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Analysis of unsteady flow effects on the Betz limit for flapping foil power generation

Published online by Cambridge University Press:  14 September 2020

John Young*
School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia
Fang-Bao Tian
School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia
Zhengliang Liu
Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Joseph C. S. Lai
School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia
Nima Nadim
School of Civil and Mechanical Engineering, Curtin University, Bentley, WA6102, Australia
Anthony D. Lucey
School of Civil and Mechanical Engineering, Curtin University, Bentley, WA6102, Australia
Email address for correspondence:


A control volume based analytical method for calculating the efficiency $\eta$ of flapping foil power generators was developed for single and tandem foil configurations. Ignoring unsteady effects and non-uniform pressures resulted in theoretical limits identical to the Betz ($\eta =16/27$ for a single turbine) and Newman ($\eta =16/25$ for tandem turbines) limits. Inclusion of unsteady flow and non-uniform pressure distributions produced theoretical efficiency maxima in excess of these limits. Simulation of single and tandem foil cases to determine the magnitude of these effects showed that the Betz limit would not be exceeded by a single foil system in practice, but that it is conceivable that a tandem foil system could exceed the Newman limit due to the strong unsteady vortex wake of the upstream turbine entraining additional energy into the path of the downstream turbine and maintaining pressures in the wake below ambient.

JFM Papers
© The Author(s), 2020. Published by Cambridge University Press

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