Direct periodic solutions of rotor free wake calculations by inversion of a linear periodic system
Periodic Inversion is a new approach for the calculation of rotor free wakes which guarantees periodically steady-state solutions, and provides the means to solve for wake dynamics at all advance ratios including low speed and hover. The method is based on enforcing periodic boundary conditions over 1/B of a rotor revolution, where B is the number of blades. This is accomplished by defining a new set of wake variables with periodic behavior, and writing the governing equations in a linear perturbation form. The method is used to examine the low speed wake structure, which exhibits three unique 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. Extensions of the method to allow coupling of the wake dynamics with panel methods and rotor dynamics are discussed, as are eigenvalue stability analysis and local element refinement.
