Non-normality and transient growth in stall flutter instability.

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.

Experimental investigation on the synchronization characteristics of a pitch-plunge aeroelastic system exhibiting stall flutter.

This study focuses on characterizing the bifurcation scenario and the underlying synchrony behavior in a nonlinear aeroelastic system under deterministic as well as stochastic inflow conditions. Wind tunnel experiments are carried out for a canonical pitch-plunge aeroelastic system subjected to dynamic stall conditions. The system is observed to undergo a subcritical Hopf bifurcation, giving way to large-amplitude limit cycle oscillations (LCOs) in the stall flutter regime under the deterministic flow conditions. At this condition, we observe intermittent phase synchronization between pitch and plunge modes near the fold point, whereas synchronization via phase trapping is observed near the Hopf point. Repeating the experiments under stochastic inflow conditions, we observe two different aeroelastic responses: low amplitude noise-induced random oscillations (NIROs) and high-amplitude random LCOs (RLCOs) during stall flutter. The present study shows asynchrony between pitch and plunge modes in the NIRO regime. At the onset of RLCOs, asynchrony persists even though the relative phase distribution changes. With further increase in the flow velocity, we observe intermittent phase synchronization in the flutter regime. To the best of the authors' knowledge, this is the first study reporting the experimental evidence of phase synchronization between pitch and plunge modes of an aeroelastic system, which is of great interest to the nonlinear dynamics community. Furthermore, given the ubiquitous presence of stall behavior and stochasticity in a variety of engineering systems, such as wind turbine blades, helicopter blades, and unmanned aerial vehicles, the present findings will be directly beneficial for the efficient design of futuristic aeroelastic systems.

Effect of parameter mismatch and dissipative coupling on amplitude death regime in a coupled nonlinear aeroelastic system.

Amplitude death (AD) has been recently identified as a phenomenon that can be exploited to stop unwanted large amplitude oscillations arising from instabilities in engineering systems. These oscillations are a consequence of the occurrence of dynamic instability, for example, the flutter instability, which results in the manifestation of sustained limit cycle oscillations. Recent studies have demonstrated amplitude death in coupled aeroelastic systems with identical parameters using suitable reactive coupling. Deriving impetus from the same, the dynamical signatures of coupled non-identical aeroelastic systems under a variety of coupling characteristics are investigated in the present study. The coupling characteristics between the individual airfoils here are assumed to possess both reactive and dissipative terms and are represented via a linear torsional spring and a damper, respectively. Explicit parameter mismatch is introduced via the use of different structural parameters such as frequency ratio and air-mass ratio for the individual airfoils. We demonstrate that a nonlinear coupled aeroelastic system with parameter mismatch and combined coupling characteristics gives rise to broader regimes of AD in aeroelastic systems. Specifically, the possibility of encountering large amplitude oscillations, usually found with pure reactive coupling can be avoided by adding a dissipative coupling term. On introducing dissipative coupling, the regime of AD was found to increase substantially, for both identical and non-identical scenarios, which in turn aids in serving as an effective tool to be developed further toward the application of flutter instability suppression.

Synchronization of pitch and plunge motions during intermittency route to aeroelastic flutter.

Interaction of fluid forces with flexible structures is often prone to dynamical instabilities, such as aeroelastic flutter. The onset of this instability is marked by sustained large amplitude oscillations and is detrimental to the structure's integrity. Therefore, investigating the possible physical mechanisms behind the onset of flutter instability has attracted considerable attention within the aeroelastic community. Recent studies have shown that in the presence of oncoming fluctuating flows, the onset of flutter instability is presaged by an intermediate regime of oscillations called intermittency. Further, based on the intensity of flow fluctuations and the relative time scales present in the flow, qualitatively different types of intermittency at different flow regimes have been reported hitherto. However, the coupled interaction between the pitch (torsion) and plunge (bending) modes during the transition to aeroelastic flutter has not been explored. With this, we demonstrate with a mathematical model that the onset of flutter instability under randomly fluctuating flows occurs via a mutual phase synchronization between the pitch and the plunge modes. We show that at very low values of mean flow speeds, the response is by and large noisy and, consequently, a phase asynchrony between the modes is present. Interestingly, during the regime of intermittency, we observe the coexistence of patches of synchronized periodic bursts interspersed amidst a state of desynchrony between the pitch and the plunge modes. On the other hand, at the onset of flutter, we observe a complete phase synchronization between the pitch and plunge modes. This study concludes by utilizing phase locking value as a quantitative measure to demarcate different states of synchronization in the aeroelastic response.