Upper limit for tidal power with lateral bypass

P. F. Pelz, M. Metzler, C. Schmitz, T. M. Müller
2020 Journal of Fluid Mechanics  
We derive the upper limit for power extraction from an open-channel flow with lateral bypass representing tidal power or run-of-river plants for the complete range of blockage σ , Froude number Fr 2 and turbine head H T . For this, a generic turbine model is used: a momentum and energy sink distributed over the geometric blocking σ of the channel allowing lateral bypass. It is indicated that existing models neglect important aspects of the free-surface deformation due to the energy extraction,
more » ... ielding unphysical behaviour at high blockage, high Froude number or high turbine head. The asymptotic validity of existing theories for σ → 0, Fr 2 → 0, H T → 0 becomes evident: firstly, by comparing existing theories with the presented general theory; and secondly, by the experimental validation of the existing and presented theories. The accompanying systematic experimental study comprises a wide range of blockage ratios, 0.25 σ 1.0, of downstream Froude numbers, 0.2 Fr 2 0.5, and of different turbine heads, H T , measured in multiples of the specific energy E 0 of the undisturbed flow. The subsequent model-based optimisation allows an indication of the optimal turbine head H T,opt /E 0 as well as the maximal obtainable coefficient of performance C P,opt as a function of σ and Fr 2 or downstream water depth h 2 /E 0 , respectively. The theory reveals points of operation in which there is a surge wave in the tailwater. The new physical insight and optimisation results may serve for plant design and operation, as well as for investment decisions.
doi:10.1017/jfm.2020.99 fatcat:a3qg4qnl5jffzbhp2hlbu3leuy