Abstract
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.
Highlights
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 Betz limit [1] expresses the currently accepted theoretical limit on the power conversion efficiency of fluid dynamic energy harvesting devices operating in unbounded flow
Modern wind and hydrokinetic energy conversion devices in nominally unbounded flow exhibit efficiencies below the Betz limit, tacitly supporting its veracity [2]. Fundamental to both the Betz limit and the design of typical fluid dynamic energy conversion devices is an assumption that the flow is nominally steady
Summary
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. Fundamental to both the Betz limit and the design of typical fluid dynamic energy conversion devices is an assumption that the flow is nominally steady. This steady flow assumption inextricably links the pressure and the velocity along streamlines upstream and downstream of the energy conversion device.
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