CFD analysis of Darrieus-Type wind turbine in skewed flows

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Ringraziamenti

Ringrazio in primis l’Ing. Stefania Zanforlin per avermi pazientemente se-guito durante tutto l’arco della tesi, per il supporto datomi anche durante il periodo di studio all’estero.

Ringrazio l’Ing. Maurizio Collu e il Prof. Andrew Shires, che, congiunta-mente con l’Ing. Zanforlin, mi hanno dato la possibilit´a di lavorare a questo progetto di ricerca e mi hanno seguito in qualit´a di supervisor durante il periodo a Cranfield. Ringrazio il Prof. Giovanni Lombardi, che ha fornito un aiuto importante durante lo svolgimento della tesi.

Ringrazio l’Universit´a di Pisa e la Cranfield University per aver contribuito al concretizzarsi di questa esperienza.

Grazie a tutti i compagni dell’universit´a, tra cui Domenico, Massimo, Danila, Beatrice, Rosanna, Andrea, Giorgio, Luigi, Simone e tutti gli altri con cui ho condiviso gioie e dolori della carriera universitaria.

Grazie anche agli amici della Contrada e di paese, che mi hanno regalato momenti felici anche durante il periodo in Inghilterra.

Ringrazio in maniera particolare la mia famiglia, sempre vicina e paziente con me in questi anni e specialmente in questo periodo. Sempre particolar-mente, ringrazio la mia fidanzata Caterina, cos´ı indispensabile e unica nel darmi la forza per raggiungere ogni traguardo.

Un grazie ai miei zii, a tutti i parenti e ai genitori della mia fidanzata per aver sempre creduto in me. Ringrazio anche Gabriele, compagno di avven-ture fin dall’infanzia e amico fedele.

Un grazie enorme allo zio Mauro, ai miei nonni Rovaldo, Miranda, Miranda e maggiormente a Corrado, che da lass ´u mi ha aiutato nei momenti difficili e che ha contribuito insieme agli altri al raggiungimento di questo impor-tante obiettivo.

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List of Figures

1.1 Modern HAVT (left), windmill (center), American multi-bladed wind-pump (right). . . 16 1.2 Different types of VAWTs. . . 17 1.3 Cp as function of TSR for different types of wind turbines. . . 18 1.4 3.8 MW ´Eole VAWT (left), 0.5 MW VAWT-850 H-rotor

(right-top), Mono V-VAWT concept (right-bottom). [Shires, 2013] . 20 1.5 NOVA V-VAWT concept (left) and Aerogenerator-X (right). . 21 1.6 The progression of substructures from shallow water to deep

water. [Jonkman et al., 2007] . . . 22 1.7 Artistic view of the concept. [Vita, 2011] . . . 23 1.8 FAWT-S (left) and FAWT-C (right) concept. [Akimoto et al.,

2011] . . . 24 1.9 FAWT in operating condition. [Akimoto et al., 2011] . . . 24 1.10 Vertiwind project. [Cahay et al., 2011; Vita, 2011] . . . 25 1.11 Flow velocities of a lift-driven wind turbine. [Islam et al., 2006] 26 1.12 Sign convention used for force coefficient. [Akins, 1989] . . . 27 1.13 Betz streamtube. [Leucci, 2010] . . . 29 2.1 Development of dynamic stall on an blade. [Larsen et al.] . . 33 2.2 Different phases occurring in the dynamic stall. [Carr et all.,

1996] . . . 34 2.3 Example of PIV measurements: streamlines visualization (up)

and vorticity magnitude measurements (down). [Ferreira et al., 2008; Fujisawa et al., 1998] . . . 35 2.4 Semi-emphirical models compared with experimental

mea-surements. [Larsen et al., 2007] . . . 37 2.5 Flow visualization trough PIV and numerical models. [Barakos

et al., 2003] . . . 38 2.6 Principle of Multiple streamtube model divided by uniform

M_{θ. [Beri et al.] . . . .} ₄₂ 2.7 Airfoil velocity and force diagram. [Beri et al.] . . . 43 2.8 Improvements of DMST model. [Batista et al., 2012] . . . 44 2.9 Velocity flowfield got by CFD simulation. [Howel et al.] . . . 45 2.10 Comparison between LES and URANS models regarding the

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2.11 Numerical and experimental tangential and normal force

co-efficient at λ = 1.11 and λ = 0.70 . [Li et al., 2013] . . . 48

2.12 Tangential and normal forces coefficient for RANS model. [Li et al., 2013] . . . 48

2.13 Power coefficient got from URANS simulation. [Zhang et al., 2013] . . . 49

2.14 Comparison of torque generation between 2D and 3D models for a H-type VAWT. [Howell et al., 2010] . . . 50

2.15 Contours of vorticity magnitude for a S-VAWT at a wind speed of 5.07 m/s. [Howell et al., 2010] . . . 51

2.16 Power coefficient for a S-VAWT at a wind speed of 5.07 m/s. [Howell et al., 2010] . . . 51

3.1 Wind turbine scheme . . . 53

3.2 DOE/SANDIA 17m Darrieus Wind Turbine. [Johnston, 1982] 54 3.3 2D domain geometry. . . 56

3.4 2D mesh. . . 57

3.5 Detail of the 2D mesh. . . 57

3.6 Detail of 2D mesh near to the blade. . . 58

3.7 3D grid geometry. . . 59

3.8 Detail of the 3D geometry of the wind turbine. . . 59

3.9 Surface mesh on the blades. . . 60

3.10 Volume mesh: all mesh (top), mesh details around blade (bottom-left) and prism layers at leading edge (bottom-right). . . 61

3.11 H-Darrieus Wind Turbine analized in open jet wind tunnel test of Delft University of Technology.[Mertens, 2002] . . . . 61

3.12 3D grid geometry for small H-Darrieus Wind Turbine. . . 63

3.13 Surface mesh. . . 63

3.14 Surface mesh details: dynamic mesh (left) and blade surface mesh (right). . . 64

3.15 Volume mesh: all domail (top), mesh details at leading edge(bottom-left) and trailing edge(bottom-right). . . 64

3.16 Wall-type boundaries: SANDIA 17m Darrieus-Type Wind Tur-bine (left) and H-Darrieus Wind TurTur-bine (right). . . 66

4.1 Cm as function of flow time for TSR=4.6 . . . 69

4.2 Ct values at TSR=4.6 (low wind-speed case)for three different meshes: coarser (620 nodes on airfoil), medium (1240 nodes on airfoil) and finer (1920 nodes on airfoil). . . 69

4.3 Normal (top) and tangential (bottom) forces at TSR=2.33 (high wind-speed case). . . 71

4.4 Angle of attack (AoA) at different TSRs. . . 71

4.5 Normal (top) and tangential (bottom) forces at TSR=4.6 . . . 72

4.6 Blade passing in downwind part at TSR=4.6 . . . 73

4.7 Pressure field around blade at θ=100°and θ=240°. . . . 73

4.8 Normal (top) and tangential (bottom) force coefficients at TSR=3.09 . . . 74

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4.9 2D streamlines at TSR=3.09. . . 75 4.10 Turbulence field: around the all turbine (top) and around

blade in the downwind part (bottom). . . 76 4.11 Normal (top) and tangential (bottom) force coefficients at TSR=2.33 . . . 77 4.12 2D streamlines at TSR=2.33 . . . 78 4.13 Details of pressure (Pa)(left), vorticity (1/s)(center),

turbu-lence (%)(right) field in upwind zone at TSR=2.33 , obtained by the 2D model. . . 79 4.14 Pressure field in x − z plane at θ=110°for TSR=2.33 . . . . 80 4.15 Details of pressure field (top) and relative velocity vectors

coloured by turbulence intensity around blade, in x − z plane at θ=110°for TSR=2.33 . . . . 81 4.16 Detail of pressure field on suction surface of the blade at

θ=110°for TSR=2.33 . . . . 82 4.17 Cp and power curve as function of TSR at 42.2 RPM . . . 82 5.1 Cm as function of the flow time for TSR=3 . . . 85 5.2 Mesh sensitivity analysis between MESH 4 and MESH 5 (finer)

at TSR=3 in normal flow condition. . . 85 5.3 Cp curve for experimental H-Darrieus wind turbine. . . 86 5.4 Pressure on blades fork-ε RNG model (top) and k-ω SST model

(bottom) at TSR=3.4 . . . 86 5.5 Wall shear on blades for k-ε RNG model (top) and k-ω SST

model (bottom) at TSR=3.4 . . . 87 5.6 Total torque coefficient (Cm) for k-ε RNG and k-ω SST model

at TSR=3.4 . . . 87 5.7 Cp ratio fot small H-Darrieus Turbine at different tilt angles. 89 5.8 TSR ratio fot small H-Darrieus Turbine at different tilt angles. 89 5.9 Normal force (top) and tangential force (bottom) coefficients

as function of azimuthal angle at TSR=3 and different tilt an-gles. . . 90 5.10 Pressure field around blade section in correspondence of the

equatorial plane in upwind part, for normal flow (left) and Φ = 15◦(right) condition. . . 91 5.11 Pressure field around blade section in correspondence of the

equatorial plane in downwind part, for normal flow (left) and Φ = 15◦(right) condition. . . 92 5.12 Velocity field at different tilt angles. . . 93 5.13 Streamlines about absolute velocity, for Φ = 0◦ and Φ = 15◦

tilt conditions. . . 94 5.14 Pressure coefficient distribution at different chord ratio and

at different x/z ratio, considered at different angles in down-wind zone, for Φ = 0◦ (blue curve) and Φ = 15◦ (red curve) conditions. . . 95

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5.15 Pressure coefficient distribution at different chord ratio and at different x/z ratio, considered at different angles in down-wind zone, for Φ = 0◦ (blue curve) and Φ = 15◦ (red curve) conditions. . . 96 5.16 Vorticity contours at Φ = 0◦(top) and Φ = 15◦(bottom). . . 97

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List of Tables

2.1 Main features of 2D and 3D CFD analysis. . . 49

3.1 Wind turbine characteristics . . . 53

3.2 Pressure probes location on the blade . . . 55

3.3 Details of employed grids. . . 58

3.4 Details of 3D grid. . . 59

3.5 H-Darrieus Wind Turbine details. . . 62

3.6 Main wind tunnel features. . . 62

3.7 Details of 3D grid for H-Darrieus small turbine. . . 63

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Introduction

The wind energy is one of the main sources of renewable energies that has seen a big growth in the last 20 years, becoming the second power source behind the hydropower generation. The worldwide wind capacity reached 336 GW by the end of June 2014, and it grew by 5,5% within 6 months, after 5% in the same period in 2013 and 7,3% in 2012.(WWEA report, 2014)

Currently most wind power systems consist of horizontal axis wind bines (HAWTs), in mid to large-scale wind farms. These conventional tur-bines are often favoured due to higher efficiency, but they are not neces-sarily suitable for all purposes. During the first decade of 21st century a resurged and increasing interest for the vertical-axis wind turbines (VAWTs) occurred. VAWTs have been considered a promising alternative to HAWTs especially for off-shore applications, due to intrinsic characteristics of this type of wind turbine (Collu et al., 2014), and for micro-generation in urban environment (Mertens, 2002).

The aim of this work is to asses if a 3D CFD model can be used as a forecast instrument to analyze the performances of VAWTs, especially of Darrieus-Type turbine, underlining its main features and limits.

In Chapter 1 and 2, the general aspects of these wind turbine are showed, describing the differences between HAWTs and VAWTs. After a brief state of art of the lift-driven vertical axis wind turbines, some off-shore applica-tion concepts are resumed, and general mathematics correlaapplica-tions useful for the analysis are defined. After, the principal phenomena which take places in the aerodynamic charaterization of VAWTs are briefly described, doing also a comparison of the forecast models used across the years to evaluate the power output by these turbines.

Chapter 3 shows the methodological approach to the problem using a CFD model, both 2D and 3D, and the main settings for the CFD simula-tions.

Chapter 4 displays the validation of the model described in the previous chapter, assessing the features and the limit of both 2D and 3D simulations. The prediction of aerodynamic forces acting on turbine represents a chal-lenging analysis and this chapter describes the ability of the 3D model to

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do it, more than the 2D one.

Finally, Chapter 5 describe the performances of a small-scale H-Darrieus wind turbine assumed mounted on a floating platform for off-shore appli-cation in deep-water loappli-cation. This analysis is based on quasi-static simu-lations, in order to compare simulated and experimental result, and shows the influence of the skewed flow on the aerodynamic forces, resulting in a augmentation of the power coefficient at higher tilt angles of the axis of the turbine.

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Chapter 1 General aspects

This chapter gives an overall description of the main characteristics of the Vertical Axis Wind Turbines (VAWT), with a focus on the state of art of lift-driven VAWTs, subjects of the present work. After, a brief description of the existing floating platforms for off-shore applications of wind turbines are described, in order to contextualize the possible use of Darrieus-Type in that field. At the end, an overview of the main parameters, used for the analysis of VAWTs, is showed.

1.1 Di

fferent types of Wind Turbines

It is possible to divide briefly all the wind turbines in two main classes, based on the different direction of the axis of revolution: Horizontal Axis Wind Turbine (HAWT) and Vertical Axis Wind Turbine (VAWT)

1.1.1 HAWT

The HAWTs are characterized by an horizontal axis of revolution, and they are mainly composed of a tower, used as support, and a rotor which includes a different number of blades depending on the model adopted. A first rude example of this turbine is thewindmill, developed in Europe from the 12th century for grinding grain applications; it was followed by the American multi-blade wind-pump, composed of an high number of blades and self-orienting rotor according to the wind direction.

The modern wind turbine provides different configurations, different sizes according to the power output (from hundreds of W to hundreds of MW) and are used to be installed in wind farm. The dimensions are variable and they can provides towers 90 meters high and rotor diameters till 150 meters.

The main features of this class of wind turbine are:

• the possibility of changing the pitch angle, in order to optimize the efficiency of the turbine;

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Chapter 1. General aspects

Figure 1.1: Modern HAVT (left), windmill (center), American multi-bladed wind-pump (right).

• high efficiency, with all blades rotating in direction opposite to the wind, which generate power during the all revolution;

• difficulties and costs of installation, due to the big dimensions; • high environmental impact;

• complex control system, able to change the rotor orientation so that it is always oriented to the main wind direction.

1.1.2 VAWT

This class of wind turbines is characterized by the vertical direction of the axis of revolution. They do not need a control system to change the rotor orientation according to wind direction changes, but they get the disadvan-tage of a pulsating torque. Different configurations can be adopted, that prevents the installation directly on the ground or with the use of tower.

The VAWTs include varying type of turbine, and the most common ones are showed below:

• Darrieus wind turbine: developed by the namesake engineer, it has a good efficiency but self-starting problems and it needs external sources for the starting;

• Giromill (or H-Darrieus wind turbine): it belongs to the Darrieus-Type turbine, with straight blades;

• Cycloturbine: it is mainly like a Giromill turbine with the possibility of change of relative angle of pitch with respect to the axis of revo-lution, with the advantage of a power output value almost constant. Generally, it is use in three-blades configuration;

• Savonius wind turbine: it is use in low-power demanding application, where the main goal is the low cost instead of efficiency. This type of

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Chapter 1. General aspects VAWT is used for domestic power generation purposes, and it have not self-starting problems.

Figure 1.2: Different types of VAWTs.

The main features of VAWT are summarized below:

• the facility of maintenance due to the installation of the main control systems and of the generator near the ground;

• the possibility of not using pitching control systems for the blades and orientating system for the axis of revolution;

• the possibility to integrate the VAWTs in buildings;

• they need low wind-speed to start and not high wind speed for the functioning;

• the independence of functioning from the wind direction;

• less efficiencies and power outputs that the HAWT, but new develop-ments tested efficiencies close to the one reached by horizontal axis turbine especially for Darrieus Type turbines;

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Chapter 1. General aspects • the presence of the pulsating torque, which introduces additional stresses

to the structure of the turbine;

• the possibility of packing the VAWTs closer than the HAWTs, because the wake in the downwind part of the rotor dissipates much quicker than those of HAWTs (Borg et al., 2012).

The Darrieus wind turbine, Giromill and Cycloturbine can be grouped in the class of the so-calledlift-driven turbine, while the Savonius wind tur-bine belongs to thedrag-driven turbine class.

The different types of VAWT summarized above are only the most known one, but there are many other types and configurations which also includes hybrid vertical axis wind turbines, composed of lift-driven and drag-driven aero-generator.

Figure 1.3: Cp as function of TSR for different types of wind turbines.

Fig.1.3 shows the coefficient of power (Cp), defined as the ratio between the power output and the maximum power which can be extracted from wind, as function oftip-speed ratio (TSR), i.e. the ratio between the tangen-tial velocity calculated at the tip of the blade and the undisturbed velocity of the wind. As it is possible to see, VAWTs take places in the low Cp field, while the high speed propellers, that mean HAWTs, can reach the highest values of Cp. For this reason, the last ones are adopted for big power output applications and, during the past years, they were fully studied to get very high efficiencies (Leucci, 2009/2010).

The attitude of VAWTs to work at lower wind speeds than the HAWTs is also displayed in the graph; if the rotational velocity of the turbine is kept con-stant, the latests verify high Cp at high wind speed velocities, while the

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Chapter 1. General aspects former reach the maximum power output at low wind speed. Only the Darrieus-Type wind turbines can approach the efficiencies showed by the horizontal axis wind turbines, more and more closer over the years thanks to a renewed interests for the reasons showed above.

1.2 State of art for Darrieus-Type wind turbines

While early examples of VAWTs were developed by the Persians over 1000 years ago, the modern VAWT was developed in the years following the first oil crisis of 1973. These later designs are based on an idea patented in 1922 by the French engineer, Georges Darrieus, with straight or curved ”lifting” blades rotating about a vertical tower.

During the 1970s and 1980s significant research and development ef-fort in both the USA ans Canada led to several curve-bladed (oreggbeater) Darrieus test turbines. These prototypes proved to be quite efficient and reliable (Eriksson et al., 2008).

The largest turbine, built in 1986, was 96 m tall ´Eole Darrieus wind turbine pictured in Fig.1.4, located at Cap-Chat, Qu ˜A¨bec, Canada. With a rated maximum power of 3.8 MW, it produced 12 GWh of electric energy during the 5 years it operated but was shut down in 1993 owing to a failure of the bottom bearing.

Attempts to commercialise the results of the analysis done were mad in USA during the 1980s by FlowWind Ltd. Several wind farms were built based on tests done on 17 m diameter Darrieus turbine by Sandia National Laboratories. Although these machines worked efficiently, they experienced fatigue problems with the blades (Eriksson et al., 2008).

The straight-bladed Darrieus turbine or H-rotor (Fig.1.4) was largely de-veloped in the UK by Peter Musgrove during the 1980s and 1990s. The H-rotor could reduce the blade manufacturing costs and use a simpler struc-ture than the one adopted for the Darrieus turbine common-shape. It also caused the use of a shorter tower and it avoided the adoption of guy sup-ports wires. Several test machines. ”Several test machines were constructed in the UK by VAWT Ltd (Clare and Mays, 1989), the largest being the 0.5MW 850 machine pictured in Fig.1.4 built in 1990. However, the VAWT-850 suffered a blade failure after a few months of operation due to a man-ufacturing fault that curtailed any further VAWT developments”(Shires, 2013).

The V-rotor, developed by Olle Ljungstrom in 1973 (Ljungstrom, 1986), aimed to reproduce the lower half of the eggbeater Darrieus turbine. The main advanteges were a shorter tower than the one used for H-rotor and the aforementioned eggbeater turbine, and avoiding horizontal blade-to-blade struts, that could increase drag forces (Fig.1.4).

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Figure 1.4: 3.8 MW ´Eole VAWT (left), 0.5 MW VAWT-850 H-rotor (right-top), Mono V-VAWT concept (right-bottom). [Shires, 2013]

Despite these VAWT developments, problems with fatigue failures due to the high dynamic loads and a poor wind energy market in the USA con-tributed to a reduction in financial support for VAWT development projects in the 1990s. The last of the Sandia VAWTs was dismantled in 1997 af-ter cracks were found in its foundations (Eriksson et al., 2008). However, the quest for larger offshore turbines that can deliver economies of scale and a need for deep water solutions have led to a recent resurgence of in-terest in VAWTs. In a recent review of VAWT technologies and economics Sandia concluded that VAWTs ”have significant advantages over HAWTs in off-shore applications” (Sutherland et al., 2012) and that H or V-rotor de-signs are likely to be more cost effective. (Shires, 2013).

Recent development of VAWT machines includes in 2009 a 35 kW proto-type of the VertiWind concept in France. This H-rotor has helical blades to reduce the torque and OTM ripple and is supported on a tilting base which can simulate the operation on a floating platform (Snieckus, 2012). After this prototype, the project includes to install a 2 MW floating wind turbine. In 2010 Vertical Wind installed a grid-connected 200 kW three-bladed H-rotor near Falkenberg, Sweden, with no gearbox and a direct driven genera-tor at the base of the tower (www. verticalwind.se). Thanks to a high genera-torque value and low RPM, it is likely that a novel drivetrain will be required par-ticularly for large offshore machines. Other recent research interest largely

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Chapter 1. General aspects focuses on the dynamics of floating VAWTs (Akimoto et al., 2011; Vita et al., 2009) and improving blade section aerodynamic performance including blade pitching concepts or giromills (Kirke and Lazauskas, 2008). How-ever, most research and development activity is focused on H or curved-bladed F-rotor concepts and research to advance the V-rotor concept is lim-ited (Shires, 2013). Examples of the aforementioned turbine are the ones derived from the NOVA project, the NOVA V-VAWT concept and its devel-opment, the Aerogenerator-X, which is projected to produce 10 MW (Shires, 2013; www.windpoweroffshore.com).

Figure 1.5: NOVA V-VAWT concept (left) and Aerogenerator-X (right).

As regards the micro-generation, a spread interests was born for the use of lift-driven turbines for urban environment in the last years. The main idea is to include small-scale wind turbines in buildings for domestic power production, on order to help the penetration of the renewable energy also in this sector (Mertens, 2002).

As regards the methods adopted to asses the efficiencies of this type of VAWTs, many forecast models have been developed in order to analyze the main characteristics of lift-driven turbines. Starting from empirical mod-els to give an overall description of this aero-generator, the research has tended toward more and more detailed analysis. One of the most known one is Paraschivoiu’s model, based onDouble Multiple Stream-Tube (DMST) model (see Chapter 2), that could obtained good results for full-scale tur-bines.

As regards Darrieus wind turbines in urban environment, there are many examples in literature about these applications, including Merten’s works onmomentum-theory models for analyzing VAWTs on roofs of buildings (used as reference for the end part of this work). The tendency of the last years, in agreement with the increased computational capacities of calculators, is the use ofCFD simulations to asses the performances of these VAWTs in details, more than the previous models could do.

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1.3 Floating platforms for o

ff-shore applications

As told before, the off-shore applications for VAWTs are the next challenge in increasing power production from renewable sources. The advantages listed above suggest the interest in it and many solutions has been studied and are still studied nowadays.

The development of floating platform is linked to the economic feasibil-ity. In fact, the most of the off-shore plants in United States, China, Japan, Norway and may other countries is available in water less deep than 60 metres. Also European plants are set in waters with a depth of 20 me-tres and prevents fixed-bottom structures (Jonkman et al., 2007). This type of anchoring becomes too expensive for water deeper than 60 metres, and the floating structures starts to be interesting from the economic feasibility point of view (Fig.1.6).

Figure 1.6: The progression of substructures from shallow water to deep water. [Jonkman et al., 2007]

There are many types of floating platform, developed thanks to the ex-perience archived in the Oil& Gas industry. The main subjects of research in this field are described below:

DeepWind concept

Fig.1.7 shows the DeepWater concept, which consists in a Darrieus rotor whose tower is extended underwater in order to act as a spar buoy. The wa-ter works as a rolling bearing, damping the dynamic effects of the bending moment on the turbine. The concept was studied for different sizes: 2 MW and 5 MW.

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Figure 1.7: Artistic view of the concept. [Vita, 2011]

The blades are twice or three times longer than a HAWT with the same swept area and they are installed in Troposkien configuration, i.e. without the use of blade-to-blade struts. The generator is set at the bottom of the submerged structure and it works as a motor to start the rotor since it is not self-starting, and it has to operate at variable speed to control the tur-bine operation. The torque generated by the rotor is transmitted trough the tower to the bottom of the structure. The forces are transferred through the mooring lines, but two or more rigid arm are necessary to take the torque. Due to the simple configuration, the whole structure, without counterweight, can float and lay horizontally on the water line. Counterweight can be grad-ually added, to tilt down the turbine.

However, this concept is not free from challenges. In facts, the rotating tower is subjected to hydrodynamics loads, overloading the submerged plat-form, and there are also some losses due to the friction of the platform in the water. Another disadvantage is the fact that the generator is at the bottom of the rotor tube, resulting in complicated maintenance operations (Vita, 2011).

FAWT concept

Floating Axis Wind Turbine (FAWT) concept includes a Darrieus-Type wind turbine and the floating structure is a buoy. The turbine can have straight blades (FAWT-S) or curved blades (FAWT-C) as showed in Fig.1.8. Although a FAWT looks like a spar buoy VAWT, its bearings for the turbine axis are not on its central tower. A cylindrical float rotates with the upper struc-tures of the turbine. The torque of the turbine is converted to electricity by bearing rollers and generators above the sea surface. In fact, the axial

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Figure 1.8: FAWT-S (left) and FAWT-C (right) concept. [Akimoto et al., 2011]

load is supported by the float and the bearing mechanism has to resist only to thrust force of the turbine, which is less than 1/10 of the weight of the VAWT mechanism. Power output from the turbine is obtained from torque of the rotating float by rollers contacting on the cylindrical surface of the float (Fig.1.10). Since the drive train is not subject to small and compact spaces like the shaft of a common VAWT, the restrictions are lighter than those in other turbines.

Figure 1.9: FAWT in operating condition. [Akimoto et al., 2011]

Lighter restrictions are also on structural requirements, since the weight and the bending moment do not act directly on the drive train. Gyroscopic moment of the turbine and the float stabilize the direction on the turbine

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Chapter 1. General aspects axis in wind fluctuations.

This concept also does not require particular structures of the installation. Since it is a concept, it has to be analyzed more from a structural point of view and it needs tests and numerical simulations before its realization (Akimoto et al., 2011).

The Vertiwind project

Figure 1.10: Vertiwind project. [Cahay et al., 2011; Vita, 2011]

The Vertiwind projects plans to install a floating VAWT of 2MW around 5 km offshore Fos-Sur-Mer, in France. It provides the use of a 3-bladed H-type Darrieus rotor at the beginning, replaced by its evolution, composed of semi-twisted blades.

The floater concept retained is of a semi-submersible design and is called ”multifloater”. It results as a very stable structure. The VAWT is located in the centre of the structure ensuring that the centre of gravity, the boyoancy and the convergence point of the mooring lines are all on the same axis (Cahay et al., 2011). This configurations highly reduces the sway and yaw response of the floater subjected both to the wind and the waves actions. The complete unit is anchored to the seabed and linked to the network by a compliant subsea cable. The structures can experience loads very close to on-shore configuration (Vita, 2011).

One of the main disadvantages of this structure is the fact that it has the largest value of displaced water among the three described configurations and the installation could be difficult because of the anchors. Other diffi-culties are linked to the cost of installations and to the possible failure of one of the wires, which could cause the collapse of the turbine in the water.

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1.4 General mathematics expressions for

aerody-namic analysis of lift-driven VAWTs

The aerodynamic analysis of the performances of Darrieus-Type wind tur-bine can be done using mathematical correlations to define parameters use-ful to compare the results obtained.

1.4.1 Variation of local angle of attach (AoA)

Figure 1.11: Flow velocities of a lift-driven wind turbine. [Islam et al., 2006]

The velocity through the rotor is not constant. From Fig.1.11 , it is pos-sible to observe that the fluid is considered to occur in the axial direction. The chordal velocity component Vc and the normal velocity component Vn

are obtained from the following relations:

Vc= Rω + Vacosθ (1.1)

Vn= Vasinθ (1.2)

where Va is the axial flow velocity (i.e. induced velocity) through the

rotor, ω is the rotational velocity, R is the radius of the turbine and θ is the azimuth angle. θ is equal to 0 when the nose of the airfoil is opposite to the

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Chapter 1. General aspects wind direction.

The AoA can be expressed as:

α = tan−1 Vn Vc

!

(1.3) Substituting the value of Vn and Vc and non-dimensionalizing with

re-spect to thefreestream wind velocity V∞, it becomes:

α = tan−1 " sinθ (Rω/V∞)(V_a/V∞) + cosθ # (1.4)

1.4.2 Normal and tangential force coefficients

System of reference adopted for the calculation of normal and tangential force coefficients, respectively Cn and Ct is the following:

Figure 1.12: Sign convention used for force coefficient. [Akins, 1989]

It is possible to define the force coefficients as:

Cn= Fn 1 2ρcW 2 (1.5) Ct= Ft 1 2ρcW 2 (1.6)

where Fnand Ft are, respectively,normal force and tangential force to the

blade, ρ is the air density, c is the chord of the blade and W is the relative velocity:

W = q

Vc2+ Vn2 (1.7)

This definitions, normalized with the relative velocity, are adopted only for the chapter about validation of the CFD model (see Chapter 4), while a most common definition of force coefficients is based on the freestream velocity: Cn= Fn 1 2ρcV 2 ∞ (1.8) 27

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Chapter 1. General aspects Ct= Ft 1 2ρcV 2 ∞ (1.9)

These correlations are used for the analysis of the rotor in skewed flow.

1.4.3 Pressure coe

fficient

Pressure coefficient is defined as:

Cp= P − P0 1 2ρV 2 ∞ (1.10)

1.4.4 Reynolds number and Tip Speed Ratio

In order to define the turbulent condition of the flow acting on the blade, Reynolds numberRe is another useful parameter:

Re =U L ν =

ρωRc

µ (1.11)

where ν is the kinematic viscosity, L is the characteristic length scale and µ is the dynamic viscosity.

Tip Speed Ratio is the ratio between the blade tip velocity Vbt and the

freestream velocity: T SR = Vbt V∞ = ωR V∞ (1.12)

1.4.5 Torque coe

fficient

Since tangential forces are depends on the azimuthal angle θ, it is possible to calculate an average tangential force Ftaon one blade as:

Fta= 1 2π Z 2π 0 Ft(θ)dθ (1.13)

The total torque Q for N -number of blades is:

Q = N FtaR (1.14)

Thetorque coefficient Cm is calculated as:

Cm= Q 1 2ρARV 2 ∞ (1.15)

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1.4.6 Power coe

fficient

To evaluate the efficiency of a wind turbine, power coefficient CP is used and

it is defined as the ratio between the power output from the turbine and the maximum available power from wind:

CP = P 1 2ρAV 3 ∞ (1.16)

where P is the power output calculated as:

P = Q · ω (1.17)

1.5 Betz law

Considering the rotor as a plate with a surface S and a control volume like the one showed in Fig., section 1 and section 2 indicates the upwind and downwind flow.

The following hypothesis are considered:

• the rotor is composed of an infinite number of blades with no shear; • the inlet and outlet flow to the rotor is uniform and has an axial

direc-tion;

• the fluid is incompressible with constant density and there is no heat transfer between the turbine and the fluid.

Figure 1.13: Betz streamtube. [Leucci, 2010]

Indicating the upstream and downstream sections of central one S with avg−and avg+, the law of conservation of mass can be written as:

˙

m = ρA1v1= ρSvavg− = ρSv_avg+= ρA₂v₂ −−−−−−> v_avg− = v_avg+ (1.18)

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Chapter 1. General aspects The momentum equation allows to calculate the force of the wind on the rotor:

F = ρv1A1v1·n1+ ρv2A2v2·n2= ˙m(v1−v2) = ρSvavg(v1−v2) (1.19)

Applying the Bernoulli’s theorem to path 1−avg−and 2−avg+, we obtain:

pavg− = p₁+1 2ρ(v 2 1−v2avg−) p_avg+= p₂+1 2ρ(v 2 2−vavg2 +) (1.20) The force expressed by the moving fluid is:

F = (pavg+−p_avg−)S =1 2ρS(v

2

2−v12) (1.21)

with vavg−= v_avg+and p₁ = p₂.

Now, it is possible to equal the equations (1.5) and (1.5) and we get the velocity in correspondence of the rotor:

vavg =

v1+ v2

2 (1.22)

The maximum obtainable power can be reached multiplying equation (1.5) for vavg:

P = 1

2ρSvavg(v

2

1−v22) (1.23)

Substituting the expression of vavg in equation (1.5), it becomes:

P = 1 2ρS 1 2(v1+ v2)(v 2 1−v22) = 1 4ρSv 3 1 1 − v2 v1 !2 +v2 v1 − v2 v1 !3! (1.24)

Doing the derivative of the previous equation with respect to v2 v1

, the maximum value of v2

v1

is 1/3. Substituting this value in the expression of power, it gives: P = 1 2ρSv 3 1 16 27 (1.25)

Thus, the maximum theoretical value of CP is 16/27 ' 0.593 .

Further details in references (Betz, 1966).

The Betz theory is the base of many models which share the concept of streamtube (i.e. multiple streamtube, double multiple stream tube, etc) showed briefly in Chapter 2.

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Chapter 2 Main issues concerning the

analysis of Vertical Axis Wind

Turbines

The analysis of the performances of a VAWT is characterized by the occur-ring of different complex aspects, due to the physic of the phenomena which takes place, and to the methodology used. These two aspects are bound to-gether and it complex to split one to another. One of the phenomena that occurs is thedynamic stall. It influences the aerodynamic forces on the blade of the turbine, causing changes in the power production and adverse con-ditions of working. However, this complex phenomenon is not the only one that occurs in the characterization of a VAWT, and the right methods and models used to investigate how the wind turbine can or could work are cru-cial.

For this reason, the two main features that affect the description of VAWTs are showed in the next sections:

• Dynamic stall;

• Approaches used for the performance prediction.

2.1 Dynamic Stall

Thedynamic stall is one of the most important phenomena which influences the performances of VAWTs and HAWTs. This strong influence was firstly discovered in 1988 and affected not only wind turbines, but also helicopter blades and turbomachinery blades (Ekaterinaris et al., 1995). The stall con-dition is due to an increase in the angle of attack (AoA), that leads to a separation of the flow from the airfoil, and causes a loss in the lift forces and an increase in the drag ones. Due to the motion of the blade of the wind turbine, the airfoil experiences a unsteady and rapid variation of the AoA during the revolution. This changes leads to an initial lift augmenta-tion, overcoming the non-linear behaviour of the lift curve which reaches

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Chapter 2. Main features affecting analysis of a VAWT relatively high AoAs (Spentzos et al., 2004). The increase in the value of lift force is due to the formation of vortices, originated at the leading edges, which pass on the upper surface of the airfoil and modify the pressure dis-tribution along the chord of the blade. This is translated in a production of transient forces that cause a different situation from the static stall condi-tion. After the creation of this vortices at the leading edge, they detach from there and are shed downstream producing a deep loss in the lift, more than the static situation.

This condition lasts till the AoA is above the static stall limit; when the AoA is below this value, the flow reattachment occurs.

Figure 2.1: Development of dynamic stall on an blade. [Larsen et al.]

During the dynamic stall, many situations happen in the flow field, such as (Barakos et al., 2003):

• Boundary-layer growth; • Separation;

• Unsteadyness;

• Shock/boundary layer and inviscid/viscous interactions; • Transition to turbulence and flow re-laminarization.

A good description of this situation, and of dynamic stall in general, is important not only in the estimation of power output as regards wind turbines, but also the presence of stall vortices produces problems such as aero-elastic vibrations and noises from the blades and the fatigue of the blade material caused by the unsteady forces (Fujisawa et al., 2000). To ap-preciate the dynamic stall behaviour on an airfoil, we can consider a blade starting from an average AoA, afterwards increased with a sinusoidal oscil-lation motion.

A typical representation of this phenomena is the hysteresis cycle defined by the angle of attack and the forces acting on the blades. As we can see in the figure below, both the static stall and the dynamic stall condition are

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Chapter 2. Main features affecting analysis of a VAWT represented. The picture shows also the different phases of the hysteresis cycle. In the first phase of the phenomena, called a in the picture below, the increased value of lift, respect to the static stall condition, is showed. After that, a recirculation of the flow nearby the profile appears and more the AoA increase, more the boundary layer becomes thicker and the recir-culated flow affects more surface in the outer part of the airfoil (phase b to d). At this point, vortex forms at leading edge and slides toward the trail-ing edge. Suddenly, the stall begins, the drag force (linked with the pitch-ing moment coefficient due to the pitchpitch-ing motion of the blade) reaches its maximum value and there is a drop in the lift force. Reducing the AoA, a re-attachment of the flow is verified (Carr et all., 1996).

Figure 2.2: Different phases occurring in the dynamic stall. [Carr et all., 1996]

Dynamic stall was studied in many different ways, starting from experi-mental tests to CFD simulations, developed in the last years. All this differ-ent approaches are found out to discovered which one of them can describe better this phenomena affecting the performance of a wind turbine so much.

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Chapter 2. Main features affecting analysis of a VAWT

2.1.1 Experimental tests

One of the previous tests carried out to asses the incidence of this phe-nomena were the experimental ones. Most of them are based on the PIV measurements of the flow field around the wind turbine, and moreover on vertical axis wind turbine. PIV (Particle Image Velocimetry) system allows to describe the behaviour of the flow on the airfoil surface and which passes trough the rotor swept area. This technique usually provides the use of a tracer (steam or liquid), injected in the form of microspheres by nozzle (about 40 µm), for the visualization of the flow field and the streamlines in the zone interested by the passage of the blades. The flow field is visual-ized with the use of light sheet (generated by laser or stroboscopes located in specific position in the test section) and the observation of it is possible with the use of a CCD camera (Fujisawa et al., 1998).

Figure 2.3: Example of PIV measurements: streamlines visualization (up) and vor-ticity magnitude measurements (down). [Ferreira et al., 2008; Fujisawa et al., 1998]

This type of tests can describe the development of the wake during the passage of a blade in the flow field and of the vortices generated by the local high AoA. As it is possible to see from the pictures Fig 2.3 (Ferreira et al., 2008; Fujisawa et al., 1998), both streamlines and vorticity field can repre-sent the behaviour of the flow that encounters the blade surface. According with Fujisawa et al., it is possible to distinguish different types of dynamic stall, depending on the vortices that develop at different azimuthal position of the blade during a revolution (Fig. 2.3).

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Thevantages of this method are:

• the direct visualization of the occurring dynamic stall through pic-tures;

• the visualization of the development of the vortices from the blades; • the use measurements, such as PIV pictures of vorticity, to convalidate

other models. Thedisadvantages are:

• requirement of specific experimental apparatus;

• no pointed but averaged (in space and time) measurements; • poor spatial resolution of the PIV system;

• uncertainty due to the experimental procedure and factors (determi-nation of the AoA, blockage factor of wind tunnels, size of interroga-tion window).

2.1.2 Semi-emphirical models

Another way to study this complex phenomenon is the use of empirical and semi-empirical model. The use of these methods to describe the stall process spreads until the 1970’s thanks to the less computational resources needed by the two type of models, while theoretical methods (moreover nu-merical ones) were prohibitive at that time.

Their methodology is often based on a collection and a resynthesis of aerodynamic test data from unsteady airfoil test or from static condition measurements. The main drawback of these models is that they use an in-terpolation of the collected values or curve fittings techniques to determine quasi-static values and specific correlations on which they are based (Eka-terinaris et al., 1995).

The goal of semi-empirical model is not to capture every variation of the loads on the blade of the wind turbine, but to describe and model the main characteristics in fast way (Larsen et al., 2007). If from one hand this ap-proach could be efficient from an engineering point of view, from the other hand it can not be generalized. In fact, the major problem of both empirical and semi-empirical models is uncertainty about their application to a range of airfoils, blade shapes and rotors size.

Examples of these models are:

• the so-called gamma function model, developed by Boeing and Vertol, based on this empirical function which depends on airfoil geometry and the Mach number;

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Chapter 2. Main features affecting analysis of a VAWT • a time domain unsteady aerodynamic model, developed by the United Technologies Research Center (UTRC), based on the collection of data regarding the instantaneous angle of attack, or the geometric angle of attack, the non-dimensional pitch rate, and another parameter which represents the relation between the instantaneous angle of attach and the effective angle of attack. This model keeps into account also the time history of the effects due to the variation of the AoA;

• the ONERA method, which consists in a system of differential equa-tions to fit the experimental forces and the pitching moment data (Ekaterinaris et al., 1995).

Figure 2.4: Semi-emphirical models compared with experimental measurements. [Larsen et al., 2007]

Therefore, we can identify the mainadvantages of this method which are: • the use of less computational resources and time consuming behaviour; • a good accuracy considering the resources needed and the results

ob-tained from this type of models. On other hand, thedisadvantages are:

• a not generalized approach for different wind turbines and airfoil ge-ometries, that could cause a loss in the accuracy changing the subject of the analysis;

• a poor description of the stall condition. 37

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2.1.3 Numerical models

Numerical models is another way to investigate dynamic stall phenomenon. This models were bounds to the development of computing capacity in the last few years, permitting very detailed simulations. This means a higher accuracy about time and space resolution, using dense meshes. The cost of performing wind tunnel experiments and the lack in the description of the stall condition using empirical/semi-empirical models suggest analysis through numerical models even more (Ekaterinaris et al., 1995).

Furthermore, an advantage of this type of models is the possibility of obtain many different results, unlike the experimental tests where the achievement of data is linked to instrumental constrains.

Figure 2.5: Flow visualization trough PIV and numerical models. [Barakos et al., 2003]

Most of the numerical models are based on the Navier-Stokes equations for compressible and incompressible flow, the ones on which we will focus attention in this work.

These models can describe the flow behavior and help in the understand-ing of these complex phenomena quite well, but this analysis is not free from many challenges. In fact, the validation of the Computational Fluid

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Chapter 2. Main features affecting analysis of a VAWT Dynamic (CFD) models and feasibility of their use, is linked to the their ca-pacity of describing the turbulent flow and modelling the transitional flow regions in the flowfield (Barakos et al., 2003); algebraic, one-equation and two-equation models, and multi-equation models affect the correct calcula-tion of the results got from simulacalcula-tions (Ekaterinaris et al., 1995).

As regards dynamic stall also, numerical simulations will only contribute to a better understanding of mechanisms and improvements in predictive ability of this phenomenon if progress in numerical schemes is paced di-rectly by an improved ability in resolving turbulent flow (Barakos et al., 2003).

In Fig.2.9 , it is possible to see an example of the description of the dy-namic stall trough a CFD analysis: the visualization of the flowfield near the blade agrees with well with the PIV images at the same airfoil position. The pictures show the typical rise of the dynamic stall condition, as described before. In fact, it is possible to see the detachment of the flow starting from the leading edge, with vortex that increase gradually along the suction sur-face of the blade. Then, other vortices forms nearby the nose of the airfoil while the ones generated at the trailing edge dominates the flow over the airfoil and the ones formed before shed at the wake.

As said before, the turbulent behaviour of the fluid leads to the presence of different time and length scales, which proliferate with the increasing in the Reynolds number. The calculation of these scales can be done using different approach, that prevent the use or not of additional external infor-mation and correlation (Ekaterinaris et al., 1995).

In fact, CFD models can be divided into three different types: • DNS (Direct Numerical Simulation) models;

• LES (Large Eddies Simulation) models;

• URANS/RANS (Unsteady/ Raynolds Averaged Navier-Stokes Simula-tion) models;

that contain a different treatment for the resolution of the governing equations, and the main features will be described in the next sections.

At the end of the day, it is possible to identify the main advantages and disadvantages of the numerical methods.

Advantages:

• Numerical simulations can describe better the development of the dy-namic stall in different flow condition, overcoming the problem due to instrumentation constrains in experimental tests;

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Chapter 2. Main features affecting analysis of a VAWT • These models are cheaper than wind tunnel or flight experiments in

unsteady flows, from the economical point of view;

• Choosing the right turbulent model, it is possible to not consider sim-plification for predicting the dynamic stall (completely turbulent or completely laminar flow) but to study directly the phenomena occur-ring in the near-wall flow.

Disadvantages:

• These models require high computational resources;

• The results obtained from these models are very affected by the tur-bulent scheme used;;

• Being time demanding, they are not very suitable for an overall eval-uation of performances.

2.2 Approaches used for the performance

predic-tion

As we have said before, the dynamic stall is a complex feature of the VAWTs, but the right description of it is not enough to evaluate the performances of the entire turbine. Many other factors, such as the influence of the wake generated by the others blade on one of it or the blade tip losses, occur in the real operation of the turbine.

It is possible to predict the performances of vertical axis wind turbine with different methods, and the most used ones can be grouped in two groups:

• Computational models; • Numerical models.

2.2.1 Computational models

In the past, several mathematical models were adopted for the performance prediction and design of VAWTs. The main features of these models are (Islam et al., 2008):

• calculation of local AoA and local realative velocities at different TSR and azimuthal position;

• calculation of ratio of induced to freestream velocity (Va/V∞)

consid-ering the blade/blade-wake interactions;

• mathematical expressions based on different approaches (Momentum, Vortex or Cascade principles) to calculate normal and tangential forces; ’Pre-stall Airfoil Characteristics’ (Cl, Cdand Cm) for the attached regime

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Chapter 2. Main features affecting analysis of a VAWT • ’Post Stall Model’ for stall development and fully stall regime;

• ’Finite Aspect Ratio consideration’;

• ’Dynamic Stall model’ to consider the unsteady effects;

• ’Flow Curvature model’ to consider the circular blade motion. The most studied and used models can be classified into three groups:

• Momentum model (based on the consideration on the momentum of the air related with forces acting on blades);

• Vortex model (potential flow models based on the calculation of the velocity field about the turbine through the influence of vorticity in the wake of the blades);

• Cascade model (used the cascade flow phenomenon already studied in the turbomachines).

Momentum models is the class of models most used for the study of VAWT; for this reason it will be described below.

Momentum model

Different momentum models (or BEM - Blade Element-Momentum - mod-els) are based on the calculation of the flow velocity trough the turbine by equating the streamwise aerodynamic force on the blade with the rate of change of momentum of air, which is equal to the overall change in the mass flow rate. According to these models, the turbine is considered inside a streamtube, where Bernoulli’s equation is applied. This method includes different approaches: Single streamtube model, Multiple streamtube model and Double Multiple streamtube model [Islam et al].

We will focus the attention on Multiple streamtube model, since it is one of the most used method for a preliminary evaluation of the performance of a Darrius-Type VAWT.

This method belongs from the simpler Single streamtube model and the swept volume is divided into a series of adjacent, aerodynamically indepen-dent parallel streamtubes. The model includes the concept of the windmill actuator disk teory, according to which the induced velocity is assumed to be constant throughout the disc and is obtained by equating the streamwise drag with the change in axial momentum. This theory takes into account the effects of the airfoil stalling on the performance characteristics, and also the influence of geometric variables such as blade solidity and rotor aspect ratio. Wind shear effect is not incorporated into the model. The flow ve-locity is considered constant throughout the upstream and the downstream side of the swept volume by the blades and it is equal at:

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Figure 2.6: Principle of Multiple streamtube model divided by uniform M θ. [Beri et al.]

Va=

V∞+ V_w

2 (2.1)

where Vais the induced velocity and Vwis the wake velocity [Islam et al.].

Each streamtube is subjected to a loss in momentum and to two impulses of aerodynamic forces during each revolution of the rotor. It is possible to calculate this loss only knowing the induced velocity. To discover Va, the

stream tube model equals the variations in axial momentum with the aero-dynamic forces. The forces act on the blades only twice (once in upwind and once in downwind part) and for the rest of the time (the most) they are considered zero.

So this model averages all the variables to find out an average value, as-sumed constant during all the revolution acting on a streamtube.

When Vais calculated, the velocity field can be determined, and at this time

also aerodynamic forces at different azimuthal angle can be [Strikland]. Some relations for this model are showed below.

The time averaged thrust force acting in a streamtube byN blades and twice per revolution can be expressed as:

Ta= N ∗ Ti∗

∆θ

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Chapter 2. Main features affecting analysis of a VAWT where VRis the relative velocity and Ti is the instantaneus trust:

Ti=

1 2ρV

2

R(hc)(Ctcos ϑ − Cnsin ϑ) (2.3)

with h the blade height and c blade chord length.

Figure 2.7: Airfoil velocity and force diagram. [Beri et al.]

The average aerodynamic thrust can be characterize by a non-dimensional Thrust Coefficient CT: CT = Ta 1 2ρV 2 R(hR∆ϑ sin ϑ) = _{N C} 2R _V R V∞ 2₂ π Ct cos ϑ sin ϑ −Cn (2.4)

where V∞is the undisturbed velocity of the flow, R the radius of the turbine,

Cnand Ct normal and tangential force coefficient defined as:

Cn= CLcos α + CDsin α (2.5)

Ct= CLsin α − CDcos α (2.6)

CL and CD are, respectively, lift and drag force coefficient, and α the angle

of attack.

The average torque Qaon rotor by N blades in one complete revolution is

Qa= N ∗ 2m X i=1 1 2%VR2(hc)Ct∗R 2m (2.7)

where the term into square brackets is the instantaneous torque Qi for one

blade.

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Chapter 2. Main features affecting analysis of a VAWT At the end, the torque coefficient CQand the power coefficient CP are:

CQ= Qa 1 2%VR2(Dh) ∗ R = _{N C} D _X2m i=1 VR V∞ 2 Ct 2m (2.8) CP = CQλ (2.9)

New improvements of this model includes also the real geometry of the turbine and skew direction of the incident flow (Fig.2.8).

Figure 2.8: Improvements of DMST model. [Batista et al., 2012]

2.2.2 Numerical model

The numerical models, especially CFD models, are the new way to describe the behaviour of VAWT. It can analyse all the phenomena which affected this type of wind turbines, such as the dynamic stall already described in previous paragraph.

In theory, with sufficient grid refinement, the solution of the governing equations yields a flow that is a sufficient approximation of the reality, underlying the assumption used to derive the model equations (i.e incom-pressibility, instationarity, etc.) [Sumner et al.].

Numerical models are affected by the methods used to resolve the gov-erinig equations. We can distinguish three different groups of models:

• DNS (Direct Numerical Simulations). The model resolves directly the Navier-Stokes equations without any turbulence model. So, the

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Figure 2.9: Velocity flowfield got by CFD simulation. [Howel et al.]

whole range of spatial and temporal scales of turbulence must be re-solved. This fact led to the use of fine meshes, which contains from grid elements of the order of Kolmorov scale η (η ∼ L/(Re)3/4)up to the integral scale L. The computational cost of DNS is very hight and, in the most of the industrial cases, the computational resources would exceed the capacity of the most powerful computers currently avail-able.

• LES (Large Eddy Simulation). To overcame the problem of resolution of the small scales of turbulence, LES model divides the scales into two groups: the big ones (large eddies) are directly resolved, the small ones (small eddies) are simulated using sub-grid models. In fact, the rationale behind LES can be summarized as follows:

– Momentum, mass, energy and other passive scalars are trans-ported mostly by large eddies. The latter are more problem-dependent, since they depend on the geometries and boundary conditions of the flow.

– Small eddies are less dependent on the geometry , tend to be more isotropic and consequently more universal.

The result of this different treatment of the turbulent scales by the model is a much less computational requirement than the one re-quired by DNS. (mesh sizes are generally one order of magnitude smaller than with DNS). Furthermore, the time step sizes will be pro-portional to the eddy-turnover time, which is much less restrictive than with DNS. However, the use of fine meshes is still required. • RANS (Reynolds-averaged Navier-Stokes equations). RANS models

is the most economic approach for computing complex turbulent in-dustrial flows. These models simplify the problem to the solution of two additional transport equations and introduce an Eddy-Viscosity (turbulent viscosity) to compute the Reynolds Stresses. More com-plex RANS models are available which solve an individual equation

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Chapter 2. Main features affecting analysis of a VAWT for each of the six independent Reynolds stresses directly plus a scale equation (Reynolds Stress Models - RSM), simpler one uses only one equation that solves a modeled transport equation for the kinematic eddy (turbulent) viscosity (Spalart-Allmaras model). There are other models based on two-equations, such as k − ω and k − ε models. 2.2.2.1 Differences between different models

As regards analysis of VAWTs and blade profiles, the use of different ap-proach to model turbulence causes differences in the solutions. Many pa-pers and articles have been published about the attitude of LES, DES (De-tached Eddy Simulation) and URANS (Unsteady Reynolds averaged Navier-Stokes equations) in predicting the rise of dynamic stall and the separation of the flow from the blade surface.

In Fig.2.10, we can see a comparison between LES and URANS models rela-tive to the vorticity contours. The analysis refers to a 2.5D simulation, that is a simulation in which the spanwise direction of the model is not fully represented. Vorticity is a useful scalar to describe the presence of separa-tion of flow, and it is related to the increase of turbulence. The figure shows generally a better definition of the grown of the dynamic stall given by LES model than the one given by URANS, at different angle of attack (AoA). The situation represents the upwind part of a revolution of a straight-blade Dar-rieus turbine. Even if there is not a scale to quantify the vorticity showed in the picture, it is possible to see that the increase in the vorticity magnitude is more emphasized in LES simulation starting from ϑ = 90◦.

In fact, both LES and URANS predict the vortical field in a similar way till ϑ = 72◦azimuthal angle [Li et al.].

The detachment of the flow from the surface occurs at one third of the cord according with URANS, while LES model shows clockwise vortices shed-ding from the leashed-ding edge region and propagating over the inner surface of the airfoil (Li et al., 2013). This leads to a differences in the pressure field nearby the blade, as we can see in Fig. 2.10 .

The rise of separation of the flow from the inner surface of the airfoil is translated in a loss in lift force and in the beginning of the state of stall.

In Fig 2.11, tangential and normal forces are showed. The graphs, more-over the one about tangential forces coefficient Ct , show that LES matches

well the experimental data, obtaining a peak in the upwind part close to the one got from measurements. This is due to a good description of dynamic stall, better than the one given by the URANS. In fact, this model fails to capture the occurrence of the separation of the flow and delays the stall of the blade. All these factor induces to a overprediction of lift and power out-put.

However, the URANS models, although give a worse description of dynamic stall and flow separation that LES models in most cases, give an appreciable

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Figure 2.10: Comparison between LES and URANS models regarding the contours of vorticity magnitude.

overall prediction of the flow dynamics and is useful for a fast design and research especially for low Reynolds number airfoil.

In Fig. 2.12 , tangential force coefficient and normal force coefficient from measurement are compared with the ones calculated with URANS model (using a k − εRN G model for turbulence modelling) for a S-VAWT. Using a mesh with specific features (such as a right value of the

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Figure 2.11: Numerical and experimental tangential and normal force coefficient at λ = 1.11 and λ = 0.70 . [Li et al., 2013]

Figure 2.12: Tangential and normal forces coefficient for RANS model. [Li et al., 2013]

sionless wall distance y+, it gives a sufficient description of the dynamic involving the flow that ”hit” the surface of the blade.

The curve which represent the simulated results not only follow the trend of the measured values, but also matches well the experimental data also from a quantitative point of view. As regards the tangential forces, that are linked with the power production of the turbine, the simulation verifies a good agreement with experimental data in the upwind half of revolution, and an overpredicted stall in the downwind part. This good agreement is reflected into the calculation of the power coefficient, that differ from mea-surements at lower TSR, but the two sets of data coincide very well at higher tip speed ratio (Zhang et al., 2013).

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Figure 2.13: Power coefficient got from URANS simulation. [Zhang et al., 2013]

2.2.2.2 2D and 3D CFD models

With the growth in computational resources in the last years, the 3D analy-sis of VAWT has taken more place. While, before, numerical methods were applied to 2D problems in most of the cases, the use of 3D simulation has become more and more important to enhance the knowledge of phenomena bound with this type of wind turbine.

Doing a comparison between 2D and 3D CFD analysis, it is possible to focus their principal features in Tab.2.1 .

2D CFD analysis 3D CFD analysis

• it is less computational de-manding;

• it can’t give a complete description of phenomena involved (dynamic stall, tip losses, etc.);

• it can be used for an quali-tative faster analysis. • more used in industry.

• it requires more computa-tional resources;

• it can give a more ac-curate description of dy-namic stall and other phe-nomena;

• it can give a qualitative and quantitative analysis; • used manly for research

purposes.

Table 2.1: Main features of 2D and 3D CFD analysis.

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Chapter 2. Main features affecting analysis of a VAWT The extra difficulty of 3D analysis, linked to more computational require-ments, is bound to the extension of the mesh to incorporate the third dimen-sion. This led to an increased number of nodes, reaching generally about two order of magnitude more than the 2D analysis, and an additional mo-mentum equation.

Another important feature of 3D models is that they can describe better the complex dynamics of the flow. Indeed, phenomena like dynamic stall, have a complicated nature that can be investigated in a better way using 3D models, since it is a three-dimensional phenomenon.

This models are useful to describe also the effect due to the finite blade on the performance of VAWTs, such as the vortices formed at tips that led to differences in the pressure field compared with the one calculated with a 2D model.

Figure 2.14: Comparison of torque generation between 2D and 3D models for a H-type VAWT. [Howell et al., 2010]

Not only the tip losses, but also wake interactions with oncoming blade influence the aerodynamic forces on the airfoil surface. Fig.2.14 shows the torque generation for one blade of a 3 blade H-type VAWT [Howell et al.]. The torque curves are similar in shape but the one representing torque val-ues for 3D model is shifted downwards. This means an average torque of 40% lower than the one got with 2D simulation. It can be explained con-sidering trailling vortices generated by blade-tip, that interact with the fol-lowing blade, and the flow interactions due to the presence of the shaft and support arms (Howell et al., 2010). In another work of Howell et al. about a S-VAWT, all these factor are underlined showing the vorticity field. A strong presence of vortices at blade-tips and wakes generate by the shaft and the passage of the blades confirm a lower prediction of torque and power coef-ficient for 3D simulation than the 2D analysis (Fig. 2.15 ).

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Figure 2.15: Contours of vorticity magnitude for a S-VAWT at a wind speed of 5.07 m/s. [Howell et al., 2010]

Figure 2.16: Power coefficient for a S-VAWT at a wind speed of 5.07 m/s. [Howell et al., 2010]

CFD analysis of Darrieus-Type wind turbine in skewed flows

Ringraziamenti

Contents

List of Figures

List of Tables

Introduction

Chapter 1

General aspects

1.1

Di

fferent types of Wind Turbines

1.1.1

HAWT

1.1.2

VAWT

1.2

State of art for Darrieus-Type wind turbines

1.3

Floating platforms for o

ff-shore applications

1.4

General mathematics expressions for

aerody-namic analysis of lift-driven VAWTs

1.4.1

Variation of local angle of attach (AoA)

1.4.2

Normal and tangential force coefficients

1.4.3

Pressure coe

fficient

1.4.4

Reynolds number and Tip Speed Ratio

1.4.5

Torque coe

fficient

1.4.6

Power coe

fficient

1.5

Betz law

Chapter 2

Main issues concerning the

analysis of Vertical Axis Wind

Turbines

2.1

Dynamic Stall

2.1.1

Experimental tests

2.1.2

Semi-emphirical models

2.1.3

Numerical models

2.2

Approaches used for the performance

predic-tion

2.2.1

Computational models

2.2.2

Numerical model