DIRECT PERIODIC-SOLUTIONS OF ROTOR FREE WAKE CALCULATIONS

Periodic Inversion is a new approach for the calculation of rotor free wakes which solves directly for periodically steady-state solutions, at all advance ratios including low speed and hover. This is a unique capability as traditional time marching solutions can fail to converge at low advance ratios. The method is based on enforcing a periodic boundary condition on the wake over one rotor revolution. The resulting system of nonlinear equations is linearized, then iteratively solved for perturbative corrections to the wake geometry. The method is used to examine the low speed wake structure, which exhibits three distinct forms depending on advance ratio: a helical structure from hover to some lower bound advance ratio, a roll-up structure above some higher bound advance ratio, and a rapid transition region between the two. Performance curves are generated by varying trim parameters between iterations.