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Title: Mathematical modelling and optimisation of Venturi-enhanced hydropower
Author: Benham, Graham P.
ISNI:       0000 0004 7430 6192
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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In this thesis we study a novel type of hydropower generation which uses a Venturi contraction to amplify the pressure drop across a turbine, allow- ing for cost-effective hydropower generation in situations where the head drop is small, such as in rivers and weirs. The efficiency is sensitive to how the secondary flow, which passes through the turbine, mixes with the accelerated primary flow, which is diverted around the turbine, within the confines of a closed geometry. In particular, it is important to understand the behaviour of the turbulent shear layers between the primary and sec- ondary flows, which grow downstream, mixing the flows together. The behaviour of the shear layers in the expanding part of the Venturi con- traction is strongly dependent on the shape of the channel. An important consequence of the channel shape, and hence the flow behaviour, is the degree of pressure amplification across the turbine, which determines the amount of generated power. We focus on mathematically modelling the mixing of the flows in turbu- lent shear layers, and we investigate two different ways to increase pres- sure amplification: optimising the shape of the channel, and using swirl to enhance mixing. The channel shape optimisation reveals an interest- ing balance between the effects of mixing and wall drag. Wide channel expansion tends to accentuate non-uniform flow, causing poor pressure amplification, whilst shallow expansion creates enhanced wall drag, which is also detrimental to pressure amplification. We show how the maximum power is generated with a channel shape that strikes a balance between these two effects. We find that swirl enhances mixing by increasing shear layer growth rates, but it produces large pressure losses in doing so, and for large amounts of swirl a slowly recirculating region can form along the channel centreline. Whilst swirl does not improve efficiency, there may be some inevitable swirl present in the flow, and we show how this affects the optimum channel shape. We also establish the criteria for the existence of such a recirculation region so that it may be avoided.
Supervisor: Hewitt, Ian ; Please, Colin Sponsor: VerdErg Renewable Energy
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Applied mathematics ; Fluid mechanics ; Mathematical modelling ; Optimisation ; Optimal control