Universal Energy Extraction Limit in Open-Channel Flow

Main result:
Maximum theoretical efficiency in free-surface flow occurs at
Froude number Fr ≈ 0.3094
with an energy extraction limit of
η ≈ 34.52%.

Background

During the development of a free-flow micro-hydropower concept, a fundamental question arose: how much energy can actually be extracted from an open-channel flow?

In wind energy, the well-known Betz limit defines the theoretical maximum amount of energy that can be extracted from the wind. However, for free-surface hydraulic flows without dams, such a universal limit had not been clearly formulated.

Main idea

This work analyzes the energy balance of open-channel flow with energy extraction. By minimizing the specific energy of the downstream section, an optimal regime is obtained.

The analysis leads to a universal optimum at:

This result plays a role analogous to the Betz limit in wind energy, but for open-channel hydrodynamic systems.

Full paper

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Diagram

Energy extraction diagram

Keywords

open-channel flow, Froude number, hydropower, hydrokinetic energy, free-flow turbines, energy extraction limit