2.2.1. Physical Similarity Relationships

The size of the turbine model is constrained by the dimensions of the recirculating flume. A turbine height of 87.5 mm is chosen so it could occupy ~1/3 of 0.3 m water depth. The size of the turbine is 1:8 of the physical model in paper [25]. Rotor radii of 56.3, 45.9, and 37.4 mm were set-up to ensure the solidity of turbine within the scope of 1.09 to 1.64 to investigate the impact of rotor radius on turbine scour. This solidity has been proved to show grea<sup>t</sup> energy extraction efficiency [25]. The turbine model represents a ratio of approximately 1:60 of full scale Darrieus-type tidal current turbine like Kobold project [26]. The ratio of turbine height and water depth was the same as Kobold. The inlet velocity is set as 0.23 m/s ensuring the clear water scours at initial scour stage. In addition, the tip speed ratio (TSR) is an important dimensionless number to influence the hydrodynamic performance of Darrieus-type tidal current turbine. The TSR is designed to be same as paper [25] to make sure the turbine has enough energy extraction efficiency. The TSR can be calculated by Equation (1):

$$\text{TSR} = \frac{a\mathcal{R}}{\mathcal{U}\_c} \tag{1}$$

The Reynolds number of the turbine wake induced by the Darrieus-type turbine model used in the experiment was ~287,500, which is calculated using Equation (2).

$$\text{Re} = \frac{\rho l L\_c D\_t}{\mu} \tag{2}$$

where ρ is density of water (kg/m3), *Uc* is mean current velocity (m/s), *Dt* is turbine diameter (m), and μ is the dynamic viscosity of water (*Pa s*). Rajaratnam [27] suggested the effect of viscosity could be neglected as long as the Reynolds number of propeller jet was more than 10,000. Therefore the viscosity effect could be neglected in the analysis of our turbine model.

#### 2.2.2. Scaling Effects of Experimental Setup

The mean sediment diameter was kept at 1.1 mm by filtering the layers of the sieves in the current experiment. The scour depth can be impacted by the critical startup shear stress of sediment with different diameter [10]. However, our research focused on the influence of turbine's tip clearance and rotor radius on temporal scour depth; the impact of sediment diameter is not a main variable. In previous experimental study of scour, the sediment size *d*50 was the same size as naturally occurring sediments—from 0.5 mm to 2.0 mm—such as [18,28]. We choose 1.1 mm sediment size as a normal prevailing condition to ensure that the sand is under clear water scour at the initial stage, in line with reality.

The size of water flume used in our experiment is shown in Figure 2. The fixed wall surfaces on both sides of flume have influence the flow distribution and experimental accuracy. The flume width is

0.35 m, which is ~6 times than turbine radius and 35 times the supporting pile diameter. In Roulund's experiment of scour around pile [29], the flume width was 36 times than pile diameter, which is almost same as our flume. In addition, based on existed experimental research of flow field around tidal current turbine [16], the operational turbine can disturb flow around it, but shows little impact on flow more than 3R distance in radial direction. Hence the flume is wide enough for our experiments.

During the experiments, the incoming velocity is maintained as 0.23 m/s measured by pitot tube in experimental flow region. This flow velocity is less than critical current speed. The formula to calculate the critical current speed can be found in paper [11]. It appears as clear water scour at first, but the initial flow cannot sweep the sediment and the scour phenomenon only occurs around the turbine's supporting pile. It should be pointed out that due to our innovative type of horizontal recirculating flume the flow on the outside of flume is a little quicker than the inside flow at the corner. When the flow moves out of the corner and towards the experimental area, the flow-equalizing equipment can reduce the speed difference and turbulence intensity to make the flow more stable. In addition, the distance between the turbine center and flow-equalizing equipment is ~10*R.* This distance is long enough to minimis the influence of uneven velocity distribution and produce uniform flow in the measurement area. To verify the reliability of flow uniformity in measurement area, the 3D shape of scour hole and the sand dune downstream is shown in Figure 3. In Figure 3, the flow moves from right to left. The white pile is supporting pile of turbine. The outline of scour hole and sand dune is indicated by white line and the centerline of sand dune is sketched by black line. The scour shape shows grea<sup>t</sup> symmetry downstream. However, the outside tail of the sand dune is a little longer than the inside tail. This is due to the wake asymmetry of Darrieus-type tidal current turbine which has been proposed in paper [17].

**Figure 3.** The sediment bed after scour equilibrium in case *C*/*H* = 1.0, *R*/*D* = 5.63.

In summary, the turbine model used in our experiments is small scale model compared with real tidal current turbine under the constraints of the experimental setup. However, the hydrodynamic performance of the turbine can be guaranteed based on reasonable TSR and turbine solidity. Meanwhile, the recirculating flume is wide and long enough to ignore the wall boundary's impact on scour process, and ensures the accuracy of experiments. Our primary purpose is to investigate the temporal development of scour depth induced by turbine with different rotor radius and tip clearance, and our experimental conditions are qualified for this work.

#### **3. Temporal Variations of Scour Profiles**

Darrieus turbine induced scour has limited data compared to the horizontal turbine induced scour. Previous works simplified the rotating turbine in the scour predictions [20]. Tip-bed clearance and the turbine radius are two main parameters of turbine to influence scour processes. In the current works, the temporal scour evolution are discussed in Section 3 with particular focusses on the influences of tip-bed clearance in Section 3.1 and turbine radius in Section 3.2. The turbine-induced contracted flow leading to scour is considered to occur on top of the monopile scour due to horseshoe e ffects.

Selected cases with various tip-bed clearances and turbine radii were tested to produce data to investigate the impact of Darrieus turbine to seabed scour. Seabed scour reached equilibrium after ~150 min in the experiments. The temporal variations of scour profiles are presented at 30 min, 90 min, and 150 min. Tip-bed clearance ( *C*) was nondimensionalized by using the turbine height ( *H*). In the first four cases, the turbine rotor remained 56.25 mm. The equilibrium scour hole depth is 2.2 *D*, 2.2 *D*, 1.7 *D*, and 1.6 *D* in cases with di fferent tip clearance ( *C*/*H* = 0.25, 0.5, 0.75, and 1.0 respectively). In other two cases, the tip clearance is remained as 0.5H, and the equilibrium scour hole depth reaches 2 *D* when *R* = 45.9 mm, and 2.6 *D* when *R*= 37.4 mm.

#### *3.1. Temporal Seabed Scours at Various Tip Clearance*

The measured temporal developments of the scour profiles of turbine are presented in Figures 4 and 5 at di fferent tip clearances. Four tip-bed clearances of *C*/*H* = 1, 0.75, 0.5 and 0.25 respectively were examined. The nondimensional temporal variations of the scour profiles at 30 min, 90 min and 150 min are plotted in the figures. Figure 4 shows scour profiles at centerline of supporting pile (y = 0), and Figure 5 shows scour profiles at y = 0.5 *D*. For the x-axis, the x/*D* = 0 is located at monopile central line. For y-axis, *S*/*D* is the scour depth nondimensionalized by monopile diameter ( *D*) in the vertical direction.

**Figure 4.** Temporal seabed profiles with different tip clearance at location y/<sup>D</sup> = 0. (**a**) Tip clearance =1H, (**b**) tip clearance = 0.75H, (**c**) tip clearance = 0.5H, and (**d**) tip clearance = 0.25H.

**Figure 5.** Temporal seabed profiles with different tip clearance at location y/*<sup>D</sup>* = 0.5. (**a**) Tip clearance = 1*H*, (**b**) tip clearance = 0.75*H*, (**c**) tip clearance = 0.5*H*, and (**d**) tip clearance = 0.25*H*.

## 3.1.1. Size of Scour Hole

The size of the scour holes increases with time up to 150 min with limited impact of tip-bed clearances. Tip-bed clearance gives significant impacts to the scour depth (*S*/*D*), but insignificantly influences the growing trend of the size of scour hole. The size of scour hole increases over time from 30, 90, and 150 min at all tip clearance *C*/*H* = 1, 0.75, 0.5, and 0.25. In all cases, the scour holes were rapidly developed in the beginning process. Temporal scour depth can reach 75% of the final depth after initial 30 min in the model tests. The increase rate of scour depth slows down with time. After scour equilibrium, the scour depth no longer increases. However, the horizontal size gradually increases with time. For the clearances at *C*/*H* = 0.25 and 0.5, the deposition moves back quickly, and the deposition mound cannot be observed in the range of −4*D*–8*D* along x-axis after 150 min. The deposition wedge moves backwards during the scour process.
