Thesis: Scott Draper

Doctor of Philosophy, St Catherine's College, University of Oxford, Trinity Term 2011

Tidal Stream Energy Extraction in Coastal Basins

In recent years the extraction of energy from tidal streams has grown in popularity as a potential source of clean renewable energy. To extract this energy, tidal devices, resembling underwater turbines or hydroplanes, are deployed in a fast moving tidal stream. However, an important consequence is that the devices then act as a resistance to the tidal stream, which can inuence local and far eld natural tidal hydrodynamics and ultimately the power potential. This thesis is concerned with modelling idealised tidal stream devices deployed in a number of generic coastal basins, or sites, to better understand these effects on natural tidal ows and the potential to generate power.

Firstly, to describe the operation of an ideal tidal stream device Linear Momentum Actuator Disc Theory (LMADT) is applied to a porous disk placed in a steady uniform tidal stream of nite Froude number. A device eciency is derived, which is dened as the power available to the device relative to the total power removed, or extracted, from the tidal stream including downstream mixing losses in the immediate wake of the devices.

A line sink of momentum is then proposed to represent a fence, or row, of ideal tidal devices in a 2D depth-averaged shallow water tidal ow. It is suggested that LMADT can be used to dene this momentum sink in terms of the local Froude number, the spacing and size of devices, denoted by a blockage ratio, and the porosity of the devices. Implementation of the line sink of momentum into a numerical solution of the Shallow Water Equations (SWEs) using the Discontinuous Galerkin (DG) nite element method is outlined.

Extraction of energy from tidal channels, oscillating bays and an idealised coastal headland are analysed numerically and analytically using the proposed line sink of momentum. In general a maximum amount of energy extraction is calculated because the ow through the turbine fence reduces as the resistance of the fence increases. For each coastal geometry this maximum is not related in any simple way to the natural rate of energy dissipation due to bed friction or the undisturbed kinetic ux (despite the fact that both of these metrics have been used in the past to predict power extraction). The available power to devices within a tidal fence is maximised if large and closely packed turbines are adopted. Moreover, unless devices within the fence are perfectly ecient the maximum available power does not generally coincide with maximum power extraction.

For tidal channels and enclosed oscillating bays energy extraction tends to reduce tidal currents and tidal range, which may have environmental implications. In contrast energy extraction is found to increase tidal range in non-enclosed oscillating bays that are longer than a natural resonant length. Energy extraction is also found to augment tidal dispersion around coastal headlands.

A survey of real coastal sites and details of a numerical code, developed in this thesis to solve the SWEs to arbitrary spatial order of accuracy using the DG nite element method, are given in Appendices.