wind turbine response to variation of analytic inflow vortices

8/6/2019 Wind Turbine Response to Variation of Analytic Inflow Vortices

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Wind Turbine Response to Parameter Variation of Analytic Inow Vortices

M. Maureen Hand * and Michael C. Robinson, National Wind Technology Center, National Renew-able Energy Laboratory, 1617 Cole Blvd, MS 3811, Golden, CO 80401, USAMark J. Balas, Electrical and Computer Engineering, University of Wyoming, PO Box 3295, Laramie,WY 82071-3295, USA

As larger wind turbines are placed on taller towers,rotors frequently operate in atmospheric conditions that support organized, coherent turbulent structures. It is hypothesized that these structures have a detrimental impact on the blade fatigue life experienced by thewind turbine. These structures are extremely difcult to identify with sophisticated anemometry such as ultrasonic anemometers. This study was performed to identify thevortex characteristics that contribute to high-amplitude cyclic blade loads, assuming that these vortices exist under certain atmospheric conditions.This study does not attempt todemonstrate the existence of these coherent turbulent structures.In order to ascertain theidealized worst-case scenario for vortical inow structures impinging on a wind turbinerotor, we created a simple, analytic vortex model.The Rankine vortex model assumes that the vortex core undergoes solid body rotation to avoid a singularity at the vortex centreand is surrounded by a two-dimensional potential ow eld. Using the wind turbine as asensor and the FAST wind turbine dynamics code with limited degrees of freedom,we deter-mined the aerodynamic loads imparted to the wind turbine by the vortex structure. Wevaried the size, strength, rotational direction, plane of rotation, and location of the vortex over a wide range of operating parameters.We identied the vortex conformation with themost signicant effect on the blade root bending moment cyclic amplitude. Vortices withradii on the scale of the rotor diameter or smaller caused blade root bending moment cyclic amplitudes that contribute to high damage density.The rotational orientation, clockwiseor counter-clockwise, produces little difference in the bending moment response. Vorticesin the XZ plane produce bending moment amplitudes signicantly greater than vortices inthe YZ plane.Published in 2005 by John Wiley & Sons, Ltd.

Received 9 April 2004; Revised 14 March 2005; Accepted 19 August 2005

WIND ENERGYWind Energ. 2006; 9:267280Published online 13 October 2005 in Wiley Interscience(www.interscience.wiley.com) DOI: 10.1002/we.170

Published in 2005 by John Wiley & Sons, Ltd.

Research

Article

* Correspondence to: M. M. Hand, National Wind Technology Center, National Renewable Energy Laboratory, 1617 Cole Blvd,MS 3811, Golden, CO 80401, USAE-mail: [email protected] article is a US Government work and is in the public domain in the USA.

IntroductionThe current design trend for wind turbines is towards large-diameter rotors on tall towers, each in excess of 100 m. At this scale, fatigue loads become critical design loads for wind turbine blades. 1 Blade fatigue loadsare driven by the stochastic nature of the turbulent wind inow. Damage density for composite materials isdominated by low-cycle, high-amplitude stresses. 2 Thus turbulent inow that causes large, cyclic blade rootbending moment uctuations contributes to fatigue damage.

Understanding the rotor/inow interaction driving the stochastic wind turbine loads has proven elusive toresearchers. Several researchers have studied the effect of inow turbulence on the structural response of wind

Key words:vortex; modelling;coherent turbulence;stable boundary layer


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turbines 38 in various inow environments, e.g. multirow wind parks, near complex terrain, smooth terrain.Coherent turbulence (as revealed by the Reynolds stress eld) and atmospheric stability were identied as para-meters contributing to large load excursions. Researchers have measured instantaneous Reynolds stresses thatexceed those generated with normal turbulence models. 9 All these studies were performed on wind turbinesthat operated primarily in the surface layer of the planetary boundary layer (050 m above ground level).

The planetary boundary layer is divided into several atmospheric layers that radically change throughout

the diurnal cycle. The layer near the ground is the surface layer, bounded above by the mixed layer during theday and by the nocturnal, or stable, boundary layer at night. The depth of each layer grows and shrinks as thedynamic stability promotes or restricts the development of turbulence. 10 Now that wind turbines are operatingat heights in excess of 100 m, they frequently operate within the stable boundary layer. Atmospheric phe-nomena such as low-level jets, gravity waves and KelvinHelmholtz instabilities occur within this boundarylayer. 1113 Coherent turbulence may result from these atmospheric phenomena, and these structures may causeblade load amplitudes that contribute to fatigue damage.

Although low-level jet formation has been observed from Texas to Minnesota, 10 the most frequent low-level jet activity occurs near the Oklahoma panhandle and extends into Kansas and Texas. 14 Researchers detectedthe existence of the low-level jet near Lamar, Colorado with a highly instrumented, 120 m tower as well as aSODAR (sonic detection and ranging) system. 13 The jet formed nearly every night during the summer monthsalong with associated coherent turbulence. Because this Great Plains region of the USA has a signicant docu-

mented resource15

and is currently being considered for wind energy development, it is important to explorethe implications of operating wind turbines in the presence of coherent turbulence.

Very few experimental data that include detailed turbulence measurements and corresponding wind turbineresponse measurements exist for large wind turbines. Initially we used experimental data obtained from theNational Renewable Energy Laboratorys (NRELs) long-term inow and structure test (LIST) to establish acorrelation between inow parameters, such as Reynolds stresses, and wind turbine response, such as bladeroot ap bending moment. This correlation was not clearly identiable with standard 10 min record statistics. 16

Additional complicating variables included rotor teeter dynamics and blade pitch motion for power regulation.Although the unique inow array, consisting of ve sonic anemometers, provided more spatial resolution thanprevious experiments, the delity was insufcient to produce the detail necessary to establish this causal rela-tionship. Atmospheric conditions suggested that the turbine layer frequently exhibited characteristics of thestable, nocturnal boundary layer. The turbine operated in the stable boundary layer for 30% of the entire windseason for which data were collected. 16 However, this turbine operated in a layer from 15 to 58 m, which ismuch lower than the turbines proposed for the Great Plains region. Finally, the normal turbulence model speci-ed by the International Electrotechnical Commission standard IEC 61400-1 17 assumes surface layer scalingand neutral atmospheric stability, which may not always apply at heights exceeding 50 m.

Measurement campaigns to date 39 have relied upon turbines that operate primarily in the surface layer. Theseexperiments found that Reynolds stresses, which suggest coherent turbulent ow, and atmospheric stability arerelated to large load excursions. However, the spatial delity of these experiments was not sufcient to estab-lish a causal relationship between turbulent uctuation parameters and wind turbine response. As turbine hubheights approach 100 m, operation in the stable, nocturnal boundary layer is more likely to occur. Within thenocturnal boundary layer, coherent turbulence can be generated from atmospheric phenomena that are not cur-rently modelled with turbulence models that rely upon surface layer scaling parameters. Experiments withspatial delity to establish a direct relationship are very difcult and expensive to conduct. Until such data areavailable, this analytic study was designed to begin to understand the conformation of coherent, vortex struc-tures that cause high-amplitude cyclic blade loads, assuming that these structures exist under certain atmos-pheric conditions.

We developed a simple vortex model that convects at a specied mean wind speed. This analytic model wasinterfaced with the commonly used wind turbine aerodynamics model AeroDyn. 18 The wind turbine structuraldynamics code FAST 19,20 simulated the wind turbine response to the vortex. By restricting the degrees of freedom in the model to rotor rotation only, the turbine model isolated the aerodynamic load introduced by thevortex to the wind turbine blade. We used experimental data to establish an upper bound of circulation strength

268 M. M. Hand, M. C. Robinson and M. J. Balas

Published in 2005 by John Wiley & Sons, Ltd. Wind Energ 2006; 9:267280DOI : 10.1002/we


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and vertical wind speed. We created response surfaces illustrating the blade root bending moment induced byvortices of varying radius, circulation, location with respect to the wind turbine hub, rotational direction andplane of rotation. The similarity between aerodynamic response to a vortex from two- and three-blade turbinesis clear. This study identies the size, circulation strength, orientation and position of vortices that cause high-amplitude cyclic loads.

Rankine Vortex The Rankine vortex is modelled as a potential vortex with a vortex core of variable radius undergoing solidbody rotation to avoid a singularity at the vortex centre. Parameters that are varied include the vortex radius,the circulation strength, the location of the vortex centre with respect to the turbine hub, the orientation of thevortex ow, i.e. clockwise or counter-clockwise, and the plane in which the vortex rotates, i.e. XY , XZ or YZ .Figure 1 is a diagram of the wind turbine co-ordinate system with a counter-clockwise rotating vortex in the

XZ plane. Note that the origin is located at the intersection of the wind turbine tower centreline and the hubheight. If the vortex centre is ( x0, y0, z0) in the aerodynamics code co-ordinate system, and the co-ordinates of the blade elements provided by the aerodynamics subroutine are ( x, y, z), then the following equations describevelocity components at the ( x, y, z) location that result from a vortex rotating clockwise in the XZ plane for

r R:(1)

(2)

(3)

The following equations describe the velocity components when r < R:w x x= -( )0 w

v = 0

u z z V = - -( ) + 0 w

Wind Turbine Response to Inow Vortices 269


x

z

Winduw

R

( xo, yo, zo)

v

y

Figure 1. Wind turbine co-ordinate system with counter-clockwise rotating vortex of radius R in the XZ plane. Thevortex convects to the left by adjusting x 0 by V Dt at each simulation time step.


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(4)

(5)

(6)

The vortex convects at a specied mean wind speed from - x to x by shifting x0 by V Dt at every simulationtime step. In the case of the vortex in the YZ plane, shown in Figure 2, the vortex convects laterally across therotor from - y to y by shifting y0 by V Dt at every simulation time step. We designed this numerical study toquantify the wind turbine response to the passage of an isolated vortex through the rotor. Thus we selected1 0 m s - 1 for the convection speed for all simulations in this study. At this wind speed the wind turbineoperates below the rated wind speed where the aerodynamic performance is optimized.

To map the response of the wind turbine to vortices in the inow, we varied the radius of the vortex and itscirculation strength. The radius was varied from 1 to 100 m to encompass a range that included scales of theturbine such as the blade chord (0.75 m) and the rotor radius (21.5 m). Using available experimental data, wedeveloped an upper bound for the circulation strength.

Experimental DataWe used data collected from the NRELs LIST to bound the simulated vortex circulation strength and verticalwind speed component. We conducted this eld experiment at the National Wind Technology Center (NWTC)near Boulder, Colorado from October 2000 to May 2001. A planar array consisting of ve sonic anemometerslocated 1.5 diameters upwind of the advanced research turbine (ART) collected three-component wind veloc-ities in 10 min records at 40 Hz. 9 Figure 3 shows the inow array. The ART is a two-blade, upwind, 43 mdiameter wind turbine with a teetered hub at 37 m. 21,22 Strain gauges measured the blade root bending moments.

w x x

x x z z= -

-( ) + -( )

G 2

0

02

02p

v = 0

u z z

x x z zV = - -

-( ) + -( )

+

G 2

0

02

02p



View of rotor,looking downwind

Windvw

z

R

( xo, yo, zo) x

u

Figure 2. Wind turbine co-ordinate system with counter-clockwise rotating vortex of radius R in the YZ plane. Thevortex convects to the left by adjusting y 0 by V Dt at each simulation time step.


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The spatial resolution of the four anemometers corresponding to the circumference of the rotor permits com-putation of the vorticity in the YZ plane according to the equation

(7)

The entire database of 10 min records in which the turbine operated throughout the record, consisting of 1941records, was processed to compute vorticity at each time step. The instantaneous maximum and minimumvalues (positive suggests clockwise rotation and negative suggests counter-clockwise rotation from a referencepoint upwind of the turbine) were 0.38 and - 0.43 s -1 respectively. These vorticity values correspond to circu-lation using the following relation, where RS represents the radius of the circle formed by the sonic anemome-ters, 21 m:

(8)

The highest circulation strength for a vortex in the YZ plane observed in the LIST experimental data was then526 or - 582 m 2 s- 1. Limiting this study to a maximum circulation of 1000 m 2 s-1 provides a conservative over-estimation of the circulation observed in the data. Because experimental data were not available to computevorticity in other planes, our conservative assumption was that the circulation strength of vortex structures inthe XY and XZ planes would not be substantially different from the circulation in the YZ plane.

Another restriction to the simulation parameters was based upon the vertical velocity component measuredin the data. The maximum, instantaneous, vertical velocity, or w component, in the database of records wherethe turbine operated throughout each record was 12.2 m s - 1. By restricting the simulation to vortices where thevertical velocity component did not exceed 16 m s - 1, another conservative overestimation of observed owparameters created a limit for simulation conditions. This limited the circulation for vortices of radius 1 m to

G = = r rw w p x x A

n A Rd S2

rr

w

x

w

y

v

z

i= -



T

, DP, BP BPBP

FT

FT

cup anemometer hi-resolution sonic anemometer/thermometer wind vane

T temperature DP dew point temperature

temperature difference FT fast-response temperature BP barometric pressure

Legend

Figure 3. Inow instrumentation array viewed from upwind


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100 m 2 s-1, vortices of radius 3 m to 300 m 2 s-1 and vortices of radius 5 and 7 m to 500 m 2 s-1 in additionto the restriction for all other radii introduced by the measured circulation strength, which was restricted to1000 m 2 s-1.

Figure 4 graphically depicts the population of root ap bending moment range (difference between 10 minrecord maximum and minimum) measurements for the entire database containing those records where theturbine operated throughout each record. The subset of those records corresponding to an average wind speedwithin the range 10 1 m s -1 is also included. The line in the centre of the box represents the median valueof the population. The box represents the lower and upper quartiles of the population. The whiskers extend to150% of the inner quartile range. The outliers are represented by the + symbol. A similar graphical repre-sentation of the population of circulation strength maxima and the absolute value of circulation strength minimais shown in Figure 5. Again, the entire database is contrasted with those records that fall within the 10 m s -1

mean wind speed bin for comparison.



0

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R o o

t F l a p

B e n

d i n g

M o m e n

t R a n g e

( k N m

)

All Wind Classes0

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R o o

t F l a p

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d i n g

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10 m s -1 Wind Bin

Figure 4. Root ap bending moment ranges from LIST experiment for all wind speed bins and for 10 m s -1 wind speed bin

CW CC0

100

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Y Z P e a

k C i r c u

l a t i o n

S t r e n g

t h ( m

2 s -

1 )

All Wind ClassesCW CC

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600

Y Z P e a

k C i r c u

l a t i o n

S t r e n g

t h ( m

2 s -

1 )

10 m s -1 Wind Bin

Figure 5. Circulation strength measured in YZ plane from LIST experiment for all wind speed bins and for 10 m s -1

wind speed bin. CW, clockwise rotation; CC, counter-clockwise rotation.


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Wind Turbine SimulationThe wind turbine geometry simulated using the FAST code was that of the ART, a two-blade, teetered hub,constant speed wind turbine with blade pitch control to regulate power above rated wind speeds. 21,22 This turbinehas a rotor radius of 21.5 m and produces 600 kW at rated wind speeds. This simulation study restricted themodelled degrees of freedom to rotor rotation at a constant speed only. This limited degreeoffreedom turbinemodel allowed isolation of the aerodynamic forces imparted to the turbine by the vortex structure.

Because wind turbines are designed for optimal aerodynamic performance at rated wind speeds or lower,we selected an operating point of 10 m s -1. The rated wind speed for the ART is 12.9 m s -1. If the ART oper-ated at variable speed, the corresponding rotational speed at a wind speed of 10 m s -1 would be 37.1 rpm andthe corresponding pitch angle to achieve maximum power capture would be 1. We specied the convectionspeed for the vortex to be 10 m s -1 for all simulations in this study to correspond to this turbine operating point.Under these conditions the ow remains attached across the majority of the blade span except for the rootsection. Little lift is generated in this section owing to the relatively small chord length and generally cylin-drical shape.

The study estimated aerodynamic loads using the AeroDyn subroutines incorporated in the FAST code. Forsimplicity, we did not simulate dynamic stall and we used the equilibrium wake model. These simplifyingassumptions did not affect the relative response from one simulation condition to another, but the magnitudeof the response may be underpredicted. Minor modications to the code permitted the inclusion of the vortexmodel in a fashion similar to the hub height wind le option. In other words, the velocity components at eachblade element were computed analytically at each time step using equations (1)(6).

We ran simulations at the operating point mentioned above with several inow vortex permutations. Wevaried the vortex radius from 1 to 100 m. We varied the circulation strength from 10 to 1000 m 2 s-1 with theadditional restriction that resulted from the vertical velocity limitation for radii 7 m. The centre of the vortexwas varied from hub height to the top of the rotor. We performed this series of 455 permutations using themodels representing a vortex rotating in the YZ and the XZ plane for both clockwise and counter-clockwiseorientation. We assumed that the XY vortex would be symmetric to the XZ vortex and so it was excluded. Thepredicted blade root ap bending moment statistics, including mean, range (difference between maximum andminimum values) and standard deviation, were obtained for each simulation run.

Wind Turbine Response to Vortex To visualize the turbine response to relative vortex scale variations, we generated surfaces illustrating the bladeroot ap bending moment statistics. Figure 6 shows the mean, range and standard deviation for the clockwiserotating vortex in the YZ plane. The vertical gradation of the surfaces represents the effect of shifting the vortexcentre with respect to the turbine hub height. The bottom surface represents a vortex centred at the hub ( z0 =0 m); the top surface represents a vortex centred at the top of the rotor plane ( z0 = 21.5 m); intermediatesurfaces correspond to a vortex centred at equally spaced vertical positions along the blade between the huband the tip. Similar surfaces representing a clockwise rotating vortex in the YZ plane and a counter-clockwiserotating vortex in the XZ plane are shown in Figures 7 and 8 respectively.

All surfaces show similarities in turbine response. The mean bending moment shows almost no variationwith the scale and position of the vortex. The bending moment cyclic range and standard deviation, whichcontribute to fatigue damage, both increase as the radius of the vortex decreases and the circulation strengthincreases. Vortices with radii greater than 2030 m appear to contribute very little to load variation. This sug-gests that vortices on the scale of the rotor (turbine radius 21.5 m) or smaller produce the load variation thatleads to fatigue damage.

The clockwise rotating vortex in the YZ plane has the same rotational orientation as the wind turbine, so therotational velocity of the vortex adds to the rotational velocity of the wind turbine. Intuitively, one would expecthigher loads when the velocities add as compared with the case where the velocities subtract, the counter-clockwise rotating vortex in the YZ plane. However, comparison of the bending moment range and standard




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deviation for both the clockwise and counter-clockwise rotating vortex in the YZ plane (Figures 6 and 7 respec-tively) shows similar magnitudes for the vortex centred at the hub. The counter-clockwise rotating vortex pro-duces bending moment ranges exceeding those produced by the clockwise rotating vortex by approximately20 kN m when the vortex is centred at the top of the rotor plane. In general, the loads produced when thevortex is centred at the hub are slightly higher than at any other location.



0 500 1000050100

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Gamma (m 2 s -1)Radius (m)

B l a d e

R o o

t F l a p

B e n

d i n g

M o m e n

t M e a n

( k N m

)

0 500 1000050100

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B l a d e

R o o

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n t R a n g e

( k N m

)

0 500 1000050100

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B l a d e

R o o

t F l a p

B e n

d i n g

M o m e n

t S t d

. D e v .

( k N m

)

Figure 6. Clockwise rotating vortex in YZ plane with 10 m s -1 convection speed

0 500 1000050100

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Gamma (m 2 s -1)Radius (m)0 500

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( k N m

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B l a d e

R o o

t F l a p

B e n

d i n g

M o m e n

t S t d

. D e v .

( k N m

)

Figure 7. Counter-clockwise rotating vortex in YZ plane with 10 m s - 1 convection speed


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B l a d e

R o o

t F l a p

B e n

d i n g

M o m e n t

S t d

. D e v .

( k N m

)

Figure 8. Clockwise rotating vortex in XZ plane with 10 m s - 1 convection speed

Figure 9 illustrates time-series traces of the blade bending moment for the most extreme hub-height vortexin each rotation orientation. The centre of the vortex passes through the wind turbine rotor at 120 seconds. Thesymmetric nature of the response explains the relatively small differences between the clockwise and counter-clockwise rotating vortices.

For comparison, Table I lists the magnitudes for both orientations at the edge of the surface with the highestmagnitude. For vortices centred at hub height, the counter-clockwise rotating vortex in the XZ plane has asteeper slope of blade bending moment range at the edge corresponding to small radius and high circulation

strength. On average, both clockwise and counter-clockwise rotating vortices produce similar magnitudebending moment ranges for all vortex centre locations. The vortex centred at the hub produces higher magni-tude range loads than at any other vertical location. The bending moment range for a vortex centred at the topof the rotor plane produced about half the cyclic load as the vortex centred at the hub. However, the vortexcentred at the top of the rotor could contribute to extreme peak loads. The vortex in the XZ plane producescyclic range variations that exceed those produced by a vortex in the YZ plane by 210 times.

The highest magnitude bending moment range of 629 kN m that results from a vortex of 10 m radius and1000 m 2 s- 1 circulation strength rotating counter-clockwise in the XZ plane compares favourably with theextreme range measured on the operating turbine in the 10 m s -1 wind speed bin shown in Figure 4. There areseveral complicating factors in this comparison. For example, the operating turbine has a teetered hub and themeasured blade bending moment could include the result of teeter stop impact. Also, the blade bending momentresponds with higher cyclic uctuation when the blade pitch is adjusted to regulate power production. Lastly,the mean wind speed over 10 min can uctuate signicantly and the range statistic would not necessarily rep-resent a single inow event. The simulation does not include any pitch control or turbine dynamics in orderto isolate the aerodynamic load induced by a vortex in the inow. Regardless, the relative magnitude of bendingmoment ranges produced by the simulated vortices compares favourably with those observed in the experi-mental data.

We performed a preliminary investigation of approximating the vortex ow eld by using the hub heightwind input le capability of the AeroDyn code. The horizontal, or u, velocity component produced by a 10 mradius, 500 m 2 s-1 circulation vortex at the top and bottom of the rotor was used to compute a time-varying,


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110 112 114 116 118 120 122 124 126 128 1300

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Time (s) B l a d e

R o o

t F l a p

B e n

d i n g

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t ( k N m

)

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t ( k N m

)

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Time (s)

R = 10 m, G = 1000 m 2 s -1; centred at hub height

YZ Vortex, CWYZ Vortex, CCXZ Vortex, CWXZ Vortex, CC

YZ Vortex, CWYZ Vortex, CCXZ Vortex, CWXZ Vortex, CC

R = 10 m, G = 1000 m 2 s -1; centred at top of rotor

Figure 9. Time series traces of simulated root ap bending moment that result from vortex passage

linear, vertical shear across the rotor. Similarly, we extracted the hub height vertical, or w, velocity componentfrom the vortex at each simulation time step. We used these values to create hub height wind les that variedthe vertical shear only, the vertical wind component only and the combination of the two. Note that AeroDyn

assumes specied vertical wind velocity components to be uniform across the entire rotor. Figure 10 illustratesthe time-varying bending moment response to the vortex as well as these three approximations. The amplitudeof the bending moment produced by the vortex exceeds all three approximations. Of the three approximationsthe vertical shear alone most closely reproduces the cyclic response and amplitude that result from vortexpassage. However, the vortex model induces some cyclic bending moment variation at the peak amplitudesthat is not captured by the approximations.

The aerodynamic response of a wind turbine to a vortex in the ow eld should not be substantially differ-ent for two- or three-blade machines. This is demonstrated in Figure 11, where a dimensionless representationof the response surfaces for the bending moment coefcient range for the two-blade turbine is compared withthat of a three-blade turbine where the vortex was centred both at the hub and at the top of the rotor. The three-blade turbine model is a 46 m, 750 kW rotor based on an initial iteration from the WindPACT study. 1 It wasmodelled with only the rotor degree of freedom in the same manner as the two-blade turbine model. The vortexradius was normalized with the turbine rotor radius ( R / RT). The vortex circulation was normalized with theparameter

(9)

The blade root bending moment was normalized with the parameter

(10)

where

B Q Ro T= p 3

G R V o T= 2p


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Table I. Simulated root ap bending moment values that result from vortex passage: (a) z0 = hub height; (b) z0 = top of rotor plane a

Vortex in XZ Vortex in XZ Vortex in YZ Vortex in YZ plane, CW plane, CC plane, CW plane, CC

Range (SD) Range (SD) Range (SD) Range (SD)(kN m) (kN m) (kN m) (kN m) (kN m) (kN m) (kN m) (kN m)

(a) R = 1 m, 270 12.4 223 10.2 27 5.6 28 5.7G = 100 m 2 s-1

R = 3 m, 507 26.9 367 23.2 68 7.5 71 7.5G = 300 m 2 s-1

R = 5 m, 514 36.7 459 32.6 105 10.3 101 10.2G = 500 m 2 s-1

R = 10 m, 551 48.3 629 47.4 199 17.4 185 16.8G = 1000 m 2 s- 1

(b) R = 1 m, 64 8.2 84 8.5 38 5.2 53 5.9G = 100 m 2 s-1

R = 3 m, 164 17.8 194 20.1 57 5.9 81 7.6G = 300 m 2 s-1

R = 5 m, 226 26.0 226 29.6 76 7.3 93 9.6G = 500 m 2 s-1

R = 10 m, 285 39.8 282 47.2 123 11.5 140 14.5G = 1000 m 2 s- 1

a CW, clockwise rotation; CC, counter-clockwise rotation; SD, standard deviation.

114 115 116 117 118 119 120 121 122 123 124200

250

300

350

400

450

500

550

600

Time (s)

XZ vortex, R = 10 m, G = 500 m 2 s -1

Vertical shearw componentVertical shear and w component

B l a d e

R o o

t F l a p

B e n

d i n g

M o m

e n

t ( k N m

)

Figure 10. Comparison of wind eld approximations of vortex with actual vortex-induced bending moment

(11)

The bending moment ranges for the two- and three-blade turbines are similar whether the vortex is centred atthe hub or at the top of the rotor. The three-blade turbine has a slightly steeper slope as the normalized radiusis decreased and the normalized circulation is increased. However, the similarity in the aerodynamic responseof the two turbines is conrmed.

Q V = 12 2r


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Summary This analytic study identies the aerodynamic response of a wind turbine to analytic vortex structures in the

inow. The vortex variation included radius, circulation strength, location with respect to the hub height, ori-entation and plane of rotation. We obtained blade response under each permutation through simulation usingthe FAST wind turbine dynamics code. We presented the blade responses in surface plots that illustrate thevariations in blade load as a result of vortex passage through the rotor. Owing to symmetry, the turbine responseto clockwise and counter-clockwise rotating vortices was similar for vortices in the YZ plane as well as forvor-tices in the XZ plane. We assumed that this would also be true for vortices in the XY plane. A counter-clockwise rotating vortex in the XZ plane and aligned with the hub produced the greatest load variation.We observed decreased load variation as the vortex was moved vertically to the top of the rotor plane, butthese loads still exceeded those observed as a result of passage of a vortex in the YZ plane. We assumed thatvortices in the XY plane would be symmetric to those in the XZ plane. Vortices of radii less than 2030 m, onthe scale of the rotor or smaller, produce substantial, cyclic, bending moment uctuations. Similar bendingmoment response is produced by a three-blade turbine, as would be expected. Vertical shear across the rotor

approximates the vortex-induced bending moment cyclic variation more closely than the hub height verticalwind component or a combination of vertical shear and vertical velocity. However, the amplitude of the vortex-induced bending moment is underestimated and some higher-frequency dynamics are not captured.

ConclusionsBecause high-amplitude cycles contribute to high damage density in composite materials, coherent vortexstructures cause cyclic blade amplitudes that contribute to fatigue damage. This analytic study identies the



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most likely conformation of vortices to produce large, cyclic blade amplitudesa vortex on the scale of therotor or smaller rotating in the XZ plane. This type of vortex is representative of that which could occur inassociation with atmospheric phenomena such as KelvinHelmholtz instabilities. Recent work by atmosphericscientists suggests that coherent turbulence may frequently form at heights wind turbines now occupy.

This parameter variation study of the wind turbine/vortex interaction provides a starting point for furtherresearch into the implications of wind turbine operation in the presence of coherent turbulence. This study

demonstrates that purely analytic vortices can cause blade load cycles commensurate with those observed inwind turbine measurements. Obviously coherent turbulent structures would be superimposed on normal tur-bulence in the atmosphere. Experimental data consisting of detailed inow measurements and the corre-sponding wind turbine response at a height of 80 m are currently being collected. Until additional data areavailable, this analytic model will be used for the design of wind turbine control systems that mitigate theeffect of coherent vortices impinging upon the wind turbine blades.

Appendix: NomenclatureDt simulation time step, 0.004 s

A area of integration Bo constant for normalization of blade root bending moment (kN m)CC counter-clockwise rotationCW clockwise rotationG or G vortex circulation strength (m 2 s-1)Go constant for normalization of vortex circulation (m 2 s-1)

unit vector along x-axisunit normal vector

w vorticity (s -1)Q dynamic pressure over rotor based on mean convection speed (Pa)r air densityr radial distance from vortex centre to ( x, y, z) position (m)

R radius of vortex (m) RS radius of circle formed by sonic anemometers, 21 m RT radius of wind turbine (m)u, v, w wind velocity components corresponding to x, y, z co-ordinates respectively (m s - 1)V convection speed of vortex (m s -1)

x, y, z blade element co-ordinates in aerodynamics code co-ordinate system (m)x0, y 0, z 0 position of vortex centre in aerodynamics code co-ordinate system (m)

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wind turbine response to variation of analytic inflow vortices

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