In order to perform experiments in a controlled environment, we are using the L1B wind tunnel of the von Karman Institute: a low speed, closed-loop wind tunnel with rectangular test section. The flow is driven by a fan with contra-rotating blades, powered by a 580 kW DC motor with variable speed controller. In the center of the test section, the flow velocity can range from 1 to 60 ms-1 in the 1000 hp configuration and from 1 to 22 ms-1 in the 100 hp configuration. A schematic of the facility is provided in Fig. .

The test section is 2 m high, 3 m wide, and ∼20 m long; more detailed dimensions are provided in Fig. . This closed test section is used to immerse the experimental wind turbine in a turbulent boundary layer, similarly to the atmospheric boundary layer to which full-scale wind turbines are exposed. An atmospheric turbulent boundary layer is generated in the wind tunnel using a set of roughness elements on the bottom floor, complemented by a grid and fence at the inlet, to create velocity gradients and turbulence. This allows one to reduce the streamwise distance needed to obtain a well-developed velocity profile at the back turntable, where the experiment is performed. A detailed verification of the wind tunnel's suitability for atmospheric flow modeling can be found in . The position of the wind turbine is defined to be sufficiently downstream for a well-developed flow while allowing for enough streamwise distance to measure the wake. In Fig. , the wind turbine is positioned at the back turntable, with a more detailed schematic in Fig. .

The flow measurements are performed using hot wire anemometry along vertical lines in the test section. Three locations have been used for the measurements, labeled 1, 2, and 3 in Fig. . Due to the probe holder's maximum displacement of 1.35 m, the inlet measurement (labeled 1) was performed in two parts to capture the full height. Locations 2 and 3 are limited to the first 1.25 m due to space constraints, yet sufficient to cover the region of interest. All point measurements were sampled at 20 kHz for 5 min each. The uncertainty quantification is described in the following section.

Previous research has shown that scaled-down wind turbines can produce a similar wake as full-scale turbines, given that the main aerodynamic parameters that affect wake behavior remain similar. For this purpose, a few main dimensionless numbers should be matched to ensure that a full-scale wake is reproduced at scale . First, the tip speed ratio (TSR), that is, the ratio between the incoming flow speed unaffected by the wind turbine and the blade tip speed (Vt=Ω⋅R), should be preserved. The TSR determines the advection speed of the vortex generated by the blade tip, thereby triggering turbulent structures in the wake that are key contributors to wake breakdown and recovery. Then, we consider the thrust coefficient (Ct) defined as 4Ct=T12ρV2A, with T being the thrust force exerted streamwise by the wind turbine and opposing the flow, ρ – the air density, V – the upstream wind velocity, and A=πD2/4 – the area swept by the wind turbine. This thrust is responsible for the velocity deficit in the wake.

Finally, the power coefficient (Cp) is defined as 5Cp=P12ρV3A, with P being the mechanical power extracted from the flow by the wind turbine, as considered at the shaft of the turbine.

Scaled-down experimental wind turbines are typically designed to have a similar TSR and Ct as compared to the full-scale wind turbine, as those parameters are the main factors influencing the resulting wake. At this smaller scale, the wind turbine blades operate at lower Reynolds number (Re), by about 2 orders of magnitude, which impacts the flow behavior locally and the capability to provide lift. Airfoils composing the blade of a model-scale wind turbine must be tailored for low-Re applications. Small-thickness airfoils are selected with a good lift-to-drag ratio and reduced sensitivity to the flow separation at low Reynolds numbers. designed in reality.

In addition, scale model testing introduces a blockage effect due to the closed environment of the wind tunnel. The blockage ratio is defined as the ratio of rotor swept area A, divided by the wind tunnel cross-sectional area. Although it cannot be avoided, it is minimized such that its effect on the flow is reduced. According to , the blockage ratio should be <10 %, and the minimum distance to a wall should be >1D. The wind turbine designed in our work has D=0.80 m and a hub height of 0.61 m. According to the above definition, the blockage is thus A(2×3)≃8.4 %. A more appropriate blockage concept in the present case consists of ignoring the region below the hub height, because this region is where the ground effect on the wind turbine is intentional. That blockage is obtained as A/2(1.39×3)≃6.0 %. Above the wind turbine, the clearance to the top wall is 1.0 m (or 1.25D), and it is the closest wall (excluding the ground).

We also wish to produce a wake whose statistics are independent of the Reynolds number, which for turbulence quantities is reached, above Re≃9.3×104 as shown in (with Re based on the rotor diameter and free steam velocity). The present wind turbine model operates at Re≥35×104, which should ensure Reynolds independency of the wake for the mean velocity and second-order statistics.

The blades were produced using a 3-D printer of UCLouvain, as illustrated in Fig. . The material is a PLA+ plastic, a more ductile variety of PLA. The ductility of the material allows the blade to flex under load without breaking. The airfoil used for the blades is the SD7037-092-88 airfoil, shown in Fig. . In the operating conditions used for this experiment, the Reynolds number of the airfoil based on the chord is ≃5.0×104 throughout the length of the blade.

At the tip of the blade, the Reynolds number is 6Rec=Ucν=29.9×0.02591.54×10-5≃5.0×104withU=(73.3×0.40)2+6.02≃29.9ms-1. Close to the root of the blade (at 10 % of the radius): 7Rec=Ucν=9.5×0.08141.54×10-5≃5.0×104withU=(73.3×0.10)2+6.02≃9.5ms-1.

At this range of Reynolds number, the flow is in the laminar regime. Consequently, any surface roughness introduced by the 3-D printing process is not expected to significantly affect the flow behavior or promote the onset of transition to turbulence. Therefore, the blades did not go through a surface smoothing process, as this could alter the intended geometry.

The twist angle and chord distribution of the blades have been designed using a BEM approach using the airfoil SD7037 shown in Fig. , and the resulting distribution is provided in Fig. .

For future projects, a revised blade design could further improve the total power extraction, mostly affecting the aerodynamics in the region close to the blade root, but the current design already serves as a validation case with the main parameters being matched in the ALM model. This design has been simulated using OpenFAST to obtain the Cp and Ct plots shown in Fig. , for varying blade pitch angle and TSR, in order to be compared with experimental values.

Experimentally, the power curve was derived from electrical power measurements, at a pitch angle of 0°. As anticipated, a discrepancy exists between the measured electrical power and the theoretical aerodynamic power output predicted by OpenFAST. This deviation can be attributed to several sources of mechanical and electrical inefficiency: bearing friction, losses in the bevel gear transmission to the generator, suboptimal generator efficiency (particularly below rated operating speed), and additional losses incurred during AC-to-DC conversion where electrical measurements are acquired. In addition to the mechanical power losses, the numerical simulation may overestimate the power output. This can occur when the lift and drag coefficients are overestimated relative to experimental conditions, which can be affected by the critical number parameter in XFoil.

This experimental power curve is compared to the OpenFAST simulations, as shown in Fig. . This corresponds to a vertical line in Fig. . The experimental measurements have been repeated at various inflow velocities close to the operating conditions of this experiment to assess the sensitivity to the Reynolds number. The results indicate no significant deviation of the curve across different inflow velocities.

As mentioned before, the turbine model diameter is D=80 cm. The wind turbine support, indicated in Fig. , allows for adjusting the yaw and the hub height of the model (set here to 61 cm). In an attempt to maintain a realistic ratio between nacelle size and swept diameter, the generator is placed under the wind tunnel. The power is then transmitted from the horizontal shaft to a vertical shaft through a set of spiral bevel gears, as shown in Fig. . Other components are placed within the nacelle, resulting in a diameter of 8 cm, thus 10 % of the swept diameter. The total length of the nacelle, from the base of the blade support to its furthest part downstream, is 23.1 cm, thus approximately 3 times the nacelle diameter. The blades can operate in cyclic and collective pitch control. In the scope of this work, the pitch angle remains constant throughout the experiment.

The aerodynamic power is transferred to the three-phase BLDC generator, to convert to electrical energy. This electrical energy is then rectified to DC using a full bridge rectifier and then used in a series of resistances where the load can be controlled by changing the total resistance. Changing the load is the easiest way to change the reactive torque on the wind turbine and hence control the rotational speed. Twelve resistances are used, each having an ohmic resistance value double of the previous one. This results in a 12 bit binary code for the load of the wind turbine, which provides 4096 possible load values, hence a set of loadings that can be considered continuous. The measurement of power is done on the AC side (before the rectifier to DC) by measuring the voltage and current on one line. In this configuration, the electrical power is measured before the losses in the conversion to DC. The electrical power is computed as 3 times the average power of one line, leading to P=33VLIL, where VL is the instantaneous line voltage, and IL is the instantaneous line current.

In the scope of this study, the TWIST wind turbine is operated at constant rotational speed, as it experiences a steady inflow. The encoder of the generator is used to obtain the rotational speed of the wind turbine during operation, connected to an Arduino microcontroller which also controls the set of relays to act on the resistive load. An integral controller was added to maintain the rotational speed, as it was found to vary otherwise due to changes in resistance caused by temperature fluctuations. Nevertheless, some variability in the rotational speed is still observed, as shown in Fig. . Indeed, the controller was tuned to compensate for the heating of the electrical resistances, which is the slowest process, but some fluctuations remain present due to low inertia of the rotor and the flow turbulence.

In order to reproduce blockage effects numerically, the first computational domain corresponds to the wind tunnel test section dimensions, and it includes both the bottom and top walls. It is used to obtain a fully developed turbulent flow with properties similar to those of the experiment. This is achieved by using a recycling method with added forcing, which is described later. To reduce the computational cost, the side walls are not represented, as they are sufficiently far away from the wind turbine not to affect the flow in the mid-vertical plane of interest. Instead, a periodic boundary condition is applied to the sides.

The second domain, which is the main domain, is continuously fed at its inlet using the turbulent flow field sampled at the recycling plane of the first domain simulation. This second domain contains the wind turbine, with blades modeled using an ALM. Both domains have the same cross-section but different lengths, as shown in Fig. .

The mesh is refined vertically close to the bottom and top walls to capture the wall-induced shear, and also in the zone of the wind turbine, especially near the tip, as illustrated in Fig. . In the cross-section, the mesh is composed of 133 elements in the inner part of the wind turbine region, 360 elements around the tip region, 216 elements close to the bottom wall, 189 elements close to the top wall, and 252 elements in the remaining zones, which totals 1150 elements. The size of each element is constant in the bulk of the rotor swept area, with a refinement applied in the tip region to allow for a sharp transition and to accurately capture the tip vortices. Excluding tip refinement, the mesh can be described as having nine spanwise elements per blade. With a seventh-order polynomial discretization, this corresponds to 63 degrees of freedom, which is directly comparable to 63 cells in a finite difference method. Including the tip refinement increases this number to 77 degrees of freedom. In length, the mesh of the recycling domain is composed of 32 equally spaced elements. The recycling plane is at 5.4 m from the inlet, which is sufficiently far from the outlet to avoid spurious numerical effects. This mesh was created using the GMSH software .

For the main domain, the length is 9.4 m with 80 elements. The element size streamwise starts identically to that of the recycling domain in the zone upstream of the wind turbine, then becomes finer at the location of the wind turbine, and it is then only slightly coarsened to still properly capture the wake. The wind turbine represented using the ALM is placed at 2.84 m (3.55D) from the inlet.

The bottom and top wall of both domains use a shear stress boundary condition, where the value of the shear is obtained from the experimental profile. The value for τwall used in the LES simulation was obtained by fitting a log law from the experimental profile. The velocity field at the inlet of the recycling domain is updated at each time step, using a rescaling of the velocity field measured at the recycling plane. Finally, the outlet of both domains is a Neumann open boundary condition with specified pressure.

The co-simulation described in Sect.  is used to generate an inflow for the main domain, matching as closely as possible that of the experiment, both in terms of mean velocity profile and of turbulence level; more detailed results are presented in .

The mean flow is reconstructed using a modified version of the “Recycle and Rescale Method” (R2M) , also described in . Unlike the original approach, this method does not apply a vertical scaling to match the boundary layer height. Instead, a scaling is performed at every grid point. A moving average of the simulated flow is calculated and divided by the experimental mean velocity profile to generate a spatial scaling factor field. This factor is then applied to the instantaneous flow at the recycling plane before re-introducing it at the inlet. The technique ensures that the inlet profile matches the experimental profile in its time-averaged value, while allowing the turbulence to naturally develop within the recycling region.

However, the turbulence level that naturally develops in the domain remains lower than what is observed experimentally in some regions. This is attributed to upstream elements (grid and fence) that are not reproduced numerically and generate additional turbulence in the experiments. To better match the experimental inflow conditions, a forcing term is introduced in the recycling domain to increase the turbulence level in a controlled manner.

The forcing is constructed as a superposition of sine waves with a wavelength on the order of the integral length scale of the flow. These waves are defined with spatial dependence in the three directions (x, y, and z). In each direction, a set of 10 sine components is used, with a slightly randomized wavelength around the base wavelength, resulting in a total of 30 closely spaced but distinct frequencies. This approach distributes the injected energy over a finite spectral band, avoiding artificial concentration at discrete modes and preventing the appearance of sharp spectral peaks that would require a longer domain to dissipate. This design injects energy primarily at large scales, which then naturally redistributes across the spectrum through the turbulent cascade. In addition, the phases of the sine waves evolve in time, promoting mixing and decorrelation of the perturbation. As a result, by the time the flow is recycled back, the forcing exhibits a more randomized behavior. Spectral analysis at the recycling location confirms that the initially imposed discrete contributions are no longer identifiable and are fully blended into the broadband turbulent spectrum.

Finally, the forcing introduces only a limited quantity of additional energy relative to the already developed turbulence in the flow. This ensures that it acts as a mild correction to the inflow conditions rather than imposing a dominant artificial structure. The amplitude of the forcing is controlled using an integral controller at every grid cell, with the control strategy illustrated in Fig. .

A smoothing function is used to remove the forcing near the inlet and the recycling plane, also for numerical stability. The main advantage of the present method is that it allows one to increase the level of turbulence in needed regions, without having to tweak any parameters, since this action is handled by the controller.

The amplitude of the forcing is illustrated in Fig. . In this illustration, it appears that the forces are needed only in the lower region, which is confirmed by the vertical profile in Fig. . The use of a smoothing function near the inlet and recycling plane is evident from the amplitudes, which vanish in those regions. Within the recycling region, where the forcing is applied, the amplitude of the forces gradually decreases along the streamwise direction. This trend arises from the controller's local operation at each grid point: in the upstream part, stronger forces are initially required to generate the desired turbulence level; moreover, as the flow propagates downstream, the incoming fluctuations begin to resemble those of the experimental profile, hence reducing the need for additional forcing. An important consequence of this approach is that, by the time the flow reaches the recycling plane, the imposed perturbations have largely dissipated. As a result, their influence on the turbulent spectrum becomes negligible, allowing the flow to naturally exhibit the desired turbulence characteristics downstream without contamination from artificial forcing.

The resulting mean velocity profile shown in Fig.  matches exactly the experimental profile, which is expected since it is imposed in the recycling method. No significant difference is observed in the turbulence fluctuation profile in regions where the experimental turbulence is lower than the numerical prediction (that is, above 0.75 m), which is also as anticipated. Below this height, the turbulence level is increased by the forcing method. To quantify this improvement, the mean absolute percentage error (MAPE) between the experiment and LES in this region was calculated: 31 % without volume forcing, and 16 % with it, representing a 50 % reduction in error.

With the successful alignment of the mean inflow profile and the enhancement of the fluctuating velocity field, the baseline flow now replicates the experimental conditions very closely. This minimization of inflow-induced discrepancies better ensures that remaining differences observed between the experimental and simulation results can be more likely attributed to the modeling approaches, rather than to inflow mismatches.

The core principle of the ALM is to compute and apply the force induced by the wind turbine on the flow, without explicitly representing it. This method is typically used for the blades. However, in this work we expand the same principle for all three parts of the wind turbine, namely the blades, the nacelle, and the tower.

Both the blades and the tower have a slim aspect ratio, hence it is assumed that using the coefficients of lift (Cl) and drag (Cd) from a 2-D simulation representing the local geometry constitutes a good approximation over most of the span. As for the nacelle, it is assumed to be a bluff body with an associated drag coefficient.

The different steps of the continuous ALM as implemented for the blades are presented hereafter. At each time step and every grid point, the wind speed components are sampled and transformed into a local coordinate system for each blade, as shown in Fig. a. This local coordinate system is positioned in the domain at the location of the wind turbine based on the hub height and yaw position. The rotation of the wind turbine blades around the axis of rotation is applied to this coordinate system, which makes it easy to change between using a controller or a fixed rotational speed. In this case, a fixed rotational speed is used.

In Fig. b, the airfoil composing the blade is shown with a non-zero angle of attack. The forces of lift Fl and drag Fd are, by definition, those aligned with the flow and perpendicular to the flow, respectively. The angle between the effective position of the airfoil and the flow direction is the angle of attack. As shown in the figure, the airfoil is angled in space, labeled ϕ as the sum of the pitch angle and the twist angle (as a function of r). Based on this, the angle of attack labeled ϑ is ϑ=ψ-ϕ.

The forces of lift and drag are obtained using 8dL=12⋅ρ⋅Vr2⋅Cl⋅c⋅dr,9dD=12⋅ρ⋅Vr2⋅Cd⋅c⋅dr, with dL: the discretized fraction of lift force (N); dD: the discretized fraction of drag (N); Vr: the measured relative velocity (ms-1); c: the chord length (m); dr: the discretized fraction of radius (m). The lift and drag coefficients, Cl and Cd, are obtained from the tabulated data using the measured angle of attack and Reynolds number Rec=Vrc/ν. These data were obtained using XFoil at Rec≃5×104, Ncrit=9, and for the range of angles -7.5 to 12.5°, which is sufficient for the simulation in normal conditions.

The values of lift and drag could be obtained from experimental datasets such as ; however in the scope of this work, we used numerical data from XFoil for a generalized approach that can be applied to airfoils for which experimental datasets are not always available at all Reynolds numbers (such as some airfoils used in full-scale wind turbines).

Close to the blade root, there is a transition from the airfoil to an ellipse, and then to a circle. The lift and drag coefficients for the ellipse were computed using OpenFoam, and the drag coefficient for the circle was taken from . It is worth stressing that, in this region, there is a sharp transition in geometry, and the main hypothesis of the ALM to use 2-D polar curves can be questioned. The coefficients used for the lift and drag are shown in Fig. .

One of the key contributions of this work is the way the wind velocity is sampled and the forces distributed in the grid. The wind speed is sampled at every grid point in the mesh, and the lift and drag are computed at the same grid point, unlike most ALM implementations that consider the center of the actuator line to sample the velocity. This is one of the key differences between cALM and most other implementations, which comes with a scaling computational benefit of removing all the overhead of data transfer in the domain by keeping every node cell independent. We also use a kernel along the actuator line which avoids any smoothing in the radial direction , hence providing a better radial resolution. The Gaussian spreading of the force solely acts in a plane perpendicular to the blade direction. In opposition to standard ALMs, which use a number of actuator points on which a 3-D kernel is applied, this 2-D kernel is applied continuously along the line, using the mesh as a discretization rather than actuator points. The 2-D Gaussian kernel is thus 10fx,y=12πσ2e-dp22σ2, with σ its core size and dp the distance from the actuator line to the point (x,y) in that plane. The value of σ is chosen as a function of the mesh created for the wind turbine : σ=2.5l/n, where l is the blade length, and n is the number of GLL points along the blade: the number of elements times the degrees of freedom per element (= polynomial order). This guideline applies to a mesh without tip refinement; in this case, the dimensionless value used is σ/l=2.5/(9×7)=0.040.

Because a two-dimensional spreading formulation may lead to numerical instabilities at the blade tip when the local mesh is insufficiently refined, an optional tip-spreading correction was implemented. This correction is based on a modified Heaviside function with a smoothing parameter consistent with that used in the two-dimensional Gaussian kernel. In the present simulations, the mesh resolution near the blade tip was sufficiently refined, and the tip spreading was therefore disabled, allowing for a more physically realistic formation and advection of the tip vortex in the wake.

Regarding the velocity sampling method in the cALM, it is evaluated at each nodal point rather than at the center of the line. The sampling velocity used for force computation is therefore obtained independently at every nodal point (i.e., at every degree of freedom within each element). Combined with the continuous kernel representation, this ensures that the computation at each node remains fully independent, significantly improving parallelization and, consequently, computational efficiency.

As a first qualitative view of the resulting flow field, a plot of the velocity magnitude in the vertical symmetry plane is provided in Fig. . The differences in boundary layer height between the two walls are clearly visible, due to the increased roughness at the bottom. At the outlet, a flow acceleration that is introduced for numerical stability reasons is also visible, although its effect remains very localized. The tip and root vortices shed by the blades are clearly noticeable. The near-wake is coherent, but it quickly loses its coherence and become fully turbulent, due to the interaction of the tip and root vortices with the tower and the turbulent inflow.

The tower is represented by a non-moving, vertical actuator line at a distance of 13 cm from the center of the blades, which is the distance of the experimental wind turbine design. It is a cylinder of constant diameter (D=60 mm), for which the drag coefficient is taken from the literature . Its Reynolds number is of the order of 104; therefore the drag coefficient is taken as Cd=1.4.

At the top of the tower, while the actuator line also stops sharply, the numerical effects are not as significant as those at the blade tip because of the much lower relative velocity. Nevertheless, a similar spread as for the tip has been applied for consistency.

The nacelle is a bluff body without longitudinal extent; hence its effect cannot be represented using an actuator line. The drag of the nacelle is computed using the local flow velocity and a drag coefficient, and the resulting force is distributed using a 3-D Gaussian ellipsoid. Its effective frontal area is approximated as a circle with a radius equal to the distance from the turbine center to the blade root A=π⋅0.0432=5.8⋅10-3 m2. Determining the drag coefficient of the nacelle is not trivial, as it is not an enclosed body. Therefore, we have adjusted the coefficient empirically until the wake in this region appeared to match observations, resulting in a value of Cd=2. To assess the sensitivity of the results to this modeling choice, an additional simulation was performed with the nacelle drag entirely disabled. In this configuration, the resulting difference remained confined to a narrow vertical band between 0.52 and 0.65 m at location 2 (1.41D downstream), with differences in streamwise velocity not exceeding 0.15 ms-1. Given the limited spatial extent and small magnitude of this effect, the nacelle drag is not expected to significantly influence the dominant wake features generated by the rotating blades or the principal conclusions of this study.

Starting with the numerical approach, we employ a structural solver to translate the aerodynamic loads applied to the wind turbine blade into resulting deformations. The solver calculates how the blade deforms under a defined loading condition. The primary goal is to determine the deformation in the flapwise direction (perpendicular to the plane of rotation), the spanwise direction (in the direction of blade rotation), and the combined out-of-plane component of twist, which arises from the interplay of both flapwise and spanwise bending.

The applied load includes the aerodynamic lift and drag on each blade section, a centrifugal force due to the rotation (which is also significant considering the rotational speed). The component of gravity is here negligible. Based on previous work on the topic for large wind turbine in turbulent wind with unsteady loads , it appears that approximating the flow behavior using the average aerodynamic load already provides good results for the blade mean deformation. In this study, we therefore use the average aerodynamic loads to compute the blade deformation.

The distribution of forces along the blade could not be obtained experimentally, so the values are exported from the previously shown LES with the cALM. Those forces along the blades are shown in Fig.  for the axial (streamwise) direction and the tangential (rotational) direction. Here, an instantaneous snapshot is shown. The axial forces increase linearly with radius, while the tangential forces remain relatively constant. This is a result of the blade design and is expected to showcase this behavior. Each curve represents an individual blade; one of them experiences a lower amplitude of the force applied because it is in the lower part of the boundary layer where the flow velocity is lower. General fluctuations are attributable to flow turbulence, while an additional effect can be observed in the region between 0.3 and 0.4 m, where the curve becomes more linear; this behavior is linked to the tip refinement, which reduces the Gibbs phenomenon. Another particular aspect visible here is that, at 0.4 m, the loading stops abruptly: this is not typical of most actuator line methods and is again due to the way the cALM was implemented and which allows for a sharp transition (when the mesh is refined enough at the tip). This provides a better flow representation of the tip vortex, and it reduces the error in the computation of the power produced. For simplicity, the distribution of forces is approximated using the two lines in Fig. , which then represents the average load used in the structural solver.

These forces are applied to the blade geometry, resulting in a deformation shown in Fig. . In this figure, the arrows represent the forces applied, with the vertical ones representing the constant tangential forces, the diagonal ones representing the axial forces, and the red arrow at the base indicating the rotation of the blade inducing a centrifugal force. The gravity component is ignored. The fixture of the part is represented with green arrows for the anchor point.

The geometry used for the structural solver is the CAD used for printing the blade. The material properties used in the simulation are provided from . There are however some differences between the intended design and the resulting 3-D printed blade. The blade was printed vertically, starting at the root. The outer layer, shaping the aerodynamic profile, is printed from a continuous filament, with the goal of having a better surface for aerodynamics. With this printing method, the inside of the blade consists of a honeycomb pattern, which is more compliant than a solid block. It is thus expected that the physical blade deforms slightly more than the simulated one.

The blade deforms mostly in the flapwise direction (the most compliant direction), as shown in Fig. , where this deformation is highlighted with arrows. This behavior is expected since the majority of the axial loading acts in this direction. The largest deformation occurs at the blade tip, where a maximum deflection of 2.88 mm is predicted.

A measurement of the experimental deformation of the blades provides further insights, complementing the numerical prediction. A significant uncertainty from the structural solver prediction comes from the fact the real blade is partly hollow, and hence it is deformed more than the simulation results. The goal of this experiment is to measure the flapwise deflection at the tip and compare it to the simulation.

For this study, the wind turbine was placed in the wind tunnel, as described in Sect. , with a camera placed outside of the wind tunnel, perpendicular to the plane of rotation. First, a calibration pattern was placed in front of the wind turbine, as shown in Fig. a. This calibration pattern is placed at the center of the wind turbine to avoid distortion due to perspective. The wind turbine was then rotated slowly manually, without any flow, to record a baseline (location of the blade tip when not loaded). The wind turbine is then operated with the wind tunnel turned on (as described in Sect. ). The camera recorded a video with the blades loaded in their defined operating condition.

In Fig. b, the two videos are overlaid. A ghosting effect is used on the unloaded case to show the blade tips at the top and bottom in their initial state, and a single image from the video of the loaded case is used to show the deformed state. The initial state is more faint but outlined by an arrow on the image.

A detection algorithm was developed to measure the position of the blade tip at the top and at the bottom. A snapshot of the resulting video with the detected tips is shown in Fig. c, where an “x” indicates the detected tip. The algorithm for computing the blade deflection consists of the following steps:

Convert the video to black and white, and increase the contrast such that the white blade is clearly identifiable against the black background.

This algorithm is applied to each frame. Finally, a manual check of the video ensures that the algorithm correctly identified the tip at each frame.

At each frame from Fig. c, a distance is obtained from the unloaded point to the tracked point of the frame: this distance is in pixels. The calibration pattern then allows one to convert pixels to millimeters to quantify the deflection of the tip in the flapwise direction. The evolution of this deflection is provided in Fig. d. The mean blade tip deflection is 7.5 mm at the top and 6.2 mm at the bottom (lower, as it is less loaded), which is significantly more than the predicted 2.9 mm obtained when assuming that the blade is not partly hollow. Yet, it amounts to 2.0 %–2.4 % of the blade's active span (which is ∼30 cm), which is still moderate even though the PLA+ material used for the blade is rather flexible.