Non-normality and transient growth in stall flutter instability

Abstract

The non-normal nature and transient growth in amplitude and energy of a pitch-plunge aeroelastic system undergoing dynamic stall are explored in this paper through numerical and supporting experimental studies. Wind tunnel experiments, carried out for a canonical pitch-plunge aeroelastic system in a subsonic wind tunnel, show that the system undergoes stall flutter instability via a sub-critical Hopf bifurcation. The aeroelastic responses indicate a transient growth in amplitude and energy—possibly triggering the sub-criticality, which is critical from the purview of structural safety. The system also shows transient energy growth followed by decaying oscillation for certain initial conditions, whereas sustained limit cycle oscillations are encountered for other initial conditions at flow speeds lower than the critical speed. The triggering behavior observed in the wind tunnel experiments is understood better by resorting to study the numerical model of the nonlinear aeroelastic system. To that end, a modified semi-empirical Leishman–Beddoes dynamic stall model is adopted to represent the nonlinear aerodynamic loads of the pitch-plunge aeroelastic system. The underlying linear operator and its pseudospectral analysis indicate that the aeroelastic system is non-normal, causing amplification in amplitude and energy for a short period.