\chapter{Conclusions and future work}\label{Final_conclusions}

Section \ref{CH7:Conclusions} summarises the conclusions made in this thesis, primarily from the analysis in Chapters \ref{Chapter3}, \ref{Chapter4}, \ref{Chapter5} and \ref{Chapter6}. Suggestions for future work are made in Section \ref{CH7:FW} and a summary of the contribution of this work in the tidal stream energy research space is made in \ref{CH7:Contribution}.

\section{Conclusions}\label{CH7:Conclusions}

%purpose
% As an emerging form of renewable energy, there is pressure on tidal device designers to improve cost efficiency by reducing the levelized cost of energy. This is achieved through the development of more efficient and robust designs and control strategies. In the case of a turbine fence one such method to address these criteria is to reduce the end-loss towards the edges of a fence. 

Methods to improve turbine performance by reducing turbine fence end-losses have been investigated in this thesis. End-losses are a reduction in power and an increase in unsteady blade loading for the outer turbines within a fence due to anisotropic blockage conditions (flow expansion constraint from adjacent turbine on the inboard side, no constraint on the outboard side). This loss, and potential mitigation methods have been examined in this thesis for short turbine fences. 

% summary of work
The work presented in this thesis has discussed the impact of lateral confinement on short tidal turbine fences through both a physical barrier (end-wall) and turbine fence controls (yaw). Both of these methodologies act to reduce the flow component in the cross-stream direction. 

% End losses
End-losses were investigated using a RANS-BE model with gradually decreasing inter-turbine spacing. As expected greater end-losses were observed under higher local blockage conditions. Greater power can theoretically be produced by closely-spaced tidal turbines, and it is more likely to be preferred by manufacturers as a closer packed fence has the potential to reduce device costs. For this reason, the minimum practical spacing of $s=0.25D$ was used in this study for the investigation of end-loss mitigation strategies. 

% Summary of findings for end-wall
\subsection{End-wall}
Both numerical and experimental investigations of a turbine fence end-wall were conducted. The end-wall geometry was designed using a parametric design process which added camber and thickness to an elliptical cross-section. RANS-BE modelling suggested that the best performing geometry gave a 3.95\% improvement in turbine fence $C_p$ and a modest reduction in $C_t$ (0.67\%) due to the reduced $\lambda^*$ the turbine operated at when accompanied by the end-wall. The introduction of additional infrastructure reduced the overall efficiency with which power was extracted (basin efficiency) due to parasitic drag from the end-wall (0.9\% reduction). Given the improvement in $C_p$ further analysis was carried out with physical experimentation in a towing tank facility. 

Towing tank test were conducted at SSPA in Gothenburg, Sweden using two 1.2 m diameter turbines close to the side of the tank which acted as a symmetry plane to emulate a fence of four rotors. The turbine fence end-wall, shaped out of marine grade plywood using a CNC router to match the geometry from the numerical study, was placed at half the inter-turbine spacing (0.125D) away from the end of the fence. The results from the experiment did not show as strong support for the use of an end-wall as the numerical model with a 1.5\% improvement in outboard turbine $C_p$ (5.6\% in numerical study) and a 0.8\% decrease in inboard turbine performance (2.4\% increase in the numerical study). The cause for this discrepancy was due to the limitations of both the experiment and RANS-BE models. The noisy data in the experiment made it difficult to determine the optimal turbine operating point and the use of the tank sidewall was not a perfect symmetry plane. This is due to a speed differential between the sidewall and water which occurs as a result of the thrust from the turbines and leads to the formation of a boundary layer. Nevertheless the end-wall was shown to improve the overall fence power and reduce the amplitude of root bending moment loads on turbine blades. It was also suggested that the use of an end-wall may have an additional purpose as a buoyancy aid for floating devices. 

% Turbine Design
\subsection{Turbine design}
Comparing experimental and RANS-BE results of the four turbine fence demonstrated some limitations in model accuracy when analysing closely-spaced turbine fences. Predictions of turbine power and thrust were up to 21.3\% and 6.1\% off respectively, when compared to experimental data. The cause of this is, in part, due to the cross-stream forces which help to squeeze and accelerate bypass flow between closely spaced turbines. The RANS-BE formulation assumes azimuthal flow symmetry over the rotor swept area and no radial flow components; assumptions which are not met within a closely spaced turbine fence. Consequentially a higher order model is required with less restrictive assumptions to further analyse closely spaced turbines and end-losses. A blade-resolved sliding-mesh RANS model was adopted for further study of these systems. While resolving the turbine geometry is possible with the mesh, it is not practical to resolve the near-wall region, and an appropriate turbulence model is needed ($k-\omega$ SST). The existing turbine design used in the end-wall study was not suited to this model due to transitional flow which was present over the blade. To model this, a more complex four equation turbulence model with higher near-wall resolution is required; this model was prohibitively computationally expensive to use for this study. Instead, lateral constraint was further analysed using a newly designed turbine of 8 m diameter ($\lambda^*=4.5$). This design ensured fully turbulent flow over the blades. 

The design for an 8 m diameter turbine was carried out for operating conditions informed by Strangford Lough (a potential site for tidal stream energy extraction) using the RANS-BE method of \cite{McIntosh2011} . A modification to this method was made to facilitate the interpolation across 2D aerofoil data with respect to turbulence intensity, Reynolds number and trailing edge thickness. This method allowed rapid prototyping of designs without the need to continually generate 2D aerofoil data for the flow conditions. For this design study, operation close to the surface posed a cavitation risk. This was mitigated through the implementation of a conservative operating condition based on an adjustment to \cite{Wimshurst2018}. This specified the highest $\lambda$ where cavitation is likely to be avoided ($\lambda=4.5$) and was used as the design speed of the turbine.

Blade resolved simulations compared both structured and semi-structured meshes in 120$^\circ$ wedge MRF and sliding mesh simulations. It was found that both mesh schemes produced roughly equivalent results with the semi-structured having a smaller run-time and requiring less user input in the meshing process. As a result, the semi-structured mesh was used for further analysis. This analysis included an investigation into the tip shape of the turbine, comparing between a rounded and flat tip. It was found that a flat tip offered better performance than a rounded tip as the rounded tip encouraged equalisation of pressure between the pressure and suction surfaces through greater tip loss. This design and mesh was used in the yawed turbine simulations.  

% Summary of Findings for yaw control
\subsection{Yaw controls}

The use of yaw adjustment on the outermost turbine within a four turbine long fence was investigated using an unsteady sliding-mesh RANS simulation. The action of yawing the outboard turbine slightly improved its power generation up to an angle of 2.5$^\circ$ however this came at a cost of inboard turbine power as the adjustment of turbine position reduced the lateral confinement on the inboard turbines. Similarly, yawing the outer turbine away from the centerline of the fence improved the inboard turbine's performance and reduced the outboard turbine's performance; this result was consistent whether the turbines were co-rotating or counter-rotating. The results highlight the balance between flow alignment and flow confinement which needs to be struck to efficiently operate a turbine fence. 

Despite the optimal power being generated when the rotors were all aligned normal to the free-stream flow, unsteady loading on the outer turbine was shown to be a reason a turbine operator may wish to adjust the yaw angle. Due to the end-loss effect, a cross-stream flow component is present on the turbine which induces a blade advancing and retreating effect. It was shown that by adjusting the outboard turbine yaw angle to 2.5$^\circ$, the flow was better aligned and the unsteady loading component was reduced to less than inner turbine's fluctuations (reduction of 47.5\%). 

Yaw adjustments in conjunction with differential speed controls were combined into a operation strategy to balance loading and reduce load amplitude along the fence. It was demonstrated that a fence with its outboard turbines yawed at 5$^\circ$ would experience a reduction in fence power of 0.3\% (relative to optimal operation of the fence using synchronised control) alongside a 1.5\% reduction in thrust. This condition coincided with even thrust on the turbines and reduced the loading amplitude of root bending moment on the outer turbine from 50\% higher than the inboard turbine to 25\% lower.

\section{Future work}\label{CH7:FW}

The work undertaken in this thesis has shown that closely spaced turbines can have both positive and negative impacts on performance and loading. While this work has presented two different methods which improve the power output or the reduce the amplitude of unsteady loading cycles experienced by the rotor, additional exploration of flow confinement may further improve turbine fence design. Specifically, investigations of the vertical position of the turbine in the water column and the effect that it has on loading would provide additional insights for improved power generation. Similar to the end turbine within a fence, asymmetric flow confinement conditions are present above and below a turbine (close to the water surface or sea floor). The way in which this positioning affects power and loading may suggest additional operational adjustments such as a pitch control.  

The work in this study has focused on idealised uniform flow conditions. An important next step in transferring this work into real world designs is evaluating it under more realistic flow conditions; this would include a shear profile and waves. Given the improvement on the uniform-steady flow cases, some improvement is expected as the turbine will be better aligned to the mean flow condition. This suggests that on average a perturbation, such as a wave, will have a smaller impact as the flow misalignment on the blade. Yawing a turbine with respect to a wave may also reduce peak loading as the wave does not propagate through the rotor at once. 

Incorporating the findings on outer turbine yaw from this thesis into a practical design would require scale testing prior to implementation. This could take the form of a towing tank test (similar to the sidewall analysis). An ensemble of tests at different yaw angles could be compared to the blade resolved CFD results to validate the observations from the model. Further to this, realistic design conditions (such as waves) should also be tested.

\section{Contribution of work}\label{CH7:Contribution}

\subsection{RANS-BE modelling of turbine fences}
A comparison between RANS-BE and experimental results showed that the RANS-BE method is not sufficient for accurately resolving the key physics at play for closely spaced turbines due to a violation of both the no span-wise flow assumption and azimuthal asymmetry. This is due to an interplay between adjacent turbines which impose lateral forces on the flow as it diverts around the rotor. Consequentially, this type of model is not expected to accurately simulate the improvement in performance due to local blockage. This study also highlighted the complexities of towing tank testing, in particular using the tank sidewall as a symmetry plane. In reality the sidewall is not a true symmetry plane as the thrust from the turbine induces a small boundary layer in the vicinity around the turbine, reducing the turbine performance when positioned close to the wall. 

\subsection{Development of new turbine geometry for fence scale simulation}
A new rotor design and computational mesh has been purpose built and calibrated for turbine fence simulations. This design was created to ensure fully turbulent flow over the blades (permitting the use of the $k-\omega$ SST turbulence model) and targeted a reduced cell count in regions where detail is not required using an semi-structured mesh. This design is a computationally efficient and detailed model which can be used to explore the operational parameter space within a turbine fence and may be useful in future detailed operational studies. 

\subsection{Turbine fence end-loss load correction}
This study has furthered the understanding of turbine fence end-losses through the use of blade resolved simulations. These simulations have demonstrated that an effect, similar to the blade advancing and retreating effect for yawed flows, is present on the outer turbines within closely spaced turbine fences. Through the implementation of a yaw correction or a turbine fence end-wall this effect can be controlled for, leading to reduced load disparity between turbines and amplitude of the blade root bending moments.

\subsection{Papers and planned publications}

Work from the initial turbine fence end-wall experimentation has already been published in \cite{Ettema2020}, with contributions of this work earning a co-authorship in \cite{McNaughton2020} and paper currently under review as second author \citep{McNaughton2021}. Two additional first author papers are currently being interally reviewed with the intension to publish soon. These are \textit{Investigations into short tidal turbine fence performance with the inclusion of an end-wall} and \textit{Hydrodynamic yaw control within a tidal turbine fence}.
