Analysis and Validation of Glauert Rotor Design

The design of industrial wind turbine rotors is generally based on the blade-element/momentum (BEM) approach introduced by Glauert (1935). Essentially, the theory consists of combining a blade-element approach with axial momentum theory, and then introducing a tip correction to account for the finite number of rotor blades.

This is required, as the momentum theory is based on representing the rotor by a disk, corresponding to a rotor with infinitely many blades. The optimum design properties are obtained by optimizing the local power coefficient at each blade element. This is typically accomplished by solving a simple analytical system of equations for the axial and tangential inductions factors, ignoring at first the tip correction.

The tip correction is subsequently introduced to correct the design variables. In the present work we analyse the implications of including the tip correction directly in the optimization. As a result of the analysis, we find the somewhat surprising result that the maximum optimal interference factor is not 1/3, as normally encountered for optimum rotor design, but 2/5.

In the paper we prove this analytically and use the theory to design optimum rotors, which subsequently are benchmarked by comparison to results from a numerical lifting line model.