Chris Vogel

Doctor of Philosophy, Magdalen College, University of Oxford, Trinity Term 2014

Theoretical Limits to Tidal Stream Energy Extraction

Tidal stream energy has gained attention as a source of predictable and renewable energy. Devices resembling underwater wind turbines, placed in fast tidal streams, have been proposed to extract this energy. Arrays of many such devices will need to be deployed to deliver a significant amount of energy to the electricity grid. One
consequence of energy extraction is that the array provides a resistance to the tidal stream, which may change the local and far field hydrodynamics, which in turn affects the power available to the array. Array-scale hydrodynamic changes affect the flow presented to the devices, which in turn affects the total resistance the array provides to the flow. This thesis is concerned with the interactions between device, array, and the tidal stream resource, to better understand the power potential of turbine arrays.
Linear momentum actuator disc theory is employed to describe the operation of an idealised turbine array partially spanning a wide channel. The model is comprised of two quasi-independent sub-models, an array-scale model, describing flow phenomena around the array, which provides the upstream boundary condition to the device-scale model, describing the flow around a device. The thrust applied by the array is the sum of the thrust applied by the devices, completing the sub-model coupling.
The numerical simulation of arrays in depth-averaged simulations is then investigated using the two-scale concept developed in the analytic partial-array model. It is shown that the device-scale flow must be modelled with a sub-grid scale model in order to correctly describe the unresolved device-scale flow and hence estimate the power available to an idealised array. Turbulence modelling in depth-averaged simulations of turbine arrays is also discussed.
Temporal variations in tidal amplitude and strength mean that generator capacity will need to be economically matched to the available resource. As device performance may consequently depart from the relationship derived in idealised models when power capping is employed, blade element momentum theory is modified to parameterise tidal turbine performance during power capping. The array-scale effect of power capping is studied in depth-averaged simulations, in which it is shown that a significant reduction in device thrust may occur during power capping, reducing the impact of energy extraction from the tidal stream.

Thesis (4.88Mb, pdf)