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Wind tunnel experiments were performed, where the development of the wake of a model wind turbine was measured using stereo Particle Image Velocimetry to observe the influence of platform pitch motion. The wakes of a classical bottom fixed turbine and a streamwise oscillating turbine are compared. Results indicate that platform pitch creates an upward shift in all components of the flow and their fluctuations. The vertical flow created by the pitch motion as well as the reduced entrainment of kinetic energy from undisturbed flows above the turbine result in potentially higher loads and less available kinetic energy for a downwind turbine. Experimental results are compared with four wake models. The wake models employed are consistent with experimental results in describing the shapes and magnitudes of the streamwise velocity component of the wake for a fixed turbine. Inconsistencies between the model predictions and experimental results arise in the floating case particularly regarding the vertical displacement of the velocity components of the flow. Furthermore, it is found that the additional degrees of freedom of a floating wind turbine add to the complexity of the wake aerodynamics and improved wake models are needed, considering vertical flows and displacements due to pitch motion.

Wind energy has become a major contributor to energy from renewable sources and is still projected to increase its portion to the overall energy supply in the future. Offshore wind energy is found to have the highest potential to fulfill these demands, due to sustained winds which are unaffected by complex terrain [

The additional degrees of freedom of a floating platform will cause different operational conditions compared to fixed foundations. A detailed understanding of the influence of the added degrees of freedom on aerodynamic performance, fatigue loads and finally the costs of floating wind turbines would allow an optimized design of floating wind turbines [

The influence of various motions such as pitch, sway and heave on the aerodynamics of the rotor and the wake characteristics are important in determining the design space for proper load and fatigue calculations [

Feasibility studies have been performed to define the constraints for floating turbines installations [

Matsukama

Experimental investigations have been done on the structural response of floating support structures by Utsunomiya

A preliminary study using the time averaged Unsteady Reynolds Averaged Navier-Stokes (URANS) method to simulate the aerodynamic interaction of the flow and pitch platform motion was performed by Matha

Sebastian and Lackner [

Jonkman

Wake measurements of offshore wind turbines were performed and compared with six different wake models [

The objective of this study is to investigate the influence of pitch motion on the wake of a model wind turbine. Wake measurements have been performed in a wind tunnel using stereoscopic particle image velocimetry (SPIV). The flow field, including mean and fluctuating components of the flow, are analyzed for a fixed versus an oscillating turbine under the same inflow. These results are then compared with existing wake models to determine their ability to capture such pitch motion effects.

For steady, incompressible and inviscid flows, the Reynolds-averaged Navier-Stokes (RANS) equations are given by:
_{i}_{i}_{i}_{xi}

Multiplication of _{i}

Several terms of the momentum in

Both the mean momentum in _{i}_{i}

Wake models that solve systems of partial differential equations are often summarised as field models. While the numerical solution of the continuity and momentum equations in three dimensions with a turbulence model and viscosity effects is obtained in computational fluid dynamics (CFD), also systems of reduced complexity are often considered. The model by Ainslie [

Further simplified descriptions are given by analytical wake models. These follow from momentum balance considerations in a specific control volume, together with model-specific assumptions. One widely used example is the model by Jensen [

Herein, short summaries of the Jensen model, the Larsen model, the Ainslie model and a CFD actuator disk model are provided, before comparing the results to data obtained from wind tunnel experiments. The governing equations of the wake models can be found in

For the calculation of the wake models, _{⋆} denotes the friction velocity; and _{0} denotes the roughness length.

The Jensen model wake is characterised by linear wake expansion as a function of the downstream distance from the rotor plane [

The Larsen model [

Like the Larsen model, the Ainslie model [

Discretised versions of the RANS equations can be solved on a three-dimensional mesh with methods from computational fluid dynamics. The simplest representation of the rotor is the actuator disk approach with uniform forcing [_{0} = 0.0046 m.

The experiments were performed in the wind tunnel at Portland State University. The test section of this closed-circuit tunnel is 5 m in length with a height of 0.8 m and a width of 1.2 m. The free stream velocity can be set between 2 m/s and 40 m/s with low turbulence intensity.

The hub height of the turbine was 25 cm. The wind tunnel speed was set to 6.05 m/s at hub height of the turbine and the model wind turbine was placed 2.01 m downstream of the passive grid.

The model wind turbine shown in _{p}_{p}_{T}

The SPIV setup consisted of a

The freestream inflow conditions without the turbine present were measured using SPIV 1.5

For each measurement plane, 2500 samples were taken for the fixed and floating case. A convergence test was carried out by calculating ensemble averages of 500, 1500 and 2500 samples. The results between 1500 and 2500 samples match very well so statistical convergence of means and higher order moments is assured. Spurious vectors were excluded from statistical calculation using a normalized median test according to [

This work compares the wake development of the fixed case and the floating case. The fixed case represents the wake of a classical bottom-fixed turbine. The floating case represents the same turbine which has the freedom to incline in the streamwise direction (pitch motion). Due to the mean inflow velocity and its fluctuations, the turbine pitches downstream and oscillates, as described earlier in this work. Therefore, only the influence of dynamic pitch on the wake is discussed.

For the fixed turbine, the sampling frequency for the SPIV system of 1 Hz was used. In the floating case, the image acquisition was triggered to a fixed amplitude of oscillations in the downstream direction to ensure the same influence of the oscillation on wake structures for each image. Therefore, a reflective strip was placed on the tower of the oscillating turbine. A

Measurements of the flow field obtained via SPIV for the fixed and floating turbine cases are compared. Contour plots are presented pairwise where the upper plot (

_{hh}_{hh}

_{hh}_{hh}

_{hh}_{hh}

_{hh}

_{hh}^{2}) from

_{hh}_{hh}

In the floating case (_{hh}_{hh}_{hh}_{hh}_{hh}

Profiles of _{hh}

_{hh}

Near wake profiles of spanwise velocity are presented in

_{hh}

Above the top tip,

In the floating case, the peak above top tip is lower with

In

In the fixed case, positive

^{2}/s^{2}, while for the fixed case, the highest ^{2}/s^{2}. For the fixed case, the turbulent kinetic energy from above tip top spreads and moves downward with increasing

^{3}/s^{3}. In contrast, in the floating case, the area of positive flux increases more slowly with increasing distance. Also at the top tip of the rotor, the flux of mean kinetic energy increases in magnitude as the flow advects downstream for the floating case as well as moving away from the top tip rotor location. The large negative blue area is restricted to

The contours of vertical flux of this normal Reynolds stress component
^{3}/s^{3}. For the floating case,
^{3}/s^{3}. Although these components are small compared to

Measured profiles of _{hh}

For the fixed case, all wake models with the exception of the Larsen model overestimate the wake expansion at 1.5

At larger distances

In stark contrast to what was observed for the fixed case, the models do not manage to capture the vertical shift to higher

In fact, both the Jensen and Ainslie models assume an axial symmetry in the wake. As a result of the pitch motion not being well represented in the models, the wake is then directed towards the wall. Therefore, the overall effect is reduced to a change in both thrust and power coefficients. The RANS model was implemented differently than the other models in that the RANS model was tilted by 15° and the rotor position was shifted accordingly. Even though these changes are implemented, the RANS model still is not able to capture the behavior as that observed in the experimental data. This disparity is then attributed to the fact that rotation was not represented in the applied actuator disk model. Consequently, it cannot capture the anisotropy as observed by the wake.

Platform pitch and streamwise oscillations have a strong impact on the mean shape of the wake as well as the magnitudes of all velocity components. Due to the oscillations in the floating case, the turbine experiences a variable shear flow. The pitch motion of the platform with an average inclination angle of 17.6° skews the mean streamwise velocity component in the wake with a positive slope, with an angle of approximately 3°. This observation is comparable to results observed in yawed turbines with a yaw misalignment of 20° [

The increase of the wall-normal mean velocity in the floating case is of importance, since vertical flow is often not considered in wake models. This is certainly true considering the development of _{hh}_{hh}

When evaluating the out of plane component, that is the spanwise component of the mean velocity, _{hh}

Furthermore, the oscillations and inclination experienced by the turbine have a strong impact on the fluctuations of the flow and on the features of turbulent kinetic energy in the wake, where in the top tip of the fixed case, the features of

From the point of view of a downwind turbine, the shear stress distribution in the fixed case leads to negative fluctuating shear forces above hub height and positive fluctuating shear forces below the hub. Similarly, strong fluctuations are observed at the nacelle. In the floating case, most of a downwind rotor potentially experiences positive fluctuating shear forces, but a strong transition from positive to negative shear force occurs at the blade tips.

Turbulent kinetic energy is a measure for the amount of kinetic energy that is contained in the fluctuations. For the fixed case, the rotor of a downwind turbine would be exposed to strong fluctuations above hub height. In the floating case, the smaller

Almost no vertical transport of vertical fluctuations can be observed in the fixed case, which compares well to findings of [

The comparison with wake models shows that for the fixed case, the shape and magnitudes of the streamwise component of the wake in midrange distance (

Wind tunnel experiments were performed to compare the wake development of a fixed and a streamwise oscillating wind turbine model using stereo PIV. Statistical analysis of wake development from 0.7_{hh}_{hh}

The authors would like to thank Stefan Ivanell for providing the blade design, Carlos Peralta for providing the turbulence model implementation for the actuator disk model simulation. This work was supported in part by grants from the Federal Environmental Foundation (DBU), Germany.

The authors declare no conflicts of interest.

The wake diameter _{w}_{0} and thrust coefficient _{T}

In the Larsen model [_{w}^{2}_{1} and _{0} follow from fits to measurement data at 9.5

The effective wake diameter _{eff} and wake radius _{9}_{.5} at distance 9.5

The latter relation was found empirically, with hub height _{a}

The solution for the wake deficit to second order is:

The second order solution contains a sum over functions:

The solution of the radial velocity component was ignored in this work.

The Ainslie model flow has an axial component, denoted as _{c}

The solution of _{max} does not influence the final wake size after convergence. The initial field ^{initial}(

The momentum

Wind tunnel setup. The scales are changed for visual clarification.

Wind turbine model with gimbal support. The gimbal is blocked for fixed case measurements. Scale 1:400, with _{p}_{T}

Normalized streamwise velocity component _{hh}_{hh}

Profile of a logarithmic fit to inflow and near wake profiles of _{hh}

Profile of a logarithmic fit to inflow and far wake profiles of _{hh}

Normalized wall normal velocity component _{hh}_{hh}_{hh}

Near wake profiles of _{hh}

Far wake profiles of _{hh}

Normalized spanwise velocity component _{hh}_{hh}

Near wake profiles of _{hh}

Far wake profiles of _{hh}

Contour of the normalized

Contours of Reynolds shear stress

Near wake profiles of

Far wake profiles of

Contours of turbulent kinetic energy

Contours for the flux of Reynolds shear stress

Turbulent kinetic flux in the wall normal direction component

Comparison of measured mean profiles of _{hh}

Comparison of measured mean profiles of _{hh}