The Effect of Wake Dynamics on Rotor Elastic Flap-lag Damping in Hover and Forward Flight

This paper describes the formulation and validation of a three-dimensional rotor blade-wake coupled system in both hover and forward flight conditions. The matrix form of elastic flap-lag coupling inflow differential equations is derived in order to determine unsteady inflow effect on aerodynamic damping. For this eigen-analysis, the blade-wake coupled system is represented by a set of periodic-coefficient differential equations. Results indicate that three-dimensional effects are more important for flapping dynamics than for inplane dynamics. For a four-bladed rotor, the two-dimensional inflow theory is most accurate near the bending stiffnesses that result in integer-multiple elastic frequencies (0,4,8), for which shed vorticity dominates, in contrast to other stiffnesses where wake layering does not occur (and for which three-dimensional trailing vorticity dominates). In forward flight applications, the induced flow still has a profound effect on blade dynamics even at high advance ratios. The effect may cause an earlier unstable condition for a helicopter rotor system.