Rui Vasconcellos

Airfoil control surface discontinuous nonlinearity experimental assessment and numerical model validation

A variety of dynamic behaviors that may be encountered in aeroelastic systems with discontinuous nonlinearities has motivated investigations that may support future applications in flight controls design, flutter prediction, instability characterization and energy harvesting. In this paper, the case of an airfoil with control surface freeplay is assessed experimentally and modeled numerically using an alternative continuous approximation for the discontinuous nonlinearity based on hyperbolic tangent function representation. The unsteady aerodynamic loads are computed using the modified unsteady Theodorsen approximation for arbitrary motions. The validity of the proposed freeplay representation is performed through comparison with experimental data. Adjustments to the pitching restoring moments have been carried out to account for a smooth polynomial concentrated nonlinearity. Data analysis is performed to characterize and investigate the experimental signals. Sub-critical bifurcation behavior is observed from both experimental data and the numerical model prediction. The results confirm the validity of hyperbolic tangent function combinations for freeplay nonlinearity representation for the experimental setup conditions.

Chaotic Patterns in Aeroelastic Signals

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincare sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincare mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

Nonlinear airfoil torsional response induced by separated flows

Stall-induced vibrations are nonlinear aeroelastic phenomena. Helicopter rotors, wind turbine blades, or other rotating components interacting with an airflow may vibrate in stall condition. Despite a significant effort to model the aerodynamics associated to the stall or separated flows, nonlinear aeroelastic behavior prediction and analysis in such flow regime remain a formidable challenge. Another source of nonlinearity with influence to aeroelastic response may be associated to the structure dynamic response. The combination of both separated flow aerodynamics and structural nonlinearities lead to complex dynamics, for instance, bifurcations and chaos. The purpose of this work is to present the analysis of stall-induced vibrations, or separated flow effects, of an airfoil in pitching when concentrated nonlinearities are associated to the structural dynamics. Limit cycles oscillations at higher angles of attack and complex nonlinear features are analyzed for different representations for concentrated restoring pitching moment. The pitching-only typical section dynamics is coupled with an unsteady aerodynamic model based on BeddoesLeishmann semi-empirical approach to produce the proper framework for gathering time series of aeroelastic responses. The analyses are performed by checking the amplitude of the aeroelastic responses in limit cycle oscillations. Evolutions on limit cycles amplitudes are used to reveal bifurcation points also admitting Mach numbers range up to 0.7, thereby providing important information to assess, characterize, and qualify the nonlinear behavior associated with combinations of different forms to represent concentrated pitching spring of the typical section. The concentrate structural nonlinearities under investigation are the hardening and softening cubic, free-play, and hysteresis. Results reinforce that oscillations under the effects of stall are mostly determined by the flow field. The structural nonlinearities are most relevant at lower airspeeds. Different bifurcations can be observed in Mach evolutions of LCOs, in which structural effects can be important to delay its onset.

PHENOMENA AND BIFURCATION ANALYSIS OF AN AEROELASTIC SYSTEM WITH IMPACT EFFECTS

Impacts can happen in real aircraft movable surfaces, such as ailerons, flaps, rudder, elevators, trim tabs among others secondary control surfaces leading to complex, dangerous and unpredictable transitions. In a real mechanism, impacts can occur when the surface displacement increases and then regions of higher stiffness or impacts can take place. Abrupt transitions from LCO to chaos and secondary complex transitions are directly related with the discontinuous nature of impact systems, these abrupt transitions caused by impacts are different from the well-known routes to chaos. In this work, numerical simulations generate the data basis for the analysis of a two degrees of freedom aeroelastic wing with a nonlinearity in the pitch stiffness simulating an impact at higher angles. The objective is to characterize the behavior of this system with parametric variation and understand the mechanisms related to the observed bifurcations.Copyright

On Grazing Bifurcations in an Aeroelastic System With Multi-Segmented Nonlinearity in the Pitch Degree of Freedom

A nonlinear characterization based on modern methods of nonlinear dynamics is performed to identify the effects of a multi-segmented nonlinearity on the response of an aeroelastic system. This system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The multi-segmented nonlinearity is associated with the pitch degree of freedom and contains two different boundaries. The results show that the presence of this multi-segmented nonlinearity results in the presence of a subcritical instability. It is also shown that there are four main transitions or sudden jumps in the system’s response when increasing the freestream velocity. It is demonstrated that the first and second sudden jumps are accompanied by the appearance and disappearance of quadratic nonlinearity induced by discontinuity and static positions. The results show that the first transition is due to a near grazing bifurcation that occurs near the first boundary of the multi-segmented nonlinearity. As for the second transition, it is demonstrated that the sudden jump at this transition is associated with a tangential contact between the trajectory and the first boundary of the multi-segmented nonlinearity and with a zero-pitch velocity incidence which is a characteristic of a grazing bifurcation. In the third and fourth transitions, it is demonstrated that there are changes in the response of the system from simply periodic to two periods having the main oscillating frequency and its superharmonic of order 3 and from chaotic to two periods having the main oscillating frequency and its superharmonic of order 3. Using modern methods of nonlinear dynamics, it is shown that this transition is due to a grazing bifurcation at the second boundary of the multi-segmented nonlinearity.Copyright