A two-dimensional rotor inflow model developed in closed form from a galerkin approach

Finite-state wake models have proven themselves very useful for rotorcraft design. However, current theories have some remaining unanswered questions. In this paper, a complete two-dimensional rotor inflow model is developed for axial flow. The new theory includes previously unaccounted for inflow modes that are zero on the rotor disk but present otherwise. The theory is developed from a Galerkin approach using potential functions that correspond to both pressure and mass source terms. The new model is used to compute results for various frequencies and pressure distributions. These results are then compared to current theories and to an exact solution in the frequency domain found by a convolution integral. The new theory gives the exact solution at zero frequency, and the infinite inflow modes are well approximated by the finite expansion terms used in the theory. Results show that the new theory agrees with the exact solution. Errors associated with the old theory are presented for the entire frequency range.