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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 Open the ORCID record for John Young[Opens in a new window] ,
Fang-Bao Tian Open the ORCID record for Fang-Bao Tian[Opens in a new window] ,
Zhengliang Liu ,
Joseph C. S. Lai Open the ORCID record for Joseph C. S. Lai[Opens in a new window] ,
Nima Nadim  and
Anthony D. Lucey
John Young*
Affiliation:
School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia
Fang-Bao Tian
Affiliation:
School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia
Zhengliang Liu
Affiliation:
Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Joseph C. S. Lai
Affiliation:
School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia
Nima Nadim
Affiliation:
School of Civil and Mechanical Engineering, Curtin University, Bentley, WA6102, Australia
Anthony D. Lucey
Affiliation:
School of Civil and Mechanical Engineering, Curtin University, Bentley, WA6102, Australia
*
†Email address for correspondence: j.young@adfa.edu.au
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Abstract

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 classification

Mathematical Foundations: General fluid mechanics Wakes/Jets: Vortex streets Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A30
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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