CFD Simulation of Two Tandem Floating Offshore Wind Turbines in Surge Motion

High-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) CFD simulation is employed to investigate the variations in the power performance of two tandem in-line floating offshore horizontal axis wind turbines for the scenario in which the upstream rotor is oscillating in surge motion and the downstream rotor is positioned in a distance of 3D (D: turbine diameter) and is stationary. The rotors are the NREL-5MW reference turbine. The platform surge period and wave amplitude are 9 s and 1.02 m, respectively. The results are presented for 100 full surge periods. It is found that the surge motion of the upstream rotor results in: (i) sinusoidal fluctuations in the power and thrust coefficients (CP and C T) of the upstream rotor with a standard deviation (std) of 9.7% and 5.5%, respectively; (ii) such fluctuations in CP and CT are less regular with a std of 4.2% and 2.8% for the downstream rotor, respectively. A low-frequency oscillating mode with a period nearly 10 times the surge period is also observed for the downstream rotor. The mean Cp and Ct of the downstream rotor are 28.9% and 38.5% of the upstream one.


Introduction
Floating offshore wind power has received wide attention in order to take advantage of the largely unexploited deep offshore wind potential. The technology is still hindered by high Levelized Cost of Energy (LCOE) (see Bosch et al. [5] and Kausche et al. [10]) and technological challenges such as those associated with mooring, electrical cables and floaters (see for example [3]). Rotor aerodynamics, despite the knowledge accumulated for the fixed rotor case, e.g. [18], reveals new challenges in view of the unsteady nature of the flow as is the case with floating platforms. Effectively a floating wind turbine rotor has six degrees of motion which are largely dependent on the coupled wind-wave action. These result in highly complex 3D blade motions which further complicate the resulting wake flows [2]. Furthermore, in a continuous effort to upscale rotors beyond 15MW, new challenges can arise such as flow compressibility, addressed by Sørensen et al. [23] towards the blade tip which is not usually considered for even the largest (non-flying) machines in existence today.
While the problem of floating offshore wind turbines is a multi-physics one involving complex aerohydrodynamic coupling, most of the research has been targeted at investigating the hydrodynamics and the aerodynamics in isolation with some assumed boundary conditions. Research articles on the wake aerodynamics of platform pitching motion by Wen et al. [26] reveal the influence on power with varied tip speed ratio and reduced frequency as a result of the pitching motion. They show that The power variation increases with increasing tip speed ratio and reduced frequency. Another article on the effect of platform pitching motion by Jeon et al. [9] using a vortex lattice method shows the presence of a turbulent wake state under low-speed inflow conditions. Another study by Tran et al. [24] investigates the effect of platform pitching motion on the unsteady aerodynamics of the rotor. Lin et al. [11] also report full body rotor Computational Fluid Dynamics (CFD) computations involving pitching and surging motion.
The research focus on floating offshore wind turbines has been mostly dedicated to surge motion in isolation. Some examples include Bayati et al. [2], Micallef and Sant [12], Farrugia et al. [7] and [6]. These authors investigate the wake and loading characteristics of floating offshore wind turbines at different tip speed ratios. Information such as transient inductions, angle of attack and loads has been reported numerically. Experiments such as Sant et al. [19] also report transient inductions using hot-wire measurements but in general there is a need for more experimental evidence of the wake behavior.
The approaches used for rotors on a fixed platform have found widespread use in floating offshore rotors. Blade Element Momentum (BEM) approaches have been used by Tran et al. [24] and Farrugia et al. [7]) with dynamic wake corrections such as by Pitt and Peters [14] and [22]. In view of the fact that the wake behavior is not directly modeled, such approaches have just been used as a code-to-code comparative analysis. Sant and Micallef show that these models do not compare well with more advanced methods [20]. The Generalized Dynamic Wake (GDW) method has also received some attention (see for instance Micallef and Sant [12]) in view of the fact that it considers the wake dynamics. Nonetheless, like BEM it has been mostly employed for comparative purposes rather than as a benchmarking tool. Despite this, the AeroDyn FAST solver [13] which employs both BEM and GDW can be used to couple the aerodynamics with the hydrodynamics which can hence resolve the platform dynamics. With this approach, under given wave amplitudes and frequencies, the platform motions can be established and used as inputs to investigate the wake aerodynamics. More advanced methods include the free-vortex, lifting-line methods such as that developed by Sebastian and Lackner [21]. Navier-Stokes based Actuator Disc (AD) and Actuator Line (AL) models have also been utilized in the literature such as by de Vaal et al. [6].
Studies on multiple floating wind turbines, as found in wind farms of the future, have found little attention particularly on the turbine-to-turbine wake interactions. Such studies are on the other hand common for rotors on a fixed platform, especially during the last decade (see for instance Troldborg [25]). One issue is that multiple floating turbines interacting with each other have coupled aerodynamics, hydrodynamics and platform dynamics, and this dramatically increases the complexity of the analysis. The principal aim of the current work, however, is to study the variations in the aerodynamic performance of two in-line floating horizontal axis wind turbines in a tandem arrangement oscillating in surge motion. Therefore, a decoupled aerodynamic analysis with a prescribed surge motion is performed. The surge motion characteristics are set based on previous work by the au-  [12]. The de-coupling simplicity provides us with the opportunity to focus on the aerodynamic interactions due to the surge motion. The analysis will focus on the variations in the turbines power and thrust coefficients where the upstream rotor is oscillating in surge motion and the downstream rotor is stationary.
The outline of the work is as follows. The details of the actuator disc modeling and the CFD simulations are given in Sec 2. The results are discussed in Sec. 3 and the conclusions are provided in Sec. 4.

Overview of the methodology
The approach used to answer the main research question is based on numerical simulations of two tandem, in-line floating offshore wind turbines oscillating in surge motion for the following scenario: oscillating upstream turbine, stationary downstream turbine with 3D (D: turbine diameter) streamwise distance in between. Note that 5D distance is the more typical value in the farms, nevertheless, as the focus of the present study is on the wake interactions and the resultant oscillating power performance of the rotors, the smallest applicable distance is selected to ensure the maximum interactions.
In the present study, high-fidelity CFD simulations are performed, where the influence of the turbines on the flow field due to the rotor loading are taken into account using the actuator disc (AD) model coupled with the CFD simulation through a User Defined Functions (UDF).
The AD model, see Sec. 2.3, is coupled based on the work by Micallef and Sant [12] and Bezzina et al. [4]. In the present study, this model has been adapted to accommodate two tandem in-line rotors. The analysis is performed for a given surge amplitude and frequency, see Sec. 2.5. Table 1 lists the geometrical and operational characteristics of the National Renewable Energy Laboratory (NREL) 5MW reference wind turbine, which is used in the simulations. Figure 1 shows a schematic of the two tandem floating offshore wind turbines in surge motion. The turbines have a collective pitch angle of 0 • .

Actuator disc model
The actuator disc model used for the two in-line rotors is based on the formulation by Micallef and Sant [12] and de Vaal et al. [6] but extended in the present study to accommodate two rotors. The rotor loading is modeled as a source term in the momentum equations. These forces are first established using the Blade Element Theory (BET). Due to the surging motion, the relative flow angle will vary with time in a transient manner. The velocity diagram is shown in Fig. 2 with the rotor surging downstream. The blue vectors represent the rotor velocities while the red vectors indicate the aerodynamic velocities. The relative flow velocity V rel and the angle of attack α are used in conjunction with 2D airfoil polars to find the lift and drag forces and hence the thrust and torque acting on a particular radial element and correct for tip/root loss effects using a Prandtl correction [8]. These forces are input as momentum source terms (axial and tangential).
The rotor surge motions (position and velocity) are input as sinusoidal motions with given amplitudes X j [m] and frequencies ω j [rad/s], see Eq. 1 -2, where j = 1, 2. Fig. 3 shows the rotor position For convergence issues, the imposed aerodynamic forces are blurred using a Gaussian function to avoid issues of singularities, which might lead to solution divergence. This is given by Eq. 3: The i is a scaling factor, see Eq. 4, and according to de Vaal et al. [6] should be 1 ≤ i ≤ 2. Micallef and Sant [12] found 2.5 as a proper choice, also used here.
The source term vector is applied by convoluting the force F and divided by the volume of each annular element ∆V .
The main assumption used in the current model is that the platform motions of both turbines are treated in a decoupled manner as a first approximation in order to limit down the complexity of   hydrodynamic and dynamic effects. In reality, the platform motions of the downstream turbine will not be identical to that of the upstream turbine due to the wake interference effects, which will somewhat alter to system dynamics. The iterative methodology is given in the flowchart, see

CFD computational settings
2D axisymmetric incompressible unsteady Reynolds-Averaged Navier Stokes (URANS) simulations are performed. The commercial CFD software package ANSYS Fluent v16.1 [1] is used. The computational domain size is 28D×10D where D is the turbine diameter. The distance from the upstream turbine to the domain inlet is 5D. A fully-structured computational grid with refinement in the rotor region and the wake area is generated, see Fig. 5. The total number of cells is 75,152 cells with 63 cells along the blade radius. The boundary condition at the domain inlet and outlet is uniform velocity inlet and zero static gauge pressure outlet and the domain top side is symmetry (slip) wall. Turbulence is modeled using the two-equation SST k − ω model. The model is shown to give accurate predictions of aerodynamic performance of wind turbines in different operating regimes, from optimal to dynamic stall, in comparison against experimental data and more complex scale-resolving simulation approaches, see [16,15,17]. SIMPLE pressure-velocity coupling scheme is employed. The time step is 0.04 s with 20 iterations per time step.
The simulations procedure is as follows. The steady RANS simulation is performed to have converged solution for 2 steady rotors. The solution is employed to initialize the transient simulation, where the upstream rotor is oscillating in surge motion with the amplitude and period given in Sec. 2.5.

Test matrix
The test matrix, given in Table 2, provides the details of the surge motion for the upstream rotor and the rotor settings for both rotors. The reference wind speed refers to the value employed in BEM calculations to calculate the relative velocity and the angle of attack.
Note that as shown in Sec. 3, the downstream rotor is experiencing much lower incident-flow velocity, i.e. 5.5 m/s. Therefore, its rotor settings is set differently than the rated conditions to  Figure 5: Computational domain and grid for the CFD simulation. operate optimally and it has a rotor speed of 0.84 rad/s according to the NREL design curve, see Table 2. Thus, as obvious, the two rotors are not operating with the same rotor speed and tip speed ratio.

Results
Fig . 6 shows the time-averaged contour plots of the pressure coefficient and normalized velocity magnitude for the streamwise positions x/D = -1 -10, with respect to the upstream rotor. It can be seen that due to the small distance between the two rotors, the incident-flow for the downstream rotor is on average significantly dropped due to the wake of the upstream rotor. The area-weighted average velocity along the rotor span is nearly 5.5 m/s. As indicated in Sec. 2.5 and table 2, hence the downstream rotors settings are adjusted according to the NREL design curve. Fig. 7 shows the variations of the thrust force and torque of the two rotors in 45 full surge periods. Fig. 8 shows the thrust and power coefficients (C T and C P ) of the two turbines normalized with the mean coefficient values of the upstream rotor. Fig. 9 shows the spatiotemporal contour plots of angle of attack, thrust force and torque for the oscillating upstream rotor (rotor 1) and the stationary downstream rotor (rotor 2).
A first observation is that the thrust and torque of the upstream rotor vary in a quasi-sinusoidal manner with some noise at the maximum and minimum positions of the surging rotor. The reason  Figure 6: Dimensionless (time-averaged) axial velocity and pressure, (instantaneous) vorticity fields.
for these are the sudden changes in loads also shown in Fig. 9 occurring every 1 2 surge period. The angle of attack, the spanwise distribution of normal and tangential forces of the upstream rotor are noticeably different during the fore and aft motions of the rotor.
The oscillatory behavior of the upstream rotor loading has 180 • phase difference with the rotor surge speed, meaning that the maximum thrust force and torque corresponds to the most negative surge velocity (when surging upstream). This is expected considering the velocity diagram shown in Fig.  2.
The C P and C T values of the surging upstream rotor have a standard deviation of 9.7% and 5.5%, respectively.  The surge motion of the upstream rotor significantly influences the thrust force and torque of the stationary downstream rotor located 3 rotor diameter downstream. The fixed downstream rotor experiences a non-sinusoidal behavior due to the resulting wake dynamics of the upstream rotor. The behavior of the oscillating loads of the downstream looks more complex with more harmonics of different frequencies other than only the surge frequency, due to wake interactions. Frequency analysis of the instantaneous C P and C T signals of the two rotors shown in Fig. 10, however, reveals that the dominant frequency for both upstream and downstream rotors is still the surge frequency, i.e. 0.11 Hz. For the downstream rotor, moreover, a low-frequency oscillating mode with a period nearly 10 times the surge period is also observed. Further analysis of this low-frequency mode is considered for future research. Note that the frequency analysis is based on the time series for 100 full surge periods.
The mean C P and C T of the stationary downstream rotor are 28.9% and 38.5% of the upstream    11 shows the spanwise distribution of the normal and tangential loads for the oscillating upstream rotor and the stationary downstream rotor. In addition to substantially lower normal and tangential forces observed on the downstream rotor, its spanwise normal force distribution is found to be much more uniform than the upstream rotor, and has comparatively limited variations from root to tip. The tangential load distribution of the downstream rotor also decays in the outer spanwise extent of the blade for r/R > 0.7 due to the wake of the upstream rotor. Figure 11: Spanwise distribution of normal and tangential loads for the oscillating upstream rotor (rotor 1) and the stationary downstream rotor (rotor 2) in the last time step.

Conclusions
The following conclusions can be drawn from this study: • Thrust and torque of the upstream rotor vary quasi-sinusoidally, due to the imposed sinusoidal surge motion of the rotor, with some discontinuities at the maximum and minimum peaks.  11 • The thrust and torque of the downstream rotor is directly influenced by the wake dynamics of the upstream rotor in a non-sinusoidal manner.
• frequency analysis of the turbine forces reveal the dominance of the surge frequency for both upstream and downstream rotors.
• The C P and C T values of the surging upstream rotor have a standard deviation of 9.7% and 5.5%, respectively.
• The mean C P and C T of the stationary downstream rotor are 28.9% and 38.5% of the upstream one and have a standard deviation of 4.2% and 2.8%, respectively.

Acknowledgments
The 1st author is currently a postdoctoral fellow of the Research Foundation Flanders (FWO) and is grateful for the financial support (project FWO 12ZP520N).