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

A control volume based analytical method for calculating the efficiency η 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 (η =16/27 for a single turbine) and Newman (η =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.