Theoretical framework to surpass the Betz limit using unsteady fluid mechanics

TL;DR

This paper introduces a theoretical framework that relaxes steady flow assumptions, suggesting that unsteady fluid motions can potentially surpass the Betz limit in energy extraction efficiency.

Contribution

It extends the Betz limit derivation by incorporating unsteady flow dynamics, broadening the conditions under which higher energy conversion efficiencies are theoretically possible.

Findings

Unsteady motions can lead to efficiencies exceeding the Betz limit.

The generalized framework allows for transient and time-averaged efficiency improvements.

Physical implementations of unsteady flows are hypothesized.

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.