LAUSR

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 $\unicode[STIX]{x1D70E}$, 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 $\unicode[STIX]{x1D70E}$ 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, yielding unphysical behaviour at high blockage, high Froude number or high turbine head. The asymptotic validity of existing theories for $\unicode[STIX]{x1D70E}\rightarrow 0$, $Fr_{2}\rightarrow 0$, $H_{T}\rightarrow 0$ 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, $0.25\leqslant \unicode[STIX]{x1D70E}\leqslant 1.0$, of downstream Froude numbers, $0.2\leqslant Fr_{2}\leqslant 0.5$, 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 $\unicode[STIX]{x1D70E}$ 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.