Stéphane Barre Benoit

Augier Guillaume

PAILLARD Maurice Benoit

Christophe Sicot

Audrey Hassan

Marie-Pierre Thierry

Manon Wessel

avec la participation active de

L'équipe algecos

Les équipes techniques "un café?" Florian Aurélien "pas de café pour moi" Agathe Pascal "le café est prêt" Saïd François "où est mon filtre a café" Sacha Muriel "où est le relais?!" Simon Jean-Marc "I ground the coffee my self" Nidiana "Je vais pas dire non à un café" Romain

Les accros de la grimpe

La famille "oups j'ai loupé un point" Kevin Céline "Quel instinct de survie."

ABBREVIATIONS

BEM

Context

Nowadays, a transition to renewable energy sources has begun all over the world. Whether it is to limit dependence on fossil fuels or to supply remote areas, renewable energies are on the rise.

Renewable electricity can, among others, be produced by hydroelectric facilities, solar panels, geothermal plants, or wind turbines. This thesis deals with wind energy, and we will focus on this particular energy source.

After the first oil crisis of 1973 -1974, the study of renewable and of wind turbines generated more interest. Many laboratories developed and tested different wind turbine technologies. Horizontal axis wind turbines (HAWT) received as much attention as vertical axis wind turbines (VAWT).

The figure 1.1 illustrates the two concepts with the two radically different designs. Research in Europe with [START_REF] Vries | On the Theory of the Horizontal-Axis Wind Turbine[END_REF]], in the United States such as [START_REF] Hibbs | HAWT performance with dynamic stall[END_REF]] and in Japan advanced the knowledge of the aerodynamics of horizontal axis wind turbines. In the United States, the Sandia laboratories work on vertical axis wind turbines [START_REF] Blackwell | Wind tunnel performance data for the Darrieus wind turbine with NACA 0012 blades[END_REF] Worstell 1978], expanding on the National Research Council of Canada (CNCR) research.

Developing this vertical axis technology turned out to be technically challenging. Several incidents such as the failure of a FloWind-19 wind turbine in 1986 or an accident during the assembly of a Darrieus wind turbine by the Canadian consortium DAL in 1983 stopped the development of vertical wind turbines for decades to come.

After the abandonment of vertical axis wind turbines, the industry converged on the design of horizontal axis tri-blade wind turbines that we all know. These turbines, ever bigger and more powerful, made the price of the electricity produced, often quantified with the Levelised To further reduce the LCOE, the industry has turned toward offshore wind turbines fields (illustrated in the figure 1.2). The more favorable wind conditions allow the exploitation of more substantial and more constant winds, thus increasing the load factor. The load factor is the ratio of the total amount of energy produced and the amount of energy the turbine would have made if it were operating at full power over the said time interval. Thus, increasing the load factor reduces the LCOE and increases the reliability of the energy source. Going offshore allowed Denmark to install several gigawatts worth of offshore production, producing up to 47% of its electricity thanks to wind turbines [Gronholt-Pedersen 2020]. Similarly, England produced more than 40% of its electricity thanks to its wind farms in the first quarter of the year 2020, and Ireland produced 32.5% of its electricity thanks to the wind in 2019 [START_REF] Djunisic | Wind produces 32.5% of Ireland's power in 2019[END_REF]].

Fixed foundation offshore wind farm are still developing. Areas such as the American East coast are planing on installing hundreds of MWs worth of wind turbine. But those vast open seas can actually be crowded. The Exclusive Economic Zones, where wind farms are installed also need to accommodate for activities such as marine traffic, fishing ground, military activities and protected areas. Fixed offshore wind farms also have their constraints. On top of the wind resource, fixed foundations are installed in shallow water (generally less that 50m) where the cost of the foundation is kept a reasonable price. With those constrains, space can be at a premium for wind industry. Fortunately, installing structures in deep water has already been done for decades.

By using the technologies developed for offshore oil & gas stations, floating wind turbines will make possible to unlock new wind sources further from the coast, on sites where the ocean depth exceeds 50m. These sites offer better wind conditions, thus further increasing the load rate while reducing the visual impact of the wind turbines on locations less needed for other usages. However, this transition to a new market can only happen when the technology will be mature.

Today, the HyWind, Floatgen, and WindFloat projects have demonstrated the technical and economic feasibility of floating wind power. However, those projects use horizontal axis wind turbines and their nacelle located at the top of the mast generates engineering challenges. They have an inherently high center of gravity which reduces their stability. In addition, the position of the nacelle imposes a strong lever arm on the floater, makes the machines sensitive to the motion of the floats, and renders maintenance more complex.

Vertical axis wind turbines, with nacelles located at the base of the mast, might bring a solution with good arguments to the installation of floating wind turbines. Their lower center of gravity reduces the stresses on the structure, and their generators located lower on the mast allow a more accessible intervention. Furthermore, using VAWTs might reduce the size and cost of the floats while allowing for easier maintenance. The reduced size of the VAWT's wake also makes the technology attractive as it will enable denser parks meaning more energy production on the same surface and reduced costs for the transportation of the electricity from the turbines to the sub-station. But the technology raises new issues such as a cyclic thrust and the moment on the yaw axis. It is in this context that this thesis is conducted.

Floats technologies

Derived from the Oil & Gas industry, floats are grouped into several categories, described here by Thiagarajan et al [START_REF] Thiagarajan | A Review of Floating Platform Concepts for Offshore Wind Energy Generation[END_REF]].

There are three major stability mechanisms: ballasting, mooring, and buoyancy. the bottom of the float. They offer a lowered center of gravity compared to the center of buoyancy. They gain their stability from the distance between those two points. In addition, their small section allows them to be very little influenced by the waves. Their main disadvantage is their draught making their transportation on-site more complex and imposing depths of 100m or more for the installation sites. This type of float is used for the Hywind project by Equinor (illustration in figure 1.5a), where each 6MW turbine is positioned on a float with a 78m draft.

Semi-submersibles: Derived from oil platforms, these structures obtain their stability thanks to a combination of their large size and their mooring system. This technology allows for low drought making it easier to build and tow to the installation site. These floats generally require active ballasting. The catenary anchors are used to maintain the float's stability and position. Principle Power's WindFloat (illustrated in figure 1.5b) and Idéol's Floatgen demonstrators use this technology.

TLPs: For Tension Leg Platform are structures maintained by their anchoring under tension. These structures are particularly stable once installed. However, some designs are not stable during transportation. This technology is particularly used in the Oil and Gas industry. To the author's knowledge, no floating wind turbine demonstrator uses this technology at the moment but SAIPEM's HexaFloat concept is a good illustration of the concept. This scale is used when modeling a phenomenon is taking place at the free surface. However, when the object of study is immersed in the medium, the Reynolds scaling is commonly used to maintain the ratio between inertial and viscous forces. Heller's course [START_REF] Heller | Model-Prototype Similarity[END_REF]] on scaling describes the different scaling methods.

F r = U 2 gL (1.1) Re = ρU L µ (1.2)
Within the framework of the study in a basin, the float model must thus follow the Froude scaling, whose velocity scale is described by the equation (1.1) whereas the behavior of the wind turbine is governed by the Reynolds number described in equation (1.2). If we follow the Froude scaling, the aerodynamic performance of the wind turbine will not be preserved. The interaction between the motion of the float and the turbine will not be correctly reproduced. Indeed the average Reynolds number on the blades will not be conserved and the wind speed variations won't match either. With offshore wind energy development, many projects have been testing models of floating wind turbines in wave tanks. These tests are essential for the development of a concept and aim at calibrating the models and measuring the response of the system in a set of environmental conditions. Thanks to the increased interest on those problematic, different solutions to circumvent the Reynolds/Froude incompatibility have been explored. The bibliographical study, presente in the chapter 2, will aim to present the main tests in wave-tank and the models of the behavior of the wind turbine employed. 2. To propose a simplified simulation of the aerodynamics of vertical and horizontal axis wind turbines for the experimental comparison of the two concepts.

The flow velocities in the

λ V = λ L (1.3) λ V = 1/λ L (1.4)

Framework and objectives of the thesis

3. Compare the behavior of a float with the vertical axis wind turbine to the behavior of the same float supporting a reference horizontal wind turbine of identical power.

4. Develop a Windquest wind turbine model to reproduce representative movements of the float and measure their impact on the thrust coefficient of the wind turbine.

5. Analyze these measurements to describe the influence of the movements of the wind turbine on its thrust coefficient and compare these results to the hypotheses used for the wave-tank tests. The literature review in this chapter is divided into two parts. The first part focuses on the experimental study of the offshore behavior of floating wind turbines. We will discuss publications describing small-scale basin or sea trials. As experiments can not be detached from simulations an overview of the Floating Offshre Wind Turbine (FOWT) numerical models will be given.

The second part will focus on the aerodynamic study of vertical axis wind turbines in wind tunnels and on the reproduction of the dynamics and movements of floating wind turbines.

VAWTs have an unsteady behavior, the thrust, the stresses in the structure and the generated power varies according to the position of the rotor. We will therefore browse references describing this phenomenon. Furthermore, the turbine's wake and it's interaction with the environment and the other turbines will be studied for both HAWT and VAWT. The subject is not directly tackled in this thesis but having a basic understanding of wakes is important to get a better understanding of the wind turbines' challenges. Finally, we will discuss publications describing the use of actuators to reproduce the motion of a floating wind turbine in a wind tunnel.

Study of the behavior of floating wind turbines at sea

The Finally the third part develops the study of floating vertical axis wind turbines concepts and the comparison with the horizontal axis.

Research projects on floating wind energy

The The material is appreciated for its worldwide availability as well as its low production and recycling costs. The second, the Nautilus, is a four-column steel float. Slightly smaller than the OO-Star, it uses active ballasts to ensure its stability. Note that, even if the two floats use the same wind turbine the mast needs to be modified in order to accommodate for the differences between the two floaters.

The whole system must be adapted to the installation site. In an effort to use the most realistic Finally, it is worth mentioning the DeepCwind consortium. The paper by Robertson et al.

[ Robertson et al. 2013a] describes tank tests of three generic floats at 1 50 scale: a SPAR, a TLP, and a semi-submersible. The structures are designed to support the replica of a 5MW turbine.

For these tests, a low Reynolds turbine and a wind generator are used.

These tests have provided recommendations on the methodology to be followed during smallscale tests. The article highlights the effect of the onboard sensors and wiring on the model, the importance of using representative wind conditions, and the need to obtain nominal performances for the wind turbine to avoid modifying the simulations. The limitations of FAST for modeling viscous phenomenons or anchoring are also discussed.

The DeepWind project extensively describes the work needed for developing a Darrieus vertical floating wind turbine optimized for floating applications. The process is described in the paper by Polsen et al. [START_REF] Uwe | Outcomes of the DeepWind conceptual design[END_REF]]. This publication mainly investigates the aerodynamic performance and stresses generated by the turbine to compare the behavior of the vertical wind turbine to the NREL 5MW reference turbine described here [START_REF] Jonkman | Definition of a 5-MW Reference Wind Turbine for Offshore System Development[END_REF]].

Modeling of a floating horizontal axis wind turbine during wave-tank tests

Literature review

Two reviews of the literature are presented here. Then come the review of SiL tests with a thrust generator. This solution is adaptable as it allows the production of many wind conditions and directions for different turbines without installing a wind tunnel. However, this solution also has its shortcomings since the aerodynamic moment, and the gyroscopic effect of the turbine is not reproduced. Therefore, research is still in progress and necessary on this technology.

Rotors and wind generation

First, there are the low Reynolds turbines. A turbine and a fan are used to reproduce the aerodynamics of the wind turbine during the tank tests. If the first tests used geometrically scaled blades, the latest designs generally use a different airfoil than the full scale and with longer chords to reproduce the expected aerodynamic thrust at low Reynolds. By using a wind generator placed above the wave tank, the turbine's performance and its interaction with the float can be reproduced with a high degree of fidelity. This solution is, however expensive and challenging to implement. Thus, these tests agree with the literature on the importance of modeling the mechanical links.

However, by considering an infinitely rigid masthead, OpenFast underestimates the stresses in the structure.

Thrust generators

Another solution to model the behavior of a wind turbine is the use of thrusters coupled to a Software in the Loop (SiL). This solution is less present in the bibliography. However, some references are very instructive.This technology is still under development and many advances are seen in the literature.

The first reference is the thesis of S. Kanner We thus find the use of 'drag disc'. These porous discs are sometimes used in wind tunnels to obtain a first approximation of the drag of a wind turbine as in the articles Bossuyt et al.

[ This configuration studies the adaptation of a Darrieus turbine to a floating applications. The design lowers the center of mass and thrust of the turbine to alleviate stress on the float. It also is producing more energy at low wind speeds while generating less structural stress in the turbine and on the floater.

The publication by Huijs et al. [START_REF] Huijs | Integrated design of a semi-submersible floating vertical axis wind turbine (VAWT) with active blade pitch control[END_REF]] describes the Nenuphar vertical-axis floating wind turbine concept. The three-bladed H-shaped turbine is positioned on a tri-float. A unique feature of the concept is that the blades use variable pitch, changing change their angle of attack during a revolution. This solution is studied numerically by modeling the implementation of a 6MW concept off the French coast in the Mediterranean sea. The study shows that, for this float design, the Yaw moment imposed by the wind turbine is not a problem for the float.

The distance of the columns and anchor points from the Yaw axis generate stiffness on this axis. Furthermore, this lever arm allows generating a righting moment with the anchor and damping with the columns. The study estimates that the wind turbine would reduce the size and, therefore, the float price by about 20 %.

The paper by Griffith et al. [START_REF] Griffith | A study of rotor and platform design trade-offs for large-scale floating vertical axis wind turbines[END_REF]] presents a parametric study of vertical axis turbines on two floats. The mass and performance of a vertical axis wind turbine depend on some known parameters such as chord, maximum radius, materials used for the blades, or the number of blades. By varying these parameters on two turbine geometries (a Darrieus and a V-VAWT) it is possible to obtain wind turbines whose masses, centers of gravity, aerodynamic performances and torque applied on the generator are computed and optimized. Therefore the author tests a set of wind turbine concepts of the same power (here 5MW) on a spar float and a semi-submersible float. By fixing a criterion of static pitch angle and natural frequency, the author varies the size of the float following a Froude scaling. The objective is thus to obtain the smallest possible float supporting a 5MW turbine. The author, therefore, estimates that using a vertical axis wind turbine would make it possible to reduce the mass of the spar float by approximately 25% and 18% for the semi-submersible. The authors estimate the influence of each design parameter of the Levelised Cost of Energy and identify the most important ones.

The study of a floating wind turbine involves a part of the mechanical analysis of the structure.

Vertical axis wind turbines are subject to very strong cyclic aerodynamic loads. This particularity must be studied with great care for large wind turbines. wind turbines, the bibliography abounds with studies on these turbines. Some references aim to refine the understanding of aerodynamic phenomena within the turbine, such as dynamic stall.

Other articles aim to understand better the influence of design parameters such as the solidity of the blade profile used on the aerodynamic performance of the machines. The approach of NENUPHAR with active blade pitching should also be noted [START_REF] Huijs | Integrated design of a semi-submersible floating vertical axis wind turbine (VAWT) with active blade pitch control[END_REF]. Finally, some authors try to understand better the particular wakes of these machines and their operation in parks. We are interested in the use of VAWT for floating applications. To the best of the author's knowledge, there is no published study reproducing the behavior of a floating vertical axis wind turbine in a wind tunnel. However, several references study the behavior of floating HAWT. We can draw a lot of information from them. Therefore, this section on the aerodynamic study of VAWTs will be divided into four sections, each dealing with one of the issues mentioned above.

Turbine design parameters and their influence

Designing a vertical axis wind turbine involves finding the right balance between aerodynamic performance, mechanical stresses in the structure, sizing of transmission and generator performance. Choosing a high solidity will reduce the rotational speed and centrifugal forces but will impose high constraints on the generator. Increasing the number of blades will reduce the amplitude of torque variations imposed on the transmission but will make the turbine heavier and more expensive. In a nutshell, designing a vertical axis turbine is a matter of compromise where the suitable parameters must be chosen while keeping in mind all the constraints related to the technology. If HAWT has converged to a three-blade upstream of the mast solution, VAWT still proposes many designs. The research presented below aims to study the influence of the different design parameters of vertical axis wind turbines while trying to maintain or increase the power coefficient Cp (equation (2.1)). Many researchers have been interested in design parameters such as blade profile, blade angle, or blade chord to improve the performance of vertical axis turbines.

The solidity, in equation (2.2) with N the nulber of blades, C the chord and R the rotor radius, is a predominant factor on the VAWTs aerodynamics.

C p = P wind turbine P wind (2.1)

S = N C R (2.2)
The Sandia Laboratories report of 1975 [START_REF] James | The Darreus Turbine: A Performance Prediction Model Using Mltiple Streamtubes[END_REF]] gives a good state of the art after the first phase of research on the vertical axis in the 70s. The Darrieus wind turbine in the form of a Troposkin is then the reference. In this article, the author develops and studies a 'Multiple Streamtube Model'. Model's validation is based on comparisons with experimental results. These studies focus on the impact of solidity and Reynolds number on the performance of the turbine.

The experiments showed maximum performance for solidities between 0.2 and 0.3 (defined by the equation (2.2)). These values are still considered today as a classical solidity. Measurements were made at two Reynolds 0.3 × 10 6 and 3 × 10 6 . The higher Reynolds increased the efficiency of the wind turbine by about 10%. The report also investigates the energy production participation of each zone of the turbine. The figure 2.5 extracted from the report shows that the central zone dominates the energy production. The author explains that the central 60% of the turbine produces 84% of the energy. The blade tip and root zones do not operate at optimal TSR, generate more drag, and are in fact driven by the rest of the turbine.

More recently, in the article by Miller et al. [START_REF] Miller | Rotor solidity effects on the performance of vertical-axis wind turbines at high Reynolds numbers[END_REF]] the authors study the influence better performances with a solidity of 0.67 than with the highest solidity of 1.12. Knowing that changing the solidity implies changing the speed of rotation, the authors used the formula (2.3) incorporating the relative speed created by the movement of the blades. In the equation ρ stands for the air density, c the chord length, U the wind speed, θ the rotor rotation speed, r the rotor radius and µ the air dynamic viscosity. Using this quantity allowed to show that, whatever the solidity of the turbine, its reaction to Reynolds number variations is the same. A plateau in performance is measured for Re c > 1.5 × 10 6 .

Re c = ρc(U + θr) µ (2.3)
Howell et al. [START_REF] Howell | Wind tunnel and numerical study of a small vertical axis wind turbine[END_REF]] are also interested in the influence of different parameters on the performance of a Darrius H turbine. The author measured the power coefficient of the turbine at different Reynolds for a coarse surface finish and then with a smooth surface finish.

At low Reynolds, below 30,000, the rough surface finish increases the turbine's performance. The previous studies, although they find a higher optimal pitch angle at -7.8°. However, we note the higher solidity of the last turbine studied. It would also be interesting to consirere the study of Armstrong et al. [START_REF] Armstrong | Flow separation on a high Reynolds number, high solidity vertical axis wind turbine with straight and canted blades and canted blades with fences[END_REF] aiming at the measurement of the pitch angle and the blade tilt impact on the performances of a 2.5m in diameter Darrieus H turbine.

Here, an optimal blade pitch of -6°is observed. We note that here the difference with a lower angle, here -3 °, is minimal. For the inclined blades, we note a decrease in performance of about 10%. The author notes that the flow dynamics changed radically with the tilt of the blades, thus modifying the optimal TRS. In the configuration where the blades are inclined, the maximum Cp is obtained for a pitch of -3.5°.

The article by Mohamed [START_REF] Mohamed | Performance investigation of H-rotor Darrieus turbine with new airfoil shapes[END_REF]] describes the use of CFD tools to study the influence of design parameters on an H-turbine. In this study, the author explores many airfoils, symmetrical or not. By testing other airfoils than NACA, he observes that the S-1046 airfoil is the most efficient section with a Cp of 0.4051, which is 10.87% more than the second airfoil, the NACA0018 at 0.2964. However, the asymmetric airfoils degrades the dynamic stall behavior of the turbine and thus lessen the performance. During the study of the solidity the author observed better performances for a solidity of approximately 0.1 which is lower than what is generally observed in the bibliography.

In the paper by Elkhoury et al. [Elkhoury, Kiwata, and Aoun 2015] the influence of variable pitch, airfoil, and airfoil camber are studied on a high solidity turbine (0.75). The study compares experimental results with simulations. For the experimental part, an eccentric mechanism is used to actuate the blades and varying their pitch angle during the revolution. The comparison of a NACA0018 to a NACA0021 showed that the thicker airfoil allows for a better Cp for a high solidity turbine operating at low TSR (around 1). Next, the camber of the airfoil is studied by comparing the performances of a NACA0021 to a NACA63 4 -221. In this configuration, the symmetrical profile is slightly more efficient. Finally, the influence of the variable pitch is studied. The active pitch is more efficient for low TSR and up to the optimal TSR (about 1).

Above this limit, the difference is reduced and reversed for the turbine using the NACA0021 profile from a TSR of 1.35.

The study by Lohry and Martinelli [Lohry and Martinelli 2016], using URANS simulations, investigates the influence of turbine strength and size on the power coefficient of a three-blade Darrius H-axis vertical wind turbine. As the turbine size increases, the solidity is kept constant, thus increasing the Reynolds number. First of all, the study indicates that the turbine performance is almost unchanged for solidities ranging from 0.13 to 0.25. The lowest solidity maintains better performances once the optimum λ is passed than the highest solidities. The lower the solidity, the smaller the induction zone downstream of the turbine. When the size of the turbine is studied, the authors note that, when the turbine operates in a turbulent regime, the Cp max is obtained at the same TSR whatever the size of the turbine. Thus, the Cp max increases asymptotically with the size of the turbine.

Aerodynamics of vertical axis wind turbines

The study by Fujisawa and Shibuya [START_REF] Fujisawa | Observations of dynamic stall on Darrieus wind turbine blades[END_REF] investigates the dynamic stall phenomena on a single-bladed H-shaped darus turbine. The tests are conducted in water, in a current vein. Turbulence is studied using a PIV system. The study is conducted in two reference frames: the first part studies the behavior of the turbine in its entirety. Formation of pairs of counter-rotating vortices is observed. They form before and after the blade is perpendicular to the flow axis. The second part of the study is placed in the reference frame of the blade. They noticed that, at higher λ, the dynamic stall is delayed and occurs at higher angles of attack.

The study of SimaoFerreira et al. [START_REF] Simão | Visualization by PIV of dynamic stall on a vertical axis wind turbine[END_REF]] takes place in a wind tunnel and uses the same process to study the dynamic stall. The same observations as [Fujisawa and Shibuya 2001] are made. The authors tried to observe an influence of the Reynolds number.

However, performing measurements at Re = 5 × 10 4 and Re = 7 × 10 4 did not allow to observe an influence of this parameter.

The study of Buchner et al. [START_REF] Buchner | Dynamic stall in vertical axis wind turbines: Comparing experiments and computations[END_REF]] is similar to [START_REF] Simão | Visualization by PIV of dynamic stall on a vertical axis wind turbine[END_REF]] but this time, the experiment uses a two-bladed turbine. The measurements are compared to simulations.

The influence of the stall and the angle of attack on the performance of the turbine is studied. At low TSR the stall decreases the airfoil performances. At higher TSR, the dynamic stall angle is increased, but the angle of attack is low, thus decreasing the capacity of the turbine to generate torque.

Investigation the unsteady forces typical from VAWTS, the experimental work by LeBlanc and Ferreira [Leblanc and Ferreira 2018a] investigating the aerodynamic loadings of the VAWTS.

The work pretender in this paper gives great intel on how to measure forces of a VAWT model.

In

Wake and interaction between VAWT

Vertical axis wind turbines are studied for their faster wake recovery than HAWTs and their ability to be position closer on from each other in farm configuration.

The experimental study by Rolin and Porté-Agel [Rolin and Porté-Agel 2018] observed the wake of a vertical axis turbine in a wind tunnel using a PIV stereo system. These measurements illustrate the asymmetry present in the wake of a VAWT with a stronger kinetic energy deficit on the downstream side (blades moving up-wind into the flow direction) of the turbine. In addition, the study observed the formation of two counter-rotating vortices. The study concludes that, while the observations presented agree with the literature, the results presented may vary significantly. If the solidity of the wind turbine seems to be a primary factor explaining in part the great diversity of the observed wake, the phenomenon remains partially unexplained.

If the previous study focuses on the case of an isolated turbine, the article by [START_REF] Posa | Wake characterization of coupled configurations of vertical axis wind turbines using Large Eddy Simulation[END_REF] studies, thanks to an LES model, the wake of a double turbine. The paper presents the impact of a configuration where two turbines are coupled. Numerical results illustrate the influence of the direction of rotation of the turbines. The author observes a strong blocking effect between the two turbines, thus increasing the flow velocity in the interstice and downstream from the turbine, thus favoring its integration in a farm. In these results, the coupling of two turbines showed a wake smaller by two to three diameters than with a single turbine in the stream wise direction. the paper shows that turbines operating at higher TSRs have a more rapidly resorbed wake.

Ahmadi

Furthermore, the measurements showed that turbines produce slightly less energy if they are positioned in the wake. But the turbines placed at the edge of the wake on the positive side(blade going upwind) produced 10% more power than the same isolated turbine and 20% more on the negative side (blade going downwind). The authors believe that this phenomenon is related to the ability of vertical turbines to capture the kinetic energy of the wind regardless of its direction.

Wake interaction between HAWT

Above are presented papers on the VAWT's wake. But, considering that HAWT is the standard for the industry, a short review of HAWT's wake measurement is useful.

The technology being more mature studies are conducted in wind tunnels as well as on industrial farms as. For the latter configuration, most of the case studies are onshore. Small models are required for wind tunnel campaigns to fit several turbines in the wind tunnel. In the article by Aubrun et al. [START_REF] Aubrun | Wind turbine wake properties: Comparison between a non-rotating simplified wind turbine model and a rotating model[END_REF] show that when comparing a porous disk to a rotating three blades HAWT model, the wakes properties are similar for both models. This implies that porous disks can be used for studying HAWT farms in wind tunnels with a setup reproducing the atmospheric boundary layer.

The use of porous disks is, for example, used in the articles of Bossuyt et al. [Bossuyt et al. 2016b] and [Bossuyt et al. 2016a] where the technology is used to study the power output of a 100 wind turbines farm at a wind tunnel scale. The turbines are placed 7 diameters apart (in the wind direction). The wind speed is reduced by 20% by the front row generating a 50% power This study showed how a wake could be skewed when closely interacting with another wake and how the wake interaction can affect the turbine's power production, the wake velocity deficit, and the turbulence intensity.

When the needs are more specialized arises, the literature showcases experimental setups that expand on the classical usage. For example, Wildmann et al. [START_REF] Wildmann | Coplanar lidar measurement of a single wind energy converter wake in distinct atmospheric stability regimes at the Perdigao 2017 experiment[END_REF] used a set of two lidars to get a 2D measurement of the wind speed. Another example of specialized LiDAR use is described in the article by Kelberlau et al. [START_REF] Kelberlau | Taking the motion out of floating lidar: Turbulence intensity estimates with a continuous-wave wind lidar[END_REF] where the use of floating LiDARs is investigated.

Wind tunnel study of floating wind turbines

Tests in wave-tank allowed to reproduce for reproduction of the float's hydrodynamics. Same

St = L m t m U m = L r t r U r (2.4)
In wind tunnel tests of floating wind turbines, the float is replaced by actuators. The Lifes50+ project published the design and manufacturing process of two of these systems. The first one, illustrated in figure 2.9 and described in [START_REF] Bayati | Wind tunnel tests on floating offshore wind turbines: A proposal for hardware-in-the-loop approach to validate numerical codes[END_REF], proposes an actuator reproducing only the pitch and surge movements. These are the two most important degrees of freedom, especially if we reproduce conditions where the waves and wind are aligned. It is also possible to reproduce all six degrees of freedom with a solution using linear actuators. The one developed for Lifes50+ is described in [Bayati et al. 2018a]. Another design compatible with the Polimi wind tunnel is presented in [START_REF] Bayati | Design of a 6-DoF robotic platform for wind tunnel tests of floating wind turbines[END_REF]].

These tests have two main interests: the measurement of aerodynamic forces and the study of the generated wake. The first measurement is particularly useful for the analysis of floating wind turbines. Measuring the forces generated by the wind turbine on the float, allows the validation of models used for simulations but also the tests in basin using the same calculations for a software in the loop. For the study of the DTU 10MW HAWT turbine the validation of the AeroDyn model is described in [START_REF] Bayati | D3.1 AeroDyn validated model[END_REF]].

To study the aerodynamics and wake of the turbine, PIV measurements are performed in con- . Low values of V * W are synonymous with an unsteady regime and high values of a quasi-static regime. The impact of the float movements on the drag is more easily observed in the quasi-static regime and/or when the blades are tilted. In these conditions, the velocity spectrogram is smoother, and the float movements' impact is more easily identifiable.

The article [Bayati et al. 2018b] takes the conclusions made on the wake measurement by hot wire anemometer and adds the findings of the PIV measure. The author shows that it is challenging to describe the wake by averaging it with the float movements. It is more appropriate to describe and average it according to the angular position of the rotor. We thus find visible structures in the wake. The author also notes that the "information" of the structure is mainly at the level of the blade tips because the dynamics of the wake is only slightly visible at the center of the turbine.

V * W = V ∞ f.D (2.5)
The references presented so far use a wind turbine with blades adapted for the wind tunnel.

There is a second approach using a porous disk. It is, for example, described in the articles of Sandrine Abrun [START_REF] Aubrun | Round-robin tests of porous disc models[END_REF]] and Benyamin Schliffke [Schliffke, Aubrun, and Conan 2020]. This solution is more adapted to the study of the interaction of the wind turbine with the wind conditions of its environment or the study of the interaction between turbines in a farm configuration.

Conclusions

The literature review presented in the section illustrated the research on floating wind turbines.

Extensive research has been done on the study of floating horizontal axis wind turbines. Those This chapter describes the floater's preparation, the mooring lines reproduction, the instrumen- The wind turbine's aerodynamics should also be reproduced as it is strongly coupled with the floater's hydrodynamics. These campaigns use a Software in the Loop approach to simulate the rotor. Propellers are used for the reproduction of the turbine's thrust. A software computing the turbine's reaction to solicitations measured in the wave tanks and fed in real-time to the simulation defines the propeller's set-points. This chapter describes the propeller's integration on the model. The computations will be explained in the next one.

Figure 3.4 -Floater's degrees of Freedom

To reproduce the Nautilus-10 properties fitted with both turbines, we need to pay attention to the set of properties described below. This chapter, while explaining the scale model's preparation, addresses all but the last point:

1. The hydrodynamics, governed mainly by the floater's geometry, mass, inertia, and water density. Using accurate geometry and saltwater is one part of the equation. The mass and inertia should also be reproduced with great care. A chapter describes this operation.

Reproducing those parameters is the first step to getting sea-keeping properties from the scale model accurate to the full-scale FOWT.

2. The moorings lines should have similar stiffness. Due to the wave tank's depth simplifications were done for this campaign. They will be described in the mooring section.

Scaling laws

Model-scale testing requires the use of scaling laws in order to get representative properties from the scale model. All the scaling laws first consider the geometrical similitude defined by the equation (3.1). This scaling factor implies the scale model's length, surfaces, volumes, masses, and angles. Table 3.1 indicates those scaling factors for the two similitudes.

λ L = L scale model L f ull scale = constant (3.1)
Hydro and aerodynamics also drive the floating wind turbine's properties. Therefore, those two fields use two different scaling laws.

-The Reynolds scaling aims at keeping the ratio between inertial and viscous forces. This scaling law, used for aerodynamics, keeps the same Reynolds number between full scale and model scale.

Equation (3.
2)is used with ρ the fluid's density, V the flow speed, L the characteristic linear dimension, and µ the dynamic viscosity of the fluid.

Re = ρV L µ (3.2)
m λ L λ L Mass kg λ 3 L λ 3 L Forces kg.m.s -2 (N) λ 3 L 1 Speed m/s λ 0.5 L 1 λ L Time s λ 0.5 L λ 2 L Acceleration m/s 2 1 λ -3 L Inertia kg.m 2 λ 5 L λ 2 L
-The Froude scaling is the standard approach for marine engineering. It aims at considering the ratio between inertia and gravity forces by keeping accelerations the same between modelscale and full-scale. Equation (3.3) defines the Froude number with V the flow speed g the gravitational acceleration and L the characteristic linear dimension.

F r = V √ gL (3.3)
From those equations scaling laws are given in the table 3.1 with λ the model scale. Wave tank testing uses the Froude scaling laws while the turbine's aerodynamics uses the Reynolds scaling, conserving the Reynolds number in equation (3.2). One can note that if most of the scaling factors match between the two similitudes, speed factors will not. This topic is discussed more in-depth in the SiL chapter. However, even if the turbine is adapted to get the correct average Reynolds number, the speed variations imposed by the Froude scaling will not match the Reynolds for the blade. Variations will thus not match. This implies that the turbine's dynamic response will probably not match the full scale values. A Software in the Loop is thus used here. The solution is used as a workaround the Froude/Reynlods incompatibility and uses a propeller to generate thrust. The thrust set-points is computed in real time and uses the scale-model's motion as an input in order to model the interaction between the hydrodynamics and the aerodynamics.

Floater and wind turbines scale models preparations

The model needs to reproduce the FOTW specifications at model scale such as length, mass, inertia or center of gravitiy. The scale model's specification are derived from the full-scale specifications using the Froude scaling. This section describes the floater and wind turbines specifications for the wave tank testing. We first explain the pendulum methodology used in order to measure the scale model's inertia. The Center of Gravity is also measured and adjusted. During this process the model is divided into two sub-assemblies: the floater and the topsides. The topsides are carbon structure used to reproduce the wind turbine. For the experimental study presented here two topsides are used, one for the DTU-10WM HAWT and an other one for the WindQuest-10 VAWT concept. They are swapped depending on the wind turbine that is being studied.

The floater: Nautilus-10

For the floater, the Nautilus-10 semi-submersible is selected 2. It is well described during the Lifes50+ project, making it a better choice for academical studies of FOWT.

3. It uses a catenary mooring. Even if simplifications need to be done it can be easily reproduced in the wave tank contrarily to the TLP moorings.

As described in the Lifes 50+ project, the floater was designed to demonstrate the feasibility of a 10MW floating wind turbine. Such structure would be installed on locations with a water depth of 50 meters or more. The mooring system needs to be adapted for each location. The The scale is fixed at 1:42 using Froude scaling to fit the wave generator and fabrication cosntraints as weight, height and column diameter. Figure 3.6 illustrates the wave generator capabilities, the main constraint was to keep the wave-height and periods bellow the breaking limit on the left side of the curve. The table 3.2 is referencing the floater's main specifications at the wave tank scale. Figure 3.7a shows a CAD model of the floater as described by literature, and figure 3.7b shows a picture of the scale model. The pontoons seen in figure 3.7a, that don't impact the floater's hydrodynamics, are removed in order to meet the center of gravity (CoG) specification.

Floater weight and center of gravity

The floater model in figure 3.8 is built from wood for the heave plates and PVC for the columns.

In order to weigh it, steel weights are integrated into the heave plates. In order to match the correct center of gravity, the scale model is built lighter than the target mass, saving mass for weights in the columns. Using the threaded rods illustrated in figure 3.8b cast-iron weights are placed in each column. The CoG is measured by balancing the floater on a rope placed at the targeted CoG. The weights are moved until the desired CoG is obtained. From the literature, The WindQuest configuration barely had any margins and required that we overshot the target mass to get the center of gravity right. The final top-side weight could reproduce a 1200 tons wind turbine (instead of 1100 tons).We chose to match the CoG that the mass as the CoG depends on the rotor's geometry, but the actual mass is more subject to variations. We explain in the next section how the masses are installed to meet both mass and inertia specifications.

The figure 3.9 illustrates both configurations.

Inertia measurements (pendulum methodology)

I g = mg(d 1 + d 2 )T 2 0 4π 2 L (3.4)
Scale model's inertia is calculated using the formula (3.4) with "m" the scale model's mass, "g" the gravitational acceleration, "d1" and "d2" the distances between the rotation center and the wires, T 0 the oscillation period and L the length of the cables. The methodology is illustrated in the figure 3.11. The test consists in measuring the oscillation period of the pendulum system to determine the model's inertia. We need to measure T 0 in order to measure the inertia. The formula uses the oscillation period squared. It is thus crucial to reduce the uncertainty as much as possible. We thus measure the time elapsed for 20 oscillations, dividing by 20 the absolute uncertainty on T 0 . As the scale models are designed to be slightly lighter than the target weights the measurement allows for the placement of weights this process allows for the tweaking of the model inertia though the positioning of weights over the model.

Floater and wind turbines scale model: conclusions

Mass and inertia are two critical parameters for the reproduction of a FOWT's sea-keeping properties. It partly defines how strong the floater's response to the waves will be. Reproducing mass and inertia with precision is thus highly important. By designing the scale model with the idea of adding mass during preparation, it is possible to match the model-scale properties of the Nautilus-10 semi-submersible fitted with the DTU-10 reference HAWT and the WindQuest-10MW VAWT. For this last one, the correct center of gravity is chosen over the specified weight.

As for the inertia, the measurements match specifications reasonably well for the WindQuest configuration, while the DTU HAWT configuration proved to be harder to match due to the smaller margin for tuning the masses positions.

Moorings lines

This section describes the theoretical mooring properties and the assumptions and installation of the model's mooring.

Mechanical specifications

The theoretical mooring lines (represented in figure 3 The catenary mooring lines are thus replaced by springs and Dyneema lines installed as illustrated in figure 3.12. It is called "aerial mooring," as the mooring lines are installed above the MSL. The mooring is simplified to a solution with stiffness only on ⃗ X and ⃗ Y . The ⃗ Z is neglected, and the catenary mooring weight is replaced by added weights in the floater's columns to pull the floater in its waterline. When the floater is pitching or drifting on the surge axis, the catenary mooring will be pulled and rise from the bottom. This will thus increase the mooring's stiffness.

Unfortunately, the "aerial mooring" solution with spring has a constant stiffness. With will be presented in the results.

The mooring's stiffness is computed thanks to an OrcaFlex simulation ran by Kevin Mehring.

The anchoring is represented as a rotula on the ground following the geometry presented in This implies that we reproduce a 21 886 N/m stiffness and a 557 801 N tension in the line. For

Installing the mooring lines

In figure 3.16 and 3.12, the scale model in the wave tank, maintained in position by the four mooring lines, is ready for testing. The mooring lines are 90°from each other, oriented 45°from

the wave direction and parallel to the water surface. Each line is thus 7.453m long with the spring-loaded for the pretension and fitted with a load cell. In order to get the correct length and tension in the mooring lines, they are prepared using the setup illustrated in figure 3.17.

First, the operator attaches the sensor, the spring, and the mooring line on the left side picture

Conclusions on the mooring lines

As explained at the beginning of the chapter, mooring lines play a crucial role in the FOWT's sea-keeping properties. The theoretical mooring, a catenary solution, could not be reproduced due to the wave tank depth. An aerial elastic mooring is thus used instead using spring and lines above the surface. The solution only reproduce the mooring in the XY plan when Z is not considered. Thanks to Orcaflex simulations, equivalent stiffness and tension are computed, keeping the same resonance frequencies as those generated by the catenary lines when the floater is around its neutral position. Selecting the right spring stiffness and carefully measuring the line's length while under tension allows for the correct oscillation periods while performing decay tests. However, this solution hase a constant stiffness, when a catenary mooring stiffness increases with the displacement from the 0 position. This limitation should be kept in mind while discussing the results.

Electronics and instrumentation

The last two sections described the scale model's conception and preparation. After explaining how to get the correct sea keeping properties, it is necessary to explain how they are measured.

Finally, this section describes the instrumentation, the electronics, and the acquisition devices necessary for the experimental campaign.

Motion tracking: Qualisys

Studying the model's reaction to the waves requires measuring its position without interfering with the motion. Qualisys is a videogrammetry system frequently used in wave tanks. A prevision of about one millimeter is appreciated in order to get consistent uncertainty with the wave gauges. In order to meet these requirements and needs, the Qualisys motion tracking system is employed. It uses markers and infrared cameras illustrated in the figure 3.18 in order to measure the generate marker's motion in a volume in from of the cameras. Thanks to a calibration, the Qualisys system generates a reference frame and reconstitutes the motion of a Rigid body composed of the markers as illustrated in the figure 3.19. Such a system allows for a submillimeter uncertainty on the rigid body's position. A trigger synchronizes the motion tracking system with the other instruments. Those measurements, acquired at 100 Hz, are transmitted via a TCP-IP connection to the acquisition system to generate the measurement files and to the Software in the Loop to compute the Floater's motion in real-time.

Waves probes

In order to study the model's dynamic response to waves measuring the solicitation is necessary. As the wave tank has the particularity of being filled with salt water, the resistive gauges commonly used in wave tank will not work. Instead, electronically control wave gauges as used as they can operate in salt water. The wave gauge transmits the surface elevation to the acqui-

Mooring sensors

A sensor capable of being installed above the water while being immersed recurrently is thus needed. Their position is illustrated in figure 3.5, the strain gauge sensor is illustrated in figure 3.21. At one end, it is connected to the rails on each side of the wave tank. On the other end, the sensor is connected to the spring of the mooring line. Its output is connected to the acquisition system. The acquisition rate is chosen to compromise the need to capture high-frequency phenomenons such as wave impacts and slow frequency phenomenons such as the scale model's surge motion.

High-frequency phenomenons are restricted by the Nyquist frequency (half of the sampling frequency). Low-frequency phenomenons are impacted by the frequency resolution defined by equation (3.5) with F s the acquisition frequency and N the number of samples. As PSD analysis requires windowing, the frequency resolution is the most constraining factor. At the end of each test, the acquisition program merges together its measurements with the measurements of the Qualisys motion tracking system. An individual file containing all the measurements from the experiment is thus generated.

F res = F s N (3.5)
Figure 3.22 -Acquisition system

Propeller's power supply

The propeller's power supply is separated from the scale model in order to meet the mass and inertia specifications. It is thus placed on the walkway in front of the scale model, and a power supply line runs from the walkway to the scale-model. This system fits one primary need: Each motor consumes up to 310W continuous and is sensitive to power losses. The power supply needs to be able to supply this wattage while mitigating the constraints listed below 1. The power lines need low electric resistance to reduce Ohm losses as the motors are sensitive to voltage variations and only run on 24V.

2. The wires should be as flexible and light as possible in order to reduce its influence on the model's motion.

From those needs and constraints, the power supply illustrated in figure 3.16 is used. A beam with a carbon fiber tube supports most of the cable's weight. The carbon tube can be retracted of extended, allowing for the tuning of the cable's position depending on the scale model's surge motion. Using this solution mitigates the cables' impact on the scale model and allows for good repeatability as the stick's position can be marked and repeated from one test to the next one.

The cables are 4mm 2 sections allowing for voltage drop lower than 1V when considering the whole system's electric resistance.

Conclusion on the campaign's electronics and instrumentation

This section gives an overview of the technical constraints and needs for the power supply, waves probes, sensors, and acquisition devices used for this experimental campaign. Those requirements on the measurements are specified to extract valuable information on the FOWT's properties.

Though those measurements the 6 DoF model position, the wave elevation, generated thurst and tension in the elastic lines are simultaneously measured at 100Hz. The power supply is needed for the wind generation and everything is made to limit the effects of the cables. Exploiting those measurements is the topic of the chapter 5.

Numerical tools

Numerical tools are part of the development and testing of Floating Offshore Wind Turbines.

Therefore, those tools need to be used together with the experimental tools. This thesis is no exception to the rule. We thus needed numerical tools in order to validate and extrapolate from our experimental results. The chapter 5 presents the experimental results. The DTU HAWT configurations is also simulated with OpenFAST in order to compare a model to the experiment.

The simulations presented in this thesis is sourced from the public OpenFAST model released for the Lifes50+ project. This section will thus describe the simulation tool.

OpenFAST is an open-source wind turbine simulation tool first developed by the National Renewable Energy Laboratory (NREL). OpenFAST is thus using a "Glue code," allowing for communication between the different modules. Each code is specialized for one type of computation.

The solver is bringing together aerodynamic computations by AeroDyn, hydrodynamic by Hy-droDyn, servo, and elastic engineering models. We will only describe the Aerodynamics and Hydrodynamics module here.

Conclusions

This section described the design and preparation process of the scale model for the wave tank measurements campaign. The process aims at getting a model with properties as close as possible from the scaled-down Nautilus-10 semi-submersible floater, DTU10 reference HAWT, and WindQuest 10MW VAWT. This preparation is done in order to model the sea-keeping properties of the floating wind turbine in the wave tank. As the scale-model couldn't perfectly fit the numerical model modifications are made to the simulations in order to match, for example the VAWT's mass and inertia.

First, great care was paid to reproduce the floater's geometry, mass, and inertia. Those parameters will define the floater's response to the waves solicitations. A significant part of the model's preparation was thus dedicated to matching the floater's weight, the center of gravity, and inertia by using weights distributed all over the model.

Then, Closely coupled to the hydrodynamics are the mooring. Few modifications are made to simplify the mooring model. For simplicity and feasibility reasons, the chains mooring is modeled by an "aerial elastic mooring" in the wave tank. A spring connected to a rope holds the floater into position. This solution will only reproduce the catenary mooring's stiffness on XY plan and around the zero position.

Also crucial to the modeling of a FOWT is the tower stiffness. However, for simplicity reasons, these parameters were not considered, and guy ropes are used to stiffen the topsides.

Instrumentation was selected in order to get as much information as possible from the experimental campaign. Those measurements, once processes are fitted with simulation for further study of the concept.

Introduction

When going offshore, the floater and wind turbines experience a strong coupling. Previously in the Material and methods, we explained how turbine inertia, mass and mooring properties could affect the floater sea-keeping properties. Wind turbine thrust plays a similar role. As the turbine is exposed to wind, it will generate thrust, and phenomenons such as floater motion or tower bending will vary that thrust. Hence the importance of modeling this phenomenon for wave tank testing. In order to fulfill that need, several solutions are available and described in the literature review in chapter 1. Each solution has its advantages and disadvantages. For this Ph.D. thesis, Software in the Loop (SiL) is used.

The Software in the Loop approach is derived from Hardware in the Loop, used in industry. Both technics aim at testing a sub-structure without integrating it into the whole system. Here the SiL will replace the aerodynamics by a simulation and a actuator to test the platform reaction to wind and waves. However, why not use a VAWTS or HAWT scale model installed on top of the sub-structure? There are two main technical challenges:

First, as explained in chapter 3 on the material and methods, respecting design mass and inertia is highly important. These specifications play a huge role on the FOWT response to waves.

Furthermore, it is challenging, even impossible, to match these criteria with an functional VAWT at a wave tank scale. Using a propellers and a SiL approach is thus also helping achieving a more true to model experiment before turning on the thrust generation. 1. The thrust generated as a reaction between the wind turbine and both the environmental wind and the apparent speed. The SiL developed for this campaign and described here reproduces this thrust.

2. The gyroscopic forces are due to the rotating mass. This phenomenon is non-negligible as it brings stability to the system. However, reproducing such forces would make the scale model more complex. In the following article, Desmond, Hinrinchs, and Murphy [Desmond, Hinrichs, and Murphy 2019] describe the use of such system and its impact on uncertainties. Indeed reproducing the gyroscopic forces implies the use of rotating masses. This would result in more complicated inertia to match when preparing the scale model. On top of this first difficulty modeling both VAWT and HAWT would require two different systems as the blades are not rotating on the same axis. Similarly, reproducing aerodynamic moments implies using several propellers and a more complex simulation that would go against our will to use simplified computations.

The following sections will first develop on the SiL concept which is decomposed into two parts: control laws and propellers applying those control laws. First will be a more in depth description of the SiL concept then, this section will tackle the description and the characterization of the propellers in charge of making those computations a reality.

Follwing the propellers calibration, the nest sections describe the computations used for the SiL specially developed during this thesis for the simulation of the DTU-10MW HAWT and the WindQuest 10MW VAWT wind turbines. As explained above, one of this thesis purposes is to investigate the effects of different SiL hypotheses on the float. A constant thrust generation is thus compared to two drag disk based computations: the constant thrust and the constant Tip Speed Ratio. The effects of those control laws will the be studied as a conclusion for this chapter.

Software in the Loop: the concept

A Software in the Loop approach aims at emulating the wind turbine aerodynamics in a wave tank environment where Froude scaling is used. The SiL will consider the environmental wind speed and the apparent wind speed due to floater motion to compute a resulting aerodynamic response of the wind turbine. This response will also depend on the operating parameters such as rotation speed and blade pitch angle. Computing the resulting thrust is just a simulation. The specificity of the SiL approach is to feed the model response in real-time to those simulations to give those results as a set-point to the propeller emulating the wind turbine. This section describes the process used for the experimental setup developed for this thesis. Before installing the propeller system on a FOWT model, calibrations and characterizations are needed to understand the system better. Therefore, the next few subsections will go through the main tests run on the system, such as static calibration of the rotor thrust, influence of air-gap between the rotors, delay to the response, or dynamic response of the system.

Static calibration

The static calibrations aim at characterizing the propeller thrust. It is essential to carry out this measurement with the thrust generators in their final configuration to account for the impact of the counter-rotating configuration, the fairings, the mast, the power supply, and the Joule losses in the electric cables. In addition, running those calibrations allows for measuring the relationship between the throttle and the propeller thrust.

For the calibration, the propellers are installed on a 6-DoF balance. The same power supply is used to fit the test conditions with the setup used in the wave tank. Then, the LabVIEW Both upstream and downstream propellers are thus first tested independently and then together. This process indicated that the upstream propellers are not affected but the downstream propellers are.

Air-gap, blockage and propeller efficiency

The design chosen for the propeller system uses a counter-rotating system in order to achieve a wider thrust range into the same volume. However, this solution implies that one rotor will be operating downstream from another propeller and will also see its incoming air-stream blocked by the structure. Fortunately, the literature gives information on the parameters influencing the propeller thrust. For example, the article by Simoes [Simões 2015] discusses on the choice of blade pitch on the performances, and Theys et al. [START_REF] Theys | Influence of propeller configuration on propulsion system efficiency of multi-rotor Unmanned Aerial Vehicles[END_REF]] discuss the impact of the propellers configurations for a counter-rotating cluster of propellers.

The study described here does not aim to find optimal parameters, but a basic study is still appreciated. Indeed, this system does not need to extract the most thrust out of the propellers.

Nonetheless, knowing the influence of the air-gap (the distance between the rotors) and the influence of the structure on the downstream propellers is valuable for designing the system.

In order to quantify the influence of the rotor distance a setup similar to [START_REF] Theys | Influence of propeller configuration on propulsion system efficiency of multi-rotor Unmanned Aerial Vehicles[END_REF] is used. Rotors face each other with a distance varying from 0.1 to 2 rotor diameters. Using the 6 DoF scale measurements, the downstream propeller efficiency is measured. The efficiency is defined in equation (4.4) as the ratio between the downstream and the upstream propeller thrust. Figure 4.8 illustrates the measurements of the downstream rotor efficiency depending on the air gap. Operating downstream from a first rotor will result in 17 to 22% less thrust generated. A clear trend is observed, the further the propellers are from each other, the worst it will be for the downstream propeller. With only a 5% difference between the two extremes, the distance between rotors is a factor to consider when designing the system but is not crucial.

Ef f iciency = T hrust downstream T hrust upstream (4.4) As a conclusion on those design parameters studying the influence of the air-gap and the fairing gave good insights on how the system should be designed. First, the system should be designed so that the two propellers are operating as close to each other as possible. Similarly, a fairing can be used without fear as its influence is small and could even be compensated by reducing the distance between the propellers.

Conclusion on propellers

The section described the Propellers used for the SiL. Choosing the solution with versatility in mind allows for the thrust reproduction of both wind turbines with the same experimental setup.

Indeed, by generating a thrust of up to 25N, the generator is suited for most use cases. This includes the DTU 10MW HAWT and the WindQuest 10WM VAWT using one set of propellers for each rotor.

The thrust generator having the particularity of using a counter-rotating the interaction between the two propellers is investigated. Through the investigation of the effects of the air-gap, the fairing, and the support structure, it has been demonstrated that operating the two propellers as close to each other as possible is the most crucial parameter varying the downstream thrust by 5%. Fairing and structure also proved to have a small influence. Therefore, their effects on the thrust are deemed negligible.

Once the design parameters are fixed, and the system is built, a characterization is needed.

Static and dynamic calibrations help validate the thrust generation system. First, the static calibration determines the trust range and defines the relationship between throttle and thrust.

This calibration made clear that no throttle above 80% is usable, resulting in a maximum thrust of 25N with both propellers operating. This combined operation proved that the final system reduced the downstream propeller thrust by 19%.

A dynamic qualification is realized after studying the design parameters and calibrating the propeller. First, a 170ms delay between the set-point and thrust response is measured through a cross-correlation study. Next, a frequency analysis pushes further the dynamic characterization of the propellers. They use set-points generated with OpenFAST, which allowed for the generation of representative set-points by the propellers before integrating the propellers into the whole system. This frequency analysis highlighted a globally good response from the propellers. Though the propellers are deemed satisfying for usage, there is still room for technical improvements.

For example, generating and implementing a transfer function for the set-point would allow for a thrust generation more true to the computed thrust.

Thrust computation and hypotheses

This section aims at explaining the computations used for those wave tank campaigns. However, some context would be helpful before diving into mathematics. The model developed for this new SiL considers the wind turbine as a homogeneous surface with constant properties. Due to time constraints and as the first comparisons with OpenFAST are deemed satisfying, the wind turbine interaction with its wake is not considered. It is thus a simplified drag disk model incorporating the pitch and surge motion on top of the environmental wind speed to compute the wind turbine thrust. As the floater is moving the wind turbine TSR will vay thus inducing thrust coefficient variations.

⃗ T = 1 2 ρSC t ⃗ V 2 rel (4.5) ⃗ V rel = ⃗ V 0 + ⃗ V a (4.6) T = 1 2 ρSC t (V 0 + ẋ + θR) 2 (4.7)
In order to acknowledge this fact and model the phenomenons, three hypotheses are used during the wave tank campaign: the constant thrust, the constant Tip Speed Ration, and the constant rotation speed. The first one, constant thrust, is not a SiL approach. The propellers are set for a pre-defined thrust and will not vary that set-point as the floater is moving. This option being the most basic, it is taken as a reference point when the other hypotheses are compared to OpenFAST BEM model. The subsections below describe each hypothesis. The first assumption is the one of a constant thrust. Environmental wind speed is the only parameter for thrust computation. This assumption does not take into account the floater motion. Equation (4.6) is simplified to V = V 0 . In figure 4.15 the thrust coefficients used for this computation. This hypothesis is using the work already done at the Ifremer Brest wave tank in an effort to introduce SiL to the available tools.

Constant thrust

Constant TSR

For the second hypothesis, the wind turbine constantly adapts its rotation speed, operating optimal TSR. For each time step and depending on the apparent wind speed, the controller adapts the rotation speed in order to follow the curve presented in figure 4.15. This hypothesis simulates a configuration where the wind turbine controller knows the platform attitude and uses the information to maximize power production. Thrust is computed by using the apparent wind speed and the resulting thrust coefficient in the equation (4.7). The last hypothesis reproduces a wind turbine operating at a constant rotation speed. The parameter is set depending on the environmental wind speed. The TSR (defined in equation (4.8) with r the rotor radius θ the angular volocity of the rotor and V the whind speed) is thus varying with the floater motion. The rotation speed is defined with the environmental wind speed. However, as the floater moves, the apparent wind speed will vary (such as in equations (4.6) and (4.7)). For each time step, the resulting tip speed ratio is computed, and the thrust coefficient is computed with the curve illustrated in figure 4.16 before being used as input into equation (4.7) with the apparent wind speed.

Constant rotation speed

Influence of the control laws on the WindQuest FOWT

As explained above two control laws are implemented to the SiL on top of the constant thrust:

the constant Tip Speed Ratio and the constant RPM. Those different control laws have an influence over the FOWT response to waves. After describing the differences between those two control laws, the next section will aim at describing those differences through the experimental results. First, using decay tests allows for the measurement of the FOWT damping. Though the testing of different wind speeds. Two regular waves tests are also presented in order to give a first illustration of the hypotheses influence over the FOWT response to waves. Finally irregular tests are showcased in order to observe the influence of the control laws in representative conditions.

Control laws and negative damping for the WindQuest 10 turbine

During the wave tank campaign, the WindQuest configuration was tested with two different control laws. The first one emulates a wind turbine adapting its rotation speed for each time step in order to maintain the optimal tip speed ratio. This hypothesis is not realistic as it would impose high constraints on the generators and the rotors. However, this control was still used as it matches the DTU HAWT emulation (that brought good results) and thus makes the comparison of the two turbines possible.

To study the WindQuest turbine with a more representative control law, a second hypothesis is implemented to the SiL: the constant rotation speed. The wind turbine maintains a constant rotation speed defined by the environmental wind speed. It is not adapting anymore to the floater motion. Figure 4.17 illustrates the RPM and TSR setpoint used for turbine control depending on the wind speed. Bellow the rated wind speed (at at 11.4 m/s) the TSR is maintained at optimal (the rotation speed is thus proportional to the wind speed) to maximize the power production.

Above the rated wind speed, the TSR is modulated in order to keep the power constant.

The following paragraph will evoke the concepts of positive and negative damping. Those terms refer to a system (here the FOWT) oscillation. A system oscillation can be described using the equation (4.9) with A the amplitude of the motion, Λ the decay rate, t the time, ω the angular frequency, and ϕ the phase angle. The equation (4.10) computes the damping ratio from the decay rate. If ζ is positive, the system motion is dampened and, the motion amplitude will decrease with time if no energy is brought to the system. On the other side, if ζ is negative, the system motion will increase over time. The terms of positive and negative damping come from this formulation. Negative damping is a critical problem. For HAWT, using a land-based controller generates negative damping when the turbine is operating above the rated wind speed With the same wind speed variations, its thrust will decrease, thus amplifying the floater motion and generating negative damping. the difference between the two control laws is marginal. On the other side, when operating at the rated wind speed, the constant tip speed ratio controller generates oscillations 36% higher than the constant RPM controller. Those two tests illustrate the influence of the computations presented above. to ease the comparison between the two load cases.

For the normal sea states, where aerodynamic forces play a significant role on the FOWT response (more on this in the next chapter) the constant TSR hypothesis generates a strong response on both the pitch and the surge resonance frequency. This is the most notable result and the only significant difference for the surge axis.

Conclusions on the control laws

Through this section the divergences between the constant thrust, the constant Tip Speed Ratio and the constant rpm SiL hypotheses are described. If at low wind speed modeling a wind turbine thrust with a TSR or a rpm set-point introduces only few divergences, the situation changes drastically at rated wind speed and above. Each control law will sustain the float motion instead of damping it at different wind speeds. Finally, using the SiL proved to have an effect of the FOWT sea keeping properties. Its response to waves spectra is lowered when modeling the wind turbine with a dynamic representation of the thrust (constant TSR or constant rpm) when compared to a constant thrust hypothesis. Moreover the last hypothesis will exhibit strong peaks of energy at pitch and surge frequency while the first hypotheses won't.

Software in the Loop: Conclusions

The Software in the Loop approach is a solution to the Froude/ Reynolds incompatibility.

Directly inspired by the Hardware in the Loop approach, the solution simulates the wind turbine interaction with the floater thanks to propellers and real-time thrust computations.

In the course of this chapter the design of the propellers system is described. In order to maximize the thrust range, a counter rotating system is used. This solution required more forethought as propellers are interaction with each other and with the structure. After studying the influence of the air-gap and blockage the propeller system is characterized in order to know it static and dynamic properties. Through this process, the system proved it capability to accurately reproduce the wind turbine thrust at the model scale.

Those propellers apply set-points determined by control laws modeling the wind turbine. In this SiL the measurements are used to feed drag-disk models of the wind turbine computing it thrust from the Qualisys live streamed measurements. Even though these hypotheses are basic compared to the state of the art they proved to be able to model the interaction between the turbine and the floater thus influencing damping and reaction to wind and waves solicitations.

For future works, there are two axes of improvements for the system. First, the propellers could receive improvements. Reducing the system response time and further pushing the propeller calibration with a control solution considering the propellers' transfer function would make the system more accurate with the set-point. On the computation side of the SiL, the simple drag disk representation fits the campaign needs. Nevertheless, similarly to Arnal [START_REF] Arnal | Modélisation expérimentale d'une éolienne flottante par une approche « software-in-the-loop[END_REF] work, having more refine simulations for VAWTs such as those developed by Leroy [Leroy et al. 2018] would be interesting. Such simulations, computing forces such as aerodynamic torque and rotor inertial would benefit from the multiple DoF propellers system, further enhancing the SiL fidelity.

Finally, on the influence of the control laws. The model designed to match the DTU HAWT thrust represents a wind turbine adapting its rotation speed to the floater motion keeping its TSR constant. However, when modeling the wind turbine, this is not the most representative solution.

A second model reproducing the WindQuest thrust with constant RPM is thus implemented and compared to the first one. Similar to the HAWTs controller, the model gives roughly the same turbine response for both models. However, when the turbine operates at or above the nominal wind speed, the differences become significant. At nominal wind speed, maintaining the optimal λ generate significant negative damping maintaining the FOWT oscillations and increasing the fatigue loading while a constant RPM law will dampen the float motion. Conversely, when operating above nominal wind speed, the constant RPM will generate negative damping while adapting the tip speed ratio will dampen the floater motion Chapter 5 The chapter follows this plan. First, the repeatability is verified. Indeed, as the measurements were carried out during two campaigns several months apart, assembling and disassembling of the model was needed. It is thus necessary to verify that this process did not affect the model properties.

WAVE TANK RESULTS

Contents

Then come the decay tests and measurements of the capsizing moment. Those tests respectively measure the FOWT natural frequencies and the wind turbine capsizing moment. Those two tests are carried out without any wave generation and give a first insight into the FOWT properties.

Here, replacing the DTU HAWT with the WindQuest VAWT proved to influence the float significantly. The experimental results will explain why and how.

Third comes the validation of the SiL with OpenFAST. From this point, results with SiL in irregular waves are presented. The section thus aims at qualifying the simplified Drag Disk approach by comparing the experimental results with the reference simulations of OpenFAST.

Finally, the influence of the SiL on the scale model sea-keeping properties is investigated by analyzing the FOWT Response Amplitude Operator (RAO). This frequency analysis gives the float response to representative sea states.

Verification of the repeatability between test campaigns

The objective of the first measurements is to verify the repeatability between two campaignes realised five months apart. Those two campaigns implied assembling and disassembling the model twice. A lot of care has been taken for positioning and mooring. To ensure the test repeatability and the results continuity, we compare the motion signals for the main three DoF: pitch, surge, and surface elevation by testing the model with regular or irregular waves and with or without thrust generation. Note that, for irregular waves, the JONWSAP spectrum is reproduced in the wave tank. The article by [START_REF] Isherwood | Technical note: A revised parameterisation of the Jonswap spectrum[END_REF]] describes the wave spectrum and defines the parameters such as the significant wave height and period.

Thus, the first tests of the second campaigns are identical to a subset of those carried out during the first campaign. Those measurements will be used for comparisons. First, the time series were

Decay tests

Wave-tank testing usually starts with decay tests. The float at rest is excited with a pole, oscillating it according to degrees of freedom. The floating wind turbine behaves as a dampened mass-spring system and oscillates at its resonance frequency. Each degree of freedom has its natural frequency measured during those tests.

As presented in the previous chapter, the model is fitted with Qualisys markers, allowing its position measurement through time thanks to the videogrammety system Qualisys. For the Surge, Yaw, and Heave DoFs presented in table 5.2, the differences are relatively small between the two FOWTs. Indeed, the floater hydrodynamics and moorings mainly govern motion on those axes. On the other side, the pitch period shows a 25% difference. Movement is influenced by the FOWT inertia on the Y-axis (the pitch rotation axis). As explained in the chapter 3, the DTU HAWT pitch inertia is 155% the WindQuest VAWT, hence the difference on the two pitch periods.

The VAWT shorter pitch period of oscillation makes this design more sensitive to the typical spectrum of the exciting wave of the Gulf of Main reproduced for these campaigns. On the other side, the DTU 10MW HAWT designed pitch period is significantly lower. The effects of this pitch period will be discussed in more details in section 5.5. A frequency approach with Power Spectral Density analyses is used in a second time. This methodology allows for identifying the phenomenons responsible for the differences quantified by the cross-correlation.

Wind turbine capsizing moment

We are introducing the concept of wind driven and wave drive Design Load Case (DLC). The concept is seen in the report D4.6 from Lifes50+ [START_REF] Lemmer | D4.6 Model validation against experiments and map of model accuracy across load cases[END_REF]] and describes conditions where the floater motion on a certain degree of freedom is mostly influenced by the waves or the wind forcing. Therefore, keeping this concept in mind is useful in order to get a better understanding of the results.

Statistical comparison

First, and to quantify the effects of the SiL, the wave tank tests with a constant λ SiL hypothesis and the tests without any thrust generation are compared to OpenFAST using the cross-correlation. The method used here will compute the cross-correlation between two signals using equation (5.4) with x and y the two vectors and d the phase difference. This methodology will give similar results to the correlation but accommodate for phase difference when the experimental files are manually synchronized.

crosscorrelationx, y(d) == Σ n i=1 (x(i) -x)(y(i -d) -ȳ) Σ n i=1 (x(i) -x) 2 Σ n i=1 (y(i) -ȳ) 2
(5.4) First, the cross-correlation between the SiL thrust and the OpenFAST thrust indicates that the simplified approach gives valid results. This computation can be used as the first approach in between inserting itself between inertia tests (without thrust) and SiLs powered by OpenFAST.

The high cross-correlation indicates that this SiL should reproduce not all but most of the phenomenons.

The pitch cross-correlation between OpenFAST and experiments is used for the platform motion as the key metrics. Indeed, this DoF is very sensitive to the action of the wind turbine. The constant thrust tests, are taken as a reference to compute the gains obtained thanks to the SiL computations and thrust reproduction. DLCs with higher wind speeds show the most significant improvements as a wind forcing strongly influences the floater motion. On the other side, waves driven DLCs showcase decreased correlation delta. Two reasons can be suggested. First, the wind forcing is decreased, and the waves are forcing increases reducing the aerodynamics influence on the floater motion. Second, one can note that the absolute correlation decreased. For those DLC, moorings play a more significant role in the floater movement. The differences between model aerial mooring and the theoretical catenary mooring are highlighted.

PSD analysis

Using Power Spectral Density analysis is a current practice when models are compared to experiments for frequency analysis. Therefore, the solicitations will be similar. The Heave PSD shows slight variations between the experiment and the model but is globally matching. For pitch and surge PSD the response to waves is almost the same. However, the model reaction is stronger on lower frequencies, around the pitch and surge natural frequencies. The SiL absorbs a significant part of the energy on that frequency but divergences between the model and the simulation are still observed.

For the Normal Sea States, illustrated in figure 5.6 similar observations are made. Though a global statement is made. This is probably due to the smaller waves and motion decreasing the signal-to-noise ratio. For Heave and Surge, the observations are similar to the Extreme Sea

States. The biggest differences are observed on the pitch PSD. Without the SiL, the model demonstrates a big spike of energy at the pitch natural frequency. However, the SiL almost eliminates that spike and generates a PSD matching fairly well the OpenFAST computations.

To conclude, using PSD analyses proved to be a valuable tool for the qualification of the SiL fidelity when taking OpenFAST simulations as a reference. The analysis demonstrated that the FOWT response to wave globally fits the OpenFAST simulation. Moreover, using the SiL proved to dampen a big energy spike present in the experimental measurements without SiL and not

A note on the reproduction of the mooring lines

The chapter on the materials and methods explains how the model was designed, stating that the mooring lines were built as springs connected to the model by thin lines running above the water. This essentially turns the model into a mass-spring system with small damping generated by the FOWT hull. When excited by the waves, the system is thus constantly oscillating around its natural frequency. This phenomenon was expected, and its influence is mostly visible when observing the Surge PSD. This phenomenon generates the clear energy spike observed in chapitre 4/figures 5.5 and 5.6. But on those chapitre 4/figures, the Surge PSD computed from the OpenFAST model is not visible.

Response Amplitude Operator and comparison of the two

FOWTs

Finally comes the comparison of the two FOWT responses to wind and waves solicitations.

To pursue this comparison, several tools are available, but the one fitting best our needs is the Response Amplitude Operator (RAO). This measurement essentially defines the floater function transfer to waves solicitations. The Response Amplitude Operator (RAO) is defined by the function in equation (5.5) and quantifies the floater response to the sea, P SD dof (f ) is the floater Power Spectral Density on a degree of freedom, P SD waves (f ) is the waves PSD and γ 2 i is the coherence.

The FOWT RAO is measured through the reproduction of irregular sea states. This measurement was repeated for several sea states. Through this process, the differences between the two FOWT and the influence of the SiL are observed. Results will show that the RAO is similar from one test to another, but the signal-to-noise ratio varies greatly. The following few paragraphs will thus present those measurements before explaining the averaging process used to get cleaner values on the lower frequencies. The RAO measurements presented until now allowed for a couple of observations to be made but they unfortunately lack of precision on the lower frequencies around the pitch and surge natural frequencies. To improve this measurement, longer tests would help as they would decrease the measurement uncertainties and, most importantly, reduce the RAO measurements frequency resolution. But, to mitigate that problem and enhance the measures a post-process solution is proposed.

RAO dof (f ) = P SD dof (f ) P SD waves (f ) withγ 2 i (f ) > 0.
All the RAO measurements are averaged out to mitigate the strong signal-to-noise ratio on the lower frequencies. The process is illustrated in figure 5. [START_REF] Bayati | A wind tunnel/HIL setup for integrated tests of Floating Offshore Wind Turbines[END_REF]. The orange plots are the experimental As a conclusion on the RAO, this section described the use of the Response Amplitude Operator for the study of the two FOWTs models. Running this analysis highlighted the changes generated by the replacement of the DTU HAWT with the WindQuest VAWT (with lower CoG, mass and Inertia). On the pitch axis, the response to waves is stronger for the VAWT, presenting a higher pitch natural frequency closer to the wave spectrum. On the other side, the surge shows the same response to the waves an there is only a small variation of the response amplitude at the surge natural frequency. Invariant from the turbine, using the SiL proved to significantly dampen the energy levels on those natural frequencies while having a smaller influence on the waves bandwidth.

Finally, for this thesis, those results bring more to this work than just giving information over the sea-keeping properties of the FOTWs. Measuring the RAO or function transfer of the FOWTs is key information for the next chapter on the wind tunnel study of the WindQuest VAWT.

Knowing the response to the most probable wave height and period is part of the fundamentals But before jumping to the next phase of this thesis, there is one last result that deserves attention: the extrapolation of a 13MW design intended to fit better the Nautilus-10 semi-submersible. This extrapolation is founded on all the results presented from the beginning of this chapter and is shown in the section 5.6. -It would lower the LCOE by minimizing the cost of the float.

-It would have a mass and inertia closer to that of the DTU 10MW HAWT, allowing the float to work in conditions closer to those for which it was designed.

The turbine is up-scaled by using the static capsizing moment measured experimentally. Measurements showed that the VAWT has a 53% lower capsizing moment. The development ex-plained below aims at matching that capsizing moment with the DTU-10WM HAWT. In order to get a first approximation of the target power, the Froude scaling is used.

Be M the static moment of inertia. It can be considered as roughly proportional to the turbine thrust and its size. The assumption is described in equation (5.6). It is thus possible to consider the static moment of inertia is proportional to the turbine size cubed. From Froude scaling, the power is defined as being a function of λ 7/2 . From this scaling factor, the ratio between inertia and power is computed in the equation (5.7). From this equation, the turbine nominal power is computed in order to fit the static moment criterion in the equation (5.8). From those equations, a 13MW WindQuest VAWT turbine should have inertia closer to the DTU 10MW

HAWT, making the float more stable while reducing the LCOE.

M ≊ F.l ≊ f 2 l ≊ l 3 (5.6) M P = λ 7/2 λ 3 = λ 3/2
(5.7)

P = M 2/3 = 1.55 2/3 = 1.34 (5.8)

Concept of a WindQuest 13MW turbine

By using in house code developed by HydroQuest and by knowing the new target power, a

WindQuest 13 MW VAWT concept is drawn. The tool takes several parameters such as the nominal power, the aspect ratio, or the number of tension cables in the blades to estimate the properties of a WindQuest turbine. The code uses the material properties of carbon fiber to estimate the aerodynamic and centrifugal forces on the turbine blade. The turbine is then modeled as a set of beams as illustrated in the figure 5.16. The table 5.4 sums up most of the parameters used for the design of that turbine, and most importantly, the table 5.5 includes the numbers that will be necessary to compute the seaworthiness of such a concept.

These parameters allow the generation of a 1548 tons rotor with blade stresses similar to those calculated for the WindQuest 10MW VAWT. To calculate the mass and inertia of the overall wind turbine, it is explained above that the routine considers beam elements. Their length and their linear mass thus define these sections. Here we will consider that, to upscale from 10 to 13MW that the reinforcement mass is proportional to the blade mass. Thus we multiply the linear masses of the 10MW by a factor k defined in the equation [8.20] to obtain the characteristics of the WindQuest 13MW VAWT presented in the table [5.5]. This turbine has a mass very close to the DTU-10MW HAWT (1560 tons) and a center of thrust closer but still slightly lower than the 119m of the horizontal axis. frequencies. The DTU HAWT response, plotted in green, is our reference. The lighter WindQuest 10MW VAWT has a slightly higher resonance frequency (peak shifted to the right). Inversely, the natural pitch frequency is shifted to a lower value for the heavier WindQuest 13MW VAWT with more inertia. Note that, for the WindQuest 10MW VAWT, the second resonance peak, located around 0.45 Hz, overlap with the high frequencies of the waves spectrum.

On the contrary, the other two wind turbines show a response shifted towards the low frequencies.

They are therefore less sensitive to swell frequencies. As a result, their RAO is lower on the interval 0.05 Hz -0.175 Hz, excited by the swell. The amplitude of the float movements over this frequency range will therefore be lower for the two heaviest FOWT.

Influence on Levelised Cost of Energy

The WindQuest turbine was introduced to decrease the Levelized Cost of Energy through lighter machines and faster wake recovery, allowing for the reduction of the floater cost and densification of the offshore parks thus reducing the cost of the interconnections. Concerning the first parameter, studies such as [START_REF] Lerch | Sensitivity analysis on the levelized cost of energy for floating offshore wind farms[END_REF]] state that turbines, substructure, and mooring manufacturing costs play a significant role in the computation of the LCOE. The low TRL of the WindQuest VAWT makes it challenging to estimate the impact of the wind turbine over the LCOE. However, it is still possible to estimate the impact of a smaller sub-structure with a 10MW turbine. The resulting LCOE can then be estimated. With a measured 53% lower pitch torque, the floater righting moment can be equally lower.

Following Froude scaling, this dimension is related to the floater scale power four (λ 4 ). The resulting semi-submersible would then be 85% of its original size. If the cost is proportional to the structure volume, the resulting floater would be 72% its initial price. If the results presented in [START_REF] Lerch | Sensitivity analysis on the levelized cost of energy for floating offshore wind farms[END_REF]] for the Golf de Fos are linearly extrapolated, then fitting a WindQuest turbine would result in a 7% decrease of the LCOE via lower sub-structure costs.

Moreover, thanks to faster wake recovery, VAWT can be packed closer in a wind farm configuration. Even if this question is not investigate in the present work this property might help reduce the LCOE of VAWT farms.

Conclusions

This chapter presented the results from the experimental campaigns led at the Ifremer Brest deep waves basin. Those tests were aimed for the experimental comparison of the WindQuest 10MW

VAWT with the DTU 10WM HAWT. As those turbines are designed for floating applications, both wind turbines are installed on the Nautilus-10 semi-submersible float. This float is designed to support the HAWT. In this way, the measurements contribute, with a new experimental approach, to answer that question: "How would a float designed for HAWT react when fitted with a VAWT?".

A SiL approach is used during this experiment. A simplified tabulated approach is used. More versatile, the solution allows for the modelling of both HAWT and VAWT. But, the most important result is that this approach proved to enhance the fidelity of the tests. When the experimental measurements are compared to the OpenFAST simulations the tabulated SiL reproducing the rotor thrust increased the fidelity when compared to constant thrust measurements. Similarly when observing the PSD or RAO of the floats the influence of the SiL is observed both on the low frequency response and on the response to waves. Improvements are of course still possible, but the first technological bricks are laid at the Ifremer Brest wave tank and will allow the development of more complex solutions with time and resources.

The exploitation of the experimental results is segmented into four sections. The first one aims at the comparison of the experimental results obtained with SiL to OpenFAST models. Those simulations were first calibrated during the Lifes50+ project and are considered as the reference. The SiL proved to significantly improve the model response fidelity, especially for wind-driven DLCs.

The pitch response, very influenced by the turbine aerodynamics, is significantly improved. However, discrepancies are still observed for the pitch and surge low-frequency response. Refining the SiL computations could help make the experimental model more accurate throughout all the wind and waves conditions. In order to pinpoint precise effects, a "model of the model" simulation in OpenFAST would be useful.

The second point concerns the comparison of the DTU HAWT and the WindQuest VAWT sea-keeping qualities. The lower mass and center of thrust of the VAWT reduce the capsizing moment by 53%. This observation is in line with the arguments in favor of the HAWTs. However, the drawback is that, a smaller wind turbine implies lower inertia. Measuring the model RAO and natural frequencies showed that the VAWT has natural frequencies closer to the waves spectrum and is more sensitive to the swell forcing.

Finally, to extend on the experimental results, an HydroStar model of the floating wind turbines is used. Measuring the response to waves showed that having a lighter wind turbine on the same float is not profitable for the FOWT response to waves. Turning this downside into an advantage, a concept matching the DTU HAWT static capsizing moment is proposed. This turbine would have a similar weight and slightly lower center of thrust than the DTU 10WM HAWT. However, the VAWT would have a nominal power of 13MW. This process results in a wind turbine being less sensitive to waves while reducing the share of the float price to the total cost, thus lowering the LCOE by 7%.

Introduction

This chapter and the next two will present the experimental setup and results from the wind tunnel campaign aiming at experimentally testing the WindQuest VAWT turbine with an hybrid approach. The methodology aims at testing a subsystem before its integration into the whole system. Here the wind turbine is tested without integrating the floater with a reproduction of the hydrodynamics. Instead acutators reproduce the floater's response, hence the hybrid approach. By submitting the wind turbine to wind conditions and motion representative to the actual conditions, conclusions can be drawn on the VAWT's aerodynamic response to the solicitation. Before developing on the actuation system and the results this chapter aims at laying the foundations needed for future work. Though the next few pages the scaling laws and the requirements for the actuators are developed.

Demonstrating a concept's feasibility, such as the WindQuest-10MW, often implies small-scale testing to decrease the risks and better understand the system. Here, the Strouhal scaling is used in order to compromise between the Froude and Reynolds scaling laws traditionally used for hydrodynamics and aerodynamics. Describing the scaling law and hypotheses is thus the first goal of this chapter.

The scaling laws are deeply connected to the specifications the actuators will need to meet for the hybrid approach. The second part of the chapter will thus focus on the floater's motion at the wind tunnel scale, and the influence of the reproduced swell on the needs for the actuation system.

Wind tunnel scaling 6.2.1 Strouhal scaling

When studying aerodynamics in a wind tunnel, scientists and engineers generally use Reynolds scaling. That similitude is ideal for studying a lifting body, it is neither the only nor the most adapted methodology for characterizing a floating wind turbine. For the former situation, Strouhal scaling, defined in equation (6.1), is used for the small-scale study of oscillating and unsteady phenomenons. The adimensional number is defined with L, the specific length, t the time, V 0 the flow speed. Those values keep the Strouhal number the same at the model and full scale. Using the methodology, the base foundations are the geometric scale λ L and the wind speed scale λ V . The other scaling factors, such as time λ t , mass λ m , linear acceleration λ a or angular acceleration λ aa , are derived from those two first factors. The table 6.1 describes the computation for the scaling factors, and the rest of the section will go through the process of selecting those scaling ratios used for designing the wind tunnel experiment.

St = L m t m V m = L r t r V r = f L V 0 (6.1)
L = L r /L m speed λ V = V r /V m time λ t = λ L /λ V mass λ m = λ 3 L angular acceleration λ aa = 1/λ 2 t linear acceleration λ a = λ 2 V / λ L force λ F = λ 2 L λ 2 V

Wind tunnel

The wind tunnel's specifications are the main constraint on the speed and length scales. The model's size needs to be large enough so that Reynolds numbers thus performances and thrust are high enough to be measured while small enough to keep the blockage ratio at reasonable values. Similarly, setting the wind speed balances the minimum wind tunnel's speed and the wind speed should make for a reasonable speed ratio as literature indicates that 2 ≤ λ V ≤ 3 make for a good compromise between the constrains on such an experiment.

Q v = S 1 × V 1 = S 2 × V 2 (6.2)
Similarly, the length scale is set at 182. This scale is chosen in order to get two 0.5m wide rotors at model scale from the 91m wide and 136.5m high turbines of the 10MW design.This size is a compromise between the two constraints: the model and the tunnel's size. Let's recall here that the goal of the present experimental work is to measure the temporal oscillation of the turbine's thrust when exposed to pitch and surge motion. Knowing that force measurements can be a difficult task, the choice of the biggest possible model leads to increase in both the quality and the precision of such measurements. Indeed the length factor plays a significant role in the accelerations imposed on the actuators and the model. The bigger the turbine, the smaller the accelerations will need to be.

But, as stated above, the wind tunnel also constrains the model's size as the blockage should be contained. This factor is used in order to account for the increased velocity in the test section caused by the presence of the model. The computation described bellow comes from [START_REF] Blackwell | Wind tunnel performance data for the Darrieus wind turbine with NACA 0012 blades[END_REF].

The blockage factor is described in equation ( 6.3) as the sum of the wake blockage and the solid blockage. The wake blockage is described in equation (6.4) with ∆ V te velocity deficit, V 0 the tunnel's wind speed, S the surface swept by the VAWT set at 0.75 m2, C the tunnel's section of 8.11 m2 and C d the turbine's drag coefficient. The solid blockage, computed in equation (6.5), is composed of the sum of the blockage from the blades and of the support structure. The blades' surface is neglected and the structure's surface is computed with the CAD model illustrated in figure 6.2. A blockage ratio ϵ t of 2.24% is thus computed. With the equation (6.6) the wind speed can be corrected. But note that a correction of 2.24% would be similar to the measurements uncertainties.

ϵ t = ϵ wb + ϵ sb (6.3) ϵ wb = ∆ V V 0 = S 4C × C d = 0.75 4 × 8.11
× 0.85 = 19.6 × 10 -3 (6.4)

ϵ sb = ϵ sb (blades) + ϵ sb (structure) = 0 + S strcuture 4C = 0.84 -0.75 4 × 8.11 = 2.77 × 10 -3 (6.5) U 0C = U 0 (1 + ϵ t ) (6.6)

Scaling factors

Throughout this section, the scaling process is described in detail with the thoughts, constraints, and hypotheses needed to develop the experiment. It is now time to present the resulting scaling factors. The scaling ratio presented by now will consider a wind speed of 5 m/s in the wind tunnel.

This statement comes from the PIV measurement illustrated in figure 6.3. The measurement was obtained by Van Der Deijl [Torque 2022] through PIV measurements. Now that the wind speed is known with precision, the scaling factors are extrapolated and presented in the table 6.2. Those scaling factors make the best use of the wind tunnel's specifications, set the base for the model's design and allow for the design of the actuator's specifications presented in the next section.

λ L = L r /L m 182 speed λ V = V r /V m 2.28 time λ t = λ L /λ V 79.8 mass λ m = λ 3 L 6 × 10 6 angular acceleration λ a a = 1/λ 2 t 1.57 × 10 -4 linear acceleration λ a = λ 2 V / λ t 2.86 × 10 -2 force λ F = λ 2 L λ 2 V 1.72 × 10 5

Hybrid approach: simulating the floater's motion

Now that the scaling law is defined the actuation hypothesis and specifications for the motion system are described. First the process for scaling the floater's motion is described. This scaling is the base concept used to defined the actuators' specifications. The pretense study focuses on the reproduction of sinusoidal motion similar to regular waves. The reason why will be discussed in this section.

Scaling down the float's motion

The actuator's specifications are based around the reproduction of the floater's Response Amplitude Operator. Those measurements, carried out during the wave tank campaign are presented in chapter 4. Figure 6.4 illustrates the floater's pitch and surge RAO experimentally measured during the wave tank campaign. Those measurements are presented full scale and need to be scaled down to wind tunnel scale.

The scaling process is carried out by using scaling factors presented in table 6.2 on the full scale RAO. The first step is to scale down the frequency axis using the time scale factor λ t . This results in the RAO illustrated in figure 6.5. The floater's motion is computed using equation (6.7) from [Orcaflex n.d.] with x the vessel displacement, R the RAO amplitude, a the wave amplitude, ω the pulsation, t the time and ϕ the RAO phase. Note that, in our situation, there is no real need to consider the RAO phase. This process is used to compute the float' response to wave heights of 2 to 8m full scale or 11 to 44mm at wind tunnel scale (with λ L = 182). The Figure 6.4 -pitch and surge RAO full scale result of this process is illustrated in figure 6.6. Theses responses to different waves heights will be used in order to design the actuators system presented in the next chapter.

x = R.a.cos(ωt -ϕ) (6.7)

Note that the process is carried out and illustrated with regular wave heights following equation (6.7). Reproducing regular waves is chosen over the irregular waves as using regular sinusoidal motion is more adapted of the study of the VAWT's aerodynamics as it allows for the study of each parameter such as motion's frequency and amplitude independently one of each other while requiring less powerfull (and bulcky) actuators.

Conclusion

This chapter presented the scaling laws used to design the wind tunnel experimental campaign and the resulting specifications for the actuator.

First, the Strouhal scaling is presented. The similitude is used for oscillating motion reproduction based on the model's geometric scale and the wind speed scale to keep the adimensional number constant. Thus the process leading to the selection of those two scaling factors is presented with the specifications for the model and the constraints imposed by the Hardware in the Loop approach and the wind tunnel specifications.

Introduction

This chapter describes the experimental setup used for characterization of the WindQuest aerodyanamics for floating applications. Each section will go through the specifications needed, the design process and the final design of each sub-assembly. Speaking of witch, the figure 7.1 illustrated the wind-tunnel model's CAD with it's main sub assemblies highlighted. As for any The blades are thus shaped with a NACA 0018 profile without any blade pitch. Independantly from the scale factor λ L and in order to match the full scale VAWT, the rotor hase a solidity of 0.3 using equation (7.1) where n is the number of blades, C the profile chord and R the rotor's radius. Dictated by the rotor specification and the scale factor come the rotor radius and height respectively set at 0.25m and 0.75m.

σ = nC R (7.1)

Actuators design and specifications

This first section describes the actuator's system used for reproduction of the floater's motion for the Hardware in the Loop approach. It was decided to focus on reproduction of pitch and surge sinusoidal motion. This next few paragraphs will explain how this process lead to the system illustrated in figure 7.1.

The actuation solution selected is inspired by design used at PoliMi and described by Bayati et al. in [Bayati et al. 2017a]. In figure 7.2 the 3D representation of the actors dynamic schematic.

The scale model is placed on a pivot located on the mast. At the bottom of that mast, a ball joint connects the pitch actuator to the scale model. By retracting and extending that actuator, the scale model will pitch. Next, the pitch actuator is hinged on a pivot to get an isotactic solution.

That whole structure is positioned on rails, allowing for it's translation, and connected to the surge actuator. With a rail solution, the entire system can translate forward and backward, reproducing the surge motion. The actuator's range of operation is mostly defined by the workload, stroke, maximum speed, and maximum acceleration. Knowing that the actuators will play sinusoidal motions actuator's stroke is defined by equation (7.2) with A the motion's amplitude, ω the motions pulsation ant t the time. The actuator's speed is defined with equation (7.3) and acceleration is defined in (7.4). From those equations, it is possible to overlay the actuators operating range to the desired motion.

x = Asin(ωt)

(7.2) ẋ = Aωcos(ωt) (7.3) ẍ = -Aω 2 sin(ωt) = -ω 2 x (7.4)
The actuator's translation needs to be converted into the scale model's rotation for the pitch axis of rotation. This is done thanks to the law of cosines illustrated in figure 7.3. The AB and AC distances are fixed and defined by the frame's geometry. From the equation (7.5) the pitch angle can be computed using equation (7.6). From this formula, the maximum actuator stroke is converted into a maximum pitch angle. The maximum pitching speed and pitching acceleration is computed similarly with equations (7.2), (7.3) and (7.4).

AB 2 + AC 2 -BC 2 = 2 × AB × AC × cos(α)c 2 + b 2 -a 2 = 2bc × cos(α)a 2 = b 2 + c 2 -2bc × cos(α) (7.5) α = arccos( AB 2 + BC 2 -AC 2 2 × AB 2 × BC 2 ) (7.6)
Once those equations are defined, the actuator's envelop can be compared to the FOTW's response. The process establishing the response to regular waves and scaling this to wind tunnel scale is presented in the previous chapter. This process is presented with the LEY63T8B-300 from SMC as the actuator used for the campaign. Table 7.1 sum-up the main actuator's specification.

In figure 7.4 the envelops computed using previous equations.

In figure 7.5 the scale model's CAD with the actuation system highlighted. The surge actuator is connected to the main frame (bolted on the ground) via a pivot connection and to the pitch structure via a ball joint to get an isostatic solution. The whole pitching structure is positioned on rails, allowing for the surge translation. The scale model is connected to that structure via the pitch pivot. The pitch actuator is connected to the lower part of the scale model's mast using the same solution as the surge actuator. For thrust measurements, two solutions have been studied. The first one is the use of a piezoelectric sensors-based scale already developed at the ENSMA. The solution is bulky and imposed its installation at the scale model's foot. The second option is the use of strain gauge sensors. Those sensors would be installed on the model's nacelles. This is the selected option. As explanations are needed, the following section explains why the piezoelectric-based sensor is not used and why we chose the strain gauge technology.

Why not measuring the total thrust at the scale model's foot?

When motion is imposed to the scale model, aerodynamics and inertial loads are superposed.

If the scale is placed at the model's foot, the measurements include the whole model's inertia.

From the CAD model, the wind turbine model's mass and inertia are computed. Those values are then used to quantify the inertia loads in operation and compare them to the aerodynamics loads. Table 7.2 sums up those informations.

Inertial forces are computed out using equation (7.7). With x, y and z the translations around the axes ⃗ x, ⃗ y and ⃗ z and rx, ry and rz the rotations around these same axes. xg, yg and zg are the distances between the center of rotation and the center of gravity. For the accelerations and angular speeds, the maximum values admitted by the actuators are used. The maximum angular speed of 0.83 rad/s is computed using equation (7.8) and with a lever arm of 0.3 m (distance between the scale and the pitch axis of rotation). The maximum angular acceleration of 15 rad/s 2 is computed using equation (7.9). Using the numerical values given above, the equation (7.7) returns a maximum inertial load of 229N. With a wind speed of 4 m/s, the average thrust is 6.7 N. This would represent 3% of the inertial load. The acquisition offers a resolution equivalent to 1% of the measurement range at best. These two factors make the load sensors installed on the tower base unfit for studying the evolution of the drag coefficient with a motion imposed to the scale model.

F = m ×         ẍ ÿ z    +     rx ry rz     ∧     xg yg zg     +     ṙ x ṙy ṙz     ∧     ṙ x ṙy ṙz     ∧     xg yg zg         (7.7) θ = ẋ r (7.8)

Instrumented nacelles: the final design

Sensors are thus installed on the nacelles, illustrated in figure 7 On the polar plot, the orange plot represents the theoretical measurement if the sensor has zero coupling. This plot is computed using equation (7.10) with m the weight's mass, g the gravitational acceleration, and θ the pulling angle. This line stays inside the confidence interval, indicating that if there is any coupling, it is smaller than the sensor's uncertainty. Note that a first wind tunnel campaign highlighted several design or manufacturing issues. The design presented here is the last one after applying the necessary modifications. -in the carbon structure with both upper and lower arms not being aligned, making the nacelles not perfectly above one each other.

-the motor which is not perfectly aligned with the reducer, generating vibrations when the motor is working -The rotor's blade is not the same length and weight, generating traction and compression as the rotor is turning. Figure 7.11 illustrates that last point.

After a couple of iterations, both upper and lower nacelles have been designed to accommodate those imperfections. Figure 7.12 shows a picture of both nacelles. The upper nacelle has a simple design. It acts like a ball joint while allowing for the upward and downward translation of the shaft coming from the rotor.

The lower nacelle is more complex. Going from bottom to top first comes the motor with its planetary reducer and the encoder. The motor is held in place with the red support bolted to the scale model. This fixation should reduce the amount of vibrations transmitted to the As the blade is 250 mm in radius, the rotational speed is computed θ = V r = 76rad/s = 12Hz. We therefore have a 2P excitation mode at 24 Hz.

The resonance modes of the model should thus not be in the interval 2P ± (2P ± 2 √ 2 ) to prevent the scale model from being excited by the rotor. The natural frequencies must therefore be located outside the interval [START_REF] Bossuyt | Wind tunnel study of the power output spectrum in a micro wind farm[END_REF][START_REF] Bredmose | The Triple Spar campaign: Model tests of a 10MW floating wind turbine with waves, wind and pitch control[END_REF][START_REF] Bredmose | D2.4 Collation of offshore wind wave dynamics[END_REF][START_REF] Brownstein | Performance enhancement of downstream vertical-axis wind turbines[END_REF][START_REF] Buchner | Dynamic stall in vertical axis wind turbines: Comparing experiments and computations[END_REF][START_REF] Carpenter | Effect of a Rapid Blade-Pitch Increase on the Thrust and Induced-Velocity Response of a Full-Scale Helicopter Rotor[END_REF][START_REF] Chabaud | Multiple-degree-of-freedom actuation of rotor loads in model testing of floating wind turbines using cable-driven parallel robots[END_REF][START_REF] Cheng | Assessment of performance enhancement of a semi-submersible vertical axis wind turbine with an optimized Darrieus rotor[END_REF] to meet this request.

A set of parameters have been tested when modeling the wind turbine. For the sake of clarity, only the ones relevant for the last design will be presented: the nacelles weight and the mast diameter.

In figure 7 The mast and arms are hollow circular sections. The horizontal arms have little influence on the modal analysis' output. Their diameter is selected to accommodate the Z6 sensors for thrust measurement. Carbon fiber is defined with Young's modulus of 85,000 MPa and a density of 1 600 kg/m 3 . RDM7 only considers isotropic materials, an approximation is thus necessary for the carbon fiber. Steel is defined as having Young's module of 210,000 MPa. Aluminum for the mass of the nacelle is modeled with a density of 2 712 kg/m 3 . The nacelle's weight is extracted from the CAD model. The mast's diameter is studied. This is, by far, the most crucial parameter. In table 7.3 the diameter and thickness parameters tested. Those parameters come from the supplier's website.

The simulations indicated that the last reference should be selected as it is the only one with a vibration frequency high enough. The next DRM7 model is designed to study the nacelle's weight impact on the structure's vibration frequencies. Swapping the hub's materials from steel to aluminum shaves 0.2 kg from each nacelle. This small weight difference greatly influences the model's vibration modes as the first mode, originally at 39.1 Hz, is increased to 43.8 Hz. This weight difference shows similar results when compared to guy wires reinforced structure. This result is the reason why the guy wire structure on the scale model is removed.

The RDM7 study presented in this subsection explains how the scale model's structure was designed. From the blade's rotation frequency, the minimum mast vibration frequency is defined at 31 Hz. Using the simplified representation proposed by RDM7 allowed for rapid iteration.

Parameters as mast diameter, nacelles weight, and guy wire structure are tested. This allowed for the optimization of the model's design. This proved the importance of the weight of the nacelles. Shaving off 200 grams had similar results when compared to a guy wire structure on the scale model. The resulting scale model has a first frequency mode at 43.8 Hz, fitting the specifications with margins. Thus, the study allowed for the simplification of the scale model while retaining similar performances.

Balancing the rotor's blades for minimal vibrations

Ax explained previously mechanical vibrations are generated by the model's imperfections such as weight imbalance of the rotor. This section describes how those vibrations are measured and how the weight imbalance is corrected in order to decrease the vibrations as much as possible. This indicates that forces measured are probably generated by centrifugal forces.

Placing counter weights

The measurement of the centrifugal forces for the left rotor is presented in figure 7. [START_REF] Bayati | Wind tunnel tests on floating offshore wind turbines: A proposal for hardware-in-the-loop approach to validate numerical codes[END_REF]. This plot is the phase average of the sensors' measurements at 500rpm. During the measurement, the other rotor is not turning to prevent coupling between the two rotors.

From the figure 7.16 it is possible to observe a positive force of about 2 N on each sensor when the rotor is around the 100°position. This means that the blade on that side is heavier. To balance this weight difference, a mass m must be placed on the balancing disk as desplay in equation (7.12) with θ is the rotor's rotation speed, F is the force measured, and R is the balancing plate's radius. The balancing is done as an iterative process by placing screwns, nuts and washers on the balancing disk as illustrated in figure 7.17. After installing the first mass, the centrifugal forces are measured again, and adjustments are made. Repeating the operation two to three times with masses smaller and smaller using nuts and washers allows for a fine balancing of the rotor.

The tipping point is observed when adding a mass as small as a washer reverses the sinus phase.

The operation is illustrated in figure 7.18. The "too heavy" and "too light" signals are in phase opposition as the lighter side of the rotor becomes heavier and vice versa. Installing one last washer got the rotor to the final configuration. However this solution is requiring too much torque on the slave motor. A new control is the designed and implemented by Wessel Van Der Deijl. The slave rotor speed is controled in order ti maintain the synchronization while the master rotor is set for a constant speed. This synchronization is illustrated in the figure 7.25a, note that the phase difference is computed on a 180°modulo. First the two rotors are independently accelerating up to the desired rotation speed. Once achieved, the "master" rotor keeps its speed constant and the slave speed is set via a PID controller. The input is the phase difference and the output is the speed. The PID gains are tweaked in order to limit the torque needed for the synchronization. By doing so the the Through careful design, a wind turbine model was conceived and built. Using the structure calculation software RDM7 the width of the sections, the nacelles weight, and the guy rope depending on the tip speed ratio λ and the azimuth position of the rotor θ. These measurements give information on the wind turbine response to steady-state wind conditions. Note that this kind of response was used to model the wind turbine with the SiL.

The second part of the results investigates the dynamic reaction of the VAWT when submitted to pitch or surge motion. The tip speed ratio, motion frequency, and amplitude influence on the rotor thrust are investigated. Finally, those unsteady measurements are compared to the static response of the wind turbine to validate or invalidate a static model for floating applications.

Unfortunately, the pitch results are not exploited due to lack of time, and analyses are only made on the surge measurements.

The second part of the results gives details on the dynamic reaction of the VAWT when submitted to surge motion. The tip speed ratio, motion frequency, and amplitude influence on the rotor thrust is investigated. Just as for the previous analysis, the same filtering solution is applied to the measurements with the the analysis and filtering of the perturbations induced by the actuators. Note that, even if measurements have been carried out to study the influence of pitch motion, no results are presented. Due to time constraints, those measurements haven't been analyzed in depth.

Static characterization of the wind turbine

This first section describes the results from the so-called "static driven tests". During those experiments, the wind turbine rotors rotate at a constant rpm and is not actuated in pitch or surge. Those tests have been realized with and without wind and are averaged over several minutes to acquire points for the measurement to converge. Realizing all those measurement points aims to know the wind turbine's static characteristics in and out.

The analysis of the measurements follows this process: first, the convergence of the measurements is checked through the use of the Normalised Root Mean Square Error (NRMSE) indicator.

Second, quantification of the measurement uncertainties is also explained as this value will be necessary for the presentation of the following results. Once those verifications out of the way the results of the static driven measurements can be presented.

First, the chapter presents the results for the measurement of the average C t as a function of the tip speed ratio λ. For those results, the unsteady characteristics of the vertical axis are averaged. The thrust coefficient curve obtained through this process is similar to the one used for SiL calculations.

Then the unsteady C t is measured as a function of the rotor position θ and a several tip speed ratios λ. This static driven result focuses on the osculating specification of the VAWT. To get this last results a significant amout of signal processing was needed. Frequency analysis is run, signals are processed, and filters are applied to the measurements to retain only the aerodynamics and

N RM SE = RM SE i RM SE n = Σ n i=1 (T n -T i) 2 n /RM SE n (8.1)
time interval = [t 0 , i × (t f -t 0 ) n ] (8.2)

Measurement's uncertainties estimation

To pursue the qualification of the measurement, quantification of the uncertainties is essential.

It's another information crucial when the measurements are exploited. The uncertainties on the thrust coefficient are estimated through a statistical approach. The measure of the average Ct without static pitch angle the model at λ=3.14 was repeated at the beginning of each day to verify the repeatability of the measurements from one day to the other. Those measurements are also used to estimate the uncertainties.

The sensor resolution is negligible, the distribution of Ct measurements is supposed to be a Gaussian phenomenon. In this situation, the true value will have 95% chances ok being in interval: measure ±2σ with σ the standard deviation. The Ct measurement at λ=3.14 was repeated eight times. A standard deviation of 0.006 was measured, indicating that we should consider the measures with the interval of ±0.012 for a 95% confidence interval.

Average thrust coefficient measurements

C t = 2T ρSV 2 0 (8.4) Re c = ρc(V 0 + r θ) µ (8.5)

Dynamic thrust coefficient measurements

VAWTs have deeply unsteady aerodynamics, though a rotor turns the apparent wind speed and angle of attack drastically varies, modifying the thrust coefficient. The thrust coefficient is measured through a phase average over the azimuth position of the rotor θ for several TSR to measure this phenomenon. The process is illustrated in figure 8.4 and starts by first running tests at the same RPM with and without wind to measure the forces generated by the rotor imbalance. Note that, in all those results, the sensor's offset is subtracted. Then the time series are filtered with a low pass filter at 2.5P (with P the rotation frequency), and a band stop at 1P are applied. This combination is chosen after a frequency analysis illustrated in figure 8.5. This filtering solution filters most of the 3P that we don't want to focus on here and the 1P generated phenomenon is probably due to the structural interaction generating parasite forces at 0°and 180°. Take, for example, the phase average measured at 300 and 600 rpm illustrated in figure

Influence of the static pitch angle over the thrust coefficient

Measuring the influence of the static pitch angle is the last test that's needed. Indeed, when the wind turbine is tested with a Pitching motion, it is crucial to know whether or not the observed effects are dynamic. The wind turbine is thus tested with a static pitch angle varying from -10°t o +10°. In addition, the offset generated by the rotor's weight is measured before each test to subtract it from the measurements. Finally, all the tests are realized at 600 rpm or λ=3.14. itch. Note that no point is out of this interval, and no trend is observed. This thus means that if there is any influence, it is too small to be measured by the present experimental setup. .

Conclusions on the static driven measurements

Measuring the static thrust coefficient gave great and valuable pieces of information on wind turbine aerodynamics. First, measuring the average thrust coefficient as a function of λ gives a comparison point for the unsteady measures presented in the next section.

Measuring the thrust coefficient over rotor position θ also gives interesting information as the C t is evolving with a behavior similar to the models. It is good to see that the methodology is viable from a technical point. However, the discrepancies observed between the expected and the observed behavior indicate that the structure is probably still too flexible. If no guy-rope is used, this measure is probably very sensitive to the structure stiffness as aerodynamics interact with the thrust sensors. Three ways to improve this problem would be: to stiffen the arm structure, use strain gauges glued on the ars to eliminate the sensor's flexibility or use the stiffer piezoelectric sensors instead of a strain gauge load sensor.

Finally, no influence of the static pitch angle is observed. This indicated that whenever the measurements with pitch motions will be used, then any influence of the pitch observed on the C t will come from the unsteady response of the wind turbine.

Now that the static driven measurements are presented, it is time to go to the next step: the unsteady surge driven measurements.

Analysis of the surge motion

The main objective of the present study is to measure the dynamic response of the wind turbine when submitted to pitch and surge motion. This response is quantified through the measurement of the VAWT's thrust coefficient. This section describes the hypotheses needed, the test matrix used, and how the measurements are post-processed to characterize the dynamic response to surge motion. Finally, those measurements will be compared with the static driven measurements presented above.

Definition of the dynamic thrust coefficient

The dynamic thrust coefficient C tV rel is defined in equation (8.6) with T the turbine's thrust, ρ the air density, S the VAWT's swept surface and V rel the apparent wind speed. The apparent wind speed is composed of the sum of the environmental wind speed and the motion speed.

For surge, the apparent wind speed is defined in equation (8.7) with V 0 the environmental wind speed, A the motion amplitude, and ω the motion pulsation. If the notion of apparent wind speed is used, the apparent Tip Speed Ratio also needs to be defined. Hence the definition in equation (8.8) with r the rotor radius, θ the VAWT's rotation speed and V rel the apparent wind speed. Theses definitions are used for the rest of the chapter in order to quantify the thrust coefficient and tip speed ratio as the VAWT is submitted to surge motion.

C tV rel = 2T ρSV 2 rel (8.6) V rel = V 0 -Aω.cos(ωt) (8.7) λ V rel = r θ V rel (8.8)

Convergence study

Similarly to the static characterization of the VAWT, the convergence of the surge measurements needs to be measured. The same process using the Normalized Root Mean Square Error is used. The temporal analysis is carried out by plotting the phase average of the thrust signal processed with three low pass Butterworth filters set to apply a low pass frequency at 100, 20 and 6 times

Inertia extraction and measurement of the dynamic thrust coefficient

The thrust sensors, placed on the rotor's nacelles, measure the reaction of the rotors. There is thus the aerodynamics but also the force generated by the acceleration of the rotor mass: the inertia. This physical quantity is specific to the scale model, is not part of this study's topic, and should thus be removed from the measurements.

Figure 8.12 illustrates the inertia extraction from the phase averaged thrust measurements allowing us to isolate the aerodynamics from the measurements. For this hybrid approach, the floater's motion is modeled as a sinus. The surge motion, position, speed, and accelerations are described in equation (8.9). The acceleration is proportional to the model's position. A linear fitting can thus be extracted from the measurements, with its slope being the inertia loads.

Subtracting the slope of the curve removes the inertial forces from the measurements. Once the inertia is extracted, the dynamic thrust coefficient C tV rel is computed with equation (8.6). The figure 8.13 illustrates this result for the same conditions as illustrated in figure 8.12.

Note that this last figure shows a cosinus shape centered around the static thrust coefficient and in phase with the ẋ. Now that the analysis is demonstrated on one configuration, the same process is repeated for all the configurations given in the table 8.3 to gain an understanding of the parameters influencing the dynamic response of the VAWT.

Comparison of the dynamic measurements with the static model

Now that C tV rel is measured for the set of surge motion, the dynamic measurements are compared to the static model. This model is extracted from the static driven measurements presented in the section 8.2.2. As explained, the static C t0 is fitted with a polynomial curve. This result is used here with the definition of a static thrust coefficient depending on λ V rel as shown in equation (8.10).

C t0 = 0.0362λ 2 V rel + 0.0257λ V rel + 0.1071 with R 2 = 0.9939 (8.10) This static model is used for comparison with the dynamic measurements in figures 8.14 and 8.15. In these two figures, the thrust coefficients are plotted as a function of λ V rel . When taking a look at the two plots and especially at the figure8.15, two conclusions are drawn from the plot: first, the values from the static and dynamic driven measurements are widely different.

For low frequencies the static and dynamic models have slightly different slopes, but at higher frequency, the slopes of the two curves exhibit opposed signs. For example, as the wind turbine is going upwind (λ V rel < λ 0 ), where the thrust is the highest, the static model predicts a thrust coefficient lower to the measure. The dynamic measurements realized for this study show, for frequencies high enough, the inversion of the slope for the function of C tV rel = f (λ V rel ) defining the dynamic thrust coefficient as a function of the apparent TSR.

Two more observations are made when comparing the static model to the dynamic data. First, as the apparent wind speed variations increase, the average C tV rel appear to drop bellow C t0 the static thrust coefficient. This phenomenon is illustrated in the figure 8.16. This figure shows the C tV rel is constant but above that point C tV rel decreases. This phenomenon is independent from the tip speed ratio. Indeed the Ct loss apears at the same moment for all tested tip speed ratio.

δ V = V 0 + Aω V 0 (8.11)
The second observation is on the effects of the frequency on C tV rel slope. The figures 8.14 and 8.15 illustrates the disagreement between the static model and the dynamic measurements. The surge motion frequency apprears to be the parameter influencing the rate at which C tV rel varies.

This observation is first illustrated in the sub-figure 8.17a. Here the surge frequency appears to be the parameter influencing the slope of the C tV rel plots. The amplitude of the motion is influencing the amplitude of those variations.

To investigate this hypothesis, linear fittings are made for each curve plotting C tV rel as a function of λ V rel . The slope of the curve is then plotted in the figure 8.17b as a function of the Strouhal Number defined in equation (8.13) with f the surge motion frequency, D eq the turbine equivalent diameter (0.977 meter defined in equation (8.22)) and V 0 the wind tunnel wind speed. Note that very little dispersion is observed between the experimental points at the same frequency. This observation corroborates the hypothesis stating that the surge frequency can be of first order D eq = 4s π (8.12)

S t = f D eq V 0 (8.13)
This analysis proved that using a static model is not sufficient for the description of the dynamic response of the wind turbine. The static model and the dynamic measurements could even exhibit curves of opposite sign. Further investigating the question shows that the evolution of C tV rel appear to be influenced by the frequency of the surge motion and the tip speed ratio of the wind turbine. This hypothesis is further investigated in the next section with the definition of the new dynamic model.

T = m a dV i dt + 2ρAV i V Z (8.14)
small induced velocity variations.

∆V i = -kAωcos(ωt) = -kbV 0 with b = Aωcos(ωt) V 0 (8.17)

In the case of the static model (instantaneous relation of the system to upstream velocity fluctuations) and if the nominal induction factor a 0 has a linear relationship with λ 0 (a reasonable approximation for the studied TSR interval 2.41< λ 0 <4) then we have a 0 δλ 0 = δ r θ V 0 = V i V 0 . This indicates that V i = δ r θ and then should be constant when considering a constant rpm operation for the rotor in the static approach. Finally, the V z fluctuations is described using equation (8.18) leading to the new expression of ∆T T 0 in equation (8.19) where χ 0 only depends on λ 0 .

∆V Z = [V 0 -(V i0 -kAωcos(ωt)) -V 0 + V i0 ] = kbV 0 (8.18) ∆T T 0 = -kbV 0 aV 0 + -kbV 0 V 0 -V i0 = -kb a + -kb 1 -a 0 = kb[ 1 1 -a 0 - 1 a 0 ] = kbχ 0 (8.19)
From the equation (8.19) the factor k is described in equation(8.20), thus quantifying the impact of the V rel fluctuations on the induced speed thus the thrust variations. When the phase is comprised in the interval -π 2 < ωt < π 2 the wind turbine is going downwind and receives energy from the environment. Most of the time, during this phase V rel ≤ V 0 , most of the time ⃗ T will thus be lower than ⃗ T 0 . When the FOWT in on the interval π 2 < ωt < 3π 2 of the surge motion and going upwind, the VAWT dissipates energy. In this situation V rel ≥ V 0 and thus ⃗ T ≥ ⃗ T 0 .

Thus the amplitude of W will be determined by the drag differential between the "upwind" phase and the "downwind" phase. The drag differential will therefore be proportional to the quantity ∆T T 0 over a cycle. We can therefore write W ∼ ∆T max A . The expression is developed in equation (8.30) leading to the final expression of the work through a surge phase in equation (8.31). The result of this equation is plotted in the figure 8

Conclusions

In conclusion, this chapter presented the experimental results of the test campaign where the WindQuest VAWT design is tested through an hybrid approach at the ISAE-ENSMA wind tunnel. The objective of the present study is to measure the unsteady response of the wind turbine when submitted to floater motion.

The model first goes through a static qualification to measure the thrust coefficient as a function of λ the Tip Speed Ratio and θ the azimuth rotor position. The first measure averages the rotor thrust over a long period to smooth the thrust variation over θ and only observe the influence of the tip speed ratio. This section also presented the signal processing needed to extract the valuable data out of the sensors' time series.

Measurements of C t over λ gives an upward slope with C t varying from 0.25 to 0.8. This measurement is coherent with the expected results. In the second part of the chapter, this result is used to establish a static model compared to the dynamic response of the VAWT. Measuring C t over θ is an interesting result in its own right. But it also helps qualify the experimental setup.

Indeed, at low TSR the C t over θ follows a sinus shape, but at higher TSR, the sinus shape flattens? This phenomenon correlates with the convergence time increasing for those TSR, probably due to aerodynamic forces interacting with the structure that would need to be stiffened.

The second part of the chapter presents the dynamic results obtained through the measurement of C tV rel the thrust coefficient of the wind turbine when it's submitted to surge motion. After extracting the inertia loads from the sensors measurements, C tV rel is computed, and divergences are observed between the dynamic response of the wind and the static model. This observation leads to the definition of a new model based on the relationship between the induced velocity and the floater motion. This approach proved that the thrust variations could be defined as a function of the static thrust, the motions frequency, the static TSR, and the TSR variations.

This new model gives excellent results as it shows a great agreement with the experimental data.

These results would make for a good methodology when developing an enhanced version of the Software in the Loop presented in this thesis. Unfortunately, it was not adapted to the pitch measures due to lack of time.

Conclusions

The main conclusions of the study presented in this Ph.D. thesis are emphasized as follows.

VAWT and HAWT can be reproduced at model-scale by propellers controlled by

SiL The propellers used for this thesis are placed in a counter-rotating configuration in order to increase the range of thrust that the system can generate, making it more versatile for the reproduction of the HAWT and the VAWT turbines. A calibration of the system has been realized covering the relationship between the throttle and the generated thrust but also the frequency Wessel Van Der Deijl, also supervised by S. Barre already reused the model for PIV characterization of the VAWT's wake. Thus as the SiL, this tool is and will be reused for future researches.

Perspectives

Thre results presented in this Ph.D. lay the foundation for further work and developement in the scope of model scale testing in wave tank and wind tunnel but also on VAWT modelization.

This last section presents the main points of improvements and future work.

Improvement of the propellers system. The propellers system proved to have satisfying characteristics. But, none the less they would benefit from five major improvements. First, the function transfer is not perfectly constant through the frequencies. Implementing a compensation for that function transfer would allow for a better fidelity between the set-point and the generated thrust. Second, the delay between the set-point and the response of the propellers could be shortened. Testing difference ESCs and observing their response time would be useful.

Indeed, those commercial controllers have widely different response time from one mode to the other. The controller with the shortest response time could be selected. Third, a faster computation rate could improve the global performances of the system. This solution could be easily implements with faster communications between the Arduino on the model and the cRIO. With faster computations more advanced signal processing is needed to reduce the noise transmitted from the measurements to the set-point. Fourth, would be the reproduction of more DoFs by the SiL. The literature includes several references enhancing the fidelity of wave tank experiments by including the reproduction of rotor inertia, or aerodynamic torque generated by the wind turbines. Similar improvements could be made to the system though those solutions would probably imply some loss of versatility for the system. For example, rotating masses can be added to the scale-model, reproducing inertia but the system would need to be tailored for each wind turbine and each scale. Finally, the system could implement a prediction of the thrust at the next time step thus removing the inherent delay caused by the refresh rate of the measurements and computations. This operation could be carried out by a variety of technical solutions such as, wave elevation time series defined before the tests and given to the SiL or upstream measurements given to the SiL and implemented to the control with solutions such as a Kalman filter.

Improvement on the SiL computations. The SiL computations could also be improved.

Two options are available. First, the tabulated approach is kept. The computations could include the oscillating thrust typical from VAWTs. Note that this oscillating thrust would be very demanding on the propellers and a design modifications might be needed. Then, though a tabulated approach, the dynamic model developed during the wind tunnel campaign could be implemented. Such solution would increase the fidelity of dynamic simulations of the VAWT for floating applications studied in wave tank. The second option would deviate from the tabulated approach and implement high fidelity models such as OpenFAST for HAWT and CACTUS for VAWT in order to have an option on the simulations' level of fidelity.

Improvements on the wind tunnel Harware in the Loop setup. Similarly the HiL setup proved to work but enhancements could be made to the system in order to expand the field of results. On the selection of the actuators, fitting more powerful hydraulic or three phase electric actuators could bring two benefits. First this would allow for a wider range of motion thus increasing the field of validity of the models generated from the measurements. Second would lower the constraints on the Strouhal scale, thus allowing for higher wind speeds, bigger model and higher Reynolds numbers ultimately enhancing the quality of the measurements. Minor improvements to the mechanical design of the system could be made. Adjusting the rails and chariots position with machined parts and stiffening the support structure would reduce the noise levels in the surge measurements. Similarly improving the pitching system would yield better results when the model is pitching. A measurement of the model's frequency response would be useful in order to know if the model needs to be stiffen. If the resonance frequency significantly higher than the 2P aerodynamic excitation then the thrust sensors should be replaced by a less flexible solution. This last improvement would allow for higher quality static measurements. Abstract: Floating offshore wind turbines experiences motions due to waves and wind that might impact their performances. In this thesis we focus on the effect of surge and pitch on an original design of a counter rotating vertical axis wind turbine (VAWT). For this study, we develop hybrid experimental set up, both in wind tunnel and wave tank, to model the behavior of the VAWT subject to waves and wind. In the tank, the model is submitted to waves when the wind is simulated with the help of a fan controlled by "Software in the Loop" (SiL). The SiL calculates and adjusts the thrust in real-time from the captured motions. In the wind tunnel, the scale-model of the wind turbine is tested when the motions are simulated by actuators. Both approaches highlights the strong interactions between the wind and waves loadings and their combined impacts on the floater behavior and turbine performance.

LIST OF FIGURES 1 . 1

 11 Schematic comparison of HAWT and VAWT . . . . . . . . . . . . . . . . . . . . 1.2 Fixed foundation offshore wind turbine park (©Van Oord) . . . . . . . . . . . . . 1.3 Stability triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Illustration of the float's technologies (source: energy.gov) . . . . . . . . . . . . . 1.5 Illustration of the Hywind Spar and WindFloat semi-submersible . . . . . . . . . 1.6 illustration of the TRL ladder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Speed scale for Froude and Reynolds scaling . . . . . . . . . . . . . . . . . . . . . 2.1 Schematic representation of the SINTEF actuator system. source: Valentin Chabaud et al 2018 J. Phys.: Conf. Ser. 1104 012021 . . . . . . . . . . . . . . . . . . . . . 2.2 Test campaign lead by the DTU at the Ifremer Brest wave tank with a low Reynolds rotor and a wind tunnel on top of the wave-tank . . . . . . . . . . . . . 2.3 Precision and accuracy for metrology . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Thrust generation by Desmond et al. credit: Desmond et al. 2019 . . . . . . . . 2.5 Energy production for the different turbine sections [Stickland 1975] . . . . . . . 2.6 VAWT model used by Miller et al. for studying the impact of a VAWT solidity on its performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Blades position through the turbine's rotation . . . . . . . . . . . . . . . . . . . . 2.8 Illustration of the desert VAWT farm studied by Brownstein et al. credit:Brownstein et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 2D HiL setup in the Politecnico de Milano wind tunnel . . . . . . . . . . . . . . . 3.1 CAD model of the IFREMER Brest wave tank . . . . . . . . . . . . . . . . . . . 3.2 CAD model of the IFREMER Brest wave tank with their respective wind turbines overlaid behind the scale-models . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 WindQuest specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Floater's degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Upper view of the wave tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Wave generator limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Nautilus-10 scale model's CAD and picture . . . . . . . . . . . . . . . . . . . . . 3.8 Floater specifications and mass distribution . . . . . . . . . . . . . . . . . . . . . 3.9 Topsides picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.10 Topsides: carbon structure and guy ropes . . . . . . . . . . . . . . . . . . . . . . 3.11 Measuring the scale model's inertia . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 Model position in the wave tank . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13 Theoretical catenary moorings described in Lifes50+ reports . . . . . . . . . . . . 3.14 Mooring stiffness computed with Orcaflex for one line . . . . . . . . . . . . . . . 3.15 Rigging for mooring lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16 Mooring lines installed on the scale model, ready for testing . . . . . . . . . . . . 3.17 Schematic representation of a mooring line's preparation . . . . . . . . . . . . . . 3.18 Qualisys cameras and markers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 Model in the wave tank with the rigid body generated by Qualisys overlaid . . . 3.20 Wave gage near by the scale model . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21 Mooring sensor zoom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.22 Acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Froude Reynolds incompatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 schematic representation of a SiL operation . . . . . . . . . . . . . . . . . . . . . 4.3 Software in the Loop components and communication . . . . . . . . . . . . . . . 4.4 Software in the Loop CompactRIO architecture . . . . . . . . . . . . . . . . . . . 4.5 Test setup for propellers calibrations . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Counter rotating propellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Thrust generator calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Counter rotating propellers efficiency depending on the rotor air-gap . . . . . . . 4.9 Influence of the fairing on the downstream rotor thrust . . . . . . . . . . . . . . . 4.10 Propeller delay between set-point and response . . . . . . . . . . . . . . . . . . . 4.11 Propeller delay between set-point and response . . . . . . . . . . . . . . . . . . . 4.12 Propellers response compared to setoint for severe sea states . . . . . . . . . . . . 4.13 Propellers response compared to setoint for normal sea states . . . . . . . . . . . 4.14 Floating wind turbine degrees of freedom . . . . . . . . . . . . . . . . . . . . . . 4.15 WindQuest VAWT and DTU HAWT thrust coefficients over the wind speed . . . 4.16 WindQuest Ct over the TSR by G. Maurice -HydroQuest . . . . . . . . . . . . . 4.17 TSR and RPM setpoints used for thrust calculation with the constant RPM hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.18 Comparing the constant λ and the constant RPM thrust at different wind speeds 4.19 Exploration of the control laws influence through decay dests, observation of the hydrodynamic damping being canceled by the wind turbine . . . . . . . . . . . . 4.20 Comparison of the control laws on the floater pitch oscillation bellow and at rated wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21 Wave spectrums for normal, severe and extreme sea states overlaid with the float pitch and surge resonance frequencies for both WindQuest VAWT and DTU HAWT configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Observing the influence of the SiL control law on the floater for normal sea state 4.23 Observing the influence of the SiL control law on the floater for severe sea state . 5.1 Pitch, surge motion and wave elevation for the same Design Load Case repeated during the two experimental campaigns . . . . . . . . . . . . . . . . . . . . . . . 5.2 Illustration of a pitch decay test for the WindQuest configuration -Left: illustration of the time series -Right: PSD of the same signal . . . . . . . . . . . . . . . 5.3 Experimental measurement of the pitch angle for the HAWT and the VAWT on the Nautilus-10 semi-submersible model . . . . . . . . . . . . . . . . . . . . . . . 5.4 Illustration of the energy spreading the frequency domain . . . . . . . . . . . . . 5.5 PSD analysis of the floater response for Severe Sea State . . . . . . . . . . . . . . 5.6 PSD analysis of the floater response for Normal Sea State . . . . . . . . . . . . . 5.7 PSD analysis of the Surge for Severe Sea State with a logarithmic scale, observing the divergences in between the model spring mooring and the OpenFAST catenary mooring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 pitch RAO for both configurations with and without SiL for Severe Sea State Hs=7.69m Tp=12.5s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Surge RAO for both configurations with and without SiL for Severe Sea State Hs=7.69m Tp=12.5s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 pitch and surge RAO for the first operational conditions . . . . . . . . . . . . . . 5.11 pitch and surge RAO for the second operational conditions . . . . . . . . . . . . 5.12 pitch and surge RAO for the third operational conditions . . . . . . . . . . . . . 5.13 illustration of the RAO averaging with all the experimental RAO overlaid with the average RAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 Averages pitch RAO for the WindQuest VAWT and DTU HAWT models . . . . 5.15 Averages Surge RAO for the WindQuest VAWT and DTU HAWT models . . . . 5.16 Beam representation of the WindQuest 13MW . . . . . . . . . . . . . . . . . . . 5.17 pitch RAOs computed with HydroStar . . . . . . . . . . . . . . . . . . . . . . . . 6.1 ISAE -ENSMA Poitiers "concrete" S620 wind tunnel . . . . . . . . . . . . . . . . 6.2 Modelling the blockage of the scale model in the wind tunnel . . . . . . . . . . . 6.3 Measuring the velocity field around the wind turbine . . . . . . . . . . . . . . . . 6.4 pitch and surge RAO full scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 pitch and surge RAO at wind tunnel scale . . . . . . . . . . . . . . . . . . . . . . 6.6 Floater's surge and pitch response from RAO . . . . . . . . . . . . . . . . . . . . 8.10 PSD of the thrust signal with a surge motion at f=0.46Hz A=75mm and a rotor frequency at 10Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.11 phase average of the same thrust signal for the surge motion at f=0.46Hz A=75mm and a rotor frequency at 10Hz with three low pass filters compared . . . . . . . . 8.12 inertia extraction from the thrust measurements at λ=3.14 for surge motion f = 0.93Hz A = 100mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.13 Dynamic thrust coefficient measured at λ=3.14 for surge motion f = 0.93Hz A = 100mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.14 static thrust coefficient model compared to the dynamic for a subset of surge motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.15 static thrust coefficient model compared to the dynamic for the following configuration λ=3.14 f=0.93Hz A=100mm . . . . . . . . . . . . . . . . . . . . . . . . . 8.16 Observation of the average thrust coefficient drop as a fonction of δ V . . . . . . . 8.17 Illustrations of the influence of the motion frequency on C ′ tV rel . . . . . . . . . . 8.18 Illustration of the VAWT stream tube with induced and fluid axial velocity . . . 8.19 Scatter plot of the k values a as a function of the Strouhal number S tV z0 . . . . . 8.20 Comparison of the measurements with the dynamic model described in equation (8.28) for all three Tip Speed Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 8.21 evolution of the wind turbine's work through a surge phase as a function of kb max χ 0 .186 LIST OF TABLES 3.1 Froude and Reynolds scalings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Nautilus-10 scale model specifications . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Target and measured scale model's masses . . . . . . . . . . . . . . . . . . . . . . 3.4 Topsides mass for both configurations . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Comparison of theoretical and measured inertia . . . . . . . . . . . . . . . . . . . 4.1 Propellers throttle and thrust measurements . . . . . . . . . . . . . . . . . . . . . 5.1 Cross correlation of the DoFs in between the two campaings . . . . . . . . . . . . 5.2 Experimental resonance frequencies for both WindQuest VAWT and DTU HAWT configurations at scale 1:1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Cross correlation of the experimental measurements with OpenFAST . . . . . . . 5.4 Specifications used for designing the WindQuest 13MW . . . . . . . . . . . . . . 5.5 WindQuest 13MW mass and inertia . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Mass and inertia of the Nautilus-10 floater fitted with the WindQuest 13MW . . 5.7 Error between experimental measurements and HydroStar model . . . . . . . . . 6.1 Strouhal scaling factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Strouhal scaling factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Actuator's operating range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Scale model' mass and inertia from CAD . . . . . . . . . . . . . . . . . . . . . . . 7.3 mast profiles tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Test matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Convergence time for different rotaton speeds . . . . . . . . . . . . . . . . . . . . 8.2 Comparison of the phase average with the time averages for the Thrust coefficient 8.3 Test matrix for the surge tests measuring the VAWT dynamic response to surge motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INTRODUCTION Contents 1 . 1 19 1. 2 21 1. 3 24 1. 4

 11192213244 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Floats technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Small-scale experimental study of the behaviour of floating wind turbines at sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Framework and objectives of the thesis . . . . . . . . . . . . . . . . . 25

Figure 1 . 1 -

 11 Figure 1.1 -Schematic comparison of HAWT and VAWT

Figure 1 . 2 -

 12 Figure 1.2 -Fixed foundation offshore wind turbine park (©Van Oord)

Figure 1 . 3 (

 13 extracted from [Thiagarajan and Dagher 2014] ) places the main types of floats on a stability triangle illustrating the mechanisms used. If four floats are presented on this figure, there are three main types of floats present in the literature and the industry (barges receiving marginal interest compared to other technologies). They are illustrated in figure 1.4, and here is the list SPAR: Single Point Anchor Reservoirs are long cylinders with a heavy ballast placed at

Figure 1 . 3 -Figure 1 . 4 -Figure 1 . 5 -

 131415 Figure 1.3 -Stability triangle

Figure 1 . 6 -

 16 Figure 1.6 -illustration of the TRL ladder

  Froude scale follow the equation (1.3) while the flow velocities in the Reynolds scale are governed by the equation (1.4) with λ L the model scale. Thus the motions of a floating wind turbine model do not allow maintaining the Reynolds number on the wind turbine blades. The figure 1.7 illustrates this situation.

1. 4 .

 4 Framework and objectives of the thesis

Figure 1 . 7 -

 17 Figure 1.7 -Speed scale for Froude and Reynolds scaling

  report [MÜLLER et al. 2014] makes a review of the tests campaigns in wave-tank and mentions the principal projects having been made public at the time of its publication. In this report, the European Wind Energy Association (EWEA) draws up a balance sheet of the floating wind market and describes the various floating wind turbine concepts. The report describes the different concepts of floating wind turbines, including grid-connected demonstrators such as Hywind, Windfloat, or the Kabashima Iceland and Hakatara Bay demonstrators in Japan. The reference also describes some wave-tank trials such as DeedCWinnd, blue H, and Deepwind. In this section, the study of floating wind turbines is divided into three parts. The first part describes the research projects that have contributed to advancing knowledge on floating wind turbines, both for the vertical and horizontal axis. The second part deals with the wave-tanks tests and the solutions to model the action of the wind turbine on the float with Froude scaling.

  European project Lifes50+ has conducted studies of twol horizontal axis floating wind turbine concepts aiming for the development f the technology. The 10MW reference wind turbine described in the DTU report by Bak et al. [Bak et al. 2013] is positioned on two semi-submersible floats. The report by Yu, Müller, and Lemmer [W. Yu, K. Müller and Lemmer 2018] describes the public version of the two float concepts. The first floater, the OO-Star is a star-shaped semi-submersible consisting of three columns positioned around a central fourth column. The design develops the concept of concrete floats.

  conditions possible, three potential implantation sites for floating wind projects are studied: the Gulf of Fos in the Mediterranean sea, the site west of the Barra Islands off the coast of Scotland, and the Gulf of Main, on the west coast of the United States. The different locations and their wave, current, and wind conditions are described in the report by Bredmose et al. [Bredmose 2012]. The Gulf of Main was selected for further development. Simulations of the FOWT are the backbone of the project.They are ran with OpenFAST, an open source simulation first developed by NREL and expanded during the project in order to fit as closely as possible the expected performances of the DTU 10MW reference HAWT. The report by Pegalajar-Jurado et al. [Pegalajar-Jurado et al. 2018] describes how the simulation was set up and tweaked to reproduce the FOWT response to wind and waves solicitations. To adjust and validate the models of the float, model-scale tests have been carried out. The behavior of the FOWT subjected to swell and the wind interaction is studied at the SINTEF basin in Trondheim, Norway. The aerodynamic solicitations are reproduced thanks to a cable actuator described in the article by Chabaud et al [Chabaud et al. 2018] and illustrated in figure 2.1. The results of the tests, as well as the comparison with simulations, are detailed in the report of Madsen et al. [Lemmer et al. 2016].

Figure 2 . 1 -

 21 Figure 2.1 -Schematic representation of the SINTEF actuator system. source: Valentin Chabaud et al 2018 J. Phys.: Conf. Ser. 1104 012021

  First, the article by Stewart and Muskulus [Stewart and Muskulus 2016] in the journal Energy Precedia presents the different approaches. This includes the DeedCwind campaigns using a geometrically scaled rotor, the Software in the Loop trials conducted at ECN, or lesser-used systems such as the porous disks used for the Wind-Float campaign at Berkley [Roddier et al. 2010] and the cable actuators used at MARNITEK [Chabaud et al. 2018]. Next comes the article by Muller et al. [MÜLLER et al. 2014]. This article, after a complete review of tank trials, looks at the advantages and disadvantages of each technology. The review of the technologies starts with the description of the rotors where either the blades are adaptedto generate the right thrust, or the wind speed is adapted. Design of the rotor will have a strong influence on the aerodynamics, the rotor torque and the amplitude of the 3P stresses. All those parameters influence the forces exercised by the turbine on the float. The solution will be expensive. But it will allow the study of details points (but important) such as the influence of the control laws of the turbine on the behavior of the structure.

Figure 2 . 2 -

 22 Figure 2.2 -Test campaign lead by the DTU at the Ifremer Brest wave tank with a low Reynolds rotor and a wind tunnel on top of the wave-tank

  [Kanner 2013]. Two thrusters rotating around two vertical axes are reproducing the behavior of a set of two vertical axis wind turbines. The cyclic nature of the thrust of vertical axis wind turbines is reproduced by modulating the thrust of the rotating thrusters. The purpose of these tests is to study the drift of the float in the long term. His work gives a great insight into what can be achieved with a simple thrust control solution as he gets interesting results. Kanner's work is a unique case (to the author's knowledge) demonstrations of modeling a VAWT's oscillating aerodynamics in a wave tank. However, his solution does not include any SiL technology that would allow for modeling the VAWT's response to the waves' induced motion. Publications by Azcona et al. [Azcona et al. 2014], and Oguz et al. [Oguz et al. 2018a] present the use of a ducted fan coupled with OpenFAST for modeling the behavior of floating horizontal axis wind turbines. This solution was developed in partnership with CENER. The technical solution and its limitations are described in [Azcona et al. 2014]. Both papers make an extensive comparison of tests to simulations. In Desmond, Hinrichs, and Murphy paper [Desmond, Hinrichs, and Murphy 2019] the authors took a metrological look at the use of thrusters. The system also uses a rotating mass to simulate rotor inertia. The system is illustrated in the figure 2.4. The article shows that the introduction of a thruster reduces precision. However, the accuracy of the measurements is improved by the addition of the thruster. The reproduction of the inertia of the rotor allowed a better fidelity of the measurements. Those metrological concepts are illustrated in figure 2.3. The authors suppose that this phenomenon comes from the gain of stability allowed by the rotor's inertia. More recently, in his thesis manuscript [Arnal 2020], Vincent Arnal describes the use of a SIL driven by OpenFAST calculations to simulate the behavior of horizontal axis floating wind turbines of up to 15MW at the Centrales Nantes test facilities. The thrust calculation by OpenFAST is compared to simpler assumptions to illustrate the advantages and limitations of the different thrust calculation solutions. In an effort to increase the fidelity of thruster/SiL systems, Pires et al. [Pires et al. 2020] present

Figure 2 . 3 -

 23 Figure 2.3 -Precision and accuracy for metrology

Figure 2 . 4 -

 24 Figure 2.4 -Thrust generation by Desmond et al. credit: Desmond et al. 2019

Figure 2 . 5 -

 25 Figure 2.5 -Energy production for the different turbine sections [Stickland 1975]

Figure 2 . 6 -

 26 Figure 2.6 -VAWT model used by Miller et al. for studying the impact of a VAWT solidity on its performances

Figure 2 . 7 -

 27 Figure 2.7 -Blades position through the turbine's rotation

  The parper by Roy et al.[START_REF] Roy | Design of an offshore three-bladed vertical axis wind turbine for wind tunnel experiments[END_REF] describes the use of a double multiple stream tube model for the design of a three blades H VAWT prior to wind tunnel tests. The model was first validated with the experimental data published by the Sandia lab [Worstell 1981]. The paper describes the process leading to the selection of the blades profiles, solidity and axpect ratio leading to good performances in the low Reynolds environment of the wind tunnel.

  -baloutaki et al. [Ahmadi-baloutaki, Carriveau, and Ting 2016] explain that while horizontal axis wind turbines are typically placed 6 to 10 diameters downstream from each other, vertical axis turbines can be placed 3 to 6 diameters apart and still produce 90% of the energy that a single turbine would produce. The author also explains that installing a counter-rotating configuration allows for a slight increase in turbine output. The downstream turbines can also benefit from the turbulence of the upstream turbines, as a more turbulent flow can delay dynamic stall. The study by Brownstein et al. [Brownstein, Kinzel, and Dabiri 2016] investigates the interaction of VAWTs in a farm configuration. For this purpose, a wind tunnel study is conducted before switching to full-scale experiments in the desert, illustration in figure 2.8. Performance measurements are performed by testing different designs, including the use or not of counter-rotating turbines and by varying the arrangement of the turbines. The literature review presented in

Figure 2 . 8 -

 28 Figure 2.8 -Illustration of the desert VAWT farm studied by Brownstein et al. credit:Brownstein et al.

  loss. When transitioning to full-scale measurements, the Light Detection And Ranging (LiDAR) technology are often used. Based on a Doppler velocity measurement LiDARs allows for the wind speed measurement in a volume around the wind turbine. The article by Käsler et al. [Käsler et al. 2010] describes the use of LiDAR for measurements of a wind turbine wake. The technology is now used to study the wave interaction in wind turbines farms. The articles by Hegazy et al. [Hegazy et al. 2022] and Torres Garcia et al. [Torres Garcia et al. 2019] use the technology to observe the turbine wake.

  effort are made in wind tunnel to study at model-scale the behavior of a wind turbine subjected to the action of the wind and floaters motion. The same problems of compatibility between the Froude scale and the Renolds scale are present, requiring compromises. Report D7.9 of the Lifes 50+ [Thys et al. 2019] project describes the issues and recommendations for such tests. The wind turbine model used for the references bellow is presented in [Matha et al. 2015]. In these configurations, the Strouhal similarity, described in the equation (2.4) and allows for the preservation the dynamics of the wake, is used. The scaling is thus governed by the geometric scale of the model λ L and by the scale of the wind speed λ V . The paper by Bayati et al. [Bayati et al. 2018a] described in detail the problematic as well as the similarities employed during the Lifes50+ campaign at the Polimi wind tunnel. From the velocity and length scales, it is possible to deduce the other scale factors for mass, time, frequency, and forces. Belloli's paper [Belloli et al. 2020] describes the tests and the method used to drive the actuator for the calculations of the OpenFAST model.

Figure 2 . 9 -

 29 Figure 2.9 -2D HiL setup in the Politecnico de Milano wind tunnel

3 . 1 50 3. 2 53 3. 3 54 3. 3 . 1 55 3. 3 . 2 56 3. 3 . 3 58 3. 3 . 4 59 3. 3 . 5 60 3. 3 . 6 61 3. 4 61 3. 4 . 1 64 3. 5 65 3. 5 . 1 65 3. 5 . 2 67 3. 5 . 3 67 3. 5 . 4 69 3. 5 . 6 70 3. 6 70 3. 7 71 3. 1 Introduction

 31502533543155325633583459356036614614164565516552675367546956706707711 studies use both numerical and experimental tools. The Lifes 50+ project is the prime example of such research with the OpenFAST model being calibrated with experimental data from wave tank and wind tunnel measurements. Vertical axis wind turbines received less attention. Numerical models of floating VAWT have been developed. Leroy's model developed with INNOSEA and the Ecole Centrale de Nantes is a great example of such model. Unfortunately experimental studies are very rare. Kanner's thesis is one of the rare examples describing an experimental study. But not low Reynolds rotor or SiL setup have been used in wave tank to the author's knowledge. And the experimental studies on VAWT mainly focus on the power production. A lack of experimental research for VAWT is observed. This thesis will thus aim at filling part of that gap in knowledge. HAWTs experiments built up on decades of research that lead to systems such as OpenFAST powered SiL and HiL allowing for high fidelity reproduction of floating HAWT in wave tank and wind tunnel. By proposing and implementing technological bricks in the Ifremer Brest, LEGI and ENSMA laboratories this thesis will hopefully help laying foundations for high fidelity floating VAWT models in wave-tank and wind tunnels. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scaling laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Floater and wind turbines scale models preparations . . . . . . . . . The floater: Nautilus-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . Floater weight and center of gravity . . . . . . . . . . . . . . . . . . . . Scale models of the wind turbines . . . . . . . . . . . . . . . . . . . . . Inertia measurements (pendulum methodology) . . . . . . . . . . . . . . Measuring the floater's inertia . . . . . . . . . . . . . . . . . . . . . . . . Floater and wind turbines scale model: conclusions . . . . . . . . . . . . Moorings lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical specifications . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4.2 Rigging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.4.3 Installing the mooring lines . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.4.4 Conclusions on the mooring lines . . . . . . . . . . . . . . . . . . . . . . Electronics and instrumentation . . . . . . . . . . . . . . . . . . . . . Motion tracking: Qualisys . . . . . . . . . . . . . . . . . . . . . . . . . . Waves probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mooring sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acquisition device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.5.5 Propeller's power supply . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion on the campaign's electronics and instrumentation . . . . . Numerical tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . As a part of the Ph.D., two wave tank campaigns are lead at the IFREMER Brest Deep Wave Basin facilities (illustrated in figure 3.1) in July and November 2019. The wave tanks uses salt water, is 50m long, 12.5m wide and is 10m deep (with a 20m deep pit used to test sea worthy equipment) and a wave generator is used to generate waves up to 55cm high. Those campaigns aimed at answering this question: What are the floater's hydrodynamic performances when fitted with the HAWT it was designed for and with a VAWT adapted onto the floater? Quantifying the performances, a few metrics such as resonance frequency or the Response Amplitude Operator can be measured. Experimentally quantifying those metrics requires both the floater and the wind turbine reproduction at model-scale for their experimental study in the wave tank.

Figure 3 . 1 -

 31 Figure 3.1 -CAD model of the IFREMER Brest wave tank

Figure 3 . 2 -Figure 3 . 3 -

 3233 Figure 3.2 -CAD model of the IFREMER Brest wave tank with their respective wind turbines overlaid behind the scale-models

3 . 4 .

 34 Structural properties of both the floater and the wind turbine need to be reproduced. The mechanical stiffness is complicated to reproduce. It is common to approximate the scale model to a rigid body. That is what is done for this experimental campaign. The aerodynamics also play an essential role in the FOWT's sea-keeping properties. This last point is handled by the Software in the Loop and treated in the chapter 4.2. The next paragraphs will describe sub-assemblies presented in the CAD model of the model in the wave tank illustrated in figure 3.5. First, there is a FOWT model on the 25m mark of the wave tank. In stead of the four cantenry mooring lines, aerial elastic mooring lines oriented 90°from each other and 45°from the wave direction maintain the model in position. Each mooring line is equipped with a strain gauge sensor placed between the line and the connection to the wave tank. Two wave gauges are installed. A first one, on the 25m mark is aligned with the model. A second one is level with the upstream mooring sensors. The measurements from this wave gauge are not exploited in this thesis. Finally, the power supply line runs from the scale-model to the pontoon.

Figure 3 . 5 -

 35 Figure 3.5 -Upper view of the wave tank

  [Pegalajar-Jurado et al. 2018; W. Yu, K. Müller and Lemmer 2018]. This floater was selected for the following reasons 1. It is a semi-submersible. When the floater has been selected semi-submersibles and spars floaters are the two technologies the most developed for FOWT. And semi-submersibles are more versatile than spars limited by their bigger draught.

  studied concept is designed for installation in the Gulf of Main, of the USA's East Coast. In the report [Pablo Gómez et al. 2015] authors describe the wind and wave conditions.

Figure 3 . 6 -

 36 Figure 3.6 -Wave generator limitations

Figure 3 . 8 -

 38 Figure 3.8 -Floater specifications and mass distribution

Figure 3 . 9 -

 39 Figure 3.9 -Topsides picture

  Figure 3.3 presents the main full-scale specifications. The two topsides illustrated in figures 3.2,3.10 and 3.9 are used.The structure is composed of a carbon section. We need a stiff and modular structure to match the CoG and CoT of the two wind turbines concepts. A carbon structure is built and stiffened by Dynameema shrouds. The structure is aligned and straightened using a laser level. How those specifications are achieved will be discussed in the next sections.

Figure 3 .

 3 Figure 3.10 -Topsides: carbon structure and guy ropes

  .13 are described in [W. Yu, K. Müller and Lemmer 2018]. The floater is held in position by four 833.24m long catenary moorings. The chain weighs 188.2 kg/m. At scale, the wave tank would have to be 3 m deep (130 m full scale) to simulate the catenary mooring with chains. It is thus not possible in the wave tank to reproduce the mooring illustrated in figure 3.13.

figure 3 . 13 .

 313 figure 3.13. Imposing the floater's surge position allowed the measurement of the mooring's stiffness and tension. The figure 3.14 illustrates the computed stiffness. In order to get the right pitch, surge, sway, and yaw frequencies for decay tests, the mooring's stiffness and tension are set to reproduce the catenary mooring line around the floater's neutral position (0 m surge).

Figure 3 .

 3 Figure 3.12 -Model position in the wave tank

Figure 3 . 14 -

 314 Figure 3.14 -Mooring stiffness computed with Orcaflex for one line

Figure 3 . 15 -

 315 Figure 3.15 -Rigging for mooring lines

Figure 3 . 16 -

 316 Figure 3.16 -Mooring lines installed on the scale model, ready for testing

Figure 3 . 17 -

 317 Figure 3.17 -Schematic representation of a mooring line's preparation

Figure 3 . 18 -

 318 Figure 3.18 -Qualisys cameras and markers

  sition via a voltage signal proportional to the position of the gauge probe with a measurement uncertainty of ±3.56mm (k=2) or 0.150mm full scale. As explained at the beginning of the chapter, two wave gauges are installed (positions illustrated in figure 3.5). The first one is placed on the 25 meters mark, is level with the scale model. This wave gauge is seen in figures 3.16, 3.19 and 3.20. The second one is placed on the walkway in front of the model, the measurements from this sensor are not used in this thesis.

Figure 3 . 20 -

 320 Figure 3.20 -Wave gage near by the scale model

Figure 3 . 21 -

 321 Figure 3.21 -Mooring sensor zoom

The

  Aerodynamics are simulated by AeroDyn, an aerodynamic module using a Blade Element Momentum (BEM) model splitting each place into several elements. The C l and C d coefficients of each section are used in order to compute the rotor's reaction to the wind. AeroDyn is in constant evolution with empirical corrections implemented to the computations. DydroDyn [Jonkman, Robertson, and Hayman 2015] is the module used for hydrodynamics computations. Potential-flow theory solution, a strip-theory solution, or a mix of both can be used by the software in order to compute the constraints applied on the structure. First, the software needs to know the wave elevation. Here the simulation is given the wave eleveation time series measured during the wave tank experiments. The wave gauges signal is computed full scale and fed into the HydroDyn computations. The open-source model allows any user with the skill set to refine, modify or adapt the computations. OpenFAST is thus growing more robust and more reliable as industries and research teams work with the tool. Examples of such uses are NREL's work on MoorDyn [Andersen et al. 2016], about DeepCWind using the software in order to compare wave tank campaigns with FAST simulations [Robertson et al. 2013b] or Lemmer et al. [Lemmer et al. 2020] who used the software to develop a new floater concept.

  Moreover, the Froude and Reylods incompatibility is making things harder. As explained in the Wave tank material and methods chapter, wave tank testing uses the Froude scaling, keeping the Froude number defined by the equation (4.1) constant. On the other hand, the wind turbine aerodynamics require a constant Reynolds number (equation (4.2)). From those equation, using the model geometrical scale defined in equation (4.3) with L f the full-scale size and L m the model size, one can define the speed from Froude scaling λ vF roude = √ λ L and for Reynolds scaling λ vReynolds = 1/λ L . It is simply not possible to match the Reynolds wind speeds while enforcing the Froude similitude for the hydrodynamics reproduced in the wave tank. This incompatibility is illustrated in figure 4.1. Solutions solving this incompatibility exist with low Reynolds blades, adapted wind speeds, drag disks, and SiL. That last approach is the one we selected as it is the most versatile allowing for the reproduction of both VAWT and HAWT with several controls laws and wind speeds.

Figure 4 . 1 -

 41 Figure 4.1 -Froude Reynolds incompatibility

3 .

 3 The wind turbine generates aerodynamic moments around the yaw and roll axis. Reproducing such forces requires having propellers away from the center of thrust. Pires et al. describe the CENER system in the conference article [Pires et al. 2020].

Figure 4 .

 4 Figure 4.2 illustrates the basic principle of a Software in the Loop operation. First, the platform motion measured in the wave tank is fed in real-time to the simulation. Next, those motions are scaled up to the full scale. The simulation then computes the platform and the wind turbine velocity. The apparent wind speed is computed as a vectorial sum of the environmental wind speed (infinity wind speed in the figure) and the FOWT motion. The simulation computes the resulting thrust with the apparent wind speed and the wind turbine operating parameter. Next, the computed thrust is scaled down to the model scale. Finally, through the calibration, the thrust is converted into a throttle given to the fans reproducing the wind turbine thrust and influencing the floater motion. The process repeats during the whole test duration.The fidelity of that computation may range from a simple low fidelity drag disc representation as used in our case to the BEM simulation ran by OpenFAST. As for a reference and context, Kulunk et al. work[START_REF] Kulunk | Aerodynamics of Wind Turbines, Fundamental and Advanced Topics in Wind Power[END_REF]] gives an excellent overview of the various levels of fidelity for

Figure 4 . 2 -

 42 Figure 4.2 -schematic representation of a SiL operation

Figure 4 . 3 -Figure 4 . 4 - 4 . 4 4 . 4 . 1

 434444441 Figure 4.3 -Software in the Loop components and communication

Figure 4 . 5 - 4 . 4 . 2

 45442 Figure 4.5 -Test setup for propellers calibrations

Figure 4 . 6 -

 46 Figure 4.6 -Counter rotating propellers

  SiL software (running on a host computer and the cRIO) transmits the throttle set-point to an Arduino via the Wifi connexion. Next, the LabVIEW program converts the thrust into a throttle set-point using the static calibration during the tests. However, the throttle set-point is used without a Thrust/PWM conversion to run the first calibration. Finally, the Arduino sends the throttle set-point to the ESC via a TTL signal (0 -5V numerical signal). The WindQuest configuration uses two thrust generators to reproduce the twin-rotor configuration of the VAWT.The calibration is thus repeated once for each thrust generator.

Figure 4 . 7 -

 47 Figure 4.7 -Thrust generator calibration

Figure 4 .

 4 Figure 4.7 illustrates the results. Operating downstream from the structure proved to have a small but non-negligible impact with a 6.5% thrust loss at the maximum throttle compared to the upstream propeller.Both propellers operating in a counter-rotating configuration with one propeller operating downstream from the other one, proved to have much more impact. The downstream propeller operates with reduced thrust. The figure 4.7 illustrates a maximum thrust reduced by 19% for the downstream propeller. Comparing both sets of counter-rotating thrust generators shows little difference. A 1% difference in the measured thrust for the same throttle is observed. This difference, probably under the uncertainty levels, is deemed negligible.

Figure 4 . 8 -

 48 Figure 4.8 -Counter rotating propellers efficiency depending on the rotor air-gap Similarly, the propeller should integrate a fairing to protect the strain-gauges and the electronics from the blades. Then again, Theys et al. [Theys et al. 2016] indicate that the fairing should generate a small thrust decrease. The parameter is thus tested, and the results are illustrated in the figure 4.9. A thrust difference of 1N is observed at full thrust, making the fairing worth the thrust loss.

Figure 4 . 9 - 4 . 4 . 5

 49445 Figure 4.9 -Influence of the fairing on the downstream rotor thrust

Figure 4 . 10 -

 410 Figure 4.10 -Propeller delay between set-point and response

Figure 4 . 12 -

 412 Figure 4.12 -Propellers response compared to setoint for severe sea states

Figure 4 . 13 -

 413 Figure 4.13 -Propellers response compared to setoint for normal sea states

Figure 4 . 14 -

 414 Figure 4.14 -Floating wind turbine degrees of freedom Thrust is computed using equation (4.5) with ρ the air density, S the swept area, C t the thrust coefficient, and V rel the relative wind speed. For the whole campaign, we only consider constant environmental wind speeds V 0 and the fluctuations due to turbulent wind speed are not reproduced. Those fluctuations can generate a very low frequency excitation on the FOWT but the present study does not aims at integrating this parameter into the equation of the sea-keeping

( a )

 a WindQuest thrust coefficient over wind speed by G. Maurice -HydroQuest (b) DTU 10MW HAWT thrust coefficient over wind speed

Figure 4 . 15 -

 415 Figure 4.15 -WindQuest VAWT and DTU HAWT thrust coefficients over the wind speed

Figure 4 . 16 -

 416 Figure 4.16 -WindQuest Ct over the TSR by G. Maurice -HydroQuest

Figure 4 . 10 )

 410 Figure 4.17 -TSR and RPM setpoints used for thrust calculation with the constant RPM hypothesis

Figure 4 .

 4 [START_REF] Bayati | A formulation for the unsteady aerodynamics of floating wind turbines, with focus on the gloabal system dynamics 11/07/2017 Terms of Use[END_REF] illustrates those differences on the thrust generated by the wind turbine when it is operating around tree wind speeds bellow, at and above the rated wind speed.Bellow rated wind speed (11.4 m/s), the two control laws are similar with linear responses to the wind speed variations. The constant RPM law will generate smaller thrust variations than the constant λ set-point. At rated win speed, The two control laws showcase drastically different reactions to the apparent wind speed variations. The constant TSR will generate big negative damping. When the wind speed varies, the aerodynamic drag acting against the floater motion decreases, thus amplifying the floater motion. The constant RPM controller will still dampen the floater motion by generating a thrust proportional with the apparent wind speed. Above rated, the controller reactions reverse. The constant λ controller generates positive damping. The turbine thrust increases with wind speed variations (both negative and positive), thus opposing its forces to the floater motion. The constant RPM controller now generates negative damping.

Figure 4 . 18 -Figure 4 .

 4184 Figure 4.18 -Comparing the constant λ and the constant RPM thrust at different wind speeds

Figure 4 . 19 - 4 . 6 . 2

 419462 Figure 4.19 -Exploration of the control laws influence through decay dests, observation of the hydrodynamic damping being canceled by the wind turbine

  (a) Comparison bellow rated wind speed (b) Comparison at rated wind speed

Figure 4 . 20 -

 420 Figure 4.20 -Comparison of the control laws on the floater pitch oscillation bellow and at rated wind speed

Figures 4 .

 4 Figures 4.22 illustrate the influence of the SiL hypothesies for Normal Sea State with 10.3 m/s wind speed, slightly bellow rated. Similarly figure 4.23 illustrates the response of the floater for severe sea state and 7 m/s. Both abscissa and ordinate axes scales are kept the same in order

Figure 4 .

 4 23a also shows that the floater has a slightly stronger reaction the the waves on the pitch axis. This response is indicated by increased levels of energy on the 0.1 to 0.15 Hz bandwidth. The two SiL hypotheses have similar levels of energy indicating a similar response to waves on the bandwidth.When observing the FOWT response to Severe Sea State on the pitch axis, the main difference comes from the constant thrust hypothesis which displays stronger response to waves and two clear energy spikes on the pitch and surge frequencies. With constant thrust and constant TSR

Figure 4 . 21 -

 421 Figure 4.21 -Wave spectrums for normal, severe and extreme sea states overlaid with the float pitch and surge resonance frequencies for both WindQuest VAWT and DTU HAWT configurations

  (a) Floater pitch PSD for normal sea state (b) Floater surge PSD for normal sea state

Figure 4 . 22 -

 422 Figure 4.22 -Observing the influence of the SiL control law on the floater for normal sea state

Figure 4 . 23 -

 423 Figure 4.23 -Observing the influence of the SiL control law on the floater for severe sea state

5. 1 102 5. 2 103 5. 3 105 5. 4 108 5. 5 Response Amplitude Operator and comparison of the two FOWTs 111 5. 6

 110221033105410851116 Verification of the repeatability between test campaigns . . . . . . . Decay tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wind turbine capsizing moment . . . . . . . . . . . . . . . . . . . . . Software in the Loop: validation and fidelity gains for DTU HAWT configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4.1 Statistical comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.4.2 PSD analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enhanced stability and lower LCOE: upscale the WindQuest VAWT to 13MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.6.1 Extrapolation of the new nominal power . . . . . . . . . . . . . . . . . . 117 5.6.2 Concept of a WindQuest 13MW turbine . . . . . . . . . . . . . . . . . . 118 5.6.3 HydroStar study of the WindQuest 13MW FOWT . . . . . . . . . . . . 120 5.6.4 Influence on Levelised Cost of Energy . . . . . . . . . . . . . . . . . . . 121 5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 This chapter presents the experimental results of the wave tank campaign. Note that all the results in this chapter are presented full-scale. The main scientific objective is to investigate the changes and improvements of the SiL on the FOWT models sea keeping properties. The model response to waves will thus be studied with and without the use of a SiL in order to establish its influence. This investigation on the SiL is carried out though the study of the sea-keeping properties of the Nautilus-10 semi-submersible with one HAWT: the DTU-10MW, and one VAWT: the WindQuest-10WM. The wind turbines are installed on the Nautilus-10, a semi-submersible first designed for the DTU HAWT. The study will present results such as measurements of the capsizing moment, decay tests, and irregular waves. Most of the results discussed in this chapter have been introduced in the Torque 2020 conference article [Matoug et al. 2020].

Figure 5 . 1 -

 51 Figure 5.1 -Pitch, surge motion and wave elevation for the same Design Load Case repeated during the two experimental campaigns

Figure 5 . 2 illustrates

 52 the measurement realized during the pitch decay test of the model in WindQuest VAWT configuration. Like all decay tests, this test is realized without generating thrust with the propellers. Looking at those signals, we see a dampened sinusoidal oscillation. The PSDshows that the signal energy is located at one frequency. This is the process for experimentally measuring the resonance frequency. The operation is repeated for Surge, Heave, and Yaw degrees of freedom on both the WindQuest VAWT and the DTU HAWT configuration. Table5.2 presents the results of those measurements.

Figure 5 . 2 -

 52 Figure 5.2 -Illustration of a pitch decay test for the WindQuest configuration -Left: illustration of the time series -Right: PSD of the same signal

  As explained previously and described by the literature, VAWT can have an advantage for static stability. The article by Borg and Collu [Borg and Collu 2015] gives excellent insight on the comparison of HAWT and VAWT for floating applications. The capsizing moment tests aim at measuring the difference between the two wind turbines. This measurement is crucial as it gives insights into the floater size needed for the wind turbine. The capsizing moment is thus measured by applying a constant thrust to the model with the propellers.

Figure 5 . 3 -

 53 Figure 5.3 -Experimental measurement of the pitch angle for the HAWT and the VAWT on the Nautilus-10 semi-submersible model

  For example, both those references by Arnal [Arnal 2020] and Madsen et al. [Madsen et al. 2016] use this process. For reference, figure 5.4 represents the typical semi-submersible response to wind and waves. On the higher frequencies is the floater response to waves. This response generally spreads on a large frequency. Then comes the pitch natural frequency generating a spike of energy on a lower frequency. Finally, on the lowest frequencies is the natural surge frequency.

Figure 5 . 4 -Figure 5 . 5 -

 5455 Figure 5.4 -Illustration of the energy spreading the frequency domain

Figure 5 . 6 -

 56 Figure 5.6 -PSD analysis of the floater response for Normal Sea State

Figure 5 .

 5 Figure 5.7 is illustrating the same response as in figure5.5 but with a logarithmic scale. This allows for a finer observation of the surge response. Note that both the catenary mooring and the spring mooring have a similar response to waves at 0.05 to 0.12 Hz intervals. But on the Surge frequency, the catenary mooring has a response of about 10 time smaller as the one observed on

Figure 5 . 7 -

 57 Figure 5.7 -PSD analysis of the Surge for Severe Sea State with a logarithmic scale, observing the divergences in between the model spring mooring and the OpenFAST catenary mooring

Figure 5 . 2 Figure 5 . 3 Figure 5 .

 52535 Figure 5.10 -pitch and surge RAO for the first operational conditions

Figure 5 .

 5 Figure 5.13 -illustration of the RAO averaging with all the experimental RAO overlaid with the average RAO

Figure 5 . 14 -

 514 Figure 5.14 -Averages pitch RAO for the WindQuest VAWT and DTU HAWT models

Figure 5 . 15 - 5 . 6 . 1

 515561 Figure 5.15 -Averages Surge RAO for the WindQuest VAWT and DTU HAWT models

Figure 5 . 16 - 10 )

 51610 Figure 5.16 -Beam representation of the WindQuest 13MW

6 . 1 6 . 3

 6163 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.2 Wind tunnel scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.2.1 Strouhal scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.2.2 Wind tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.2.3 Scaling factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Hybrid approach: simulating the floater's motion . . . . . . . . . . . 130 6.3.1 Scaling down the float's motion . . . . . . . . . . . . . . . . . . . . . . . 130 6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Figure 6 . 2 -

 62 Figure 6.2 -Modelling the blockage of the scale model in the wind tunnel

Figure 6 . 3 -

 63 Figure 6.3 -Measuring the velocity field around the wind turbine

Figure 6 . 5 -

 65 Figure 6.5 -pitch and surge RAO at wind tunnel scale

Figure 7 . 1 - 7 . 2

 7172 Figure 7.1 -Wind tunnel model with the main sub-assemblies highlighted

Figure 7 . 2 -

 72 Figure 7.2 -Actuator's dynamic schematics

Figure 7 . 3 -

 73 Figure 7.3 -Actuator's translation to rotation motion conversion

Figure 7 . 4 -Figure 7 . 5 - 7 . 4

 747574 Figure 7.4 -Floater's surge and pitch response from RAO

. 6 .

 6 In this situation, only the rotor's inertia overlays on top of the aerodynamics. The process is repeated but with the 1.05 kg rotors. The average thrust is thus 3.35 N per rotor. To compute the inertia acting on each sensor, the rotor is split into two half rotors. Their CoG is positioned at 35% of the half rotor's height, the carbon fiber blades being 0.3 kg while the aluminum hubs weight 0.12 kg (illustration in figure7.7). This would result in inertial loads of 7.4 N for the lower nacelle sensors and 9.4 N for the upper nacelles censors. The average aerodynamics then represents 48 % to 56 % of the inertia. This is much more favorable to the measurement of unsteady aerodynamics.

Figure 7 . 6 -

 76 Figure 7.6 -Illustration VAWT scale model

FFigure 7 . 9 -

 79 Figure 7.9 -Z6 sensor response to angles constraints

Figure 7 . 10 - 7 . 5 . 1

 710751 Figure 7.10 -WindQuest turbine model for wind tunnel

Figure 7 . 11 -

 711 Figure 7.11 -Discrepancies in the blades' length

Figure 7 . 12 -

 712 Figure 7.12 -Upper and lower nacelles of the scale model

  .14 the RDM7 model of the VAWT scale-model. It is simplified into a set of beam elements. Masses are added to each nacelle to represent the mass of the engines and rotors. Only the rotor's mass is included here. Their stiffness is not modeled. The light blue star structure models the strouds structure. If the final design will be a foam plate sandwiched by two carbon sheets, it is represented in RDM7 as a set of hollow rectangular beams. Tiis structure is rendered obsolete as the final design does not includes shrouds.

Figure 7 .

 7 Figure 7.14 -RDM7 model

7. 6 . 1 Figure 7 . 15 -

 61715 Figure 7.15 -Observing the centrifugal forces due to blades' weight imbalance

Figure 7

 7 Figure 7.16 -Centrifugal forces measurements

Figure 7 . 17 -Figure 7 . 18 - 7 . 6 . 3

 717718763 Figure 7.17 -Balancing plate with weight installed

Figure 7 . 19 -

 719 Figure 7.19 -Before and after balancing both rotors

Figure 7 . 20 -

 720 Figure 7.20 -Interaction between rotors whent they are both operating

Figure 7 . 22 -

 722 Figure 7.22 -Actuator cRIO logigram

Figure 7 . 25 - 9 Conclusions

 7259 Figure 7.25 -Illustrations of the rotor synchronization and residual phase difference

Figure 8 .

 8 Figure 8.2 illustrates the measurement of the wind turbine's average thrust coefficient over the Tip Speed Ratio (TSR). The TSR is defined in equation (8.3) with r the rotor radius, ω the rotor's rotation speed in rad/s, and U the wind tunnel's wind speed. During those tests, the wind speed is maintained constant at 5 m/s, and the VAWT's rotation speed is set. Each point represents a measurement point at a fixed rotation speed ranging from 350 rpm to 750 rpm. As expected, the measurements follow an upward trend that is almost linear.The thrust coefficient is extracted from the thrust measurements using equation (8.4) with T the measured thrust (sum of all four thrust sensors), ρ the air density measured for each measurement

Figure 8 . 2 -

 82 Figure 8.2 -Measure of the average thrust coefficient

  by the imbalance in the rotors. The measurements without wind are then subtracted to the measurements with wind only to retain the aerodynamic forces. Once this process is completed, the sensors measurements are summed. The figure8.3 illustrates the process on one censor. It is repeated on each sensor.

Figure 8 . 3 -

 83 Figure 8.3 -Measuring the efforts generated by the rotor's imbalance and suppressing them from the aerodynamics

Figure 8 . 4 -

 84 Figure 8.4 -The process of measurement the thrust coefficient illustrated at 600 rpm

Figure 8 . 5 -Figure 8 . 6 - 71 Figure 8 . 7 -

 85867187 Figure 8.5 -PSD analysis of the signal before and after filtering

Figure 8 .

 8 Figure 8.8 illustrates the result of those measurements. The scatter plots the results for each experimental point and, on top of this result is the uncertainty interval centered on the C t at 0°p

Figure 8 . 8 -

 88 Figure 8.8 -C t for static pitch angles varying from -10°to +10°8

Figure 8 .

 8 Figure 8.9 illustrates the result obtained of a typical configuration. The measurement for all four sensors converged at 200 seconds as the surge motion started at 111.5s. The measurement converged within a hundred seconds. This observation is similar for all the measurements ran for this study. Also note that the two top sensors are slower to converge. This is probably due to the vibrations generated by the surge system. As they are transmitted to the mast of the VAWT the vibrations' amplitude is increased introducing more noise into the top sensors. Those vibrations are studied in greater details in the next section as the filtering solution is presented.

Figure 8 . 9 - 14 8. 3 . 3

 891433 Figure 8.9 -C tV rel convergence using the NRMSE criterion for surge motion f=0.46Hz A=75mm at λ=3.14

Figure 8 .

 8 Figure 8.10 -PSD of the thrust signal with a surge motion at f=0.46Hz A=75mm and a rotor frequency at 10Hz

Figure 8 .

 8 Figure 8.11 -phase average of the same thrust signal for the surge motion at f=0.46Hz A=75mm and a rotor frequency at 10Hz with three low pass filters compared

x

  = A.sin(ωt) ẋ = Aω.cos(ωt) ẍ = -Aω 2 .sin(ωt) = -xω 2

(8. 9 )Figure 8 .Figure 8 . 13 -

 98813 Figure 8.12 -inertia extraction from the thrust measurements at λ=3.14 for surge motion f = 0.93Hz A = 100mm

Figure 8 .

 8 Figure 8.14 -static thrust coefficient model compared to the dynamic for a subset of surge motions

Figure 8 .

 8 Figure 8.15 -static thrust coefficient model compared to the dynamic for the following configuration λ=3.14 f=0.93Hz A=100mm

Figure 8 . 16 -Figure 8 . 17 - 8 . 4 8 . 4 . 1

 81681784841 Figure 8.16 -Observation of the average thrust coefficient drop as a fonction of δ V

Figure 8 . 19 - 2 ( 1 +

 81921 Figure 8.19 -Scatter plot of the k values a as a function of the Strouhal number S tV z0

Figure 8 . 20 -

 820 Figure 8.20 -Comparison of the measurements with the dynamic model described in equation (8.28) for all three Tip Speed Ratio

. 21 .Figure 8 .

 218 Figure 8.21 -evolution of the wind turbine's work through a surge phase as a function of kb max χ 0 .

  This Ph.D. thesis addresses the experimental study of floating offshore wind turbine with a focus on a counter rotating vertical axis wind turbine concept: the WindQuest 10MW. Using an hybrid approach in the Ifremer Brest wave tank, the study investigates the sea keeping properties and the interaction of the VAWT with the semi-submersible floater originally designed for horizontal axis wind turbines. The influence of the wind turbine on the floater is studied though the use of a Software in the Loop modeling the wind turbine in the wave tank with a propeller controlled by real-time computations. The VAWT aerodynamics when submitted to the floater motion are studied at the ENSMA wind tunnel with a Hardware in the Loop approach. Here the model of the wind turbine is submitted to motion generated by actuators reproducing the pitch and surge response of the floater to waves. This last chapter presents the results and conclusions of those topics with recommendations for future works.

  response and the time delay between the set-point and the thrust output. If the results are satisfying for the present experiments the limitations such as time delays and imperfect function transfer of the system have been highlighted. Improving on those points is part of the future work possibilities that will be discussed later in this chapter. On the topic of the control laws, the wind turbines are modeled as uniform surfaces. Their response is computed from tables of the static response of the wind turbine at different tip speed ratios. Three hypothesis are used for this model: the constant thrust, the constant Tip Speed Ratio and the constant rpm. The influence of those controle laws on the FOWT model is presented in the next paragraph.Tabulated approach for SiL increases the fidelity of the HAWT and VAWT simulationsThe SiL used in this thesis uses tables and not simulations such as OpenFAST or CACTUS. This approach prove to have significant effects on model's response to sea. The pitch response, influenced by the aerodynamics of the wind turbine shows the most significant improvements with the SiL. First, when comparing the experimental measurements of the DTU-10MW configuration with the calibrated OpenFAST simulations. The constant thrust experiments are taken as a reference. It is shown that the use of SiL increase significantly the correlation of the measured motion with the simulation (OpenFAST), specially for wind driven conditions.Second, the PSD and RAO illustrate the influence of the SiL on the motion by generating a damping. The damping is reducing the FOWTs response both on the waves spectrum and on the low frequencies around the pitch and surge natural frequencies. Third the three control laws, generating a constant thrust, a wind turbine operating a constant Tip Speed Ratio and at constant rotations speed, proved to capture the dynamics of the different control laws on the FOWT. The first one is used in the present thesis as a reference when comparing the experimental results with simulations. The later two hypothesis yield similar results when the wind turbine is operating bellow its rated speed. When the damping effect is more realistic above at and above the rated wind speed, the different hypotheses prove to have a significant impact of the aerodynamic damping of the wind turbine. The tabulated approach captured the dynamics of the different control laws. Depending on the control law, the tabulated SiL modeled positive and negative aerodynamic damping from the wind turbine on the FOWT, highlighting once again the importance of control laws adapted to floating applications.An off the shelf SiL for the Ifremer Brest wave tank. The system presented and developed for this Ph.D is calibrated and has been tested. The tabulated approach and the versatility of the propellers are qualifying the system for future use in the wave tank. The system has already been used once for a campaign unrelated to the present work and ready to be reused after the conclusion of this Ph.D. thesis.Replacing the DTU-10MW HAWT with theWindQuest-10MW on the Nautilus-10 semi-submersible has a significant impact on sea-keeping properties. The FOWT natural frequency is strongly impacted by the reduction in weight and inertia of the VAWT especially on the pitch axis. It has the advantage of reducing the FOWT capsizing moment when submitted to wind but also increases the response to waves. A solution studied in this Ph.D.thesis is to increase the size and power production of the wind turbine while keeping the same floater size. This option is studied with an HydroStar model calibrated with the measurements and apears to be a viable option to restore the sea-keeping properties of the float while reducing the Levelized Cost Of Energy.Designing a VAWT scale model for wind tunnel testing with Hardware in the Loop approach and Strouhal scaling. When testing the VAWT at the ENSMA wind tunnel the Strouhal similitude is used in order to study the unsteady aerodynamics of the VAWT positioned on actuators. This process is a fine act of balance between the wind tunnel characteristics and the actuators specifications. This approach also proved to generate strong constraints on the model that need to be considered. Those constraints resulted in the choice of generating sinusoidal oscillations on pitch and surge axes. From frequency analysis of the structure to instrumentation and rotors balancing nothing was left to change. Once this process carried out, and in order to get the model ready for the wind tunnel campaigns, adjustments are still needed. Iterating on the nacelles design, tweaking the actuators structure and balancing the rotors the scale models proved to be a key element to the proper operation of the VAWT model. Remaining improvements on the model will be discussed in the perspective. surge significant impact on the VAWT thrust from the Hardware in the Loop approach. During the experimental wind tunnel campaign the static and dynamic thrust coefficients of the wind turbine are measured thanks to the instrumented model positioned on pitch and surge actuators. For the static response, the wind turbine thrust coefficient is measured as a function of the Tip Speed Ratio and the rotor azimuth angle. Then measurements are then carried out with the wind turbine submitted to pitch and surge motion. The surge results shows a dynamic response drastically influenced by the motion frequency. At lower frequency the static and dynamic responses are similar, but for higher frequencies, the dynamic response is opposed to the static response of the wind turbine. Consequently, a static model such as those used in the wave tank campaign fails at capturing the correct response of the wind turbine for floating applications. The TSR and the frequency of the surge motion proved to influence the evolution of the thrust coefficient in those unsteady situations. A new model based on the relationship between the induced velocity and the motion frequency is thus proposed. This model proved to have a very good agreement with the experimental measurements for all the motion frequencies and tip speed ratios tested in the present study.A VAWT model reused for more experimental campaigns. The VAWT model is being used for other experimental campaigns at the ENSMA wind tunnel. For his own Ph.D. thesis

  Exploring the VAWT's dynamic response when submitted to pitch and combined motion. Measurements in the wind tunnel have been carried out when the model is submitted to pitch ans surge motion. They still need to be processed in order to propose a model describing the unsteady reaction of the VAWT to pitching motion. This objective could hopefully be achieved for the defense of this Ph.D. thesis. Once a pitch model is defined, in a more distant future, experimental measurements of the VAWT thrust submitted to both pitch and surge motion could be carried out. Such measurements would allows for the validation of invalidation of the current laws for combined motion. Such laws would be of a great use for the tabulated SiL approach explored in this Ph.D. thesis. Titre : Etude expérimentale du comportement marin d'une éolienne flottante à double rotor Mot clés : éolienne flottante, axe vertical, Software in the Loop, Hardware in the Loop ,bassin, soufflerie Résumé : Les éoliennes offshore flottantes subissent des mouvements dus aux vagues et au vent qui peuvent avoir un impact sur leurs performances. Dans cette thèse, nous nous concentrons sur l'effet du cavalement et du tangage sur un design original d'éolienne à axe vertical contrarotatif (VAWT). Pour cette étude, nous développons un dispositif expérimental hybride, à la fois en soufflerie et en bassin à houle, pour modéliser le comportement de l'éolienne VAWT soumise aux vagues et au vent. En bassin, le modèle est soumis aux vagues alors que le vent est simulé à l'aide d'un ventilateur contrôlé par le "Software in the Loop" (SiL). Le SiL calcule et ajuste la poussée en temps réel à partir des mouvements mesurés. En soufflerie, la maquette d'éolienne est étudiée lorsqu'elle est soumise à des mouvements de flotteurs simulés par des actionneurs. Les deux approches mettent en évidence les fortes interactions entre les charges du vent et des vagues et leurs impacts combinés sur le comportement du flotteur et les performances de l'éolienne. Title: Experimental study of the sea keeping properties of a counter rotating vertical axis wind turbine Keywords: floating offshore wind turbine, vertical axis, Software in the Loop, Hardware in the Loop, wave-tank, wind tunnel

REVIEW Contents 2.1 Study of the behavior of floating wind turbines at sea

	Chapter 2
	LITERATURE

. . . . . . . . 28 2.1.1 Research projects on floating wind energy . . . . . . . . . . . . . . . . . 28 2.1.2 Modeling of a floating horizontal axis wind turbine during wave-tank tests 30 2.1.3 Floating vertical axis wind turbines: numerical studies . . . . . . . . . . 35 2.2 Experimental and numerical study of the aerodynamics of vertical axis wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2.1 Turbine design parameters and their influence . . . . . . . . . . . . . . . 38 2.2.2 Aerodynamics of vertical axis wind turbines . . . . . . . . . . . . . . . . 42 2.2.3 Wake and interaction between VAWT . . . . . . . . . . . . . . . . . . . 43 2.2.4 Wake interaction between HAWT . . . . . . . . . . . . . . . . . . . . . . 44 2.2.5 Wind tunnel study of floating wind turbines . . . . . . . . . . . . . . . . 45 2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.1.3 Floating vertical axis wind turbines: numerical studies

	In this publication, floats from the WindFloat and Hywind industrial projects are adapted for a
	Darrieus 5MW turbine. VAWT design parameters are modified to find the most suitable center
	of gravity and inertias. The designs are chosen according to the pitch period, static pitch angle,
	RAO, and anchoring choices resulting from the floater/turbine combination.
	In 2012 DeepWind published a reference design for a vertical axis floating wind turbine in the
	paper by Paulsen et al. [Paulsen et al. 2012]. This study aims to propose a design, a reference
	Bossuyt et al. 2016b; Bossuyt et al. 2016a] (more on this subject later). This solution was used design that can be carried forward into future work. The study uses available manufacturing
	for the basin tests of the WindFloat floating wind turbine [Roddier et al. 2010] at Berkely in methods, proposes design parameters of the conventional turbine, and uses references of gener-
	2010 in conjunction with an inertia wheel, thus generating the necessary thrust and inertia. Full ators available on the market. If the proposed floating wind turbine is not the most efficient,
	scale atmospheric conditions imply turbulence of the wind and thus of the thrust. If this solution it allows underlining the technical difficulties and the design problems such as a high solidity
	does not aim at controlling and reproducing this turbulence, the wind blower still generates is leading to a rotor too heavy and with rotation speeds to low for the selected generators. On the
	own turbulence influencing the FOWT. Thus, even if we do not choose the level of turbulence other hand, increasing the rotation speed of the wind turbine decreases the size of the generator
	and the frequency of these disturbances, turbulence linked to the wind tunnel is created and and improves its performance.
	applied to the model. The studies presented above consider aerodynamic performance and structural issues. However,
	The Lifes 50+ trials saw the use of cable actuators. This solution is described in detail in the other studies also seek to optimize aerodynamic performance and energy production. One could
	publication by Chabaud et al. [Chabaud et al. 2018]. Six cable actuators are connected to a cage for instance, mention the study of Cheng et al. [Cheng, Wang, and Ong 2018] on VAWT concepts
	located on the nacelle of the model. The solution reproduces the thrust, the force perpendicular developed during the European DeepWind project [Paulsen et al. 2012; Paulsena et al. 2013].
	to the thrust, the moments in Yaw and pitch, and the generator's torque.
	The development of floating wind turbines led to a renewed interest in vertical axis wind turbines
	from industries and research institutes. The Sandia National Laboratory, with a long culture of
	vertical axis, is the part of the first to explore the use of vertical axis for floating applications. In
	this poster, Griffith et al. [Griffith et al. 2000] present the interests of the vertical axis: a lower
	center of gravity, easier maintenance and installation, less complex machine and smaller floats,
	and leading to less expensive electricity. This study and most of those that will follow present a
	single-rotor Darrieus troposkine or H.
	In the article by Borg and Collu [Borg and Collu 2015] this topic is developed. The authors
	compare a vertical axis wind turbine to an horizontal axis wind turbine. A static study shows
	that VAWTs are more favorable for floating applications due to a lower capsizing moment and
	more flexible design criteria. However, the oscillating nature of the thrust can excite the float on
	frequency bands close to or superimposed on the swell. The Yaw moment should also be studied
	carefully as some types of floats, like spars, have a low righting moment on the Yaw axis.
	In the previous study, the float design was taken from a concept developed for the horizontal
	axis. Adapting floaters designs from horizontal to vertical axis wind turbines is interesting as
	a wide variety of substructures already exist for HAWT. This is what was done by the three
	researchers of the Sandia national lab: Fowler, Bull, and Goupee [Fowler, Bull, and Goupee 2014].

2.2 Experimental and numerical study of the aerodynamics of vertical axis wind turbines

	Owens and Griffith [Owens and Griffith
	2014] propose a methodology coupling an aerodynamic analysis to a structural analysis using an
	open-source tool. The publication describes results for two Darrieus and V-VAWT wind turbines
	with carbon fiber or fiberglass blades. This first study suggests that the safety margins taken for
	these designs are sufficient to withstand the aerodynamic instabilities and constraints associated
	with floating VAWT.
	More recently V.Leroy explored the numerical modeling of both HAWT and VAWT during his
	Ph.D. thesis [Leroy 2018]. In his conference article [Leroy et al. 2018] Leroy describes the sea
	keeping properties of a Daerius VAWT on the OC3Hywind spar. The wind turbine is modeled
	using both the low computational cost Double Multiple Streamtube and the more expensive
	Free Vortex Wakes computations. Results of both methodologies are compared using the OC3
	load cases.
	After the first surge in researches on VAWT (with examples such as [Worstell 1978; Sheldahl,
	Klimas, and Feltz 1980; Ashwill 1992; Sidney F., Johnston 1982; Mays 1978; Ashwill et al.
	1986; Klimas and Worstell 1981; Stickland 1975]) and with the renewed interest in vertical axis

Table 3 .

 3 1 -Froude and Reynolds scalings

	Physical quantity	Unit	Froude scaling Reynolds scaling
	Length

Table 3 .

 3

	2 -Nautilus-10 scale model specifications
	Nautilus floater	1/42	1/1
	Mass	105.01 7.78 10 6 kg
	Height	0.62	26	m
	Width	1.55	65.25	m
	Columns diameter	0.25	10.5	m
	CoG (from the keel) 0.232	9.7	m

Table 3 .

 3

	3 -Target and measured scale model's masses
	DTU configuration: target mass	128.40 kg
	DTU configuration: measured mass	128.52 kg
	Error	0.1	%
	WindQuest configuration: target mass	121.17 kg
	WindQuest configuration: measured mass 124.98 kg
	Error	3	%

the target weight is 105.01 kg (floater with full ballasts) with a CoG 0.232 m above the keel. All the results with the topsides are presented in the table 3.3. By carefully placing the topside's lead weights, the CoG is obtained with a precision greater than ±2.5mm, the Dyneema rope's radius.

Table 3 .

 3 4 -Topsides mass for both configurations

		Wind Quest	DTU
	unloaded mass (kg)	14.39	11.004
	target mass (kg)	14.847	20.967
	measured mass (kg)	16.2 (error 9%)	21 (error 0.15%)
	unloaded CoG (m)	0.931	0.568
	CoG target (m)	1.297	1.659
	CoG measured (m) 1.298 (error = 0%) 1.659 (error = 0%)
	Center of thrust (m)	98.5	119

Table 4 .

 4

	1 -Propellers throttle and thrust measurements
	Throttle (%) Thrust (N)
	20	1.17
	30	4.37
	40	8.01
	50	12.34
	60	17.07
	70	21.3
	80	24.8

  As explained in the literature review, for the simulation of HAWT, most simulations use AeroDyn, and OpenFAST [Oguz et al. 2018b; Azcona et al. 2014; Chabaud et al. 2018]. Comparable to OpenFAST for VAWT applications, V.Leroy [Leroy et al. 2018] work uses CACTUS for the simulation of floatingVAWTs. Unfortunately, his solution is an internal tool for INNOSEA, and we cannot use it for this campaign. In conclusion, even though those tools offer excellent fidelity and have already been presented in the literature, they're not the best solution if the need for a cheap and readily employable tool is predominant.

Table 5 .

 5

	Jonswap	10.92	15	0	0.979	0.955	0.971
	Regular	4.2	9.72	7	0.994	0.985	0.998
	Jonswap	10.92	15	7	0.989	0.992	0.989

1 -Cross correlation of the DoFs in between the two campaings wave signification wave Peak period WSPD Corr Corr Corr spectrum height (Hs) [m] (Tp)[s] [m/s] (waves) (pitch) (surge)

Table 5 .

 5

	2 -Experimental resonance frequencies for both WindQuest VAWT and DTU HAWT
	configurations at scale 1:1
		DTU 10MW HAWT WindQuest 10MW VAWT
	surge[s]	114.1	109
	heave[s]	19.8	19.44
	pitch[s]	31	23.3
	yaw[s]	90.9	94.6

Table 5 .

 5

		3 -Cross correlation of the experimental measurements with OpenFAST
	Waves	Wind	HS	Tp	WSPD No SiL pitch SiL pitch	pitch Thrust
	strength strength (m) (s)	(m/s)	correlation	correlation ∆	correlation
	+	+	1.26 7	5	0.60	0.67	+0.07 0.78
	+	++	1.68 7.97 7.1	0.63	0.75	+0.12 0.9
	+	+++	2.18 7.94 10.3	0.64	0.78	+0.14 0.9
	++	+	7.7	7.7	5	0.75	0.81	+0.06 0.79
	+++	++	10.9 15	7	0.67	0.70	+0.03 0.81

Table 5 .

 5 3 includes the wind and waves conditions with the cross-correlations of the pitch and thrust times series with OpenFAST. Wave and wind driven DLCs are visualized thanks to colors and + marks. The + indicated normal sea states and/or mild wind conditions. ++ marks indicate severe sea stats and/or potent wind seeds. Finally, +++ marks are given for severe sea state or wind speed close from nominal.

  Those measurements are obtained by soliciting the FOWT with irregular waves. Here the JON-SWAP spectrum with a significant wave height of 7.69m and a pic period of 12.4s is reproduced at model scale. Furthermore, when the turbine aerodynamics are reproduced, a wind speed of 7m/s is modeled. Those conditions are one of the Design Load Cases used for designing the DTU 10MW & Nautilus-10 FOWT and are extracted from the Lifes50+ report[START_REF] Lemmer | D4.6 Model validation against experiments and map of model accuracy across load cases[END_REF].Two main observations are drawn from chapitre 4/figures 5.8 et 5.9. First, on the waves frequency bandwidth, the VAWT has a stronger response than the HAWT on the pitch DoF. On the surge, the two FOWTs have similar responses. The SiL has a negligible impact on the system response.

	Pitch Response [°/m]	1.0 1.5 2.0 2.5 3.0 3.5 Surge Response [m/m]	0 2 4 6 8 10 12	0.00	0.05	8 WindQuest SiL DTU no SiL DTU SiL 0.15 0.20 Frequency [Hz] RAO 0.10 Normalised waves PSD 0.25 WindQuest no SiL RAO DTU no SiL DTU SiL WindQuest no SiL WindQuest SiL Normalised waves PSD 0.30	(5.5)
		0.5
		0.0	0.00	0.05	0.10	0.15 Frequency [Hz]	0.20	0.25	0.30
	Figure 5.8 -pitch RAO for both configurations with and without SiL for Severe Sea State
	Hs=7.69m Tp=12.5s
	chapitre 4/figures 5.8 et 5.9 respectively represent the WindQuest and DTU FOWTs' pitch

and surge RAO with both "no wind" and "wind" configurations in a severe sea state. The first configuration is obtained by measuring the model response without generating thrust with the propellers. The second one is obtained with the SiL reproducing a wind turbine operated for maintaining the optimal λ, thus maximizing the power production.

Second, several observations are made on the lower frequencies around the pitch and surge natural response. First, the measurements have a rough resolution. Nonetheless, the spikes in Figure 5.9 -Surge RAO for both configurations with and without SiL for Severe Sea State Hs=7.69m Tp=12.5s the natural frequency are observed. Both FOWTs have a natural frequency measured at 0.007 Hz or 140 seconds on the Surge DoF. The measure is noisy on the pitch axis, but two spikes are observed. The first spike, with lower frequency is measured at 0.007 Hz indicating a probable interaction between the pitch and the surge. The second spike is observed at 0.03 Hz or 33 s for the DTU HAWT and at 0.042 Hz or 24 s for the WindQuest VAWT. The measurements match pretty well the results from the decay tests, and once again, the lower mass and inertia of the WindQuest VAWT is modifying the float natural frequency on the pitch DoF.

Figures 5.10

, 5.11 and 5.12 illustrate the same process but for operational conditions where waves forcing is smaller while wind forcing, gets proportionally stronger. In those conditions, the results presented previously will still apply. The WindQuest FOWT has a stronger pitch response to the waves. Observing the Surge RAO shows similar responses for both configurations though the VAWT has a slightly stronger wave response.

Table 5 .

 5

	4 -Specifications used for designing the WindQuest 13MW
	Parameter	Value	Unit
	Diameter	104	m
	Height	156	m
	Nb of cables	2	[-]
	Aero power	7.123	MW
	Blade profile	NACA18	[-]
	λ opt	3.8	[-]
	Aspect ratio	1.5	[-]
	Profile chord	7.8	m
	blade skin thickness	21	mm
	ρ glass fiber	2500	kg/m3
	solidity	0.15	[0]
	Table 5.5 -WindQuest 13MW mass and inertia
	Mas	1548.8 Tons
	I xx	1.70x10 10 kg.m2
	I yy	1.93x10 10 kg.m2
	I zz	2.75x10 10 kg.m2
	Center of thrust	103m
	center of gravitu	82.4m
	RPM at λ opt	8

Table 5 .

 5

	6 -Mass and inertia of the Nautilus-10 floater fitted with the WindQuest 13MW
	Mas	9.51× 6 kg
	I xx	3.3185 × 10 10 kg.m2
	I

zz 3.5 × 10 10 kg.m2

Figure 5.17 -pitch RAOs computed with HydroStar Table 5.7 -Error between experimental measurements and HydroStar model

Table 6 .

 6

	1 -Strouhal scaling factors
	physical quantity	scaling formula
	length	λ

Table 6 .

 6

	2 -Strouhal scaling factors
	physical quantity	scaling formula	scale
	length

Table 7 .

 7

	1 -Actuator's operating range
	Specificatio	range	unit
	Stroke	300	mm
	Max speed	250	mm/s
	• Max acceleration 5000 mm/s 2
	Work load	38	kg

Table 7 .

 7

	2 -Scale model' mass and inertia from CAD
	Mass	14.2 [kg]
	CoG	0.746 [m]
	Ixx	11.355 [kg.m2]
	Iyy	10.36 [kg.m2]
	Izz	1.02 [kg.m2]
		θ =	ẍ r	(7.9)

Table 7 .

 7

	3 -mast profiles tested

Table 8 .

 8

	1 -Convergence time for different rotaton speeds
	Rotor rpm convergence time to 5% [s]
	350	50s
	350	50s
	450	65s
	550	73s
	650	74s
	750	56s

Table 8 .

 8 2 -Comparison of the phase average with the time averages for the Thrust coefficient

	RPM C t phase average [-] Average C t [-]
	300	0.26	0.25
	400	0.18	0.21
	500	0.45	0.45
	600	0.58	0.57
	700	0.74	0.72

Table 8 .

 8 3 -Test matrix for the surge tests measuring the VAWT dynamic response to surge motion

	Frequency Amplitude	TSR
	[Hz]	[mm]	[-]
	0.46	25	2.41, 3.14, 4
	0.46	50	3.14
	0.46	75	3.14
	0.46	100	2.41, 3.14, 4
	0.93	25	2.41, 3.14
	0.93	50	2.41, 3.14, 4
	0.93	75	2.41, 3.14, 4
	0.93	100	2.41, 3.14, 4
	1.5	25	3.14
	1.5	50	3.14
	1.93	50	2.41, 3.14, 4
	1.93	75	2.41, 3.14, 4

Remerciements

Table of contents

Measuring the floater's inertia

Using the formula (3.4) the floater's inertia is measured. The results are given in the table 3.5.

In those results the following coordinate system is used: ⃗ x is the wind and wave propagation axis facing toward the wave generator, ⃗ z is the vertical axis facing up and ⃗ y is defined by the two other vectors to define a Cartesian coordinate system. Those results are obtained after adjusting the model's inertia. Ixx is tweaked by moving masses along the mast and Izz by moving masses toward or away from the mast. The model does not allows for Izz to be modified. But, as the experiments focus on conditions where wind and waves are aligns the Yaw response is not studied and constraints on this axis are thus lower. On the Ixx and Izz axis the measures are within 10% from the target which is considered to be a good result. However note that the WindQuest inertia is lower than target while the DTU HAWT is higher that target. This result will thus increase the differences of the two FOWTs on their pitch response.

Frequency analysis

A frequency analysis helps gaining a better understanding of the propeller dynamic response.

From OpenFAST simulations, the wind turbine thrust in normal, severe, and extreme sea states conditions is scaled-down and used as set-points for the propellers. In figures 4.12 and 4.13 the measured PSD for respectively a severe and a normal sea state. The first energy spike at 0.4Hz (floater natural frequency) is very well reproduced. At 0.8Hz, where the waves forcing generates thrust variations, the propeller thrust fits reasonably well the set-point. However, one can note that the accuracy (metrology speaking) is not optimal as one measure is below set-point while the other is slightly above.

For the normal sea state, part of that divergence is due to the motor noise levels being higher when compared to the weaker normal sea state thrust signal. With the signal-to-noise ratio being low, the accuracy is mathematically reduced. However, another phenomenon should be taken into consideration: the system frequency response. Any system has a function transfer making its response to a solicitation (or a set-point here) different depending on the frequency.

The static calibration used and presented in the thesis will not accommodate this. Thus, using a "dynamic compensation" similar to the one used in Arnal thesis [START_REF] Arnal | Modélisation expérimentale d'une éolienne flottante par une approche « software-in-the-loop[END_REF]] and inspired from [Goodwin, Graebe, and Salgado 2000] would help make the set-point and response better.

have the same swept surface to a small margin leading to the same thrust at a set wind speed.

The only difference in capsizing moment will thus come from the turbine weight and CoG height.

Before commenting on the results, we should note that the model has two limitations that will affect the measurements. First, the Nautilus-10 is designed with active ballasts, modifying the float CoG to balance the wind turbine thrust. Our scale model is not equipped with such a system. Second, the aerial mooring used for the model (presented in chapter 3) will not have the same response to the FOWT pitch angle than the catenary mooring shown in the design. Those two differences influence the pitch angle value, but the comparison of the capsizing moment is still valid.

For the WindQuest VAWT configurations, the pitch angle is 53% lower than for the DTU HAWT configuration. This measurement fits with the statement indicating that VAWT allows for a smaller floater for the same turbine power. The measurement of this pitch angle will be used later to elaborate on a new floater/turbine combination designed to optimize the turbine seaworthiness and Levelized Cost of Energy (LCOE).

Software in the Loop: validation and fidelity gains for DTU HAWT configuration

Next comes the comparison of the experimental measurements with OpenFAST computations.

Those tests aim at qualifying the Software in the Loop by simulating the measures with Open-FAST. Two different hypotheses are compared to OpenFAST: the no SiL without any thrust and the SiL hypothesis reproducing the constant Tip Speed Ratio (TSR) λ assumption described in the previous chapter. The TSR is defined in equation 5.3 with r the rotor radius, θ the rotor rotation speed and V 0 the wind speed. OpenFAST is chosen as a reference for two reasons: first, it is well presented and validated in the literature, and second, calibrated models of the Nautilus-10 and DTU 10 WM HAWT are available on a repository. An important note is the the OpenFAST are modified to match the model mass and inertia. But the numerical mooring is still a catenary mooring and not an aerial spring mooring as in the wave tank.

To run this comparison, two methodologies are used and described in this chapter: First is presented the statistical analysis using the cross-correlation between the experiments and the OpenFAST simulations. If this approach does not explain how the differences are made between the SiL hypotheses but rather quantifies the gains and losses.

actuator's capabilities. Indeed, for Strouhal scaling, the motion's speed is directly proportional to the wind speed. A lower wind speed (i.e., higher λ V ) will decrease the actuators' constraints as speeds and accelerations will be spaller. But the counterpart is that this will also decrease the measured thrust with a square law. In order to understand the scaling selection, a presentation of the wind tunnel is needed. For this campaign, the scale model is placed a few meters downstream from the main test section. This choice is made to reduce the wind speed on the scale model and the blockage ratio.

The tunnel's section expands by 30% between the main section and the actual model locating.

Knowing that the volumetric flow rate, described by the equation (6.2) is conserved, the wind speed is expected to reduce by the same 30%. However, if the wind turbine's blockage is not negligible, the wind speed will not decrease as much. Following this reasoning, if the wind tunnel is operating at its lowest operational set-point, the wind speed on the scale model should be somewhere between 4 and 5 m/s. This would result in 2.28 The first key element of the model that needs to be set and defined is the actuators. The constraints on this element are mostly defined by the scaling law and the floater's response that needs the be reproduced for the hybrid approach.

Then, before going forward on the model's design, a focus on the strain sensor's selection is needed as this choice deeply influence the design of the VAWT's model.

The third section descibes the design of the scale-model's carbon fiber structure. Developing a scale-model with trust measurements in mind while placed on top of actuators system for Hardware in the Loop in a wind tunnel imposes some constrains and requires careful design.

This design includes mechanical conception of the nacelles but also a modal analysis of the carbon structure and of the rotor.

Going forward on the process of preparing the VAWT for wind tunnel testing, designing the model is only the first part of the equation. Once the system is assembled the rotors need balancing. Placing counter-weights in order to bring back the rotor's CoG on the rotation axis is essential for good rotor operation and exploitable thrust measurements. The fourth section will go though this process.

Finally, all this mechanics needs instrumentation and electronics in order to run. The last section of this chapter will thus described the instrumentation and the actuator's control needed for the effective operation of the scale-model.

Once this first issue solved another one needs to be checked. The thrust of a vertical axis turbine is oscillating [Leblanc and Ferreira 2018b]. The norm of the thrust vector varies, the direction also oscillates. Therefore, it can be dissociated into two components: the drag (Fx), exerted in the direction of the wind flow, and the thrust perpendicular to the drag (Fy). When modeling a floating wind turbine, Fx is the most critical force to reproduce. We have reproduced this thrust in a basin and that we are now seeking to study in a wind tunnel. It is, therefore, necessary to decouple the two stresses generated by the turbine.

Sensors placed on the nacelles of each rotor must allow the decoupling of the stress. Due to their construction, the bending sensors generally make it possible to decouple the forces on Fx from Fy. However, we are looking to verify this hypothesis on HBM's Z6 sensor (sensor selected for the thrust measurements). A calibrated mass is used to apply this constrain. Next, the sensor is secured onto a profile. This profile can be rotated in order to adjust for the angle at which the force is applied.

How to drive the design changes?

The designs changes are mostly driven by the mechanical perturbations measured by the thrust sensors. Figure 7.13 illustrates how the selection of designs operates.

Modal analysis of the structure with RDM7

The structure does not directly match the concept's design scaled down. It is designed to handle and operate with the harsh constraints imposed by the wind tunnel and the hybrid setup. To accommodate for the rotor's excitation, the structure needs to be stiffer than what is needed for static and inertial loads. Previous wind tunnel campaigns used Guy rope structure to stiffen the wind turbine. The wave tank model also uses that solution. The full-scale design also incorporates this solution. But the small footprint of the actuator system would not allow for the use of the guy wires to a base.

The aerodynamics excitation, also called 2P from the two rotors blades, should not excite the structure. Else the measurements won't be exploitable and the structure integrity might be

Actuators: Testing the control system

The actuators are tested using Qualisys, the wave tank's motion tracking system, to validate the speed control, figure 7.23 illustrates the setup. Four cameras are positioned around the actuator.

After calibrating, the Qualisys track manager reconstitutes the tracker's 3D motion. One of them is positioned on the actuator and the others are used for reference. The average oscillation amplitude is measured through phase averaging.The phase averages for amplitudes of ± 20mm and ± 100mm at 1 Hz are given as examples and displayed in figures 7.24a and 7.24b. The Qualisys measurement has an uncertainty of ± 2 mm. This uncertainty can vary from one test to another. 2 mm is the highest uncertainty observed. The average amplitudes fit the setpoint with an error of less than a millimeter. The standard deviation on this amplitude is less than ± 5%. This error is of the same order as the Qualisys measurement uncertainty. This result is similar throughout all the frequencies and amplitudes tested. This allows us to affirm that the instruction is respected and the speed control is validated.

Acquisition device

As explained previously, the wind tunnel campaign sees a slightly modified version of the acquisition used at the wave tank. The compact RIO is now running at 1 kHz to get a more satisfactory resolution on the measurement over a rotor's turn. This acquisition rate is the highest allowed by the cRIO before needing to switch the cRIO's programming to FPGA.

Added to the tension channels and the Wheatstone bridges channels, two encoder counters are added thanks to the ni 9401 digital input module. The module can count the quadrature encoder channels and directly output the motor's position. Note that the absolute position is returned.

The rotor's angular position is computed in the post process.

Synchronized rotors: the control strategy for the motors

The motors actuating the rotors are Maxon brushed DC motors controlled by EPOS 2 controllers.

The motor -controller assembly is chosen as system offers position, speed or torque control of the motors. The plan was first to use what is called the "master encoder mode" where one rotor is following a speed set-point while the second one is position controlled over the position of the first one. This mode developed for robotics applications allows for a perfect synchronization of the two motors.

structure were tuned to fit the needs for a structure stiff enough not to be excited by the high rotor rpm. Through several design iterations, the rotor performed as well or even better than expected. Balancing the blades reduced the centrifugal forces observed by the sensor to low levels compared to aerodynamics. Even though the wind turbine's mast and arms are designed with great care, not using guy ropes proved to be challenging with the coupling observed between the two rotors. Similar phenomenons have been observed during the wind tunnel campaign and will be discussed in the next chapter.

Choosing an actuation solution required compromises. Reproducing the motion from irregular waves proved to be out of the electric drive actuators capabilities. A system was thus designed to generate a sinusoidal oscillation on the pitch and surge degrees of freedom. Those motions' frequency and amplitude reproduce the floater's response to regular waves. This solution also has the advantage of being more adapted to studying the vertical axis wind turbine's aerodynamics.

Once again, after a few iterations, the design gave great results, but improvements can still be made and will be discussed in the next chapter.

Introduction

This chapter goes through the main experimental results obtained during the wind tunnel campaign. Measurements are regrouped into two categories: static and dynamic driven measurements. First, the static experiments aim at measuring the thrust coefficient of the wind turbine filter out the structure's vibration.

Uncertainties and convergence

Convergence study

The first convergence tests are run to ensure that the acquisition time is long enough so that the measurement converges towards the final value. This section will thus explain the convergence study realized for the static thrust measurements. when the VAWT is submitted to surge oscillations is thus proposed with T 0 the nominal thrust, V i0 the nominal induced velocity defined by V i0 = a 0 V 0 and V z0 the velocity deficit defined by

The induced velocity variation is defined with the equation (8.17). ∆V i represents the induced velocity fluctuations while the relative wind speed varies by Aωcos(ωt). The parameter k is thus representing the ratio between the two speeds and depends on the system's time constant. This constant may describe the fact that, depending on some parameters, the system might generate strong Vz variation or, on the contrary, will show little sensibility to the surge motion, generating