Generalized limits for energy extraction in a linear constant velocity flow field



The Lanchester–Betz limit has long been established as setting an upper bound on the power performance coefficient of an energy extraction device operating in isolation in a linear constant velocity flow field. However, the ideal limiting performance of energy extraction devices operating in conjunction with ducts, diffusers or any systems that further modify inflow local to the plane associated with energy extraction has not been previously established.

The present analysis derives the limiting performance in such cases, with the Lanchester–Betz limit emerging as the special case of energy extraction in open flow. The key to this analysis is the characterization of an ideal system in terms of the axial induction that would exist at the plane of energy extraction in the absence of the energy extraction system. The concept of an ‘ideal system’ as one that matches the flow field in every state of loading of the energy extraction device is also crucial.

Computational Fluid Dynamics (CFD) analysis of a system with a diffuser provides preliminary validation of the new theory. Generalization of the standard blade element theory is outlined, and the implications for the development of a rationalized design approach and optimization of a system with a rotor operating in a diffuser are addressed.

The theory has obvious applicability to systems that are purposefully designed to augment flow, but a wider relevance to wind technology in situations where terrain or other wind turbines modify the flow field is also suggested. Copyright © 2008 John Wiley & Sons, Ltd.