The near wake of the VAWT: 2D and 3D views of the VAWT aerodynamics

The near wake of the VAWT

2D and 3D views of the VAWT aerodynamics

Carlos Simão Ferreira

The near wake of the VAWT

Stellingen

behorende bij het proefschrift

The near wake of the VAWT

2D and 3D views of the VAWT aerodynamics.

Carlos Jos´e Sim˜ao Ferreira

1. Vergeleken met vortex modellen is het gebruik van impulsbehoudmodellen (de ”BEM”, ”MST”) traag, duur, inaccuraat en onnodig. Voor VAWT, BEM is dood; voor HAWT (dankzij de lineaire vortex modellen) zal deze methode ook spoedig afgedankt worden. 2. De aanname in deze thesis over de ineffici¨entie van de achterrandvorticiteit van de 3D

VAWT is incorrect aangezien de energie extractie in 4D plaats vindt.

3. Dynamische overtrek kan het rendement van de VAWT vergroten. Het oprollen en het transport van het zog tijdens een dynamische overtrek resulteert in een overdracht van inductie tussen de voorste en achterste trekkende schijf wat een extra ontwerpvariabele oplevert.

4. Als de constante gebonden circulatie over de bladen van de VAWT een invloed heeft op het vermogen van de 2D VAWT, dan is dat een vergelijkbaar effect als bij ommantelde rotoren, maar nu veroorzaakt door roterende bladen.

5. Het simuleren en het ontwerpen van een lift-aangedreven verticale-as golfrotor vereist een nauwkeurig werveldissipatiemodel; het toerental zal voornamelijk worden bepaald door de superpositie aan de lijwaarts en loefwaarts van de gegenereerde vorticiteit, en minder door de invalshoek die de bladen ondervinden.

6. De tipwervel van een lift-aangedreven verticale-as golfrotor levert de grootste ontwerp-beperking voor de grootte van de rotor; als verkeerde afmetingen worden gekozen, zal de ontstane tipvorticiteit aan de stroomopwaartse zijde van het blad het midden raken van de twee bladen die stroomopwaarts passeren.

7. De verbetering in wervelkernmodellen voor zogmodellering is ondergeschikt aan een nauwkeuriger model van de tipwervel-convectie en het oprollen en insluiten van het zog door de tipwervel. 8. De beruchte lage kwaliteit van stellingen bij proefschriften, waarover het College voor Promoties van de TUDelft zich zorgen maakt, wordt veroorzaakt door Artikel 17 van de Promotiereglement van de TUDelft, die de te verdedigen stellingen reguleert; dit is een goed bedoeld, maar vreselijk artikel. Verandering van een enkel woord in Artikel 17.1 maakt een groot verschil.

9. Wind turbine aerodynamici zouden financi¨ele theorie moeten studeren. De HAWT is veel ineffici¨enter dan de VAWT door financieel mismanagement. De HAWT betaalt geld aan zijn energieleverancier, terwijl de VAWT een krediet betaalt over een halve omwenteling. Dus bij het aerodynamisch ontwerp moet rekening worden gehouden met het rendement op investering van de aerodynamica.

10. Slapende Engelse windturbines zijn effici¨enter dan slapende Nederlandse windturbines, om-dat ze geen inductie veld genereren.

Deze stellingen worden opponeerbaar en verdedigbaar geacht en zijn als zodanig goedgekeurd door de promotoren, Prof. dr. Gerard van Bussel and Prof. dr. ir. Gijs van Kuik.

Propositions

accompanying the thesis

The near wake of the VAWT

2D and 3D views of the VAWT aerodynamics.

Carlos Jos´e Sim˜ao Ferreira

1. Compared to vortex models, the use of streamtube momentum balance models (”BEM”, ”MST”) is slow, costly, inaccurate and unnecessary. For the VAWT, BEM is dead; for the HAWT, by taking advantage of the linearity of vortex models, BEM can soon be retired. 2. The characterization in this thesis of the trailing vorticity of the 3D VAWT as an inefficiency

is incorrect, as energy must be extracted in 4D.

3. Dynamic stall can increase the efficiency of the VAWT. The roll-up and transport of the wake during dynamic stall implies in a transfer of induction between the upwind actuator disk and the downwind actuator disk, resulting in an additional design variable.

4. If the constant bound circulation on the blades of the VAWT is to have an impact on the power of the 2D VAWT, then it is by a similar effect to shrouded rotors, caused by the rotating blades.

5. Simulating and designing of a lift-driven vertical-axis wave-rotor requires an accurate vor-ticity dissipation model; the rotational velocity will be determined more by the need to superimpose leeward- and windward-generated vorticity, than by the angle of attack expe-rienced by the blades.

6. The tip-vortex of the lift-driven vertical-axis wave-rotor is the main design constraint for the size of the rotor; get the wrong size-relations and the tip vortex generated upwind will hit the midspan of the two upwind blade passages.

7. The improvement of vortex-core models for application in wake models is secondary to a more accurate modeling of tip-vortex convection and the entrainment of the wake by the tip-vortex.

8. The infamous low quality of PhD propositions, that so much worries the TUDelft Board of Doctorates, has its source in Article 17 of the Doctorate Regulations of the TUDelft, which regulates the propositions to be defended; this article, as many things done with good intentions, is terrible. Changing a single word in Article 17.1 would go a long way. 9. Wind turbine aerodynamicists should study financial theory; the HAWT is much less

effi-cient than the VAWT due to financial mismanagement. The HAWT pays cash to its energy supplier, while the VAWT pays with a letter of credit valid over a half-rotation; thus, the aerodynamic design must account for a Return on Investment on the aerodynamics. 10. Let sleeping turbines lay. Sleeping turbines are just much more efficient as they experience

no induction field.

These propositions are considered opposable and defendable and as such have been approved by the supervisors, Prof. dr. Gerard van Bussel and Prof. dr. ir. Gijs van Kuik.

The near wake of the VAWT

The near wake of the VAWT

2D and 3D views of the VAWT aerodynamics

PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. dr. ir. J.T. Fokkema,

voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op maandag, 26 oktober 2009 om 15.00 uur

door

Carlos Jos´

e Sim˜

ao Ferreira

ingenieur luchtvaart- en ruimtevaart

engenheiro aeroespacial, Universidade T´

ecnica de Lisboa

geboren te Figueira da Foz.

Dit proefschrift is goedgekeurd door de promotor: Prof. dr. G.J.W van Bussel

Prof. dr. ir. G.A.M. van Kuik

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. G.J.W van Bussel Technische Universiteit Delft, promotor Prof. dr. ir. G.A.M. van Kuik Technische Universiteit Delft, promotor Prof. dr. ir. drs. H. Bijl Technische Universiteit Delft

Prof. dr. F. Scarano Technische Universiteit Delft Prof. dr. R. Galbraith University of Glasgow Dr. D. Berg Sandia National Laboratories

Dr. H. Madsen Technical University of Denmark & Risø Na-tional Laboratory for Sustainable Energy

Printed by W¨ohrmann Print Service, Zutphen, The Netherlands Copyright c 2009 by C.J. Sim˜ao Ferreira

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author.

Typeset by the author with the LA_{TEX Documentation System.}

Acknowledgements

So many of you have supported and encouraged the birth of these roughly three hundred pages; family, friends, students and colleagues who have become friends, all of you directly and indirectly contributed to the good end of this journey. You did not forget me from my time as your student; you gave me a job doing what I was born to do; you provided that I had resources so that my ideas would not be limited; you spent hours with me in the wind tunnel and made doomed experiments come to life; you were family; you were a role model; you sat beside me behind a computer; you have challenged and criticized me, and over and over again you have changed my mind; you invested in me; you were patient and listened to me, receptive to what I was trying to teach you, and with that I learned so much; you were a friend; you worked hard to help me, even when you were tired; you were a pal; you shared your knowledge and experience; you advised me; you demanded more and better; you complimented me; you were generous with your time; you were patient; you were family; you were neighbors; you forgave me when I was rude; you were professional and demanded the same; you went and got me a cup of tea without being asked, because you thought I needed it. I have written you name in the next page, as a way to say thank you.

In between all these very dear names there are secret messages, important guide-lines for having a prime good time; to find them, just follow the best advice in the galaxy and DON’T PANIC!!

Thank you so very much!! Carlitos

ii ACKNOWLEDGEMENTS I f y d o a u h h t w e a e c a n j t u n w t n u s w i o t s u a f m t u h i t r e v l m u i d e e e y v n u d r w e m o c d i n v u o e l t l h a t t p j e l m e r m c s o n e v l c s o a c y i e t o i u h a n v a e f r a g a v x y y o h a i n h a i o t d n t a s h i f t y o d a t e c r t a d k r n t o r y d o i d w s a w e d e w d o h e e h n b a s s e d r u l h w s a r e n e i y h f e o e u s i i e n e l e w t s r e l c w t e r o t s a t n s e o t w i c a e a l e t f l s i w s l l b a i s r s p m u p e t a m a f h h i s f e r e e k o t c a s n v h f a s c a s l e y d f i o k a p a s s t g c c t c a s o o t o f g f n u t l b o a e e t i e v i b e t y t g n e n i s b s b e a t i e n i g u h l i r o b a u s l c j t c h m l e p e w h e d n g d o a o g i r d o r h t n n t r e l a o i n o t n a a w w t e u g r a d a e e r c s h f o e e a y o n e e h w c t d e u k j o t c a t f o t o t h l n o t e r a r i o i o t w d m r y d s r t r n o b d f s o r y p s a d e u i d o r a v t i t d n s v n z e h a o n y l f o i p e i r e y s o f i a g r o l i t l v s r t e o o e a g t e s e u e t f m a t t o z r e h r b n f p e a n i t t g o r s v h o i o r n r n l s n t r u t r s r f n h n a a e d e a a g a e l n n o o d f d t a i m n i r mm d e t v r e p w s e s o a e t t i o s r s e i n o a s a r r l t i r w n o g n e o i w o h e a l w o g t t r a l h i j a n a o j c d d c d m d d i h o w a l t r o u t n i f h r i a i u e r i t a d a o l o n r n m i t u a k r i i l e s f l c f a t q e e n a o t n t n p r e s h a i n y m j g c l d a r l r f e i l u j e o t r i n t u d t d t e i t i h w d a s e k n a i e d e f f l e e r l e h n a i t s i r k h r t i e d w t t c f o h i t m l v i e s n c m r m e i e r r o e l h g s c n h a o t d w r l m a a t a o n a n u t o a r a i i s a a m e d n a i s r e e o t o a a u e n d o e t o r c t l r s d d o u w w a r s a n r r l t c i n t l o t r n h n o v t u e e u s h r d k i a t a w b e z c t n i b k c i d g i s c e o u f b d u u r f e w d m k t a e e g e p x h n i l h b o b e t m o t a u t n t r s h e r m i n i a v a t e r s e n r b e x v i e d r a s o s e g a e a i v e a t e y a n u h a s s i e n n t d a i r o o y n p e s s t r d i e l m s y k n n a a b s a m p n i s t j k o s i i h r c g n a l t e e f w i h l e v m t g x o n i g wm a x l o o i i n w i r n t t h e e i n a h p e t s t a z e b p o o l i e t e d r a n r e b f o u m s e s e a a mm p o r n t c t h r r b v e t e a r m y s r r h t v e o t f l t o g p m l k s l n h p n o e i o c a e a i o e o i n s t e i d a f r h l d e s t c l r k l e e a u y t e a i t s n o u t n t e u r f p t s s n n e i v e l o e f e r a h m d i e n n d n i w u d o a g r r i e e n r o t v l a e t a a d o t e o j h n a n a t h i i t d l o b b c t r w o t a o e d c a t h o h g x u c d u a t u r a f c n x d c d e n h t t t o l t i s t f i t n d v e t o e r o e t m c f a r n g t n l e i i i o y s k m h i t u o o s c i a u e a t o d t r r t i s s b u o l t i i i w a m b m v f o i u e e n t n a n b a t l c v l o r b e i o e h t m a r r c e r m e i i r r y a n i t s i r c d d d t y u n i s o v s t y c s t x r h o l a t i x e i n l i l p n d t t y d u d g e c f h a s o f a r e u i t x t o g t e r a t h Hm d o i l a g m a r i l e n a e w e h t t a m g t t t l p c h o h r e h i d n e e o c s a v e c o c a e v n n e p o i s i y e s e h d a i o e i e f e g n t m e c a h n o n s c m i y v k i r e a w w w n i r e p i d o r l c c r t b t m e e r p k e n a g d t t i t e m t a v h a t d i n a g c o o m b b i u i i i y l t a t r h r

Summary

The analysis, modeling and design of the lift-driven Vertical Axis Wind Turbine (VAWT) has challenged the wind energy community for many decades; this limited progress in knowledge has severely impaired the development of the VAWT, giving rise to the myth that the VAWT rotor is inherently inefficient (in comparison with the more conventional Horizontal Axis Wind Turbine - HAWT) or too complex for commercial implementation.

In this research work, we take a new path on the analysis of the VAWT: instead of considering a rotor that creates a perturbation on the flow (wake and induction field), we consider an unsteady wake, to which a rotor energy-conversion system is associated, obtaining the loading on the blade by better understanding the flow. The research aims at understanding the wake and its relation with energy conversion and the loading on the rotor system.

Four main questions drive this research:

• What is the relation between blade loading and energy conversion? • How does the near wake of the VAWT develop?

• What is the difference between the 2D and the 3D wake? • How does understanding the near wake improve our design?

At the end of this dissertation we achieve a clear and insightful view on the 2D and 3D aerodynamics from the point of view of the wake, that significantly improves the aerodynamic design and optimization of new VAWT rotors for energy conversion and propulsion, opening a new design space and methodology.

The results and discussion presented in this dissertation are organized in five steps (see thesis outline, Chapter 1):

• Part I: understand the fundamental VAWT aerodynamics and how these relate

with the research presented in this dissertation.

• Part II: understand the energy exchange process in the 2D plane by

under-standing the shedding of the wake over the rotation, and the wake expansion in 2D. Analyze the impact of dynamic stall on the near wake evolution, and how to extract blade load information from the near wake in dynamic stall.

• Part III: understand the impact of the spanwise dimension of the rotor and

the role of the consequent trailing vorticity. Investigate the little known skewed iii

iv SUMMARY

flow.

• Part IV: understand better the energy exchange process, the wake’s

genera-tion and the decoupling between loading and energy conversion. Propose new approaches and guidelines for the aerodynamic rotor design.

• Part V: discuss the main results and conclusions of the research, and its

im-pact on new aerodynamic research and design approaches, both for 2D and 3D VAWT rotors.

In Part I (Chapter 2) we frame our research approach, analyzing the VAWT from a wake perspective, by considering both 2D and 3D aerodynamics of the VAWT at two different scales: aerofoil/blade scale and rotor scale. We divide the rotor in windward (315◦ < θ < 45◦), upwind (45◦ < θ < 135◦), leeward (135◦ < θ < 225◦) and downwind (225◦ < θ < 315◦) regions of the rotation. This approach obsolesces the conventional division of the rotor into upwind and downwind halves; while the upwind/downwind division is driven by angle of attack considerations (blade loading problem), this new segmentation is determined by the shedding of vorticity (energy conversion problem), a more useful and effective approach. The wake is also split into shed vorticity due to the time gradient of the bound circulation, and trailing vorticity due to the spatial gradient of the bound circulation; this division leads to our 2D and 3D analysis of the flow.

In Part II, we analyze the 2D rotor and wake at two scales: rotor and blade. The two flow scales are obviously related, in the sense that the rotor’s aerodynamics are the result of the wakes generated at the several blades and the blade experiences an induction field due to the vorticity distributed over the wake at the rotor scale. The separation in blade and rotor scale is in fact a separation of two views on the total system:

• The rotor, as an energy exchange system, where the energy exchange results in

a wake and streamline expansion.

• The blade, as an aerodynamic loading system, where the design-objective

load-ing is associated with an equivalent bound circulation. The time variation of this bound circulation results in a shed wake.

The 2D potential-flow analysis (Chapter 3) shows that:

• the conventional breakdown of the VAWT into upwind and downwind actuator

systems is incorrect, leading to an overestimation of energy conversion on the upwind half of the rotation and an underestimation in the downwind half.

• contrary to the HAWT, the induction is not a function of the total loading, but

only of the load component associated with the azimuthally varying circulation.

• it is possible to significantly improve Double Multiple Streamtube models by

incorporating a better description of the flow. The proposed improved model clearly surpasses conventional models on the prediction of the induction and loading.

v

to the time-varying bound-circulation term; therefore, the induction field of the 2D VAWT in potential flow can be defined by only the number of blades, rotor solidity and tip-speed ratio. This allows for the obsolescence of streamtube momentum models, replaced by faster and more accurate potential flow vortex models.

In Chapters 4 and 5 we visualize and quantify, experimentally and numerically, the flow field in the near wake of the blade during the upwind and leeward segments of the motion, at tip-speed ratios λ = 2, 3 and 4, using Particle Image Velocimetry (PIV). An interesting physical aspect of the vortical flow in dynamic stall, especially at low tip-speed ratios, is the transport of the shed vorticity with the blade. This transport of the vortical structures with the blade means that the geometry of the wake, due to viscous effects, differs from what is obtained with potential flow. A different spatial distribution of the shed vorticity implies a different induction field, which might imply a reduction of the effectiveness of momentum models and simple potential-flow models and change the rotor’s performance. The results show two important effects:

• At the rotor scale, the transport of vorticity with the blade, rolled in the leading

edge/trailing edge separated vortices.

• At the blade scale, the importance of the small scale vortices for the oscillations

on pressure distribution and loads.

In Chapter 6 we use the experimental and numerical data from the previous chap-ters to evaluate the feasibility of extracting information from the flow/wake measured with PIV, even in dynamic stall, for improving flow analysis and model validation.

In Part III we introduce the fourth dimension of our problem: the spanwise direc-tion. The finite span leads to a non-constant spanwise distribution of circulation on the blade, and this distribution leads to the release of trailing vorticity, of which the blade tip vortex is the most prominent component. In Chapter 7 we measure the wake at the tip-vortex region of the VAWT; in Chapter 8 we combine these experimental results with 3D unsteady free-wake potential-flow simulations to:

• experimentally and numerically observe, quantify and analyze the generation

and convection of the 3D tip vortex of the VAWT.

• experimentally, numerically and analytically investigate the effect of blade-tip

shape on the generation and convection of the tip vortex, with focus on the added circulation due to the motion of the blade.

• combine experimental measurements and numerical simulations to analyze: the

3D wake of the VAWT; the interaction between shed and trailing vorticity; the roll-up and expansion of the wake in the leeward and windward regions; the in-rotor convection and inboard/outboard motion of the tip vortex; the 3D induction field; the 3D blade wake interaction during the downwind blade passage; and the effect of trailing vorticity in the spanwise distribution of cir-culation, including the 2D to 3D load direction reversal in the downwind blade passage.

The spanwise dimension of the flow also gives rise to a new form of misalignment between the flow and the axis: skewed flow. In Chapter 9 we analyze the physics

vi SUMMARY

of skewed flow, flow asymmetry, near wake development, blade-wake interaction and impact on energy conversion.

The analysis of the VAWT from the point of view of the 2D and 3D near wake is shown to be very effective in understanding: the physics of the flow; the energy exchange process; how the total energy exchange over one rotation actually relates to the local aerodynamic loading on the blade; the impact of implementing an essen-tially 2D energy conversion process into a 3D aerodynamic system; and the resulting inefficiencies due to the finite span and trailing vorticity.

In Part IV (Chapter 10) we show that it is possible to decompose the VAWT de-sign problem into dede-signing for loading and dede-signing for energy conversion, opening a large design space and proposing a new methodology, impacting both 2D and 3D flow. We also show that, although the 2D wake does not vary significantly with vari-ation in the pitching axis locvari-ation and blade camber, the 3D wake and performance are significantly affected by these variations. This is due to the impact that varying the bound circulation has on the release of trailing vorticity; a larger trailing vorticity generated during the upwind blade passage implies a larger induction due to trailing vorticity, and a worse interaction at the downwind blade passage. The effects of vari-ation of camber and/or pitching axis in 2D and 3D performance are contradictory and complementary and can be simultaneously optimized.

In Part V (Chapter 11) we further develop these and other main conclusions, discussing their impact on VAWT aerodynamics. The research here presented implies a break from conventional approaches to the VAWT aerodynamics, allowing for the development of new research and models, both in 2D flow (aerofoil design, rotor energy conversion optimization) and 3D flow (blade and rotor shape, non-uniform flows).

Samenvatting

Het analyseren, modeleren en ontwerpen van een Verticale As Wind Turbine (VAWT) is al decennia lang een uitdaging voor de windenergie gemeenschap. De beperkte voortgang in kennis heeft de ontwikkeling van de VAWT ernstig gehinderd, wat heeft geleid tot de mythe dat de VAWT inherent minder effici¨ent is dan de Horizontale As Wind Turbine (HAWT) of te ingewikkeld om commercieel toe te passen.

In dit onderzoek kijken we op een nieuwe manier tegen de analyse van de VAWT aan: in plaats van de rotor te zien als een voorwerp dat de stroming verstoort, kijken we naar het instationaire zog veroorzaakt door de rotor, waarna met een goed begrip van de stroming de belasting op de rotorbladen bepaald kan worden. Het onderzoek richt zich op het begrijpen van het zog en de relatie tot de conversie van energie en de belasting op de rotor.

Vier hoofdvragen sturen dit onderzoek:

• Wat is de relatie tussen de bladbelasting en de energieconversie? • Hoe ontwikkelt het zog zich dichtbij de rotor?

• Wat is het verschil tussen het 2D en het 3D zog?

• Hoe verbetert het begrijpen van het dichtbije zog ons ontwerp?

Bij het einde van het proefschrift hebben we een heldere en inzichtelijke kijk op de 2D en 3D aerodynamica van het zog, waarmee het aerodynamisch ontwerp en optimalisatie van nieuwe VAWT rotors significant verbeterd wordt, en ruimte geeft voor nieuwe ontwerpen en methodes.

In het proefschrift worden de resultaten en discussie in vijf stappen ondergebracht (zie de opzet van het proefschrift, Hoofdstuk 1):

• Deel I: het begrijpen van de fundamentele VAWT aerodynamica, en hoe deze

zich verhoudt tot het in het proefschrift gepresenteerde onderzoek.

• Deel II: het begrijpen van het energie conversie proces in het 2D vlak door

te begrijpen hoe het zog tijdens een omwenteling gecre¨eerd wordt, en hoe de zogexpansie in 2D is. Het analyseren van de invloed die dynamische overtrek heeft op de nabije zog ontwikkeling en hoe informatie over de bladbelastingen te krijgen uit het nabije zog tijdens dynamische overtrek.

• Deel III: het begrijpen van de invloed van de spanwijdte van de rotor en de rol

van de hierbij horende tipwervels. Het onderzoeken van de stroming wanneer vii

viii SAMENVATTING

de wind niet loodrecht op de as staat.

• Deel IV: het beter begrijpen van het energie conversie proces, het cre¨eren van het

zog en het loskoppelen van bladbelasting en energie conversie. Het voorstellen van nieuwe methodes en richtlijnen voor het aerodynamisch ontwerp van de rotor.

• Deel V: het bediscussi¨eren van de belangrijkste resultaten en conclusies van

het onderzoek, en de gevolgen hiervan voor nieuw aerodynamisch onderzoek en ontwerpmethodes, zowel voor 2D als voor 3D VAWT rotors.

In Deel I (Hoofdstuk 2) kaderen we de onderzoeksaanpak in, analyseren we de VAWT gezien vanuit het zog, door zowel de 2D als 3D aerodynamica van de VAWT te beschouwen op twee verschillende schalen: die van het profiel en blad, en die van de rotor. We verdelen de rotor in de loefwaarts (315◦ < θ < 45◦), stroomop-waartse zijde (45◦ < θ < 135◦), lijwaarts (135◦ < θ < 225◦) en stroomafwaartse zijde (225◦ < θ < 315◦). Hiermee maken we de conventionele verdeling in een stroomop- en afwaartse helft achterhaald. Deze verdeling is zinnig wanneer de in-valshoek beschouwd wordt (een bladbelasting probleem) terwijl de nieuwe verdeling gebaseerd is op beschouwingen over het loslaten van wervelsterkte (een energie con-versie probleem) wat een effectievere manier is. Het zog is ook verdeeld in afgeschudde wervelsterkte die het gevolg is van de in tijd vari¨erende gebonden circulatie, en de tip-wervelsterkte ten gevolge van de ruimtelijke gradi¨ent van de circulatie. Deze splitsing leidt tot onze 2D en 3D stromingsanalyse.

In Deel II analyseren we de 2D rotor en het zog op twee schalen: die van de rotor en die van het blad. Het is evident dat de twee schalen gerelateerd zijn, aangezien de aerodynamica van de rotor het resultaat is van het door de verschillende bladen gegenereerde zog, en omdat een blad een ge¨ınduceerd snelheidsveld ondervindt door de wervelverdeling in het zog. Bij een splitsing in blad- en rotorschaal kijken we als het ware vanuit twee gezichtpunten naar het totale systeem:

• Vanuit de rotor als een energieomzettingssysteem, waarbij de omzetting van

energie resulteert in een zog en een expanderende stroomlijnen.

• Vanuit het blad als een aerodynamisch belast systeem, waarbij de belasting

waarvoor het blad ontworpen wordt gekoppeld is aan een equivalente gebonden circulatie. Het vari¨eren van deze gebonden circulatie met de tijd resulteert in een afgeschud zog.

De analyse van de 2D potentiaalstroming (Hoofdstuk 3) toont aan dat:

• De conventionele scheiding van de VAWT in een stroomopwaartse en

stroom-afwaartse kant (actuator) niet juist is, wat leidt tot een overschatting van de energieconversie aan de stroomopwaartse kant en een onderschatting aan de stroomafwaartse kant.

• In tegenstelling tot de HAWT is de inductie niet een functie van de totale

belasting, maar slechts van dat deel van de belasting dat veroorzaakt wordt door het met de azimuthoek vari¨erende deel van de circulatie.

• De Double Multiple Streamtube modellen kunnen significant verbeterd worden

ix

overtreft duidelijk de conventionele modellen wat betreft de voorspelling van de inductie en de belasting.

• De invloed van het constante deel van de bladgebonden circulatie is klein ten

opzichte van het in de tijd vari¨erende deel van de bladgebonden circulatie. Daarom kan het ge¨ınduceerde snelheidsveld van de 2D VAWT in een poten-tiaal stroming gedefinieerd worden met alleen het aantal bladen, de rotorvol-heidsgraad en de snellopendheid als parameters. Hierdoor kunnen stroombuis impuls modellen als verouderd beschouwd worden, en kunnen ze vervangen wor-den door snellere en nauwkeuriger potentiaal stroming wervelmodellen.

In Hoofdstukken 4 en 5 wordt het stromingsveld in het nabije zog gevisualiseerd en gekwantificeerd (zowel experimenteel met behulp van Particle Image Velocime-try (PIV) als numeriek) in het stroomopwaartse en stroomafwaartse gedeelte van de beweging, bij snellopendheden van λ = 2, 3 and 4. Het transport van de wervel-sterkte afgeschud door het blad gecombineerd met dynamische overtrek is, vooral bij lage snellopendheden, een interessant fysisch aspect van de wervelstroming. Dit transport van wervelstructuren met het blad betekent dat, door viskeuze effecten, de geometrie van het zog verschilt van die verkregen met een potentiaalstroming. Een andere ruimtelijke verdeling van de afgeschudde wervelsterkte impliceert een ander ge¨ınduceerd snelheidsveld, hetgeen een vermindering kan geven van de effectiviteit van impuls modellen en simpele potentiaalstroming modellen en een verandering in het vermogen van de rotor. De resultaten laten twee belangrijke effecten zien:

• Op rotor schaal, het transport van wervelsterkte met het blad, oprollend in de

gescheiden voorrand- en achterrandwervels.

• Op blad schaal, het belang van wervels op kleine schaal voor de oscillaties in

drukverdeling en belasting.

In Hoofdstuk 6 worden de experimentele en numerieke gegevens van de vorige hoofdstukken gebruikt om te kijken of met stromings- en zoginformatie uit PIV de stromingsanalyse en modelvalidatie verbeterd kan worden, zelfs in dynamische overtrek.

In Deel III introduceren we de vierde dimensie van ons probleem: de spanwijd-terichting. De eindigheid van het blad veroorzaakt een in spanwijdterichting ver-lopende circulatieverdeling. Deze verdeling zorgt voor het ontstaan van loslatende wervels, waarvan de tipwervel het meeste opvalt. In Hoofdstuk 7 meten we het zog in de buurt van van de tipwervel van de VAWT. In Hoofdstuk 8 combineren we deze experimentele resultaten met 3D simulaties met een potentiaalstroming en een vrij zog, om:

• het ontstaan en het transport van de 3D tipwervel van de VAWT experimenteel

en numeriek te bekijken, kwantificeren en analyseren.

• de invloed te onderzoeken, experimenteel, numeriek en analytisch, van de vorm

van de bladtip op het ontstaan en transport van de tipwervel, met speciale aandacht voor de circulatie door de beweging van het blad.

x SAMENVATTING

van de VAWT te analyseren op vlak van: de wisselwerking tussen afgeschudde en losgelaten wervelsterkte; het oprollen en uitdijen van het zog in de loef-en lijzijdes; het transport van de tipwervel binnloef-en de rotor loef-en de beweging van de tipwervel naar binnen of buiten; het 3D ge¨ınduceerde snelheidsveld; de wisselwerking in 3D tussen het blad en het zog tijdens de passage van het blad aan de lijzijde; het effect van de losgelaten wervelsterkte op de circulatieverdeling in de spanwijdterichting van het blad, met inbegrip van de omkering van de belasting, in 2D en 3D, tijdens de passage van het blad aan de stroomafwaartse kant.

In 3D kan er sprake van zijn van een nieuwe vorm van scheefstand, wanneer de stromingsrichting en de as van de turbine niet loodrecht op elkaar staan. In Hoofdstuk 9 analyseren we de fysica hiervan, de stromingsasymmetrie, de ontwikkeling van het zog dichtbij de rotor, de wisselwerking tussen blad en zog, en de invloed op de energieomzetting.

De analyse van de VAWT vanuit het 2D en 3D dichtbije zog blijkt zeer effectief om de eigenschappen van de stroming te begrijpen, even als de energieomzetting, de verhouding tussen de lokale bladbelasting en energieconversie gedurende ´e´en rotatie en de invloed van het toepassen van een in principe 2D energieomzettingsproces in een 3D aerodynamisch systeem, en de verliezen door de eindige bladlengte en de afgeschudde wervels.

In Deel IV (Hoofdstuk 10) tonen we dat het mogelijk is het ontwerpprobleem van de VAWT op te splitsen in een ontwerp voor belasting en een ontwerp voor energieomzetting. Dit opent een breed ontwerpspectrum en stelt een nieuwe ontwerp-methode voor die zowel op de 2D als 3D stroming invloed heeft. We tonen ook dat ondanks het feit dat een zog in 2D nauwelijks varieert bij een verandering van de positie van de pitch as (as waarom de positie van het blad wordt ingesteld) en van de welving van het blad, het 3D zog en de prestaties wel aanzienlijk veranderen. Dit komt door de invloed die een verandering van de gebonden wervelsterkte heeft op de afgeschudde wervelsterkte; de productie van grotere afgeschudde wervels tij-dens de passage van het blad aan de stroomopwaartse zijde zorgt voor een grotere ge¨ınduceerde snelheid door deze wervels, en een slechtere wisselwerking tussen zog en blad tijdens de stroomafwaartse blad passage. Veranderingen in welving van het blad en/of locatie van de pitch as hebben een gelijksoortige invloed op de 2D en 3D prestaties, waardoor deze tegelijk geoptimaliseerd kunnen worden.

In Deel V (Hoofdstuk 11) gaan we verder in op de belangrijkste conclusies van dit werk, en de invloed hiervan op de aerodynamica van VAWTs. Het onderzoek dat hier gepresenteerd wordt houdt een breuk in met conventionele aanpak van VAWT aerodynamica, en geeft mogelijkheden voor nieuw onderzoek en nieuwe modellen, zowel in 2D (ontwerp van profielen, optimalisatie van de energieomzetting in de rotor) als in 3D stromingen (vormgeving van het blad en de rotor, niet-uniforme instroming).

Contents

Acknowledgements i

Summary iii

Samenvatting vii

1 Thesis outline 1

1.1 The research question . . . 2

1.1.1 What is the relation between blade loading and energy conver-sion? . . . 2

1.1.2 How does the near wake of the VAWT develop? . . . 2

1.1.3 What is the difference between the 2D and the 3D wake? . . . 3

1.1.4 How does understanding the near wake improve our design? . . 4

1.2 Structure of the dissertation . . . 4

1.2.1 Introduction . . . 4

1.2.2 The 2D Near Wake . . . . 4

1.2.3 The 3D Near Wake . . . . 6

1.2.4 Impact on aerodynamic design . . . 6

1.2.5 Conclusions and impact on future research . . . 6

I

Introduction

9

2.2 2D VAWT aerodynamics . . . 12

2.2.1 Rotor scale . . . 16

2.2.2 Aerofoil scale . . . 18

2.3 3D VAWT aerodynamics . . . 22

2.3.1 Spanwise vorticity distribution and tip vortex . . . 22 xi

xii CONTENTS

2.3.2 Skew angle . . . 23

2.4 Impact of the near wake on aerodynamic design . . . 24

2.5 Chapter nomenclature . . . 24

II

The 2

D Near Wake of the VAWT

27

3.1.1 Section description . . . 30

3.2 Introduction . . . 31

3.3 Multiple streamtube models for VAWT . . . 31

3.3.1 Potential flow models applied to VAWT . . . 32

3.4 2D potential-flow panel-model of the VAWT . . . 33

3.5 Reference simulation . . . 33

3.5.1 NACA0015, B = 3, σ = 0.15, k = 0.05, λ = 4 . . . . 33

3.5.2 The flow field . . . 34

3.6 The two-actuator disk approach . . . 36

3.7 The effect of the constant bound circulation due to blade pitching . . 40

3.8 Comparing vortex model with DMST model . . . 44

3.8.1 Accounting for pitching in the 3D flow case . . . 45

3.9 Modeling the induction term a_⊥ . . . 46

3.9.1 Induction surface . . . 46

3.9.2 Modifying the DMST model to account for a_⊥ . . . 49

3.9.3 Comparison of the DMST model with and without correction to the vortex model . . . 49

3.10 Solving the downwind half of the rotation . . . 52

3.11 Validation of the proposed method . . . 56

3.12 Alternative forms of calculating a_⊥ . . . 59

3.13 Conclusions . . . 60

3.14 Chapter nomenclature . . . 63

4 2D Particle Image Velocimetry of the wake of the VAWT in dy-namic stall 65 4.1 Chapter outline . . . 65

4.2 Introduction . . . 66

4.3 Experimental apparatus and procedure . . . 68

4.3.1 Wind Tunnel facility . . . 68

4.3.2 The rotor . . . 69

4.3.3 Diagnostic apparatus . . . 69

4.4 Phase averaging of the velocity field . . . 71

CONTENTS xiii

4.4.2 Determining the phase-averaged and random components of the leading-edge vortex . . . 72 4.4.3 Uncertainty associated with the experimental procedure . . . . 74 4.5 Variation of shed vorticity with azimuth angle . . . 76 4.5.1 The λ = 2 case . . . . 76 4.6 Evolution of counter-clockwise vorticity . . . 78 4.7 λ = 3 and λ = 4 . . . 80 4.8 Conclusions . . . 82 4.9 Chapter nomenclature . . . 83

5 2D CFD simulation of dynamic stall on a VAWT 85

5.1 Chapter outline . . . 85 5.1.1 Section description . . . 86 5.2 Introduction . . . 86 5.3 Motion and aerodynamics of a VAWT . . . 88 5.4 Simulation definition . . . 89 5.4.1 Model geometry . . . 89 5.4.2 Computational space grid . . . 89 5.4.3 Simulated flow conditions . . . 90 5.5 Validation of the results of different turbulence models . . . 91 5.5.1 URANS models . . . 92 5.5.2 LES . . . 92 5.5.3 DES . . . 96 5.5.4 Comparison of force simulation . . . 97 5.6 Verification of grid sensitivity . . . 97 5.6.1 Time step refinement . . . 97 5.6.2 Space grid refinement . . . 100 5.7 Verifying high-frequency variation in force . . . 100 5.8 Experimental validation of leading-edge separated-vortex circulation . 102 5.9 Conclusions . . . 105 5.10 Chapter nomenclature . . . 107

6 Estimating blade loads on a VAWT from velocity data 109

6.1 Chapter outline . . . 109 6.1.1 Section description . . . 110 6.2 Introduction . . . 111 6.3 Theoretical background of the method . . . 112 6.4 Verification of sensitivity of the method to data resolution with

NS-simulation data . . . 114 6.4.1 Validation of the calculation of the pressure gradient . . . 114 6.4.2 Comparison of the different formulations of the Flux Equation 115 6.4.3 Sensitivity to spatial grid resolution . . . 115 6.4.4 Sensitivity to phase/time grid resolution . . . 117 6.4.5 Comparison along rotation . . . 117

xiv CONTENTS

6.5 Evaluation of phase-averaged forces with phase-locked average data . . 118 6.6 The effect of measurement uncertainty . . . 120 6.7 Application to experimental force estimation . . . 123 6.7.1 Experimental setup . . . 123 6.7.2 Data acquisition and processing . . . 124 6.7.3 Phase averaging . . . 125 6.7.4 Flow acceleration term . . . 125 6.7.5 Analysis of the determination of blade loads . . . 127 6.8 Conclusions . . . 127 6.9 Chapter nomenclature . . . 129

III

The 3

D Near Wake of the VAWT

131

7 Experimental investigation of the tip vortex of a VAWT 133

7.1 Chapter outline . . . 133 7.1.1 Section description . . . 134 7.2 Introduction . . . 135 7.2.1 Experimental campaigns . . . 136 7.3 Smoke visualization and hot-wire measurements of the flow field in the

tip-vortex region . . . 136 7.3.1 Rotor model and experimental setup . . . 137 7.3.2 Spanwise wake expansion of the H-VAWT, smoke visualization

and hot-wire anemometry . . . 137 7.3.3 Upwind hot-wire measurements . . . 140 7.4 PIV experimental setup and flow conditions . . . 140 7.4.1 Rotor model and experimental setup . . . 140 7.4.2 Measurement planes and fields of view . . . 142 7.4.3 3D vorticity iso-surface representation . . . 143 7.4.4 2D tip-vortex slices in xz-planes . . . 144 7.5 Tip-vortex convection . . . 144 7.5.1 Trajectory in the z-direction . . . 153 7.5.2 Induction in the x-direction . . . 153 7.6 Evolution of tip-vortex strength . . . 154 7.7 The effect of tip shape on tip-vortex strength . . . 155 7.8 Conclusions . . . 158 7.9 Chapter nomenclature . . . 160

8 3D dynamics of the near wake of the VAWT 161

8.1 Chapter outline . . . 161 8.1.1 Section description . . . 162 8.2 Introduction . . . 162 8.3 The 3D free-wake panel model of the VAWT . . . 163 8.4 Development and convection of the tip vortex generated upwind . . . 163

CONTENTS xv

8.5 Validation with experimental results . . . 166 8.5.1 Location of the tip vortex . . . 166 8.5.2 Tip vortex strength . . . 169 8.6 Asymmetry in the y-direction of the wake sheet expansion and roll-up 171 8.7 3D wake effects on the downwind blade passage . . . 173 8.8 Wake at midspan . . . 177 8.8.1 Wake convection velocity . . . 177 8.8.2 Comparison with experiment . . . 181 8.8.3 2D vs 3D bound circulation and normal force . . . 182 8.9 The 3D effect of the pitching motion of the VAWT blade. . . 184 8.9.1 The effect of tip shape . . . 184 8.10 Conclusions . . . 186 8.11 Chapter nomenclature . . . 187

9 The impact of the 3D skewed wake of the VAWT 189

9.1 Chapter outline . . . 189 9.1.1 Section description . . . 190 9.2 Introduction . . . 191 9.3 Wake convection in skewed flow . . . 192 9.3.1 Experimental Investigation with PIV . . . 194 9.4 Asymmetry of the induction in the z-direction during the upwind

blade-passage . . . 197 9.4.1 Induction due to trailing vorticity . . . 197 9.4.2 Induction due to shed vorticity . . . 200 9.4.3 Induction in spanwise direction . . . 200 9.4.4 Influence of the skew angle on the tip vortex movement . . . . 200 9.4.5 Validation of the effect of skew on tip vortex strength . . . 201 9.5 Asymmetry in the z-direction of wake roll-up and expansion in the

leeward and windward regions . . . 203 9.6 Perpendicularity of the vortex sheet . . . 204 9.7 Effect of skew in bound, trailing and shed vorticity . . . 206 9.7.1 Trailing vorticity . . . 207 9.7.2 Bound vorticity . . . 207 9.7.3 Shed vorticity . . . 211 9.8 Smoke visualization validation of the convection of the

downwind-generated tip vortex . . . 213 9.9 Validation with experimental power measurements . . . 213 9.10 Conclusions . . . 221 9.11 Chapter nomenclature . . . 222

xvi CONTENTS

IV

Impact on aerodynamic design

223

10 2D and 3D effects of varying the constant bound circulation by

varying pitching axis and camber 225

10.1 Chapter outline . . . 225 10.1.1 Section description . . . 226 10.2 Introduction . . . 226 10.3 The effect of varying pitching axis in 2D . . . 229 10.3.1 Pitching axis location . . . 229 10.3.2 Effect on shed vorticity and power . . . 229 10.3.3 Effect on pressure distribution and loads . . . 232 10.4 Effect of camber . . . 234 10.4.1 Camber geometry . . . 234 10.4.2 Effect on shed vorticity and power . . . 236 10.4.3 Effect on pressure distribution and loads . . . 237 10.5 Impact of viscous effects . . . 238 10.6 3D effects . . . 242 10.7 Conclusions . . . 249 10.8 Chapter nomenclature . . . 250

V

Conclusions

251

11 Conclusions and recommendations 253

11.1 Contributions to the state-of-the-art . . . 253 11.2 Discussion of the conclusions . . . 256 11.2.1 2D wake . . . 257 11.2.2 3D wake . . . 263 11.2.3 Using the blade’s constant circulation term as a design variable 265 11.2.4 The end of streamtube models for VAWT . . . 266 11.3 Recommendations on future research . . . 267 11.3.1 2D flow research . . . 267 11.3.2 3D flow research . . . 268

Bibliography 271

CHAPTER

1

Thesis outline

The aerodynamics of the lift-driven Vertical Axis Wind Turbine (VAWT) are defined by a rotational motion of the blades around an axis perpendicular to the flow direction. The energy conversion is based on the azimuthal variation of the bound circulation on the blade, with an inherently unsteady operation, resulting in a wake composed of shed vorticity, and, in 3D flow, also trailing vorticity.

The geometry of the rotor implies the occurrence of blade-wake interaction, and, commonly, dynamic stall.

The analysis, modeling and design of the VAWT has challenged the wind energy community for many decades; this lack of knowledge has severely limited the devel-opment of the VAWT, giving rise to the myth that the VAWT rotor is inherently inefficient (in comparison with the more conventional Horizontal Axis Wind Turbine - HAWT) or too complex for commercial implementation.

The current momentum balance models for VAWT tend to underestimate the contribution of the leeward, downwind and windward regions of the rotation. The analysis is based on an erroneous and misleading division of the VAWT into upwind and downwind actuator disks, where the downwind actuator disk would be operating in a flow with a lower content of energy.

In this research work, we take a different path on the analysis of the VAWT; instead of considering a rotor that creates a perturbation on the flow (wake and induction field), we will consider an unsteady wake, to which a rotor system is associated.

At the end of this dissertation, we aim at presenting a clearer and more insightful understanding of the 2D and 3D aerodynamics from the point of view of the wake, that will simplify and significantly improve the aerodynamic analysis, design and optimization of new VAWT rotors for energy conversion and propulsion.

2 THESIS OUTLINE 1.1

1.1

The research question

The research developed for this thesis aims at understanding the wake, and its relation with energy conversion and the loading on the rotor system.

Four main questions drive this research:

• What is the relation between blade loading and energy conversion? • How does the near wake of the VAWT develop?

• What is the difference between the 2D and the 3D wake? • How does understanding the near wake improve our design?

We will now analyze each of the main research questions.

1.1.1

What is the relation between blade loading and energy

conversion?

The total energy extracted from the flow by the VAWT is the result of the work of the forces over the full rotation of the blade. There is thus a relation between the loading on the blade and the energy exchanged by the rotor. The objective of the aerodynamic design is to maximize the extraction of energy for a given expenditure of resources; this expenditure is highly affected by the aerodynamic loading on the blades.

The wake is a consequence of the energy exchange on the rotor, consisting of a pressure/vorticity structure which induces a velocity/pressure field around the blade. In this thesis, we analyze the generation of the wake, how it relates to blade loading and the induction field, both in 2D and 3D flow. We decouple blade loading from energy exchange, taking advantage of the properties of the shed vorticity; we thus can split the rotor design into design for energy conversion and design for loading, decreasing the constraints. The results have significant impact on the design of the rotor.

We propose a new view on rotor and blade design, decoupling the design into rotor scale and blade scale for 2D flow and energy exchange, and coupling it again in 3D flow, aiming at decreasing the impact of finite span effects.

1.1.2

How does the near wake of the VAWT develop?

To analyze the wake and the rotor we will consider two scales: rotor scale and blade scale.

At the rotor scale, the wake development expresses the energy exchange process; understanding the wake at the rotor scale allows us to maximize the energy extraction, especially in 3D flow.

Contrary to the common division into upwind and downwind actuators, we split the rotor scale into four regions: windward (315◦ < θ < 45◦), upwind (45◦ < θ <

135◦), leeward (135◦< θ < 225◦) and downwind (225◦< θ < 315◦) (see Figure 2.1 in Chapter 2). This segmentation is necessary to correctly understand the induction field, and accurately account for the downwind region and development of the wake inside the rotor volume.

1.1 THE RESEARCH QUESTION 3

The wake at the rotor scale is in fact generated at the blade scale, by the interaction between the boundary condition of the blade and the flow; this connects the question of energy conversion and blade loading. Understanding this connection allows us to separate the two design constraints of load and power.

At the blade scale, the VAWT commonly experiences dynamic stall and blade vortex interaction. These local events will actually affect the distribution of vorticity at the rotor scale, changing the induction field and the energy conversion process. We must then evaluate the evolution of the convection of vorticity in dynamic stall and the blade-vortex interaction.

To understand the development of the near wake, we must be able to experimen-tally visualize and quantify it, and afterwards model/reproduce it.

Measuring and visualizing the near wake of the VAWT

The simulation of the near wake is impaired by the specific limitations of each model. Experimental aerodynamics not only provides data for validation of the models, it is also an important tool to visualize and quantify effects that the numerical models might not reproduce, or that the analysis might disguise.

In this thesis, we use Particle Image Velocimetry, rotor loading measurements, hot-wire anemometry and smoke visualization to measure and analyze the 2D (Chap-ters 4, 5 and 6) and 3D (Chap(Chap-ters 7, 8 and 9) near wake flow.

Modeling the near wake of the VAWT

Three types of models are commonly used in the analysis of the VAWT.

Multiple streamtube models are the most common approach to model the VAWT. These are actuator momentum-balance based models, which estimate the induction by balance of the average work of the forces applied at a certain section of the rotor area. Multiple streamtube models have difficulty accounting for the dynamics of the wake. Current formulations of these models commonly disregard the lateral expansion of the wake and treat the VAWT as two independent actuator disks.

Vortex models use a Lagrangian approach to account for the evolution of the wake; due to the complexity of the VAWT, the correct modeling of the wake is essential. The vortex model presents a challenge in the time integration of the wake when vortex-vortex interactions and blade-wake interactions occur, and in its high computational cost when trying to model viscous effects.

NS models are commonly referred to as CFD simulations and can be used to

investigate the impact of viscous effects of vorticity, such as dynamic stall. But what is the impact and the importance of correctly modeling the shed vorticity?

1.1.3

What is the difference between the 2

D and the 3D wake?

The lift-driven VAWT is, aerodynamically, a 2D wind-energy conversion system. The energy conversion process is defined in the plane normal to the axis of rotation, and

4 THESIS OUTLINE 1.2

the wake is composed of shed vorticity.

However, the construction of a real VAWT implies the existence of a finite blade span, and thus a 3D flow with spanwise distributions, the appearance of trailing vorticity, and in particular, the tip vortex. The dynamics and induction of the 3D flow are then significantly different from the 2D flow, both at the rotor and blade scales, in particular, at the blade tips and downwind blade passage.

The third spatial dimension also allows for the occurrence of a misalignment be-tween the direction of the flow and the normal to the rotor axis, resulting in skewed flow. Skewed flow has not previously been thoroughly researched, despite its impor-tance for urban and wave-energy conversion applications.

1.1.4

How does understanding the near wake improve our

de-sign?

The design process is a balance of constraints, trying to fulfill the objective of the system with the lowest expenditure of resources. A conflict usually arising in wind turbine rotor design is the maximization of energy conversion and the concurrent minimization of loads.

The generation of the wake is a result of the spatial and temporal distribution of the loading at the blade scale. By understanding the generation of the wake, we can thus understand the loading experienced by the blade, or at least, how to vary the loading while still generating the wake we require for the energy exchange process.

In this, we analyze the vortical field by breaking it down into bound, shed and trailing vorticity, which for the lift-driven VAWT, correspond to analyses on blade loading, energy exchange and 3D inefficiency, respectively.

We thus stop analyzing the blade as a load generating element, and instead analyze it as a wake generating element, moving the analysis from loading (a design constraint) to energy exchange (our design driver).

1.2

Structure of the dissertation

1.2.1

Introduction

Chapter 2 - Introduction to the aerodynamics of the VAWT In the last

years, the development of VAWT rotors for the built environment wind-energy con-version, wave/water current-energy conversion and large scale offshore wind-energy conversion has lead to an increasing research of the VAWT.

In Chapter 2 we review some of the most important topics on the aerodynamics of the VAWT, as they relate to the research questions stated in Section 1.1.

1.2.2

The 2

D Near Wake

Chapter 3 - Improving on Double Multiple Streamtube models for the

VAWT using Vortex Models In this section we propose a new approach to the

conventional Double Multiple Streamtube model. The proposed method significantly improves performance prediction by taking into account the expansion normal to the

1.2 STRUCTURE OF THE DISSERTATION 5

incoming flow, and developing a new approach to model the wake expansion inside the rotor and at the downwind part of the rotation.

The work also tackles and defines the pitching movement/flow curvature effect as a form of varying a constant bound circulation term, decoupling the different components of loads, wake generation, energy exchange and induction.

The analysis in the chapter, combined with Chapter 10, leads to the conclusion that momentum methods are no longer necessary for the VAWT, as they are much less accurate and computationally more costly than a vortex model approach.

Chapter 4- 2D Particle Image Velocimetry of the wake of the VAWT in

dy-namic stall Dynamic stall is dominant in the aerodynamics of high-solidity VAWT

at low tip-speed ratios.

This chapter presents the results of a 2D Particle Image Velocimetry experimental research on a single-bladed VAWT at low tip-speed ratios. The results quantify the location and strength of the shed vorticity, clearly showing its impact on the flow field in comparison with attached flow conditions.

We also analyze the interaction between leading-edge and trailing-edge vorticity, and in particular, the convection by the blade of the shed vorticity, in the leeward region of the rotation.

Chapter 5- 2D CFD simulation of dynamic stall on a VAWT The near

wake shed during dynamic stall has a large effect on the development of the flow, both around the airfoil and in the rotor space, as seen in Chapter 4. Chapter 5 presents the results of a 2D numerical Navier-Stokes simulation of the flow experimentally observed in Chapter 4. The impact of correctly modeling the shedding of the near wake is verified, as well as the effect of modeling the cluster of small vortices, instead of a single large vortex.

Chapter 6 - Estimating blade loads on a VAWT from velocity data The

experimental measurement of blade loads with conventional approaches is not feasible in almost all cases; the load data is usually limited in that it cannot account for friction and is of low accuracy.

The use of Particle Image Velocimetry enables the quantification of the flow ve-locity field; by applying the integral momentum equation, it is possible to determine the loads on the blade from the velocity field. Using the results of Chapters 4 and 5, and data from a new experiment, in Chapter 6 we evaluate the feasibility of using the method for determining the forces on moving blades in dynamic stall, including estimation of the impact of unsteadiness and uncertainty.

The integration of the forces from the velocity field overcomes the difficulties and limitations presented by pressure sensors for local section loads.

The analysis closes the approach in 2D flow for understanding all the scales of the rotor aerodynamics, by analysis of blade scale from the near-wake point of view.

6 THESIS OUTLINE 1.2

1.2.3

The 3

D Near Wake

Chapter 7 - Experimental investigation of the tip vortex of a VAWT The

exchange of energy, the shedding and expansion of the wake, of the VAWT occurs in the 2D plane perpendicular to the axis of rotation. However, the existence of a blade tip in the 3D VAWT generates an additional tip vortex; this tip vortex has a severe impact on the 3D flow, and its dynamics change both in terms of its generation at different azimuthal positions and in terms of its trajectory and dissipation. Chapter 7 presents the experimental (PIV, smoke visualization and hot-wire anemometry) in-vestigation into the generation and development of the tip vortex, including the effect of tip shape.

Chapter 8 - 3D dynamics of the near wake of the VAWT Chapter 8

com-bines the experimental measurements from Chapter 7 with simulations of the VAWT from a 3D unsteady free-wake panel model, to understand the dynamics of the 3D near wake; convection, expansion of the wake, vortex roll-up and the induction field, decomposed into trailing and shed vorticity effects.

Chapter 9 - The impact of the 3D skewed wake of the VAWT The

oper-ation of the VAWT in urban environment, and as a wave-energy converter, leads to the operation of the rotor in conditions where the flow is not normal to the axis of rotation - skewed flow. Chapter 9 presents experimental and numerical research on the generation and development of the wake in skewed flow. Experimental perfor-mance measurements and flow visualization/quantification with smoke visualization and PIV are used in combination with 3D free-wake panel model simulations to un-derstand the asymmetry of the flow in relation to the induction field, blade flow, wake dynamics, and impact on energy conversion.

1.2.4

Impact on aerodynamic design

Chapter 10 - 2D and 3D effects of varying the constant bound circulation

by varying pitching axis and camber In Chapter 10, we analyze the constant

term of the bound circulation of the blade and demonstrate how it can be used for decreasing the 2D viscous inefficiency and the 3D inefficiency due to trailing vorticity. We use the analysis of the previous chapters to dissociate the different components of the wake and loading, and analyze its isolated effects.

1.2.5

Conclusions and impact on future research

Chapter 11 - Conclusions and recommendations In Chapter 11 we discuss the

main conclusion of this research work and the implications for VAWT aerodynamics, design and future research.

1.2 STRUCTURE OF THE DISSERTATION 7

Chapter 3 Improving on Double Multiple Streamtube models for the VAWT using Vortex Models

Chapter 4 2D Particle Image Velocimetry of the wake of the VAWT in dynamic stall

Chapter 5 2D CFD simulation of dynamic stall on a VAWT

Chapter 7 Experimental investigation of the tip vortex of a VAWT Chapter 8 3D dynamics of the near wake of the VAWT

Chapter 9 The impact of the 3D skewed wake of the VAWT

Chapter 10 2D and 3D effects of varying the constant bound circulation by varying pitching axis and camber

Chapter 2 Introduction to the aerodynamics of the VAWT 2D Near Wake

3D Near Wake

Implications on VAWT design VAWT Aerodynamics

Chapter 6 Estimating blade loads on a VAWT from velocity data Part I

Part II

Part III

Part IV

Chapter 11 Conclusions and recommendations Part V

Part I

Introduction

CHAPTER

2

Introduction to the aerodynamics of the VAWT

2.1

Vertical Axis Wind Turbine aerodynamic

re-search

The research on Vertical Axis Wind Turbine aerodynamics had its peak during the 1980’s, with the maturity of streamtube momentum-balance models and the first development of vortex models and CFD simulations (see Wilson (1980), Kirke (1998) and Paraschivoiu (2002)).

The downturn of the wind energy industry in the US and Canada, and the pro-gressive development of the Horizontal Axis Wind Turbine led to the acceptance of the HAWT as the standard for megawatt scale wind energy conversion. As a conse-quence, wind turbine rotor aerodynamics research became dominated by the HAWT, and much of the aerodynamics research on the VAWT was discontinued, despite the success of the first generation of VAWT (for an historical overview see Gipe (1995)). Throughout the 1990’s and early 2000’s it is still possible to find some research on the aerodynamics of the VAWT, much of it a follow-up/improvement on models initially developed during the previous decade.

The recent exponential development of wind energy and wind energy research has provided for a new interest on VAWT, no longer for application on the 1M W scale wind conversion systems, but on the extremes of the range:

• Small rotors (< 100kW ) for application in the urban environment. • Multi-megawatt (> 10MW ) floating offshore VAWT.

• Wave/tidal/current rotor application.

However, for the aerodynamicist, the most important consideration is the com-plexity of the aerodynamics of the rotor. The VAWT is by far the more interesting of the two mainstream lift-driven conversion systems:

• The energy conversion is based on the variation in time of the circulation on

12 INTRODUCTION TO THE AERODYNAMICS OF THE VAWT 2.2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −1.5 −1 −0.5 0 0.5 1 1.5

Figure 2.1: Representation of the 2D VAWT and notation of azimuthal position. the blade, with an inherently unsteady operation.

• The geometry of the rotor implies the occurrence of blade-wake interaction,

including interaction between blade and multiple wakes at one instant/location.

• The occurrence of dynamic stall is a common event.

• The wake is necessarily composed of shed and trailing vorticity.

• The actuator surface of the rotor is double (upwind and downwind halves),

operating in 4D (space and time).

• The blade experiences both translation and pitching, with the suction and

pres-sure sides of the blade interchanging during the revolution

• The flow is inherently asymmetric.

• Although insensitive to yaw, it is sensitive to skewed flow, which results in a

spanwise asymmetry.

In this chapter we will review some of the aerodynamic research topics essential for VAWT aerodynamics and related to the research questions posed for this thesis.

2.2

2D VAWT aerodynamics

The lift-driven VAWT is, aerodynamically, a 2D wind-energy conversion system. The energy conversion process occurs in the plane normal to the axis of rotation, contrary to the HAWT, where the energy conversion occurs in the volume derived from the revolution of the plane including the axis of rotation.

Figure 2.1 shows the geometry of the lift-driven VAWT (example with 3 blades) in the flow plane. The blades are at a radial distance R from the axis, rotating at

2.2 2D VAWT AERODYNAMICS 13

Figure 2.2: Representation of a 2D VAWT and wake (see also Figure 3.1). an angular velocity ω. The axis of rotation is aligned with the z-axis, normal to the unperturbed incoming flow U_∞.

In this thesis, we analyze the VAWT from the perspective of the wake. The wake of the 2D VAWT is generated as a consequence of Kelvin’s theorem, which states that, for an incompressible inviscid fluid flow, the total rate of change of circulation is null, for a given fluid region consisting of the same fluid particles (see Katz and Plotkin (2000)). The wake of the VAWT is composed of shed vorticity that balances the blade’s bound circulation, as the bound circulation varies along the rotation. Figure 2.2 shows an example of the wake of a 2D vertical axis wind turbine.

The energy extracted by the rotor results in an induction field generated by the rotor and wake; thus, the energy conversion is based on a azimuthal variation of the circulation on the blade, which results in the shed vorticity of the wake.

We can compare the vertical axis rotor configuration with the currently more industrially applied Horizontal Axis Wind Turbine (HAWT) configuration. Figure 2.3 shows a representation of a HAWT and its wake, with the rotation axis aligned with the unperturbed wind velocity U_∞.

The wake generated by the HAWT is composed of trailing vorticity, a result of Helmholtz’ second theorem (see Katz and Plotkin (2000)), which states that, for an incompressible inviscid fluid flow, a vortex filament cannot start or end in the fluid, and must therefore form a closed path. The bound circulation at the finite rotor blade must be continued as trailing vorticity in the flow, closing the vortex filament ring at the start-up shed vortex located infinitely downwind. Helmholtz’ third and fourth theorems (see Katz and Plotkin (2000)) require the strength of a vortex filament to be constant along the filament. Thus, the strenght/circulation of the wake is defined by the total bound circulation on the blade.

14 INTRODUCTION TO THE AERODYNAMICS OF THE VAWT 2.2

Figure 2.3: Representation of the 3D HAWT and wake.

Vertical Axis Wind Turbine and the wake of the Horizontal Axis Wind Turbine:

• In the VAWT, the wake is composed of shed vorticity, a result of the energy

exchange process that implies a variation over the rotation of the blade’s bound circulation. In the HAWT, the wake is composed of trailing vorticity, a result of the finite span of the blade.

• In the VAWT, the strength of the wake is determined by the component of the

blade’s bound circulation which varies during the rotation. In the HAWT, the strength of the wake is determined by the total bound circulation on the blade. A base tool for the analysis of propellers and horizontal axis wind turbines is the actuator disk concept (see Burton et al. (2001) and Glauert (1947)). For the HAWT, the 3D rotor is primarily reduced into a 2D actuator surface (by eliminating the thickness of the rotor) and furthermore, by taking into account the axisymmetry, reduced into a 1D actuator strip in an axisymmetric flow.

Figure 2.4 shows an axisymmetric actuator strip representation of the HAWT; a streamtube, delimited by two streamlines that intersect the rotor diameter at the tips, expresses the expansion of the flow. The velocity decreases along the streamtube as a function of the induction generated by the wake, and the pressure drop at the actuator strip balances the force applied by the rotor on the flow. The difference in the kinetic energy of the flow infinitely farupwind and infinitely fardownwind in the streamtube (where the local pressure equals the unperturbed static pressure value) balances the work on the flow due to the force exerted by the rotor (the energy balance).

The actuator strip on a streamtube concept thus connects the loading on the rotor with energy exchange and the wake’s induction and expansion.

2.2 2D VAWT AERODYNAMICS 15                    !  "  $ %  

Figure 2.4: Actuator disk representation of a HAWT rotor.

 

  

Figure 2.5: Wake model on actuator disk representation of the HAWT rotor; grey region

representing wake.

wake model. For the HAWT, the strongest trailing vorticity (usually) occurs at the blade root and tip. We can simplify the rotor wake model as single vortex filaments emanating from the tip and root; the (symmetric and overlapping) root vortices cancel each other out, and the result is the actuator strip representation, with a continuous vorticity distribution along the streamline that crosses the blade tip (Figure 2.5).

The success of this method has lead other authors to apply it to the VAWT (see Templin (1974) and Wilson and Lissaman (1974)). In the case of the VAWT, the simplification of the actuator system consists on collapsing the circular rotor in wind direction, resulting in the exact same actuator strip concept as described in Figure 2.4. The same result as for the HAWT can be obtained for the simplified wake model applied to the actuator strip model of the 2D VAWT. The strongest shed vorticity is shed at the leeward and windward regions (see Figure 3.6 in Chapter 3). We can simplify this by assuming that all vorticity is shed at exactly θ = 0◦ and θ = 180◦; in our actuator strip, the wake is then shed at the extremities, resulting again in the representation of Figure 2.5.