Browsing by Author "Draper, S."

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    Flow through a very porous obstacle in a shallow channel
    (The Royal Society, 2017-04-26) Creed, M. J.; Draper, S.; Nishino, Takafumi; Borthwick, A. G. L.
    A theoretical model, informed by numerical simulations based on the shallow water equations, is developed to predict the flow passing through and around a uniform porous obstacle in a shallow channel, where background friction is important. This problem is relevant to a number of practical situations, including flow through aquatic vegetation, the performance of arrays of turbines in tidal channels and hydrodynamic forces on offshore structures. To demonstrate this relevance, the theoretical model is used to (i) reinterpret core flow velocities in existing laboratory-based data for an array of emergent cylinders in shallow water emulating aquatic vegetation and (ii) reassess the optimum arrangement of tidal turbines to generate power in a tidal channel. Comparison with laboratory-based data indicates a maximum obstacle resistance (or minimum porosity) for which the present theoretical model is valid. When the obstacle resistance is above this threshold the shallow water equations do not provide an adequate representation of the flow, and the theoretical model over-predicts the core flow passing through the obstacle. The second application of the model confirms that natural bed resistance increases the power extraction potential for a partial tidal fence in a shallow channel and alters the optimum arrangement of turbines within the fence.
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    Performance of an ideal turbine in an inviscid shear flow
    (Journal of Fluid Mechanics, 2016-04-28) Draper, S.; Nishino, Takafumi; Adcock, T. A. A.; Taylor, P. H.
    Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines.