Performance and Wake Comparison of Horizontal and Vertical Axis Wind Turbines under Varying Surface Roughness Conditions

This is a version of a publication in Please cite the publication as follows: DOI: Copyright of the original publication: This is a parallel published version of an original publication. This version can differ from the original published article. published by Performance and Wake Comparison of Horizontal and Vertical Axis Wind Turbines under Varying Surface Roughness Conditions Mendoza Victor, Chaudhari Ashvinkumar, Goude Anders Mendoza, V., Chaudhari, A., Goude, A. (2018). Performance and Wake Comparison of Horizontal and Vertical Axis Wind Turbines under Varying Surface Roughness Conditions. Wind Energy. Pp. 1-15. DOI: doi.org/10.1002/we.2299 Final draft Wiley Wind Energy doi.org/10.1002/we.2299 © Wiley 2018 This is the peer reviewed version of the following article (cited above) which has been published in final form at https://doi.org/10.1002/we.2288. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. Performance and Wake Comparison of Horizontal and Vertical Axis Wind Turbines under Varying Surface Roughness Conditions VICTOR MENDOZA * Department of Engineering Sciences, Division of Electricity, Uppsala University, Uppsala 751 21, Sweden victor[email protected] ASHVINKUMAR CHAUDHARI CEID, School of Engineering Science, Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland ANDERS GOUDE Department of Engineering Sciences, Division of Electricity, Uppsala University, Uppsala 751 21, Sweden Abstract A numerical study of both a horizontal axis wind turbine (HAWT) and a vertical axis wind turbine (VAWT) with similar size and power rating is presented. These large scale turbines have been tested when operating stand-alone at their optimal tip speed ratio (TSR) within a neutrally stratified ABL. The impact of three different surface roughness lengths on the turbine performance is studied for the both turbines. The turbines performance, the response to the variation in the surface roughness of terrain and the most relevant phenomena involved on the resulting wake were investigated. The main goal was to evaluate the differences and similarities of these two different types of turbine when they operate under the same atmospheric flow conditions. An actuator line model (ALM) was used together with the large eddy simulation (LES) approach for predicting wake effects, and it was implemented using the open-source CFD library Open-FOAM to solve the governing equations and to compute the resulting flow fields. This model was first validated using wind tunnel measurements of power coefficients and wake of interacting HAWTs, and then employed to study the wake structure of both full scale turbines. A preliminary study test comparing the forces on a VAWT blades against measurements was also investigated. These obtained results showed a better performance and shorter wake (faster recovery) for a HAWTcompared to a VAWT for the same atmospheric conditions. Keywords: Atmospheric Boundary Layer (ABL), Vertical Axis Wind Turbines (VAWTs), Horizontal Axis Wind Turbines (HAWTs), Actuator Line Model (ALM), Dynamic Stall Model (DSM), Large Eddy Simulation (LES) *Corresponding author 1 1 Introduction The majority of the currently deployed wind turbines are horizontal axis wind turbines (HAWTs). A renewed interest has been brought for vertical axis wine turbines (VAWTs) for offshore arrays, since they have several advantages over the conventional HAWTs, and their implementation can potentially mitigate the new challenges the offshore environment presents [ 1 , 2 , 3 ]. The omni-directionality allows them to operate with the incoming flow from any direction, further simplifying the mechanical design, since there is no need for a yawning mechanism (and often the pitching system). This characteristic is considerably appreciated in offshore environments where operation and maintenance are relevant items contributing in the total energy production cost. Another advantage of VAWTs is the availability to place the generator at the sea level, reducing the complexity involved in the installation and maintenance. This improves the stability of the overall structure and reduces the size and cost of the base, and moreover, it minimizes the concerns related to the dimensions and weight of the generator allowing the installation of heavy direct drive generators with permanent magnets [ 4 ]. On the other hand, VAWTs have a much lower power coefficients and suffer from vibration problems complicating their industrial models production. However, this study is limited to rather aerodynamic issues (power performance, wake development and recovery, etc.) and not to operational factors. It is well known that the general structure of a turbine wake is directly related to the inflow characteristics, turbulence produced by the turbine, and operational conditions (blade pitch, yaw condition, tip speed ratio [TSR], etc). Considering both HAWT and VAWT stand-alone turbines, the common profile of velocity deficit is characterized by a Gaussian-like distribution (besides in the near wake) with a peak close to the region where the hub is located [ 5 , 6 ]. The near wake is where the main contribution of its structure comes directly from the turbine, while the far wake is characterized by (dissipative) turbulent structures, the recovery process, and a Gaussian profile of velocity. The turbulence intensity level in the incoming flow contributes considerably to a faster wake recovery as it has been reported in experimental [ 7 , 8 , 9 , 10 , 11 ] and numerical studies [ 5 , 12 , 13 , 14 ]. In a qualitative study [ 15 ] over the performance of a large wind farm, this effect showed that the downwind turbines decreased considerably the power deficit because of an increasing of the turbulence intensity within the incoming flow, highlighting the important role of the atmospheric turbulence in the total power output. There are several well known studies in which the performance and wake characteristics of HAWTs [ 5 , 16 ] and VAWTs [ 6 , 17 , 18 , 19 ] were investigated; however, these works have been carried out separately for each type of turbine. Thus, a direct comparison in terms of aerodynamic performance between the two turbine types is perhaps difficult. The presented study provides results for both turbines under the same atmospheric flow conditions, with the aim of evaluating the differences and similarities of these two devices. Testing the both turbines with their best operating TSR conditions as well as under the same atmospheric flow conditions provided a fair comparison in terms of the aerodynamic performance, response to the atmospheric turbulence variation, and the resulting flow pattern. For this purpose, an actuator line model (ALM) has been implemented using the open-source computational fluid dynamics (CFD) toolbox library OpenFOAM [ 20 , 21 ] to solve the governing equations and to compute the resulting wake. Both an HAWT and a VAWT under a neutrally stratified atmospheric boundary layer (ABL) condition (i.e., no influence of vertical temperature profile) were tested for varying surface roughness conditions. These large scale turbines have similar size and power rating, operating at their optimal TSR. The HAWT employed is a well-documented large scale turbine NREL-5MW [ 22 ] and the VAWT is a proportionally scaled version of a 12-kW straight-bladed turbine [ 23 , 24 ] with almost the same rotor projected area as the HAWT. 2 The model is first validated using the wind tunnel measurements of the power coefficients and velocity flow field (wake) of two interacting HAWTs [ 25 ]. Additionally, the normal forces on one blade of a VAWT operating in an open site have been reproduced and compared with experimental data [ 23 , 24 ]. The employed model is characterized by stability and accuracy, which makes it a potential tool in the design of large scale wind turbines. 2 Methodology An ALM coupled to a dynamic stall model (DSM) has been employed to solve the blade force equations and model the turbine operations. The ALM samples the local velocity from the flow solver and then it calculates the angle of attack and relative velocity for each blade element, while the DSM calculates the unsteady lift and drag forces, which the ALM impart back as body forces into the flow solver. The present work is focused on evaluating the turbines aerodynamic performance and the wake modeling part. To do this, the library turbinesFoam developed by Bachant et al. [ 26 , 27 , 28 ] has been used as implementation of the ALM. To overcome the representation of a proper inlet boundary condition, the so-called recycling technique was used to generate the inflow turbulence for the flow. A detailed description of the ALM and DSM used in the present study can be found in [ 27 ] and [ 29 ], respectively, since only a brief explanation of the ALM is given further in this section. 2.1 Actuator Line Model Based on the classical blade element theory, the ALM has been developed by Sørensen and Shen [ 30 ], and it is a three-dimensional and aerodynamic unsteady model used to study the resulting flow around (and within) wind turbines. This technique divides the blade into n -elements that have a two-dimensional airfoil behavior on which (normal and tangential) forces are determined using a DSM commonly based on empirical data. The implementation of the ALM requires the values of the lift and drag coefficients for the different angles of attack and Reynolds numbers locally involved. The geometrical relation between the tangential speed of the blade Vblade =Ωr , where Ω is the angular velocity and r is the radius to the element, and the incoming flow Vin (which usually is smaller in magnitude than the free-stream velocity V∞ ) is used for the calculation of the relative flow Vrel and the angle of attack α, Vrel =Vin −Vblade (1) The angle of relative wind ϕ is represented by the sum of the angle of attack α and the blade pitch angle γ . Figure 1shows an illustration of the velocities and acting forces on the cross-sectional airfoil element for both HAWTs and VAWTs. The inflow velocity considered in each element is the averaged velocity value of a number of samples around the element, which are symmetrically distributed. Once α and Vrel are obtained (with the spanwise component removed from the latter), the lift and drag forces per spanwise length unit can be calculated as fL=1 2ρc CL|Vrel|2(2) 3 fD=1 2ρc CD|Vrel|2(3) where CL and CD are the lift and drag coefficients, respectively, which are dependent on α and the local Reynolds number. The lift component is perpendicular to Vrel and the blade span component, while the drag has the same component as Vrel. The chord length is represented by cand the density by ρ. The same method is employed to obtain the forces on the towers, nacelle (for HAWTs) and struts (for VAWTs). Once all the forces in the lines of elements are calculated, these are added as a source of body force per unit of density into the momentum conservation equation 5. The elements are moving in space, for every time-step within the fixed volume (domain), as they are in a turbine. 2.2 The Large Eddy Simulation framework In order to use the LES approach the original Navier-Stokes equations have been filtered, and based on the incompressible flow case are expressed as ∂˜ ui ∂xi =0(4) ∂˜ ui ∂t+∂˜ ui˜ uj ∂xj =−1 ρ ∂˜ p ∂xi +ν∂2˜ ui ∂xj∂xj −fi ρ−∂τij ∂xj (5) with ˜ ui and ˜ p representing the grid-filtered velocity and pressure values, respectively, ν the kinematic viscosity, fi the acting body forces (blades) and τij the sub-grid scale (SGS) stress defined as τij = g uiuj−˜ ui˜ uj. In order to parameterize the deviatoric part of the SGS strees, the Smagorinsky model [ 31 ] was employed as τij −1 3δijτkk =−2(CSe ∆)2|e S|(6) with e Sij =1 2∂e ui ∂xj+∂e uj ∂xi representing the resolved rate-of-strain tensor, e ∆ is the grid size and CS= 0.1667 as the Smagorinsky constant (usually it has a value between 0.1 and 0.2). 2.2.1 The recycling method for simulating the atmospheric boundary layer (ABL) In LES modelling, the correct reproduction of transient inflow condition is crucial for a proper modelling of ABL interaction to wind turbines. Previously, in many LES studies dealing with ABL modelling (e.g. [ 32 , 33 ]), a separate precursor LES calculation for ABL flow over a homogeneous terrain has been used to generate transient inflow boundary conditions. However, this method is very time consuming as it requires the entire simulation to be performed in two different stages: (1) precursor simulation for ABL flow over a horizontally-homogeneous flat surface (i.e. without turbine) to produce and store the instantaneous field data from each time-step, and (2) to utilize this time-dependent data for the main simulation (i.e., ABL with turbine). In this study, the so-called recycling inflow method is employed for generating the fully developed ABL flow profiles before the turbines. Chaudhari et al. [ 34 , 35 , 36 ] have studied the applicabilities of the recycling inflow method for ABL flow modelling over complex terrains, and further they have shown 4 the validation of the method against field measurements. A more detailed description of the recycling method can be found in [34,35,36], and only a brief explanation is given further in this section. Using the recycling approach, the precursor simulation is combined with the main simulation, as shown in Figure 2. During the simulation, the flow variables, mainly velocity, temperature, SGS turbulent kinetic energy, etc., are sampled on a crosswind plane (i.e. recycling plane in Figure 2), which is sufficiently downstream from the inflow plane. The sampled data is then recycled back to the inflow plane. This process is repeated for each time step, creating a recycling section between the inflow and recycling planes, in which the flow becomes fully developed gradually. The method is very sensitive to the recycling length Lr and the distance between the inflow and recycling planes. After testing various recycling lengths, Chaudhari et al. [ 34 , 36 ] suggested that the recycling length Lr should be at least 3δ (i.e. Lr≥3δ ), where δ is the ABL height and it is fixed to be δ=5D (since the domain should be high enough to avoid any flow disturbances due to turbine wake [ 37 , 38 ]). This restriction is needed to avoid any artificial turbulence structures within the recycling section due to too short recycling length. In addition to recycling the data, the method also uses the fixed velocity flux through the inflow plane (boundary) in order to maintain the same amount of volume flow rate throughout the entire simulation. The main advantage of the method is that precursor simulation is avoided, and the entire simulation is performed at once on a single computational domain as shown in Figure 2. The fully developed ABL profiles obtained using the recycling method are compared with the logarithmic profile and are presented in Figure 11 in Section 3.2. 2.2.2 Wall-function modeling The surface boundary condition is also one of the challenges in LES modelling. In order to avoid massive computational resources required due to the finer mesh resolutions near the surface, the use of the wall-function approach has become standard in LES modeling of ABL flows (e.g. [ 16 , 5 , 34 , 35 , 36 ]). In addition, the surface roughness parameters (height or length) of a rough surface are often implemented via a wall-function model. In this work, a wall function model based on the well-known logarithmic law of a rough surface, implemented in OpenFOAM by Chaudhari et al. [34,36], is used on the lower surface. The logarithmic law of the wall over rough surface is given by Vx=Vx∗ κln z+z0 z0(7) where z0 is the ground roughness length, κ=0.41 is the von-Kármán constant, and Vx∗ is the instantaneous frictional velocity. More information on the implementation of this wall-function can be found in [34,36,39]. 3 Results and Discussion In this section, results from the validation tests and the study of the influence of varying surface roughness conditions are presented. For the validation cases, similarities and discrepancies between numerical and experimental values are discussed. 5 3.1 Numerical model validation Two different experimental studies have been chosen to validate the employed numerical model. The first case is focused on the proper representation of the velocity field (wake structure) and the performance (power coefficients) of two interacting HAWTs within a wind tunnel, while the second one simulates the normal forces acting on the blades of a 12 kW VAWT, located in an open site. 3.1.1 Two in-line wind turbines with spanwise offset The test case chosen for the power coefficient ( CP ) and wake validation is based on the experiment reported by Krogstad et al. in [ 25 ]. This work has been carried out in a wind tunnel facility and consists in two HAWTs, which are separated by a distance of 3D in the streamwise direction and around 0.415D ( 0.4 m) in the crosswind direction. The downstream rotor has a diameter of D2=0.894 m (further denoted as D in this section) with a stepped tower consisting of four cylinders of different diameters while the upstream turbine has a slightly larger diameter of D1=0.944 m with and a tower with constant diameter. The arrangement of the experiment is such that the projection of the area from the upwind rotor covers half of the downwind turbine. The measurements of the streamwise velocity component were done in two spanwise lines, located 1D and 3D behind the downwind turbine at the height of the axis. Figures 3and 4show more details about the wind tunnel and the dimensions of the test configuration. In this work, two different levels of turbulence have been tested. First, a turbulence intensity level of TI=0.23% in the location of the upwind turbine rotor, which corresponds to the measurements when the wind tunnel is empty and it is hereafter referred to as Case A. Then, in order to consider the effects of atmospheric turbulence, a large grid was used in the entrance of the chamber (shown in Figure 3) producing a higher level of turbulence intensity measured of TI=10% , this is referred as Case B. The synthetic turbulence generator turbulentInlet, from the standard library of OpenFOAM, is employed to introduce the different levels of turbulence at the inlet of the studied domain. The ABL profile is not considered for the wind tunnel experiments, because the dimensions of the experimental chamber were not large enough to fully develop ABL conditions (see Figure 4). The employed lift and drag coefficients into the ALM are taken (digitized) from the work of Cakmakcioglu et al. [ 40 ], and they correspond to the Reynolds number equivalent to Re=105 . The upwind and downwind turbine are further denoted as T1 and T2 , respectively. The domain has been discretized using a mesh topology with a uniform hexahedral distribution of cells in every direction, considering a grid resolution of 16.8/D cells in the whole domain and a local refinement of 68/D cells in the region around the rotor and behind the turbines in order to capture the details of the resulting wake. This mesh configuration has been chosen based on the criteria presented in [ 41 ] (as well for the meshes in subsequent sections). The DSM has not been used for these cases. The specifications of the tested turbines and experiments are listed in Table 1. Power and thrust coefficient curves Power coefficients of the both turbines are evaluated over a wide range of TSRs, but in the case of the downwind turbine, its performance has been obtained while the upwind turbine is operating at its optimal TSR of design λ1=Ω1R1/V∞=6 , where Ω1 represents the angular speed of the upwind turbine rotor. The reference velocity considered for calculations is V∞=10 m/s. The power and thrust 6 coefficients of the turbines are defined as CP=P 1 2AρV3 ∞ (8) and CT=T 1 2AρV2 ∞ (9) with P as the average power and T as the average thrust for the rotor obtained over one revolution. Experimental and numerical results of the turbines performance for cases A and B are depicted in Figure 5. For the case A, with low turbulence levels, it is observed that there is a good agreement in the identification of the region where the turbines operate at the maximum power coefficient (optimal λ ), and in general, with the trend of the curves. The numerical accuracy has to be highlighted for the power coefficient prediction in the upwind turbine for λ1≥5 , unlike for the lower TSRs, where discrepancies occur when reproducing the curve in the stall condition with a maximum error of 28%. The numerical results of the downwind turbine show concordance with the lower TSRs, while there is an overestimation of the CP values for λ2>4 . The interaction of the wake with the downwind turbine is also captured and the power curve of T2 is characterized by lower values than the curve of the upwind turbine due to the reduction in the available kinetic energy. The experimental thrust coefficient data, which was expected to demonstrate increased CT values with increasing TSR, was very similar for both turbines, revealing that almost the same physical forces are applied on the rotors, while differing available kinetic energy. The upwind turbine has a considerably good agreement with the experimental values, while the numerical thrust coefficient curve of the downwind turbine shows an underestimation for all the tested TSRs, with a maximum error around of 12%. For the test case B, with high levels of turbulence on the freestream flow, again there is a good identification of the region where the turbines achieve the highest power coefficients. A better numerical representation of the power curve is made for λ1>4 for the upwind turbine, and for the downwind turbine, this occurs at λ2≤5 , with a maximum error of 21%. With respect to the thrust coefficients values, there is an overestimation in the upwind turbine at λ2≥4 and an underestimation for the downwind one for all the studied TSRs with a maximum error around of 20%. Wake The downwind turbine has been tested at three different TSRs, while the upwind turbine is operating at its optimal TSR λ1=6 , in order to study the resulting velocity field of interacting wakes. The three tested TSR conditions correspond to partially stall, optimal TSR and high TSR with λ2=3.5, 4.75 and 8.0 , respectively. These conditions cover from the stall regime to the rotor almost working as a propeller. As mentioned earlier, the streamwise velocity component has been measured in a horizontal line in the crosswind direction at the hub height at distances x/D=1 and x/D=3 behind the downwind turbine (see Figure 4), which allows us to identify the general structure of resulting flow from the interacting wakes. These results for the normalized streamwise velocity deficit profiles for all the tested cases and TSRs are displayed in Figure 6, where the radius rhas been used to normalize the spanwise position. 7 In both cases, for the section x/D=1 behind the second rotor, the numerical and experimental results agree in the representation of the wake geometry and size, as well as the asymmetric behavior. Small discrepancies in some details of the velocity profile are revealed with a maximum error of 25% for particular regions. Three different regions can be identified in the velocity profile; in −1.5 <y/r< −0.5 where the resulting flow comes mainly from the upwind turbine, at −0.5 <y/r<0.5 both turbines give a contribution to the wake, and 0.5 <y/r<1.5 where only the effects of the second rotor are present. A particular condition is observed for the highest TSR (λ2=8.0) , since there is a relevant flow obstruction (velocity deficit) close to the blade tips due to the high rotational speed of the blades, and in the other hand, at the root location the opposite effect is noticed. Regarding the wake at x/D=3 , a change is observed from an irregular shape of the velocity profile at x/D=1 to a smoothly one, specifically a Gaussian wake deficit profile. Therefore, in this section the wake recovery process already started and the direct contribution from the rotors into the flow is dissipated by the turbulent structures. In general, there is also a good agreement in numerical and experimental values in the regions outside the wake. The effects of the added turbulence (Case B) are not significant in the near wake general structure (at x/D=1 ). Moreover at this location, it is noticed that for both cases A and B the velocity profiles do not differ considerably, more evident changes are present at the far wake section. The authors believe that discrepancies between numerical and experimental values mainly can be caused by: • The simplified implementation of the turbulence inlet generator is not realistic since it adds random noise to the specified inlet mean velocity from a defined turbulence level • More detailed input data of CL and CD for a wider range of the Reynolds numbers is needed. Currently, only data for Re =105 has been considered which can not be appropriate for all the diversity of studied cases, since the employed ALM is highly sensitive to the input coefficients for a correct blade force projection • Potential improvements of the numerical simulations can be achieved in the outer wake zones with the fully resolved wall boundary layer, which was not applied in this work 3.1.2 ABL flow through a 12 kW straight-bladed VAWT in an open site A 3-bladed 12 kW VAWT located in the North of Uppsala (Sweden) has been chosen to validate the model under the influence of the ABL. The turbine has three rotor blades projected from a NACA0021 airfoil profile with a chord of 0.25 m and 6.48 m of diameter, the blade length is 5 m. This turbine is placed at an open site and it is surrounded by mild vegetation which is mostly composed by grass and small bushes. The normal forces on one blade and its struts were measured using four load cells. The experimental activity and results as well as more detailed specifications of the device are available in [ 23 ] and [ 24 ]. These forces have been used as the validation parameters for a TSR of λ=3.44 (close to the optimal one). Additionally, obtained results for the same VAWT under the influence of a wind shear (only a constant mean wind profile without turbulence) are also shown for a comparison analysis. For this study, the operating conditions of the turbine are such that the freestream velocity at the blade equatorial plane ( z=5.75 m) is V∞=6.4 m/s. A roughness length of z0=0.025 m is considered for representing the place where the turbine is located. The lift and drag coefficients for the ALM are taken from the report of Sheldahl and Klimas [ 42 ]. The specifications of the modeled turbine are listed in Table 2. The employed discretization mesh has a hexahedral cell distribution over 8 [47] J. Gottschall and J. Peinke, “How to improve the estimation of power curves for wind turbines,” Environmental Research Letters, vol. 3, no. 1, p. 015005, 2008. [48] E. Möllerström, F. Ottermo, A. Goude, S. Eriksson, J. Hylander, and H. Bernhoff, “Turbulence influence on wind energy extraction for a medium size vertical axis wind turbine,” Wind Energy, vol. 19, no. 11, pp. 1963–1973, 2016. [49] P. Krogstad and L. Sætran, “Invitation to the 2013 blind test 3 workshop two in-line wind turbines with spanwise offset,” Department of Energy and Process Engineering, NTNU, Trondheim, Norway, 2013. 15 Table 1: Nominal parameters of the tested turbines and experiments. Turbines Experimental cases T1T2A B Number of blades 3 V∞[m/s] 10 Diameter [m] 0.944 0.894 TI[%] 0.23 10 Hub height [m] 0.817 Blade profile NREL S826 Chord length [m] variable Table 2: Nominal parameters of the modeled 12kW VAWT. Number of blades 3 Diameter [m] 6.48 Hub height [m] 6 Blade profile NACA0021 Chord length [m] 0.25 V∞[m/s] 6.4 TSR 3.44 Table 3: Aerodynamic performance of the tested turbines for the different terrains. Turbine z0[m] CPP[MW] CTT[MW] VAWT 0.0005 0.346 1.579 0.688 0.402 0.025 0.321 1.500 0.702 0.410 0.1 0.338 1.546 0.673 0.393 HAWT 0.0005 0.558 2.003 0.870 0.399 0.025 0.556 1.997 0.860 0.394 0.1 0.496 1.780 0.761 0.348 16 Figure 1: Illustration of velocity vectors and forces acting at the cross-section airfoil element for a HAWT (left) and a VAWT (right) and a schematic with the lines of elements. Note: For HAWTs, ˆ θ denotes the tangential direction of the blade while θis the azimuthal angle for VAWTs Figure 2: Schematic views of the domain and relevant dimensions for the application of the recycling method: perspective (left), side (upper right) and top (lower right). 17 Figure 3: Model in the wind tunnel [49]: perspective (left) and from downwind (right) views. Figure 4: Schematic view of the wind tunnel domain: from the upper part (top) and perspective (bottom). The first two perpendicular sections (in black) represent the rotor planes of the turbines, while the two sections after the turbines (in red) represent the plane where the measurements were done, specifically in a crosswind line at the rotor height. 18 0.0 0.1 0.2 0.3 0.4 0.5 CP 0 2 4 6 8 10 λ 0.00 0.25 0.50 0.75 CT T1 Experimental T2 Experimental T1 ALM T2 ALM 0.0 0.1 0.2 0.3 0.4 0.5 CP 0 2 4 6 8 10 λ 0.00 0.25 0.50 0.75 CT T1 Experimental T2 Experimental T1 ALM T2 ALM Figure 5: Power coefficient and thrust coefficient for the case A with low turbulence level (left) and the case B with high turbulence level (right). −2 −1 0 1 2 λ2= 3.5 y/r x/D = 1, Case A Experimental ALM x/D = 3, Case A Experimental ALM x/D = 1, Case B x/D = 3, Case B −2 −1 0 1 2 λ2= 4.75 y/r 0.0 0.4 0.8 1.2 Ux/V∞ −2 −1 0 1 2 λ2= 8.0 y/r 0.0 0.4 0.8 1.2 Ux/V∞ 0.0 0.4 0.8 1.2 Ux/V∞ 0.0 0.4 0.8 1.2 Ux/V∞ Figure 6: Normalized mean streamwise velocity profiles along a crosswind (horizontal) line through the rotor center. 19 Figure 7: Normalized instantaneous streamwise velocity at the vertical middle plane: ABL (top) and wind shear (bottom). 0 45 90 135 180 225 270 315 360 Azimuthal degree [◦] −400 −300 −200 −100 0 100 200 300 400 FN[N] Experimental ABL Wind shear Figure 8: The normal force response under the influence of the ABL and a wind shear. Figure 9: Illustration of the main characteristic dimensions of the tested turbines. 20 0 2 4 6 8 10 12 λ 0.0 0.1 0.2 0.3 0.4 0.5 CP HAWT VAWT Figure 10: CPas funcion of λfor both a VAWT and a HAWT in full scale. Figure 11: Vertical profile of the mean streamwise velocity for the inflow conditions. 21 Figure 12: Normalized instantaneous streamwise velocity in the vertical plane at the centre of the turbine for different terrains. 22 Figure 13: Normalized mean streamwise velocity in the vertical plane at the centre of the turbine for different terrains. 23 Figure 14: Normalized streamwise velocity at different representative sections perpendicular to the flow for different terrains with z0=0.0005 m (top), 0.025 m (center) and 0.1 m (bottom). 24