simulation of wakes behind wind farms

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Acad Year

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Project No. C032

SIMULATION OF WAKES BEHIND LARGE WIND

FARMS

Abdulqadir Aziz Singapore Wala

SCHOOL OF MECHANICAL AND AEROSPACE ENGINEERING

NANYANG TECHNOLOGICAL UNIVERSITY

Year 2011/2012

SIMU

LATIONOFWAKESBEH

INDLARGEWINDFAR

MS
http://www.google.com/imgres?q=ntu+logo&um=1&hl=en&sa=N&rls=com.microsoft:en-sg:IE-SearchBox&rlz=1I7RNRN_enSG424&biw=1280&bih=784&tbm=isch&tbnid=kC1zEging1hpwM:&imgrefurl=http://research-tlh.appspot.com/&docid=vYqSeR_xlQGkAM&imgurl=http://research-tlh.appspot.com/pics/NTU_Logo.png&w=176&h=237&ei=EeR7T6SHI8SgmQWd5anlCw&zoom=1&iact=hc&vpx=527&vpy=325&dur=764&hovh=189&hovw=140&tx=101&ty=61&sig=116094330542508210768&page=1&tbnh=132&tbnw=98&start=0&ndsp=24&ved=1t:429,r:8,s:0,i:100


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Title Page

SIMULATION OF WAKES BEHIND LARGE WIND FARMS

SUBMITTED

BY

ABDULQADIR AZIZ SINGAPORE WALA

SCHOOL OF MECHANICAL AND AEROSPACE ENGINEERING

A final year project report

presented to

Nanyang Technological University

in partial fulfilment of the

requirements for the

Degree of Bachelor of Engineering (Mechanical Engineering)

Nanyang Technological University

Academic Year 2011/2012


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Abstract

Computational fluid dynamics simulations of wind turbines are an essential aspect of

wind turbine design. Also very important is the simulation of many turbines in arrays, as they

are arranged in wind farms. This allows for the understanding of the effect of upstream

turbines on downstream ones, allowing for planning of the most efficient placement of wind

turbines as well as understanding the aeroelastic loads on wind turbines for a more efficient

maintenance schedule.

Given the computationally intensive nature of accurate wind turbine simulations even

when using simple two-equation Reynolds Averaged Navier-Stokes (RANS) models, simulations

of wind farms cannot be conducted through modeling the geometry of each wind turbine. Each

turbine needs to thus be simplified to a model that maintains the effects of the wind turbine on

the flow, while significantly reducing the size of the computational mesh required for the

simulation.

Since the far-wake structure of wind turbines are relatively steady in nature, actuator

disc models have become a popular choice for the simulation of wind farms. Actuator discs

model the blade forces of the wind turbines as pressure drops across infinitely thin discs.

However, to produce such a model, an aerodynamicist must know the blade forces. To this

effect, the Blade Element Momentum (BEM) theory has become a popular method to predict

the blade forces as input parameters for the actuator disc. However, being based on one-

dimensional theory and using two-dimensional airfoil data for its predictions, the BEM theory is

fraught with complications. Empirical corrections are often employed to make up for these, to

limited success.

Nevertheless, if direct rotor modeling and even accurate and detailed wind tunnel

experiments are used in the design process of wind turbines, this information can be used to

extract the blade force data needed for the actuator disc models. A complication is the

extraction of the axial and tangential induction factors required to model the variation of

pressure drop against local velocity for each actuator disc.


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Bak et al employed several methods to extract cross-sectional aerodynamic data from

wind turbines (Bak, Fuglsang, Sorensen, Madsen, Shen, & Sorensen, 1999). These included one

based on an inverse BEM method, by using blade force data to find the axial and rotational

induction factors of the blade element, and an actuator disc-based method, which used the

exact pressure drop for each specific wind speed to create a model of pressure drop against

local velocities. This report will investigate the accuracy of actuator disc models based on direct

rotor modeling data, by creating actuator discs through extraction of the induction factors

using the methods described earlier. The wake parameters from these models will then be

compared with traditional BEM-based actuator discs and a direct rotor model simulation. The

two present methods used were found to possess similarly high accuracies in wake prediction

in comparison to the direct rotor model, and displayed the ineffectiveness of an actuator disc

model based on a traditional BEM algorithm using 2-dimensional airfoil data. It is thus proven

that extraction of aerodynamic force data from direct modeling simulations or experiments can

be done in a manner useful to the prediction of the performance of a wind farm.


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Acknowledgements

Every endeavor requires inspiration and perspiration, and this project was no different.

My inspiration, has always been, and will always be, my spiritual leader, Dr Syedna

Mohammed Burhanuddin Saheb (TUS), who is my motivation and guiding light. He has taught

me to never hold back in the pursuit of knowledge, and this has given me clarity in my life. His

successor, Syedi wa Maulaya Aali Qadr Mufaddal Bhaisaheb Saifuddin (TUS) has been a shining

example and constant reminder that the true sign of knowledge and intelligence is humility.

Special thanks must be reserved for my project supervisor, Associate Professor Ng Yin

Kwee, who rather than stifle me with instructions and rigidity, encouraged me to be creative

and plan the project on my own. He constantly supported me with invaluable guidance and

advice, without which this project by no means would have been complete.

I would also like to thank my dad, who has shown me nothing but support and belief in

my abilities, and has spent many long hours worrying about the hours I have spent working, my

mum, who has shown me by example that no mountain is too high to scale, my beautiful wife,

Fatema, who has been a constant pillar of support, and my brother and his wife, Hozefa and

Ummehani, who have believed in me even more than I did myself.


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Table of Contents

1.0 Introduction ...................................................................................................................................... 1

2.0 Literature Review .............................................................................................................................. 4

2.1 Aerodynamics of Wind Turbines ................................................................................................... 4

2.1.1 Blade cross-sectional geometry and three-dimensional flow .............................................. 4

2.1.2 One-dimensional momentum theory ................................................................................... 5

2.1.3 Blade element momentum theory ........................................................................................ 8

2.1.4 Wind turbine wakes ............................................................................................................ 12

2.2 Rotor Modeling ........................................................................................................................... 13

2.2.1 Generalized actuator disk models ....................................................................................... 13

2.2.2 Direct modeling ................................................................................................................... 16

2.3 Experiments ................................................................................................................................ 18

3.0 Objectives and theoretical premise for project .............................................................................. 22

3.1 Development of simulation methodology for accurate actuator disc models ........................... 22

3.2 Inverse BEM Approach ................................................................................................................ 23

3.3 Actuator disc approach ............................................................................................................... 24

4.0 Computational Methodology .......................................................................................................... 25

4.1 Fluent computational fluid dynamics software .......................................................................... 25

4.2 Direct Modeling ........................................................................................................................... 25

4.2.1 Computational set-up ......................................................................................................... 25

4.2.2 Validation ............................................................................................................................ 30

4.2 Actuator disc models ................................................................................................................... 31

4.2.1 BEM based actuator disc model .......................................................................................... 32

4.2.2 Inverse BEM based actuator disc models ........................................................................... 32

4.2.3 Actuator disc based actuator disc model ............................................................................ 33

5.0 Results and Discussion .................................................................................................................... 34

5.1 Comparison of accuracy between direct rotor model and BEM theory ..................................... 34

5.2 Axial Velocity ............................................................................................................................... 35

5.2.1 Wake flow visualization ...................................................................................................... 35

5.2.2 Vertical profiles of axial velocity ......................................................................................... 39


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5.2.3 Horizontal profiles of axial velocity ..................................................................................... 42

5.3 Turbulence Intensity ................................................................................................................... 45

5.3.1 Wake flow visualization ...................................................................................................... 45

5.3.2 Vertical profiles of turbulence intensity ............................................................................. 48

6.0 Conclusion ....................................................................................................................................... 53

6.1 Project outcomes and objectives ................................................................................................ 53

6.2 Limitations of project .................................................................................................................. 54

6.3 Future work ................................................................................................................................. 54

7.0 References ....................................................................................................................................... 56

Appendix A ................................................................................................................................................ A-1

Appendix B ................................................................................................................................................ B-1


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List of Figures

Figure 1 Graph showing development and prognosis of total installed wind capacity in the

world from 1997-2020 (World Wind Energy Association, 2011) .................................................................. 1

Figure 2 Figure showing flow velocities and angle, angle of attack and airfoil pitch (Hansen,2008) ............................................................................................................................................................. 4

Figure 3 Figure showing cylindrical control volume for axial momentum equation (Hansen,

2008) ............................................................................................................................................................. 5

Figure 4 Figure showing streamlines past the rotor and graphs showing axial velocity and

pressure upstream and downstream of the rotor (Hansen, 2008) .............................................................. 6

Figure 5 BEM algorithm for WT_perf design code (Maniaci, 2011) ............................................................ 12

Figure 6 Comparison of actuator disk without (dashed line) and with rotation (solid blue line),

actuator line (black dots) and experiments (red circles), in terms of time-averaged velocity

against height at several down stream positions. Reproduced from (Porte-Agel, Lu, & Wu, 2010) .......... 14

Figure 7 NREL UAE Phase VI turbine in the NASA Ames wind tunnel (Hand, et al., 2001) ......................... 19Figure 8 Wind tunnel size for NREL UAE Phase VI Experiment (Simms, Schreck, Hand, &

Fingersh, 2001) ............................................................................................................................................ 19

Figure 9 NREL S809 airfoil section ............................................................................................................... 20

Figure 10 Distribution of blade cross-sectional chord length, c (m) against non-dimensionalized

rotor radius ................................................................................................................................................. 20

Figure 11 Distribution of blade pitch, () against non-dimensionalized rotor radius .............................. 21

Figure 12 Inverse BEM alogorithm for present study ................................................................................. 23

Figure 13 Computational gird intersecting the wind turbine blade ........................................................... 26

Figure 14 Computational gird intersecting the wind turbine blade in a closer view .................................. 27

Figure 15 Figure showing the computational grid adjacent to the blade ................................................... 27

Figure 16 Figure showing the computational grid around the blade tip .................................................... 28

Figure 17 Figure showing computational grid around the blade hub ........................................................ 28

Figure 18 Comparison of computed and experimental torques ................................................................. 30

Figure 19 Comparison of computed and experimental thrust ................................................................... 31

Figure 20 Radial discretization of actuator disc .......................................................................................... 32

Figure 21 Comparison of computed torques for CFD and BEM theory ...................................................... 34

Figure 22 Comparison of computed thrusts for CFD and BEM theory ....................................................... 35

Figure 23 Contour plot of axial velocity for wind speed of 7m/s................................................................ 36

Figure 24 Contour plot of axial velocity for wind speed of 10m/s .............................................................. 36




Figure 28 Vertical profiles for axial velocity for wind speed of 7m/s ......................................................... 39

Figure 29 Vertical profiles for axial velocity for wind speed of 10m/s ....................................................... 40



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Figure 33 Horizontal profile of axial velocity for wind speed of 7m/s ........................................................ 42

Figure 34 Horizontal profile of axial velocity for wind speed of 10m/s ...................................................... 43

Figure 35 Horizontal profile of axial velocity for wind speed of 15m/s ...................................................... 43Figure 36 Horizontal profile of axial velocity for wind speed of 20m/s ...................................................... 44

Figure 37 Horizontal profile of axial velocity for wind speed of 25m/s ...................................................... 44

Figure 38 Contour plot of turbulence intensity for wind speed of 7m/s .................................................... 46

Figure 39 Contour plot of turbulence intensity for wind speed of 10m/s .................................................. 46




Figure 43 Vertical profiles for turbulence intensity for wind speed of 7m/s.............................................. 49

Figure 44 Vertical profiles for turbulence intensity for wind speed of 10m/s............................................ 50





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List of Symbols

Angle of attack of airfoil

Pitch angle of wind turbine blade, with respect to plane of rotation

Angle of relative wind at wind turbine blade cross-section, with respect to

plane of rotation

Wind turbine rotation speed

Va Air axial velocity at wind turbine

V0 Freestream wind speed

Vrot Relative wind rotation speed

a Axial induction factor

a Rotational induction factor

R Wind turbine rotor radius

D Wind turbine rotor diameter

r Local radius from rotor center

c Local true chord of rotor-cross sectional airfoil

Cl Coefficient of lift of airfoil

Cd Coefficient of drag of airfoil

Cn Coefficient of force of airfoil normal to plane of wind turbine rotation

Ct Coefficient of force of airfoil tangential to plane of wind turbine rotation

CT Coefficient of thrust of wind turbine

CP Coefficient of power of wind turbine

x Displacement in axial direction, normal to rotor plane, in the direction of wind

(position of rotor plane is at x=0)

z Displacement in upwards direction, from rotor centre (rotor centre is at z=0)


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1.0 Introduction

Over the last two decades, many large wind turbines have been installed globally, and they

now contribute to 2.5% (World Wind Energy Association, 2011) of the global electricity supply.

This trend has been continually increasing and is expected to increase further, as shown in

Figure 1 below.

Figure 1 Graph showing development and prognosis of total installed wind capacity in the world from 1997-2020

(World Wind Energy Association, 2011)

Wind turbines are commonly grouped together in large wind farms. The reason for this is

that single wind turbines cannot generate enough power to be a useful producer of electricity,

and maintenance costs are reduced due to economies of scale. However, this results in wind

turbines operating in the wakes of other wind turbines. One of the problems that results from

this is reduced overall performance of the wind farm in comparison to a single wind turbine.

For example, (Neustadter & Spera, 1985) found that the power output for three turbines, each

separated by 7 rotor diameters was reduced by 10%. Another problem is the decrease in

lifespan of the rotors due to an increase in turbulence intensity in the wake. (Sanderse,

Aerodynamics of Wind Turbine Wakes, 2009)


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Effective computational aerodynamic simulation of a wind turbine, and by extension, a

wind farm, is an elusive goal for many aerodynamicists. Of particular interest from

computational simulations of wind turbines are the aerodynamics of the wakes. Three

particular tasks were listed by (Sanderse, Aerodynamics of Wind Turbine Wakes, 2009) with

regard to the simulation of wind turbine wakes:

1.

Calculating rotor performance and wind farm efficiency, requiring time-averaged

velocity profiles behind the turbines,

2.

Calculating the blade loading of the turbines in the wakes of other turbines and

fluctuations in electrical energy output, requiring turbulence fluctuations and intensity

of the wake,

3.

And calculating wake meandering, requiring large atmospheric eddies being taken into

account.

However, there are inherent difficulties associated with computations of wind farms,

including high computational costs due to the turbulent nature of the wind turbine wakes as

well as the rotation of the rotor, resulting in difficulties creating a suitable computational mesh.

(Sanderse, Aerodynamics of Wind Turbine Wakes, 2009)

While the computational methods theoretically exist to simulate the operation of

single wind turbines, the more accurate methods require a large computational cost to be

realized. These methods mostly involve direct modeling of a particular wind turbine, by means

of modeling its geometry and applying appropriate turbulence models such as RANS, DES or

LES. When considering the size of wind turbines and the Reynolds Number of the simulation, it

can be seen why such simulations would be computationally costly, especially since heavy

refinement of the computational mesh would be required close to the surfaces of the wind

turbine, to accurately compute the effects of the boundary layers. (Sanderse, van der Pijl, &

Koren, Review of CFD for wind-turbine wake aerodynamics, 2011)

To reduce the computational requirements of simulating wind turbines, several

models, generally classified as generalized actuator disk models, have been created to

accurately simulate the wind turbine, or the aerodynamic or aeroelastic effects of the wind

turbine, while keeping computational costs low. In these models, the aerodynamic properties


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of the wind turbine are traditionally derived using momentum theory. While momentum

theory, can be used as part of an initial design stage of wind turbines, it is not highly accurate,

resulting in a flawed actuator disc design to begin with.

Of the generalized actuator disc models, it is still found that only the actuator disc

model allows for a simulation of a wind farm since the others are still too computationally

demanding (Sanderse, van der Pijl, & Koren, Review of CFD for wind-turbine wake

aerodynamics, 2011).

It shall thus be the purpose of this research to develop a methodology through which

accurate actuator disk models can be generated using aerodynamic data extracted from direct

modeling of wind turbines, then comparing this methodology to conventional momentum

theory-based actuator disc models.


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2.0 Literature Review

2.1 Aerodynamics of Wind Turbines

2.1.1 Blade cross-sectional geometry and three-dimensional flow

The local angle of attack of a wind turbine blade is given by:

( 1 )Where is the pitch of the airfoil, the angle between its chord and the plane of rotation, and

is the flow angle, given by

( 2 )

Where Vais the axial flow velocity, and Vrotis the rotational velocity of the air.

Figure 2 Figure showing flow velocities and angle, angle of attack and airfoil pitch (Hansen, 2008)

Given that the blade is not dissimilar to a finite wing, tip vortices must exist. The

system of vortices introduces an axial velocity component opposite the direction of the wind,

and a tangential velocity component opposite the direction of blade rotation. The induced axial

velocity component is aVa,where ais the axial induction factor. The induced tangential velocity

component in the wake is 2ar where ais the tangential induction factor. Since there is no

rotation of the air upstream of the rotor, the induced tangential velocity within the rotor plane

is ar. is the angular velocity of the rotor, and r is the radial distance of the rotor from its

axis of rotation.


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Knowing the two induction factors, the axial and rotational velocities of the air in the

rotor can be found:

( 3 )

( 4 )

With these, the angle of attack of the blade cross-sections can be found. If the lift and

drag characteristics of the blade cross-sections are known, the force distribution along the

blade, and thus power output and aeroelastic forces can be computed.

2.1.2 One-dimensional momentum theory

Employing the cylindrical control volume shown inFigure 3 below, the axial momentumequation in integral form becomes:

( 5 )

Figure 3 Figure showing cylindrical control volume for axial momentum equation (Hansen, 2008)

The variations of pressure and velocity with axial distance both upstream and

downstream of the rotor is shown inFigure 4 below.


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Figure 4 Figure showing streamlines past the rotor and graphs showing axial velocity and pressure upstream and

downstream of the rotor (Hansen, 2008)

Using the law of conservation of mass, the mass flow through the rotor can be found:

( 6 )The law of conservation of axial momentum results in:

( 7 )

Using the law of conservation of energy, the shaft power, P, is equal to the loss of

kinetic energy in the air:


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( 8 )

Since this power is equal to the power performed by the thrust T,on the disc:

( 9 )Equating( 8 ) and( 9 ) gives us:

( 10 )Substituting equation( 3 ) into equation( 10 ) then the equations for power( 8 )and

thrust( 7 ) gives:

( 11 )and

( 12 )

The total kinetic energy of the air passing undisturbed through the same area as the

rotor, and its total momentum is equal to:

( 13 )and

( 14 )Non-dimensionalizing the power and thrust with respect to these, gives us the

coefficients of power and thrust:

( 15 )and

( 16 )


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To find the maximum power coefficient of the wind turbine, the derivative of the

coefficient of power with respect to the axial induction factor must be equated to zero. This

would give a value of CP=16/27 for a=1/3. This is called the Betz limit, the theoretical maximum

for an ideal wind turbine.

However, this one-dimensional momentum theory is not valid for values of agreater

than 0.4, because the velocity deficit in the wake would result in large shear forces between

the wake and freestream, causing eddies which transport momentum from the freestream into

the wake. Another obvious shortcoming is its inability to account for shear and turbulent

effects.

So far, the assumption has been that there is no rotation in the wake. However, most

wind turbines are single stage, having no stators or secondary contra-rotating rotors to keep

the flow steady.

With the definition of the rotational induction factor from equation 4, the azimuthal

velocity component in the wake is:

( 17 )The optimal relationship between aand ais found to be:

( 18 )

It can thus be seen that the Betz limit is arrived when a=0, consistent with the

momentum theory. This was found to occur at an infinite rotational speed of the blades.

2.1.3 Blade element momentum theory

The blade element momentum theory (BEM theory) can be viewed as a refinement of

the one-dimensional momentum theory. Instead of using the momentum balance across the

whole cylindrical control volume, the momentum balances across many annular control

volumes are calculated. This is done using two-dimensional airfoil data for various blade cross-

sections. It is an iterative process, since the axial and rotational induction factors are unknown


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for the blade cross-sections, thus the angle of attack is unknown. Hence, at every iteration, the

induction factors and the angle of attack is updated, requiring new values of lift and drag to be

determined from the airfoil lift curve.

The force coefficients normal and tangential to the rotor disc can be found from the lift

and drag curves using:

( 19 ) ( 20 )

The solidity, , is defined as the area of the annular element covered by aBnumber of

blades:

( 21 )

Using momentum theory, it can then be found that:

( 22 )

( 23 )

The equations for the axial and rotational induction factors, a, and a, are:

( 24 )

( 25 )


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The iterative method for deriving the blade forces thus involves an initial guess of a and

a, followed by finding and the appropriate lift and drag forces and then new values of aand

awhich are sued in the following iterations until the difference in aand abetween two

consecutive iterations are tolerably small, as defined by the aerodynamicist. Each control

volume is assumed independent, thus the procedure should be repeated for every discrete

annulus that the rotor is discretized into. This assumption of independent annular control

volumes is valid at lower values of a, but becomes inaccurate at higher values of a, due to the

mixing of the flows caused by increased wake turbulence and free shear effects (Hansen, 2008).

This can be rectified with empirical Glauert corrections, which will be discussed later.

Using these results, local loads on blade segments can be calculated. These results can

then be used to estimate fatigue and failure conditions for the turbine blades.

The BEM method shown thus far is based on the 1-dimensional mass and momentum

balance through annular stream tubes. This leads to obvious inaccuracies in the theory, which

does not account for the effects of blades of finite length, which result in tip and root vortices,

the finite number of blades which changes the vortex system in the near wake and the

significant free shear effects at larger axial induction factors. To correct for these, there are two

main corrections, one to correct for the infinite-blade assumption of the 1-dimensional theory,

and the other to correct for higher axial induction factors.

Prandtls tip loss factor

Prandtls tip loss factor is shown here without derivation, and the reader is directed to

Glauert, 1935 for a full derivation.

Equations( 24 ) and( 25 ) for aand aare replaced by:

( 26 )

( 27 )

Fis computed as:


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( 28 )Where:

( 29 )

Bis the number of blades, R is the radius of the rotor, ris the local radius of the annular control

volume, and is the local flow angle.

The tip loss factor corrects for the assumption of an infinite number of blades (Hansen,

2008). Alone, it will still have the limitation of inaccuracy at higher values of the axial induction

factor, a,due to mixing of flows arising from increased turbulence. This can be corrected

empirically using a Glauert correction.

Glauert correction for high axial induction factors

The corrections for high axial induction factors (high values of a) are empirical (Hansen,

2008). Thus, a number of different corrections have been proposed over the years, but they all

have the commonality of imposing different corrections for different values of a. They are all

classified as Glauert corrections. The equations described below are used in the WT_perf

design code by the National Wind Technology Centre in the United States. The tangential

induction factor, a,remains unchanged after this correction. More details of the model can be

found in Hibbs et al (Hibbs & Radkey, 1982):

{

( 30 )

WT_perf design code

The WT_perf design code was created by researchers at the National Wind Technology

Centre in the United States. The objective of this code was to provide researchers worldwide

with a simple program capable of BEM computations. It was developed as an open source

code, thus allowing researchers the flexibility of implementing their own algorithms and

modifications. The algorithm used in the WT_perf design code is described in the flow chart in


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Figure 5.The radial center of the blade elements are regarded of representative of the

sectional forces.

Figure 5 BEM algorithm for WT_perf design code (Maniaci, 2011)

The iterations do not use any form of relaxation, unless under-relaxation is needed to

handle divergence. Over-relaxation is unnecessary due to the quick convergence of the

algorithm, usually converging in a few iterations (Maniaci, 2011). The typical tolerance and

maximum number if iterations for the certification tests run with the WT_perf code are 10e-5

and 5 respectively.

2.1.4 Wind turbine wakes

The wake of a wind turbine is the region of airflow behind the wind turbine. This is

further subdivided commonly into the near-wake and far-wake regions (Vermeer, Sorensen, &

Crespo, 2003). In the near wake region, shear stresses are generally very high due to the large

difference in velocity between flow in the wake and outside of it. The number of blades can be


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discriminated, and tip vortices are clearly present. More than 1-2 rotor diameters downstream,

these effects become less discernible, and the flow properties are more axisymmetric, self-

similar and Gaussian. Turbulence effects are dominant, coming from three sources:

atmosphere, rotor blades and tip-vortex breakdown. In wind farm setups, downstream wind

turbines lie in the far wake region of upstream ones. In the far wake, large-scale effects such as

wake meandering are important, as are the effects of topology on the wake. (Sanderse, van der

Pijl, & Koren, Review of CFD for wind-turbine wake aerodynamics, 2011)

2.2 Rotor Modeling

2.2.1 Generalized actuator disk models

In the generalized actuator disk models, the computation of the boundary layers (and

by extension the computational resources required to accurately resolve it) is circumvented by

modeling the effects of the turbine itself on the airflow. The wind turbine is represented by a

body force, averaged over a disk, line or surface. The turbine is modeled using the momentum

balance expressed in the Navier-Stokes equations. In cylindrical coordinates and integral form,

( 31 )

The last term, the force term, results in a discontinuity in pressure. This is formulated in

different ways to result in the different generalized actuator disk models. In addition, a good

model should also introduce the turbulence generated by the blades.

Actuator Disk Model

The actuator disk model is a disk that represents the rotor plane. The force,f,is

equivalent to the thrust produced by the rotor. This can either be modeled as the average

thrust over the whole disk (uniformly loaded), or piecewise concentric thrusts (non-uniformly

loaded). Generally, the thrust is enforced as a pressure drop, which is equivalent to the thrust

divided by the area it is applied on. Since the model assumes an infinite number of rotors, the

force is equivalent to the time-averaged effect of the force on the blade. This was practiced by

(Raichle, Melber-Wilkending, & Himisch, 2008) and (Ammara, Leclerc, & Masson, 2002) using

the following equation:


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( 32 )Where the surface force,fs, is equal to the blade force,fr,multiplied by Bnumber of blades

divided by the circumference of the circle the element covers.

While turbulence effects on the rotor would be inherent in the modeling of the rotor

force, turbulence generated by the rotor is also dispersed into the wake, which is not explicitly

simulated by the actuator disk. This turbulence can be added at the disk location. However, in

comparison with wake turbulence (due to shear) and atmospheric turbulence, its effect is small

(Sanderse, van der Pijl, & Koren, Review of CFD for wind-turbine wake aerodynamics, 2011).

Another effect not simulated by the original actuator disk model is rotational effects,

which will have an effect on wind shear, and thus wake turbulence. Porte-Agel et al (Porte-

Agel, Lu, & Wu, 2010) showed that this would have an effect on both time-averaged velocity

and turbulence intensity in the wake, as shown inFigure 6 below.

Figure 6 Comparison of actuator disk without (dashed line) and with rotation (solid blue l ine), actuator line (black

dots) and experiments (red circles), in terms of time-averaged velocity against height at several down stream

positions. Reproduced from (Porte-Agel, Lu, & Wu, 2010)


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The main method used to determine the blade forces required to model the actuator

disk is the blade element momentum method, which, as described earlier, uses an iterative

method that utilizes information from the lift curve slopes of the airfoils at various segments to

determine the local annular momentum balance. The BEM theory will be explained in detail

later in this report. This method has been the more common method, probably because it is

the least computationally intensive method. The BEM method to determine the rotor

properties poses a very one-dimensional problem that can be resolved very quickly in an

iterative process. This indeed was used in LES simulations by Porte-Agel et al (Porte-Agel, Lu, &

Wu, 2010) and Wolton (Wolton, 2008). Ammara et al (Ammara, Leclerc, & Masson, 2002)

applied a BEM-generated actuator disk concept to simulate a coned rotor. Simulations by

Sorenson et al (Sorensen & Kock, A model for unsteady rotor aerodynamics, 1995) used a

similar approach, but the force was averaged over the whole disk, as compared to one that is

dependent on radial position. Studies could not be found that compare the number of

concentric actuator disks used in a non-uniformly loaded actuator disk to the accuracy of the

simulation.

A study by Harrison et al (Harrison, Batten, & Bahaj, 2010) showed increased accuracy

of wake predictions when using an actuator disc discretized into concentric discs as compared

to a uniform one for application in tidal stream turbines.

Another possible method to determine the blade forces has been through direct

modeling. This was done by Hartwanger et al (Hartwanger & Horvat, 2008). In this case, time-

averaged velocity and pressure information was extracted just upstream and downstream of

the rotor. These were then directly used to model the actuator disk pressure drop and

rotational velocity. However, it is unclear how the planes from which data was extracted were

chosen. It is probable that planes too close to the surface of the rotor would be affected by the

boundary layer on the rotor, while planes too far away would not give reliable information on

the flow just upstream and downstream of the rotor. Furthermore, the planes would be at

different distances from the rotor surfaces, due to twist and taper of the rotor, further

exacerbating the problem.


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Actuator Line Model

The actuator line model is an extension of the non-uniformly loaded actuator disk,

developed by (Sorensen & Shen, Numerical modeling of wind turbine wakes, 2002). The

difference is that in the actuator disk model, the blade forces are time-averaged over the whole

rotor disk, while in the actuator line model, the blade forces are not time-averaged, and remain

as line forces. This means that distinct tip vortices can be computed, for more accurate flow

visualization.

However, this unsteady modeling of the rotor results in an increase in computational

costs, which restricts its use to single wake LES simulations, while most LES wind farm wake

simulations are still performed using actuator disk modeling.

2.2.2 Direct modeling

Direct modeling is performed by modeling the entire rotor of the wind turbine, with a

body-fitted grid. Ideally, this would be the best method to represent the rotor for

computations of wakes behind wind turbines and wind farms, since the rotor is represented

completely, rather than just its assumed effects on the flow. However, there are many

problems associated with modeling the rotor directly.

Firstly, direct modeling is computationally very expensive. Direct modeling requires

that the boundary layers formed be adequately resolved to give an accurate representation of

transition, separation and stall effects (Sanderse, van der Pijl, & Koren, Review of CFD for wind-

turbine wake aerodynamics, 2011), which have direct impact on the aerodynamic forces of the

blades. This requires a high mesh resolution near surfaces, especially with high Reynolds

numbers.

Secondly, generating a mesh of sufficient quality to resolve the flow is not trivial.

(Sanderse, van der Pijl, & Koren, Review of CFD for wind-turbine wake aerodynamics, 2011).

This can be achieved using a chimera (overset) grid, in which a separate grid is made for the

moving surfaces, and the grid is overlapped onto a background grid, and these communicate

with each other. Another method commonly used is a sliding mesh approach, in which the

rotor resides within a cylindrical or spherical fluid domain. The rotor is stationary with respect

to this domain, and the domain itself moves, communicating with the cells in the stationary


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domain. The last method commonly used is that of the moving reference frame. In this

method, the mesh would be similar to that of the sliding mesh approach. This method is

simpler than the sliding mesh approach, given that the flow field rotates, and not the rotor. The

unsteady flow thus becomes a steady one with respect to the rotating frame of reference. This

reduces computational costs and simplifies post-processing (Sagol, Reggio, & Ilinca, 2012).

Potsdam et al (Potsdam & Mavripilis, 2009) compared structured, unstructured and structured

chimera grids to find no significant difference in their accuracies. However, the ease of creation

of the chimera grid, without the need to re-mesh the whole domain, needs to be weighed

against the grid-adaptation and refinement that can be achieved with regular grids.

Lastly, the high grid resolution limits the turbulence models that can effectively be

applied to direct modeling to RANS. Large Eddy Simulation (LES) (Lesieur & Metais, 1996)

models are too complex for such applications, and even the fastest supercomputers would not

be able to satisfactorily solve the simulation within a short enough time frame. Detached Eddy

Simulation (DES) (Spalart, Detached-Eddy Simulations, 2009) models have been used before by

Johansen et al (Johansen, Sorensen, Schreck, & Michelsen, 2002). however, no significant

improvement was found over RANS in predicting blade characteristics. Similar comparisons

were carried out by Sorensen et al (Srensen, Johansen, & Conway, 2004) who concluded that

while there was no significant difference in predicting the blade characteristics, the DES was

significantly better for flow visualization. Benjanirat et al (Benjanirat & Sankar, 2003)

performed simulations using the Bladwin-Lomax (Bladwin & Lomax, 1978), Spalart-Almaras

(Spalart & Allmaras, A one-equation turbulence model for aerodynamic flows, 1994) and k-

(Launder & Spalding, 1974) models and found that the models were reasonably accurate in

predicting normal forces of the blades, but sensitive to near-wall modeling in terms of chord-

wise forces. Sagol et al (Sagol, Reggio, & Ilinca, 2012) compared the k- (Launder & Spalding,

1974), Renormalization Group (RNG) k- (Yakhot & Orszag, 1986), Realizable k- (Shih, Liou,

Shabbir, Yang, & Zhu, 1995) and k- Shear Stress Transformation (SST) (Menter, 1994) models

and concluded that the k- SST model was the most accurate for the application of direct

modeling of wind turbines.

The simulations by Hartwanger et al (Hartwanger & Horvat, 2008), mentioned earlier,

made use of the k-turbulence model. The k-SST model has been proven to be more popular


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among aerodynamicists for the direct modeling of rotors. Indeed, it was also used in

simulations of wind turbines by (Le Pape & Lecanu, 2004) and in simulations for helicopter

rotor performance by (Le Pape & Beaumier, 2003).

Bak et al (Bak, Fuglsang, Sorensen, Madsen, Shen, & Sorensen, 1999) made use of

direct modeling to attain airfoil aerodynamic properties of wind turbine blades. This was done

using simulations with the k-SST turbulence model. The lift and curve slope derived for the

airfoil cross sections, which were specific to the flows found in wind turbines, could be used to

form more accurate actuator disc models through a more accurate BEM computation. Two

methods were used to derive the airfoil characteristics, the first of which was an inverse BEM

method. In this, the already known forces from the simulation were used (as compared to

forces being taken from lift and drag curves) and the axial and tangential induction factors

computed iteratively. In the second method, the forces, both axial and tangential, were placed

into an actuator disc. The resultant axial and induction factors, based on the speed of the

airflow at the disc, were used to compute the wind speeds and angle of attack. Both methods

were found to be in good agreement.

2.3 Experiments

Many experiments have been conducted by researchers to learn about wind turbine

aerodynamics. With the many problems inherent in CFD simulations of wind turbines,

experiments remain the only means of attaining absolutely accurate results. Of particular

interest is the National Renewable Energy Laboratory (NREL) Unsteady Aerodynamics

Experiment (UAE). This involved testing wind turbines both in wind tunnel and field conditions.

The results have been collated, arranged and made available to researchers.

In the NREL UAE Phase VI experiment (Hand, et al., 2001), a 10.058m diameter, 2-

bladed rotor was tested in the NASA-Ames 24.4m by 36.6m wind tunnel, as shown inFigure 7

andFigure 8.The wind tunnel has a turbulence intensity of 0.5%. The blades of the wind

turbine are twisted and tapered, and measurements include the coefficient of pressure

distribution at certain span sections, thrust, torque, and blade root flap bending moment. This

makes it an excellent validation case for CFD analyses, and will be simulated for this project.


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Figure 7 NREL UAE Phase VI turbine in the NASA Ames wind tunnel (Hand, et al., 2001)

Figure 8 Wind tunnel size for NREL UAE Phase VI Experiment (Simms, Schreck, Hand, & Fingersh, 2001)


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The experiments were conducted for a wide range of wind speeds, and the rotor speed

was controlled at 72rpm. The blades were composed entirely of the NREL S809 airfoil shown in

Figure 9,from 1.257m span to the blade tip. It transitions from a cylindrical shape to the NREL

S809 airfoil from 0.883m to 1.257m, although little is known about this transition and the form

of the blade tip, so some degree of assumption is necessary. The blade taper and pitch for a 3

pitch at the tip are shown inFigure 10 andFigure 11 respectively.

Figure 9 NREL S809 airfoil section

Figure 10 Distribution of blade cross-sectional chord length, c (m) against non-dimensionalized rotor radius

-0.15-0.1

-0.05

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1 1.2

Chordlength(m)

Non-dimensionalized rotor radius (r/R)


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Figure 11 Distribution of blade pitch, () against non-dimensionalized rotor radius

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1 1.2

Ptich()

Non-dimensionalized rotor radius (r/R)


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3.0 Objectives and theoretical premise for project

3.1 Development of simulation methodology for accurate actuator

disc modelsActuator disc models are the only method available currently for an accurate

simulation of the wakes behind wind turbines in a large wind farm. Current research, however,

centers on the simplest application of the actuator disc model, where the parameters are

based on the simple but inaccurate BEM theory. Research has barely brushed the possibility of

using direct modeling, or experimental results (both in much the same way) to attain a more

accurate actuator disc model.

This is likely to be due to the fact that direct modeling and experiments are both very

time consuming and expensive, compared to using the BEM theory, which can deliver a result

in seconds. However, the applications of direct modeling and actuator disc models are

dissimilar. Direct modeling can be used to optimize the design and understand the

aerodynamic and aeroelastic properties of a single wind turbine. Actuator disc models, on the

other hand, can be used to optimize wind turbine placement in wind farms, understand the

maintenance requirements for the wind farm, and possibly be used to design wind turbines for

subsequent arrays after the first, that are optimized to operate in the wake of upstream

turbines. This would create a far more efficient wind farm, decreasing costs and increasing the

energy output from the wind farm.

Thus, the objective of this research is to develop a framework through which the

essential information can be passed from wind turbine manufacturers to wind farm operators,

for the accurate simulation of wind farms using the actuator disc model. The same framework

can be used by wind turbine manufacturers to work with wind farm operators and produce

wind turbines suited to their position within a wind farm.

This project will attempt to fulfill this objective using two approaches, similar to the

approaches used by Bak et al (Bak, Fuglsang, Sorensen, Madsen, Shen, & Sorensen, 1999) to

attain the airfoil characteristics for wind turbine blade cross sections, and will be elaborated on

in later sections. This will be carried out by means of first conducting a direct modeling of the


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NREL UAE Phase VI rotor. The wakes of the actuator discs will be compared to the wakes of the

direct models as well as actuator discs developed using the BEM theory, and the accuracy of

the developed approach will be assessed.

3.2 Inverse BEM Approach

This approach will use the same BEM algorithm used in the WT_perf design code,

except that the forces extracted from the direct simulation will be used. Thus, there will be no

reference to the lift and drag curves, since the forces are already known. The algorithm is

summarized inFigure 12,was applied using Microsoft Excel and run for 50 iterations, and the

blade discretized into 20 sections of 5% span length. The radial center of this section will be

used to represent the sectional forces.

Figure 12 Inverse BEM alogorithm for present study

The extracted awill be directly used to form the relationship between pressure drop

and axial velocity as well as model the swirl velocity in the actuator disc. The same disc model

will be run for all wind speeds.


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3.3 Actuator disc approach

In this approach, the pressure drops computed from the direct simulation and will be

run as fixed (not velocity-dependent) pressure drops in actuator discs specifically for each of

the wind speeds. The axial velocity will be extracted at each blade section at each wind speed,

which will be used to form an overall pressure drop against velocity model. This new model will

be used in the actuator disc run for all cases, which will be used for comparison.

The present study will only cover axial flows, and will not include a tangential force

component, like the one used in the simulations by Bak et al (Bak, Fuglsang, Sorensen, Madsen,

Shen, & Sorensen, 1999).


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4.0 Computational Methodology

This section will highlight the mesh properties and boundary conditions used in all the

CFD computations in this project. 5 wind speeds were simulated, 7, 10, 15, 20 and 25 m/s.

These were all run for the specific case of 0 yaw and 0 coning angle of the wind turbine. The

pitch of the wind turbine at the blade tip was 3. The hardware used was a computer with an

Intel Xeon 5650 processor and 16GB of RAM. This enabled large simulations to be run quickly

by parallel processing among the 6 cores, which ran at 3.06GHz.

4.1 Fluent computational fluid dynamics software

The simulations were run on ANSYS Fluent 6.3.26. Fluent is an Eulerian, finite-volumes

based CFD software. As a commercial CFD tool, it is a powerful software used by many

industries, including aerospace, automotive and marine. It comes packaged with many

numerical solving methods and turbulence models, giving the user many options. It also has the

capability of parallel processing, allowing the user to perform larger simulations with multi-core

or network processors.

Fluent comes packaged with the grid generation software, Gambit, which was used to

model the computational meshes for this project.

4.2 Direct Modeling

4.2.1 Computational set-up

The direct modeling for this project used the multiple reference frames approach. In

this approach, the air in the wind tunnel would be computed in a stationary frame of reference,

while the flow field would rotate in the cylindrical control volume around the blade, simulating

a rotating blade. While many researchers have used a cylindrical domain for the farfield

boundary, it was not practiced in this project. Instead, the domain was shaped to match the

wind tunnel in which the experiment was conducted, for a more meaningful validation. Since

the experiment has a periodic symmetry of 180, a periodic simulation was run, using only one

blade and half the wind tunnel cross-sectional geometry, thus requiring only half the number of

mesh cells.


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The computational mesh was composed of 2 primary fluid domains, the rotor zone and

the tunnel zone, and was entirely composed of an unstructured tetrahedral mesh. The rotor

zone had a radius of 5.5m, to allow a large enough gap between the blade tip and the edge of

the rotor zone so as to prevent interference with the fluid flow. The rotor zone also extended

0.15D upstream and 0.15D downstream of the rotor centroid. The mesh size was 8mm at the

rotor and expanded at a growth rate of 1.25 to a maximum size of 4cm, giving a total of

5,479,781 cells.

Figure 13 Computational gird intersecting the wind turbine blade


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Figure 14 Computational gird intersecting the wind turbine blade in a closer view

Figure 15 Figure showing the computational grid adjacent to the blade


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Figure 16 Figure showing the computational grid around the blade tip

Figure 17 Figure showing computational grid around the blade hub

The rotor domain extended to 18.3m in height, half the width of the NASA-Ames wind

tunnel, and from -12.2m to 12.2m from the rotor centroid in width, matching the height of the


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NASA-Ames tunnel. The inlet and outlet boundaries were located at 10D form the rotor

centroid, to ensure the boundaries cannot significantly affect the flow. The mesh size grew

from 4cm at the boundary of the rotor zone at a rate of 1.4 to a maximum size of 73.8cm,

corresponding to the largest chord length in the rotor geometry. This resulted in a total of

3,185,465 cells in the tunnel zone. Thus, the total number of cells for the direct model was

8,665,246 cells.

The velocity inlet and outflow boundary conditions were applied to the inlet and outlet

boundaries respectively, no-slip wall condition for the tunnel walls and rotor, and periodic

condition for the boundaries of rotational symmetry. The rotor zone was given a rotational

speed of 72rpm, and the rotor given 0 rotational speed with respect to the adjacent rotor zone.

A k-SST turbulence model (without transitional flows) was applied. The reason the

transitional flows wall function was not applied was that it required a cell y+ of 1 to 10 to be

optimum, which was not the case for this simulation. Without transitional flows, a y+ of 30 to

300 was appropriate, which matched the y+ range of the rotor. The k-SST turbulence model

was chosen because of its proven accuracy in wind turbine simulations, resulting in its

popularity as a turbulence model for direct modeling simulations, most likely due to its high

accuracy in both near wall flows and flows away from the wall, as well as its ability to handle

rotational flows.

A steady-state simulation was first attempted. While the torque output was tolerably

accurate, within 10% of the experimental torque, the torque output was noisy, constantly

changing with every iteration. Thus, a pseudo-steady state method was employed for wind

speeds of 7m/s and 10m/s, whereby an unsteady simulation was run, but with a time step

equivalent to 1 revolution of the rotor. This allowed for a rather steady-state output, and the

results at every 10 revolutions from the 250th

to 400th

revolution were taken and averaged.

However, at 15m/s, this approach became inaccurate, exceeding a 15% deviation from

experimental torque. This was probably because of the onset of flow separation, which made

the flow more complex. The time step was reduced to a 2 rotation of the blade per time step.

After 9 rotor revolutions, the simulation was deemed to have converged, since the peaks and

troughs of the oscillations for the torque output were similar, and this provided enough time

for wind with 15m/s speed to reach the outlet boundary from the rotor and the rotor from the


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inlet boundary. From here, the data from every 20 turn of the rotor was taken and averaged

for one rotor revolution. This was done to have an azimuthal average of the various rotor and

flow properties, such as coefficients of pressure and wake velocities. The large angle of 20

between each data set was used to simplify this averaging process, but small enough to ensure

a fair averaging process. A similar approach was practiced for the other wind speeds. The

simulations of wind speeds of 20m/s and 25m/s were deemed to have converged after 7 and 5

revolutions respectively and thus were run for 8 and 6 revolutions respectively.

4.2.2 Validation

The results of the simulation were validated against experimental results, and showed

good agreement. All torque and thrust values were tolerably accurate (within 12% of

experimental values) as shown inFigure 18 andFigure 19 respectively. In addition, force

coefficients normal to the chord at various cross sections (30%, 63% and 95% span sections)

were in similarly close agreement. The distribution of the coefficients of pressure for these

span sections were also compared for a pre-flow separation case (7m/s) and post-flow

separation case (25m/s) and found to be in close agreement. The comparisons of the force

coefficients and the coefficients of pressure distribution can be viewed in Appendix A.

Figure 18 Comparison of computed and experimental torques

0

200

400

600

800

1000

1200

1400

1600

1800

5 10 15 20 25

Torque(N.m

)

Wind Speed (m/s)

NREL UAE Phase VI

CFD Predictions


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Figure 19 Comparison of computed and experimental thrust

4.2 Actuator disc models

The actuator disc models were created with a similar domain size as the direct model,

for a fair comparison. The actuator disc is modeled in Fluent as a fan boundary condition.However, this boundary condition can only create a uniform pressure drop across the disc,

which can vary with local axial velocity at the fan boundary. To create the actuator discs for this

study, many concentric fan boundaries were used, thus effectively discretizing the actuator disc

radially. The actuator disc models were also composed of tetrahedral unstructured meshes.

The mesh size on the actuator disc was equal to the sectional length, 5% of the blade span.

From here, the mesh was expanded to a maximum size of 0.5R (2.5145m) at a growth rate of

1.25. A diagram illustrating the radial discretization of actuator disc is shown inFigure 20.

800

1300

1800

2300

2800

3300

3800

4300

5 10 15 20 25

Thrust(N)

Wind Speed (m/s)

NREL UAE Phase VI

CFD Prediction


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Figure 20 Radial discretization of actuator disc

Each discrete concentric actuator disc was given a pressure drop function of velocity,

modeled using a 4thorder polynomial shown in equation( 33 ).

( 33 )

where Ciis the coefficient for each power of velocity.

4.2.1 BEM based actuator disc model

The BEM design code, WT_perf, was used to perform the BEM computations to findout the forces on the blade sections. Since no lift or drag curves could be input for the

cylindrical section, the whole section was modeled as a hub. In addition, the transition section

from the cylindrical section to the blade proper was modeled as having the same airfoil as the

blade. The input file for the WT_perf code is shown in Appendix B.

To match the output from the program, the hub was modeled as a circular wall of 0.2R

radius. Thereafter, there were 16 concentric fan boundaries, with each pressure drop being

modeled with the 4

th

order polynomial shown in equation( 33 )

4.2.2 Inverse BEM based actuator disc models

The inverse BEM model was created based on the algorithm explained in section3.2

Inverse BEM Approach.Using this model, all sections of the blade could be modeled,


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and so no wall was used to simulate the hub. Instead, 20 concentric fan boundaries were used,

with each pressure drop being modeled with the 4th

order polynomial shown in equation( 33 )

4.2.3 Actuator disc based actuator disc model

In this model, one set of actuator discs were created with a constant pressure drop,

independent of axial velocity, and simulated at their specific wind speeds to find the local axial

velocity at the actuator disc, with each pressure drop being modeled with the 4thorder

polynomial shown in equation( 33 )


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5.0 Results and Discussion

5.1 Comparison of accuracy between direct rotor model and BEM

theoryTo better understand the comparative accuracies between the actuator disc methods

presented in this report and one based on BEM theory, a comparison is done for the torques

and thrusts for the rotor attained by the two methods. These are presented inFigure 21 and

Figure 22.

Figure 21 Comparison of computed torques for CFD and BEM theory

0

200

400

600

800

1000

12001400

1600

1800

5 10 15 20 25

Torque(N.m

)

Wind speed (m/s)

NREL UAE Phase VI

CFD Predictions

BEM


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Figure 22 Comparison of computed thrusts for CFD and BEM theory

It can be seen that BEM theory is highly inaccurate, due to the fact that two-

dimensional airfoil data is used, which does not account for rotational effects of the rotor that

can suppress stall effects. Thus can give an idea of the inaccuracies associated with a BEM-

based actuator disc approach, will be better qualified and quantified in the coming sections.

5.2 Axial Velocity

5.2.1 Wake flow visualization

Contour plots of axial velocity in the wake are shown for each wind speed in figures 23

to 27, for the direct rotor model (DRM), actuator disc-based actuator disc model (ADM-AD),

inverse BEM-based actuator disc model (ADM-IB) and BEM-based actuator disc model (ADM-

BEM).

800

1300

1800

2300

2800

3300

3800

4300

5 10 15 20 25

Thrust(N)

Wind speed (m/s)

NREL UAE Phase VI

CFD Prediction

BEM


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Figure 23 Contour plot of axial velocity for wind speed of 7m/s



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It is clear from the contour plots that the two present methods, the actuator disc-based

actuator disc model (ADM-AD) and inverse BEM-based actuator disc model (ADM-IB) have

produced highly similar results. Furthermore, their wake structures appear to be similar to the

wakes from the direct rotor model (DRM), although less turbulent. The axial velocities appear

to be in similar range, but the contours contain less detail. They appear to be more accurate in

comparison to the BEM-based actuator disc model, ADM-BEM, which generally displays lower

axial velocities.

A possible explanation for the differences between the both the ADM-AD and the

ADM-IB and the DRM is the lack of tip vortices produced by the actuator disc model. Also, the

flows in the actuator disc models are purely axial, and no rotational flows were simulated. This

may have contributed to the less noisy and smoother contour lines. Lastly, some of the lacks of

detail in the actuator disc models may be due to the coarser mesh used in the actuator disc

models compared to the DRM, resulting in a much poorer resolution of detail.


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5.2.2 Vertical profiles of axial velocity

To ensure a more meaningful, quantitative comparison, the vertical profiles of the non-

dimensionalized axial velocities, local velocities divided by the inlet velocity, from the rotor

center were plotted at 4, 6 and 8 rotor diameters downstream of the rotor (x/D = 4, 6 and 8

respectively), to compare the accuracy of the wakes and wake degradation. These profiles are

used to compute downstream rotor performances in wind farms, and thus are of great

importance. These are shown in figures 26 to 30 below.

Figure 28 Vertical profiles for axial velocity for wind speed of 7m/s


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The ADM-AD and ADM-IB models have shown a similar performance, with relatively

accurate prediction of the wake velocities, significantly more accurate than the ADM-BEM

results. However, slight inaccuracies can be seen at the rotor hub and tip regions. This may

possibly be due to the lack of rotational flows in the actuator disc models, which could add

additional shear forces in the flow that would create a steeper velocity gradient. Another

possibility may be the need to refine the discretization of the actuator disc model into

concentric actuator discs near the hub and tip regions.

5.2.3 Horizontal profiles of axial velocity

Axial velocities along the axial direction for radii of 0R, 0.25R, 0.5R and 0.75R (z/R=0,

0.25, 0.5 and 0.75 respectively) at a 0 azimuth (12 0clock position) for each of the simulations

are compared and shown for each wind speed in figures 33 to 37.

Figure 33 Horizontal profile of axial velocity for wind speed of 7m/s


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These profiles indicate that downstream wake degradation patterns in the ADM-AD

and ADM-IB models are similar to the DRM simulations, with very few variants. The high

accuracy in prediction of axial velocities even at large downstream distances from the rotor

indicates that the ADM-AD models and ADM-IB models will be highly successful in terms of

wind farm wake prediction. These results also indicate that the relative coarseness of the

meshes used in the actuator disc models do not affect the general flow physics adversely.

The profiles from the ADM-BEM simulations indicate a very low accuracy, which will

result in a highly inaccurate wind farm simulation, as these errors will be compounded in

downstream actuator discs.

5.3 Turbulence Intensity

5.3.1 Wake flow visualization

Contour plots of turbulence intensity in the wake are shown for each wind speed in

figures 38 to 42, for the direct rotor model (DRM), actuator disc-based actuator disc model

(ADM-AD), inverse BEM-based actuator disc model (ADM-IB) and BEM-based actuator disc

model (ADM-BEM).


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Figure 38 Contour plot of turbulence intensity for wind speed of 7m/s



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It is immediately apparent that both the ADM-AD and ADM-IB methods do not produce

enough turbulence to replicate the DRM result. In fact, the turbulence for these two models

are almost non-existent. This can possibly be attributed to the fact that rotational flows were

not simulated, and that the actuator discs do not simulate tip vortices, which can cause

shearing effects and eventual mixing, which result in turbulence. Also, the lack of any physical

wall means that boundary layer turbulence cannot develop.

Indeed it is likely to be the flat circular wall used to model the hub of the rotor in the

ADB-BEM model, which has resulted in the high levels of turbulence in those simulations.

However, this is not comparable with the turbulence from the DRM simulation, as the location

and intensity differs. Thus, it is likely that turbulent source terms must be included in the ADM-

AD and ADM-IB models to create a similarity with the actual flow.

5.3.2 Vertical profiles of turbulence intensity

To ensure a meaningful, quantitative comparison of axial velocities for the purposes of

wind farm wake simulation (for placement optimization, performance prediction and loads


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prediction), axial velocity profiles at 4, 6 and 8 rotor diameters downstream of the rotor (x/D =

4, 6 and 8 respectively) were compared, in figures 43 to 47.

Figure 43 Vertical profiles for turbulence intensity for wind speed of 7m/s


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These profiles confirm that the present methods do not produce enough turbulence to

accurately simulate the wind turbine. Using a wall boundary condition for the hub, as used in

the ADM-BEM method, produces too much turbulence, and does not generally follow the same

pattern as the DRM simulations. It is noticeable that above the rotor, turbulence from the

three actuator disc models are similar and higher that the DRM simulations. This is likely to be

due to the relative coarseness of the actuator disc meshes, which are not refined enough to

accurately simulate the wind tunnel wall boundary layer.

It is likely that turbulence source terms are needed to accurately account for the

turbulence generated by the rotor. The rotor is seen to develop more turbulence at the tip at

higher velocities, and the source terms need to account for this as well.


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6.0 Conclusion

6.1 Project outcomes and objectives

Two methods of creating actuator disc models have been presented, both involving theextraction of axial induction factors for discrete blade segments and blade forces directly from

a direct rotor modeling of a wind turbine. The first method, ADM-AD, involved using a fixed

pressure drop across the actuator disc for each wind speed, finding the local velocity normal to

the actuator disc for each blade segment, and using the data to form a pressure drop against

velocity profile, for a more general actuator disc. The second method, ADM-IB, used the BEM

algorithm, but with the fixed blade force data, to find the axial induction factor, based on which

the pressure drop against velocity profile for the actuator disc was formulated. The actuator

discs were made up of 20 discrete segments to increase the accuracy of the actuator disc.

Results showed little difference between the results of the ADM-AD and ADM-IB

methods. This was to be expected, since previous work by Bak et al (Bak, Fuglsang, Sorensen,

Madsen, Shen, & Sorensen, 1999) showed good agreement between similar two methods for

formulating airfoil lift and drag coefficients. More significant was the high accuracy of

prediction of axial velocity in the wake, even at large distances downstream of the rotor, in

comparison to the direct rotor model (DRM). In addition, this accuracy was significantly higher

than for the actuator disc constructed using a traditional BEM method (ADM-BEM). This shows

that the availability of direct rotor modeling results, or detailed experimental results both of

which would likely be produced at a design stage of a commercial wind turbine, can increase

the accuracy in which wind farm simulations are conducted. This can allow for far more

efficient placement of wind turbines in wind farms, as well as accurate prediction of blade

aeroelastic loads for a more cost-effective maintenance schedule.

However, prediction of turbulence intensity in both the ADM-AD and ADM-IB models

were highly inaccurate. This is due to the fact that the actuator disc forms only a pressure

discontinuity, and has no physical presence in the flow. These low turbulence intensities from

the ADM-AD and ADM-IB models may have been compounded by the fact that the present

study did not include rotational flows. Rotational flows may increase the shear in the wake to a

level that increases the turbulence intensity. From previous literature, it can be concluded that


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this is unlikely to be enough, and turbulence source terms would be needed in the actuator disc

to improve accuracy. However Sanderse et al noted in their review of wind turbine wake

aerodynamics that in the case of an atmospheric boundary layer, the turbine-generated

turbulence would be insignificant compared to atmospheric turbulence (Sanderse, van der Pijl,

& Koren, Review of CFD for wind-turbine wake aerodynamics, 2011). This needs to be

investigated with present models using atmospheric boundary layers.

Overall, this project was successful in producing accurate actuator disc representations

of the NREL Phase VI wind turbine by means of extraction of aerodynamic data from the direct

rotor CFD model. This success suggests that accurate and detailed experimental results would

be well suited to produce even more accurate actuator disc models for wind farm wake

simulation.

6.2 Limitations of project

All research has shortcomings, but effective assessment of these will allow the

discerning scientist or engineer to formulate better conclusions. One shortcoming of this

project was the assumption that the wake from the DRM simulation was an accurate

representation of the actual wind turbine wake. This is a safe assumption, since not only overall

torque and thrust data was highly accurate, but blade sectional force distribution and the local

cross-sectional coefficient of pressure distribution were found to be accurate. While this is an

intuitively safe assumption, this could not be validated due to the lack of particle image

velocimetry (PIV) or anemometry data.

In future, it is hoped that more experiments such as the NREL UAE phase VI will be

conducted, with a wide and detailed variety of data that includes detailed wake profiles. This

would allow for better validation of CFD data.

6.3 Future work

Present research focused on only axial flows for the actuator disc models. However,

this is by design, rather than a shortcoming, to reduce the number of variables. The work

presented here can be extended in several directions, including:


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1.

Exploring the relationship between the number of blade segments used and the

accuracy of the actuator disc model, and if a suitable coarse but accurate model can be

created.

2.

Exploring the same models presented here including rotational flows, to assess the

accuracy of the new model, with the added parameter of rotational velocity of the

wake.

3.

Exploring the addition of turbulence source terms in the actuator disc models

presented to improve prediction of wake turbulence.

4.

Investigating the effect of outdoors simulation, using the atmospheric boundary layer,

to assess the viability of the models in a true wind farm setting.

5.

Comparing the accuracy of the present models in arrays, with experimental results

involving similar wind turbine arrays.

It is the hope of this author that such studies and more will result in highly accurate

wind farm wake simulations, for more efficient and cheaper wind farms in the future.


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7.0 References

Ammara, I., Leclerc, C., & Masson, C. (2002). A Viscous Three-Dimensional

Differential/Actuator-Disk Method for the Aerodynamic Analysis of Wind Farms.

Journal of Solar Energy Engineering, 124(4), 345-356.

Bak, C., Fuglsang, P., Sorensen, N. N., Madsen, H. A., Shen, W., & Sorensen, J. (1999).Airfoil

Characteristics for Wind Turbines.Riso National Laboratory, Technical University of

Denmark. Roskilde, Denmark: Riso National Laboratory. Riso-R-0165 (EN).

Benjanirat, S., & Sankar, L. N. (2003). Evaluation of turbulence models for the prediction of

wind turbine aerodynamics. 41st Aerospace Sciences Meeting and Exhibit.Reno,

Nevada, USA: AIAA. AIAA-2003-0517.

Bladwin, B. S., & Lomax, H. (1978). Thin Layer Approximation and Algebraic Model for

Separated Turbulent Flow. 16th American Institute of Aeronautics and Astronautics,Aerospace Sciences Meeting.Huntsville, Alabama: AIAA. AIAA-1978-257.

Glauert, H. (1935). Airplane Propellers. In W. F. Durand,Aerodynamic Theory, Vol IV(pp. 169-

360). Berlin, Germany: Springer Verlag.

Hand, M. M., Simms, D. A., Fingersh, L. J., Jager, D. W., Cotrell, J. R., Schreck, S., et al. (2001).

Unsteady Aerodynamics Experiment Phase VI: Wind Tunnel Test Configurations and

Available Data Campaigns.Golden, Colarado: National Renweable Energy Laboratory.

NREL/TP-500-29955.

Hansen, M. O. (2008).Aerodynamics of Wind Turbines(2nd ed.). London, UK: Earthscan.

Harrison, M. E., Batten, W. M., & Bahaj, A. S. (2010). A Blade Element Actuator Disc Approach

Applied to Tidal Stream Turbines. OCEANS 2010.Seattle, Washignton, USA: IEEE.

Hartwanger, D., & Horvat, A. (2008). 3D Modeling of a Wind Turbine Using CFD. NAFEMS

Conference, (pp. 1-14). Chaltenham, United Kingdom.

Hibbs, B., & Radkey, R. L. (1982). Small Wind Energy Conversion Systems (SWECS) Rotor

Performance Model Comparison Study.Pasadena, Cal

simulation of wakes behind wind farms

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