1.vawt_airfoil optimization_final_thesis.pdf

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Airfoil Optimizationfor vertical axis wind turbines

Rody KempMarch 13, 2015

D e l f t U n i v e r s i t y

o f T e c h n o l o g y


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A IRFOIL OPTIMIZATION

FOR VERTICAL AXIS WIND TURBINES

by

Rody Kemp

in partial fulfillment of the requirements for the degree of

Master of Science

in Aerospace Engineering

Wind Energy Research Group, Faculty of Aerospace Engineering, Delft University of Technology

at the Delft University of Technology,

to be defended publicly on Wednesday March 26, 2015 at 10:30.

Thesis committee: Dr. ir. C. J. Simao Ferreira (supervisor) TU Delft Wind Energy Ir. W. A. Timmer, TU Delft Wind Energy Ir. L. M. M. Boermans, TU Delft Aerodynamics

An electronic version of this thesis is available at http://repository.tudelft.nl/.

http://repository.tudelft.nl/http://repository.tudelft.nl/


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A CKNOWLEDGMENTS

With this thesis an end has come to my years as a student. Obviously, I could not have done this without thehelp of a lot of people. First of all I would like to thank my supervisor Carlos Simao Ferreira, he inspired me topursue VAWT research during my DSE, supported me during my internship and finally supervised my thesis.Next to this I have had invaluable help with understanding the optimizer and airfoils in general from Gael Andrade de Oliveira. Our (long) talks about airfoils, optimizers (and e-learning) made of lot of this thesis to what it is now.

On a personal level I would first like to thank my girlfriend Judit, she has always been there for me. She evenread this thesis without understanding half of it, if that isn’t love. Next thanks to my family; Martin, Marijkeand Cintha, for being proud on me and supporting me with big decisions. To my graduation buddy Dieter:Thanks for distracting me from my work and making me drink more beer than is good for me.

If I am going to thank everyone that has been important to me my thesis will probably exceed the page limit

so I will not do that. Instead I will thank you all together for making my life here in Delft awesome. It was agreat ride with all of you with lots of very good memories.

Rody Kemp

Delft, March 2015

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SUMMARY

This thesis addresses the process of airfoil optimization for vertical axis wind turbines (VAWT). The airfoilsare designed for large scale turbines above 5 MW. The VAWT concept is relevant for offshore floating windenergy, because of its low center of gravity (stability) and their simplicity (low maintenance). An optimal tipspeed ratio of 4-4.5 is chosen with an average Reynolds number of 5 million. The solidity c /R of the turbine is0.1. These operation conditions are representative for the new generation VAWT. The goal of this thesis is todevelop an optimization process for VAWT airfoils and to demonstrate it by designing an airfoil, while takinginto account airfoil soiling.

A literature review presents the previous researchin VAWT airfoil design, showing that no consensus has beenpreviously reached about VAWT airfoil design. From the literature review an optimization objective derivedby Simão Ferreira [30] is chosen. The airfoil is optimized for aerodynamic and structural performance. The

aerodynamics is assessed on airfoil level according to the objective of lift slope over drag (C l αC d

). Structurally,

the airfoil will be optimized for flapwise bending stiffness I

xx t s . Airfoil soiling is simulated on the airfoil by using turbulent transition.

A genetic optimization tool for airfoils coupled with RFOIL, an airfoil analysis tool, is used to generate VAWTairfoils. The objective function values are calculated using the aerodynamic coefficients from RFOIL andthe geometric properties of the airfoils. The optimization process is validated by analyzing the results withthree different models for full VAWT analysis. These models are: 1) an inviscid panel model coupled withRFOIL, 2) a double wake panel model and 3) a CFD model. Three airfoils resulting from the optimizationare tested using the aerodynamic models. The performance of the airfoils validates the objective functions,but performance for the soiled case is not satisfactory. These preliminary findings were presented at the 33rd Wind Energy Symposium at the AIAA SciTech conference [32], the full paper can be found in appendix B

Five different strategies are developed to optimize airfoils. The results are analyzed using a double wakepanel model. The optimization strategy in which airfoils are optimized for soiled conditions results in the

best performing airfoils. The RK2-27 is a demonstration airfoil resulting from this optimization strategy. TheC P of this airfoil for a tip speed ratio of 4 and a solidity of 0.1 is 0.53 in the clean case and 0.45 in the soiledcase. This was determined by both the inviscid panel model and the double wake panel model.

The RK2-27 has an increased C P compared to the NACA 0018 of 0.04 in the clean case at the design operatingconditions. The C P in the soiled case is only 0.02 lower than the NACA 0018. The maximum thickness of theairfoil increased by 50% from 18% to 27%. The RK2-27 has similar aerodynamic performance compared tothe traditionally used NACA 0018, while structurally it performs significantly better.

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CONTENTS

Acknowledgments iii

Summary v

1 Introduction 1

1.1 Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Vertical Axis Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Research Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Literature Review 5

2.1 Historical overview: 1970-1990 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Wichita State University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Sandia National Laboratories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.3 Queen’s University of Belfast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.4 Tokai University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.5 West Virginia University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.6 National Technical University of Athens . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.7 University of Glasgow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.8 Griffith University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Recent developments: 2005-present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Delft University of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 University of Windsor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.4 Commercial developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Airfoil Design Methodology 19

3.1 Airfoil optimization goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 Aerodynamic Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.2 Structural Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Roughness modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Optimization strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Airfoil Genetic Optimization 25

4.1 Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.1 Parameterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.2 Matlab’s Genetic Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.3 RFOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Implementation of objective functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3.1 Aerodynamic objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3.2 Structural objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Discussion on Inputs and Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Airfoil Performance Analysis 35

5.1 Inviscid Panel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2 Double Wake Panel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 CFD Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.4 Comparison between models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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viii CONTENTS

6 Results of Optimization 41

6.1 Optimization Strategy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.1.1 Inputs optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.1.2 RK1-23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.1.3 RK1-26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.1.4 RK1-32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.1.5 Discussion of strategy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.2 Adapted optimization strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7 Final Remarks 53

7.1 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Bibliography 55

A Coordinates of Results 59

B AIAA paper 65


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NOMENCLATURE

Abbreviations

AoA Angle of attack

HAWT Horizontal Axis Wind Turbine

TSR Tip speed ratio≥ΩR V ∞

¥ VAWT Vertical Axis Wind Turbine

Greek Symbols

α Angle of attack of airfoil

Γb Bound circulation on airfoil

ψ Inflow angle at airfoil

ρ Density (of air)

θ Azimuthal angle of VAWT

θta i l Trailing edge angle

Latin Symbols

B n Bernstein polynomial coefficient

C d Drag coefficient of airfoil

C l Lift coefficient of airfoil

C l α Lift slope of airfoil ≥∂C l ∂α ¥

I xx Moment of inertia around neutral axis of airfoil

N c r i t Amplification factor for XFOIL/RFOIL’s transition model

sc a ero Final aerodynamic objective function value

sc clea n Aerodynamic objective function value in clean case (free transition)

sc r o u g h Aerodynamic objective function value in rough case (forced transition)

T D Torque due to drag force

t s Skin thickness of airfoil

t ai r (x) Airfoil relative thickness

U ∞ Incoming (wind) speed

V p Perceived velocity by the airfoil

w c Weighting factor of clean case.

w s Weighting factor of soiled case.

x t r Chordwise location where forced transition is applied in XFOIL/RFOIL

z t e Trailing edge thickness

B Number of blades of turbine

c Chord of airfoil

N order of Bernstein polynomial

x Normalized x coordinate on x = [0,1]

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1INTRODUCTION

In this thesis, an approach to airfoil optimization for vertical axis wind turbines (VAWT) is outlined. First, ashort introduction into VAWT and VAWT aerodynamics will be given. Also an overview of the research goals

and the ouline of this thesis will be presented.

1.1. W IND ENERGY

The world is facing a great energy challenge. With increasing population and increasing wealth, the demandfor energy is increasing fast. The diminishing supplies of fossil fuels and the threat of global warming call forsustainable solutions. These solutions are found in a new sustainable energy mix consisting of hydro-, solar-and windpower. Wind energy, especially in Europe, South-east Asia and North America, is a fast growingindustry and will play a significant role in the solution of the energy challenge the world is facing.

Space and environmental constraints force the wind energy generation to move offshore. Onshore projectsare still developed, but are often confronted with resistance from people living nearby complaining about the

noise and shadow nuisance. In highly populated areas simply no space is available to place enough turbinesto facilitate energy for everyone. Offshore, the wind farms can be made bigger and are not hindered by noiseand shadow constraints. The drawbacks of offshore wind are higher installation costs and higher mainte-nance cost because the sites are harder to reach. Next to this, the foundation of turbines can be a problem.In shallow waters the turbines can be fixed to the ground, but for deep waters this becomes too costly. Inoffshore environments, VAWT have some beneficial characteristics which make them an interesting researchsubject.

1.2. V ERTICAL A XI S W IN D TURBINES

In the field of wind energy, the most well-known and widely used turbines are the horizontal axis wind tur-bines (HAWT) . This turbine is being used onshore as well as offshore and is available in all sorts of sizes

ranging from 1 kW up to 10 MW, with plans of even larger scales. VAWT are not well-known and not widely used yet, only small turbines in the order of 10 kW are commercially available and bigger turbines are still indevelopment. But, this has not always been the case and might not be the case anymore for very long.

HISTORY

VAWT have been present for a long time. As long as 1500 years ago a primitive version was used by thePersians, called a Panemone. These windmills were used to grind crops or pump water. The Panemoneused sails or wooden surfaces to turn around a vertical axis. The windward turning part of the windmill wasshielded by a wall to avoid it from producing drag. An example of a Panemone can be found in figure 1.1a.

The first modern VAWT for electricity generation were made during the 1970s and 80s. During this time, windenergy was in its starting days and different concepts were competing to become the preferred choice. Up

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2 1. INTRODUCTION

(a) Panemone using wood as ’sails’ [1]. (b) Schematic of Savonius rotor [2]. (c) Schematic of Darrieus rotor [3].

Figure 1.1: Different types of VAWT

until now the most successful VAWT in history was produced by a spin-off of the Sandia National ResearchLaboratories in theUS. They had a fleet of about 500 vertical axis turbines in service. These ’FloWind’ turbines were troposkien (φ) shaped turbines with a rated power of about 150-250 kW. More on this turbine can befound in section 2.1.2 and a picture of this turbine is printed on the cover of this thesis.

Around the start of the 90s, research was mainly focused on the development of the HAWT. This led to theshutdown of most VAWT research programs while HAWT programs were boosted. This is why VAWT nowa-days still lack behind their horizontal counterparts on which a few decades more of research has been de-voted. In theory, both concepts should be able to perform similarly.

VAWT CONCEPTS & WORKING PRINCIPLES

There are a variety of VAWT concepts, a first distinction can be made between drag driven and lift driventurbines. Drag driven turbines use the aerodynamic drag force to generate energy. The most famous exampleof this principle is given by a simplecup wind meter (anemometer) which uses thedifferent in drag coefficientof a convex and concave sphere to turn. A schematic of a drag driven Savonius turbine is shown in figure 1.1b,in this case the convex and concave drag characteristics are also used. Since these machines can attain only very low efficiency they are mainly used for high torque applications. They will not be considered in thisthesis.

The focus of this thesis will be on lift driven VAWT, which will be referred to as just VAWT for simplicity.Theoretical analysis shows that these turbines canattain thesame efficiency as HAWT. These VAWT are drivenby the aerodynamic lift force acting on the blades. These blades have airfoil shapes and a schematic of such arotor can be seen in figure 1.1c. There are a lot of shape variations possible when it comes to these VAWT. Themost simple one is the H-shaped (figure 1.1c), this concept can also be twisted into a helical shape. Another

promising one is the φ shaped turbine, the ’FloWind’ turbine from the 80s had such a shape. A less widely used concept is the V-shaped VAWT. In this thesis a 2D approach is taken, which implies that it can still beused in all turbines.

Since the airfoils of a VAWT are constantly changing their orientation with respect to the incoming wind, they experience changing wind speeds and angles of attack. This makes the operating regime of VAWT unsteady and the variation in angle of attack means that an airfoil should perform well at a big range of angles insteadof a small range like with HAWT. A VAWT is driven by torque that is generated by the blades, this torque isproduced by the lift force on the airfoil, a schematic of velocities and forces is shown in figure 1.2. Airfoilsproduce different lift at different angles of attack. Dynamic effects like dynamic stall make the aerodynam-ics even more complex. On top of this, a VAWT blade passes through its own wake, created on the upwindpart of the rotation, during the downwind part of the rotation. This blade-wake interaction makes the powerextraction downwind very different than upwind. The goal of this thesis is to design an airfoil which is aero-dynamically efficient and is structurally strong enough to handle the forces on the blade.


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1.3. RESEARCH GOAL 3

Figure 1.2: The working principles of a lift driven VAWT [4].

RELEVANCE OF VAWT RESEARCH

After this introduction to VAWT, the question could rise: Why investigate VAWT when HAWT are already farmore advanced and working fine? Before this question is answered the assumption is made that wind energy will have to grow fast in the coming decades to be able to provide enough ’green’ energy to substitute fossilfuels. In this growth process, VAWT could have some advantages over HAWT.

• An area where VAWT are already applied is small scale power generation. Since VAWT can capture windfrom all directions, urban areas are also suitable for VAWT. Commercial products are already availablein this range [5].

• The most promising area for VAWT application however, is offshore wind energy. Currently wind tur-bines are placed on the seabed on big submerged structures, which are only worthwhile in relatively

shallow waters. Floating turbines are a huge opportunity to not only make installment easier, but alsoto expand the area where turbines can be placed. When looking at floating turbines, VAWT have ad-vantages over HAWT like a lower center of gravity and load application point, which would make thefloater much more stable.

• Another advantage of a VAWT is the fact that upscaling of the technology is easier. Right now the bladesof HAWT are getting to their limits in terms of length and twist. VAWT blades can be supported by morethan one strut and are thus less limited in size. It has to be noted here that a VAWT is usually moreexpensive in material when you compare it to a same rotor area HAWT. This is because VAWT rotors arethree dimensional and hence mass scales with radius to the third power, while for HAWT it is a 2D rotorand thus it scales with the radius to the second power.

• VAWT show a good performance in skewed flow. This is because their actual frontal area increases. This

is a positive feature when installing turbines on rooftops but more importantly when installing VAWTon floating platforms subject to waves.

These considerations make the VAWT a viablecandidate to expand the possibilities in wind energy and hencea contribution to solve the challenge of diminishing fossil fuel supplies.

1.3. RESEARCH GOA L

The overall goal of this thesis is to lower the cost of energy produced by a VAWT by focusing on the aerody-namic efficiency of the airfoils and the structural possibilities of the airfoils. The specific goal of this researchis twofold.

1. To design an airfoil shape or family of shapes that is suitable for VAWT. This will give a general idea on what VAWT airfoils should look like and what characteristics are advised.


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4 1. INTRODUCTION

2. To validate the objective functions and optimization algorithm as an efficient optimization method todesign airfoils in future projects. For instance for different Reynolds numbers or different operatingconditions of the turbine.

The turbine considered in this research will be a large scale VAWT. As a result, theReynoldsnumber is taken tobe 5 million. The aerodynamics of a VAWT are such that the Reynolds number is notconstant, but 5 million istaken as a representative mean value. Higher Reynolds numbers lead to higher stall angles which is beneficial

for VAWT due to their wide angle of attack operation range. The solidity that is used as a reference is 0.1, fora two bladed turbine the solidity is computed using the chord to radius ratio c /R . The solidity should besimilar between turbines to compare performance. The tip speed ratio of the turbine is taken to be 4-4.5.This is where theoretically the highest efficiency can be reached. Figure 1.3 shows this.

Figure 1.3: The maximum efficiency of a VAWT is reached at a tip speed ratio of 4-4.5 [6].

1.4. O VERVI EW OF THESIS

In this thesis first a literature review of previous VAWT airfoil research will be given in chapter 2. Then thetheoretical foundation for the optimization will be discussed in chapter 3. The optimization tool with all itsinputs will be presented in chapter 4. The models with which the results of the optimization are be validatedcan be found in chapter 5, together with a comparison between all the models. Finally the results will beanalyzed in chapter 6. The thesis will end with a conclusion of the research in chapter 7. This chapter willshow the main findings of the research and give recommendations on how to use the optimization. Alsorecommendations for further research will be given in this chapter.


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2LITERATURE REVIEW

Wind energy is moving offshore. Floating wind turbines is the newest development in the field and this hassparked new interestin vertical axis wind turbines (VAWT) because of their beneficial characteristics for float-

ing structures.

The VAWT concept should theoretically be able to reach similar aerodynamic performance as the horizontalaxis wind turbine (HAWT). Compared to HAWT, an apparent advantage of VAWT is that it is less complex andshould therefore be less costly in maintenance, which is a big part of the cost for offshore wind. Next to thisthe VAWT concept seems more compatible to floating platforms because of its lower center of gravity, which will increase stability and decrease the required size of the floater.

Much research has been done on VAWT in the 1970’s and 1980’s, after this the HAWT became the dominantconcept and research efforts for VAWT faded. Recently the interest has returned. In this chapter, an attemptis made to summarize all previous research regarding airfoils for VAWT. For VAWT the airfoil can have a hugeimpact in the cost of energy (COE) of the turbine. Both aerodynamic efficiency and structural integrity of thebladesrely on thechoice of airfoil. The unsteady operation of the VAWT, with a constant variation in apparent

speed and angle of attack seen by the airfoil, complicate the design of the airfoil.This chapter will present the research done in airfoil design for VAWT. This chapter will provide an overview of clear rationales behind airfoil design and might help to provide new insights into existing challenges. Thechapter will show the main objectives of the research, the method of design and analysis and the final resultsand potential implementation.

Figure 2.1: The amount of papers published on VAWT research (based on data retrieved from [7]).

The review is divided in two parts. Figure 2.1 shows that there are two distinct time frames where most re-search took place on VAWT. These two time frames are separated in this work. Table 2.1 shows the VAWTairfoil research done in chronological order.

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6 2. L ITERATURE REVIEW

Table 2.1: List of research done on VAWT airfoils.

Year Author Airfoil Main objectives or subject

1977 T. Fukuda WSU 0015 Not found, experimental work on airfoil used [8].1978 E.G. Kadlec [9] NACA 00xx First Sandia report on airfoils for VAWT.1978 J.V. Healy [10, 11] NACA 00xx, Gö

profiles

The influence of thickness and camber on VAWT per-

formance.1980 Y. Kato, K. Seki, Y.

Shimizu [12]TWT 11215-1 Airfoil design objectives: 1) High ∂

C l ∂α , 2) Low C d , 3)

C d should be symmetric about αC l =0, 4) Large negativepitching moment.

1981 R.E. Sheldahl, P.C.Klimas [13]

NACA 00xx Full 360◦ wind tunnel tests of NACA 00xx

1983 P.G. Migliore, J.R.Fritschen [14]

NACA 00xx,NACA 6-series, WSU 0015

Review of existing airfoils withdesirablecharacteristics:

low C d and high ∂C l ∂α .

1984 P.C. Klimas [15] SAND 0015/47,SAND 0018/50,SAND 0021/50

Favourable characteristics: 1) modest values of maxi-mum lift coefficient with sharp stall, 2) low C D 0 , 3)widedrag buckets.

1988 A. Zervos [16] ARC 0015, NACA 00xx, NACA 6-series, GAW(1),NLF0416

Review of existing airfoils stressing flow curvature ef-fects.

1990 D.E. Berg [17] SAND 0015/47,SAND 0018/50,SAND 0021/50

Discussion of SAND airfoils and robustness to rough-ness.

1992 T.D. Ashwill [18] NACA 0021,SAND 0018/50

The 34 meter testbed turbine of Sandia.

1992 R.A.M. Galbraith,F.N. Coton, J.Dachun [19]

GUVA 10 Airfoil designed for stall regulation.

1998 B.K. Kirke [20] Selfstarting VAWT.

2005 J.C. Vassberg, A.K.Gopinath, A. Jame-son [21]

NACA 0015, WARP0015-RC8

Warped airfoil design on basis of CFD.

2006 M.C. Claessens [22] DU06W200 Airfoil design criteria: 1)Low Reynolds (105),2)Low C d ,3) wide drag bucket, 4) Increased thickness for struc-tural strength, 5) smooth stall for noise reduction, 6)small hysteresis loop, 7) postpone deep stall and smalldrop in C l .

2007 R. Bourguet, G.Martinat, G. Harran,M.Braza [23]

unnamed Optimization using commercially available tools.

2007 M. Islam, D. Ting, A.

Fartaj [24]

NACA 0015,

GOE 420, NACA 4415, NASA LS-0417, NASA NLF-0416,S1210, MI- VAWT1

Review of existing airfoils and design of new airfoil.

2010 T.J. Carrigan [25] unnamed Genetic optimization using NACA 4-series.2011 M.R. Castelli, E.

Benini [26]NACA 0012,NACA 0021

A comparison using CFD between two airfoils to inves-tigate the effect of relative thickness.

2012 H.J. Sutherland [27] SNLA series,S824

A review of Sandia’s VAWT research.


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2.1. H ISTORICAL OVERVIEW : 1970-1990 7

2012 L.A. Danao, N. Qin,R. Howell [28]

NACA 0012,NACA 0021,NACA 5522,LS0421

Theeffect of thicknessand camber is investigated usingthe NACA 4 series.

2012 T.J. Carrigan, B.H.Dennis, Z.X. Han,B.P. Wang [29]

NACA 0015,NACAopt

Based on his previous work ([25]).

2014 C.J. Simao Ferreira,B. Geurts [30]

DU12W262 Genetic optimization [31] airfoil design with objectivelift slope over drag.

2015 C.J. Simao Ferreiraet al. [32]

unnamed Follow up on previous research.

2.1. HISTORICAL OVERVIEW : 1970-1990

In the 1970s and 80s wind energy was emerging as a consequence of the energy crisis. The concepts for

VAWT and HAWT were competing to become the industry standard and a lot of research was done into bothconcepts. This period is when the first big research efforts were done into (lift driven) VAWT technology.In this section, these efforts will be reviewed. They are categorized by institution and will be presented inchronological order.

2.1.1. W ICHITA STATE UNIVERSITY

In 1977 a master thesis project on Wichita State University focused on a new airfoil design for Darrieus windturbines. The thesis itself is not publicly available but experimental validation of this work was done in the WSU wind tunnel using a one meter diameter, three bladed turbine with troposkien shaped blades [8]. Themain objective for the design of the airfoil of the blade found by Fukuda [33] was increasing the stall angle of the airfoil. It was found that this is mainly done by increasing the thickness of the airfoil. This also makes thepeak in performance shift towards lower TSR.

Theairfoil that wasdesigned in the thesiswas the WSU0015 and theWSU 0021, which are symmetricprofiles.The WSU 0021 is shown in figure 2.2. The experimental comparison with the NACA 0012 gave the followingresults, the NACA 0012 had a C P ,ma x of about 0.2 at a TSR of 5 and the WSU 0021 achieved a C P ,ma x of about0.25 at a TSR of 4.

Figure 2.2: The WSU 0021 airfoil [8]

2.1.2. S AN DI A N ATI ON AL L AB OR ATORI ES

The main research institute during the 70’s and 80’s was Sandia National Laboratories (SNL) based in New Mexico, USA. The research on VAWT was commissioned by the US Department of Energy and a lot of re-sources were available to carry out research. At SNL, the popularity of symmetric NACA 4-digit airfoils orig-inates. The early research focused on the NACA 0012 and NACA 0015 [9, 13]. These airfoils were originally designed for aviation purposes and were not specifically designed for VAWT. A symmetric airfoil was cho-sen because of the operational nature of the VAWT, the suction and pressure side of the airfoil change sidesduring the revolution. It was deemed important that the behavior of the airfoil sections remained the same,so symmetric sections were chosen. The NACA 00xx series was chosen mainly due to the amount of dataavailable on these airfoils. A complete dataset for the NACA 00xx series was published [13] after an extensive


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measurement campaign in which the airfoils were tested over the full range of angles of attack from -180◦ to180◦.

When SNL started to work on larger prototypes of 17 meter (and later 34 meter) the need for more structuralstiff airfoils arose. For this reason the researchers switchedto the NACA 0018, which has a higher thickness. Atthe same time new airfoil shapes were investigated by Klimas [15]. Klimas stated the desirable characteristicsof a good VAWT airfoil:

• Modest values of maximum lift coefficient and sharp stall.

• Low C D ,0

• Wide drag buckets

The first point is desirable for power regulation of the turbine at high windspeeds, the modest value of C l reduces peak loads in these conditions and the sharp stall will aid in slowing down the turbine. The secondpoint and the related third point originate from the unsteady operation of the VAWT where the angle of attack varies. Low and wide drag buckets ensure efficient operation over large ranges of angle of attack.

Airfoils possessing the characteristics mentioned above are NLF airfoils. In light of these findings SNL de-signed three NLF airfoils in cooperation with Gregorek of Ohio State University [17]. Use was made of theairfoil design code PROFILE by Eppler [34]. The airfoils were based on the NACA 00xx series and are called

the SNLA (or SAND) 0015/47, 0018/50 and 0021/50. The first four digits indicate the symmetry and thicknessand the last two digits the location in percentage of chord two where the flow is laminar. Advantages of theSNLA family over the NACA 00xx family include reduced roughness sensitivity and thus higher performance with dirty blades.

SNL’s final 500 kW ’Test Bed’ turbine was a troposkien shaped VAWT with a maximum diameter of 34 meters.This turbine utilized a NACA 0021 near the towers for structural strength and the SNLA 0018/50 near theequatorial region for aerodynamic performance [27].

The ’Test Bed’ turbine was commercialized by FloWind Corporation, using a SNLA 0021/50 instead of a SNLA 0018/50 profile. During the peak of FloWind, 500 turbines were in service. A new operating rpm led to a needof a slightly modified profile. This profile was designed by Dan Somers [35] and was called the S824 [36]. Thisprofile was used in the ’B blade’ and ’C blade’ of the FloWind turbines [37].

2.1.3. QUEEN’S UNIVERSITY OF BELFAST

At Queen’s University of Belfast, Healy [10, 11] conductedan investigation on the effectof airfoilthickness andcamber on the power output. The investigation was done for relatively small turbines with solidities from 0.1to 0.2 and Reynolds numbers of about 4 ·105. The main objective of this research was to investigate the effectof airfoilthickness andcamber for thepurpose of curvedbladeVAWT. In this research, no airfoilwas designed,but several airfoils were tested using a single actuator multiple streamtube model. Healy acknowledges thefact that this model does not have a correct treatment of the downwind halve of the turbine but states thatsatisfactory double multiple streamtube models have not been devised successfully.

The airfoils that were used for the investigation into airfoil thickness effects were the NACA 0009, 0012, 0015and 0018 [11]. Airfoil coefficient data was taken from the NACA TR-586 report [38]. The main result of this work is that airfoil thickness does not play a large role in the maximum power output at high Reynolds num-

bers in the order of 2 million. For lower Reynolds, thicker profiles are preferred.

The second investigation into camber took into account Göttingen series airfoils, for the reason that for theseairfoils data was available to do the calculations. This data was taken from [39]. Profiles were chosen tohave different cambers and were compared to two symmetric profiles, the NACA 0018 and the Gö 460. Thecambered profiles were Gö 676, 738, 735, 746, 741, 744 and 420. Of these airfoils, only the Gö 735 and 738are considered interesting because higher power coefficients were achieved and the C p −T SR curves weresmooth, making it easier for the turbine to operate in optimum conditions. It was found that both symmetricprofiles had the best performance in terms of smoothness of power curve and height of C P ,ma x . It was con-cluded that the closer the airfoil is to symmetric, the more satisfactory the power output. All airfoils were alsotested at different pitch angles. It wasfound that most profiles have a big sensitivity to this preset pitch angle.


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2.1.4. TOKAI UNIVERSITY

In light of the1970s energy crisis, countries where natural resourceswere limited invested in research on windenergy. In 1980 Tokai University in Japan carried out research on airfoils for VAWT. The analysis and experi-mental work was performed on a small 2×2.5 meter (H×D) turbine. A set of conditions for high aerodynamicefficiency was derived [12]:

• Large lift gradient

dC L

d α

• C D must be small and symmetric aboutαC L =0

• Large pitching moment coefficient

These objectives were derived using a simple streamtube model of the turbine. The dependency of C P on theairfoil coefficients was analyzed. C L , C D and C M were considered. Having a large pitching moment coeffi-cient is stressed in the paper as the most important design driver. An airfoil was designed with a S-shapedcamberline to introduce a strong negative pitching moment coefficient on the airfoil. The front part has anegative camber while the aft part of the airfoil has a positive camber. This airfoil, the T.W.T.11215-1, waseventually patented [40], but no records of commercial use were found.

Figure 2.3: Experimental results from Kato [12] showing the power coefficient (C P ) vs. tip speed ratio (β). An increase in C P ,ma x wasfound for the airfoil with the pitching moment.

Experiments on the performance of the new airfoil were performed on the small experimental turbine. Theresulting C P -TSR curve is shown in figure 2.3. It is shown that the C P ,ma x is increased when the airfoil hasa pitching moment. In the figure a positive C M is given, while the T.W.T.11215-1 has a negative pitchingmoment. This is probably a notation error.

2.1.5. W ES T V IRGINIA UNIVERSITY

Traditionally the NACA 00xx series were used for VAWT, these airfoils were designed for aeronautical appli-cations. In the early 80’s, an investigation was done at West Virginia University into other existing airfoils tosee if better performing airfoils were already available [14]. The performance was calculated using a bladeelement momentum model by Strickland [41]. A selection of airfoils was made to limit computational efforts.

The selection was based on the identified desirable airfoil characteristics, which were low drag and high lift

slope≥

dC L d α

¥. Based on these requirements 10 airfoils were selected to be evaluated. The NACA 00xx, the NACA

63b 0xx, the NACA 64b 0xx and the WSU 0015 were chosen. The NACA series were all evaluated for the relativethicknesses of 12%, 15% and 18%.

The calculations showed that the NACA 63 and 64 series had higher maximum C p over a higher TSR range.For these series the aerodynamic performance increased with increasing thickness, which is favorable forthe structural stiffness of the blade. The NACA 632015 and 633018 performed the best of all airfoils, with theNACA 632015 reaching an annual energy output of about 20% more in comparison with the NACA 0015.

Migliore is also known for his work on flow curvature effects [42]. Using the methods outlined in [43] he trans-


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Figure 2.4: Transformed shape of the NACA 632015 to correct for flow curvature effects [14].

formed the NACA 632015 to its appropriate shape. This was done for a c /R of 0.07. The original and resultingprofile can be seen in figure 2.4. It is interesting to note that this study concluded by favoring an airfoil that was designed for maximizing laminar flow. This is in line with the findings and approach of Sandia.

2.1.6. N ATION AL TECHNICAL UNIVERSITY OF A THENS

Duringthe late 80’s research on VAWT airfoil wasperformedat NTUA. The main focus of theairfoil design wasthe influence of the rotational motion that the blade makes during its revolution and how this can be usedto balance the unsteady loading on a VAWT to increase the fatigue life. Cambered airfoils could help exploitthe rotational effect for this purpose. Other researchers have also suggested this influence and proposedcorrection methods for VAWT analysis [14, 42–44]. Zervos [16] suggested to use this rotational influence as abasis for airfoil design for VAWT.

First a numerical evaluation was made on six airfoils to find the effect of thickness and camber on the un-steady loads in the VAWT. These six airfoils were: NACA 0012, NACA 0015, NACA 0018, NACA 63015, GAW(1)and the NLF 0416. The effect of thickness on the unsteady loading was found to be insignificant. Camber didhave an effect on the behavior of the VAWT, Zervos explained this through the flow curvature effect, which

makes the same airfoil in a curved flow behave differently than in a rectilinear flow. A transformation to theairfoil is made to correct for this effect by introducing a virtual angle of incidence and a virtual camber to theairfoil, as can be seen in figure 2.5.

Figure 2.5: The virtual effect of flow curvature on the airfoil according to [16, 42]

Changing the (virtual) camber and incidence of a VAWT airfoil can shift loading from upwind to downwindrotations. Zervos devised an airfoil that countered the flow curvature effect by cambering it in the opposite way (concave inwards). The camberline of the airfoil was shaped according to the arc of the circle it was flyingon, the thickness distribution was that of a NACA 0015. This airfoil was called the ARC 0015 and since the flow curvature effect changes with c /R , the airfoil is tailored to a specific c /R .


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2.1.7. UNIVERSITY OF GLASGOW

The wind energy community in Britain believed that large scale VAWT could be economically more favor-able then the HAWT. Glasgow University worked on creating VAWT design codes which focused on the mainaerodynamic features of the VAWT. The code was capable of assessing the effect of blade pitch, twist, taper,but also of airfoil section on the performance of the turbine. The assessment for the airfoils was done for astraight bladed H-type turbine.

The main goal of the airfoil design was to increase the fatigue life of the turbine through passive stall regula-tion while retaining the behavior of the NACA 0018 during normal operation [19]. Stall regulation was to beaccomplished by having a sharper drop in C L at stall.

For the design of the new airfoil possessing these characteristics a design package was made. This packagecontained two main components; an airfoil geometry generation module and a VAWT performance module.Using this package and the GUVA 3 airfoil as a basis, a serie of six airfoils was created, the GUVA 4 to 9. Of these six, the GUVA 4 and GUVA 9 had the most desirable static performance. During the assessment of theairfoils, it became clear that the airfoils were both susceptible to dynamic stall and ’were likely to producesome degree of stall regulation on a VAWT’ [19].

The GUVA 10 airfoil resulted from the design process. This airfoil was a combination of the NACA 0018 rearpart and the specially designed nose part of the GUVA 9. The rear part of NACA 0018 was used to achieve

more similar performance between the GUVA 10 and the NACA 0018. The final airfoil is presented in figure2.6.

Figure 2.6: GUVA 10 airfoil (sharper nose) compared to the NACA 0018 airfoil [19].

The design process was validated with experiments on the GUVA 10 airfoil. Both static and dynamic testsconfirmed the static and dynamic stall behavior predicted in the design process. The GUVA 10 stalls approx-imately two degrees earlier than the NACA 0018. Combined with the sharper stall, this should provide stall

regulation on a VAWT.

2.1.8. GRIFFITH UNIVERSITY

A much debated subject in the wind energy community is the ability of a VAWT to self start. An interestingapproachto this discussion wastakenby Kirke in hisPhD thesis[20]. Heinvestigated how a VAWT blade couldbe designed to self start. Although he primarily focused on variable pitch mechanisms, some interestingnotesare made on airfoil design. A first interesting note is that for VAWT operating at high Reynolds numbers, theself starting problem seems to be non existent. For small VAWT with verylow Reynoldsnumbers a ’dead band’exists where negative torque is produced. The effect of Reynolds number can be seen in figure 2.7.

Figure 2.7: C P -TSR curve for different Reynolds numbers [20].


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On airfoil shapes the following conclusions are drawn. First of all, thicker airfoils will decrease the size of the ’dead band’. The second conclusion is that cambered airfoils are favorable for self starting small windturbines. This is because performance of symmetric sections drops below Reynolds numbers of 2.5 ·105, theperformance of cambered airfoils remains good. Another reason is that cambered airfoils will be able to ex-tract more energy on the upwind pass because of higher lift coefficients there, since the incoming windspeedhere is higher, this would outweigh the loss in performance on the downwind pass.

The third and most exotic option opted are shape transforming blades. Three types are considered, fabricsails, sheetmetal blades and flexible airfoils. The idea is that the camber reverses when the sign of the an-gle of attack changes. Fabric sails and flexible sheetmetal plates will have a natural tendency to do this, buttheir basic aerodynamic performance lacks. At the time, flexible airfoils were deemed very interesting, withself starting capabilities and 40% increase in peak performance, but too hard to manufacture. With recentdevelopments and advances in structural and material engineering, this option might be interesting to rein-vestigate.

2.2. RECENT DEVELOPMENTS: 2005-PRESENT

As can be seen in figure 2.1, around 2006 VAWT research started to grow rapidly. New application of windenergy, in particular in floating offshore form, made VAWT an interesting concept again. Its advantages of

lower maintenance, low center of gravity and good performance in skewed flow are perfect for offshore float-ing conditions. The growth in computational power also changes the way in which designs are made, whichalso marks a big difference between the two periods of VAWT research.

2.2.1. DELFT UNIVERSITY OF TECHNOLOGY

At TU Delft a lot of research is being done on VAWT at the moment. This section presents the publishedresults on airfoil design for VAWT until now.

CLAESSENS

The wind energy group at TU Delft has substantial resources dedicated to VAWT research. In 2006 a masterthesis was done on the optimization of an airfoil for a small scale VAWT [22]. The airfoil was designed forthe Turby VAWT, which is a small 2.65×2 meter (H×D) VAWT for urban environments [45]. The goal for theoptimization was to design an airfoil with low drag and wide drag bucket. Contrary to the the early researchof Sandia and Glasgow University, the goal of smooth stall was set with the purpose of reducing noise. Also astiffness increase with respect to the NACA 0018 was desired.

Claessens conducted a simulation campaign in which several existing airfoils were tested in a double multi-ple streamtube (DMST) model to assess their performance. NACA 4 series, NACA 6 series, NLF airfoils andprofiles from the early VAWT period like the SNLA 0018 and the S824 were evaluated. Next to this the effectof camber and thickness was evaluated using the NACA 4 series. It was concluded that NLF airfoils would bethe best basis for the design because of the low drag coefficients combined with relatively wide drag buckets.

With the NLF profiles as basis, first the thickness and camber are set. This is done by varying them andanalyzing them with the DMST model. Optimum thickness and camber are found to be 20% and 0.8% re-

spectively. The pressure distribution and geometric features of the NLF profile are modified to improve thedrag characteristics of the airfoil. This resulted in the final DU06W200 profile which is shown in figure 2.8.

Figure 2.8: The final design of the DU06W200 compared with the NACA0018 [22]

Wind tunnel tests show that the DU06W200 behaves approximately the same as the NACA 0018 at negativeangles of attack. However at positive angles of attack theC

L ,ma x is increased. The overall drag bucket is wider


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2.2. RECENT DEVELOPMENTS: 2005-PRESENT 13

for the DU airfoil. This results in a C p curve shown in figure 2.9. An increase in C p ,ma x is observed as well asa slight shift towards the lower tip speed ratios.

Figure 2.9: The power coefficient (C p ) against the tip speed ratio, as calculated by the DMST code using experimental data as input [22].

SIMÃO FERREIRA ET AL.

Ferreira developed a generalized objective function for VAWT airfoil optimization. The principles used comefrom his previous work on VAWT wakes [46]. One important general remark in his paper is that with theincrease in computational power, more and more optimization algorithms are directly coupled with CFDsimulations. This approach lacks a clear rationale of what features an airfoil should have and is an inefficientprocess. A good objective function which links the rotor performance to the airfoil performance could po-tentially speed up the process by orders of magnitude and increase the understanding of the aerodynamicsof VAWT [30].

The basic element of wake generation of the VAWT was taken as the starting point of the objective function.Due to the azimuthal variation in bound circulation on the blade, vorticity is being shed constantly. Energy extraction is directly dependent on the shedding of vorticity, so optimizing the shedding of vorticity will op-

timize energy extraction. This means optimizing ∂Γb ∂θ which is proportional to ∂C l c ∂θ . Translating this to airfoil

properties, the lift slope should be maximized to arrive at the maximum power.

This rationale was used by Ferreira to construct an objective function for an optimization. The optimiza-tion was performed using a genetic optimizer for airfoils developed by Oliveira [31]. In this optimization theroughness sensitivity was incorporated by doing a clean and dirty simulation for each airfoil and averagingthe performance. Also a structural objective was added to increase the flapwise bending stiffness. This re-sulted in the AIR family of airfoils, which are relatively thick airfoils. Two examples can be found in figure2.10.

These high thickness airfoils are beneficial for structural purposes. The reason these airfoils come out of theoptimization is that increasing thickness, up to a limit of about 35%, has no detrimental effecton thelift slope.

As a continuation of this research, one airfoil was tested in the low-turbulence wind tunnel of the TU Delft.This airfoil was named DU12W262 [47] and can be found in figure 2.11.

Measurements were mostly taken with a PIV method which captures the flow field around the airfoil. They were performed at Reynolds numbers around 1 million. The results concluded that the DU12W262 outper-formed the NACA 4 series which were in the initial population of the genetic algorithm.

2.2.2. UNIVERSITY OF W INDSOR

At the university of Windsor in Canada, Islam conducted an investigation into desirable airfoil features for VAWT [48] and deriving from this a special purpose VAWT airfoil [24]. The airfoil was designated for smallcapacity VAWT which are characterized by airfoils operating at low Reynolds numbers in the order of 1 ·105.The main objective was to find the best performing airfoilout of a small group of six existing airfoils which aresuggested by literature. These airfoils are: NACA 0015, NACA 4415, GOE 420, NASA LS-0417, NASA NLF-0416and the S1210.

The performance was calculated using a Cascade model, with correction modules for dynamic stall and flow


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Figure 2.10: Two examples of the AIR family of airfoils [30].

Figure 2.11: A representation of the DU12W262 airfoil [47].

curvature. From this analysis, the NACA LS-0417 (or GA(W)-1, see figure 2.12) was found to be the best per-forming airfoil. This was the starting point of the airfoil design. Four aspects are taken into account in asensitivity analysis. The influence of camber, thickness, leading edge radius and trailing edge thickness aretaken into account and varied using XFOIL.

The resulting airfoil is the MI-VAWT1, see figure 2.13. The exact geometry is not known, but when comparing

it to its ’parent’ airfoil, the LS-0417, big differences are present. The MI-VAWT looks symmetric and alsoshows a lot of resemblance to a NACA 0018 with a thinner tail.

Figure 2.12: A representation of the NASA LS-0417 airfoil [48].


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2.2. RECENT DEVELOPMENTS: 2005-PRESENT 15

Figure 2.13: A representation of the MI-VAWT1 airfoil [48].

2.2.3. NUMERICAL METHODS

The field of optimization has been influenced by the enormous increase in available computational power.Heavy calculations involving panel methods or CFD calculations are becoming less expensive. This sectiongives an overview of VAWT airfoil optimization campaigns conducted in this manner.

Carrigan designed a ’proof of concept’ optimization for VAWT airfoil during his master thesis in 2012 [25, 29]. Airfoil geometries were created by differential evolution from the NACA 4-series. This constrains the opti-mization to only this family of airfoils. A mesh generation module meshed the airfoil before analyzing it in a

CFD simulation in FLUENT. As a baseline geometry the NACA 0015 was used. Two optimization cases weredone. The first case was at a TSR of 1 and a rotor solidity of 1.5, which are both unusual values for VAWT. A NACA profile with a maximum camber of 0.94% at 60% of the chord and a maximum thickness of 17.7% wasfound (close to the NACA 1618 geometry). This airfoil showed a 2.4% increase in C p when compared to theNACA 0015. The second case was run at a TSR of 3 and a solidity of 0.4, which is more toward normal VAWToperating conditions. A 10.9% thick, symmetric airfoil resulted (close to the NACA 0011 geometry). This air-foil performs 1.1% better than the baseline of the NACA 0015. According to Carrigan, the symmetric airfoilshape is due to the low solidity. With low solidity rotors, no blade-vortex interactions take place and positiveand negative angles of attack are of same magnitude.

In work of Vassberg et al. [21] CFD simulations are used to compute the performance of a modified versionof the NACA 0015, the WARP0015-RC8. This airfoil is designed using the same approach as Zervos [16], the

camber line warped along the circular path of the blade. This was done for a c /R of 0.125. Using the CFDanalysis, an increase in C p of 4% was observed.

Bourguet et al. [23] coupled the commercially available optimizer ’Optimus’ with the CFD tool ’StarCD’. Theoptimization was performed using three criteria: High nominal power production, high efficiency range andblade weight. The optimization only took into account symmetric profiles. The resulting profile was very close to the NACA 0025 and had a 28% increase in nominal power production and 46% increase in efficiency range, compared to the NACA 0015 baseline design. It is not clear from the paper how this efficiency range was measured.

Castelli [26] investigated the effect of relative thickness of the airfoil on the VAWT performance. Simulations were done using the commercially available CFD software ANSYS FLUENT. NACA 0012 and NACA 0021 were

analyzed. It was found that the NACA 0021 had a 4.5% higher maximum C p at a lower TSR compared to theNACA 0012. This wasattributed to the fact that thicker airfoils stall at a higher angle of attackthan its thinnnercounterpart.

Danao et al. [28] set up a CFD campaign to find the effect of airfoil thickness and camber on VAWT perfor-mance. Four airfoils were selected to do this investigation: the NACA 0012, NACA 0022, NACA 5522 and theLS0421. It was found that the NACA 0012 performed better than the NACA 0022 for higher TSR.

Looking at all these campaigns it can be concluded that exploring full design spaces is still too computation-ally intensive. The demanding CFD simulations are mostly used to analyze effects of changing certain airfoilcharacteristics or to check a theory. The most elaborate optimization of Carrigan was restricted to the NACA 4 series which limits the possible airfoil shapes considerably.


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2.2.4. COMMERCIAL DEVELOPMENTS

Several companies adopted the idea of offshore VAWT and are working on concepts and prototypes. A few examples of current developments are given here. Not a lot of information is available, most observations aremade from visualizations of the concepts.

• Gwind [49] is a high solidity helical H-type VAWT. The VAWT will be deployed on a floating structure

which will be stabilized by a gyroscope. At the end of 2013 the prototype Spinwind 1 was commissioned.Estimating from the size this is a prototype in the order of 10 kW.

• The Deepwind [50] project focuses on developing aφ-type floating turbine with a power rating of 5 MW.Currently tests are being performed on a small prototype in the Roskilde Fjord in Denmark.

• As part of the INFLOW project [51] Nenuphar [52] is developing a floating helical H-type VAWT. A 35kW prototype was already installed and tested. The first stage of a 2 MW onshore prototype was builtin 2014, this first stage is rated at 600 kW.

• Spinfloat [53] is developing 5 MW H-type VAWT also for a floating platform. The website mentions thatpitching blades will be part of the design, but so far no prototypes have been built.

• VertAx Wind Ltd [54] is developing a bottom founded H-type VAWT with a rating of 10 MW. Wind tunneltests were performed on a VAWT but further information is not available.

All these companies are stating that the airfoils of the turbines are also subject of research, but since they areongoing commercial developments, nothing is shared. This overview serves as a reference to the landscapeof developments currently taking place.

2.3. CONCLUSION

This review shows a summary of the research anddesign efforts into theairfoils for VAWT. In theearly days themain method to develop airfoils was to analytically derive principles which served as a basis for the design.In this period mostly existing airfoils were used and then modified to get the desired performance. A clearshift is shown in design methods with the arrival of more and more computational power. A trend is visible tolet the computer design the airfoil using combinations of optimization algorithms and aerodynamic analysiscodes, the theoretical/analytical basis is sometimes skipped. In my thesis I will try to speed up the process

by using an analytically derived function to do the optimization and then using more advanced software toassess the performance of these airfoils and validating the analytical work.

Conclusions on possible objectives for VAWT airfoil design can be drawn on basis of this review. They will bediscussed in the list below.

• The lift slope ∂C l ∂α is used by several references as an aerodynamic objective. In [12] it is used for achiev-

ing a high C l quickly, while Migliore et al. [14] and Ferreira et al. [30, 32] consider the lift slope in itself the goal and high C l values are not required. The difference between these is that Migliore et al. dis-cardsthe lift slope as an objective because too little variation can be observed between lift slope. This incontrast to the findings of Ferreira et al. that found significant differences in power performance withsmall changes in lift slope.

• The drag is also an aerodynamic objective for many researches. It shows up in different forms: low C D ,0

[15] and low C d in general [12, 14, 22, 30] are objectives that ensure the least negative torque from theairfoils. However there might be a trade off when a small increase in drag can have beneficial resultsfor other objectives. This makes it a good secondary objective. Wide drag buckets are mentioned in[15], which depends on the tip speed ratio of the turbine (TSR), at high TSR wide drag buckets arenot necessary. Finally, [12] opts that drag should be symmetric about the zero lift angle. This probably comes from the assumption that theangle of attackdistribution will be symmetric in up and downwindregions of a VAWT, which is a faulty assumption.

• Flow curvature is a phenomenon to be taken into account. Several researchers [14, 16, 21] have donethis by transforming the shape of an existing airfoil. By curving it along the streamlines the character-istics should become similar the the untransformed airfoil. By using CFD or some vortex models thisphenomenon is automatically taken into account, otherwise a correction or transformation should takeplace to produce valid airfoil designs.


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2.3. CONCLUSION 17

• The topic of roughness sensitivity is used as an objective by Sandia [17] and Ferreira et al. [32]. Soilingof wind turbine blades can have a detrimental effect on power performance. The question that needsto be answered is: What is more cost effective, designing blades that are roughness insensitive withprobable drawbacks in normal power output or cleaning wind turbine blades? This is dependent onfactors as the amount of reduction in performance with soiling, the degree of soiling and the cost of cleaning. These factors are hard to predict, so a definitive answer to whether this design approach is

necessary cannot be given at this time.• A contrast can be seen between earlier research when most airfoils were designed to be symmetric, with

Healy [10, 11] concluding ’the closer the profile is to symmetric, the higher the output’. Results of morerecent research show predominantly cambered profiles. Main reason for this is the recognition of thedifferent operation conditions between up and downwind halves of the rotor. Preset pitch and activecontrol are also ways to cope with this fact.

• The airfoil design will be impacted by Reynolds number. The upscaling of wind turbines will also setdifferent requirements for airfoils. Most research has focused on small turbines with Reynolds num-bers below a million. However, the developments mentioned in section 2.2.4 will be bigger turbinesoperating at higher Reynolds numbers. This has to be factored in into the design process.

The key challenge for VAWT airfoil development at this time is to find a consistent (set of) aerodynamic op-

timization objective(s) to be able to design airfoils for a rapidly developing and changing branch of industry.This objective is ideally applicable to a range of VAWT scales, while factoring in phenomena like roughnesssensitivity and flow curvature.


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3 A IRFOIL DESIGN METHODOLOGY

In this chapter the theory for the optimization of VAWT airfoils will be explained. First an aerodynamic andstructural goal for an optimal airfoil will be derived in section 3.1. Section 3.2 will show how the phenomenon

of blade soiling will be incorporated into the design.

3.1. A IRFOIL OPTIMIZ ATION GOALS

Theoptimizer, whichwill be explained in section4.1, works based on two objective functions. These calculatethe performance that the airfoils in the generated populations have. In this optimization an aerodynamic anda structural objective function are used. These are usually conflicting objectives in wind energy, but also inaeronautical engineering. For structural engineers it would be ideal to have thicker blades so the structuralelements could be designed more efficiently, however for aerodynamic engineers the thickness should belimited in order to limit drag. Conflicting objectives are well suited for a Pareto optimization method. Thismethod will be explained in section 4.1.2. Both objective function will be explained in more detail in thissection.

3.1.1. A ERODYNAMIC FUNCTION

The energy extracted by a VAWT is a function of the location and strength of the wake over the boundary of a control volume surrounding the VAWT [30]. The aerodynamic objective function works on the principle of optimizing this wake shedding, the derivation of this work is cited from the work of Simão Ferreira [30].

According to Kelvin’s theorem, the VAWT’s wake is generated by the temporal/azimuthal varia-tion of bound circulation on the blade; its vorticity distribution is not dependent on the averagebound circulation on the blade but only on its azimuthal variation. Implicitly, the same powerconversion (same wake) can occur as the result of different loading distributions over the ro-tor/actuator surface. The optimization of the energy conversion can be performed by optimizingthe shedding of the wake. For a 2D VAWT defined by an actuator, the optimization of the wake

generation implies the optimization of the curl of the load distribution over the surface, leavingundetermined a constant load distribution from the integral of the solution. However, an opti-mal loading distribution might in practice not be achievable or even desired. The question is asfollows: for a given wake distribution, which implies an azimuthal variation of bound circulation, which aerofoil gives the most power converted into effective torque?

For a given number of blades and tip speed ratioλ, an azimuthal (θ) distribution of shed vorticity Γw (θ) also implies a specific wake which induces a specific velocity field, resulting in a specificazimuthaldistribution of perceived velocity V p (θ) and inflow angleφ(θ). The distribution of shed

vorticity Γw (θ) implies a distribution of the gradient of bound vorticity over the rotation d Γb (θ)

d θ .

We can define d Γb (θ)

d θ = 12

d (V p C l c )d θ since, for a given wake, the local perceived velocity distribu-

tion V p (θ) is defined, a distribution of the time-derivative (or alternatively azimuth-derivative) of

19


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20 3. A IRFOIL DESIGN METHODOLOGY

bound vorticity over the rotation is equivalent to implying a distribution of dC l c

d θ .

Although there is a unique distribution d Clcd θ that satisfies the generation of the wake, there isan infinite number of suitable distributions C l c . For rotor design, these possible solutions canbe achieved by, for example, adding a fixed pitch angle β, changing the aerofoil camber or other

forms of circulation control. Additionally, we can rewrite d Clcd θ as a product of an average C l θc and

a distribution function C (θ) as

d Clc

d θ =

C l θc ·

C (θ). The term C l θc is not only a constant but specificfor a certain wake.

Ideally, we would convert the maximum of the energy extracted from the flow into mechanicalpower associated to a torque; however, we are limited by the effect of drag. The average contri-bution of drag to torque (T D ) is defined by Equation 3.1, where R is the rotor radius, ρ is the airdensity,ψ is the angle between the perceived velocity V p and the tangent to the rotor at the blade,and U ∞ is the unperturbed velocity upwind.

T D =R2π

0 R 12ρcosψV

2p C d c d θ=R

12ρ (λU ∞)

2R2π

0 A 1C d c d θ

with A 1 =cosψV 2p

(λU ∞)2(3.1)

For a given tip speed ratio, minimizing the impact of drag is equivalent to maximizing the inverseof the integral in Equation 3.1. Fixing the variablesthat are not properties of the blade section,themaximum performance can be expressed in Equation 3.2 as a maximum of the inverse of theintegral along the blade section design space variable ξ.

ddξ

µ 1R2π

0 A 1C d c d θ

∂= 0

with d2

dξ2

µ 1R2π

0 A 1C d c d θ

∂< 0

(3.2)

Since C l θc = const , Equation 3.2 can be rewritten as Equation 3.3

d

dξµ C l θ ·c R2π

0 A 1C d c d θ∂= 0

with d2

dξ2

µ C l θ

·c R2π0 A 1C d c d θ

∂< 0

(3.3)

To further simplify the analysis we define C d ·c as a product of the term C d c term and a distribu-tion function G (θ), as C d · c =C d cG (θ).

Equation 3.3 can then be simplified into Equation 3.4.

ddξ

µC l θC d

1R2π0 A 1G (θ) d θ

∂= 0

with d2

dξ2

µC l θC d

1R2π0 A 1G (θ) d θ

∂< 0

(3.4)

Equation 3.4 gives thefirst insight into the aerodynamic optimization of a VAWT aerofoil: ina firstapproximation, for a given range of angle of attack over the rotation, the aerodynamic optimiza-

tion is achieved by maximizing C l θ

C d . This result is analogous to the

C l C d m ax

optimum for horizontal

axis rotors. The term R2π

0 A 1G (θ) d θ is a weighing function which depends on the aerofoil polarand should be accounted for.

For the case of no circulation control (excluding blade pitching), the azimuthal distribution C l θcan be defined by dCldα

dαdθ , where α is the angle of attack. As

dαdθ is defined by the induction field

and blade pitch angle distribution, the maximization of C l θ

C d is equivalent to the maximization of

C l αC d

. We therefore arrive at an aerofoil aerodynamic objective function that is proportional to the

lift slope of the aerofoil C l α

and inversely proportional to drag.


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3.2. ROUGHNESS MODELING 21

This derivation is important to the strategy of this optimization. The VAWT aerodynamics are used to derivean objective on the airfoil scale, this means that for the optimization not every airfoil has to be simulated by a complete VAWT model. Instead the airfoil can be assessed using simple tools (which will be explained insection 4.1.3) which will save a lot of computational power. This means that the strategy can be implementedsuch that big design spaces can be covered to find a good airfoil design.

µC l αC d

∂ma x

(3.5)

As mentioned in the quote, the aerodynamic goal for VAWT as stated in expression 3.5 is analogous to theHAWT optimization goal of glide ratio. The different goals originate in the fact that the VAWT is in unsteady operation with constantly changing angles of attack while HAWT in principle work on fixed angles of attack.

3.1.2. STRUCTURAL FUNCTION

For the structural objective there are several options, obvious choices would be edgewise or flapwise bendingstiffness. Edgewise bending is bending parallel to the chord and flapwise bending is bending perpendicularto the chord. When thinking of wind turbines, fatigue can also be regarded as a big issue. However fatiguedepends very much on operating conditions and cannot be made into an usable objective for this optimiza-

tion. The choice between the remaining two objectives is made in favor of flapwise bending stiffness. In thisdirection the forces will be the biggest and the stiffness is generally smallest.

The structural objective is to maximize the geometrical stiffness of the airfoil. It is defined as the moment of inertia about the horizontal neutral axis I xx t s , which corresponds to the flapwise bending stiffness of the VAWTblade. The airfoil is assumed to be a thin-walled structure. This assumption makes the calculation simplerand a skin thickness does not need to be specified. By maximizing the geometrical stiffness of the blade, lessmaterial and stiffening structures will be needed to make the blade resistant to the loads. This will reduce costof the blade, but also reduce the weight, leading to less stringent requirements on other parts of the turbinelike the struts, tower, bearings etc.

In a real blade, stiffening structures will dominate the stiffness. Objective functions taking into account stiff-ening I-beams or box structures in the airfoil were investigated. This method was not adopted as the main

structural function because in this case the structure cannot be assumed thin-walled anymore, this means athickness or thickness ratio has to be chosen for the I-beams. This leads to an uncertain input because this will depend very much on the shape of the final airfoil. It will however have a big impact on the outcome of the structural function and thus have a big, uncertain influence on the optimization.

3.2. ROUGHNESS MODELING

As will be explained in more detail in section 4.1.3, airfoils operating in soiled conditions are taken into ac-count in theoptimization. Thisis done by modeling roughnesson the airfoil. In RFOIL there are threeoptions which can be used to simulate roughness.

• The N c r i t amplification factor is a measure for the disturbance (turbulence) level of the flow. The e N

model for which it is used, can trigger the transition from laminar to turbulent flow. N c r i t = 9isusedfor

stable flow comparable to standard wind tunnel flow [55]. Rough conditions will trigger transition toturbulent flow. The N c r i t does not mimic roughness but mimics the effect of roughness. This is done by placing the disturbances normally caused by roughness already in the flow, this makes the boundary layer more susceptible to transition. This is a reasonable approximation to simulate roughness. By setting the N c r i t to a low value (below 1) roughness can be simulated.

• The second tool is the manual forced transition point x t r , which can be set for both bottom and top of the airfoil. By setting thetransition point close to thenose of theairfoil, where usually therough surfaceis located, the flow will transition there always.

The airfoil soiling phenomenon needs to be studied in more detail to see which of these methods suits thesimulation. Figure 3.1 shows an example of blade soiling on a HAWT. The roughness can be caused by squashed bugs, corrosion of leading edge and buildup of ice, salt or dust particles. The roughness is mostly concentrated at the leading edge of the airfoil, the rough surface will make the flow transition from lami-


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22 3. A IRFOIL DESIGN METHODOLOGY

nar to turbulent there. The figure shows very severe soiling, normally the soiling is less and will thus impactthe transition less. There are two modeling approaches: 1) force transition at a certain point if roughness ispresent, or 2) place disturbances in the flow to make it transition earlier.

If a low N c r i t is used, the flow will transition close to the stagnation point, making the entire airfoil flow tur-bulent. A forced transition point models the physical phenomenon of roughness more accurate. But forcingtransition at a fixed point means that an estimate has to be made where flow should transition. A choice on

this position is made in section 4.1.3. Since N c r i t mimics the effects of roughness on transition better than aforced transition point, the N c r i t factor is used a the primary simulation tool for roughness.

Figure 3.1: Example of blade soiling, bugs are squashed on impacting the blade [56].

To evaluate the impact of different soiling cases, simulations were done using the double wake model [67].This is a VAWT simulation model which will be used to analyze the results of the optimization and will beexplained in section 5.2. Four cases were tested, one clean case as a reference and three soiled cases to seethe impact of surface roughness:

• Severe soiling: N=0 (flow will transition almost instantly)

• Medium soiling: N=4 and forced x t r = 0.1

• Medium soiling: N=4 and forced x t r = 0.2

• Clean case: N=9

Figure 3.2 shows the impact of these different soiling cases on the tangential force of a turbine, which is anal-ogous to the performance. This comparison was made for a 26% thick airfoil. The clean case is shown by the black line. It can be seen that the roughness cases all impact the performance, but the severity of theroughness plays a role in the amount of performance degradation. In the upwind region (0−180◦) the influ-ence is not that severe, in the downwind part (180−360◦) the influence is more pronounced. The roughnesscauses separation in the upwind region and the vortices shed will be encountered in the downwind region.Especially at 225◦ azimuth this impact is big.

3.3. OPTIMIZATION ST RATEGY The strategy to get to an optimized airfoil and a working optimization procedure is as follows. After the opti-mization tool (explained in chapter 4) has been tested and verified, a first set of inputs will be chosen to do afirst optimization. A choice will be made on the following properties/issues:

• How to model soiling in RFOIL. This involves the choice of critical amplification factor N c r i t and forcedtransition points x t r .

• Outer boundaries of optimization problem. These will be chosen to allow as much freedom as possible.More stringent constraints will be defined in these boundaries.

• Minimum trailing edge angle; this angle is set to avoid trailing edges which are to sharp for production.

• Choice of parameters defining the operation conditions of the airfoil and VAWT. This involves choosinga Reynolds number and an angle of attack range corresponding to the design tip speed ratio of the


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3.3. OPTIMIZATION STRATEGY 23

0 45 90 135 180 225 270 315 360

!0.2

!0.15

!0.1

!0.05

0

0.05

0.1

0.15

0.2

0.25

Tangential Force for TSR = 4, pitch = !4

Azimuth [°]

T a n g e n t i a

l F o r c e

[ ! ]

A!26 N = 0

A!26 N = 4, T=10

A!26 N = 4, T=20

A!26 N = 9

Figure 3.2: Impact of roughness cases on tangential force for a 26% thick airfoil.

VAWT airfoil.

• Find a suitable maximum thickness for the airfoils to avoid the inaccuracy region of RFOIL, but stillleave enough freedom for the optimization.

• A suitable weighting between clean and soiled case must be determined. This will be investigated usingthe first optimization trials.

From the results of this first optimization a few characteristic and interesting shapes will be chosen to do thefull VAWT analysis on. These shapes will be chosen not necessarily on basis of their best performance, butalso on their geometrical features. Seemingly ’weird’ geometries will be interesting to analyze to see if thesegeometries are really favorable, or enter the optimization results on basis of other reasons. These reasons arefor instance inaccurate descriptions of some aerodynamic phenomena which result in undeserved higherperformances. Three airfoils are chosen for the full analysis and the results are used to choose the inputs fora final optimization campaign. The results of these three airfoils are also published in [32].

The insight gained from this first optimization trial will be used to improve the optimization. The secondoptimization trial will involve minor changes in the aerodynamic objective function and weighting betweenclean and soiled performance. Four cases will be run, the results of these four optimizations will be analyzedand the best way will be used as an example result of a good VAWT airfoil and this process will be recom-mended as the best way to optimize VAWT airfoils.


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4 A IRFOIL GENETIC OPTIMIZATION

Designing airfoils can be done in several ways, if there is already a general shape available for the application,a popular way is to tune an existing airfoil to your needs. As can be concluded from the literature review in

chapter 2 no consensus has been reached on an airfoil shape for VAWT. This makes the possibilities of airfoiltuning limited and other methods are needed. In this research a choice was made to investigate a big designspace in search for suitable airfoil shapes. This is done by using a genetic algorithm which generates airfoilsand evaluates them according to two objective functions. For this approach a lot of airfoils will need to beaerodynamically simulated. To keep computational cost acceptable CFD methods are not feasible. To limitcomputational cost the airfoil analysis program RFOIL is used. Because RFOIL simulates airfoils and not acomplete turbine, the challenge is to come up with a good objective function which will be able to predict theperformance of the wind turbine based on airfoil coefficients. To recall, the research goals of this thesis are:

• To find an airfoil shape or family of shapes that is suitable for VAWT.

• To validate the objective functions and optimization algorithm as an efficient optimization method todesign airfoils in future projects.

A program developed by Gael de Oliveira [31] called Optiflow will be used for the optimization. Optiflow is anoptimization algorithm for airfoils which is coupled to RFOIL for airfoil analysis. The work that needed to bedone consisted of choosing and verifying boundary conditions and inputs and implementing the objectivefunctions.

This chapter will elaborate on the optimization program in section 4.1. Next the constraints are explained insection 4.2. The choice of constraints is important to the optimization because certain restrictions can have abig impact on the final shapes. In section 4.3 the implementation is shown of the objective functions derivedin section 3.1.

4.1. OPTIMIZER

The optimizer Optiflow is built upon MATLAB’s multi criteria optimization tool gamultiobj which is cou-pled to work together with the airfoil analysis tool RFOIL. To facilitate the optimization the airfoils will beparametrized. These facets of the optimization procedure will be explained here.

4.1.1. P AR AM ET ER IZ ATI ON

Normally airfoils are represented by a set of coordinate points which describe the full shape of the airfoil in(X,Y) coordinates. These are usually between 100 and 200 points. If this would be given to the optimizer as thefree parameters, the design space would be enormous. Next to this extra conditions should be implementedto ensure smoothness of the airfoil. To be able to generate airfoil shapes efficiently, the airfoil shape is param-eterized according to the Class Shape Transform (CST) method that was originally developed by Boeing [57].Theairfoil shape is

1.vawt_airfoil optimization_final_thesis.pdf

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