Cylindrical vortex wake model: right cylinder

The vortex system consisting of a bound vortex disk, a root vortex and a vortex cylinder as introduced by Joukowski in 1912 is further studied in this paper. This system can be used for simple modeling of rotors (e.g. wind turbines) with infinite number of blades and finite tip-speed ratios. For each vortex element, the velocity components in all directions and in the entire domain are computed analytically in a novel approach.

In particular, the velocity field from the vortex actuator disk is derived for the first time. The induction from the entire vortex system is studied and is seen to recall results from 1D momentum theory. It is shown that a superposition of concentric cylindrical systems predicts the independence of annuli, which is assumed in blade element theory and stream-tube analyses.

A simple example of application for the estimation of the velocity deficit upstream of a wind turbine is provided. Copyright © 2014 John Wiley & Sons, Ltd.