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Tidal stream turbines lend themselves to being placed closely together as shared infrastructure costs can be distributed amongst the devices. This has led to the development of various systems with turbines arranged in a fence formation (for example, Schottel-SME's Plat-i and Orbital Marine Power's O2). 

Close spacing between turbines can be used to realise a performance improvement through increased local blockage at reduced spacing \citep{Nishino2012}. However, flow diversion around the fence reduces the realistically achievable power compared to theoretical limits and affects, in particular, the outboard turbines within a fence. This fence-end effect results in a variation in power production and loading over the fence. The work presented in this thesis examines ways to reduce these losses and achieve more uniform power output and time-varying loading for all turbines along the fence. Two approaches are investigated in this work; a physical barrier in the form of a contoured turbine fence end-wall, and a yaw control strategy. In order to computationally examine the fluid mechanics of a turbine fence with yaw applied to end-turbines, a new rotor geometry and mesh structure is presented in this thesis. This turbine was designed at a scale to ensure fully turbulent flow over the entire blade permitting the $k-\omega$ SST RANS turbulence model to be used which facilitated computationally efficient multi-rotor blade resolved simulations.

%Two approaches are investigated in this work. The first places a physical barrier in the form of a turbine fence end-wall (which has a supplementary use as a buoyancy aid for a floating turbine) to provide a lateral constraint to flow expansion. The second examines a control method in which outboard turbine yaw adjustment is used to correct for flow diversion around the end of the fence. 

% The first approach presented in this thesis to reduce end effects investigated using a contoured turbine fence end-wall to improve the performance of a four-rotor turbine fence by realigning the flow to reduce end losses. A Reynolds-Averaged Navier-Stokes (RANS) model with an embedded blade element (BE) solver was used to investigate the variation of end losses with inter-turbine spacing. A range of turbine fence end-wall geometries were examined for turbines operating with an inter-turbine spacing of 0.25$D$, where $D$ is the turbine diameter. Numerical simulations demonstrated that overall fence performance could be increased by up to 3.95\% relative to the without end-wall case. This performance improvement coincided with a marginal reduction in mean thrust on the turbines, optimal tip-speed-ratio ($\lambda^*$), and basin efficiency (noting that the slight decrease in turbine thrust was offset by the additional thrust from the end-wall). The numerical results were compared to experiments performed in the towing tank at the SSPA facility in Sweden. This comparison showed that the RANS-BE model slightly over-estimated performance improvement due to the end-wall and highlighted some of the short comings of the numerical model.

The first approach presented in this thesis to reduce end effects used a contoured turbine fence end-wall to realign the flow normal to the turbine plane. A Reynolds-Averaged Navier-Stokes (RANS) model with an embedded blade element (BE) solver was used to investigate the variation of end losses with inter-turbine spacing. Numerical simulations demonstrated that use of an end-wall (at tip-to-wall spacing half the turbine tip-to-tip spacing of s=0.25$D$) could increase overall fence performance by up to 3.95\% relative to the without-end-wall case. This performance improvement coincided with a marginal reduction in mean thrust on the turbines, optimal tip-speed-ratio ($\lambda^*$), and basin efficiency (noting that the slight decrease in turbine thrust was more than offset by the additional thrust from the end-wall). The numerical results were compared to experiments performed in the towing tank at the SSPA facility in Sweden. This comparison showed that the RANS-BE model slightly over-estimated performance improvement due to the end-wall and highlighted some of the shortcomings of the numerical model.

The second approach used yaw control to improve the alignment of the outboard turbine to the skewed approach flow towards the ends of the fence. Blade resolved sliding-mesh simulations of a four-turbine long fence with counter-rotation about the fence centre-line, were used to adjust the yaw of the outboard turbine to align normal with the immediate inflow. The principal benefit of this was a significant reduction in unsteady, azimuthally varying blade root bending moment loads. A modest improvement in outboard turbine performance was also observed, however this was accompanied by a reduction in the performance of the inboard turbines (due to reduced lateral flow confinement) and thus had a minimal effect on total fence power.

The impact of differential turbine speed control was also investigated within the four-turbine fence with the outboard turbine aligned and yawed. Little improvement in overall fence power was found when optimising for this parameter with differential controls; however, when using the controls to balance thrust over each turbine, a reduction in thrust of 1.5\% was observed while maintaining the same power output from the synchronised operation case. When a 5$^\circ$ yaw of the outboard turbines towards the centre-line of the fence was introduced to this control strategy a similar operational condition was found with the added benefit of reducing the amplitude of the outboard turbine blade root bending moment by 49\%, bringing this loading cycle closer to that experienced by the inboard turbine. 

The use of these methods to compensate for end-losses have been shown to be effective in balancing the steady load and reducing the unsteady blade loading, with a comparatively small impact on power. Given the reduction in loading and balancing of fatigue along the fence this yaw control strategy may have the potential to contribute to reductions in the cost of energy from tidal stream systems.



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