Dynamic Wake Solutions for Rotors That Are Powered, Braking, or In Transition

The nonlinear dynamic equation for rotor induced-velocity applies to powered rotors, energy-extracting rotors, and the transition between. This inflow equation (verified by experimental data) yields interesting dynamic behavior due to the attractors, repellers, and branch cuts in the dynamic coefficient. The present paper offers some closedform results for the nonlinear system in axial flow (along with accompanying numerical solutions) that give insight into the behavior of the dynamic wake in all system regimes. The closed-form solutions also offer good benchmark cases against which to compare large-scale simulation codes. In addition, the paper offers numerical solutions in skewed flow and with an empirical vortex-ring correction.