Beating Betz: Energy Extraction Limits in a Constrained Flow Field

Abstract

Experiments with diffusers and other flow concentrating devices have shown that the power performance coefficient Cp of an energy extraction device, defined in relation to the area of flow intercepted at the device, may exceed the Betz limit. “Beating Betz,” in that sense, has been long established but no theory has existed to define in a generalized way what ideal limit may apply to Cp in such situations. Recent analysis has resolved this. This indicates that, irrespective of the presence of flow concentration systems or other influences that perturb the flow but do not in themselves extract energy, there is a universal ideal limit of energy extraction. This is found to be 89 of the upstream kinetic energy in the streamtube associated with the energy extraction. Moreover, the familiar Betz equations for power and thrust coefficients can be generalized in a simple way to express this. Although this work has been developed in the context of wind energy, it will be apparent that the results are of general significance for any application of ducted rotors or propellers in a fluid stream.