Finite state induced flow models. II - Three-dimensional rotor disk

In Part I of this two-part article, we developed a finite state induced flow model for a two-dimensional airfoil. In this second part, we develop a finite state induced flow model for the three-dimensional induced flow for a rotor. The coefficients of this model are found in a compact closed form. Although the model does not presuppose anything about the source of lift on the rotating blades, applications are given in which the Prandtl assumption is invoked. That is, the two-dimensional lift equations are used at each radial station, but with the inflow from the three-dimensional model. The results are shown to reduce (in several special cases) to Prandtl-Goldstein theory, Theodorsen theory, Loewy theory, dynamic inflow, and blade-element momentum theory. Comparisons with vortex-filament models and with experimental data in hover and forward flight also show excellent correlation.