Dynamical Behavior of Unsteady Flowfield of an Elastically Mounted Flapping Airfoil

Transition to chaos in the flow-induced vibration of a pitching–plunging airfoil at low Reynolds numbers: Ruelle–Takens–Newhouse scenario

Abstract: This study focuses on numerically analyzing the transition from periodic to chaotic dynamics in the fluid-elastic response of a 2-dof flexibly-mounted airfoil with chord-wise rigidity. The computational framework is composed of a high fidelity Navier–Stokes solver, weakly coupled with a structural model having geometric nonlinearity represented by cubic order stiffness terms. A low Reynolds number flow regime and a very low structure-to-fluid added mass ratio have been considered to simulate the flying conditions of very light-weight unmanned devices. A bifurcation analysis of the system, in the absence of actuation or control forces, is undertaken with the wind velocity as the control parameter. The route to chaos – identified to be the Ruelle–Takens–Newhouse quasi-periodic route – is established for the first time for a flexible pitch–plunge flapping system. Robust nonlinear time series analysis techniques have been implemented to characterize different complex dynamical states present in the system.

An alternative simulation approach for the ONERA aerodynamic model and its application in the nonlinear aeroelastic analysis of slender wings with pylon-store system

Abstract: The ONERA aerodynamic model is a nonlinear aerodynamic model which includes the effects of dynamic stall. With the strip theory, the ONERA model is usually used in the aeroelastic analysis of slender wings. To the classical approach for the ONERA model, the circulatory and nonlinear parts are all described by using aerodynamic elements and the simulation cost may be very high. In this paper, an alternative simulation approach is proposed to simplify the calculations for the ONERA model, in which the circulatory part of the ONERA model is solved analytically by using Duhamel integral method. In this way, the corresponding aerodynamic loads can be directly expressed in the modal space of the wing motion through only introducing two additional variables. For a slender wing model, the new simulation approach is used to analyze its nonlinear aeroelastic responses. In the simulation, the number of the state variables for the system using the proposed approach is reduced modestly comparing with that using the classical approach. In addition, for a slender wing with a pylon-store system which includes a free-play gap, both the proposed approach and the classical approach with the same number of aerodynamic elements are used to analyze the nonlinear dynamic behaviors of the system. Simulation results are given to show that the pylon-store system with a free-play gap can lead the occurrence of sub-critical Hopf bifurcation for a slender wing. Additionally, some nonlinear dynamic phenomena about the wing-pylon-store system are observed by using the new approach. But these phenomena cannot be predicted by employing the classical approach with the same number of aerodynamic elements used in the new approach. The peak of the post-critical responses obtained from the classical approach are larger than those obtained from the new approach in most range of free-stream velocity. The nonlinear flutter velocity predicted by using the classical approach is lower than that predicted by using the new approach.

Transitional Flow Dynamics Past a Passively Flapping Airfoil in Gusty Flow

Abstract: This paper investigates the transitional flow dynamics behind a passively flapping airfoil supported by nonlinear springs in the presence of gusty inflow. The fluid-structure interaction (FSI) framework is composed of an incompressible Navier-Stokes solver weakly coupled with a two degree-of-freedom (dof) nonlinear structural model. The fluid-elastic system shows a rich bifurcation behavior in terms of successive Hopf bifurcations in uniform flow condition as the mean wind speed is increased. Presence of gusty fluctuations in the inflow makes the dynamics more complex through transitional states that we refer to as ‘intermittency’ between different dynamical states. A regular intermittent state between quasi-periodic dynamics and low amplitude aperiodic response has been observed when the FSI system is subjected to a time harmonic gust in terms of sinusoidal fluctuation. A parametric study has been carried out for various amplitudes and frequencies of the sinusoidal fluctuation to demarcate the transitional regimes. Thereafter, the system is subjected to random gusts modeled as Ornstein-Uhlenbeck process and ‘on-off’ and ‘burst’ type intermittent dynamics have been observed for long time-scale and short time-scale input fluctuations respectively. The intermittent states have been characterized through time series analyses tools and the corresponding flow-field dynamics has been investigated in detail.

Entropy and fractal perspectives of a flapping wing subjected to gust

Abstract: Studies on entomopter’s performance under the influence of gust have received impetus in the past decade. There exists a dire need to ascertain the threshold of the frontal gusty conditions which w...

Independent coordinates for strange attractors from mutual information.

Abstract: The mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction. An N logN algorithm for calculating I is presented. As proposed by Shaw, a minimum in I is found to be a good criterion for the choice of time delay in phase-portrait reconstruction from time-series data. This criterion is shown to be far superior to choosing a zero of the autocorrelation function.

Determining embedding dimension for phase-space reconstruction using a geometrical construction

Abstract: We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d\ensuremath{\rightarrow}d+1. When the number of nearest neighbors arising through projection is zero in dimension ${\mathit{d}}_{\mathit{E}}$, the attractor has been unfolded in this dimension. The precise determination of ${\mathit{d}}_{\mathit{E}}$ is clouded by ``noise,'' and we examine the manner in which noise changes the determination of ${\mathit{d}}_{\mathit{E}}$. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than ${\mathit{d}}_{\mathit{E}}$. This knowledge may be useful in the practical analysis of observed time series.

Recurrence Plots of Dynamical Systems

Abstract: A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.

Recurrence plots for the analysis of complex systems

Abstract: Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980's. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e. g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system's behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. We therefore detail the analysis of data and indicate possible difficulties and pitfalls.