\doublespacing

% CV comments --

% I suggest that you treat the first chapter as a short, high level introduction to tidal energy extraction, and mention that you might want to deploy turbines in fences, and then chapter 2 is where you go into detail about performance variations, reviewing previous work, solutions people have proposed etc
% --

\chapter{Introduction}\label{Introduction}

% This chapter provides an introduction into the research by first providing an overview of the tidal energy resource in section \ref{cs:tidal_resource}, following this a overview of the current state of the art tidal energy converters is introduced in section \ref{cs:Tide_range_devices}. Finally a overview of the thesis is outlined in section \ref{cs:thesis_overview}.


\section{The tidal energy resource}\label{cs:tidal_resource}

Tidal energy is the energy associated with tidal motion. Typically this is extracted using mechanical devices, such as turbines or barrages, with greater energy extracted in regions with larger tidal ranges or high velocity tidal currents. For the United Kingdom there are several potential regions for tidal energy extraction with tidal ranges in some parts exceeding 14 m \citep{Baker1991TidalPower}.


\section{Methods of energy extraction}

There are two classes of devices used to extract tidal energy, tidal range devices and tidal stream devices, the latter being split into horizontal axis turbines (HATs) and vertical axis turbines (VATs). The work in this thesis focuses on HATs; however, for completeness, both tidal range and VATs devices are briefly discussed in this section. 


\subsection{Tidal range devices}\label{cs:Tide_range_devices}

Tidal range devices extract energy by exploiting a head difference induced by a barrier (such as a dam or a barrage) which artificially shifts the tidal phase on either side \citep{Neill2018}. The barrier is operated to discharge water during either the ebbing, flooding or a combination of both phases of the tide \citep{Burrows2009} and energy is extracted as the flow passes through turbines in the barrier. The energy produced using this method is proportional to the square of the water level difference on either side of the barrage \citep{Baker1991TidalPower,Neill2018}. As a result, regions with large tidal ranges are well suited to this type of device, such as the Severn Estuary, which has a 14 m tidal range \citep{Xia2010}. 

The Severn Estuary has been the subject of multiple studies \citep{Sathiamoorthy1994,Ahmadian2010,Xia2010} investigating tidal range devices owing to the significant potential for energy production (an estimated 17 TWh per year \citep{Xia2010}); and has been subject to several unsuccessful proposals to install tidal range devices dating back to 1920 \citep{Waters2016}. Despite the interest in the development of Severn Estuary, there are currently no tidal range devices installed due to two main challenges faced by this device type; environmental impacts and high development costs \citep{Rourke2010b,Frid2012,Waters2016}. This is a consequence of the significant change in the coastal hydrodynamics which can result from barrages. 


\subsection{Tidal stream devices}

Tidal stream devices extract kinetic energy from the flow in a similar manner to wind turbines \citep{Rourke2010b}. Like wind energy the power output is proportional to the cube of the inflow velocity focusing site selection on regions of fast currents. There are several challenges unique to tidal which are not present in wind owing to a disparity in fluid density and inflow speeds; these influence the loading and turbine geometry \citep{King2009}. The density of water is approximately 832 times greater than air improving energy density \citep{Rourke2010a}; however, smaller turbine diameter (80 - 90 m for wind compared to 8 - 20 m for tidal) \citep{Rourke2010b,Veers2003} and lower inflow speeds (7.5 - 10 m/s for wind and 2 - 3.5 m/s for tidal) \citep{Lu2017} means that the thrust of tidal and wind rotors are similar in magnitude. There are, however, some larger modern wind turbines that experience significantly higher thrusts \citep{NESFircroft2021TheWorld}. Tidal stream devices are also capable of significantly impacting the flow speed, and therefore performance, through effects associated with flow resistance and confinement; this is discussed in Chapter \ref{Chapter2}.


There are two classes of tidal stream devices, HATs; where the rotor spins about the axis parallel to the flow direction, and VATs; where the rotor spins about an axis perpendicular to the flow direction  \citep{Rourke2010b,Khan2009}. While some VAT concepts have been developed and prototyped \citep{AtlantisStrom2004,BlueEnergy2010,ORPC2019}, the dominant form of tidal stream devices appears to be HATs \citep{Siemens2015,AndritzHydro2016,SIMECAtlantisEnergy2019,OrbitalMarinePower2019}. This can, in part, credited to the extensive knowledge base of HATs from conventional wind turbines. 

\section{Support structure}

There is a significant variation in the support structures designed for tidal stream energy devices due to the complexities of installation, maintenance, geographic and hydrodynamic conditions \citep{King2009}. Broadly speaking there are two classes of support systems for tidal turbines; floating and fixed. Fixed systems are rigidly attached to the bed through support structures; such as monopiles, which are commonly used in the wind industry \citep{Arshad2013}. This type of support structure has been used in the design and installation of the SeaGen tidal rotor \citep{Siemens2015}. Despite its success and well established position in offshore wind there are limits to the depths that this support system can be used owing to increased cost with depth of installation. This is due to the bed conditions, which are more commonly scoured rock at tidal stream locations, and limited duration for access due to strong currents making it difficult for installation.

In contrast floating tidal devices may be more suitable for deep water applications where attaching a structure rigidly to the bed is cost prohibitive. This support structure type has been implemented by Orbital Marine in their O2 and SR2000 turbines \citep{OrbitalMarinePower2019} as well as by Sustainable Marine Energy in the PLAT-I and PLAT-O array types \citep{SME}. Floating tidal devices also provide the additional benefit of operating in the upper region of the water column where the currents are typically higher; this positioning also allows easier access for maintenance. Operating the turbine near the surface of the water column does risk cavitation due to the lower pressure and care must be taken when defining the operation conditions to limit this risk by restricting the operating point to a certain range \citep{Wimshurst2018}. Furthermore, floating structures and the turbines they support also experience higher wave loading, with the action of the waves causing fluctuations in velocity through the turbine. Additional challenges for floating tidal devices include platform loading and the connection to the electricity grid as the floating mooring lines require flexible electric connections \citep{Brown2001}.


\section{Tidal turbine fences}

One appealing feature of HATs over tidal range devices is the device modularity allowing additional power generation by placing more turbines in the flow. The flexibility of device placement calls to question how best to arrange tidal turbines. Work by \cite{Draper2014} suggested turbines placed in a fence formation (a single row of turbines) produced greater power than a staggered array of turbines (two rows of turbines staggered such that down-stream turbines are not in the shadow of up-stream turbines). Work performed numerically \citep{Schluntz2015,Vogel2017} and experimentally \citep{Cooke2016,McNaughton2019} has confirmed that turbines in fence formation achieve enhanced power due to the channel blockage effect (discussed in Section \ref{Ch2_Blockage}). However, as \cite{Cooke2016} showed, this performance improvement is not evenly distributed along the fence due to the diversion of inflow around the ends of the turbine fence (end losses). 

Tidal fence devices are growing in popularity with manufactures producing several prototypes including the SR2000 \citep{OrbitalMarinePower2019} and PLAT-I \citep{SME}. These devices indicate a push toward using shared infrastructure between turbines with the turbine mounted to floating support structure. This allows the turbines to achieve a performance improvement from the close proximity in the fence formation and reduces the cost as infrastructure is shared. 

\section{Thesis outline}\label{cs:thesis_overview}

This research aims to further the understanding of turbine fence end losses through CFD simulation and physical testing. In particular, this work focuses on:
\begin{enumerate}
    \item Establishing performance variation along short turbine fences
    \item Determining the azimuthal variation in blade loads between the inboard and outboard turbines
    \item Evaluating potential methods to mitigate loading and power imbalances along short turbine fences though:
    \begin{enumerate}
        \item The addition of an end-wall
        \item Yaw adjustment of outboard turbines
    \end{enumerate}
\end{enumerate}

\noindent An overview of turbine performance and relevant literature is presented in Chapter \ref{Chapter2}, and methods for numerical modelling of turbines are presented in Chapter \ref{CH3:Model_turb}. The design of a turbine fence end-wall (Chapter \ref{Chapter3}) and testing (Chapter \ref{Chapter4}) is examined. Chapter \ref{Chapter5} presents a design of a turbine of sufficient geometric scale to ensure fully turbulent flow over the entire blade tidal turbine which facilitates the detailed modelling of a yaw control strategy in Chapter \ref{Chapter6}. Finally, a summary of the finding from this thesis is made in the conclusions chapter (Chapter \ref{Final_conclusions}).




% This will then lead into your thesis outline, which sets out different ways that you might correct for such effects.



% Tidal stream energy extraction technology has fallen out of favour in recent years, partly due to the high cost of prototyping devices and complexities surrounding the resource. Whilst a promising resource with regards to energy density, a dominate technologies has yet to emerge as the most effective for energy extraction. In turn this has seen a limited number of detailed trials of new technologies undertaken the prototype scale. This section presents the technical challenges associated with the design of tidal energy extraction devices as well as the motivation for using this technology. 


% \subsection{Tidal Energy's Future Role}\label{Tidal Energy's Future Role}
% A finding from the International Energy Outlook 2017  \cite{U.S.Energy2017International2017} determined that a growth in global energy demand of 28\% is expected between 2015 and 2040. The same report also predicts the renewable energy sector to be the fastest growing averaging 2.8\% growth/year due to government incentives for sustainable technology. The effect of combined growth and pressure on the renewable energy sector to meet this demand means that there is room for emerging technologies, such as tidal stream turbines, to be developed.

% With regards to meeting the projected future demand for energy, the United Kingdom is well suited to capitalise on tidal stream generation from multiple sites around the coastline of Great Britain. Figure \ref{Figure 1.1} highlights this by illustrating the M2 (principal lunar semi-diurnal) tidal constituent for current amplitude and phase around the British Isles similar to that of Neill \cite{Neill2016TidalPhasing} with the data being sourced from the TOPEX Poseidon global tide data set \cite{Egbert2002EfficientTides}. As can be observed from Figure 1a, there are various location where strong tidal currents of up to 2m/s exist. The 2011 Carbon Trust report UK Tidal Current Resource \& Economics suggested that an average power density of 1.5kW/m2 be used as a low end cut off for site selection. The below equation can be rearranged to determine the velocity at which this criteria is satisfied. 

% \begin{equation}\label{eq1_1}
% \centering 
% P_{average} = \frac{1}{2} \rho A \frac{\int_{0}^{T}{\left | U_{M2}\sin{g_{M2}t} \right |} ^{3} dt}{T}
% \end{equation}


% Where $P_{average}$ is the average power output of a tidal cycle of length $T$, $\rho$ is the fluid density which, in the case of ocean water, is approximately 1024kg/m3, $A$ is the turbine cross-section area, $U_{M2}$ is the amplitude of the semi-major M2 current constituent. The expression can be simplified by averaging using $\int_{0}^{2\pi}{{\left | sin{x} \right |} ^{3} dx}=8/3$.

% \begin{equation}\label{eq1_2}
% \centering 
% P_{average}=\frac{1}{2} \rho A U_{M2}^3\frac{4}{3\pi}
% \end{equation}


%  \begin{figure}[!htb]
%         \center{\includegraphics[width=\textwidth]
%         {Figures/Chapter_1/1_1_M2_amplitude_and_phase.png}
%         \caption{\label{Figure 1.1} M2 tidal current amplitude (a) and phase (b) in the ocean surrounding the Great Britain (a) is a plot of the semi-major axis of the M2 tidal current ellipse and (b) is the phase lag in hours $\frac{T_{M2}\left | \sin{g_{u}}  \right |}{4}$ where $T_{M2}$ is the period of the M2 constituent (12.42 hours) and $g_{u}$ is the tidal current phase. Data sourced from the TPOX tide database \cite{Egbert2002EfficientTides}}}
% \end{figure}

% This yields a M2 tidal current constituent of greater than 0.89 m/s to achieve the minimum power output. Looking again at \ref{Figure 1.1} we see that much of the coastline far exceeds this low end criteria. 

% \subsection{Technical challenges in tidal energy}\label{Technical challenges in tidal energy}

% Broadly speaking there are three classes of problems which affect the design and performance of tidal stream technologies. These being uncertainty with regards to the design loading/resource density, the arrangement of tidal turbines and the design of individual devices. These cover regional, array and individual turbine length scales respectively. This section will give a brief overview of technical problems and current literature at these three length scales and attempt to draw parallels with the wind industry (a similar technology).

% \subsubsection{Regional/Resource Scale} \label{Regional/Resource Scale}

% With respect to power generation tidal turbines have the advantage that the energy produced from the system can be easily predicted due to the cyclic nature of the tide. This is a key advantage that tidal energy has over wind and solar where weather patterns complicate the predictability of the resource. The predictable nature of the tide means that the resource can be more precisely managed to meet anticipated demand in conjunction with complementary energy sources. 

% Despite the high certainty on the predictability of power output from tidal turbines, factors unique to the oceanic environment provide design challenges to engineers which need to be managed. 

% \begin{itemize}
%   \item Wave loading
%   \item Cavitation on blades
%   \item Storms and extreme weather events
%   \item Footings eroding
% \end{itemize}

% The above considerations are not unique to tidal turbines and accordingly there are statistical methods and guidelines to define design conditions to address and ensure they are adequately designed for. 

% Separate to the above factors, unique problems to tidal turbines emerge when investigating the efficiency and downstream wake effects of an array. Simplified methods using linear momentum actuator disc theory (LMADT) employed by Garrett \& Cummins \cite{GARRETT2007TheChannel} have provided estimates of the amount of power output which is possible to be extracted by a tidal turbine. A key finding from this paper is that the well-established Betz limit of 59.3\%; which describes the maximum amount of kinetic energy which can be extracted from an unbound incompressible flow \cite{Betz2013TheMotor}, does not apply to tidal streams. Instead, blockage ($B$) of the channel increases the theoretical limit by a factor of ${1-B}^{-2}$, where $B$ is the ratio of turbine swept area to channel cross section. An extension of this work was undertaken by Nishino \& Willden \cite{}(2012) who analysed an array of turbines using a scale separation approach and determined that inter-turbine spacing governed an upper limit to the efficiency which could be extracted from the system. This limit was determined to be approximately 0.798.  This is discussed further in Chapter \ref{Chapter2}. 


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  At the resource scale consideration has to be given not only to the turbine design but the overarching environmental impact. Whilst there is the objective to extract maximum power, care must be taken to minimise the disturbance to natural coastal possesses. This is achieved through regional scale numerical simulations taking into account key environmental details such as bathymetry, tide, atmospherics and regional ocean circulation patterns. Due to the significant difference in turbulent length scales between the turbines and basin, a sub-grid scale approach is often adopted to simulate the regional effects. A simplified model using LMADT is presented in Houlsby et al. (2008). This model has been used by Draper et al. (2010), Serhandhoglu, S. (2014) and Bonar et al. (2018) in 2D basin scale simulations with favourable comparisons to Nishino & Willden (2012). These larger scale simulations, run with the simplified sub-grid scale model, allow for computationally efficient assessments to be undertaken. This is useful when determine environmental impacts at a scoping level phase of a project where impacts on currents, sedimentation and the tidal prism may alter the site selection. 

%  The tools discussed above provide valuable insights at the regional scale fluid dynamics however, problems emerge when attempting to refine designs due to the simplifying assumptions in LMADT and the lack of experimentally collected data. For this reason more refined methods which analyse the problem at smaller length scales are typically used to determine array scale efficiency. 

% \subsubsection{Array Scale} \label{Array Scale}

% Pertinent to the design of the optimal energy extraction system is the arrangement of the tidal turbine array. Placement of turbines with respect to bathymetry and each other can be used to improve efficiency of the device though the exploitation of the blockage effect. By contrast a poorly arranged turbine array can result in the loss of efficiency, an example of this may be to place a turbine in the wake of another resulting in decreased performance. The question of how best to arrange turbines in an array is currently an active area of research due to the complex flow patterns and various degrees of freedom in this problem. Work completed by Nishino & Willden (2012) showed that for a channel of infinite width the efficiency of the turbine array depends only on the local blockage (ratio between a single device area and the local passage cross-sectional area). The result from this simplified model implies that significant efficiency gains can be obtained with the correct array lay out. Factors to be considered when analysing the layout of an array of turbines include:

% \begin{enumerate}
%     \item Channel geometry. As discussed in Garrett & Cummins (2007) and Nishino & Willden (2012), appropriate channel selection leads to an increase in performance due to the blockage effect.
%     \item Inter-turbine spacing. As discussed appropriate inter-turbine spacing is essential for extracting maximum power out of the flow field.  Vogel & Willden (2017) looked at maximising performance from tidal turbine fences for both global and local blockages. They achieved this by looking at single turbine arrays designed for a global blockage and investigated how they performed in an array with varied separation between them. The outcome of this research suggested that designing individual turbines for higher global blockage conditions was advantageous when turbines were placed in an array together.
%     \item Placement of downstream turbines. Wake recovery downstream of turbines is a very active area of research especially in the wind industry where various methods exist to predict the performance of a wind farm. Whilst possible to explicitly model the downstream flow field of an array of turbines, simplifications are often made to expedite the computationally intensive process. Gunn et al. (2016) reviewed various methods for predicting wake superposition models and determined that the all the methods used neglected important aspects of flow physics, particularly in the case of offset turbines.
% \end{enumerate}

% Further to the above point’s operational constraints also factor into how the array performs. Varying blade diameter, tip speed ratio (TSR) and even blade pitch on the revolution 

% The method for simulating the flow physics at the array scale typically involves blade element momentum (BEM) theory. This is a useful tool which makes simplification to the turbine being modelled to be able to obtain quick estimates of performance at the array scale. BEM tends to be considered a more accurate method of determining turbine performance over LMADT. Chen (2018) presented a discrepancy of up to 25\% when comparing the two models for a tidal turbine application. BEM will be discussed in detail in chapter 2 of this thesis. 

% \subsubsection{Device Scale} \label{Device Scale}

% Significant variation exists when considering the design of tidal energy extraction devices. This is in part due to the limited amount of testing which has been undertaken at device scales. One such project which tested a device of commercial scale is ReDAPT [ref]. This project manufactured a buoyant 1MW tidal generator and measured the power output as well as flow field data. This project saw a comprehensive publicly available data set be generated for the operation of this turbine.
% % [https://www.eti.co.uk/programmes/marine/redapt]

% \paragraph{Turbine}

% The design and operation of a tidal turbine is a multi-parameter problem with many unconstrained degrees of freedom. The design problem starts with the selection of a blade profile. 
% Selection of this profile involves weighted consideration of not only the lift to drag ratio of the blade at the design pitch but also the range of velocities over which it will be operating over. Typically for wind turbines blade section is varied over the length of the blade [ref] with careful consideration being given to the selection chosen in the [30-70\%] radius length range [ref] as this is the primary power producing location [ref]. 
% Complementary to the section is the way in which blade chord length and twist angle is varied along the length of the section. These parameters are typically designed using blade element momentum theory [ref] to adjust the blade twist the optimal angle to optimise lift to drag ratio and adjust the chord length to meet a target local thrust coefficient. The value for this coefficient is typically fairly constant for tidal turbines in the range of ~3 [ref].
% Alongside the geometry parameterization of the turbine, the operational strategy of the turbine can be altered to improve and manage performance. Some common strategies adopted in practise with wind turbines are pitch and feather as well as pitch and stall approaches [ref]. These methodologies adjust the blade twist angle to reduce thrust on the blades during high flow conditions. Additionally control over the rate at which the turbine spins (tip speed ratio) is also an operational parameter which needs to be designed for. Tip speed ratio is an important determinate in aerofoil selection [ref] as blade speed impacts on aerodynamic performance of the cross section. 
% The importance of the tip speed ratio to the choice of aerofoil (discussed in the first paragraph of this section) highlights the nonlinear nature of the design process for tidal and wind turbines. In order to achieve optimal performance an iterative design loop needs to be established which points towards the solution of optimal turbine performance given the design criteria. 


% \paragraph{Support Structure}
% Various options for support structure exist for tidal turbines. As yet, given the immaturity of the industry, no predominate support structure technology has emerged as the dominate option. The recent REDAPT project [ref] employed a floating support structure which was capable of swinging around with the tide. The choice of floating support structure is advantageous given that typically, stronger currents exist at the top of the water column; hence greater power generation potential is possible. This support structure design is not without its flaws as turbines blades operating near the surface of the water column are at higher risk of cavitation given the low pressure conditions near the surface. Careful consideration must be given to the design tip speed ratio when operating in these conditions.
% Another option for the primary turbine support structure is a fixed or bed mounted system. A typical example of this being monopoles for offshore wind turbines. This system, whist robust and well established, lends itself to being highly loaded if the turbines are suspended too far from the base of the support and also has . [ref] 
% Complementary to the primary function of supporting the turbine array, the support structure can be used to provide ducting to the turbine array. [ref –conor Flemming] Ducting in tidal turbines acts to increase the power production of a tidal turbine by accelerating the flows which passes into the turbine. This increased velocity and power output is at the cost of the overall basin efficiency of the system. Careful thought must be given when designing ducting for a tidal turbine array to accurately determine the downstream turbine conditions and the impacts of the efficiency of these turbines. 


% \section{Tidal turbine blockage}

% Tidal turbine blockage works to improve efficiency of a turbine by making use of nearby hard boundaries. Unlike open flow fields (such as wind) tidal channels are bounded by banks. The effects of these banks means that the flow field simply cant expand around it the turbine without doing work. The basic physics describing blockage is as follows: 
% \begin{enumerate}
%     \item Flux through turbine induced wake of slow-moving fluid downstream
%     \item Outside this wake and between the walls of the channel flow must therefore accelerate to maintain continuity (negligible drop in water level compared to its depth)
%     \item Because of this additional work the fluid has to do the path of least resistance for a high portion of incoming fluid ends up being through the turbine. This leads to greater efficiency.
% \end{enumerate}

% \subsection{Types of blockage}
% Blockage can happen over two different length scales within a channel. The first is the way described above, this is known as a global blockage where the fluid is interacting with the side walls. 
% The second type of blockage is referred to a local blockage. This type of blockage comes from the wakes of multiple turbines in a cross section interacting with each other. This effect in the local domain is analogous to the wall method in the global domain however instead of walls there is turbulent wakes from adjacent turbines interacting. 

% \subsection{Implications for design}
% The feedback loop between rotor design and blockage is non-linear. This is to say that the specific rotor design selected will have a different turbulent wake profile which effects the amount of blockage. This goes on to affect the flux through the turbine which has implications of the turbulent wake… full circle. For this reason, designing to optimize power output though maximizing power output is not well understood [ref]. 

% \subsection{Suport Structure}
% Support structures are designed provide structural support for turbines whilst reducing the net drag force on the structure (parasitic drag).  Due to this drag, support structures have a significant effect on the overall basin efficiency of the system.

% \subsection{Basin Efficiency}
% Basin efficiency is the ratio of the total power generated to the total power removed. The power removed includes wake re-mixing. Sometimes if turbines are placed in series it can work out more efficient to place the turbines in series with lower power output but higher basin efficiency. Typically maximizing power output from the system will result in running turbines below optimal performance. Blocking the channel more increases the basin efficiency, this is because the relationship between core and bypass flows do not scale evenly as blockage increases. This means that as blockage increases, the difference between the core and bypass flow are closer meaning there is less energy required to mix the flow. It is important to also not that higher flow speed through the system will maximize turbine efficiency. 


% \section{Ducted Turbines}

% Ducts can be placed on turbines to ensure flow is passing through the turbine as designed this also has the added effect of improving the operational efficiency of the turbine by channeling more flow through it. There are two flow regimes which ducted turbines operate in:
% \begin{enumerate}
%     \item Nozzle contoured flow
%     \item Separation dominated flow
% \end{enumerate}

 
% The higher thrust production is the latter of the two regimes. The reason for this is due to the localized blockage effect that happens in the separation case due to the separation around the outside edges of the duct. Whilst ducts may improve the power output for a given turbine cross section, when normalized for the intake area the power output for ducted turbines is low than their non-ducted counter parts. There is also the added disadvantage of increased parasitic drag (and hence basin efficiency) due to the duct structure. 
% Parameters critical to the design of ducting systems are the length and angle of the duct and diffuser. Shallow angles should be preference to limit the size of the pressure jump and separation of the boundary layer inside the duct. Boundary layer control slots can be placed on the downstream side of the duct to allow the boundary layer to become re-energized.
