**1. Introduction**

With the consumption of traditional fossil fuels and serious environmental pollution, more and more countries in the world begin to attach importance to the development of renewable energy. As a kind of green, pollution-free and abundant renewable energy, wind energy has great potential for development [1]. Originally, wind turbines were mainly built on land, but due to the large noise of onshore wind turbines and relatively few wind and land resources, the wind power industry gradually developed to the sea [2]. From a worldwide point of view, the sea wind is rich in resources, and the wind is stable, which has become the irresistible general trend [3]. With the large-scale capacity of the offshore wind turbine, the size of the wind turbine and the height of the tower are increasing, resulting in a more obvious tower shadow effect [4]. Therefore, it is particularly important to study the unsteady aerodynamics under the tower shadow effect of FOWT.

Offshore wind power generation has obvious advantages over onshore wind power generation; however, FOWTs produce six degrees-of-freedom (6-DOF) [5] motions under the combined action of wind, waves and currents, resulting in more complex aerodynamics compared with onshore and offshore fixed wind turbines. In recent years, many scholars have studied the aerodynamic performance and structural characteristics of FOWTs from the aspects of experiments, models, research methods, etc. The blade element momentum (BEM) theory with two widely used engineering dynamic inflow models was used by Vaal [6] to investigate the effect of a periodic surge on the wind turbine. Ma [7] investigated the effects of the control system of the wind turbine and the motion of the floating platform on the blade aerodynamic performance during the representative typhoon time history. However, the BEM methods used to research aerodynamics lack the characteristics of capturing the physical details of the flow field, which the reasonability and accuracy are suspectable. Farrugia [8] used the results from the free-wake vortex simulations to

**Citation:** Hu, D.; Deng, L.; Zeng, L. Study on the Aerodynamic Performance of Floating Offshore Wind Turbine Considering the Tower Shadow Effect. *Processes* **2021**, *9*, 1047. https://doi.org/10.3390/pr9061047

Academic Editor: Eugen Rusu

Received: 3 May 2021 Accepted: 11 June 2021 Published: 15 June 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

analyze the wake characteristics of the wind turbine under floating conditions. Complex wake phenomena under the influence of extreme wave conditions were observed. Wen et al. [9,10] also used the FVM method for numerical simulation and found that the power coefficient overshoot is caused by the time lag between the output power and the wind farm power. The time lag and the resultant power coefficient overshoot increase as the platform surge frequency increases. In pitch motion, with the increase of the reduced frequency, the mean power output decreases at a low tip speed ratio and increases at a high tip speed ratio. Salehyar [11] investigated the dynamic response of a spar-buoy-based floating wind turbine to non-periodic disturbances through a coupled aero-hydro-elastic numerical model, observing the ability of the wind turbine to recover to the balanced position after being disturbed. Lin [12] investigated the aerodynamic characteristics in system pitch and surge motions and the asymmetric and complicated wake was observed. Tran et al. [13–16] performed the CFD simulation based on the dynamic mesh technique and an advanced overset moving grid method, respectively, to accurately consider the aerodynamic loads of a three-dimensional wind turbine. Results summarized the comparisons of different aerodynamic analyses under periodic surge, pitch and yaw motions to show the potential differences between the applied numerical methods. Chen [17] proposed a model of a spar-buoy and a semi-submersible floating wind turbine to compare with the experimental results of the two. Nguyen [18] studied the fully coupled motion of FOWT and applied the six degrees-of-freedom solid motion solver to multi-motion coupling to study the coupling of the surge, pitch and yaw motions. Huang [19] discussed the dynamic response of the local relative wind speed and local angle of attack of the blade section and the wind– wave force acting on the floating platform to reveal the interaction mechanism between the aerodynamic load and the motion of the platform with different degrees of freedom. Fang [20,21] applied a 1:50 model FOWT to explore the aerodynamics and characteristics of its wake under surge and pitch motions. Chen [22,23] investigated the aerodynamic characteristics of the wind turbine under surge–pitch coupling and pitch–yaw coupling by the combination of dynamic mesh and sliding mesh. The results show that the fluctuation of the overall aerodynamic performance of the wind turbine dramatically with the increase of amplitude and frequency. Sivalingam [24] examined the predictions of numerical codes by comparing them with experimental data of a scaled floating wind turbine.

In addition to the research on changes in wind turbine performance caused by platform motions, a series of studies have also focused on the tower shadow effect of the wind turbine. Kim [25] and Quallen [26] found that the diameter of the tower has a greater effect on the wind turbine than the gap between the tower and the blade, and the root of the blade is more affected by the tower. Ke [27] proposed an effective method for calculating the aerodynamic load and aeroelastic response of a large wind turbine tower blade coupling structure under the yaw condition, taking full account of wind shear, tower shadow, aerodynamic interaction and rotation effect. Noyes [28] used unsteady aerodynamic experiments to analyze the influence of tower shadow effect on aerodynamic loads and blade-bending moments of downwind two-blade wind turbines. Zhang [29] found that the maximum displacement and Mises stress increase with the increase of the average wind speed under the tower shadow effect. Li [30] investigated the aeroelastic coupling effect under periodic unsteady inflows, indicating that the tower shadow effect causes dramatic changes in the tilting moment, thrust force and output power when the blade rotates in front of the tower. Wu [31] investigated the unsteady flow characteristics in the tip region of the blade, observing the static pressure distribution of different blades near the leading edge of the tip is very different due to the influence of turbulence intensity and tower shadow effect.

According to the above literature review, the influence of the six degrees-of-freedom motions of the platform on the FOWTs has been studied to a certain extent, and the investigations on the tower shadow effect are mostly focused on the land-based fixed wind turbine. Nevertheless, the effect of platform motions combined with the tower shadow effect is rarely mentioned. This paper aims to investigate the unsteady aerodynamic characteristics of FOWTs under surge, pitch and yaw motions based on the tower shadow effect. The unsteady dynamic numerical simulation of the aerodynamic characteristics of the full-size wind turbine model in the rotating process was carried out using a UDF (user-defined function) and embedded sliding mesh, and the unsteady Reynolds-Averaged Navier–Stokes equations (RANS) and SST k-ω turbulence model are adopted. Considering the effect of the tower shadow effect, the power, thrust and the pressure distribution of blade sections under surge, pitch and yaw motions are compared and analyzed, and the near wake and far wake flow fields of the wind turbine are analyzed.

#### **2. Model and Numerical Methods**

#### *2.1. Governing Equations and Turbulent Model*

The three laws of mass conservation equation, momentum conservation equation and energy conservation equation need to be followed in fluid mechanics. For incompressible fluids, the continuity equation and the momentum equation (Navier–Stokes equation) can be used to describe the law of conservation of mass and momentum of the fluid. Regodeseves [32] and Burmester [33] validated the accuracy of the model in simulating the aerodynamic characteristics of FOWTs by comparing the simulation results of the model with the experimental data.

The definition of the continuity equation, Reynolds equation and scalar Φ timeaveraged transport equation expressed in the tensor form are expressed as follows:

$$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x\_i} (\rho u\_i) = 0,\tag{1}$$

$$\frac{\partial}{\partial t}(\rho u\_i) + \frac{\partial}{\mathbf{x}\_j}(\rho u\_i u\_j) = -\frac{\partial p}{\partial \mathbf{x}\_i} + \frac{\partial}{\mathbf{x}\_j}(\mu \frac{\partial u\_i}{\partial \mathbf{x}\_j} - \rho \overline{u'\_l u'\_j}) + \mathbb{S}\_{i\nu} \tag{2}$$

$$\frac{\partial(\rho\phi)}{\partial t} + \frac{\partial(\rho u\_j \phi)}{\partial x\_j} = \frac{\partial}{\partial x\_j} \left( \Gamma \frac{\partial \phi}{\partial x\_j} - \rho \overline{u'\_j \phi'} \right) + S\_\prime \tag{3}$$

$$
\pi\_{i\bar{j}} = -\rho \overline{u'^{\mu'}\_{l} u'^{\nu}\_{\bar{j}'}} \tag{4}
$$

where *ρ* is the air density, *t* is the time, *ui* and *uj* represent the Reynolds mean velocity components of fluid, *p* is the pressure, *μ* denotes the coefficient of dynamic viscosity, *S* is the generalized source term (*i*, *j* = 1, 2, 3) and Γ represents the diffusivity. *τij* corresponds to six different Reynolds stress terms, which is defined as Reynolds stress.

The SST *k-w* model combines the advantages of the *k*-*w* model in the near-wall region and the far-field calculation of the *k*-*ε* model, further modifies the turbulent viscosity and adds an orthogonal diffusion term, which can well predict the separation of the fluid under the negative pressure gradient. For the aerodynamic analysis of the wind turbine in this paper, the SST *k-w* model has obvious advantages, which is used in the later simulation.

The transport equation expression of SST *k-w* is as follows:

$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho u\_i k)}{\partial x\_i} = \frac{\partial}{\partial x\_j} \left( \Gamma\_k \frac{\partial k}{\partial x\_j} \right) + \overline{\mathcal{G}}\_k - \mathcal{Y}\_k + \mathcal{S}\_{k\prime} \tag{5}$$

$$\frac{\partial(\rho w)}{\partial t} + \frac{\partial(\rho u\_i w)}{\partial x\_i} = \frac{\partial}{\partial x\_j} \left(\Gamma\_w \frac{\partial w}{\partial x\_j}\right) + G\_w - Y\_w + D\_w + S\_{w\prime} \tag{6}$$

where *Gk* is the turbulent energy caused by the average velocity gradient, *Gw* is the turbulent dissipation rate, Γ*<sup>k</sup>* and Γ*<sup>w</sup>* represent the effective diffusivity of *k* and *w* caused by turbulence, respectively, *Yk* and *Yw* are the dissipation of *k* and *ω*, *Dw* is the orthogonal divergence, both *Sk* and *Sw* represent user-defined source items.
