Tidal turbines convert the energy of a flowing tide to generate electricity. Early designs of these machines commonly ha

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Tidal turbines convert the energy of a flowing tide to generateelectricity. Early designs of these machines commonly had theirrotor attached to a supporting tower mounted on the seabed – seefor example Figure QC2.1. A representation of a tide-driven flow ofwater past a tidal turbine is sketched in Figure QC2.2. Anexpansion of the flow from d1 to d2 is imagined to occur over therotor, with half of the expansion (in area) happening upstream ofthe rotor, and half downstream.
(a) Explain why the active part of the inflow (the streamtubeshown in FigureQC2.2) expands its cross-section as it passes theturbine. (2)
Analysis for the analogous situation of a wind turbine withuniform inflow, attributed to Albert Betz and others in the 1920s,demonstrated that for optimum efficiency of energy extraction fromthe inflow, the far upstream flow speed should be reduced by theturbine such that the far downstream speed is 1/3rd of the farupstream speed.
(b) Suggest three reasons why this theoretical maximumefficiency will in generalnot be achieved in a practical tidal turbinedeployment. (3)
(c) The Alstom 1.4 MW OceadeTM turbine has a rotor diameter of18 m. Thesupporting tower has a height of 15 m and a diameter of 3 m. In a 3ms-1 tidalflow, estimate the total fluid loading experienced by the wholemachine. Stateand justify the assumptions that you make in arriving at thisestimate. (12)
(d) How would you expect to use these estimates of forces whendesigning theturbine and tower structure?