Floating wind farm experiments through scaling for wake characterization, power extraction, and turbine dynamics

In this study, wind and water tunnel experiments of turbulent wakes in a scaled floating wind farm are performed. Scaling of a floating wind farm with a scaling ratio of 1:400 is made possible by relaxing geometric scaling of the turbine platform system, such that the dynamic response can be correctly matched, and to allow for relaxing Froude scaling such that the Reynolds number can be kept large enough. Four dimensionless parameters, describing the relative importance of wind and wave loads compared to turbine inertia, are used to guide the scaled floater design. Free decay tests of the pitch and heave response confirm that the dimensionless natural frequency of the scaled model is in the typical range for full-scale floating turbines when matching the proposed four dimensionless parameters. The response and performance of a single turbine scaled model are characterized for different wind and wave conditions. Subsequently, a wind farm experiment is performed with twelve floating turbine models, organized in four rows and three columns. Particle image velocimetry measurements of the wake of the middle turbine in the third row reveal distinct differences in wake properties for different wave conditions. Conditional averaging confirms a synchronization of wake deflection with the traveling waves in the wind farm. The power outputs show distinct peaks at the wave frequencies and its harmonics, due to motions triggered by complex wave-turbine-wake interactions. The power spectrum of the aggregate power of three streamwise aligned turbines exhibits anticorrelation of motions at the wave frequency due to wave speed induced phase lag, and spatiotemporal correlations of power outputs at the frequency corresponding to the wind-convective time between two rows. These experiments using an appropriately scaled floating wind farm in a wind tunnel setup confirm distinct impacts of turbine motion on wake recovery and meandering, and measurement results highlight the intricate interactions between wave topology and wake meandering.

Figure 1

Photograph of the scaled floating wind farm setup in the Portland State University wind and water tunnel.

Figure 2

A schematic representation of several forces acting on a floating turbine, represented on the OC5 DeepCWind turbine with NREL 5 MW rotor as visualized in QBlade [76] (a), and a schematic representation of floater design parameters that can be altered to improve the response of a small-scale model (b).

Figure 3

Example of images used for water surface measurements. Standard computer vision algorithms are used to identify the air-water interface, as indicated by the red-dashed line. Panel (a) is for a wave frequency of 2.7 Hz with no wind, while panel (b) is for a wave frequency of 1.5 Hz and a wind speed of 5.4 m/s.

Figure 4

Camera snapshot used for optical tracking, with indication of tracked markers and their previous trajectory for an incoming hub wind speed of 2.9 m/s and 1.2 Hz wave conditions.

Figure 5

Schematic representation of the measurement setup in the Portland State University wind tunnel.

Figure 6

Schematic of scaled-down floating wind turbine model with key dimensions.

Figure 7

Optical measurement of impulse response with no-wind for tilt (a), roll (b), and heave (c).

Figure 8

Schematic of the mooring setup.

Figure 9

Measured wave shapes for no-wind condition, projected to spatial coordinates using the measured wave velocity. The wave shapes are shown for 2.7, 2.0, 1.5, 1.2, and 1 Hz waves, in order from smallest to largest wave length.

Figure 10

Measured wave speed as a function of wave length compared to the relation according to linear wave theory for deep water waves and transitional gravity waves [92] (a), measured wave period as a function of wave length compared to the relation for deep water gravity waves [92] (b), measured wave height as a function of wavelength (c), and the power spectrum of wave height (d).

Figure 11

The measured inflow conditions for different wave conditions used to measure the single turbine performance. The measured inflow is shown for two different wind tunnel speeds, corresponding to a free-stream velocity of 2.2 and 4.3 m/s. Black dashed lines show the top-tip, bottom-tip and hub height on the velocity profile (a) and turbulence intensity profile (b).

Figure 12

Photo of a single floating wind turbine in the wind tunnel subject to 1.2 Hz waves.

Figure 13

Motion time trajectories of a single scaled floating wind turbine subject to a hub wind speed of 2.2 m/s. Vertical colored lines in the right panels indicate the wave frequencies, and their subharmonics.

Figure 14

Motion trajectories of a single floating wind turbine subject to a wave with frequency of 1.2 Hz, and for two wind speeds. The vertical black lines in the right panels indicate the wave frequency and its subharmonics.

Figure 15

Motion trajectories of a single floating wind turbine subject to no waves and for three wind speeds. The vertical black lines in the right panels indicates the natural frequency for pitch, roll or heave.

Figure 16

The measured power coefficient for different wave paddle conditions, and for a hub wind speed of 2.2 m/s (a) and 4.3 m/s (b). The wave excitation period is indicated in the legend.

Figure 17

Power spectral density of measured motor current for a single floating turbine subject to different wave paddle conditions, and for a hub wind speed of 2.2 m/s (a) and 4.3 m/s (b). The wave excitation period is indicated in the legend.

Figure 18

Photo of the optical tracking camera setup in the wind tunnel with the floating wind farm.

Figure 19

Measured motion of the floating wind turbine model in the third row of the wind farm, for all four wave conditions.

Figure 20

Mean contours of wake velocity (top) and turbulence intensity (bottom) for all four wave conditions.

Figure 21

Relative wake power potential as calculated by the average of $U^3$ over a rotor area with spanwise position $\mathrm{\Delta }Z$ compared to the upstream turbine.

Figure 22

Conditional averages of wake phases for 1.5 Hz (a), 1.2 Hz (b), and 1 Hz (c) waves, accompanied with a plot of wave height reconstructed from all PIV snapshots, projected onto a single (a) or double (b), (c) wave period using a synchronization frequency of $1.5437\mathrm{Hz}$ (a), $1.23647\mathrm{Hz}$ (b), and $1.03116\mathrm{Hz}$ (c). The maximum velocity deficit is indicated with a red dot, and its trajectory by a red contour line. The reference rotor position is indicated by a black circle to indicate wake changes.

Figure 23

Power spectrum of turbine power normalized by its time-average ($P_i/\overline{P_i}$) for the middle turbine in rows 1–4, from top to bottom. Vertical lines indicate the wave frequencies (–), their second harmonic (– –), and subharmonic (–.).

Figure 24

Power spectrum of aggregate power of the three middle turbines in rows 2, 3, and 4. Black lines indicate: the flow-convective frequency corresponding to one and two turbine spacings $S_x$ (–), the natural frequency for heave (– –), and the natural frequency for pitch (–.). Colored lines indicate the wave excitation frequencies (–), half of the wave frequency (–.), double the wave frequency (– –), and the frequency and first harmonic related to wave speed and turbine spacing $v/S_x$ (:). A power-law scaling of -5/3-2 is shown to indicate the spatiotemporal sampling effect established for fixed bottom wind farm arrays [100].

Figure 25

Cross-correlation of turbine power signals for wind-only (a), 1.5 Hz wave (b), 1.2 Hz wave (c), and 1 Hz wave (d) conditions. Vertical lines at $t{U}_h/S_x=1$ and 2 indicate the convective flow time between rows 2 and 3, and between rows 2 and 4.

Figure 26

Effect of wave conditions on power output of the middle turbine in each row. All measured power values are normalized by the power in the first row for the wind only condition. The normalized absolute power increase of each turbine compared to the wind-only condition is indicated above each bar.

Figure 27

Dummy floater designs to explore sensitivity of pitch response to floater dimensions and ballast.