| In this research, 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 closed-form 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 and time domains. The complete velocity field above the disk is obtained in the frequency domain by this new methodology for axial and skewed flows, for various skew angles, and for different pressure distributions. These are compared with the Peters-He model and with an exact solution obtained by a convolution integral. In the time domain, the response to a step function is computed and compared with the exact solution for axial flow. |
