Flap-lag damping in hover and forward flight with a three-dimensional wake

Prediction of lag damping is difficult owing to the delicate balance of drag, induced drag and Coriolis forces in the in-plane direction. Moreover, induced drag is sensitive to dynamic wake, both shed and trailing components, and thus its prediction requires adequate unsteady-wake representation. Accordingly, rigid-blade flap-lag equations are coupled with a three-dimensional finite-state wake model; three isolated rotor configurations with three, four and five blades are treated over a range of thrust levels, Lock numbers, lag frequencies and advance ratios. The investigation includes convergence characteristics of damping with respect to the number of radial shape functions and harmonics of the wake model for multiblade modes of low frequency (<1/rev.) to high frequency (>1/rev.). Predicted flap and lag damping levels are then compared with similar predictions with 1) rigid wake (no unsteady induced flow), 2) Loewy lift deficiency and 3) dynamic inflow. The coverage also includes correlations with the measured lag regressive-mode damping in hover and forward flight and comparisons with similar correlations with dynamic inflow. Lag-damping predictions with the dynamic wake model are consistently higher than the predictions with the dynamic inflow model; even for the low frequency lag regressive mode, the number of wake harmonics should at least be equal to twice the number of blades.