*2.2. CFD Model of Reference Composite Wind Turbine Blade*

2.2.1. Control Equation, Geometric Model of Composite Wind Turbine Blade and Flow Field for CFD Simulation

In this work, the Navier–Stokes equation (RANS) based on Reynolds stress averaging was used to solve the flow field of the wind turbine blade, see Equation (1).

$$\frac{\partial}{\partial t}(\rho \stackrel{\rightarrow}{\boldsymbol{\mu}}) + \nabla \cdot (\rho \stackrel{\rightarrow}{\boldsymbol{\mu}} \stackrel{\rightarrow}{\boldsymbol{\mu}}) = -\nabla p + \nabla \left(\mu \left(\nabla \stackrel{\rightarrow}{\boldsymbol{\mu}} + \nabla \stackrel{\rightarrow}{\boldsymbol{\mu}}^T\right) - \frac{2}{3}\mu (\nabla \cdot \stackrel{\rightarrow}{\boldsymbol{\mu}})\right) + \stackrel{\rightarrow}{\boldsymbol{F}} \tag{3}$$

where <sup>→</sup> *F* is the external force applied to the fluid.

The wind turbine in this work is the NREL offshore 5 MW baseline wind turbine developed by National Renewable Energy Laboratory (NREL) [33]. The length of composite blade in the NREL 5 MW machine is about 61.63 m. The blade is artificially divided into 17 airfoils from the root to the tip, namely: Cylinder, Du40, Du35, Du30, Du25, Du21 and NACA64, respectively. Note: The detailed geometric parameters corresponding to the aforesaid airfoils can be found in Table S1, Supporting Information (SI).

The geometric model of the composite wind turbine blade can be established as follows: <sup>1</sup> Translate the aerodynamic center of the airfoil to the coordinate origin; <sup>2</sup> Rotate and

transform the airfoil coordinate in accordance with the twist and chord; <sup>3</sup> Calculate the 3D coordinate of nodes using the following equation:

$$\begin{cases} \quad \mathbf{x}' = c \cdot \frac{|\mathbf{x} - \mathbf{x\_{Aero}}|}{\mathbf{x} - \mathbf{x\_{Aero}}} \sqrt{(\mathbf{x} - \mathbf{x\_{Aero}})^2 + y^2} \cos\left(\arctan\frac{y}{\mathbf{x} - \mathbf{x\_{Aero}}} + \beta\right) \\\quad y' = c \cdot \frac{|\mathbf{x} - \mathbf{x\_{Aero}}|}{\mathbf{x} - \mathbf{x\_{Aero}}} \sqrt{(\mathbf{x} - \mathbf{x\_{Aero}})^2 + y^2} \sin\left(\arctan\frac{y}{\mathbf{x} - \mathbf{x\_{Awo}}} + \beta\right) \\\quad z = r \end{cases} \tag{4}$$

where *x* and *y* mean the normalized coordinates; *x* and *y* mean the 3D coordinates; *x*Aero means the aerodynamic center of the airfoil to the coordinate origin; *c* and *β* mean the chord and twist. Based on the aforesaid method, the 3D geometric model of composite wind turbine blade can be established using the Siemens NX 10.0 software, see Figure 1a,b.

**Figure 1.** Establishment of 5 MW wind turbine blade. (**a**) Normalized section data of airfoils. (**b**) Wind turbine blade. (**c**) Geometric overall domain. (**d**) Geometric rotation and blade domains. (**e**,**f**) Stereogram and side view of fluent mesh models. (**g**) Local fluent mesh view of blade.

The flow domain for the CFD simulation of a composite wind turbine blade was defined as: <sup>1</sup> The effects of tower and nacelle were not considered in this work; <sup>2</sup> Onethird model was chosen for the CFD simulation to reduce the computation time. Figure 1c exhibits the dimensions and boundary conditions of the CFD model, where the model consists of a rotation domain and a stationary domain. The data can be passed though the interface. The radiuses of the rotation and stationary domains were 70 m and 300 m, respectively. The inlet was 200 m from the hub center and the outlet was 500 m from the hub center.

The fluent mesh model for the CFD simulation of the composite wind turbine blade was obtained as follows: The aforesaid domains were meshed using unstructured tetrahedral element type based on the ANSYS Meshing tool. Note: although some scholars [34,35] meshed blades using the structured mesh, the unstructured mesh for blade and fluid is available by calculating Y+ values at different speeds and comparing the results of the output torque and power curves, which can obtain reasonable simulation results, see Figure 2. The mesh sizes for the rotation and stationary domains were 3 m and 1 m, respectively. Furthermore, the meshes in the symmetry surfaces, named Side\_wai1 and Side\_nei1, Side\_nei1 and Side\_nei2, were completely controlled by the periodic mesh matching using the periodic boundary constraint command to ensure that the periodic surface nodes correspond to each other, see Figure 1e,f. In order to better simulate the flow near the wall surface of the blade, the meshes around the blade surfaces were refined and fifteen expansion layers with a growth rate of 1.9 were set. The height of the first layer was 1 × <sup>10</sup>−<sup>5</sup> m, see Figure 1g.

**Figure 2.** Output responses of composite wind turbine blade based on the k-*ω* SST and k- models and FAST. (**a**) Output torque response. (**b**) Output power response. Note: the simulation model is one third of wind turbine.

#### 2.2.2. Mesh Quality and Independence Verifications

The mesh quality of the constructed CFD model was checked by using the *y*<sup>+</sup> value [36], which can be calculated as:

$$y^{+} = \mu\_{\*} y / \nu \tag{5}$$

where *u*<sup>∗</sup> is the friction speed; *y* is the nearest wall; *ν* is the kinematic viscosity of fluid. If the *y*<sup>+</sup> is less than 1, the mesh quality is reasonable. The *y*<sup>+</sup> values were calculated under the wind speeds of 7 m/s, 11.4 m/s, 15 m/s, 20 m/s and 25 m/s, respectively, see Figure S1, SI. All the values were less than 1, indicating that the constructed CFD meshing models under different wind speeds were reasonable. Apart from the validation of mesh quality, the mesh independence was also carried out to find out an appropriate mesh size in this work. The case under the wind speed of 11.4 m/s was chosen, where the wind turbine speed is 12.1 RPM and the pitch angle is 0◦. Four mesh sizes of 0.3 m, 0.2 m, 0.1 m and 0.07 m were adopted to mesh the blade surface, and the interface surface and outer surface meshes were set as 3 m and 6 m, respectively. After meshing, the amount of elements corresponding to the aforementioned mesh sizes were 3.63 million, 4.17 million, 578 million and 808 million, respectively. Table S2 (SI) shows the relationship between mesh number and calculated wind turbine torque. In view of the computation time and accuracy, the mesh size of 0.1 m was taken for the blade surface in the subsequent study of this work.
