Tidal energy theory and turbine array design in constricted channels

Abstract

This thesis extends existing tidal energy theory to include the effects of channel constriction - previous general theoretical works have been limited to unconstricted rectangular channel geometries. This work uses a combination of 1-D and 2-D mathematical modelling to explore how channel constriction affects the upper-limits of tidal energy generation, how turbine arrays should be designed in constricted channels and how turbine arrays will affect constricted channels when they are operational. 1-D modelling is fast and efficient and is particularly suitable for performing a broad systematic study. However, flow in constricted channels is a multi-dimensional phenomenon. Thus, a 2-D depth-averaged model is adopted to examine how 2-D flow, more realistic geometries, and more realistic tidal forcing impact on the derived 1-D theory. A comparison is done between the 1-D and 2-D models. As the 1-D model used here is similar to models used to build the foundations of tidal energy theory for unconstricted channels, this comparison serves to validate findings in these works also.

Initial work treats turbines as an arbitrary amount of drag in a basic 1-D channel model, this drag is increased in a myriad of test channels with differing degrees of constriction. Both channels connecting two ocean bodies (regular channels), and channels connecting an ocean body to a lagoon or bay (lagoon channels) are tested. Findings show that for channels of similar size, more constriction in the channel results in less power available for extraction (channel potential). Faster flows in the constricted region result in greater energy loss to friction and less energy is available for electricity generation. Lagoon channels can be geometrically modified (by increasing/decreasing the degree of constriction) to increase channel potential. A simple approximation for channel potential in the literature is extended to constricted channels.

An analytical turbine model is then nested into the 1-D channel model. This allowed for a systematic exploration of array design in a myriad of channel geometries. Power generation was maximised by placing one row of turbines in the smallest cross-section and filling it to maximum blockage. Arrays built outside of the constriction can generate the same amount of power as arrays in the constriction but use more turbines. Using the power-to-force ratio as an economic indicator, building stronger turbines to withstand the forces of the constriction are worthwhile in terms of enhanced power generation. Results from the 2-D model showed that large amounts of kinetic energy are lost from constricted small channels in the constriction jet. In larger channels, the jet can mix in with the surrounding flow before the channel exit. Adding turbines dampens the jet by reducing flow through the channel, this allows more of this lost energy to be captured. Turbines were found to have an effect on the channel head difference driving flow. This was not accounted for in the 1-D model. When accounted for, the 1-D model showed good agreement for large channels. Agreement was within 40% for smaller channels but the 1-D model could not account for the kinetic energy loss in the jet.