatedflow field. Blade cp distributions enabled unambiguousdetection and tracking of the dynamic stall vortex, aswell as correlation of α and Cn with dynamic stallvortex kinematics.

Blade cp histories are presented in Figures 7 through 10,accompanied by α and Cn histories. The data in thesefour figures correspond to spans 0.30, 0.47, 0.63, and0.80 for cycle number 320, and are representative of theα, Cn, and cp histories for the other 20 cycles used inthis study. During cycle 320, average hub height windspeed was 11.7 m/s, and average yaw error was 24.2°.The format is identical for all four figures, with eachfigure containing two panels. The upper panel shows13 suction surface cp histories versus instrumentedblade azimuth angle (ψ). ψ = 0° denotes the 12 o�clockposition, and the blade rotates clockwise as viewedfrom downwind. Trace 1 corresponds to the leadingedge pressure tap, with successive numberscorresponding to tap locations progressively farther afton the suction surface blade chord. Surface pressureminima corresponding to dynamic stall vortex presence[12,30] have been highlighted with an open circlesymbol. The 13 traces have been offset to facilitateviewing, and zero references have been omitted. Thelower panel contains α and Cn histories, again versusblade azimuth angle. Note that Cn magnitudes havebeen multiplied by 10 to allow plotting on the samescale with α.

In Figure 7 (0.30 span), α reaches a minimum of �0.7°at ψ = 163°, excluding tower wake effects. Thereafter,α rises with only minor monotonicity disruptions, to amaximum of 39.9° at ψ = 337°. In response toincreasing α, cp decreases at all 13 taps, although therate of decrease is noticeably faster at tap locationsnearer the leading edge. Decreasing surface pressuresculminate in well defined cp minima corresponding todynamic stall vortex presence and marked by opencircles. After cp minima are attained, surface pressuresagain increase, signaling departure of the dynamic stallvortex. These cp minima occur at later times for tapsfarther aft on the blade chord, consistent with adynamic stall vortex that initiates near the leading edge,and then convects aft toward the trailing edge.

At taps 1 through 8, between ψ = 271° and ψ = 285°, cpvariation yields troughs that are deep and narrow,indicating passage of a condensed vortex structure.Between taps 8 and 9, at ψ = 285°, these deep, narrow

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cp troughs are abruptly supplanted by broad, shallow cpdepressions, indicating sudden alteration to the vortexstructure. Subsequently, taps 9 through 13, between ψ= 331° and ψ = 347°, record similar broad, shallowdepressions, indicating passage of a more expansivevortex structure. Note that the tower wake incursion, asindicated by α, is restricted to 106° ≤ ψ ≤ 137°,allowing ample delay for the blade flow to reestablishand wake structures to convect downstream prior to thestart of the events described above.

Figure 7. Suction surface cp histories (upper panel);angle of attack and 10××××Cn histories (lower panel).Both for cycle number 320 at 0.30 span.

In Figure 7, Cn underwent fluctuations consistent withthe cp variations described above. As cp initiallydecreased uniformly over the suction surface, Cninitially increased without interruption. Cn reached alocal maximum of 1.35 at ψ = 283°, and then brieflydecreased. At the same time the deep, narrow cptroughs were supplanted by broad, shallow cpdepressions. Shortly thereafter, Cn underwent aresurgence, rising higher, and subsequently stalling at ψ= 331° at a value of 2.58, as the vortex approached theblade trailing edge.

Some surface pressure responses apparent in Figure 8(0.47 span) are quite similar to those in Figure 7 (0.30span). At ψ = 169°, α begins to increase from aminimum of 4.2°. This α increase with time proceedsunabated to a maximum of 27.3° at ψ = 355°. Inresponse, cp decreases at all 13 taps, with the rate ofdecrease being appreciably faster for tap locations inthe leading edge region. Decreasing surface pressuresculminate in unambiguous cp minima (marked by opencircles), followed shortly thereafter by pressure rises,signaling the approach, presence, and departure of thedynamic stall vortex. Surface pressure minima occur atlater times for taps farther back on the chord, indicatingvortex initiation near the leading edge followed byconvection downstream.

Figure 8. Suction surface cp histories (upper panel);angle of attack and 10××××Cn histories (lower panel).Both for cycle number 320 at 0.47 span.

However, some behaviors in Figure 8 (0.47 span) aresignificantly different from those in Figure 7 (0.30span). In contrast to Figure 7, Figure 8 shows no abrupttransition from a deep, narrow pressure trough to abroad shallow one. Instead, the Figure 8 pressuretroughs are initially narrow and deep near the leadingedge, and gradually broaden and become shallower asthe trailing edge is approached. These cp fluctuationsare indicative of progressive vortex growth with no

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major modification to overall vortex structure. As at0.30 span the tower wake crossing, as indicated by α,occurs well in advance of the event sequence ofinterest, and imparts negligible disruption.

As at 0.30 span, the 0.47 span Cn variations wereconsistent with the cp fluctuations. When cp initiallydeclined over the suction surface, Cn increased withoutsignificant interruption. However, unlike 0.30 span, Cnat 0.47 span attained no local maximum. Instead, Cnincreased without interruption, until stalling at a valueof 1.84 at ψ = 302° as the dynamic stall vortex reachedthe trailing edge.

Figure 9 (0.63 span) shows cp fluctuations stronglyresembling those observed at 0.30 span. In response torising α, cp declines at all 13 taps, producing clear cpminima that indicate dynamic stall vortex presence(marked by open circles). These cp minima occur laterfor taps farther aft on the chord, which is consistentwith a vortex initiation near the leading edge followedby convection toward the trailing edge.

Figure 9. Suction surface cp histories (upper panel);angle of attack and 10××××Cn histories (lower panel).Both for cycle number 320 at 0.63 span.

Most significant are the similarities in vortex signaturedevelopment observed between 0.30 span and 0.63span. At 0.30 span, deep, narrow cp troughs wereobserved at taps 1 through 8, and broad, shallow cpdepressions were seen at taps 9 through 13. Thetransition from the first type of cp signature to thesecond was abrupt, occurring over a brief time andshort distance. The same is seen at 0.63 span, exceptthat the transition occurred between taps 7 and 8. Inaddition, vortex initiation, convection, and sheddingfollowed extremely similar temporal and spatialcourses. As before, Cn variations reflected thefluctuations in cp, with stall taking place at a Cn

magnitude of 1.70, at ψ = 326°, as the vortex reachedthe trailing edge. However, at 0.63 span, no local Cnmaximum followed by normal force resurgencepreceded Cn stall. As before, blade passage through thetower wake did not interfere with the aerodynamics ofinterest. Virtually identical surface pressure signatureshave been observed on pitching three-dimensionalwings [12], and the associated vortex structures havebeen characterized in detail [13].

Figure 10 (0.80 span) stands in marked contrast toFigures 7 through 9. In the three previous figures, αsubstantially exceeded the 15° static stall threshold, andstall Cn levels underwent pronounced dynamicamplification beyond static levels. Concurrently,surface pressure signatures clearly revealed thepresence of energetic dynamic stall vortices responsiblefor dynamic amplification. However, at 0.80 span, thestall α of 16.2° only shallowly penetrates the static stallthreshold. Likewise, the stall Cn of 1.24 constitutesonly weak dynamic amplification. Not surprisingly, the0.80 span cp histories generally show attenuated cpminima, indicating that the dynamic stall vortices at thisspan are significantly smaller and less energetic thanthose farther inboard on the blade. In the data used forthe current effort, stall vortex signatures usually werenot evident in the surface pressure data at 0.80 span.

Surface pressure data for 0.95 span (not shown herein),are consistent with that presented previously. At 0.95span, stall α is 14.0° and stall Cn is 0.91. Since thestatic stall threshold has not been exceeded, the cphistories contain no evidence of a vortex structure, andstall normal forces exhibit no amplification. Dataemployed in the current effort showed no evidence ofdynamic stall vortex presence at 0.95 span.

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Figure 10. Suction surface cp histories (upperpanel); angle of attack and 10××××Cn histories (lowerpanel). Both for cycle number 320 at 0.80 span.

Dynamic Stall Vortex Kinematics

When present, the dynamic stall vortex dominated theflow field over the blade, prompting significant stalldelay and amplifying normal forces beyond staticlevels. To better comprehend the physics of the vortexand the influences it exercised on the bladeaerodynamics, the kinematics of the dynamic stallvortex were documented in detail.

Dynamic stall vortex convection histories wereextracted from cp histories like those shown in Figures7 through 10, and consolidated into plots similar to thatshown in Figure 11. Figure 11 documents dynamicstall vortex chordwise position versus time, where t = 0corresponds to ψ = 0° (instrumented blade at 12 o�clockposition). The data shown in Figure 11 were extractedfrom cycle 320, the same cycle documented in Figures7 through 10. Typically, the dynamic stall vortexinitiated at approximately the same time at 0.30, 0.47,and 0.63 span. As shown by the slopes of the plots,vortex convection proceeded at approximately the samevelocity (VDSV) over the forward 0.10c. Subsequently,convection velocity at 0.30 span and 0.63 span slowedappreciably between 0.66 s and 0.75 s, and then

accelerated dramatically. During this time, convectionvelocity at 0.47 span exhibited only minor variations.

0.00

0.20

0.40

0.60

0.80

1.00

0.60 0.65 0.70 0.75 0.80TIME (s)

x/c

0.30 SPAN0.47 SPAN0.63 SPAN0.80 SPAN

Figure 11. Representative dynamic stall vortexconvection histories for cycle number 320.

At 0.80 span, vortex initiation was delayedapproximately 0.06 s, relative to the three inboard spanstations. At this span, the vortex underwent nearlyuniform acceleration between 0.0c and 0.20c, and thenstabilized at approximately constant velocity. It shouldbe noted that cycle 320 is atypical in that most cyclesdid not exhibit a dynamic stall vortex at 0.80 span.

To allow consistent comparison of vortex convectionvelocities across different cycles and span locations,linear least squares fits were applied to convectionhistories like those shown in Figure 11. This yieldedaverage vortex convection velocity (VDSV) duringvortex presence on the blade surface. In addition,reduced frequency (K = cω/2ULOC) was computed ateach span location for all cycles. These twoparameters, with VDSV nondimensionalized by ULOC, areco-plotted in Figure 12. Shown on the same plot areVDSV/ULOC corresponding to sinusoidal pitchoscillations of a two-dimensional S809 airfoil in theOhio State University (OSU) wind tunnel [26].

In Figure 12, the points corresponding to the three spanlocations can be assembled into the three groupsbounded by dashed boxes. Reduced frequencydecreases monotonically for span stations fartheroutboard due to monotonically increasing localvelocity. However, VDSV/ULOC varies nonmonoticallywith span location. At 0.30 span and 0.63 span,VDSV/ULOC assumes magnitudes between 0.03 and 0.17.However, at 0.47 span, VDSV/ULOC reaches significantlyhigher values, between 0.17 and 0.30. Consistent withprevious reports [31], VDSV/ULOC for the two-dimensional OSU data increases monotonically with K.In addition, the two-dimensional OSU data lie

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approximately between the two lower point groups(0.30 and 0.63 span) and the upper point group (0.47span). Clearly, the blade vortex convection velocitiesdeviate from two-dimensional data, and fail to increasemonotonically with K. These trends indicate thatpronounced three-dimensional effects influence vortexdevelopment, even near the center span of the highaspect ratio blade.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.02 0.06 0.10 0.14 0.18REDUCED FREQUENCY (K)

V DSV

/ULO

C

OSU, 20 +/- 10OSU, 14 +/- 100.30 SPAN0.47 SPAN0.63 SPAN

Figure 12. Nondimensional dynamic stall vortexconvection velocities vs. K.

Vortex convection histories like Figure 11 wereinterpolated in time to obtain the vortex chord locationsat all four span locations at equal time intervals. Usingthese interpolated data, vortex kinematics data fromseparate span locations were assembled into vortextopologies. This methodology exploits the vortextheorem of Helmholtz regarding the continuity ofvorticity and vortex structures [32]. One such topology,for cycle 320, is shown in Figure 13. Here, the plotarea corresponds directly to the blade planform, withthe abscissa representing the blade span, and theordinate portraying the chord. Each of the individualplots in the figure corresponds to the family of surfacepressure minima at the time specified in the legend.The times in the legend are in units of seconds, with t =0 s corresponding to ψ = 0° for the instrumented blade.

Figure 13 clearly shows that the stall vortex initiatesnear the leading edge, and is highly two-dimensional atthat time. Accelerated convection at 0.47 span coupleswith impeded convection at 0.30 and 0.63 span torapidly deform the vortex, soon rendering it highlythree-dimensional. Clearly, the midspan portion of thevortex reaches the trailing edge first, followedsubstantially later by vortex segments inboard andoutboard of midspan. In contrast to the two-dimensional vortex initiation between 0.30 and 0.63span, the nascent vortex between 0.67 and 0.80 spandisplays substantial three-dimensionality. It first

appears at a later time than the vortex inboard, andalready is oriented at a considerable angle with respectto the leading edge. These temporal and spatialrelationships suggest that vorticity straining maycontribute to vortex coalescence at extreme outboardspan locations.

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.20 0.40 0.60 0.80 1.00r/R

x/c

0.62590.64510.66430.68350.70270.72190.74110.7603

Figure 13. Representative three-dimensionaldynamic stall vortex topology for cycle number 320.

Clearly, vortex convection velocities on the turbineblade fail to vary in an orderly, monotonic fashion as afunction of K. In contrast, previous efforts using two-dimensional airfoils indicate that stall vortex convectionvelocity varies monotonically, and even linearly, withunsteady pitching parameter.[31,33] This discrepancysuggests that other turbine blade aerodynamicinfluences impact dynamic stall vortex convectionvelocity in addition to K. Figure 14 shows the responseof nondimensional vortex convection velocity(VDSV/ULOC) to changes in K, (∆(VDSV/ULOC)/∆K), as afunction of yaw error (γ).

-20.0

-10.0

0.0

10.0

20.0

-50.0 -25.0 0.0 25.0 50.0YAW ERROR (deg)

∆∆ ∆∆(V

DSV

/ULO

C)/ ∆∆ ∆∆

K

0.30 SPAN - 0.47 SPAN0.47 SPAN - 0.63 SPAN

∆∆∆∆(VDSV/ULOC)/∆∆∆∆K for 2-D

Figure 14. Vortex convection velocity sensitivity toK vs. yaw error.

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Two groups of points appear in Figure 14, oneassociated with ∆K between 0.30 span and 0.47 span,and the other corresponding to ∆K between 0.47 spanand 0.63 span. Second order least squares fits havebeen applied to both point groups. For 0.30 to 0.47span, the parameter ∆(VDSV/ULOC)/∆K is generallynegative. This is because moving from 0.30 to 0.47span prompts a decline in K and an increase in vortexconvection velocity. Alternatively, for 0.47 to 0.63span, the value of ∆(VDSV/ULOC)/ ∆K is generallypositive, since both K and vortex convection velocitydecrease.

The horizontal dashed line in Figure 14, at∆(VDSV/ULOC)/∆K = 1.78, shows the sensitivity of two-dimensional vortex convection velocity to changes inK. Notably, both point sets deviate considerably fromthis line, indicating that three-dimensionality plays akey role in these vortex dynamics. In addition, the fittrendlines reveal that turbine blade stall vortexdynamics possesses a distinct sensitivity to yaw errorinfluences. Both point groups, representing twosegments of the vortex, show the largest magnitudesensitivity to changes in K at yaw errors between �5°and �10° (γ = �5° to γ = �10°). Both lower and higheryaw error angles produce attenuated sensitivitymagnitudes, approaching zero at γ = �43° and γ = +34°.These trends with respect to γ indicate that low yawerrors elicit the most pronounced vortex three-dimensionality, while larger yaw errors result in moretwo-dimensional vortex structures. That the data pointsdeviate substantially from the fit trendline indicates thatstill other influences in addition to reduced frequency(K) and yaw error angle (γ) impact the kinematics ofthe stall vortex.

Turbine Blade Vortex Structure and Dynamics

Practical considerations discourage attempts to directlyvisualize the dynamic stall vortex structure on theturbine blade. However, detailed surface pressure data,analogous to that documented herein for the turbineblade, exist for a three-dimensional wing pitching in awind tunnel. [13] Furthermore, the vortical flow fieldover the pitching wing has been thoroughly visualizedand the fluid dynamics are well understood.Comparative analyses enable knowledge regardingwing vortex structure and dynamics to be extrapolatedto the wind turbine blade.

Obviously, inflow profiles and angle of attack historiesin the laboratory wind tunnel differ markedly fromthose in the wind turbine field test environment. In thewind turbine environment alone, inflow and angle ofattack display a bewildering spectrum of permutations.

However, all turbine blade surface pressure dataexamined in the current investigation possessed highlystereotyped features indicative of dynamic stall vortexpresence, and evolved similarly with time. Asdocumented above, the data campaign used in thisstudy was typical of Phase IV data, and the cyclesselected from that campaign for analysis herein werechosen to uniformly represent elevated Cn conditions.Notably, these features and time courses were highlyanalogous to surface pressure data acquired on a wingpitching in a wind tunnel.

The turbine blade cp histories (Figures 7 through 10)bear a striking resemblance to the data acquired for thethree-dimensional wing pitching in a wind tunnel. Likethe turbine blade, pressure taps on the wing experienceddistinct cp minima in response to dynamic stall vortexpassage. Surface pressure histories at 0.47 span on theturbine blade were very similar to those near midspanon the rectangular wing. At these central span locationson both geometries, vortex passage manifests itself asdeep, narrow cp troughs that gradually broaden andbecome shallower farther aft on the chord. In addition,surface pressure histories at 0.30 and 0.63 span on theturbine blade were very similar to those recordedinboard and outboard of midspan on the rectangularwing. At these locations, vortex passage elicited deep,narrow cp troughs near the leading edge, that wereabruptly supplanted by broad, shallow cp depressionsnear midchord.

Wing surface pressure data also were exploited tocharacterize stall vortex convection velocities [34].These data were compared with turbine blade datapresented in the current work (Figure 12), and strongsimilarities were again evident. For both the blade andthe wing, stall vortex convection velocities were highestnear midspan, and decreased significantly at locationsboth inboard and outboard of midspan.

The flow field for the rectangular wing has beenextensively visualized [13], and one panel from thesequence is shown in Figure 15. In this photograph,heavy black lines near the periphery of the photographbound the wing planform. Instantaneous α is 32.9°,during a constant rate pitch up at α+ = 0.10, that startedat α = 0° and ended at α = 60°. The vortex liesadjacent to the wing surface between the root andlocation A, and between the tip and location C. Atlocations A and C, the vortex is sharply kinked andremains near the wing surface. Here, vorticitydeformation significantly augments vortex-surfaceinteraction and amplifies local suctionmagnitudes.[10,13] Finally, between locations A andC, the vortex forms an arch over the central portion ofthe wing, with the apex located near B. Vortex

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convection velocity was substantially faster at B than itwas at A or C, due to increased exposure to thefreestream flow. Notably, the shape and location of thevortex between A and C recapitulates the vortextopology presented in Figure 13.

TRAILING EDGE

LEADING EDGE

ROOT

TIP

A

B

C

Figure 15. Visualization of three-dimensionaldynamic stall vortex.

Given these strong similarities, it is likely that theturbine blade vortex qualitatively resembles the wingvortex visualized in Figure 15. Following two-dimensional initiation, some portions of the bladevortex remain near the surface and, experiencing noincrement to convective influence, continue to exhibittwo-dimensional kinematics. At the same time, othersegments of the same vortex rise above the surface andaccelerate in response to enhanced freestreaminfluence, thus producing significant three-dimensionaldeformation. Due to the dominant role played by thevortex, aerodynamic force generation exhibitscorresponding amplification.

Although not proposed previously for wind turbineblades, the dynamic stall vortex structure hypothesizedabove is not singular. Similar three-dimensional vortexstructures have been documented for lifting surfacesundergoing diverse pitching motions [9,14,35,36]. Inaddition, analogous vorticity concentrations have beenobserved on stationary wings of high aspect ratio [37].

CONCLUSIONS

Using field data acquired via the NREL UnsteadyAerodynamics Experiment, the current work providesdetailed characterization of normal forces andassociated stall vortex kinematics for a rotating, three-dimensional turbine blade in the presence of inflowanomalies. Consistent trends and structures wereevident, enabling the following conclusions to be drawnregarding the unsteady vortex mechanics of thisHAWT, operating within the range of wind speeds andyaw angles stated.

Normal force amplification occurs only when the bladepenetrates the static stall angle of attack threshold. Thisoccurs frequently during routine turbine operation at allspan locations except those very near the blade tip.Cyclic angle of attack variation, due to blade rotation atnonzero yaw error, is sufficient to elicit stall thresholdpenetration and normal force amplification. At inboardlocations, stall normal forces over three times the staticlevel are attainable, and stall normal forces twice thestatic level are common.

Penetrating the static stall threshold initiates a two-dimensional dynamic stall vortex near the blade leadingedge. This vortex rapidly convects aft, simultaneouslyundergoing dramatic three-dimensional deformation.Near center span, vortex convection is accelerated,while at locations both inboard and outboard of centerspan, vortex convection is impeded. Three-dimensionaldistortion of the vortex locally enhances vortex-surfaceinteraction, and is accompanied by distinct surfacepressure signatures. Normal forces, already amplifiedby vortex presence, are further augmented by vortexdistortion.

The dynamic stall vortex generally can occupy one-halfof the blade span and can be present for as much asone-fourth of the blade rotation cycle. Three-dimensional blade vortex kinematics differssignificantly from those observed under two-dimensional conditions, responding strongly and inorderly fashion to changes in yaw error angle as well asreduced frequency. Lower yaw errors generallyproduce greater sensitivity to changes in reducedfrequency. This, in turn, leads to more pronouncedthree-dimensionality at lower yaw errors.

Wind turbine vortex surface pressure signatures andkinematics are highly reminiscent of those observed forthree-dimensional wings pitching in wind tunnels.Based upon this, it is likely that the midspan portion ofturbine blade vortex rises above the surface andaccelerates as it encounters stronger freestreamconvective influence. Inboard and outboard ofmidspan, the vortex remains near the surface andshielded from the freestream, impeding vortexconvection. These pronounced disparities inconvection velocity engender rapid three-dimensionaldeformation of the dynamic stall vortex.

This effort has disclosed dynamic stall vortex structuresand interactions heretofore unrecognized ascontributors to HAWT aerodynamics. Theseinteractions are pronounced in terms of temporal extentand spatial duration. Most importantly, theseinteractions exercise a strong, direct impact on HAWT

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structural loads, power quality, and overall cost ofenergy. Extension and refinement of this work willhelp provide aerodynamics models of greater accuracyand robustness for wind energy machine design andanalysis.

ACKNOWLEDGMENTS

The wind turbine data used in this investigation wereacquired solely from the National Wind TechnologyCenter Unsteady Aerodynamics Experiment (Phase IV).This field experiment was designed, built, andmaintained by Mr. Jason Cotrell, Mr. Lee Jay Fingersh,and Mr. David Jager.

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