The generation of electricity from elevated water sources has been the subject of much scientific research over the last century. Typically, in order to produce cost-effective energy, hydropower stations require large flow rates of water across large pressure drops. Although there are many low head sites around the UK, including numerous river weirs and potential tidal sites, the pursuit of low head hydropower is often avoided because it is uneconomic. Thus the UK, and other relatively flat countries miss out on hydropower due to the lack of sufficient elevated water sources.

In his DPhil project, Oxford Mathematician Graham Benham, has been studying a novel type of low head hydropower generation which uses the Venturi effect to amplify the pressure drop across a turbine. The Venturi effect is similar to a mechanical gearing system. Instead of a turbine dealing with the full flow and a low head, it deals with a reduced flow and an amplified head, thereby allowing for much cheaper electricity. However, the hydropower efficiency depends on how the turbine wake mixes together with the main pipe flow – that is the key to understanding the mixing process.

Mixing occurs in a thin turbulent region of fluid called a shear layer, or a mixing layer. In their recently published research, Oxford Mathematicians Graham Benham, Ian Hewitt and Colin Please, as well as Oxford physicist Alfonso Castrejon-Pita, present a simple mathematical model for the development of such shear layers inside a pipe. The model is based on the assumption that the flow can be divided into a number of thin regions, and this agrees well with both laboratory experiments and computational turbulence modelling. Specifically the model is used to solve a shape optimisation problem, which enables the design of the Venturi to produce the maximum amount of electricity from low head hydropower.

The image above shows the assembly of VerdErg's Venturi-Enhanced Turbine Technology (VETT). VerdErg is a British renewable energy company that has patented VETT. The image was taken from Innovate UK.

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