The efficiency of a turbine in a tidal channel

TLDR

Power extraction by tidal‑channel turbines is limited by an upper bound that is achieved only when turbines occupy the channel uniformly, yet such deployment can interfere with other uses, and the mixing of wake and free‑stream flows causes additional energy loss. For short channels, the free‑stream speed outside the turbine wake is governed by exit‑channel separation, influencing power extraction. Ideal turbine models show that fractional power loss rises from one‑third to two‑thirds as turbine coverage grows from zero to nearly full channel, and that in short‑channel scenarios the maximum power is only slightly less than proportional to the occupied cross‑section.

Abstract

There is an upper bound to the amount of power that can be generated by turbines in tidal channels as too many turbines merely block the flow. One condition for achievement of the upper bound is that the turbines are deployed uniformly across the channel, with all the flow through them, but this may interfere with other uses of the channel. An isolated turbine is more effective in a channel than in an unbounded flow, but the current downstream is non-uniform between the wake of the turbines and the free stream. Hence some energy is lost when these streams merge, as may occur in a long channel. We show here, for ideal turbine models, that the fractional power loss increases from 1/3 to 2/3 as the fraction of the channel cross-section spanned by the turbines increases from 0 to close to 1. In another scenario, possibly appropriate for a short channel, the speed of the free stream outside the turbine wake is controlled by separation at the channel exit. In this case, the maximum power obtainable is slightly less than proportional to the fraction of the channel cross-section occupied by turbines.