*2.4. Geometries, Meshes and Numerical Setups*

For both cases, the 3D blade geometry is made using the open source software QBlade [21] that allows building of a blade using its various sections and twist. Two kinds of barnacles are studied to investigate the differences between them: a conical barnacle according to [13] experiment and a realistic barnacle generated using 3D digital imaging (Figure 1). The open CAD software Blender [22] is used to fix the barnacles to the structures.

SnappyHexMesh is a module of OpenFoam that generates unstructured meshes [19]. This module allows one to control the parameters of the mesh such as the number of refined layers near the walls, the size of the smallest computational cells, the skewness, the orthogonality, etc. Thus, all the meshes respect the following characteristics: skewness smaller than 4 and a non-orthogonality parameter lower than 60°. Near the walls, cells are always structured. The smallest cell length scale is 2.1875 × <sup>10</sup>−<sup>4</sup> c and 5.6 × <sup>10</sup>−<sup>2</sup> <sup>c</sup> for the biggest one. The meshes contain around 2 million cells for the motionless blade case and around 9 million for the full rotor simulation. The time step (Δ*T*) is computed by

OpenFoam using the *CFL* < 0.5 condition (Courant–Friedrichs–Lewy condition) on the computational domain to ensure the numerical stability of the code with:

$$\text{CFL} = \mu\_{\text{max}} \cdot \left(\frac{\Delta T}{\Delta \mathbf{x}\_i}\right) < 0.5,\tag{19}$$

where *umax* is the maximum velocity magnitude in the domain and Δ*x* is the length of the local cell at the *umax* position.

**Figure 1.** 3D structures of the conic (**left**) and realistic (**right**) barnacles.

2.4.1. Motionless Blade Simulation with a Single Barnacle

The blade structure made for this test is identical to that of the original experimental study [13]. This allows us to work on the validation of the full-scale model. The foil section is a 55 mm chord NACA 63-619. The barnacle is also placed at 60% of the chord at 40 mm from the centre of the blade in the y direction. The barnacle is thus located at 1/4 of the length of the blade. Half of the blade is used as a reference (clean blade), and the barnacle is placed in the middle of the second part of the blade (Figure 2). The experimental data show that the impact of the barnacle on the blade is limited to a few barnacle base diameters (0.3 c) around the barnacle. Thus, the barnacle should not impact the results of the clean part of the computational domain. Both barnacle geometries are tested and compared.

**Figure 2.** 3D geometry of the blade with one barnacle. The clean part of the blade is marked by the red arrow. The barnacle is in the middle of the section marked with the blue arrow.

Several sizes of computational domains were tested to remove the effects caused by boundary conditions for the smaller domain. Widths from 2 c to 8 c were tested and, after 3 c (1.65 m), numerical results were independent of the width. Thus the simulation channel is 1.60 m high × 8 m wide × 7.3 m long and limits the impact of the boundary conditions. The thinnest cells are located close to the blade walls to capture the boundary layer. The

dimensionless wall distance, *<sup>y</sup>*<sup>+</sup> is set to 1 on the clean section (*y*+ = *yu<sup>τ</sup> <sup>ν</sup>* , where *<sup>y</sup>* is the distance to the wall and *uτ* is the friction velocity). Mesh is structured near the blade in six successive layers with an increase ratio of 1.3 between each layer. The wake expected position is refined using a refinement box to avoid the filtering by the mesh of the wake vortices. The refined mesh is shown in Figure 3. Irregularities on the 2D cut are due to 2D projections in 3D cells which are not distorted. The fluid used in motionless blade simulation is air (supposedly incompressible). The physical simulation parameters are given in Table 2.

**Figure 3.** 3D geometry and mesh of the entire computational domain (**a**), around the blade (**b**), and around the conic barnacles (**c**). Distored cells are due to the cutting plane and do not represent the 3D cells.


**Table 2.** Summary of the physical parameters used in simulations of the motionless blade cases.

Four angles of attack were tested and compared to experimental data (5°, 10°, 14°, 15°). The Reynolds number of the motionless blade cases (with the chord (c = 0.055 m) as reference length) is *Rec* = 1.5 × <sup>10</sup>5.

### 2.4.2. Full Rotor Simulation with a Realistic Barnacle Colonisation

In this section, a full rotor simulation is presented. The rotor hub is removed to limit the computation time. The turbine used in this work has been numerically studied previously for other subjects than biofouling (e.g., flow induced rotation) with clean blades [23]. Barnacles are fixed to the blades according to the realistic implantation on the blades of the AHH HS 1000 tidal turbine shown in [13] (Figure 4). We assume that the colonisation is identical on the three blades. The barnacles are settled on the downstream part of the blade, from 60% of the chord. Moreover, a large part of them are grouped in a patch. Indeed, the barnacles seem to favour the less energetic positions of the blades and their grouping contributes to protect them from the strongest currents. The chosen mesh for the clean case is the converged one used in [23]. It has been subjected to a mesh convergence study related to the forces applied to the rotor. For the fouled case, the general parameters of the

mesh are kept, and the barnacles are taken into account as part of the solid structures. The computational domain is a cube with sides equal to 4 rotor diameters. The cells are twice as thin in the X-direction, which is the direction of the main velocity. Both meshes (clean and fouled) are composed of about 9 million points. Around the turbine, a 1.5 diameter refinement cylinder forms a moving part of the mesh. It is connected to the static zone by an Arbitrary Mesh Interface (AMI) which transfers fluid information from one zone to the other. The rotation of this cylinder generates the rotation of the rotor by sliding on the static zone. The mesh is shown in Figure 5.

**Figure 4.** 3D geometry of one of the three blades of the rotor with barnacles. Red lines are cut positions for post-processing.

**Figure 5.** Views of the X–Y (**left**) and Y–Z (**right**) planes of the computational domain including the rotor geometry. Green lines are the no-slip boundary conditions, the red line is the inlet with the velocity condition and the blue line is the pressure outlet condition.

The full rotor is moving in the water. Physical and numerical parameters are given in Table 3.


**Table 3.** Summary of the physical parameters used in dynamic simulations of the rotor

Ω*<sup>R</sup>* is the rotor's rotation speed and *I*<sup>∞</sup> is the turbulence intensity. The chord-based Reynolds number at the tip of the blades for the full rotor simulations is *Rec* = 1.7 × <sup>10</sup>5.
