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Published February 2020 | Submitted + Published
Journal Article Open

Theoretical framework to surpass the Betz limit using unsteady fluid mechanics


The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through a notional actuator disk that is stationary in the streamwise direction. The present derivation relaxes the assumptions of steady flow and streamwise actuator disk stationarity, which expands the physically realizable parameter space of flow conditions upstream and downstream of the actuator disk. A key consequence of this generalization is the existence of unsteady motions that can, in principle, lead to energy conversion efficiencies that exceed the Betz limit not only transiently but also in time-averaged performance. Potential physical implementations of those unsteady motions are speculated.

Additional Information

© 2020 American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 9 October 2019; accepted 14 January 2020; published 5 February 2020) The author gratefully acknowledges helpful feedback from Robert Whittlesey, Daniel Araya, and Jifeng Peng.

Attached Files

Published - PhysRevFluids.5.022501.pdf

Submitted - 1912.12746.pdf


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August 19, 2023
October 19, 2023