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Energy Benefit in Tidal Power Schemes' by Helen Suckling Abstract Predictions of energy output from a barrage in the Severn Estuary can be made by using a mathematical model describing the operation of the barrage linked to one of tidal flow. Estimates of the likely energy production from such a barrage have been made using a flat surface model of the estuary which incorporates real machinery operating characteristics. The flow through the barrage can be controlled optimally in order to obtain the greatest amount of energy from the tides. The energy predictions made by using the flat surface model are examined using a hydrodynamic model of flow in the estuary. A simple one-dimensional hydrodynamic model of the tidal flow in the Severn Estuary is presented. The area of the estuary under consideration is that which lies between approximately Berkeley in Gloucestershire and 11 fracombe on the North Devon coast. The only open boundary is assumed to be the seaward boundary. No account is taken of flow into the estuary from rivers. Finite amplitude shallow water wave equations, together with a representation of bottom friction, are used to describe the tidal behaviour in the estuary. The crosssectional topography of the estuary is assumed to be a rectangle. The boundary conditions are that there is no flow through the landward boundary and the water level at the seaward boundary is a known function of time. The equations are solved numerically as a system of ordinary differential equations. A simple Runge-Kutta method is used. The mqdel is used to obtain predictions of the level and time of high and low tide at certain points along the estuary. The results are compared with those obtained by using another, but more complex, onedimensional model. In the region of computation, the accuracy of the results of the two models are comparable. The effect of varying both the coefficient of friction and the form of the friction term is examined. The effect of linearizing the governing equations is also studied. A model of a tidal power barrage, sited between Weston-super-Mare and Cardiff, is then incorporated into the hydrodynamic model. The operation 'of the barrage is determined by using an open loop control, obtained by using a flat surface model of the estuary. The extent to which hydrodynamic effects may modify the energy predictions made by the flat surface are examined. variation of the time at which generation is allowed to start is found to affect the amount of energy predicted by the hydrodynamic model. The costate equations, which are necessary for the solution of the optimal control problem are derived, but the solution of these equations is not presented

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This thesis presents a detailed investigation of the capability of a modern three-dimensional Navier-Stokes solver to predict the secondary flows and losses in a linear cascade of high turning turbine rotor blades. Three codes were initially tested, to permit selection of the best of the available numerical solvers for this case. This program was then tested in more detail. Results showed that although very accurate prediction of the effects of inviscid fluid mechanics is now possible, the Reynolds stress modelling can have profound effects upon the quality of the solutions obtained. Solutions using two different calculation meshes, have shown that the results are not significantly grid dependent. The flowfield of the cascade was traversed with hot-wires to obtain measurements of the turbulent Reynolds stresses. A turbulence generating grid was placed upstream of the cascade, to produce a more realistic inlet turbulence intensity. Results showed that regions of high turbulent kinetic energy are associated with regions of high total pressure loss. Calculation of eddy viscosities from the Reynolds stresses showed that downstream of the -cascade the eddy viscosity is fairly isotropic. Evaluation of terms in the kinetic energy equation, also indicated that both the normal and shear Reynolds stresses are important as loss producing mechanisms in the downstream flow. The experimental Reynolds stresses have been compared with those calculated from the eddy viscosity and velocity fields of Navier-Stokes predictions using a mixing length turbulence model, a one equation model, and K - ϵ model. It was found that in the separated, shear flows, agreement was poor, although the K - ϵ model performed best. Further experimental work is suggested to obtain data with which to determine the accuracy of the models within the blade and endwall boundary layers.