wind farms with counter-rotating wind turbines

Original article

Wind farms with counter-rotating wind turbines

Ahmadreza Vasel-Be-Hagh ⇑, Cristina L. ArcherPhysical Ocean Science and Engineering, University of Delaware, Newark, DE 19716, USA

a r t i c l e i n f o

Article history:Received 7 September 2016Revised 10 October 2016Accepted 12 October 2016Available online xxxx

Keywords:Dual-rotor wind turbineWind farmWind powerLarge eddy simulationLESCFD

a b s t r a c t

The objective of this study is to assess the effects of using counter-rotating wind turbines on the perfor-mance of a wind farm. Large eddy simulations, coupled with the actuator line model, were conducted toinvestigate flow through a test wind farm with 48 large-scale wind turbines with the same layout asLillgrund in Sweden. Two counter-rotating cases were tested; first, an alternate-row wind farm in whicheach turbine has one rotor, rotating either clockwise or counter-clockwise, with alternating rows of clock-wise and counter-clockwise turbines throughout the farm; and second, a wind farm with dual-rotor windturbines in which each turbine has two rotors, with the first rotor rotating counter-clockwise and the sec-ond rotor rotating clockwise. It was found that both counter-rotating configurations were more efficientin power generation than the control case in which all turbines have one clockwise rotor; the alternate-row case was found to produce 1.4% more power and the dual-rotor case was found to produce 22.6%more power than the control wind farm. The wakes of the counter-rotating cases, particularly the windfarm with dual-rotor wind turbines, exhibit different characteristics from those in the control case. Thesedifferences are discussed through wind speed distribution, thrust coefficient, and power production ofwind turbines.

! 2016 Elsevier Ltd. All rights reserved.

Introduction

Energy supplies are moving away from environmentally dam-aging, finite, and expensive fossil fuels to renewable energyresources, such as wind [1,2], solar [3], biomass [4,5], geothermal[6], and hydrogen [7], through technological innovations. Windenergy conversion is one of the most promising renewable energytechnologies due to the extensive research that has been ongoingover the last decades to optimize aerodynamic performance ofwind turbines [8–10], structural design of wind turbines [11,12],control strategies [13–15], site selection [16,17], and the layoutof wind farms [18–21]. The focus of the investigations, however,has been mostly limited to single-rotor wind turbines with threeblades as the most popular wind energy conversion technology,and there are only a few studies that have taken into considerationwind turbines with double rotors, either co-rotating or counter-rotating [22–33]. These studies are briefly reviewed here.

According to the Betz’s law, the power coefficient of an isolatedsingle-rotor wind turbine cannot exceed CP;max ¼ 0.59. This maxi-mum power coefficient CP;max was deduced assuming that: theeffects of fluid rotation were negligible, the flow was axial, therewas no hub, the rotor had an infinite number of blades with no

drag force exerted on them, there was no heat transfer, the flowwas incompressible, and finally, the thrust force was distributeduniformly over the rotor. Any deviation from these ideal conditionscauses a reduction in the power coefficient. Extending from theBetz’s law, and based on similar assumptions, Newman [22] provedthat the maximum power coefficient of a dual-rotor wind turbineis CP;max ¼ 0.64. Hence, under the above mentioned ideal condi-tions, a single isolated dual-rotor wind turbine can produceapproximately 13% more power in comparison with an isolatedsingle-rotor wind turbine. Jung et al. [23] used the blade elementtheory to investigate the aerodynamic performance of a singlesmall-scale dual-rotor wind turbine (30 kW). The effect of thewake of the upstream rotor on the downstream rotor was takeninto account using the wind tunnel data obtained by Neff and Mer-oney [34]; the aerodynamic interference between the two rotors,however, was neglected. The best aerodynamic performance wasachieved with an upstream rotor half the size of the downstreamrotor, located at a distance equal to one-quarter of the diameterof the larger rotor.

Dual-rotor wind turbines have also been studied by researchersat Iowa State University. They conducted wind tunnel experimentsunder neutral stability conditions to investigate the aeromechanicsand wake characteristics of a single isolated dual-rotor wind tur-bine for both co-rotating and counter-rotating cases [24]. Therotors were the same size and were located at a distance equal

http://dx.doi.org/10.1016/j.seta.2016.10.0042213-1388/! 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: [email protected] (A. Vasel-Be-Hagh).

Sustainable Energy Technologies and Assessments xxx (2016) xxx–xxx

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to one-quarter of the rotor diameter from each other. In addition tomeasuring power output and wind loads, they used particle imagevelocimetry to quantify the flow characteristics in the near-wakeof turbines. Their measurements revealed that the power produc-tion performance of the dual-rotor wind turbines and the windloads acting on them were much higher compared to those of asingle-rotor wind turbine. Furthermore, the rotational directionof the rotors was found to have a significant effect on the aerome-chanic performance of the dual-rotor wind turbines; the counter-rotating dual-rotor wind turbine was found to harvest more energythan the co-rotating dual-rotor wind turbine. They also studied aunit of two in-line wind turbines where the upstream one hadtwo rotors and the downstream one had one rotor [25]. The sec-ondary rotor of the dual-rotor wind turbine, located immediatelyupstream of the main rotor, was approximately half the size ofthe main rotor. The single-rotor wind turbine located downstreamof the dual-rotor wind turbine was found to produce more powerin comparison with the single-rotor wind turbine located down-stream of another single-rotor wind turbine, provided that the dis-tance between downstream and upstream turbines was larger than4D, where D is the rotor diameter. In a different study, they solvedReynolds Averaged Navier–Stokes (RANS) equations to find anoptimal design for a single isolated dual-rotor wind turbine thatgives the highest power coefficient CP at one operating point[26]. Three optimization parameters were taken into account: therotor diameter, the distance between the two rotors, and the tip-speed ratio. Two two-dimensional parametric sweeps were carriedout. First, the secondary rotor size and tip-speed ratio were variedwhile the distance between two rotors was constant. An optimaldiameter of D/4 was found for the secondary rotor, where D wasthe diameter of the main rotor. Then, the distance between therotors and the tip-speed ratio of the secondary rotor were variedwhile holding the secondary rotor diameter at the optimum value(i.e. D/4). The best performance was obtained for a distance of 2D

between the two rotors, where D was the diameter of the mainrotor. The optimal tip-speed ratio was found to be 6. This optimaldesign caused the power coefficient of the wind turbine to increaseby approximately 7%. They then conducted large eddy simulationsunder neutral and stable atmospheric conditions to study theeffects of atmospheric stability conditions on the performance ofthe above mentioned optimal design [27].

Shen et al. [28] used the actuator line model along with theEllipSys3D code to simulate flow over a single isolated dual-rotorwind turbine. The EllipSys3D code, developed at the TechnicalUniversity of Denmark in cooperation with the Department ofWind Energy at Risø National Laboratory, is a finite volume dis-cretization of the incompressible Reynolds averaged Navier–Stokes(RANS) equations in general curvilinear coordinates. The dual-rotorwind turbine was assumed to have two rotors of the same sizewith a distance varying from 0.05D to 0.4D, where D was the rotordiameter. The mean power coefficient was found to be almostindependent of the distance between the rotors in the studiedrange. The amplitude of the fluctuations of the instantaneouspower coefficient, however, was found to significantly decreasewith the distance between the rotors.

In addition to the aerodynamic performance, several otheraspects of dual-rotor wind turbines, such as design, control andelectrical concerns, have been taken into consideration. Farahaniet al. [29] evaluated the fault-ride-through capability of dual-rotor wind turbines and single-rotor wind turbines under constantpitch angle and constant speed conditions, and realized that dual-rotor wind turbines introduce higher damping torque to the net-work in both constant speed and constant pitch angle modes. Byusing dual-rotor wind turbines, both steady state and transientperformance of the wind farm would be enhanced. They also eval-uated risk of subsynchronous resonance (SSR) for both single-rotorand dual-rotor wind turbines [30]. They introduced a genetic algo-rithm for optimizing the dual-rotor system design with the objec-

Nomenclature

c chord length [m]D rotor diameter [m]F force [N]f Coriolis parameter ½rad # s$1%l mixing length [m]P power [kW]p pressure [Pa]q temperature flux ½K #m # s$1%r distance between cell center and blade element [m]S strain rate tensor ½s$1%t time [s]u wind speed ½m # s$1%X X axis in Cartesian coordinatesY Y axis in Cartesian coordinatesZ Z axis in Cartesian coordinates

Greek lettersD filter width [m]d Kronecker deltae alternating unit tensorh temperature [K]m turbulent viscosity ½m2 # s$1%q density ½kg #m3%s stress tensor [Pa]U site latitude [rad]x Earth rotational speed ½rad # s$1%

SubscriptsT thrustP poweri index of X directionj index of Y directionk index of Z directionext external

AcronymsALTR alternate-rowCP power coefficientCT thrust coefficientDRWT dual-rotor wind turbineLES large eddy simulationPISO pressure implicit with split operatorPr Prandtl numberSOWFA simulator for wind farm applicationsSSR sub-synchronous resonanceRANS Reynolds averaged Navier–Stokes

ConstantsCs Smagorinsky constantg gravitaional acceleration

2 A. Vasel-Be-Hagh, C.L. Archer / Sustainable Energy Technologies and Assessments xxx (2016) xxx–xxx



tive of reducing the SSR possibility to the same level of single-rotorwind turbines. No et al. [31] presented the blade pitch controlscheme and a nonlinear simulation software for the performanceprediction of a new design for dual-rotor wind turbines. The pro-posed dual-rotor wind turbine was treated as a constrainedmulti-body system and the equations of motion were obtainedusing the multi-body dynamics approach. Blade element andmomentum theory along with a simple flow interaction modelwere used to calculate the aerodynamic forces and torques. Theeffectiveness of the proposed pitch control algorithm was exam-ined by implementing it under three different operational modes:maximum aerodynamic torque mode, optimum tip-speed trackingmode, and rpm limitation mode. Inspired by the power transmis-sion of motor vehicles, Kim [32] designed a new planetary-typepower transmission for the dual-rotor wind turbines whichdepends on the torque ratio and not the gear ratio, as in commongear systems. The experimental results showed that the proposedplanetary-type gear box caused fewer energy losses, and had ahigher efficiency and lower manufacturing costs, making it suitablefor commercial wind turbines. Habash et al. [33] engaged a newinduction generator (TRIAS generator) in dual-rotor wind turbinesthat integrates a unique symmetry winding technology with astandard generator. Both standard induction and synchronousmachines have one set of stator winding per phase, whereas theproposed generator has two stator windings per phase. The addi-tional winding creates the reactive component that provides themeans for maximum energy transfer and efficiency.

Our review on counter-rotating wind turbines indicates that theexisting literature is focused on single isolated wind turbines, andthere is a dearth of published research exploring the performanceof counter-rotating wind turbines in commercial-sized wind farms.The present study aims at filling this gap by examining the perfor-mance of contour-rotating wind turbines in a wind farm consistingof 48 wind turbines with rotor diameter and hub height of 93 mand 63 m respectively. To this aim, three large eddy simulationswere conducted under neutral atmospheric conditions in the pre-vailing wind direction (southwest). The wind farm configuration,including base locations of the wind turbines and their rotationaldirection are presented in the next section, followed by a descrip-tion of the computational methodology used in the present study.Results of the large eddy simulations will then be presented anddiscussed in three parts: the first on the aerodynamic loads actingon the wind turbines, the second on the power production perfor-mance of the wind farm, and the third on the wake characteristics.

Wind farm configurations

A wind farm with 48 wind turbines with the same layout as Lill-grund in Sweden was chosen as the test case. Wind turbines wereassumed to be SWT-2.3-93 model manufactured by Siemens AGwith a rated power 2.3 MW, rotor diameter of 93 m, cut-in windspeed ucutin = 4 m/s, rated speed urated = 15 m/s, and cut-out windspeed ucutout = 25 m/s. Large eddy simulations were conducted toexamine three configurations illustrated in Fig. 1 in the prevailingwind direction from the south-west (i.e. 225" from the north usingmeteorological convention).

The first was the control case, illustrated in Fig. 1a, in which allturbines were assumed to have a single three-blade rotor rotatingclockwise. In the second case, illustrated in Fig. 1b, an alternate-row configuration (ALTR) was investigated in which each turbinehas one single three-blade rotor, rotating either clockwise orcounter-clockwise, with alternating rows of clockwise andcounter-clockwise turbines throughout the farm. Turbines in theodd rows, including the front row, were rotating clockwise,while turbines located in the even rows were rotating

counter-clockwise. In the third case, illustrated in Fig. 1c, each tur-bine had two three-blade rotors, with the first rotor rotating clock-wise and the second rotor, located immediately upstream of thefirst one, rotating counter-clockwise. A schematic side view of eachdual-rotor wind turbine (DRWT) is depicted in Fig. 1d.

Computational methodology

The model formulation and numerical strategies employedthroughout the present study are detailed in this section.

Large eddy simulations (LES)

Large eddy simulations treat the dynamics of large eddies byremoving those with scales smaller than a filter width from theunsteady Navier–Stokes equations and parameterizing their effectsvia subgrid scale models. The filter width is defined asD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDXDYDZ3

pwhere DX; DY , and DZ are the cell size in X, Y and

Z directions respectively. The incompressible formulations of thefiltered continuity and momentum equations are as follows:

@!ui

@xi¼ 0; ð1Þ

@!ui

@tþ @!ui!uj

@xj¼ $ @p

@xi$@sDij@xj

$ 1q0

@p0ðx; yÞ@xi

þ Fext; ð2Þ

where the bar denotes spatially resolved components; i; j, and k arethe indices of the three spatial components x; y and z; u is the windspeed; t is time; p is the modified pressure defined as½pðx; y; z; tÞ=q0 $ p0ðx; yÞ=q0 þ q0gz=q0 þ ðskkÞ=3%; p and p0 are thestatic and mean pressure; q0 is the reference air density; sDij is thetraceless part of the wind stress tensor; and Fext stands for the exter-nal forces applied to the wind, including those induced by the windturbines. According to the Boussinesq eddy viscosity assumption,the traceless stress tensor sDij given in Eq. (2) is defined as:

sDij ¼ $2mtSij; ð3Þ

where the kinematic eddy viscosity mt is defined using the subgridscale model proposed by Smagorinsky [35] as:

mt ¼ ðcsDÞ2jSj; ð4Þ

in which cs ¼ 0:168 is the Smagorinsky constant,Sij ¼ ð@!ui=@xj þ @!uj=@xiÞ=2 is the filtered strain rate tensor, and

jSj ¼ffiffiffiffiffiffiffiffiffiffiffiffi2SijSij

qis the norm of the filtered strain rate tensor. The exter-

nal force Fext term in Eq. (2) includes the Coriolis force, the buoy-ancy force, and the force exerted by turbine blades that iscalculated using the actuator line model presented in the next sec-tion. Accordingly, the external force Fext can be expressed as:

Fext ¼1q0

Fi þ gh$ h0h0

" #di3 $ ei3kf uk; ð5Þ

where Fi is the force generated by the actuator line model, eijk is thealternating unit tensor, g stands for the gravitational acceleration, his the potential temperature, h0 ¼ 300 K is the reference tempera-ture, dij is the Kronecker delta, and f is the Coriolis parameter,defined as f ¼ 2xsin/, in which x is the Earth rotational speed() 2:95* 10$5 rad=s), and / is the site latitude. The followingpotential temperature equation needs to be solved coupled withEqs. 1 and 2 to obtain the potential temperature needed to calculatethe buoyancy term in Eq. 5:

@!h@t

þ @ð!uj!hÞ

@xj¼

@qj

@xj; ð6Þ

A. Vasel-Be-Hagh, C.L. Archer / Sustainable Energy Technologies and Assessments xxx (2016) xxx–xxx 3



where qj represents the temperature flux defined as:

qj ¼ $ mtPrt

@!h@xj

; ð7Þ

and Prt is the subgrid turbulent Prandtl number defined as [36]:

Prt ¼1

1þ 2 lD

; ð8Þ

in which,

l ¼min 7:6 mt

D ðs$1

2Þ;D$ %

if s > 0

D if s + 0

(ð9Þ

and

s ¼ gh0

@!h@z

: ð10Þ

Usually l ¼ D, and hence, Prt ¼ 13.

Wind turbine modelling

The actuator line model, proposed by Sørensen and Shen [37],was employed along with LES to model the wind turbines. In thismodel, the turbine blades are represented by three rotating linesthat are discretized into blade elements with centers located atðxj; yj; zjÞ. Using airfoil lookup tables, the aerodynamic forces arecalculated for each blade element f ai ðxj; yj; zj; tÞ. Summation of theaerodynamic forces of blade elements corrected via a regulariza-tion kernel yields the body force exerted by the blades onto theflow field,

Fi ¼X40

j¼1

f ai ðxj; yj; zj; tÞp3=2e3 exp $ rj

e

$ %2& '

; ð11Þ

where f ai ðxj; yj; zj; tÞ denotes the aerodynamic forces at 40 equallyspaced blade elements with centers located at ðxj; yj; zjÞ; Fi is theforce field projected as a body force onto the CFD grid, rj is the

Fig. 1. Top view of the wind farm configurations studied in the present paper; (a) control case where all turbines rotate clockwise, (b) alternate-row (ALTR) configurationwhere turbines in the odd rows rotate clockwise (in black) and turbines in the even rows rotate counter-clockwise (in red), and (c) dual-rotor wind turbines (DRWTs) casewhere each turbine has two three-blade rotors, the upstream rotor rotates counter-clockwise and the downstream one rotates clockwise. Panel (d) illustrates a schematic sideview of the dual-rotor wind turbines of the third configuration shown in panel (c). (For interpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)




distance between the cell center and the blade element, and e isused to control the Gaussian width so that it spans from the lead-ing edge to the trailing edge of the blade elements. In the presentwork, e was set to be c/4.3, where c indicates the chord length ofthe blade elements, so at both trailing and leading edges (i.e.rj ¼ c=2) the exponential term was reduced to approximately 1%of its maximum [38]. The power calculations are based on theaerodynamic torque that is exerted on the blades. Multiplyingthe aerodynamic torque by the rotational speed of the rotor yieldsthe power output.

Numerical solution

The governing equations described in two previous sectionswere solved using Simulator fOr Wind Farm Applications(SOWFA), which is a CFD solver developed by the United StatesNational Renewable Energy Laboratory [39] and is based on theOpenFOAM toolbox [40]. The equations were discretized using afinite volume formulation. A second order central differencingscheme was used to conduct the spatial discretization as largeeddy simulations are too sensitive to false numerical diffusion

Fig. 2. Thrust coefficient CT of single-rotor wind turbines of the control case (Fig. 1a) and thrust coefficient CT of rotors of dual-rotor wind turbines of the DRWTs case (Fig. 1c).




and the central differencing scheme significantly reduces thenumerical diffusion in comparison with the upwind scheme.The Pressure Implicit with Split Operator (PISO) algorithm wasused for the pressure–velocity coupling [41]. Comparing to otherpressure–velocity coupling methods, such as SIMPLE [42] andSIMPLEC (SIMPLE-Consistent) [43], the PISO algorithm requiresmore CPU time per solver iteration; however, it significantly helpsto maintain a stable calculation with larger time steps, and hence,decreases the number of iterations.

Simulation setup

The computational area was a rectangular cuboid with width,depth and height of 4000 m, 4000 m, and 1000 m respectively. Atfirst, a coarse mesh with approximately 5,900,000 hexahedralcells was created using the blockMesh utility supplied with Open-FOAM. This mesh was then refined locally around the wind tur-bines leading to approximately 42,000,000 cells. The simulationswere conducted in two steps. First, a precursor simulation was

Fig. 3. Standard deviation of the thrust coefficient of single-rotor wind turbines of the Control Case (see Fig. 1a) and the rotors of dual-rotor wind turbines of the DRWTs Case(see Fig. 1c).




carried out to develop the flow field through the computationaldomain without taking into account the wind turbines for12,000 s and then a wind plant simulation was performed for2000 s by adding the wind turbines into the developed flow field.Conducting the wind plant simulation over the above-describedcomputational domain requires approximately 60,000 CPU-hoursusing a 2.4 GHz processor of a high-performance computing clus-ter. The present study was conducted using 192 parallelprocessors.

A horizontally-averaged wind speed of 9 m/s was specified atthe height of 90 m in the south-west direction, i.e. 225" clockwisefrom the north using the meteorological convention. Wind speedat other heights was initialized using the log law under the neu-tral stability condition. The wind speed boundary conditionswere set as slip at the top and bottom boundaries, outlet at thenorth and east boundaries, and inlet with time-varying mappedfixed values at the west and south boundaries. The buoyant pres-sure boundary condition was used at all six boundaries of thedomain to define the pressure boundary field. The temperatureboundary field was set as fixed gradient with a uniform valueof 0.003 K m/s at the top boundary, zero gradient at the bottom,east, and north boundaries, and time-varying mapped fixed val-ues at the south and west boundaries. Finally, the surface rough-ness was set to be 0.016 m.

Results and discussions

Aerodynamic loads

The thrust, or axial force, acting on the rotor of a wind turbinecan be expressed as the mass flow rate of the wind flow throughthe rotor multiplied by the change in velocity in the axial direction.Hence, the reduction in wind speed, or, in other words, themomentum extracted from the wind, is directly related to thethrust coefficient of the rotor. Fig. 2 compares the thrust coefficientCT of the rotor of single-rotor wind turbines of the control casewith the thrust coefficient of the rotors of dual-rotor wind turbinesof the DRWTs case along every column of the wind farm. Thrustcoefficients presented in this figure were calculated using theundisturbed freestream velocity of wind upstream of the frontrow turbine of each column, which was 8.81, 8.4, 8.87, 8.83, 8.76,8.59, 8.66, and 8.54 m/s for columns 1 to 8 respectively. The thrustcoefficients of the upstream and downstream rotors of dual-rotorwind turbines are approximately equal for all turbines in all col-umns indicating that both rotors extract almost equal amount ofmomentum from wind. It is also observed that the thrust coeffi-cient of the rotor of single-rotor wind turbines is larger than thethrust coefficient of each rotor of dual-rotor wind turbines for allturbines in all columns. However, the total thrust coefficient ofdual-rotor wind turbines, defined as the sum of the thrust coeffi-cients of upstream and downstream rotors, is larger than the thrustcoefficient of the rotor of the single-rotor wind turbines. Hence, therotor of single-rotor wind turbines delivers better aerodynamicperformance in comparison with each individual rotor of dual-rotor wind turbines, but the overall performance of dual-rotorwind turbines is better than the overall performance of single-rotor wind turbines. As is seen in Fig. 2, the total thrust coefficientof dual-rotor wind turbines that are located in the front row ofeach column is slightly beyond 1, whereas according to the Betz’slaw, the thrust coefficient of a single-rotor wind turbine can neverexceed CT;max ¼ 1 even under ideal conditions. The variation trendof the thrust coefficient of single-rotor turbines of the alternate-row case (not shown) was similar to that of the control wind farm.

The thrust coefficients of both single-rotor and dual-rotorwind turbines suffer a significant drop as wind moves from the

front row to the second row of the wind farm. In the control case,the thrust coefficient of single-rotor wind turbines continues todrop as wind moves from the second row to the third row, whilein the wind farm with dual-rotor wind turbines the thrust coef-ficients of the third-row wind turbines are larger than the thrustcoefficients of the second-row wind turbines, indicating thatwind flow recovers faster downstream of the second-row dual-rotor wind turbines than the second-row single-rotor wind tur-bines. It should be mentioned that the jump in the thrust coeffi-cient of the forth turbine of column 4 and the third turbine ofcolumn 5 is due to the ‘‘hole” inside the Lillgrund wind farm,shown in Fig. 1. There is a relatively larger distance betweenthese turbines and their upstream turbines so the velocity deficitin the upstream wake is more eroded and wind gains moremomentum before reaching these turbines.

In addition to the aerodynamic performance, comparing thethrust coefficient of single-rotor and dual-rotor wind turbines pro-vides insights into their length of the near-wake region and thelevel of turbulence that is induced by them. According to Fig. 2,as the dual-rotor wind turbines have higher combined thrust coef-ficient than single-rotor wind turbines, the length of the near-wakeregion downstream of the dual-rotor wind turbines is longer thanthe length of near-wake region downstream of the single-rotorwind turbines, and dual-rotor wind turbines introduce larger levelsof turbulence into the flow.

Fig. 4. Time history of the mean power production of the wind farms.

Fig. 5. Time-averaged values of the mean power production of the wind farms.




The thrust force acting on the rotor of a wind turbine is adynamic load that is directly transmitted to the tower on whichthe rotor is mounted. Hence, the standard deviation of the thrustcoefficient, which is a measure of its dynamic nature, can be usedas a parameter to assess the fatigue loads acting on the wind tur-bine. In the front row of all columns, the standard deviation ofthe thrust coefficient of each individual rotor of dual-rotor windturbines is greater than the standard deviation of the thrust coeffi-cient of the rotor of the corresponding single-rotor wind turbine(Fig. 3), meaning that, in the front-row of each column, dual-rotor wind turbines are subjected to significantly greater dynamicloads in comparison with single-rotor wind turbines. As wind goes

down to the next rows of the wind farm, the standard deviation ofthe thrust coefficient of single-rotor wind turbines goes beyond thestandard deviation of the thrust coefficient of each individual rotorof dual-rotor wind turbines.

Power production

The time history of the mean power production of the windfarm for the three cases (control, ALTR, and DRWT) is illustratedover 1000 s of flow-time in Fig. 4. The mean power is defined asthe sum of the power production of all wind turbines of the windfarm divided by the total number of turbines. The amplitude of the

Fig. 6. Panels (a1) to (h1): comparison between the time-averaged power production of single-rotor and dual-rotor wind turbines in the three cases considered (control,ALTR, and DRWT). Panels (a2) to (h2): gain in power production of each wind turbine in DRWT and ALTR cases with respect to corresponding single-rotor wind turbine in thecontrol case.




fluctuations of the mean power production of the wind farm withdual-rotor wind turbines is significantly larger than that of thealternate-row and control cases. Looking at the time-averaged val-ues of the time history of mean power production of each windfarm (Fig. 5), it appears that alternating the rotational directionof wind turbines along a column improves the power productionperformance of the wind farm by 1.4%. To put this into perspective,assuming that the studied wind farm always operates under theconditions considered here, alternating the rotational direction ofthe wind turbines would increase revenue by more than $2 millionover the lifespan of the wind farm. Employing dual-rotor windturbines, however, is more effective and can boost the total powerproduction of the wind farm up to 22.6%, although the costs of

installing twice as many blades and generators would need to beconsidered too.

Fig. 6 draws a comparison between the time-averaged powerproduction of single-rotor and dual-rotor wind turbines along allcolumns of the wind farm. Adding a secondary rotor to the windturbines brings a considerable increase in the productivity of thewind turbines. The gain in power production of the wind turbinesvaries from 5% to 40% depending on their location inside the windfarm; the highest gain was observed in the front row, and thelowest gain was observed in the second row and in rows deepdownstream of the wind farm (seventh and eighth rows). Consid-ering the higher fatigue loads that dual-rotor wind turbines aresubjected to, one may argue that it is not worth it to employ

Fig. 6 (continued)




dual-rotor wind turbines in the second row and in deep rows of awind farm.

As is observed in Fig. 6, in the ALTR case, some of the wind tur-bines produce more power in comparison with their correspondingturbines in the control wind farm, while there are some other windturbines that produce less power than their corresponding turbinesin the control case. The overall impact of employing alternate rowsof clockwise and counter-clockwise turbines, however, is positiveand the mean power production of the alternate-row configurationis greater than that of the control case (Fig. 5).

Wake characteristics

No significant trend was observed by comparing the velocityfields through the control wind farm and through the wind farmwith alternate rows of clockwise and counter-clockwise turbines(Fig. 7). By employing the alternate-row configuration, some of

the turbines were subjected to higher wind speeds and some ofthem experienced lower wind speeds; the overall effect, however,was positive as the mean power production of the wind farm wasenhanced by approximately 1.4%. The wakes in the ALTR case werenot significantly different from those in the control case (Fig. 7b vs.Fig. 7a). The wind speed distribution through the wind farm withdual-rotor wind turbines, however, was found to be considerablydifferent than the control case. As is seen in Fig. 7c, the velocitydeficit downstream of dual-rotor wind turbines is larger than thevelocity deficit downstream of the single-rotor wind turbines. Itis also observed that length and width of the wake of dual-rotorwind turbines are significantly greater than those of single-rotorwind turbines. To provide further clarification, the differencebetween the mean velocity magnitude through the wind farm withdual-rotor wind turbines and the control wind farm, i.e. panels (c)and (a) of Fig. 7, is illustrated in Fig. 8. Although wind speed in thewind farm with dual-rotor wind turbines and the wind farm with

Fig. 7. Mean velocity magnitude through the wind farm over a two-dimensional slice at the hub height of wind turbines for the three cases studied here: (a) control, (b) ALTR,and (c) DRWT.




single-rotor wind turbines are approximately equal over most ofthe area (white in Fig. 8), the velocity deficit downstream of thedual-rotor wind turbines is up to 3.5 m/s larger in comparison tothe velocity deficit downstream of the single-rotor wind turbines.It is also observed that turbines located in the second row of thewind farm with dual-rotor wind turbines are subjected to a signif-icantly weaker wind comparing to the second-row wind turbinesof the control wind farm. This explains the trend observed in pan-els (a2) to (h2) of Fig. 6. Similarly, turbines located in the seventhand eighth rows of columns 2 and 3 of the wind farm with dual-rotor wind turbines experience lower wind speeds than their cor-responding wind turbines in the control wind farm, while dual-rotor wind turbines located in the third, fourth, fifth and sixth rowsof the wind farm are subjected to approximately similar windspeeds as their corresponding wind turbines in the control windfarm. This wind speed distribution supports the trend observed inthe thrust coefficient and power production of the wind farm withdual-rotor wind turbines and suggests that adding a secondary rotorto the front-row and middle-row turbines is more effective thanadding it to second-row and deep-row wind turbines, provided thatthe spacing between the rows of the wind farm is uniform. The effec-tiveness of adding the secondary rotor to the second-row and deep-row wind turbines can be enhanced by increasing the spacingbetween these rows and their upstream rows.

Conclusions

The effect of employing counter-rotating wind turbines onpower production of a wind farm was investigated using largeeddy simulations. Three configurations of a wind farm with 48large-scale wind turbines with a layout similar to Lillgrund off-shore wind farm in Sweden were studied: (I) all wind turbineswere assumed to have one clockwise rotor, (II) an alternate-rowconfiguration in which each turbine has one rotor, rotating eitherclockwise or counter-clockwise, with alternating rows of clockwiseand counter-clockwise turbines throughout the farm, and (III) allturbines were assumed to have two rotors with the first rotor

rotating clockwise and the second rotor rotating counter-clockwise. This study suggests that the rotational direction of therotor (clockwise vs. counter-clockwise) could be an additionaloptimization parameter in wind farm layout studies.

Some notable observations from the studied conditions aresummarized as follows:

1. The dual-rotor and the alternate-row configurations were foundto produce approximately 22.6 % and 1.4% more power than thecontrol case.

2. The amplitude of the fluctuations of the mean power produc-tion in the wind farm with dual-rotor wind turbines wasapproximately twice that of the control and the alternate-rowconfigurations.

3. The performance of each single-rotor wind turbine of the controlwind farm was better than the performance of each individualrotor of its corresponding wind turbine in the wind farm withdual-rotor wind turbines. The total performance of each dual-rotor wind turbine, however, was significantly greater than theperformance of its corresponding single-rotor wind turbine inthe control wind farm (5% to 40% more power production).

4. Adding a secondary rotor causes the fatigue loading acting onthe tower to increase.

5. Adding the secondary rotor to the wind turbines was mosteffective in the front and middle rows of the wind farm. Theperformance of turbines in the second row and deep rows(i.e. seventh and eighth rows) of the wind farm was negativelyaffected by the stronger upstream wakes. Hence, it is recom-mended to increase the distance between these rows andtheir upstream rows to reduce the effect of strong wakes thatare generated by the front-row and middle-row windturbines.

Acknowledgement

We would like to acknowledge Francois Souchay for bringingthe topic of counter-rotating wind turbines to our attention.

Fig. 8. Wind speed in the control wind farm subtracted from velocity field through the wind farm with dual-rotor wind turbines.




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