wind turbine simulations using actuator line model

Master’s Thesis

Wind Turbine Simulations usingActuator Line Model

Author: Andrea MATIZCHICACAUSA

Supervisor: PhD. Omar LOPEZEvaluator: PhD. Andres GONZALES

A thesis submitted in fulfilment of the requirementsfor the degree of Master in Mechanical Engineering

in the

Departamento de Ingenierıa MecanicaFacultad de Ingenierıas

Universidad de Los Andes

July 2015Bogota, Colombia

Department or School Web Site URL Here (include http://)

Faculty Web Site URL Here (include http://)

http://www.uniandes.edu.com

Declaration of Authorship

I, Andrea Matiz Chicacausa, declare that this thesis titled, ’Wind Turbine Simulationsusing Actuator Line Model’ and the work presented in it are my own. I confirm that:

This work was done wholly or mainly while in candidature for a research degreeat this University.

Where any part of this thesis has previously been submitted for a degree or anyother qualification at this University or any other institution, this has been clearlystated.

Where I have consulted the published work of others, this is always clearly at-tributed.

Where I have quoted from the work of others, the source is always given. Withthe exception of such quotations, this thesis is entirely my own work.

I have acknowledged all main sources of help.

Where the thesis is based on work done by myself jointly with others, I have madeclear exactly what was done by others and what I have contributed myself.

Signed:

Date:

i

UNIVERSIDAD DE LOS ANDES

AbstractFacultad de Ingenierıas

Departamento de Ingenierıa Mecanica

Master in Mechanical Engineering

Wind Turbine Simulations using Actuator Line Model

by Andrea Matiz Chicacausa

Computational simulations of fluid dynamics around wind turbines have become andimportant tool in the wind energy research field due to the opportunity to gain goodinsight of the physical phenomena with less expensive cost compared with experimenta-tion. However, the computational cost of such simulations is still high and efforts havebeen made in order to simplify simulations keeping the accuracy in the results. Actua-tor line is a technique proposed by Sørensen and Shen [22] to simplify such simulationsreplacing the actual geometry of a blade by a line over which punctual body forces willbe computed and projected on the flow. The use of this technique makes simulationswith fewer grid points able to resolve wake structures behind the turbine. This thesisproposes the use of this technique to simulate a full wind turbine (rotor and tower) inorder to achieve conclusions regarding the accuracy of the model to predict forces andto finally prove the capability of the model to simulate the tower. Results from the useof the AL technique and the aerodynamic response to the tower presence are shown andcompared to experimental data from UEA NASA Ames Phase VI Experiment.

Keywords: Actuator Line, CFD, NREL Phase VI, Wind Turbines

http://www.uniandes.edu.co

Faculty Web Site URL Here (include http://)

Department or School Web Site URL Here (include http://)

Acknowledgements

As always there are many people to whom I am deeply thankful. First of all, I would liketo express my deepest gratitude to my thesis supervisor Omar Lopez who was alwayspresent during this work, his constant support and patience encourage me to continueduring the most difficult parts of this work. This work could not have been possiblewithout the patient advice and time invested by Ivan Herraez who spent precious timeteaching me and discussing with me the main topic of this thesis.

This thesis would not have been possible without funding from the Turbine Simulation,Software Development and Aerodynamics Group of Fraunhofer IWES Institute and hishead Dr. Bernhard Stoevensandt who helped me even in difficult moments for the groupand himself.

Many thanks to the Turbulence, Stochastic and Wind Energy Group of ForWind Insti-tute of Oldenburg University, specially the CFD team for providing all resources needed,the productive discussions and support from colleagues made every day of work of thisthesis worth it. I am deeply indebted to Bastian Dose and Hamid Rahimi who helpedme more than needed not just for this work but also in my daily life in a foreign countryand made of my days in Germany something more than work.

Thanks to the computer time provided by the Facility for Large-scale Computations inWind Energy Research (FLOW) at University of Oldenburg. Many thanks to Dr. ScottSchreck from the National Renewable Energy Laboratory who provided the experimentaldata.

Last but not least to my family, without their support and sometimes sacrifices nothingof this could not have been possible. Finally, many thanks to Carlos Benavides for hissupport in critical moments.

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Contents

Declaration of Authorship i

Abstract ii

Acknowledgements iii

Contents iv

List of Figures vi

List of Tables viii

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Unsteady Aerodynamics Experiment Phase VI . . . . . . . . . . . . . . . 6

1.3.1 Turbine Description . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.2 Test Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Present Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Theoretical Background 11

2.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Finite Volume Method . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2 SIMPLE, PISO and PIMPLE . . . . . . . . . . . . . . . . . . . . . 16

2.3 Wind Turbines Aerodynamic and BEM . . . . . . . . . . . . . . . . . . . 19

2.4 Actuator Line Model (ALM) . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Numerical Simulations and Results 23

3.1 Computational Tools and Setup . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Navier-Stokes Solver . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.2 Mesh Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.3 Actuator Line Solver . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 CFD Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

iv

Contents v

3.2.1 Rotor-Actuator Line Simulations . . . . . . . . . . . . . . . . . . . 25

3.2.1.1 Grid dependence . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1.2 Epsilon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.2 Tower-Actuator Line Simulations . . . . . . . . . . . . . . . . . . . 29

3.2.2.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.2.2 Tower-AL . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.3 Rotor and Tower-Actuator Line Simulations . . . . . . . . . . . . . 34

3.2.4 Three-dimensional rotor and tower-AL . . . . . . . . . . . . . . . . 36

4 Conclusions 41

4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

A Blade chord and Twist Distribution 43

B k − ω SST Model: Mathematical Expressions [12]. 45

Bibliography 47

List of Figures

1.1 Wind Turbines hisctoric increment of size [15]. . . . . . . . . . . . . . . . 1

1.2 NREL Phase VI Turbine. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Design Models of Wind Turbines through complexity levels. BEM [3],Free Vortex Wake and CFD [17] . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 NREL Phase VI Blades [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Reynolds Number local to the blade distribution for different wind speeds. 8

1.6 Mach Number local to the blade distribution for different wind speed. . . 9

2.1 Structured and unstructured mesh for the finite volume method [27]. . . . 14

2.2 Schematic representation of a mesh for finite volume method [27]. . . . . . 15

2.3 SIMPLE algorithm [27]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 PIMPLE algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Acutator Disc and Stream Tube. . . . . . . . . . . . . . . . . . . . . . . . 19

2.6 Blade Element [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.7 Blade Element velocities and forces [3]. . . . . . . . . . . . . . . . . . . . . 21

3.1 Computational Domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Schematic top view of the domain and the refinement boxes. . . . . . . . 26

3.3 Output power vs. number of elements in the domain. . . . . . . . . . . . 28

3.4 Normal force coefficient along the blade. . . . . . . . . . . . . . . . . . . . 28

3.5 Tangential force coefficient along the blade. . . . . . . . . . . . . . . . . . 29

3.6 Computational Domain (Cylinder Simulations). . . . . . . . . . . . . . . . 30

3.7 Pressure distribution on the cylinder surface at Re = 2.6× 105. . . . . . . 31

3.8 Lift and drag forces from the cylinder simulation. . . . . . . . . . . . . . . 32

3.9 Forces oscillating with the actuator line model after modifying the liftand drag coefficients on the code. . . . . . . . . . . . . . . . . . . . . . . . 32

3.10 Deficit of velocity comparisson between results from simulation of a cylin-der, actuator line model and actuator line modified. . . . . . . . . . . . . 33

3.11 Vorticity produced by the Actuator Line tower. . . . . . . . . . . . . . . . 33

3.12 Output Power spectrum for U∞ = 7m/s . . . . . . . . . . . . . . . . . . . 34

3.13 Normal force coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.14 Tangential force coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.15 Normal force coefficient for 5 sections on the blade 30%, 47%, 63%, 80%and 95% at U∞ = 7m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.16 Three dimensional mesh, detail of the root of the blade. . . . . . . . . . . 37

3.17 Instantaneous y+ distribution over the blade. . . . . . . . . . . . . . . . . 37

3.18 Pressure coefficient distribution for 5 sections on the blade 30%, 47%,63%, 80% and 95% at U∞ = 7m/s . . . . . . . . . . . . . . . . . . . . . . 39

vi

List of Figures vii

3.19 Output power comparison between isolated rotor and with AL tower . . . 40

List of Tables

1.1 NREL Phase VI Turbine Dimensions . . . . . . . . . . . . . . . . . . . . . 7

1.2 NREL Phase VI Blade chord and twist distributions . . . . . . . . . . . . 9

3.1 Mesh characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Boundary Conditions for rotor and tower simulations . . . . . . . . . . . . 27

3.3 Boundary Conditions for 3D rotor and tower-actuator line . . . . . . . . . 38

viii

To Santiago

ix

Chapter 1

Introduction

The use of renewable energies to supply an increasing demand of energy over the worldseems to be the trend in the near future. So far, this kind of alternative energies are thekey to a sustainable way of progress since the use of wind or sunlight, for instance, is anunlimited, clean and free source of energy.

As the use and demand of these sources of energy increase the size of the wind turbineshas grown up as well (see Figure 1.1). According to the International Energy Outlook of2013 by the Energy Information Administration EIA, in 2010 the wind energy productionwas 2.5% of the total electricity consumed and it was estimated that for the year 2020 thewind energy generation will reach 700 GW. However, nowadays the wind installationsgrew by 44% worldwide and it is expected a generation of nearly 2000 GW by 2030 [1].

Figure 1.1: Wind Turbines hisctoric increment of size [15].

The constant increment of the wind turbines size and the complexities present in theevolution of the wind industry are the reason of the growing need for highly reliabledevices to transform the energy from the source to everyday electricity.

Moreover, the significant size that the wind turbines have achieved nowadays is an im-portant aspect that demands better/reliable design models in order to avoid expensivecosts of maintenance, that in some seasons of the year is impossible to carry out. There-fore the wind energy industry needs are clear: reliable, accurate and affordable design

1

Chapter 1. Introduction 2

models that improve the loads prediction during the operation of the wind turbine onthe field. And this is just possible by understanding the physical effects behind theoperation and states of these devices.

This section aims to present the importance of researching in wind energy field speciallyin the topic regarding to this thesis: the accurate prediction of aerodynamic loads bymeans of Computational Fluid Dynamics (CFD) models validating the Actuator Line(AL) model and the study of the aerodynamic effects.

First, it is presented the motivation for this research work. Second, it will be shownsome previous works done on this topic. And finally, the objectives proposed and theoutline of this document.

1.1 Motivation

In Wind Energy and especially regarding to wind turbines technologies, aerodynamics isone of the most important aspects. We must not forget that a wind turbine is, after all,a machine that transforms kinetic energy contained in the wind into mechanical powerthrough an aerodynamic process.

The importance of aerodynamics lies on the large amount of parameters that play a bigrole in the process of energy transformation. The current design models of the rotor arestill subject of large uncertainties due to several phenomena that can be classified in twogroups: periodic and aperiodic [10]. These uncertainties sources can be produced bythree-dimensional effects, unsteady effects, de-attached flow effects (stall), tower effects,among others [18].

These phenomena are highly difficult to measure, asses or model and the unknownresponses of the turbine under those effects, different work conditions and configurationproduce an unexpected and erratic behaviour, placing higher loads on the rotor thanthat they were designed for, and finally making a not-so-reliable device increasing thecost of energy in some cases.

The upwind configuration of wind turbines, that is when the air flow comes form thefront of the rotor, has been the most popular the last decades. The main reason for thisis the low frequency noise found in downwind turbines when the blade passes throughthe tower wake. However, downwind configuration present some advantages like theflexibility on blade design and yaw angle since the interference between rotor and toweris avoided.

In 2001 the National Renewable Energy Laboratory (NREL) invited several expertsfrom different institutes to participate in a blind prediction of loads and performance ofan instrumented wind turbine that was tested under controlled conditions in the NASAAmes wind tunnel [21]. The results from the comparison between the data measuredshowed an important lack of accuracy among the predictions; moreover, the comparisonbetween the participants shown wide variations between various design codes.

The evident and significant problems within the wind turbines designing process haveyield in making efforts to understand the complexities of the several phenomena takingplace in the wind turbines operation. A database of experimental data was obtainedby the NREL-NasaAmes Unsteady Aerodynamic Experiment (UAE) in 2001 [5] (see


Figure 1.2: NREL Phase VI Turbine.

Figure 1.2); later and with the objective to reduce the uncertainties present in designmodels, performance and loads calculations the Energy Research Center of The Nether-lands (ECN) led the Model Experiments in Controlled Conditions (MEXICO) project,which provided a experimental measurements database but with some different measuredmethods as for example Particle Image Velocimetry (PIV) [19].

Those databases sought to validate the existent engineering models and specially inthe case of MEXICO to provide a validation tool for Navier-Stokes based calculationtechniques. In conclusion, the aerodynamic modelling of wind turbines ranged from thebasic Blade Element and Momentum theory (BEM) to engineering models based onBEM and vortex wake methods to CFD methods to solve the Navier-Stokes equations(see Figure 1.3).

Although engineering models based on BEM are currently the most used methods andprovide high predictive confidence levels in the designing of wind turbines the CFDmethod is a more useful tool from which it is possible to achieve a deep insight andphysical realistic simulation of the turbine flow field, its behaviour and surrounding.

In the last decade CFD simulations have been a commonly used tool that gives goodinsight about the phenomena happening during a wind turbine operation. However, thesimulation of such big machines require to handle complex geometries and in most casessimulate transient phenomena making the method a expensive and complex technique.


Figure 1.3: Design Models of Wind Turbines through complexity levels. BEM [3],Free Vortex Wake and CFD [17]

The large amount of computational resources (memory and simulation time) needed andthe numerical issues associated plus the complexity of the phenomena to simulate haveled to developed simplified models based on actuators that capture the essence of thewind turbine behaviour reducing the computational resources needs. Although thesemodels do not describe completely the underlying physics behind the operation they areaccurate when computing specific quantities of interest.

The actuator disk concept, for example, is based on the representation of the physicalrotor as equivalent forces distributed on a permeable disc of zero thickness in a flowdomain. With a similar concept in mind Sørensen and Shen [22] proposed an actuatorline (AL) model which was later slightly modified by Michelsen [13].

The AL model combines a three-dimensional Navier-Stokes equations solver with a tech-nique where body forces are distributed along a line that represents a blade. The ad-vantage of this technique against the actuator disc model is its discrete nature that it isable to resolve tip and root vortices. Moreover, with the AL technique there is not needof resolving blade boundary layer instead the computational resources are employed tosimulate the dynamics of the flow structure [7]; therefore, information about the wakestructure and azimuthal distribution of velocity induction factors can be obtained withthe use of simple meshes.

1.2 Previous Work

Numerical simulation for wind turbines application started with a low acceptance sinceat that time they were too demanding in terms of computational resources and timeof processing. However, as the computational technologies progress they became moreaccepted and currently a powerful tool for accurate aerodynamic predictions with alower cost than required for full scale experiments in wind tunnel. These simulations arecommonly carried out by solving the three-dimensional Navier-Stokes equations bothin steady and unsteady approaches [6, 9]. Besides the computation of the governingequations the turbulence can be modelled by three main methods Reynolds AveragedEquations (RANS), LES and DES. However, those last ones are more demanding in


terms of mesh quality and computational time hence RANS modelling of turbulenceis the most commonly used. For wind turbine applications several tools have beenused, from commercial codes developed by ANSYS like Fluent to open source codes likeOpenFoam to in-house developed codes like ellipSys3D [14].

The challenges that simulate a full wind turbine present are time and computationalconsuming. First, mesh generation of complex geometries as it is the case for blades isone of the most time demanding tasks. Second, handling the relative movement betweenthe rotor and tower. And finally, to capture the unsteady phenomena happening on theflow over the rotor and surroundings in a reduced-cost way.

Different techniques have been adopted to face those challenges. Concerning the relativemovement between rotor and tower can be found for both upwind and downwind: Slidinginterface mesh [8], a General Grid Interface (GGI) method [9] and overset grid or so-called chimera grids [31] are the most used techniques.

In order to reduce the computation time, techniques based on actuators have beendeveloped. In 2002, Sørensen and Shen [22] proposed a model to study three-dimensionalflow field over wind turbine rotors. This model combined a three-dimensional Navier-Stokes Solver with an actuator line that represent the blade geometry over which theloads are distributed. The main goal of this model was to analyse and validate someengineering models.

In 2003, Michelsen [13] reformulated the AL model in terms of the primitive variables:pressure and velocity (p−V) and use the in-house Navier-Stokes equations solver ellip-Sys3D to study the aerodynamic behaviour of coned rotors, rotors exposed to yaw inflowand tunnel blockage. Besides, the AL model was used to analyse some of the assump-tions of BEM method such as tip loss correction models. Michelsen [13] also proposed athree dimensional actuator line changing the form of the regularization kernel since theoriginal model was physically inaccurate when distributing loads near the tip.

Since its formulation AL model has been subject of several studies especially directedto analyse the effect in the results when changing the parameters associated. The useof a suitable ε and its influence is one of the most studied [11, 20, 26]; however, there isnot a definitely conclusion about the best ε value.

Studies using the AL model have been often directed to analyse wake structures and tipvortices. Ivanell et al. [7] studied the behaviour of wakes behind the wind turbines withspecial interest in the structure and position of the tip vortex and the circulation on theblades. Regarding to ε it was concluded that the wake expansion does not depend onit; however, it influences the phase between the root and tip vortices; therefore, theysuggested reduce it as much as possible keeping a good agreement between numericalstability and accuracy.

Troldborg et al. [26] studied the wake behind the wind turbine operating in a uniforminflow combining LES simulations and the AL technique and, varying inflow conditionscombining AL technique and URANS computations [25]. There, it was investigated thesensitivity of the computed solutions to the regularization parameter ε. Simulationswith four different values were performed 1.5∆r, 2.0∆r, 2.5∆r and 3.0∆r where ∆r isthe cell side length in the equidistant region. As conclusion from his work it is seen thatincreasing ε causes a more smooth variation of the velocity near the root and tip. Onthe other hand if ε is chosen too large it will be difficult to distinct the pattern from


the tip and root vortices. In this work ε = 2∆r showed a good compromise betweenreducing oscillations without smoothing them out too much.

A comparison between actuator disk and actuator line was performed by Martinez et al.[11] in terms of predicting wind turbine power production and wake velocity deficits andconclusions about good practices were attempted. Besides, the parameters that affectthe performance of these models were analysed; for example, grid resolution, use of tipand root loss correction and the way the forces are projected onto the flow field. To dothese, they implemented a CFD solver in OpenFOAM and compare the results with aNREL-developed code that uses BEM theory.

From the performance of the AL model it was concluded that the power output increaseswith mesh refinement and as ε becomes larger the predicted power increases as well. Thelarger ε the smaller the rate of change of predicted power as a function of grid resolution.And as closest this parameter to the characteristic length of the blade section gives betterresults. Regarding to the actuator points were the forces will be smeared is said thatthey should be enough to predict the force field along the blades and to have a smoothdistribution through the blade, this criterion should be the basis for establishing theblade resolution. A very important conclusion is get from this work: the time step sizehave a big impact on simulation and it is restricted by the tip speed which should notpass through more than one cell each time-step. This condition is more restrictive thanthe typical Courant-Friedrichs-Lewy condition (CFL= 1).

It is evident the importance of studying the dependence between AL performance andgrid refinement level. Shives and Crawford [20] performed a numerical tests to determinemesh density and to provide force distribution guidelines. This was carried out by usingan infinite span wing and finite span wing with constant circulation distributions. Theyfound that the parameter ε should be somehow to be related to the local airfoil chordlength c. Although, they did not conclude to an specific value, they suggested the idealof defining ε based on the airfoil pressure distribution, which depends of the angle ofattack (AoA). This would means to change this parameter in each iteration.

Lately, Nilsson et al. [14] validated the capability of the AL model to capture vortexstructures in the near weak behind the MEXICO rotor comparing the simulation resultswith PIV measurement data finding good agreement between the wake expansion andtip vortex circulation.

Overall, the AL model has been tested for several cases and has showed a good perfor-mance. Although, definitely guidance with respect to the use and the influence of theparameters associated has not been completely concluded some basic assumptions arebeen made and it is clear that it has to be tested and analysed for other cases.

1.3 Unsteady Aerodynamics Experiment Phase VI

The National Renewable Energy Laboratory (NREL) of the United States conducted theUnsteady Aerodynamics Experiment (UAE) in order to provide accurate data represent-ing a wind turbine in field operation; in this way the characterization of the forces actingin a turbine to get a better understanding of the loads was possible; hence, optimizeblade and rotor designs and validate the existent models and BEM assumptions.


The experiment was performed in the NASA-Ames wind tunnel with a two-blade windturbine of 10 meter diameter. Several measurement campaigns were carried out in orderto test the wind turbine under different operational conditions and to obtain data toanalyse specific effects.

The information in this section about experiment, test turbine and test description wasfound in [5]. For detailed information refer to the reference or to other technical reports.

1.3.1 Turbine Description

The test turbine was a 10 meter diameter, stall-regulated with full span pitch controlwith a power rating of 20 kW, shown in Figure 1.4.

It was two, twisted and tapered blades and it was tested in both upwind and downwindconfigurations.

Figure 1.4: NREL Phase VI Blades [5].

The blade’s cross section is S809 airfoil designed by NREL. The S809 is a 21% thick-ness airfoil, designed for wind energy applications, specifically for horizontal axis windturbines (HAWT). It was optimised to improve wind energy power production and isless sensitive to leading edge roughness; for this airfoil there is available several datathat includes pressure distribution, separation boundary locations and drag coefficient.The two-dimensional blade profile data and, chord and twist distribution are includedin Appendix A. Some other turbine parameters are shown in Table 1.1.

Rotor diameter 10.058 m.Hub height 12.192 m.Tower Diameter 0.4 m.Tower clearance 1.401 m.

Table 1.1: NREL Phase VI Turbine Dimensions


Airfoil Data

As mentioned the blades are conformed of the S809 airfoil and its polars were took from[5] for Reynolds number ranging between 300000 and 1000000. They were obtainedat the Colorado State University for Reynolds number until 650000 and at Ohio StateUniversity for higher values.

The local Reynolds number of the blade varies in function of the chord as shown inEquation 1.1 and its distribution spam wise is shown in in Figure 1.5 for wind speedfrom 5 to 9 m/s; then, accordingly the airfoil data was setted up in the directory for ALsimulations.

Re =Ubladec

ν, (1.1)

where Ublade is the local blade velocity as express in (1.2), c is the chord and ν is thekinematic viscosity.

Ublade =√U2ax + U2

rot, (1.2)

where, Uax is the velocity in the axial direction (stream direction); and Urot is therotational speed (Urot = ωr, where r is the the radius of the blade).

Figure 1.5: Reynolds Number local to the blade distribution for different wind speeds.

The local Mach number(Ma = Ublade

a

)where a is the velocity of sound in air (343 m/s)

was computed as well in order to determine the compressibility conditions of the rotor.The distribution along the spam, shown in Figure 1.6 makes evident the incompressibilityof the flow as the Mach number is always less than 0.3.


Figure 1.6: Mach Number local to the blade distribution for different wind speed.

1.3.2 Test Description

Several measure campaigns were performed, some to emulate field operation and someother to collect data to explore specific phenomena. Tests were run in upwind anddownwind configuration. The angle of attack and dynamic pressure were measuredusing five-hole probes installed at five different spam sections over the blade. The spanposition, chord and twist distribution are shown in Table 1.2.

Radius [m] r/R [-] Chord [m] Twist []

1.510 0.30 0.711 14.2922.343 0.466 0.627 4.7153.173 0.631 0.543 1.1504.023 0.80 0.457 -0.3814.780 0.95 0.381 -1.469

Table 1.2: NREL Phase VI Blade chord and twist distributions

For the purpose of this thesis the results were compared with two specific campaigns:test sequence B and H, the downwind and upwind baseline tests. Both were performedwith a locked yaw angle, 72 RPM and wind speed ranging from 5 m/s to 25 m/s;however the numerical results were compared with the campaign at 7 m/s. The bladetip pitch was 3 constant. Data was recorded during 36 blade rotations that is 30seconds; measurements were sampled at 520.83 Hz.

The test sequence B was in downwind configuration with a teetered turbine and a coneangle of 3.4. For low wind speed yaw angles of ±180 were achieved and for high windspeed angles of −20 to 10. The test sequence H was in upwind configuration in a


rigid turbine with a 0 cone angle. For low wind speed yaw angles of −30 to 180 wereachieved and for high wind speed angles of ±10.

1.4 Present Work

The AL model has several input variables that depend strongly from each other and aresignificant for the results. Currently there are no clear conclusions about the method todetermine these parameters. This work aims to analyse how these parameters influencethe results and determine if it is possible to use the same simplification to simulate withthe AL model a tower hence to simulate a full wind turbine actuator line and achieveconclusions about the effect of the tower in the aerodynamic loads over the rotor.

To fulfil this intention the next objectives were proposed:

1.4.1 Objectives

The main objective of this thesis is to simulate the NREL- UAE Phase VI turbine indownwind configuration using the AL model.

The next specific objectives are proposed:

Specific Objectives

• To generate the mesh and simulate the rotor using the AL model.

• To analyse the influence of the level of mesh refinement on the results of thesimulation.

• To analyse the influence of the parameters from the actuator line model (regular-ization kernel ε and number of actuator points) on the results of the simulation.

• To analyse the influence of the time step (∆t) on the results of the simulation.

• To implement the actuator line model to simulate the tower.

• To simulate the full wind turbine using the actuator line model.

• To compare the results from simulations with experimental data.

1.4.2 Thesis Outline

This document is divided in five chapters. The present, Chapter 1 is devoted to explainthe motivation of this thesis, the state of art of the use of actuator line and finally tomention the objectives of this work. Next section, Chapter 2 will provide a theoreticalframe, briefly explaining the governing equations, the actuator line model and some otherconcepts used in the development of this work. Chapter 3 will show the simulationsperformed, the pre, post-processing and results. Finally, Chapter 4 will mention theconclusions, discussion and further possible work.

Chapter 2

Theoretical Background

This section introduce some basic information about Numerical Simulations, mentioningthe governing equations of fluid dynamics as a keystone upon the computational fluiddynamics; the numerical models to solve the governing equations and the methods tomodel turbulence. The Actuator Line model is explained as it was proposed.

2.1 Governing equations

The governing equations for a viscous, unsteady, three-dimensional, incompressible floware the Navier-Stokes Equations: continuity and momentum conservation equation, (2.1)and (2.2) respectively.

∇ ·V = 0 (2.1)

∂V

∂t+ [∇V] V = −1

ρ∇p+

µ

ρ∇2V + f (2.2)

where V is the velocity vector, p is the pressure ρ is the density and µ is the kinematicviscosity.

The Navier-Stokes equations were formulated after Navier and Stokes added the New-tonian viscous term to the momentum equations. Therefore in principle these equationsare in fact the momentum equations for viscous flows; however, nowadays the com-plete set of equations (continuity and momentum) is called Navier-Stokes or GoverningEquations for viscous flows.

2.1.1 Turbulence

The viscosity plays an important role in flows, it has a destabilizing effect on the fluidsyielding to random phenomena called turbulence [29].

The Reynolds number (Re) is one of the most important parameters to characterizeflows. Shown in (2.3), it is a dimensionless number that correlates the inertial and theviscous forces.

Re =ρV L

µ=V L

ν(2.3)

11

Chapter 2. Theoretical Background 12

where V and L are characteristic velocity and length scales of the flow, µ is the viscosityand ν is the kinematic viscosity.

At high Reynolds Numbers flow is considered turbulent, which means that it is subjectof high frequency, random fluctuations of various flow properties, and generation of largeeddies and vortex takes place in this regime.

Turbulence Modelling

In numerical simulations, turbulence modelling is one of the most important aspects,together with mesh generation and the implementation of numerical methods have avery important effect in the accuracy of the simulation [30]. Although not easy due tothe complex nature of turbulence ’an ideal model should introduce the minimumamount of complexity while capturing the essence of the relevant physics.(Wilcox [30])’ From Reynolds, Bussinesq, von Karman and Prandtl, many authorshave studied turbulence and attempted to predict the turbulent properties on a flow.

Prandtl attempted to develop a realistic mathematical expression to model the turbulentstresses for which he proposed a model that relates the eddy viscosity and the kineticenergy of the turbulent fluctuations k. This model was called one equation modelof turbulence. However the model was incomplete since the length scale (eddies size)was not included.

In 1942, Kolmogorov proposed his turbulence model introducing a new parameter ωthat represents the turbulence frequency Wilcox [30]. This model was called the k − ωmodel and since it satisfy another differential transport equation was also refereed astwo equation model of turbulence.

RANS and k − ω SST Model

Reynolds Averaged Navier Stokes focus on the mean value of the flow velocity field andthe sum of the mean value of the fluctuations of velocity, pressure, shear stress, etc.This lead to rewrite the Navier-Stokes equations in terms of mean turbulent variables.

Leading to expressions for the velocity components (u, v, w) and pressure field like (2.4).

u = u+ u′ v = v + v′ w = w + w′ p = p+ p′, (2.4)

where the time mean u of a turbulent function u(x, y, z, t) is (2.5) and the fluctuationu′ is the deviation of u from its mean value u: u′ = u− u

u =1

T

∫ T

0udt, (2.5)

Although the fluctuation has a mean value equal zero its mean square value (u′)2 it isnot, and measure the turbulence intensity.

(u′)2 =1

T

∫ T

0u′2dt 6= 0, (2.6)


Substituting (2.4) in (2.2) gives as result the so-called turbulent stresses which areconvective acceleration terms. These terms are unknown, therefore there are need threeadditional equations that involve unknown variables. This is known as the closureproblem since it is need to posse an equal number of equation for all the unknownquantities.

The turbulence models based on the equation for the turbulence kinetic energy k are themost used in CFD simulations. These models can be classified in: one equation modelsor incomplete models since they do not take into account the turbulence length; andtwo equation models or complete models that provides an equation for the turbulencelength scale. The k − ω, k − ε and k − ω SST models are some of the most known anduse.

The k − ω Shear Stress Tensor (SST) used in the simulations of this thesis is a twoequation model that use the formulation of Kolmogorov’s k−ω model in the inner partsof the boundary layer and is able to switch to the k − ε model when describing thebehaviour of free-stream.

This model solve two transport equations one for the turbulent kinetic energy k and onefor the specific dissipation rate or turbulent frequency ω and from them to obtain thebehaviour of the kinematic eddy viscosity ν. These equations ((B.1), (B.2) and (B.3) )can be found in Appendix B.

2.2 Numerical Methods

So far it has not been found a general solution for the Navier-Stokes equations and, asthey are a coupled system of non-linear partial differential equations it is just possibleto solve analytically very simple cases. For this reason the governing equations aresolved by means of numerical methods that seek to produce an approximate solution byiterative means.

The first step to obtain an approximate solution is the numerical discretization of thegoverning equations. This process consist of formulate each equation that is proposedover a continuous domain in discrete points or volumes in the domain. In other wordsthe partial differential equations are replaced by algebraic expressions on each node interms of the flow-field variables; for instance, velocity, pressure and temperature, asfunctions of the position on the domain (coordinates x, y and z). Therefore the flowfield is described over the complete domain where it is search a solution.

Some of the discretization techniques are: finite elements, finite differences and finitevolumes. All methods in CFD use those techniques to solve the governing equations.OpenFoam is based on finite volume discretization.

2.2.1 Finite Volume Method

This method subdivides the computational domain into control volumes where the con-servation laws have to be fulfilled locally in each one of them. For time dependent simula-tions, the time is divided in time intervals so-called time step, for each iteration/time-stepthe governing equations will be solved in the entire domain.


Figure 2.1: Structured and unstructured mesh for the finite volume method [27].

This method discretizes the governing equations presented in the conservative form(2.7). As this method works with control volumes, it can handle different kind of grids;structured or unstructured, making this method more flexible and useful for the imple-mentation on complex geometries as it is shown in Figure 2.1.

∫SρφV · ndS︸︷︷︸convection

=

∫S

Γ∇φ · ndS︸︷︷︸diffusion

+

∫ΩqφdΩ︸︷︷︸

source

(2.7)

where, ρ is the density, φ is the intensive property, Γ is a diffusive coefficient like thekinematic viscosity µ.

When the finite volume method is applied the domain is considered as a finite number ofvolumes surrounding nodal points, P , W and E, as it is shown in Figure 2.2. First, theequation (2.8) is discretized in time, then at the time tk the spatial domain is dividedinto finite volumes that have the reference point P at the center.

∂u

∂t=uk+1 − uk

∆t, (2.8)

Those control volumes have their interior boundaries placed at the points w betweenW and P ; and, e between P and E. At the nodal point P the discretization givesEquation 2.9 that in words states that the subtraction between the diffusive flux of φleaving the east face and the diffusive flux of φ entering the west face represents thegeneration of φ.∫

∆V

d

dx

(Γdφ

dx

)dV +

∫∆V

SdV =

(ΓA

dφ

dx

)e

−(

ΓAdφ

dx

)w

+ S∆V = 0 (2.9)


Figure 2.2: Schematic representation of a mesh for finite volume method [27].

where A is the cross-sectional area of the control volume face, ∆V is the volume and Sis the average value of source S over the control volume [28].

In Equation 2.9 the values of the diffusion coefficient Γ and the gradient ∂φ∂x at east (e)

and west (w) are required. To calculate them it is used the central differencing approachthat in a uniform grid linearly interpolated values for Γw and Γe are given by 2.10 and2.11.

Γw =ΓW + ΓP

2Γe =

ΓP + ΓE2

(2.10)

(ΓA

dφ

dx

)w

= ΓwAw

(φP − φWδxWP

) (ΓA

dφ

dx

)e

= ΓeAe

(φE − φPδxPE

)(2.11)

Substituting 2.10 and 2.11 into Equation 2.9 gives Equation 2.12 that can be arrangedas Equation 2.13. The finite volumes method generate algebraic expressions at thereference point based on the the values at the neighbouring points. The resulting systemof equations has to be solved simultaneously.

ΓeAe

(φE − φPδxPE

)− ΓwAw

(φP − φWδxWP

)+ S = 0 (2.12)

(ΓeδxPE

Ae +ΓwδxWP

Aw − Sp)

︸︷︷︸aP

φP =

(ΓwδxWP

Aw

)︸︷︷︸

aW

φW +

(ΓeδxPE

Ae

)︸︷︷︸

aE

φE + Su (2.13)


The system of equations resulting from the discretization process is solved by numericalmethods whose complexity depends on the dimensionality and geometry of the physicalproblem; and whether the equations are linear or non-linear. These numerical methodsare classified in direct and iterative methods [27]. The most well known direct methodis the Gauss elimination, which derives from the basis of systematic reduction of largesystems of equations to small ones; however, for large systems of equations, this methodbecomes computationally expensive. The iterative methods are based on the repetitionof an algorithm leading to a convergence of the solution. This kind of methods startwith an initial guess and use the equation to improve the solution until convergencesis achieved; therefore, it is less expensive compared with direct methods. Jacobi andGauss Seidel are some of the most common iterative methods use in CFD.

2.2.2 SIMPLE, PISO and PIMPLE

For an incompressible flow the governing equations are dependent of pressure since ineach momentum equation the fluid flow is driven by pressure gradients. Therefore,the system of equations consist of four equations: one continuity equation and threeequations for momentum conservation; all of them function of velocity V and pressurep. However, there is not an independent transport equation for pressure; hence, thegoverning equations have to be solved for pressure and velocity fields coupled.

The most common method to solve the pressure-velocity coupling issue is an iterativemethod called SIMPLE, that stands from Semi-Implicit Method for Pressure-LinkageEquations developed by Patankar and Spalding [16]. In this scheme, an initial pressurefield is guessed and used to solve the momentum equations. Then, from the continuityequation, a corrected pressure is deduced, which is used to update velocity and pres-sure fields. Through an iteration process the pressure and velocity fields are improveduntil convergence is achieved for both fields. The algorithm of this scheme is shown inFigure 2.3.

Another scheme commonly use to solve the pressure-velocity coupling is the PressureImplicit with Splitting Operators (PISO) algorithm which involves an additional pressurecorrection equation to improve convergence. The non-linear effects of the velocity areavoided by setting a small time step, leading to a Courant number1 below one. Thisscheme is an extension of the SIMPLE algorithm that has been also adapted for thecomputation of unsteady problems.

Depending on the problem keeping a Courant number below one means to set a timestep so small that the complete simulation becomes slow and computational expensive.For this reason, in transient situations, the momentum equation is solved in an outerloop while the continuity equation can be recalculated as many times as the outer loopiterations. This procedure is called PIMPLE since it is a merged algorithm from SIMPLEand PISO and it is shown in Figure 2.4.

1Courant number is a condition for convergence and stability while solving partial equations by meansof numerical methods. Co = u∆t

∆xin simple words it states that a particle of a fluid just pass trough one

cell every time step


Begin

Solve the momen-tum equations

Solve the pressurecorrection equation

Correct pressureand velocity fields

Solve all other transportequations (turbulence)

Check residuals

is solutionconverged?

End

Replacep∗ = p;

V∗ = V,

Initial guess: p∗, V∗

V∗

p′

p, V

k, ω

yes

no

Figure 2.3: SIMPLE algorithm [27].


Begin

Solve the momen-tum equations

Solve the pressurecorrection equation


Solve the second pres-sure correction equation


Solve all other transportequations (turbulence)

Check residuals

Replacep∗ = p;V∗ = V

is solutionconverged?

is solutionconverged

End

Initial guess: p∗, V∗

V∗

p′

p, V

k, ω

yes

no

no

yes

Figure 2.4: PIMPLE algorithm.


2.3 Wind Turbines Aerodynamic and BEM

The most basic and commonly used method to design rotors and compute loads is theMomentum and Blade Element theory, in short BEM. The Momentum Theory is basedon the assumptions of: i) infinite number of blades; ii) uniform thrust over the rotor;iii) non-rotating wake; and iv) infinite blade spam (two dimensional assumption).

With an infinite number of blades it is assumed that the rotor is in fact a continuous diskthat produce a drop of pressure in the stream tube, as the pressure drops it produces achange of momentum equal to the change of velocity as it is express in (2.14) and shownin Figure 2.5. (

p+d − p

−d

)Ad = (U∞ − Uw) ρAdU∞ (1− a)︸︷︷︸

Change of momentum

, (2.14)

where, U∞ is the wind free stream velocity, the subscript d indicate the conditions onthe actuator disc, Uw the far wake wind velocity and a is the induction factor which isproduct of a velocity variation induced by the disc on the free stream velocity. That

Figure 2.5: Acutator Disc and Stream Tube.

Where, V0 and P0 represent the wind free stream velocity (U∞) and pressure; and u1

the far wake velocity (Uw).

drop of pressure produces a force F on the actuator disc, known as thrust, that istransformed in power. Both thrust and power can be non-dimensionalized to give therespective coefficients (2.16) (2.17) which depend strongly of the induction factor a.

FUd︸︷︷︸Power

= 2ρAdU3∞a (1− a)2 (2.15)


CP =FUd

12ρU

3∞Ad

= 4a (1− a)2 (2.16)

CT =FUd

12ρU

2∞Ad

= 4a (1− a) (2.17)

In reality the air passing through the blades (no infinite number of blades) exerts atorque on the rotor, the reaction to this effect is an equal and opposite torque exertedon the air. This reaction makes the particles of air rotates in an opposite direction tothat of the rotor with a tangential and axial velocity components, hence the wake behindrotates.

On the other hand, the Blade Element Method (BEM) assume a infinite blade span(two dimensional assumption) therefore the aerodynamic forces can be calculated bytwo dimensional airfoil parameters for a determined angle of attack. This is done byassuming a single element of the blade as it is shown in Figure 2.6 that has not effecton the other elements.

Figure 2.6: Blade Element [3].

The angle of attack defined as the angle between the chord of the airfoil and the windspeed can be computed from the velocity components local to a blade section, the windvelocity and the rotational speed of the rotor. Knowing the angle of attack and thecoefficients of lift and drag the forces on the blade can be calculated an they are shownin Figure 2.7.

Those forces are in charge of the change of momentum on an specific element and theyare radial independent, which means that they do not affect other elements of the blade.

From Figure 2.6 and Figure 2.7 the obtained relative velocity to the blade (Equation 2.18)acts at an inflow angle φ to the rotational plane.

Vrel =√U2∞(1− a)2 + ω2r2(1 + a′)2 (2.18)

The inflow angle φ can be defined as (2.19) and the angle of attack α according toFigure 2.7 is defined as (2.20).


Figure 2.7: Blade Element velocities and forces [3].

sinφ =U∞(1− a)

Vrelcosφ =

ωr(1− a′)Vrel

, (2.19)

α = φ− β, (2.20)

where, ω is the rotational speed, a and a′ are the axial and tangential induction factorsrespectively, and β is the pitch angle.

From (2.18) it is possible to compute the lift and drag forces on a blade element of δrlength, as it is express in Equation 2.21 and Equation 2.22

δL =1

2ρV 2

relcClδr (2.21)

δD =1

2ρV 2

relcCdδr (2.22)

Nowadays, BEM is the most commonly used method to design blades and to computeloads. However, real wind turbines are subject of three-dimensional effects associateddue to the discrete number and the finite span of blades that produces changes on theaerodynamic loads. For this reason, correction models for three-dimensional, rotationaleffects as well as for other parameters such as the presence of the tower and the so-calledtower shadow have been developed, though they are not accurate enough.

2.4 Actuator Line Model (ALM)

The actuator line model was proposed as a simplified way to simulate rotors of windturbines and to solve accurately the wake and the structures on it.

This method adds to the Navier-Stokes Equations a source term related to body forces fε.These body forces are the aerodynamic loads computed with the basic BEM approach(2.23) that use two dimensional airfoil lift and drag coefficients corrected for three-dimensional effects to compute the tangential and axial force to the blade airfoil.


f2D =dF

dr=

1

2ρU2

relc (CLeL + CDeD) , (2.23)

where CL and CD are the lift and drag coefficients respectively that depend on the angleof attack (AoA) and Reynolds number (Re); c is the chord, and eL and eD are the unitvectors in direction of lift and drag.

These forces have to be smear over the line to avoid singular behaviour; therefore, bytaking the convolution of the computed normal force and a regularization kernel ηε thattakes the form of a three-dimensional Gaussian distribution function (2.25) is producedthe distributed loads fε (2.24).

fε = f ∗ ηε, (2.24)

where

ηε (r) =1

ε3π3/2exp

[−(r/ε)2

], (2.25)

where, ε adjust the distribution of the force and r is the distance between the measuredpoint and the initial force points on the blade. In this way the loads are distributedsmoothly on more than one grid point.

The three dimensional distribution presents physics inconsistency when distributingloads further than the physical tip of the blade. For this reason Michelsen [13] pro-posed a two dimensional regularization function following the form of a two dimensionalGaussian distribution shown in Equation 2.26. Besides, he reformulated the model inthe primitive variables, pressure and velocity in order to couple it with the Navier StokesEquations Solver ellipSys3D

η2Dε =

1

ε2πexp

[−(r/ε)2

]. (2.26)

Among the advantages of the Actuator Line Method are: the need of simpler mesheswith less grid points to capture the aerodynamics of the blade compared with threedimensional blade meshes; since it is a simplified model, it does not simulate the actualgeometry of the blade therefore, it is not able to resolve blade boundary layer nonethelessthe computational resources can be employed in solving other effects. Compared withother simplified methods (i.e. actuator disc) actuator line provides information aboutthe kinematics of the flow and allows for a detailed study of wake structures, tip androot vortex for instance.

Chapter 3

Numerical Simulations andResults

This chapter is devoted to describe the simulations performed and, the pre and postprocessing stages. Giving details of the domain, mesh, boundary conditions and theresults obtained.

First, a simulation of the rotor with the actuator line model was performed in orderto asses the grid dependence and regularization factor effect on the results. Second,the actuator line model was tested and implemented to model the tower, to do this,simulations around a cylinder were performed in order to produce a velocity field tocompare with the actuator line model results. Third, rotor and tower were modelledwith the actuator line aiming to determine if this simplification shows the predictedeffect of the tower on the rotor aerodynamics. Finally, the actual geometry of the rotorwith the implemented actuator line tower was simulated to observe if the tower shadowphenomena can be studied with this model.

3.1 Computational Tools and Setup

3.1.1 Navier-Stokes Solver

OpenFOAM R©(Open Field Operation and Manipulation) was used for all computationsand simulation. It is a free, open-source CFD software package that provides a largeamount of features to solve several cases involving partial differential equations com-putations, however it is mostly employed in solving an extensive range of fluid flows ofdifferent levels of complexity. It includes tools for meshing, pre and post-processing. Al-most all those features run in parallel using the Message Passing Interface (MPI) librarymaking of this package a very flexible tool. Moreover by being open source, OpenFOAMallows the user to customise and extend its functionality as long as it is desire since itis C++ based.

OpenFOAM is based in Finite Volume Method and has several numerical schemes im-plemented to carried out the time and spatial discretization. It counts as well witha wide variety of solvers to simulate different flows and different conditions. Amongothers, icoFoam a transient solver for incompressible, laminar flow of Newtonian flows;

23

Chapter 3. Numerical Simulations and Results 24

simpleFoam a steady state solver for incompressible, turbulent flow; pisoFoam a tran-sient solver for incompressible flow; and, pimpleFoam a large time-step solver for incom-pressible flow using a SIMPLE-PISO merged algorithm.

3.1.2 Mesh Generator

Meshes were generated with the mesh generator tools provided by OpenFOAM, blockMeshwhich generates meshes of blocks of hexahedral cells according to a directory that spec-ifies the points coordinates, the block orientation, and faces comformation. The toolfor unstructured meshes, snappyHexMesh was used and for three dimensional blades thein-house1 automatic Blade Block Mesher (BBM)was employed.

3.1.3 Actuator Line Solver

NREL developed a set of classes based on C++ to couple with CFD solvers basedon OpenFOAM that allow the users to investigate wind turbines and wind farms per-formance under different atmospheric conditions and terrain. This application, calledSOWFA (Simulator fOr Wind Farm Applications) includes a high fidelity analysis ofwind plant and wind turbine fluid physics and structural response [4].

SOWFA includes among other tools an Actuator Line turbine model class that does notinclude the hub nor the tower effects. However, it takes into account the geometry of theturbine (tower height and hub size) to locate the rotor on the computational domain.

The solver pimpleFoam was modified and compiled with the AL model class included inSOWFA in order to run transient simulations.

3.2 CFD Simulations

First, simulations of the NREL-Nasa AMES UAE Phase VI rotor were performed fordifferent wind speed (5, 6, 7 8 and 9 m/s) varying the mesh refinement and the regular-ization parameter ε. This was done to analyse the influence of the parameters and themesh refinement.

In order to implement the acuator line model for tower modelling, simulations of flowaround a cylinder were performed in order to stablish a reference point of the velocityfield. Then, simulations of a full wind turbine (rotor and tower) using the AL modelwere performed in order to achieve conclusions about: i) validation of AL model fortower applications; ii) accuracy of the results after simplifying the full turbine to an ALmodel; and finally, iii) effect of the presence of the tower in the rotor aerodynamics.

Lastly, a simulation of the actual geometry of the rotor and the tower AL was performedaiming to analyse the effects of the tower AL on the rotor aerodynamics and validateits implementation.

This section pretend to present the set up for the three cases performed, the character-istics of the mesh, the imposed boundary conditions and the parameters used.

1Developed by Fraunhofer IWES and ForWind Oldenburg


3.2.1 Rotor-Actuator Line Simulations

As it was mentioned simulation for wind speed between 5 and 9 m/s were performed.First to analyse the influence of the mesh in the results and to establish the character-istics for the next simulations. Second, simulations changing the regularization factorε were performed to analyse its influence on the results and to obtain a definitely andgeneral guidance about the use of this parameter for the next simulations. For this, abase case was created to start the first round of simulations and from it the parameterssubject of this work were changed.

Mesh Generation

One of the main advantages of using AL model is that there is no need of meshingcomplex geometries as it is the case when generating the mesh for full three-dimensionalblades. Just a much more simple mesh and some constraints to obtain an accurate andstable simulation are needed.

The domain, shown in Figure 3.1 and generated with blockMesh, has a rectangular shapebig enough to avoid the effect that outer boundaries can have on the vortex sheddingfrequency and the velocity field. It consist of a mesh of 10D length in the axial directionand 5D in the cross-flow direction; the length was setted 1/3 in front and 2/3 behindthe rotor.

Figure 3.1: Computational Domain.

It was designed in a way that fulfil the requirements established by SOWFA developerslisted below.

• +x must be east, +y must be north and +z must be up2.

• Use at least 20 grid cells across the rotor diameter2.

2SOWFA guidelines [4].


• Use at least 50 grid cells across the rotor diameter if it is desired to resolve tip/rootvortices2.

The base mesh follows the recommendations mentioned above and three more mesheswere generated with different refinement boxes in order to analyse the influence of thegrid on the results and to stablish the required mesh for next simulations. The schematicview of the mesh and the refinement is shown in Figure 3.1 and Figure 3.2 and thecharacteristics of each mesh is shown in Table 3.1 with the cell size in the refined part.

Figure 3.2: Schematic top view of the domain and the refinement boxes.

Refinement level Number of cells [M.] Cell size [m]

Base Mesh 6.1 0.2First box 7.4 0.15Second box 11.7 0.09Third box 20.1 0.05

Table 3.1: Mesh characteristics

Boundary Conditions

The imposed boundary conditions are shown in Table 3.2, where I is the turbulenceintensity, k turbulence kinetic energy, ω turbulent frequency, l turbulence length (l =0.07D) and Cµ is a empirical non-dimensional constant 0.09.


Boundary U p k Omega

Inlet U∞dpdy = 0 3

2 (U∞I)2 k32

kCµl

Outlet dUdy = 0 p∞

dkdy = 0 dω

dy = 0

Ground 0 dpdy = 0 dk

dy = 0 dωdy = 0

Top and sides dUdy = 0 dp

dy = 0 dkdy = 0 dω

dy = 0

Table 3.2: Boundary Conditions for rotor and tower simulations

Base Case

This case was setted with the mesh that follows the recommendations described beforewith approximately 4 million cells.

Based on the mesh, ε was setted equal to 0.4 from ε∆x = 2 and the number of actuator

points was equal to 40 following ∆b∆x = 0.753, where ∆b is the width of the discrete blade

section and ∆x is the grid resolution.

The time step is restricted by the tip speed. Since the tip of the blade should not passthrough more than one cell each time step. This condition is more important than thetypical Courant-Friedrichs-Lewi number (CFL = 1) [11] leading to a fixed time stepequal to 0.01989 s.

3.2.1.1 Grid dependence

The first parameter to analyse was the grid dependence of results. Three different caseswere performed for three meshes with different level of refinement as shown in previoussection.

Figure 3.3 shows the comparison of the rotor power for meshes with different levels ofrefinement. It is clear that the baseline guidance for mesh was not enough and the resultsstart to convergence to the experimental data (continuous line) from meshes with morethan 7 million cells which means one level of refinement and a cell size of 0.15 m in themore refined areas as it was shown in Figure 3.2 and it is 2.5 times smaller than thelength of the chord on the tip of the blade.

3.2.1.2 Epsilon

It has been proposed that ε should be related to a representative length of the blade byShives and Crawford [20] and [24] among others; because, this parameter regulates thedistance over the forces are projected. In this work it is propose a value of ε equal to thechord of the blade; therefore, simulations were performed with values equal to the chordof the blade in the positions were the experimental measurements were taken. That isε = 0.38, 0.46, 0.54, 0.63 and 0.71

Comparing the experimental normal and tangential force and the results from the nu-merical simulation good agreement was found specially for the normal force coefficient

3Recommendation by Martinez et al. [11]


Figure 3.3: Output power vs. number of elements in the domain.

(see Figure 3.4) and better agreement was obtained with lower ε values, or values closeto the chord of the tip of the blade. On the other hand, for tangential force coefficient,shown in Figure 3.5, bigger discrepancies were found specially close to outermost partof the blade; while it is true that as higher ε results seems to converge, for those valuesit is shown that they are far from the experimental data as better agreement is shownby lower values of ε; from a physical point of view as higher ε the forces will be smearedfar away from the physical blade geometry.

Figure 3.4: Normal force coefficient along the blade.

The discrepancies found close to the tip area can be explained by the two-dimensionalnature of the actuator line model and its lack of geometrical-three-dimensional correc-tions.


Figure 3.5: Tangential force coefficient along the blade.

3.2.2 Tower-Actuator Line Simulations

The actuator line model was used and modified in order to model not just the rotorboth the tower as well hence to asses the capability of the model to influence the rotoraerodynamics.

3.2.2.1 Implementation

To simulate the tower with the AL model, simulations of the flow around a cylinder wereperformed in order to obtain a reference point of the tower conditions (velocity field)and afterwards compare it with the tower-AL results.

Cylinder Simulations

First, simulations of flow around a cylinder of 0.4m diameter were performed at windspeeds between 5 and 9 m/s. The Reynolds number for this conditions varies between1.3× 106 and 2.4× 106. This range fit in the critical regime where the drag coefficientcurve is very stepped therefore that value changes greatly from one wind speed to other.

Mesh generation

A circular domain, shown in Figure 3.6, ten times bigger than the inner bluff body wasgenerated with blockMesh. Higher refinement was done close to the cylinder surface inorder to capture the stagnation and separation point, and the vortex shedding accurately.

The mesh consist of 3.3× 106 cells and the y+ was kept less than 1 (y+ = 0.08).


Figure 3.6: Computational Domain (Cylinder Simulations).

Boundary Conditions and Turbulence Properties

The boundary conditions for all cases were as follows:

• Inlet: Velocity uniform flow was specified

• Outlet: Pressure was set to a fixed value zero.

• Periodic: This boundary type simulates an infinitely long cylinder.

• Cylinder Surface: Wall conditions; pressure is set to zero gradient and velocityis set to zero.

The k−ω SST turbulence model was used for both RANS and URANS simulations dueto its wide documented well behaviour.

The values of the turbulence kinetic energy (k), the turbulence frequency ω and, theturbulence length (l) are given in (3.1), (3.2) and (3.3) according to Stringer et al.[23]; at the wall kwall is set to zero and ωwall is computed with a standard logarithmicwall function provided by OpenFOAM. Cµ is the empirical non-dimensional constant(Cµ = 0.09) and ν is the kinematic viscosity.

k =3

2(U∞I)2 (3.1)

ω =k

32

kCµl(3.2)

l = 0.07D (3.3)

where, U∞ is the free stream velocity and D is the tower diameter (0.4)m.


Validation

To validate the cylinder simulations, results were compared with experimental resultsfrom Achenbach [2] as it is shown in Figure 3.7. Grid dependence and turbulence modelcomparison were performed showing independence of results for both aspects.

Figure 3.7: Pressure distribution on the cylinder surface at Re = 2.6× 105.

For Reynolds number from 1× 105 to 1× 106 the flow is in the so-called critique regimewhere the drag coefficient drops hastily. The difficulty to validate the simulations ofthe flow around the cylinder during this regime relies in the several differences found inliterature about the critical Reynolds number at the drag drop starts. These differencesare product mainly of experimental set up, turbulence intensity and they are speciallysensitive to the surface smoothness.

The lift and drag forces oscillated trough the simulation as it is presented in Figure 3.8.The averaged drag coefficient obtained in this simulations was 0.6 that agrees with theresults reported on [2]. The averaged value for lift coefficient is zero and the Strouhalnumber St was 0.2

3.2.2.2 Tower-AL

From actuator line simulations the fluctuations reported previously could not be seeing.The reason for this is that the model takes the lift and drag coefficient from a tabulateddata depending of the angle of attack, those data remain constant during the simula-tion thus the fluctuation observed before is not reproduced; moreover such fluctuationproduce the vortex shedding behind the cylinder then the actuator line model is notreproducing that condition.

To reproduce the mentioned oscillation the code of the actuator line was modified re-placing the constant lift and drag coefficients by functions of time (3.4) and (3.5).


Figure 3.8: Lift and drag forces from the cylinder simulation.

CL = CL0 cos(ωt) (3.4)

CD = CD0 cos(2ωt) (3.5)

where CL0 and CD0 are the averaged values found in the previous section and ω = 22rad/s calculated from the Strouhal number as St = fL

V and as it is well known ω = 2πf .

The results from this modification produce the same oscillation of those coefficientsshown in Figure 3.9 improving the results when comparing the deficit of velocity behindthe tower as it can be observed in Figure 3.10 the drop of velocity with the modifiedactuator line is closer to the deficit obtained from the simulations of the cylinder.

Figure 3.9: Forces oscillating with the actuator line model after modifying the liftand drag coefficients on the code.


Figure 3.10: Deficit of velocity comparisson between results from simulation of acylinder, actuator line model and actuator line modified.

However, fluctuations of the vortex structures from the tower were not evident becausethe source of shedding is too small to be observed. Although the vortex shedding fromthe tower affects the rotor aerodynamics, Figure 3.11 shows the lack of fluctuations thatdoes not permit to properly observe the unsteady nature of the interaction between thevortex shedding from the tower and the blade.

Figure 3.11: Vorticity produced by the Actuator Line tower.


3.2.3 Rotor and Tower-Actuator Line Simulations

Finally, a simulation of a rotor and tower using the AL model was performed in orderto analyse the capability of the model to simulate a tower thus to influence the rotoraerodynamics.

The mesh and boundary conditions were the same employed in the previous simulations.From the first part, the rotor-actuator line simulations it was obtained the mesh inde-pendence study then a domain of 7 million cells was used in this simulation. Regardingthe regularization parameter, the chord of the tip of the blade was used (ε = 0.38). Tomodel the tower it was used the modified version of the model with the lift and dragcoefficients as function of time.

To accurately quantify the frequency of the effect of the tower on the rotor aerodynamics,power spectra were computed with the time records of AL and experimental data usinga Fast-Fourier Transform (FFT) algorithm. Experimental measurements were sampledat 520.83 Hz over 30 seconds for which the power spectra showed important content upto 30 Hz. Moreover, spectral peaks of significant magnitude were found in the range 0Hz to 10 Hz.

The power spectrum in Figure 3.12 shows the comparison between the actuator linemodel and the experimental data at wind speed of 7 m/s and it is evidence of the effectof the presence of the AL-tower as the highest spectral peaks are found for 2P, 4P and6P meaning that the power drops as the blades encounter the tower shadow once perrevolution (P = 1.2Hz); for the experimental data, although, the highest peak is at 2Pthere are spectral peaks every 1P due to unbalance of the turbine during the experiment.

Figure 3.12: Output Power spectrum for U∞ = 7m/s

Normal and tangential force coefficients were compared with experimental data, Fig-ure 3.13 and Figure 3.14 show the averaged coefficients for 5 section along the bladecorresponding to the pressure tap locations in the experiment. Good agreement is foundproving that the global aerodynamic parameters are well represented by the AL model.

At the root and the tip of the blade bigger discrepancies were found due to three-dimensional effects present in those locations and that they are not properly captured


Figure 3.13: Normal force coefficient

Figure 3.14: Tangential force coefficient

by the model. Although the Glauert correction F = 2π cos−1 exp(−f), where f is given

by f = B2

R−rr sin(φ) , at root and tip is applied it is not enough to accurately predict the

forces. This is shown as well in Figure 3.15 as increasing span wise from the root betteragreement is found until 80% of the blade. For the outermost part of the blade, section95%, the model does not represent properly the effect.


Figure 3.15: Normal force coefficient for 5 sections on the blade 30%, 47%, 63%, 80%and 95% at U∞ = 7m/s

3.2.4 Three-dimensional rotor and tower-AL

Rotor tower interaction was also studied with simulations performed by using a threedimensional model of the actual rotor geometry. To handle the relative movement be-tween rotor and tower while keeping a low computational cost a dynamic mesh approachwas used.

Mesh of the blades in Figure 3.16 was generated with the in-house4 automatic BladeBlock Mesher BBM, tool based on openFoam blockMesh and snappyHexMesh the result-ing domain consisting of 11.6 million cells, of cylindrical shape, 10D large and a radius

4Developed by Fraunhofer IWES and ForWind, Oldenburg.


of 3D. The rotor was placed at 1/3 of the domain length from the inlet. The y+ waskept at a maximum value of 100, as it is presented in Figure 3.17 since good results wereobtained with this mesh resolution.

Figure 3.16: Three dimensional mesh, detail of the root of the blade.

Figure 3.17: Instantaneous y+ distribution over the blade.

The Unsteady Reynolds Averaged -URANS computations were carried out using thePIMPLE algorithm to solve the coupled velocity-pressure equations and the turbulencewas modelled with the k-ω Shear Stress Tensor model. The boundary conditions inTable 3.3 were similar to the previous simulations adding the wall condition to the bladesurfaces.


The time step was kept fixed at 2.32×10−3 which means 1 of rotation per time step thatproduces an average Courant number of 0.38; however, due to the small size of the meshin some parts of the domain, specially close to the blades a maximum Courant numberof 2981 was achieved. Therefore, to asses the accuracy of the simulations the pressurecoefficient at five sections of the blade was compared with experimental data. Theresults presented in Figure 3.18 show that the simulation exhibits very good agreementcompared with experimental data.

Boundary U p k Omega

Inlet U∞dpdy = 0 3

2 (U∞I)2 k32

kCµl

Outlet dUdy = 0 p∞

dkdy = 0 dω

dy = 0

Ground 0 dpdy = 0 dk

dy = 0 dωdy = 0

Top and sides dUdy = 0 dp

dy = 0 dkdy = 0 dω

dy = 0

Wall

Table 3.3: Boundary Conditions for 3D rotor and tower-actuator line

To handle the relative motion between rotor and tower the dynamic mesh option includedin pimpleDyMFoam was used and re-compiled to add the actuator line option. This wasdone in two ways: first, placing the rotor and a rotating part that communicates withthe stationary part of the domain through a Arbitrary Mesh Interface (AMI); and secondrotating the complete domain. Both approaches produced good and almost the sameresults as it is showm in Figure 3.18 and avoiding the AMI interface the computationaltime is reduced.

The AL tower presence is proved by the drop of power in both cases. The differencebetween the isolated three-dimensional rotor and the full downwind turbine is presentedin Figure 3.19 that shows the effect of the presence of the tower as the output powerdrops every 0.41 seconds when the blades pass through the tower wake.


Figure 3.18: Pressure coefficient distribution for 5 sections on the blade 30%, 47%,63%, 80% and 95% at U∞ = 7m/s


Figure 3.19: Output power comparison between isolated rotor and with AL tower

Chapter 4

Conclusions

4.1 Conclusions

The use of the AL technique to simulate the full wind turbine and analyse the capabilityof such model to capture the tower effect on the rotor aerodynamics was the motivationof this work. To do this, numerical simulations of the NREL Phase VI turbine wereperformed for downwind configuration. First, we presented the isolated rotor where aparametric study was performed. Second, the implementation of the actuator line modeland comparison with simulations of flow around a cylinder were presented. Third, itwas performed full turbine simulations, as AL was employed to model the tower and theinteraction between both elements was attempted to be analysed.

The simulations were performed with OpenFoam using the actuator line technique im-plemented in the OpenFoam based toolbox SOWFA. Computations of the rotor weredone at wind speed of 7 m/s at a fixed yaw and pitch angle of 0 and 3 respectivelywith a constant rotational speed of 72 RPM.

Three aspects were studied: the accuracy of the actuator line model to predict loads,the effect that the parameters of the model have on the results and the performance ofthe model to simulate the rotor-tower interaction.

The results from the AL model are strongly dependent of the parameters and the meshresolution. The guidelines found in the literature regarding mesh characteristics are nottotally accurate and grid independence studies have to be performed for each case.

Other works have set ε related to the grid resolution. However, this parameter has aphysical meaning because it stablish the distance over the forces are projected on theflow. This work proposes to choose such factor from the chord length of the tip of theblade. Although for output power the results shown the solution start to converge after aregularization parameter equal to the chord at 63% regarding forces prediction this valueshown slightly discrepancies with experimental results. And as the tip speed is mostlyresponsible for the power of the turbine it is recommendable to use a regularizationparameter related to the chord of the outermost part of the blade at 80% or 95%.

Regarding the use of the actuator line technique to model the tower it was demonstratedits capability to influence the flow and affect the aerodynamic of the rotor. For full ALturbine simulations, good agreement between numerical simulations and experimental

41

Chapter 4. Conclusions 42

data was found, specially in mid sections (63% and 80%). The reason of this is thatthe flow on those sections is mostly two-dimensional while in the inner and outer partof the blade the forces are subject of three dimensional effects that the AL model doesnot capture completely.

Although it was possible to reproduce the fluctuation of the lift and drag forces thevortex shedding in the wake behind the tower was not observed and further work andinvestigation have to be done regarding the study of the unsteady nature of the vortexinteraction between the wake of the tower and blades.

The capability of the AL to model the tower was proved as well with three-dimensionalrotor simulations, as the power drops every time the blades pass behind the tower. Thiswas done with two different techniques to handle the relative movement between the twocomponents. The dynamic mesh was the more suitable technique as consistent resultswere deployed.

Simulations with full turbine actuator line were tested and proven to be a fast optionfor prediction of integral quantities like output power and aerodynamic forces when theturbine does not present dynamic stall hence it is a useful design tool. Moreover, itsapplicability in simulations of wind farms is advantageous since its simplifications allowsto obtain a general overview of the aerodynamic forces, fluid dynamics and wake profilesof several turbines while keeping low computational cost. When the aim is to analyseeffects related to the blade boundary layer like stall delay and tip loss it is better tosimulate the three dimensional model since the nature of the AL model does not allowto get such effects. Furthermore, the use of the AL as tower with three dimensionalrotor is a good compromise to get insight of the rotor aerodynamics while simulatingfull turbines and the effects associated to the tower interference.

4.2 Further Work

The regularization parameter ε has a strong influence on the results; since this parameterregulates the distance over which the forces will be distributed it is proposed to relateit to a blade characteristic length. However, as higher ε results seems to convergeto a value, although ε is larger than the physical geometry of the blade hence theapproach seems to be non-physical realistic. Moreover, it would be better to change thisparameter accordingly to the blade span. The behaviour of this parameter should befurther studied, the possibility of make it variable instead of constant as a function oftime is something that could bring improvements to the actuator line model.

On the other hand, the actuator line model has been proven to give good results whenLES is performed due to the simplicity of the mesh required makes the computationsfaster in computational terms. This work proved that the model is a fast tool to computeglobal variables and its capability as design model. Further work should be done toimprove the results presented in this work doing LES simulations. In this way it issuggested to perform LES to obtain the vortex structures that with RANS simulationswere not observed.

Appendix A. Blade chord and Twist Distribution 44

Appendix A

Blade chord and TwistDistribution

Radial

Distance

(r) [m]

Span

Station

(r/5.532)

[m]

Span

Station

(r/5.029)

[m]

Chord

length

[m]

Twist

[Degrees]

Thickness

(% chord)

[m]

Twist

axis (%

chord)

0.0 0.0 0.0 Hub -center ofrotation

Hub -center ofrotation



0.508 0.092 0.101 0.218(root hubadapter)

0.0 (roothubadapter)

0.218 50 (roothubadapter)

0.660 0.120 0.131 0.218 0.0 0.218 50

0.883 0.160 0.176 0.183 0.0 0.183 50

1.008 0.183 0.200 0.349 6.7 0.163 35.9

1.067 0.193 0.212 0.441 9.9 0.154 33.5

1.133 0.205 0.225 0.544 13.4 0.154 31.9

1.257 0.227 0.250 0.737 20.040 0.154 30

1.343 0.243 0.267 0.728 18.074 20.95% 30

1.510 0.273 0.300 0.711 14.292 20.95% 30

1.648 0.298 0.328 0.697 11.909 20.95% 30

1.952 0.353 0.388 0.666 7.979 20.95% 30

2.257 0.408 0.449 0.636 5.308 20.95% 30

2.343 0.424 0.466 0.627 4.715 20.95% 30

2.562 0.463 0.509 0.605 3.425 20.95% 30

2.867 0.518 0.570 0.574 2.083 20.95% 30

3.185 0.576 0.631 0.543 1.150 20.95% 30

3.476 0.628 0.633 0.543 1.150 20.95% 30

3.781 0.683 0.691 0.543 1.150 20.95% 30

4.023 0.727 0.752 0.543 1.150 20.95% 30

4.086 0.739 0.800 0.543 1.150 20.95% 30

4.391 0.794 0.812 0.543 1.150 20.95% 30

4.696 0.849 0.873 0.543 1.150 20.95% 30

4.780 0.864 0.934 0.543 1.150 20.95% 30

5.000 0.904 0.950 0.543 1.150 20.95% 30

5.305 1.959 0.994 0.543 1.150 20.95% 30

5.532 1.000 1.100 0.543 1.150 20.95% 30

Appendix B

k − ω SST Model: MathematicalExpressions [12].

Kinematic Eddy Viscosity

νT =a1k

max (a1ω, SF2)(B.1)

Turbulence Kinetic Energy

∂k

∂t︸︷︷︸Rate of change of k

+ Uj∂k

∂xj︸︷︷︸convective term

= Pk − βkω︸︷︷︸diffusive term

+∂

∂xj

[(ν + σkνT )

∂k

∂xj

](B.2)

Specific Dissipation Rate

∂ω

∂t+ Uj

∂ω

∂xj= αS2 − βω2 +

∂

∂xj

[(ν + σωνT )

∂ω

∂xj

]+ 2 (1− F1)σω2

1

ω

∂k

∂xi

∂ω

∂xi(B.3)

Closure Coefficients and Auxiliary Relations

F2 = tanh

[[max

(2√k

βωy ,500νy2ω

)]2],

Pk = min(τij

∂Ui∂xj

, 10βkω)

,

F1 = tanh

min

[max

( √k

βωy ,500νy2ω

), 4σω2kCDkωy2

]4

,

45

Appendix B. k − ω SST Model 46

CDkω = max(

2ρσω21ω∂k∂xi

∂ω∂xi, 10−10

),

φ = φ1F1 + φ2 (1− F1),

α1 = 59 , α2 = 0.44,

β1 = 340 , β2 = 0.0828,

β∗ = 9100 ,

σk1 = 0.85, σk2 = 1,

σω1 = 0.5, σω2 = 0.856.

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