The turbine site whose bathymetry is considered in this study was the Naru Strait in the Goto Islands, Nagasaki Prefecture, Japan, where the first tidal energy demonstration project in Japan was conducted in 2021 (Garcia-Novo et al., 2024). Naru Strait is one of the two channels (the other is Tanoura Strait) designated for tidal stream energy harvesting by the Government of Japan, among the four main channels formed by the five islands that constitute Goto (Waldman et al., 2017). The Goto Islands are characterized by narrow and relatively shallow channels and large water masses moving from the Pacific Ocean to the Sea of Japan and the Yellow Sea during flood tides and vice versa during ebb tides, generating strong tidal currents. Located between the Hisaka (west) and Naru (east) islands, Naru Strait is approximately 7 km long and 2 km wide, with a recorded vertically averaged maximum velocity of 3.1 m/s (Garcia-Novo et al., 2018). A map of the Goto Islands showing the turbine location in Naru Strait is shown in Fig. 1. The turbine location coordinates are 32°49′04.3″ N–128°54′40. 4″ E. The depth of the deepest point at the site is 50 m, and the mean water depth at the turbine location is 40 m, with a turbine hub height of 15 m above the seabed (Ministry of Environment, Government of Japan, n.d.).

A high-resolution 3D bathymetry model of the domain of interest in the Naru Strait around the turbine location was created using topological map data, as shown in Fig. 2. The bathymetry is characterized by an elongated ridge with small undulating dunes near the turbine location. The ridge is raised approximately 10 m from the lowest point in the domain and is separated from the hill to the left by a 10-m-deep valley. A steep slope exists at the end of the ridge towards the outlet end of the domain. The computational domain size was 540 × 360 m, oriented parallel to the dominant flow direction of the accelerating ebb tides, as determined by Garcia-Novo et al. (2024, 2018). The water column height in the domain varied from 50 m at the lowest point to 35 m at the highest point. The analysis domain is shown in Fig. 3, which presents the seabed, inlet, outlet, and top and side boundaries. Three cases were considered in this study: a real bathymetry with a turbine (Case 1), a flatbed with a turbine (Case 2), and a real bathymetry without a turbine (Case 3). A constant water depth of 40 m, which was similar to the depth at the turbine location, was used in Case 2. The ANSYS-Fluent computational fluid dynamics code was used to perform the 3D viscous flow analysis of the turbine using the k-ω Shear Stress Turbulence (SST) Reynolds averaged Navier-Stokes (RANS) model. Owing to tidal currents and irregular bathymetry interactions, turbulent flow exists in the water column near the seabed. Therefore, seabed boundary layers require a turbulence model to account for bathymetry roughness (Launder and Spalding, 1974). The k-ω SST model integrates the accuracy of the k-ω model in the boundary layer region close to the wall and the k-∊ model in the free stream, using a blending function. Flow separation under adverse pressure gradients (APGs) and turbulent oscillating boundary layer flows over rough bottoms can be precisely predicted using this model (Holmedal et al., 2013). The inlet boundary was located 5D upstream of the turbine and the outlet 25D downstream of the turbine. The seabed, flatbed, turbine blades, and hub were modelled as walls, whereas the sides and upper boundaries were assigned symmetry boundary conditions. Standard inflow-outflow boundary conditions were used for the inlet and outlet, with the inlet velocity taken as the depth-averaged flow velocity, U₀ = 1.5 m/s, and the outlet pressure P was set to 0 Pa. The domain was discretized using ANSYS Fluent meshing as a watertight geometry with no voids and differentiated local sizing. A polyhexcore unstructured mesh that flexibly combines polyhedral and hexahedral elements was used. The mesh consisted of 25.4 million cells. An unsteady flow analysis was conducted, and the solution was run for 960 time steps, with each time step fixed at 0.5 s. The turbine rotation speed was set according to the specifications of the turbine used in the demonstration project in the Naru Strait for an inlet current velocity of 1.5 m/s. The original turbine adopted for the analysis is shown in Fig. 4, and its description is presented in Table 1. The simulation conditions are listed in Table 2.

The turbine used for analysis is a scaled-up model of the 0.9-m-diameter HATT with a Wortmann FX 63-137 airfoil profile, which was designed in collaboration between the University of Strathclyde and Cardiff University through the Dylotta project. This HATT was tested by Allmark et al. (2020, 2021). The turbine was scaled up to 18 m, a diameter similar to that of the 0.5-MW turbine deployed in the demonstration project in Naru Strait. To ensure similarity in terms of flow characteristics between the original and scaled-up turbines, dynamic similarity should be maintained. However, while the original turbine was tested in a flume tank, where the Reynolds number (Re) and other flow parameters could be readily controlled, the scaled-up turbine operated under varying turbulent flow conditions owing to the irregular bathymetry. In this study, the characteristic curves of the non-dimensional performance parameters (power and thrust coefficients) were used to assess the Re-independence of the scaled-up turbine, as proposed by Allmark et al. (2019) and Ordonez-Sanchez et al. (2019). The instantaneous turbine torque (T), thrust (τ), power coefficient (C_P), and thrust coefficient (C_T) at the tip speed ratio (λ) resulting from Eq. (1) for the flow velocity (U) and rotation speed (ω), were used in this study. C_P and C_T are expressed as in Eqs. (2) and (3), respectively, where A is the flow area and ρ is the water density.

The turbine torque and thrust output time series are shown in Fig. 5, and the average values of the performance results are listed in Table 3. The results show that the turbine power output in the presence of irregular bathymetry was 1.84% higher than that in the flatbed case. Bathymetry contributes to improved turbine power, although with a 1.73% increase in thrust loading. Periodic fluctuations were also observed in the turbine torque and thrust outputs. The torque fluctuations in Case 1 have amplitudes 1.9× larger than those in Case 2. A similar observation was made for thrust fluctuation, but with smaller amplitudes. In both cases, the fluctuations occurred at a frequency consistent with the turbine rotational speed. This not only implies increased turbulence but also increased fatigue loading on the turbine blades in the presence of bathymetry. However, these effects require further research.

Fig. 6 shows a comparison of the power and thrust coefficient curves of the original 0.9-m-diameter and scaled-up 18-m-diameter turbines. The original turbine was tested at a tip ratio range of λ = 2–7. Table 3 summarizes the turbine performance comparison. The results show that at a tip speed ratio corresponding to the demonstration project specifications, differences of 3.93% and 4.76% in the C_P and C_T values, respectively, were observed between the original and scaled-up turbines. The close correlation between the non-dimensional performance curves indicates good scalability and Re independence for the scaled-up turbine. However, the turbine does not operate at its peak efficiency, which occurs at approximately λ = 4. Therefore, further research should be conducted under these conditions.

The streamwise velocity distribution and wake development behind the turbine in Cases 1 and 2 are shown in Fig. 7. A clear distinction exists between the wake profiles for the bathymetry and flatbed cases. The turbine in the real bathymetry case exhibited a smaller reverse-flow area compared to the flatbed case. The turbine receives an accelerated flow from the upstream hill, which induces a favorable pressure gradient. The flow was accelerated by up to 5.2% of the inlet velocity and was maintained over the ridge. Then, a reduction in flow velocity occurred, coinciding with the slope in bathymetry 7D downstream of the turbine. There is a vertical wake expansion towards the seabed and water surface owing to flow separation. This phenomenon is more pronounced near the end of the domain, where the largest depth exists, experiencing up to 8.6% reduction in flow velocity along the turbine axis and 15% velocity reduction at the deepest point of the domain.

Fig. 8 shows the streamwise velocity field over the horizontal plane at the turbine hub height. The contours in Case 3 show that the seabed topology causes high spatial variability in the average flow velocity, even without the turbine. The turbine in Case 1 operates in a complex mix of favorable and adverse pressure gradients that not only cause significant velocity distribution variations but also contribute to the wake meandering and shifting phenomena shown in Figs. 8 and 9. These effects can result in notable variations in the power output and loading on a tidal farm’s downstream turbines (Brugger et al., 2022). However, the turbine in Case 2 operates in a zero-pressure gradient and therefore experiences negligible wake-meandering and shifting effects. Furthermore, the seabed features caused faster vortex dissipation in Case 1 owing to the scattering of the vortex structures, as shown in Fig. 10. The streamwise vorticity magnitude distribution in the wake-recovery zone behind the turbine is illustrated in Fig. 11. As expected, stronger vortices were formed in the near-wake zone, followed by an initially faster dissipation. Case 1 exhibited 16.1% faster average vortex dissipation than Case 2, although comparatively stronger fluctuating vortices were observed in the far-wake zone. This could also have a negative effect on the downstream turbines in a tidal array; therefore, further research is required.

To analyze and quantify the wake recovery, the velocity deficit (U/U_o) was used in this study. This is defined as the non-dimensional ratio of the flow velocity at a downstream location U, to the inlet flow velocity U_o. The streamwise U/U_o vertical profiles are shown in Fig. 12. A 4.1% increase in the average wake recovery rate was observed over the elongated ridge-like seabed feature between 3D and 7D downstream of the turbine, where the flow was accelerated owing to the bathymetry-induced favorable pressure gradient (FPG). By contrast, the drastic slope in the bathymetry from 9D downstream of the turbine to the end of the domain caused a reduction in the average wake recovery of approximately 11.1% compared to the flatbed case. The seabed slope induces APGs that decelerate the flow. The profile for Case 3 shows that the flow was accelerated upstream of the turbine by the small hill feature and over the ridge-like feature. However, negative flow recovery was observed over the bathymetry slope, even without the turbine. Fig. 13 shows the mean pressure distribution over the vertical plane through the turbine axis. It can be observed that the wake of the turbine is subjected to varying pressure fields because of the seabed topology that induces FPGs and APGs, as indicated by the purple circles, which cause enhanced and slow wake-recovery phases, respectively.