Net Mass Flow Components in a Three-Dimensional Unsteady Rotor Inflow Model

Abstract

Potential flow equations are converted to ordinary differential equations by the Galerkin approach in which velocity and pressure potential functions are expanded in terms of closed-form solutions to Laplace’s Equation. The reduced number of generalized coordinates in a Galerkin approach gives advantages in real-time simulations, preliminary design, and dynamic eigenvalue analysis for aeroelasticity. Net mass injection from rotor sources is expected to occur in some situations, but cannot be treated by previous models. It is included in the present formulation. In this paper, frequency response due to pressure distributions corresponding to net mass flow in both axial and skew-angle flight are given. These results are compared with exact solutions obtained by the approach of a convolution integral. A brief analysis is also included with respect to numerical simulations of the Associated Legendre Functions, in which it demonstrates that net mass flow components are extremely sensitive to the recursive process of seeking Associated Legendre Functions.