We investigate the aerodynamics of a surging, heaving, and yawing wind turbine with numerical simulations based on a free-wake panel method. We focus on the UNAFLOW (UNsteady Aerodynamics of FLOating Wind turbines) case: a surging wind turbine which was modeled experimentally and with various numerical methods. Good agreement with experimental data is observed for amplitude and phase of the thrust with surge motion. We achieve numerical results of a wind turbine wake that accurately reproduce experimentally verified effects of surging motion. We then extend our simulations beyond the frequency range of the UNAFLOW experiments and reach results that do not follow a quasi-steady response for surge. Finally, simulations are done with the turbine in yaw and heave motion, and the impact of the wake motion on the blade thrust is examined. Our work seeks to contribute a different method to the pool of results for the UNAFLOW case while extending the analysis to conditions that have not been simulated before and providing insights into nonlinear aerodynamic effects of wind turbine motion.

With the wind energy market leaning heavily towards offshore turbines in recent years, floating offshore wind turbines (FOWTs) have become the focus of numerous research groups. One of the many challenges of such configurations is that, due to oceanic waves, the turbine is subjected to large amplitude motions, making its aerodynamics even more complex than that of onshore turbines. Turbines can translate horizontally perpendicular (surge) or parallel (sway) to the rotor plane. They can translate vertically (heave). They can rotate around the tower axis (yaw) or around the two horizontal axes (roll and pitch). These degrees of freedom are illustrated in Fig.

The sway and heave motion are, from a rotor aerodynamics perspective, equivalent. Rolling moves the rotor in a very similar way to sway, with an added in-plane rotation, equivalent to a change in rotation velocity. Pitching can be thought of as a combination of surge, yaw, and heave. Hence, for rotor aerodynamics, we can consider the surge, yaw, and sway as the fundamental forms of rotor motion from which the others can be derived. For this reason, in this study, we focus on these three degrees of freedom. While these rotor motions have been studied experimentally

The UNAFLOW

Degrees of freedom of a FOWT.

While BEM simulations have successfully captured dynamic inflow conditions

This work is an expansion of what was documented in a previous conference publication

With these characteristics in mind, this is an important stepping stone towards the ultimate goal of this research: aeroelastic simulations of FOWTs through a fully coupled transient aerodynamic and structural fluid–structure interaction (FSI). To our knowledge, only experimental and CFD results have been used to investigate the wake of the UNAFLOW turbine

The next objective of this work is to extend the surge analysis to sway and yaw motion. We use the UNAFLOW rotor to perform such investigations in order to contribute to the knowledge of the physics of these motions. Finally, we seek to understand the impact of the wake motion on surge, sway, and yaw. We do this by employing unique features of the free-wake panel method, allowing us to include rotor motion effects indirectly. The analysis of wake motion effects seeks to clarify mechanisms of turbine motion that will need to be accounted for when simulating FOWT motion with methods without true wake motion, such as BEM and prescribed wake vortex methods.

We employ a source and doublet panel method with free wakes

When symmetries are present, as in turbines with multiple blades and no yaw or heave, virtual bodies across symmetry planes or axes can be used

The panel method shown here was created with the intent to be faster than available methods through the use of efficient algorithms and modern acceleration techniques, such as leveraging GPUs for the calculations. At the moment, our implementation was compared to an open-source C++ panel code

The UNAFLOW turbine case

The blades are based on the SD7032 airfoil section, transitioning into a circle in the root region. For the simulations in this work, the blade geometry was constructed based on chord and twist distributions provided in the experimental data set

Panel method simulation results of the UNAFLOW rotor and its wake.

The blades are discretized with 100 chordwise panels, using a cosine distribution, and 50 equally spaced spanwise panels each, with a total of about 15 000 panels. The panel distribution is shown in Fig.

Surface mesh used for the UNAFLOW blade, showing tip region.

For a demonstration of the accuracy of the chosen time steps, simulation duration, and validation of the mean flow properties, refer to

We examine the fluctuating component of

Surge frequency effect on the amplitude of the fluctuation in the thrust coefficient. Simulations at constant

Surge frequency effect on the phase between the rotor position and its thrust. Simulations at constant

The values of

We now focus on the rotor wake. The UNAFLOW experiments included particle image velocimetry (PIV) on a vertical plane in the rotor wake, aligned with the center of the nacelle. Measurements were made at several stages of the surging motion and averaged over several snapshots, with the rotor always being in the same azimuth

Simulations are done with

UNAFLOW wind turbine (grey), wake panels (blue), and PIV plane (red).

Figures

Experimental tip vortices' position on steps 1 (green) and 5 (blue). Vorticity perpendicular to the plane shown from 0 to 300 1

Numerical wake on steps 1 (green) and 5 (blue). Vorticity perpendicular to the plane shown from 0 to 300 1

CFD simulations conducted for the UNAFLOW turbine

It is worth noting that the wind turbine wake is folding upon itself on the right side of Fig.

In this section, we seek to expand our simulations beyond the limitations of the UNAFLOW experiments. Due to the relatively small reduced frequencies involved in wind turbine surge motion

Results for simulations beyond the experimental data are shown in Figs.

Maximum surge velocity effect on the amplitude of the fluctuation in the thrust coefficient.

Maximum surge velocity effect on the phase between the rotor position and its thrust.

We can now find where

Normalizing

We now move on to simulations of the two other degrees of freedom of interest for FOWTs in this work: sway and yaw. We continue to use the UNAFLOW turbine in spite of no experimental data being available for the cases investigated in this section. Although not shown, some of the simulations in Sect.

In order to identify the dynamic effects of sway and yaw, we first need to understand the static effects of side wind. Hence, we simulate a fixed UNAFLOW rotor with side wind. This is usually referred to as a yaw case, but to avoid confusion between static and dynamic yaw cases, we refer to the static yaw cases as side wind throughout this paper and use the word “yaw” to refer to dynamic rotation around the tower axis.

We perform side wind simulations by rotating the wind vector around the vertical axis by a side slip angle

Top view of turbine with definition of side slip angle

Figure

Axial force fluctuation amplitude of single blade during rotation for different side wind angles.

We impose a swaying motion on the turbine using the same conventions of Sect.

The sway motion introduces a side velocity, which at its maximum value

Top view of turbine with definition of maximum side wind angle

Figure

Time history of blade 1 thrust coefficient for various sway frequencies. Thrust normalized with maximum rotor velocity magnitude.

Amplitude of blade thrust coefficient fluctuation for various side wind angles and various maximum side wind angles achieved during sway motion. Thrust normalized with maximum rotor velocity magnitude.

By scaling

We now take a closer look at one of the curves of Fig.

Time history of blade 1 thrust coefficient for a sway case. Vertical lines show blade azimuth.

Time history of horizontal sway velocity projected on airfoil chord at the tip of blade 1. Vertical lines show blade azimuth.

Azimuth convention used. Blade shown at

The horizontal rotor sway velocity varies with the cosine of the sway frequency

We can see that the thrust fluctuations in Fig.

The general behavior for sway motion is as follows: when the blade is pointing to either side, the sway velocity projection onto the blade chord is zero, sway effects are minimal, and the thrust is near its mean value. When the blade is pointing up or down, the potential for sway effects is maximum and the thrust can reach its maximum or minimum if this coincides with maximum sway velocity. Hence, the relationship between the rotation and sway frequencies, along with the phase between the trigonometric functions that represent those motions, will dictate the behavior of the blade thrust.

We impose a yawing motion on the turbine by rotating it around the vertical central axis using the same conventions of Sect.

Figure

Time history of blade 1 thrust coefficient for various yaw frequencies.

Amplitude of blade thrust coefficient fluctuations for various maximum surge velocities

Note that

Similar to the previous section, we now focus on a single yaw case, namely

Time history of blade 1 thrust coefficient for a yaw case. Vertical lines show blade azimuth.

Time history of blade 1 streamwise blade tip yaw velocity. Vertical lines show blade azimuth.

The general behavior for yaw is as follows: when the blade is pointing up or down, the velocity introduced by the yaw force is zero and the thrust is near its mean value. This can be seen for all cases of

The results shown so far for sway and yaw are all for single blades, which had a specific initial position, with blade 1 pointing up. The sway and yaw motions were all done with the rotor in neutral position at time equal to zero. The rotation frequency was 4 Hz, and the sway and yaw frequencies were 1, 2, 3, 4, and 5 Hz. Hence, the rotor motion and blade position were locked in phase, and this is not representative of all the possible loads blades can experience with different starting positions or with non-integer frequency ratios.

We can analyze Eqs. (

Figures

Amplitude of blade thrust coefficient fluctuation for various maximum side wind angles achieved during sway motion. Simulations results are shown, along with the theoretical possible range of results as dashed lines. Thrust normalized with maximum rotor velocity magnitude.

Amplitude of blade thrust coefficient fluctuation for various maximum tip yaw velocities. Simulations results are shown, along with the theoretical possible range of results as dashed lines.

The thrust fluctuations start by scaling linearly with the surge, sway, and yaw motions, as these motions act on the blade sections, increasing and decreasing the relative flow velocity. The surge and yaw motions act on the axial velocity of a given blade section, while the sway motion changes the tangential velocity on the blade sections. As the tangential velocity is typically much higher than the axial velocity in wind turbines, the sway motion effects are small compared to the surge and yaw. However, the sway motion moves the rotor out of the slipstream, leading to changes in axial velocity that are not due to simple changes in the kinematic velocities. This effect is quantified in the next section.

Methods such as BEM are unable to capture the detailed wake motion of wind turbines shown in Fig.

To do this, we take advantage of the properties of panel methods and model the rotor motion indirectly. The rotation of the rotor is still performed explicitly, but the surge, sway, and yaw motion are included not by displacing the turbine but by modifying the equation for the sources

The pseudo-motion method means that the wake panels are always released from the trailing edges in the fixed rotor position. The wakes are not identical to the wakes of a fixed rotating turbine, as changes in the circulation on the blades will affect how the wake is convected. However, the wakes are substantially different from the cases with real motion while still being more realistic than a frozen or prescribed wake method. With this, we seek to quantify the effect of real motion and the associated realistic wake compared to pseudo motion and the more simple wake that comes with it.

We select various frequencies from the previous sections and simulate them in pseudo motion. The results are summarized in Figs.

Ratio between mean blade thrust for pseudo-motion and real-motion simulations for various frequencies and motion types.

Ratio between amplitude of fluctuating blade thrust for pseudo-motion and real-motion simulations for various frequencies and motion types.

Figures

Wake for real (top, blue) and pseudo (bottom, orange) surge motion at

Wake for real (top, blue) and pseudo (bottom, orange) sway motion at

Wake for real (top, blue) and pseudo (bottom, orange) yaw motion at

The amplitudes and frequencies used in this paper for surge are mostly related to the UNAFLOW experiment. For sway and yaw, we decided to use the same frequencies as in surge, adapting the amplitude to obtain values of

We have shown that a free-wake panel method can accurately capture the mean and unsteady thrust of a surging wind turbine. The methodology used in this paper slightly underpredicts the mean thrust and overpredicts the amplitude of thrust fluctuations; however, results are comparable to and in line with the state-of-the-art

The effects of the rotor motion on the tip vortices was also shown to be accurately captured by the method in what we believe is the first simulation of surging wind turbine wakes that accurately reproduce experimental data. Wake vortices are particularly difficult to capture with CFD methods, as the Eulerian approach tends to dissipate them

We found that the surge frequency had to be tripled from its maximum value in the experimental campaign to reach a nonlinear response in thrust. The current method allowed us to investigate this by isolating Theodorsen effects. This means that, in reality, the nonlinear response could happen earlier due to other phenomena, such as dynamic stall.

We then studied side wind, sway motion, and yaw motion of a rotor. We demonstrated the complexity of the forces acting on the blades during sway and yaw motions even without flow separations. By comparing side wind results with sway results using the maximum sway angle and including the sway velocity in the thrust coefficient, we were able to show linear behavior for sway at low frequencies that matched the side wind trends. For the yaw motion, the blade tip surge effect was demonstrated by investigating the axial force on a single blade during a yaw cycle. For both sway and yaw, the blade force fluctuations can vary by a factor of 2, depending on the ratio between the rotor motion and rotation, as well as the blade initial position.

Finally, we used an interesting feature of the current methodology to perform what we refer to as pseudo-motion simulations, where we accounted for the surge, sway, and yaw motion on the rotor without actually performing these motions on the turbine. With this we showed the sensitivity of wake deformation on the forces on the blades. It was found that the sway motion allows undisturbed air to enter the wake, increasing the mean thrust and, in our case, reducing the dynamic loads. Surge and yaw were shown to be fairly insensitive to the wake motion, which explains the fact that methods that do not capture wake dynamics can still predict surge motion effects well.

This work is a stepping stone towards building a tool that is able to simulate FOWTs in a way that is accurate, robust, and efficient. Future work will expand to include more complex cases, such as full offshore platform motion and aeroelasticity.

The data generated in this work can be provided upon request to the corresponding author.

AFPR developed the panel code, performed the simulations, post-processed the data, and wrote the paper. DC contributed to the conceptualization of the study and the interpretation of some results. CSF contributed to the conceptualization of the study, interpretation of the results, and the development of the panel code.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are grateful to Felipe Miranda for providing the experimental data

This paper was edited by Sandrine Aubrun and reviewed by two anonymous referees.