Numerical analysis of Reynolds and Mach number effect on dynamic stall onset

The onset of dynamic stall limits the maximum airspeed of helicopters. For Reynolds numbers where laminar separation precedes transition, the bursting of a leading edge laminar separation bubble can initiate dynamic stall. Using large-eddy simulations, the effect of Reynolds and Mach number on bubble bursting is investigated for the National Advisory Committee for Aeronautics (NACA) 0012 wing section that is undergoing a harmonic pitching motion. Time histories of the lift and moment coefficient as well as the skin-friction and wall-pressure coefficient are compared for chord-based Reynolds numbers of 100 000, 200 000, and 400 000 and Mach numbers of 0.1 and 0.4. With increasing Reynolds number, the bubble size prior to bursting is diminished. For the larger Mach number, the bubble is larger and bursts earlier. To understand the observed behavior, spanwise and phase-averaged flow fields just prior to bubble bursting for Re = 100 000 are analyzed with a compressible biglobal stability computer program. The biglobal analysis reveals dominant two-dimensional modes for M = 0.1 and M = 0.4. For the higher Mach number, the growth rates are reduced, which explains the longer bubble. Observed oblique waves in the laminar separation bubble for M = 0.4 may result from the resonance of three-dimensional waves with two-dimensional shear layer waves.