Contributions to the mathematical modeling of rotor flow fields using a pseudo-implicit free-wake analysis

A pseudo-implicit predictor-corrector relaxation algorithm with five-point central differencing in space has been developed for the numerical solution of the non-linear partial differential equations that govern the helicopter rotor free-wake problem. The scheme is used to predict the locations of the vortices trailed by the rotor blades in hover and forward flight, and to predict the rotor induced velocity field. The work presented has been toward the development of a robust and versatile free-wake scheme that can be potentially used on a routine basis and incorporated into comprehensive rotor analyses.;Numerical convergence, stability, and accuracy characteristics of the methodology are discussed in detail. The pseudo-implicit numerical scheme is compared with more conventional explicit-type free-wake algorithms to demonstrate its enhanced stability and convergence trends. The method is shown to approach a grid-independent wake solution for increasing discretization resolutions, and converges to a unique solution. The use of artificial tuning parameters has also been eliminated from the formulation, resulting in a scheme that is significantly more robust and versatile than existing methods. The method is also extended to investigate the flow field structures of tandem, side-by-side and coaxial rotor configurations.;The method is applied to examine rotor wake geometries for a wide variety of geometric rotor configurations and flight conditions, including variations in advance ratio, rotor thrust, number of blades and rotor shaft angles. Comparisons between predictions and experiment are made for wake geometries, wake boundaries, rotor induced inflow distributions and flow field velocities, to help validate the predictive capabilities of the new method. The overall agreement between the predictions and experiment are demonstrated to be good.