Extension of dynamic inflow models to include mass injection and off-disk flow

In this paper, the potential flow equations are converted to ordinary differential equations through a Galerkin approach in which velocity and pressure potential functions are expanded in terms of closedform solutions to Laplace's equation. Because the method gives differential equations for the flow in terms of a relatively few generalized coordinates (that represent modes of the flow field) the resultant equations can be used effectively in preliminary design, real-time simulations, and dynamic eigenvalue analysis for aeroelasticity. This new theory is more general than the Peters-He dynamic wake model since it has a more rigorous derivation and includes inflow modes previously neglected in the Peters-He model. Results are presented in the frequency domain for simple harmonic motion. The axial velocity components are obtained by this new methodology on and off the disk, for axial and skewed flows, and for different pressure distributions and are compared with the Peters-He model and with an exact solution obtained by a convolution integral.