Jordan M. WilsonDepartment of Civil

and Environmental Engineering,

Colorado State University,

Fort Collins, CO 80523-1372

Cole J. Davis1

Department of Civil

and Environmental Engineering,

Colorado State University,

Fort Collins, CO 80523-1372

Subhas K. Venayagamoorthy2

Associate Professor

Department of Civil

and Environmental Engineering,

Colorado State University,

Fort Collins, CO 80523-1372

e-mail: vskaran@colostate.edu

Paul R. HeyligerProfessor

Department of Civil

and Environmental Engineering,

Colorado State University,

Fort Collins, CO 80523-1372

Comparisons of Horizontal-AxisWind Turbine Wake InteractionModelsIn this study, Reynolds-averaged Navier–Stokes (RANS) simulations are performed usingthe k-e and k-x shear stress transport (SST) turbulence closure schemes to investigate theinteractions of horizontal-axis wind turbine (HAWT) models in the neutrally stratifiedatmospheric boundary layer (ABL). A comparative study of actuator disk, actuator line,and full rotor models of the National Renewable Energy Laboratory (NREL) 5 MW refer-ence turbine is presented. The open-source computational fluid dynamics (CFD) codeOPENFOAM 2.1.0 and the commercial software ANSYS FLUENT 13.0 are used for simulations.Single turbine models are analyzed for turbulent structures and wake resolution in thedownstream region. To investigate the influence of the incident wind field on very largeturbine blades, a high-resolution full rotor simulation is carried out for a single turbineto determine blade pressure distributions. Finally, simulations are performed for twoinline turbines spaced 5 diameters (5D) apart. The research presented in this study pro-vides an intercomparison of three dominant HAWT models operating at rated conditionsin a neutral ABL using an RANS framework. Furthermore, the pressure distributions ofthe highly resolved full rotor model (FRM) will be useful for future aeroelastic structuralanalysis of anisotropic composite blade materials. [DOI: 10.1115/1.4028914]

1 Introduction

As concerns continue to increase over resource availability,energy prices, environmental impacts, and worldwide populationgrowth, renewable energy production becomes paramount inmeeting future energy demands. Wind energy has prevailed as themost cost effective source of renewable energy production [1].Within the United States, energy production from wind is aimedat 20% of the total energy market by 2030 [2]. As wind turbinesreach higher into the atmosphere with increasing rotor diametersand wind farms expand beyond 20 km in length, understandingthe flow dynamics imposed by the ABL and local turbine wakeinteractions becomes an essential part of wind farm design andoptimization. Wakes not only decrease the downstream mean ve-locity and corresponding power production but also increase tur-bulent fluctuations leading to structural fatigue issues. Fieldobservations provide valuable data but can only be collected fromexisting sites. Laboratory studies yield a priori information but arelimited to moderate Reynolds number flows and cannot replicatelarge mesoscale motions. CFD analysis has become an importanttool in the study of ABL flow dynamics and wind engineeringallowing unprecedented studies of wind turbine wake dynamicsand interactions (see e.g., Refs. [3–7]). As computational powercontinues to increase and numerical techniques are refined, CFDwill be at the forefront of wind turbine design and wind farmlayout.

The high Reynolds numbers of ABL flows (e.g., 107–109) dic-tate that spatial or temporal closure schemes be used to handle tur-bulence either through large-eddy simulations (LES) or RANSsimulations, respectively. Direct numerical simulation of theNavier–Stokes equations remains limited to moderately low

Reynolds numbers and simple geometries. LES provides resolu-tion of large turbulent scales but relies on less accurate subgrid-scale models for modeling smaller turbulent scales. LES requiresconsiderable computational resources especially when scaling tomultiple turbines and wind farms. On the other hand, RANS simu-lations apply temporal filtering to the governing Navier–Stokesequations providing an averaged flow field based on turbulenceclosure assumptions requiring significantly less computationaltime. The k-e turbulence model [8] is perhaps the most widelyused RANS model for engineering flows in research communitiesand industry, but most notably fails to accurately capture severelyseparated flows with adverse pressure gradients. Literature sug-gests that appropriate modifications (e.g., wall functions andboundary conditions consistent with field data and laboratoryexperiments) to the k-e scheme provide accurate simulations ofABL flow and HAWT wake dynamics [9,10]. The favorablebehavior of the k-e model in the free stream has been incorporatedinto other various RANS turbulence models through blendingfunctions. One such model is the k-x SST model [11] combiningthe k-x model [12] in the near-wall region and the k-e model inthe free-shear region.

In order to study the dynamics of large wind turbines, theNREL 5 MW reference turbine is selected [13]. While this turbinewas developed as a theoretical tool for studying power productionand structural responses in large wind turbines, the blade geome-try is appropriate for fluid dynamic analysis. The accurate depic-tion of HAWTs in a computational model is essential. An actuatordisk model (ADM) is one of the simplest representations of a tur-bine rotor applying a uniform integration of rotor forces to thecomputational domain [14,15]. Increasing in sophistication, actua-tor line models (ALMs) include nonuniform rotor forces inte-grated along discrete lines, rotational effects, and tip vortices.FRMs give a three-dimensional rotor representation to investigateblade aerodynamics, near-wake dynamics, and power production[7]. In this study, a comparison of wake dynamics for ADM,ALM, and FRM rotor representations of the NREL 5 MW refer-ence turbine are explored. To further understanding on dynamicloading of very large turbine blades, a high-resolution FRM is

1Present address: Quest Integrity Group, Boulder, CO 80301.2Corresponding author.Contributed by the Solar Energy Division of ASME for publication in the

JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING

ENERGY CONSERVATION. Manuscript received December 18, 2013; final manuscriptreceived September 8, 2014; published online November 17, 2014. Assoc. Editor:Yves Gagnon.

Journal of Solar Energy Engineering JUNE 2015, Vol. 137 / 031001-1Copyright VC 2015 by ASME

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

analyzed to highlight the pressure distributions on blade surfaces.Finally, simulations of two inline turbines spaced 5D apart areperformed to investigate wake interaction dynamics. Figure 1 pro-vides a schematic of the two inline turbines. The objective of thisstudy is to further understand the development and resolution ofturbine wakes using ADM, ALM, and FRM methods applicable tooptimization of power production and fatigue load minimization.

In the following, a brief theoretical overview of the numericalmethods, simulations, and rotor models is provided in Sec. 2.Section 3 presents the results of numerical simulations comparingsingle ADM, ALM, and FRM methods, pressure distributions onturbine blades for a high-resolution FRM, and two inline turbinemodels spaced at 5D. Results are thoroughly discussed in Sec. 4,providing a better understanding of wake interaction for largewind turbines and turbine blade loading.

2 Theory

This section is meant to highlight the turbulence closure modelsused in this study for neutral ABL flow. In the Reynolds-averaging process, an additional term is added to the momentumequation referred to as the Reynolds stress term (�u0iu

0j). Turbu-

lence closure schemes use the turbulent viscosity hypothesis todefine the Reynolds stresses shown below

� u0iu0j ¼ �t

@ �Ui

@xjþ @

�Uj

@xi

� �� 2

3kdij (1)

where �U is the mean velocity field (individual velocity compo-nents are given by �u in the x-direction (streamwise), �v in they-direction (spanwise), and �w in the z-direction (vertical)), k is theturbulent kinetic energy, dij is the Kronecker delta function, �t is

the turbulent viscosity, and @ �Ui=@xj þ @ �Uj=@xi

� �is twice the

mean strain rate tensor (�Sij). The turbulent viscosity is commonlysolved through an algebraic combination of velocity and lengthscales (�t� u*l*). These scales can be solved for through a myriadof methods ranging in complexity from zero-equation models toReynolds stress models. This study focuses on the two-equationk-e and k-x SST turbulence closure schemes described in in Sec.2.1 and 2.2, respectively.

2.1 Standard k-e Model. The standard k-e model [8] is atwo-equation closure model based on the exchanges between tur-bulent kinetic energy (k) and the dissipation rate of the turbulentkinetic energy (e). This model is widely used for simulation ofengineering and geophysical flows including HAWT interactionsin the neutrally stratified ABL [9,16–19]. This model is used forsimulations of actuator disk and line models. The governingtransport equations for k and e are given in Eqs. (2) and (3),respectively,

�Dk�Dt¼ @

@xj� þ �t

rk

� �@k

@xj

� �þ Pk � e (2)

�De�Dt¼ @

@xj� þ �t

re

� �@e@xj

� �þ Ce1

ek

Pk � Ce2e2

k(3)

where � is the molecular viscosity, Pk ¼ 2�t�Sij

�Sij is production ofturbulent kinetic energy, rk¼ 1.3 is the Prandtl number for k,re¼ 1.0 is the Prandtl number for e, and Ce1¼ 1.44 and Ce2¼ 1.92are model constants that are assigned their standard values [20].The turbulent viscosity is given by

�t ¼ Clk2

e(4)

where Cl is a model coefficient with a standard value of0.09 [20].

Numerous modifications have been suggested in literature forthe standard k-e model in ABL applications. Crespo et al. [21]used Cl¼ 0.03 to reduce excessive model dissipation. Addition-ally, Kasmi and Masson [18] suggested an extended k-e model forflow through HAWTs improving on the simple modification ofCrespo et al. [21]. Furthermore, Gorl�e et al. [22] and Parente et al.[9,17] added additional source terms to the transport equations for

k and e and cast Cl ¼ u4�=kðzÞ2 as a function of height. u�

¼ffiffiffiffiffiffiffiffiffiffisw=q

pis the shear velocity and sw is the shear stress at the sur-

face. Obviously, there is yet to be a consensus for proper modifi-cation of the standard k-e model in ABL applications whichbecomes further complicated in the presence of stratification.Stratification introduces buoyant forces that influence mixing andtransport processes of turbulent flows (see, e.g., Ref. [19]). Futureresearch will consider modifications to the k-e model but the cur-rent work uses the standard formulation along with the consis-tency condition for the turbulent Prandtl number of e [23,24]

re ¼j2

Ce2 � Ce1ð ÞffiffiffiffiffiffiCl

p (5)

where j is the von K�arm�an constant (j¼ 0.4). For Cl¼ 0.09,Eq. (5) results in re¼ 1.11 instead of the standard value of1.3 [20].

2.2 k-x SST Model. The k-x SST turbulence closure model[11] is used for the full rotor simulations due to its aptitude forsimulation of near-wall viscous effects, separated flows, and freestream conditions [25]. The governing transport equations forturbulent kinetic energy (k) and specific dissipation of turbulentkinetic energy (x) are given in Eqs. (6) and (7), respectively

�Dk�Dt¼ @

@xj� þ �t

rk

� �@k

@xj

� �þ ~Pk � Yk (6)

�Dx�Dt¼ @

@xj� þ �t

rx

� �@x@xj

� �þ Px � Yx þ Dx (7)

where rk ¼ 1=½F1=rk;1 þ ð1� F1Þ=rk;2�; ~Pk ¼ minðPk; 10b�kxÞrepresents the production of turbulent kinetic energy, Yk¼b*kx isthe dissipation of turbulent kinetic energy, rx¼ 1/[F1/rx,1þ (1�F1)/rx,2] is the Prandtl number for x, Px¼ (a�t)Pk isthe production of specific dissipation of turbulent kinetic energy,a¼ a1F1 þ a2(1�F1) is a blending function, Yx¼ bx2 is the dis-sipation of specific dissipation of turbulent kinetic energy,b¼F1bi,1 þ (1�F1)bi,2 is blending function for specific dissipa-

tion, and Dx ¼ 2ð1� F1Þrx;2 1=xð Þ @k=@xj

� �@x=@xj

� �is the

cross-diffusion term. F1 is a blending function equal to zero awayfrom the surface (k-e model) and one in the surface boundary layer(k-x model). The turbulent viscosity for the k-x SST model isgiven by

�t ¼k

x1

max1

a�;SF2

a1x

� � (8)

Fig. 1 Schematic of two inline turbines

031001-2 / Vol. 137, JUNE 2015 Transactions of the ASME

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

where a� ¼ a�1½ða�0 þ Ret=RkÞ=ð1þ Ret=RkÞ� is a damping func-tion for low-Reynolds number correction and F2 is a secondblending function. In the near-wall region the SF2/a1x term isdominant and in the free stream the 1/a* term is dominant. Table1 presents the standard model constants for the k-x SST model.This section highlights the major transport equations and terms inthe k-x SST model. Menter [11] provides a thorough explanationof the k-x SST model and numerous blending functions in theturbulence model formulation.

2.3 Numerical Framework. This study focuses on the influ-ence of very large wind turbine interactions leading to the selec-tion of the NREL 5 MW reference turbine for simulations [13].While the turbine was intended for theoretical dynamic structuraland drivetrain research for offshore wind turbines, it has beenused in CFD studies as well [6,26,27]. This study used two differ-ent CFD software packages: OPENFOAM 2.1.0. and ANSYS FLUENT

13.0.The finite-volume code OPENFOAM (open-source field operations

and manipulations) is a set of Cþþ libraries solving differentialequations of the flow equations using the finite-volume methodfor unstructured meshes and is highly parallelizable through themessage passing interface [28]. The Simple (semi-implicit methodfor pressure-linked equations) algorithm was used for steady-statesimulations of the ADMs. Transient simulations of the ALMsused the PISO (pressure implicit with splitting of operators) algo-rithm. Spatial discretizations were set to Gauss linear for gradientand divergence terms and Gauss linear corrected for Laplacianterms. First-order implicit Eulerian discretization was used fortemporal terms in the ALM model simulations.

FLUENT 13.0 is a commercially available finite-volume CFDsimulator with a built-in postprocessor [29]. The code is adaptablethrough user-defined functions (UDFs), but there is no directaccess to the source code which leads to some ambiguity in imple-mentation of modifications. FLUENT was used for the fully resolvedturbine rotor model case using a sliding mesh method. Transientsolutions again used the PISO algorithm with second-orderaccuracy in temporal and spatial discretizations.

The computational domain was sized 2D (252 m) upstream ofthe turbine, 20D (2520 m) downstream of the first turbine, 2.5D(315 m) spanwise on either side of the turbines, and 378 m inheight, where D is the rotor diameter. The total domain was2772� 630� 378 m. Considering the relatively small domain sizein the performed simulations Coriolis effects can be neglectedleaving the driving boundary conditions and surface roughness asthe primary influences on the boundary layer. The domain sizewas sufficient to not encounter boundary effects in the flow andallow downstream wake observation. The turbine models wereplaced at the hub height of 90 m. A grid independence study wasperformed to ensure solution independence for each of the rotormodels, ADM, ALM, and FRM, respectively.

2.4 Boundary Conditions. The fully developed inlet profilesof mean streamwise velocity (�u), turbulent kinetic energy (k), anddissipation rate turbulent kinetic energy (e) of Richards and Hoxey[30] were applied at the domain inlet in simulations

�u zð Þ ¼ u�j

lnzþ z0

z0

� �(9)

k ¼ u2�ffiffiffiffiffiffiCl

p (10)

eðzÞ ¼ u3�

j zþ z0ð Þ (11)

where z0 is the aerodynamic roughness length. Equations (9)–(11)are analytical solutions to the standard k-e model if the Prandtlnumber for e is defined by Eq. (5) [24]. Equations (9) and (11) arestandard boundary conditions for �u and e. The boundary conditionfor k is specified as a fixed value given in Eq. (10). A UDF wascompiled in FLUENT to implement the inlet conditions for �u, k, ande. The domain outlet was specified as pressure outlet with a con-stant value of 0 Pa (gauge). The top and side (front and back)surfaces of the computational domain were assigned a slip condi-tion. A slip condition ensures zero-gradient (@/@n) for scalar quan-tities. For vector quantities, the normal component is set to zeroand tangential components are assigned zero-gradient.

Figure 2 depicts the vertical profiles of mean streamwise veloc-ity and turbulent kinetic energy for an empty domain using theprescribed boundary conditions. The mean velocity profile ismaintained and the TKE does not exhibit a strong peak near thewall surface. A vertical gradient (wall-normal coordinate) of TKEis consistent with the numerical simulations of the neutral ABL[9,17,31]. However, maintaining the inlet TKE profile for the neu-tral ABL is a well documented difficulty and active area ofresearch in the RANS framework [30,32]. Overall, resolution ofthe mean velocity profile is of primary importance for the compar-ison of HAWT models which is achieved prior to incidence withthe upstream turbine.

2.5 Wall Functions. The bottom (or ground) surface in thedomain was treated as a fully aerodynamically rough wall. Wallfunctions are employed due to the high Reynolds number of ABLflow rather than resolving the scales near the wall. Wall-resolvingmodels require very fine mesh resolution and are not practical dueto high computational costs. The velocity and turbulent dissipa-tion rate are defined at the first cell centroid, zp, using the formula-tion of Richards and Hoxey [30] as

�uP ¼u�j

lnzp þ z0

z0

� �(12)

eP ¼C3=4

l k3=2

j zP þ z0ð Þ (13)

Table 1 k-x SST model constants

a�1 a1 b�1 a1 bi,1

1.0 0.52 0.09 0.31 0.075

bi,2 rk,1 rk,2 rx,1 rx,2

0.0828 1.176 1.0 2.0 1.168 Fig. 2 Vertical profiles of mean streamwise velocity (left) andturbulent kinetic energy (right)

Journal of Solar Energy Engineering JUNE 2015, Vol. 137 / 031001-3

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

where the subscript P denotes the value at the first grid point. Themean streamwise velocity at the first grid point is enforced byrelating the shear stress over the wall-adjacent cell to the wallshear stress (sw)

sw ¼ qu2� ¼ qC1=4

l jk1=2 �uP

lnzp þ z0

z0

� � (14)

where u� ¼ C1=4l k1=2 is the shear velocity defined using the local

equilibrium assumption. Assuming that the shear production atthe wall is given by Pk � swð@�u=@zÞ, the velocity derivative isgiven by

@�u

@z

� �P

¼C1=4

l k1=2P

jzp þ z0

z0

� � (15)

Using the relationship between wall shear stress and velocity gra-dient over the wall-adjacent cell is a more robust condition for tur-bulence models than directly applying Eq. (12) [33]. The wallboundary condition for k is set to a zero-gradient in the normaldirection

@k

@n

� �w

¼ 0 (16)

Equations (13), (15), and (16) are enforced as boundary conditionsfor e, �u, and k, respectively, in OPENFOAM and FLUENT.

2.6 Wind Turbine Models. Wind turbine computationalmodels vary in levels of sophistication, but all are based on theprinciple of momentum extraction from the fluid stream. Actuatordisk and line models are generally used to determine the influenceof a wind turbine on the ABL and wake dynamics while FRMsdetermine loads on turbine structures and power production. Ratedconditions were specified for all turbine models with a wind speedof 11.4 m/s at 90 m hub height correlating to a rotor speed of12.1 rpm at a pitch angle of 0.0 deg [13]. Figure 3 presents theresults from a grid independence study of the individual rotormodels.

2.6.1 ADM. Actuator disk theory replaces the rotor of aHAWT with a representative disk upon which blade forces aredistributed. This simplification allows for a computational modelwithout the need for a highly resolved mesh in the region of theturbine to accurately capture the boundary layer effects along theblades. Development of actuator disk methods is further describedby Madsen [15], Sørensen and Kock [34], and Sørensen andMyken [14]. The essential quantities in this formulation are thrust(T), power (P), and torque (Q), described in Eqs. (17)–(19),respectively,

T ¼ qV20

2pR2CT (17)

P ¼ qV30

2pR2CP (18)

Q ¼ P

X(19)

where V0 is the free stream velocity, R is the rotor radius, CT isthe turbine thrust coefficient, CP is the turbine power coefficient,and X is the turbine rotational speed. Equations (20) and (21) pre-scribe the volume integral for thrust and torque of the actuatordisk

T ¼ð

V

fbx dV (20)

Q ¼ð

V

fbh dV (21)

where fbx is the body force in the axial direction and fbh is thebody force in the tangential direction.

For the NREL 5 MW reference turbine, CT and CP are 0.6 and0.5, corresponding to typical operating conditions. The disk radiusis 63 m. The center of the actuator disks is located 252 m down-stream of the inlet boundary for a single turbine and 252 m and882 m for two turbines spaced 5D apart. The computational domainwas meshed to 128� 128� 256 using the meshing utility block-Mesh in OPENFOAM. The mesh was clustered in the streamwisedirection where the actuator disks were placed. The resolution pro-vided convergence of results and a reasonable computation time.Residuals of relevant flow and turbulent quantities were monitoredfor solution convergence. The ADM allows for steady-state compu-tations given the uniform force distributions.

2.6.2 ALM. ALMs allow for discretized wind turbine bladesto be represented as compact lines of body forces. A significantadvantage is that tip vortices can be captured with the ALM. Themost widely used adaptation of this technique was developed bySørensen and Shen [7] and will be used in this research as imple-mented by Churchfield et al. [35] in NRELs SOWFA (simulator foroffshore wind farm applications) solver set for OPENFOAM. Similarto the ADM, the ALM does not depict the nacelle or tower.

This model also has the ability to be dynamically controlled,responding to changes in the incoming flow field. For an RANSsimulation this feature is not essential, but is desirable when mov-ing to a higher order simulation such as LES. The velocity magni-tude and local flow angle can be computed for each of thesegments on the actuator line based on airfoil type, chord, twist,and local flow velocity. Assuming the effects of up- and down-wash are small from lift, the magnitude of lift and drag can becomputed from airfoil lookup tables as follows:

Fig. 3 Grid independence study for (a) ADM, (b) ALM, and (c) FRM rotor models.Mean streamwise velocity (�u) is measured 0.5D downstream. The number of cellsis calculated over a circular region centered at the rotor hub with a diameter of150 m (coinciding with the sliding mesh surface of the FRM).

031001-4 / Vol. 137, JUNE 2015 Transactions of the ASME

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

L ¼ 1

2ClaqV2

0 cw (22)

D ¼ 1

2CdaqV2

0cw (23)

where Cl is the lift coefficient, Cd is the drag coefficient, a is theinduction factor, c is the chord length, and w is the actuator linesegment length. From Sørensen and Shen [7], the actuator lineforces are projected onto the computational domain as a bodyforce field using a Gaussian projection given by

FTi x; y; z; tð Þ ¼ �

XN

j¼1

f Ti xj; yj; zj; t� � 1

e3p3=2exp �

�rj

e

� �2" #

(24)

where e controls the width of the Gaussian projection and its spec-ification is analyzed in detail by Matinez et al. [36]. Churchfieldet al. [35] discuss the numerical framework for their implementa-tion of the Sørensen and Shen [7] ALM. The computationaldomain was meshed to 128� 128� 256 using the meshing utilityblockMesh in OPENFOAM clustered in the regions of turbine place-ment. Grids were refined to 1 m in the streamwise direction andsufficiently fine to have at least 20 cells over the turbine area. Thisresolution provided convergence of results and a reasonable timebased on the recommendations for sufficient grid resolution [35].Again, residuals of relevant flow and turbulent quantities weremonitored for solution convergence.

2.6.3 FRM. The FRM of the NREL 5 M reference turbine wascreated in SolidWorks to the specifications of Jonkman et al. [13]for rated conditions. This geometry was exported into ANSYS

Design Modeler, where the domain geometry was created. A cy-lindrical domain 150 m in diameter and 20 m in thickness encap-sulating each turbine rotor was created to allow for sliding meshcomputations. Meshing was performed in ANSYS using an unstruc-tured tetrahedral mesh. Cell sizes were set to 1 m on the bladesurfaces and hubs and 0.5 m on the blade tips. Cells were kept to amaximum size of 15 m in the horizontal direction and 10 m in thevertical direction. Inflation layers were implemented on all solidsurfaces with a maximum growth rate of 1.2. The front and backfaces of the rotating domains were constrained to 7 m cell sizesand the circular surfaces of the rotating domains were restricted to4 m cell sizes. With these restrictions, the FRM contained approxi-mately 2.15� 106 cells. Figure 4 shows the meshed domains forthe FRM. Models were run as transient simulations until theyreached a quasi-steady state (approximately 10 min in real flowtime) with convergence of residuals.

3 Results and Discussion

This section discusses the results from single turbine simula-tions of ADM, ALM, and FRM models and compares streamwisevelocity profiles for the NREL 5 MW reference turbine. These

simulations illustrate the physics of wake formation and resolutionfor different models. A high-resolution FRM model is simulatedfor analysis of blade pressure distributions. Finally, two inline tur-bines spaced 5D (630 m) apart were simulated using ADM, ALM,and FRM. These additional simulations further illustrate wakeinteraction and resolution.

3.1 Single Turbine Simulations. Figure 5 displays velocitycontours for the single turbine simulations. Streamwise velocityprofiles for the ADM, ALM, and FRM, respectively, are presentedin Fig. 6. The velocity deficit is more pronounced for the FRMcompared with ADM and ALM. The downstream wake recoversslightly faster for the ADM as compared to the ALM while theFRM velocity deficit persists throughout the domain. To furtheranalyze the flow characteristics, contours of turbulence intensity(I ¼ u0=j �Uj) are displayed in Fig. 7. Within the RANS framework,

the fluctuating velocities, u0 are estimated by u0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffið2=3Þk

pand

j �Uj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�u2 þ �v2 þ �w2p

is the magnitude of the three-dimensionalvelocity field. Behind a single turbine, the turbulence intensity issignificantly more pronounced for ADM and ALM compared withFRM. This difference is attributed largely to the difference in k-eand k-x SST turbulence models. Notably, the k-e model overpre-dicts k in regions with adverse pressure gradients. However, theseeffects only have minor influences on the mean flow field which isof primary interest in an RANS framework.

Overall, results compare well qualitatively with literature forsimulations of the NREL 5 MW reference turbine [26,27]. Wakeeffects for large wind turbines persist further downstream thanstandard wind farm spacings of 5D–10D and may not be adequatefor optimal performance [3]. The contours and vertical profiles ofstreamwise velocity indicate a close comparison between the actu-ator disk and line models. It is well known that actuator disk andline models provide a more accurate representation of far-fieldwake effects compared with FRMs [4,26]. Additionally, actuatordisk and line models require significantly less computational timethan a comparable FRM which becomes increasingly importantwhen scaling simulations to numerous turbines in large wind farmsettings. ADM and ALM simulations present a significant increasein wake prediction compared with empirical models [37]. Finally,the large blade diameter of the NREL reference turbine experien-ces greater shear forces under neutrally stratified ABL conditions(an approximate difference of 2 m/s in incident wind velocityfrom the bottom to top of the rotor domain). When placed in anarray of turbines, this shear and the additional wake effects canpresent significant structural concerns that are important to considerfor evaluating fatigue related failures.

Fig. 4 Computational grid for FRM simulations of two turbineswith 5D spacing (left) and grid of a sliding mesh domain for aturbine rotor enclosed (right).

Fig. 5 Contours of streamwise velocity (m/s) for single turbinemodels. ADM (top), ALM (center), FRM (bottom).

Journal of Solar Energy Engineering JUNE 2015, Vol. 137 / 031001-5

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

3.2 High-Resolution FRM Simulations. To further the cur-rent study for large wind turbines, a high-resolution FRM wassimulated to analyze the pressure distributions on the blade surfa-ces. While the original converged computational grid was suffi-cient to capture flow dynamics, refinement is needed toinvestigate the surface (or near-wall) characteristics. A similarsetup was carried out for the grid independence study of the high-resolution FRM as with the single and two turbine simulations.For these models, the domain included only one rotating turbinelocated 2D from the inlet and extended only 5D downstream ofthe turbine. The mesh sizes were varied on the turbine and rotat-ing domain surfaces. Table 2 provides the mesh restrictions andmodel cell counts.

The results of this grid independence study were quite interest-ing. The FRM maximum pressure is nearly the same as the stagna-tion pressure calculated from the Bernoulli principle occurringalong the leading edge of the blade shown in Fig. 8. The pressureexerted on the blades increases dramatically and levels off at thecase of 1.09� 106 cells with a cell size of 0.65 m on the bladesurfaces. This is a very small change from the previous case butwith dramatic results. The maximum blade pressure in the singleturbine simulation is found to be approximately 1.4 kPa whichagrees well with the findings of Bazilevs et al. [38,39] in theirLES study which yielded a maximum pressure of 1.2 kPa. It is

noted that their blade configuration was slightly altered from idealoperating conditions which can explain the difference in values.Although this maximum pressure can be approximated with theBernoulli equation, the distribution of the pressure along the bladerequires CFD simulation presented in Fig. 9. This distributed load-ing by pressure forces leads to significant torque and nonlinearbending in the highly anisotropic turbine blade materials. Thesedistributions suggest that investigation into nonlinear beam effectsshould be pursued since they are likely to load the blade outsidethe limits of linear response. As wind speeds increase, theincreased pitch response would lead to a redistribution of theblade pressures and further the need for investigation of nonlinearbeam mechanics.

3.3 Inline Turbine Simulations. An investigation of wakeinteractions was performed for two inline turbines spaced 5D.Figure 10 displays the velocity contours. A clear increase in the

Fig. 6 Comparison of downstream vertical profiles of streamwise velocity (m/s)for (a) ADM, (b) ALM, and (c) FRM

Fig. 7 Contours of turbulence intensity for single turbinemodels. ADM (top), ALM (center), FRM (bottom).

Table 2 FRM high-resolution grid sizing

Blade face (m) 1 0.8 0.65 0.5 0.1Blade tip (m) 0.5 0.2 0.15 0.1 0.05Rotating domain face (m) 7 5 4 4 2Rotating domain cylinder (m) 4 4 4 4 2Total cells (� 106) 0.789 0.951 1.09 1.27 5.43

Fig. 8 Grid independence study of maximum turbine bladepressure compared to the theoretical maximum Bernoullipressure

Fig. 9 Contours of pressure (Pa) along blade surfaces

031001-6 / Vol. 137, JUNE 2015 Transactions of the ASME

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

downstream velocity deficit for the second turbine can be noticedfor all three models. Figure 11 shows the vertical profiles ofstreamwise velocity 0.5D and 4D behind the first turbine (T1) andsecond turbine (T2). Both velocity contours and streamwise veloc-ity profiles clearly illustrate ADM and ALM exhibit wake restora-tion in the computational domain. The FRM wake extends beyondthe domain limits. The contours of turbulence intensity for theinline turbine models are shown in Fig. 12. There is a noticeableincrease in the size and magnitude of the regions of turbulence in-tensity downstream of the second turbine. Behind the secondFRM there is a significant region of turbulence intensity indicativeof the onset of wake meandering effects increasing the turbulentkinetic energy [35]. Wake meandering can have significant effectson power production and fatigue loading especially in arrays withmultiple rows of turbines.

The simulations of inline turbine models reveal the strong inter-action of turbine wakes when spaced only 5D apart. Again, thecontours and vertical profiles of streamwise velocity show a goodcomparison between the actuator disk and line models. The FRMresults are well outside of the magnitudes in ADM and ALM sim-ulations again showing the weakness of the FRM in far-wake fieldprediction. Downstream of the first turbine (T1), velocity and tur-bulence intensity fields closely resemble those of the single tur-bine simulations. Significant increases in velocity deficit reveal astrong decrease in the available energy for power production. Theincrease in turbulence intensity results from a correspondingincrease in the turbulent fluctuations or analogously the turbulentkinetic energy. These fluctuations can induce strong peak loadingon downstream turbines leading to structural concerns. Overall,results indicate that 5D spacing is inadequate for large windturbines in neutrally stratified conditions.

4 Conclusions

Several important findings resulted from this study of theNREL 5 MW reference turbine. The single turbine simulations foractuator disk, actuator line, and FRMs compared well qualita-tively with literature for the NREL 5 MW reference turbine[26,27] and similar large HAWT simulations [4,10]. ADM andALM results compared closely while the FRM exhibited a moresustained velocity deficit. Wake effects were observed beyond thetypical spacing of 5D–10D and warrants further investigation intothe spacing of large wind turbines in arrays and wind farm set-tings. The k-e model yields an increased turbulence intensitybehind rotors, but ADM and ALM still represent an increase inwake prediction accuracy compared with empirical models [37].A high-resolution study of a single FRM revealed interesting pres-sure distributions for a 0.0 deg pitch angle operating at the ratedconditions. The maximum observed pressure was remarkablyclose to the calculated Bernoulli maximum pressure located onthe leading edge of the blades. The pressure distributions suggestthat the blades may be loaded beyond linear limits and requirenonlinear beam mechanics to accurately quantify the blade behav-ior. Finally, wake interactions were observed for turbines spaced5D. Results suggest that this spacing would yield a significantreduction in power production from downstream turbines. Theincrease in turbulence intensity could also lead to serious fatigueloading. While the NREL 5 MW reference turbine was used inthis study to highlight the differences between the different tur-bine wake models, it provides a base model for simulations oflarge wind turbines. As turbines continue to grow in size, a stron-ger collaboration between the research community and industry isneeded to better evaluate the physics not only involved in theinteraction of the ABL on turbines and turbine–turbine interac-tions but also the influence of turbines on atmospheric dynamics.

Future research will investigate structural dynamics and aeroe-lastic effects of large wind turbine blades based on the obtainedpressure distributions from the FRM. The potential of nonlinearbending in blades constructed with anisotropic composite materi-als presents significant structural issues. Additionally, stablystratified ABLs will be considered. Stable stratification can intro-duce high shear rates, low-level jets, and wave motions in theABL. These stable boundary layer effects lead to higher loads onblades and increased shear forces over the wind turbine rotor.

Acknowledgment

Funding for this research was provided by the Center forResearch and Education in Wind (CREW) and the Colorado StateUniversity Clean Energy Supercluster. Computational resourceswere provided by Colorado State University’s Information

Fig. 11 Comparison of downstream vertical profiles of stream-wise velocity (m/s) for (a) 0.5D downstream and (b) 4D down-stream for first and second turbines (T1 and T2, respectively)

Fig. 12 Contours of turbulence intensity for inline turbinesspaced 5D apart. ADM (top), ALM (center), FRM (bottom).

Fig. 10 Contours of streamwise velocity (m/s) for inline tur-bines spaced 5D apart. ADM (top), ALM (center), FRM (bottom).

Journal of Solar Energy Engineering JUNE 2015, Vol. 137 / 031001-7

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Science & Technology Center (ISTeC) Cray HPC System sup-ported by NSF Grant CNS-0923386.

References[1] Ball, J., 2011, “Wind Power Hits a Trough,” Wall St. J., Apr. 5, http://online.

wsj.com/news/articles/SB10001424052748704629104576190812458488694?mod=_newsreel_3

[2] USDOE, 2008, “20 Percent Wind Energy by 2030,” United States Departmentof Energy, Technical Report No. DOE/GO-102008-2567.

[3] Meyers, J., and Meneveau, C., 2012, “Optimal Turbine Spacing in Fully Devel-oped Wind Farm Boundary Layers,” Wind Energy, 15(2), pp. 305–317.

[4] Port�e-Agel, F., Wu, Y.-T., Lu, H., and Conzemius, R. J., 2011, “Large-EddySimulation of Atmospheric Boundary Layer Flow Through Wind Turbines andWind Farms,” J. Wind Eng. Ind. Aerodyn., 99(4), pp. 154–168.

[5] Calaf, M., Meneveau, C., and Meyers, J., 2010, “Large Eddy Simulation Studyof Fully Developed Wind-Turbine Array Boundary Layers,” Phys. Fluids,22(1), p. 015110

[6] Churchfield, M. J., Moriarty, P. J., Vijayakumar, G., and Brasseur, J. G., 2010,“Wind Energy-Related Atmospheric Boundary Layer Large-Eddy SimulationUsing OpenFOAM,” National Renewable Energy Laboratory (NREL), Techni-cal Report No. NREL/CP-500-48905.

[7] Sørensen, J. N., and Shen, W. Z., 2002, “Numerical Modeling of TurbineWakes,” ASME J. Fluids Eng., 124(2), pp. 393–399.

[8] Jones, W., and Launder, B., 1972, “The Prediction of Laminarization With aTwo-Equation Model of Turbulence,” Int. J. Heat Mass Transfer, 15(2), pp.301–314.

[9] Parente, A., Gorl�e, C., Beeck, J. v., and Benocci, C., 2011, “Improved k-eModel and Wall Function Formulation for the RANS Simulation of ABLFlows,” J. Wind Eng. Ind. Aerodyn., 99(4), pp. 267–278.

[10] Vermeer, L. J., Sørensen, J. N., and Crespo, A., 2003, “Wind Turbine WakeAerodynamics,” Prog. Aerosp. Sci., 39(67), pp. 467–510.

[11] Menter, F. R., 1994, “Two-Equation Eddy-Viscosity Turbulence Models forEngineering Applications,” AIAA J., 32(8), pp. 1598–1605.

[12] Wilcox, D. C., 1988, “Re-Assessment of the Scale-Determining Equation forAdvanced Turbulence Models,” AIAA J., 26(11), pp. 1299–1310.

[13] Jonkman, J., Butterfield, S., Musial, W., and Scoot, G., 2009, “Definition of a5-MW Reference Wind Turbine for Offshore System Development,” NationalRenewable Energy Laboratory (NREL), Technical Report No. NREL/TP-500-38060.

[14] Sørensen, J. N., and Myken, A., 1992, “Unsteady Actuator Disc Model for Hor-izontal Axis Wind Turbines,” J. Wind Eng. Ind. Aerodyn., 39(1–3), pp.139–149.

[15] Madsen, H. A., 1996, “A CFD Analysis for the Actuator Disc Flow ComparedWith Momentum Theory Results,” Proceedings of the 10th IEA Symposiumof Aerodynamics and Wind Turbines, Edinburgh, UK, Dec. 16–17, pp.109–124.

[16] Balogh, M., Parente, A., and Benocci, C., 2012, “RANS Simulation of ABLFlow Over Complex Terrains Applying an Enhanced k-e Model and Wall Func-tion Formulation: Implementation and Comparison for Fluent and Open-FOAM,” J. Wind Eng. Ind. Aerodyn., 104–106, pp. 360–368.

[17] Parente, A., Gorl�e, C., van Beeck, J., and Benocci, C., 2011, “A ComprehensiveModelling Approach for the Neutral Atmospheric Boundary Layer: ConsistentInflow Conditions, Wall Functions and Turbulence Model,” Boundary-LayerMeteorol., 140(3), pp. 411–428.

[18] Kasmi, A. E., and Masson, C., 2008, “An Extended k-e Model for TurbulentFlow Through Horizontal-Axis Wind Turbines,” J. Wind Eng. Ind. Aerodyn.,96(1), pp. 103–122.

[19] Rodi, W., 1987, “Examples of Calculation Methods for Flow and Mixing inStratified Fluids,” J. Geophys. Res.: Oceans, 92(C5), pp. 5305–5328.

[20] Launder, B. E., and Spalding, D. B., 1974, “The Numerical Computationof Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp.269–289.

[21] Crespo, A., Manuel, F., Moreno, D., Fraga, E., and Hern�andez, J., 1985,“Numerical Analysis of Wind Turbine Wakes,” Proceedings of the DelphiWorkshop on Wind Energy Applications, Greece, May 20–22, pp. 15–25.

[22] Gorl�e, C., Beeck, J. v., Rambaud, P., and Tendeloo, G. V., 2009, “CFD Model-ling of Small Particle Dispersion: The Influence of the Turbulence KineticEnergy in the Atmospheric Boundary Layer,” Atmos. Environ., 43(3), pp.673–681.

[23] Wilcox, D. C., 1993, Turbulence Modelling for CFD, DCW Industries Inc., LaCanada Fltrdg, CA.

[24] Hargreaves, D. M., and Wright, N. G., 2007, “On the Use of the k–e Model inCommercial CFD Software to Model the Neutral Atmospheric BoundaryLayer,” J. Wind Eng. Ind. Aerodyn., 95(5), pp. 355–369.

[25] Menter, F. R., 2009, “Review of the Shear-Stress Transport Turbulence ModelExperience From an Industrial Perspective,” Int. J. Comp. Fluid Dyn., 23(4),pp. 305–316.

[26] Tossas, L. A. M., and Leonardi, S., 2013, “Wind Turbine Modeling for Compu-tational Fluid Dynamics,” National Renewable Energy Laboratory (NREL),Technical Report No. NREL/SR-5000-55054.

[27] Sørensen, N. N., and Johansen, J., 2007, “Upwind, Aerodynamics and Aero-Elasticity, Rotor Aerodynamics in Atmospheric Shear Conditions,” EWEA, 2007European Wind Energy Conference and Exhibition, Milan, Italy, May 7–10.

[28] OpenCFD, 2014, OpenFOAM: The Open Source CFD Toolbox–User Guide.[29] ANSYS, 2010, ANSYS FLUENT User’s Guide, Canonsburg, PA.[30] Richards, P. J., and Hoxey, R. P., 1993, “Appropriate Boundary Conditions for

Computations Wind Engineering Models Using the k-e Turbulence Model,” J.Wind Eng. Ind. Aerodyn., 46–47, pp. 145–153.

[31] Yang, Y., Gu, M., Chen, S., and Jin, X., 2009, “New Inflow BoundaryConditions for Modelling the Neutral Equilibrium Atmospheric BoundaryLayer in Computational Wind Engineering,” J. Wind Eng. Ind. Aerodyn.,97(2), pp. 88–95.

[32] Spalart, P. R., and Rumsey, C. L., 2007, “Effective Inflow Conditions forTurbulence Models in Aerodynamic Calculations,” AIAA J., 45(10), pp.2544–2553.

[33] Ferziger, J. H., and Milovan, P., 1996, Computational Methods for FluidDynamics, Springer, Berlin.

[34] Sørensen, J. N., and Kock, C. W., 1995, “A Model for Unsteady Rotor Aero-dynamics,” J. Wind Eng. Ind. Aerodyn., 58(3), pp. 259–275.

[35] Churchfield, M. J., Lee, S., Moriarty, P. J., Martinez, L. A., Leonardi, S.,Vijayakumar, G., and Brasseur, J. G., 2012, “Large-Eddy Simulation of WindPlant Aerodynamics,” National Renewable Energy Laboratory (NREL), Tech-nical Report No. NREL/CP-500-53554.

[36] Martinez, L. A., Leonardi, S., Churchfield, M. J., and Moriarty, P. J., 2012, “AComparison of Actuator Disc and Actuator Line Wind Turbine Models andBest Practices for Their Use,” AIAA Paper No. 2012-0900.

[37] Stovall, T., Pawlas, G., and Moriarty, P. J., 2010, “Wind Farm Wake Simula-tions in OpenFOAM,” AIAA Paper No. 2010-825.

[38] Bazilevs, Y., Hsu, M.-C., Akkerman, I., Wright, S., Takizawa, K., Henicke, B.,Spielman, T., and Tezduyar, T. E., 2011, “3D Simulation of Wind TurbineRotors at Full Scale. Part I: Geometry Modeling and Aerodynamics,” Int. J.Numer. Methods Fluids, 65(1–3), pp. 207–235.

[39] Bazilevs, Y., Hsu, M.-C., Kiendl, J., W€uchner, R., and Bletzinger, K.-U., 2011,“3D Simulation of Wind Turbine Rotors at Full Scale. Part II: Fluid-StructureInteraction Modeling With Composite Blades,” Int. J. Numer. Methods Fluids,65(1–3), pp. 236–253.

031001-8 / Vol. 137, JUNE 2015 Transactions of the ASME

Downloaded From: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 05/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use