Bi-global Linear Stability Analysis of Laminar Separation Bubble for Helicopter Blade Section Undergoing Dynamic Stall

Helicopter blade dynamic stall is associated with the generation and shedding of large coherent flow structures. The dynamic stall vortex, which is the dominant structure, plays an important role in the non-linear lift and drag augmentation. For earlier dynamic stall blade section simulations, the dynamic stall vortex is initiated by the bursting of a leading edge laminar separation bubble which is followed by a shear layer roll-up. For these earlier simulations, the complex helicopter blade motion was decomposed into a harmonic pitching, surging, and yawing motion. A case with combined pitching and surging motion served as baseline case. For another case, an unsteady yawing motion was added for investigating the effect of harmonic cross-flow. Both cases capture a full dynamic stall cycle in accordance with the literature. For the latter case, the laminar separation bubble is shedding oblique structures and bursting sooner. A lower maximum lift coefficient can also be observed for the latter case. Simulations with improved grid resolution compared to the earlier simulations were performed to obtain additional confirmation for this behavior. A local linear stability investigation suggests that the laminar separation bubble is less unstable for the case with yawing motion compared to the baseline case. A bi-global stability analysis computer program was developed and validated for a case from the literature. The program was employed to analyze the stability of the laminar separation bubble. Similar to the local stability analysis, the bi-global stability analysis indicates a less unstable laminar separation bubble for the case with yawing motion.