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This paper presents an analytic model for the analysis of co-planar turbine fences that partially span the width of a channel in which the flow is driven by a sinusoidally oscillating driving head. The thrust presented by the turbines reduces the flow rate through the channel leading to a solution for overall power that is dependent upon turbine resistance and flow blockage as well as on channel characteristics. We introduce a return parameter, in terms of power per turbine area, to assess optimum turbine fence deployment for a given channel. We find that the optimal deployment rests on a universal curve independent of the channel characteristics, and that these characteristics – namely the integrated channel bed friction and a modified channel Froude number – move the optimum along this curve. We find that blockage considerations play a large role in the performance of a tidal farm – its achievable power, optimal return, channel flow rate reduction and device thrust – and that the scales of blockage must be considered even when designing relatively unblocked farms. The impact of the channel characteristics on the optimal arrangement, alongside environmental constraints that may limit permissible flow blockage, are quantified and discussed.

A key hydrodynamic difference between tidal current and wind turbines is the volume-flux constrained flow field in which tidal turbines operate and the resulting streamwise static pressure difference that develops in the flow passage. Blade Element Momentum (BEM) theory is extended to account analytically for the effects of blockage and the development of the static pressure difference in the flow passage and shows agreement in thrust and power predictions to within ± 3 % of equivalent blade resolved simulations. The confined flow BEM model is employed to study two different power capping strategies: varying the rotational speed with fixed pitch blades; and pitching the blades to feather at constant rotational speed. Pitch-to-feather achieves reduced thrust above rated flow speed which leads to a greater extractable resource than achievable with overspeed control, due to the feedback between device thrust and available tidal resource. Flow confinement is shown to reduce the flow speed at which rated power occurs, and increases the rotor loads and power below rated conditions. It is also shown that root bending moments, which affect fatigue damage rates, increase with flow confinement.

An embedded Reynolds-Averaged Navier-Stokes blade element actuator disk model is used to investigate the hydrodynamic design of tidal turbines and their performance in a closely spaced cross-stream fence. Turbines designed for confined flows are found to require a larger blade solidity ratio than current turbine design practices imply in order to maximise power. Generally, maximum power can be increased by operating turbines in more confined flows than they were designed for, although this also requires the turbines to operate at a higher rotational speed, which may increase the likelihood of cavitation inception. In-array turbine performance differs from that predicted from single turbine analyses, with cross-fence variation in power and thrust developing between the inboard and outboard turbines. As turbine thrust increases the cross-fence variation increases, as the interference effects between adjacent turbines strengthen as turbine thrust increases, but it is observed that cross-stream variation can be mitigated through strategies such as pitch-to-feather power control. It was found that overall fence performance was maximised by using turbines designed for moderately constrained (blocked) flows, with greater blockage than that based solely on fence geometry, but lower blockage than that based solely on the turbine and local flow passage geometry to balance the multi-scale flow phenomena around tidal fences.

An array of ten 1 MW turbines, with a one diameter inter-turbine spacing, is simulated in a hypothetical tidal channel using the depth-averaged flow solver TELEMAC-2D. It has been shown for idealised turbines that mean power extraction from tidal channels can be enhanced by tuning turbine resistance for a given channel. Blade element momentum theory is used to analyse turbine control strategies such as power capping, which can allow turbine operation to better match the dynamics of the underlying tidal resource. It is shown that choosing control strategies that limit array thrust helps sustain higher channel flow speeds, and hence can lead higher mean power production than other strategies. This has an impact on tidal farm size, where mean turbine power reduces as the number of turbines increases, due to the reducing flow rate in the channel. Adding turbines beyond the channel- and turbine-specific optimal chokes the flow, reducing overall farm power. To limit environmental impact it may be desirable to constrain the maximum flow-rate reduction. Under a 10% flow-rate reduction constraint, the lower thrust per turbine under pitch-to-feather control allows significantly more turbines to be installed and greater farm power than either pitch-to-stall or no power capping strategy.

An embedded Reynolds-Averaged Navier–Stokes blade element actuator disk model is used to investigate the performance of a closely spaced cross-stream fence of four turbines. The flow characteristics of such fences are found to be dependent on both the local turbine scale flow problem and the array in channel flow scale problem. The mean fence power is found to be less than that predicted for a single turbine with the same local blockage ratio (ratio of turbine swept area to surrounding flow passage area), but greater than that for a single turbine based on the global blockage ratio of the fence (ratio of total fence swept area to the cross-sectional area of the channel). Cross-fence variation in turbine performance is observed as a result of the differing resistance to bypass flow acceleration around the inboard and outboard turbines and depends on the operating condition of the turbines. Reducing turbine thrust, such as by changing the rotational speed of the turbine or by employing a pitch-to-feather power capping mechanism reduces turbine-turbine interactions and turbine performance becomes more uniform across the fence. An approximately 6% increase in the mean fence power can be achieved if a cross-fence differential blade pitch strategy is employed to maximise the lift to drag ratio along the majority of the blade span of each of the turbine blades.

The power available to a tidal stream turbine fence depends on the turbine resistance, the mass flux through the array, as well as the flow speed variation within the array. Depth-averaged simulations are often used to analyse the power available at a site, where the array is modelled as a region of enhanced flow resistance. Without special treatment this method can lead to errors when estimating the power available to the array as the simulated velocity at the turbine plane, and therefore the inferred power, is a spatially averaged value and does not capture flow speed variation within the array; true power being dependent on through-turbine velocity rather than array area-averaged velocity. Linear momentum theory is used to represent the turbines, which by equating the thrust of the numerically simulated array and the analytically modelled turbines enables the true power available to the array to be correctly evaluated. This power is shown to always be less than the erroneous power inferred from the simulated array area-averaged flow velocity. Array end effects, due to the skewed flow passing through the simulated turbine array region, are shown to be particularly important when estimating the power available to short and high-thrust arrays.

Commercially available wind yield assessment models rely on superposition of wakes calculated for isolated single turbines. These methods of wake simulation fail to account for emergent flow physics that may affect the behaviour of multiple turbines and their wakes and therefore wind farm yield predictions. In this paper wake-wake interaction is modelled computationally (CFD) and physically (in a hydraulic flume) to investigate physical causes of discrepancies between analytical modelling and simulations or measurements. Three effects, currently neglected in commercial models, are identified as being of importance: 1) when turbines are directly aligned, the combined wake is shortened relative to the single turbine wake; 2) when wakes are adjacent, each will be lengthened due to reduced mixing; and 3) the pressure field of downstream turbines can move and modify wakes flowing close to them.