Nonlinear flow-induced instability of an elastically mounted pitching wing

Abstract

Abstract

On the initiation and sustenance of flow-induced vibration of cylinders: insights from force partitioning

“…They showed that the energy extracted by a cylinder undergoing forced oscillations is closely related to the amplitude response of a freely oscillating cylinder under carefully matched kinematic conditions. This was also demonstrated in free oscillations of airfoils in the work of Menon & Mittal (2019) and Zhu, Su & Breuer (2020), where the computations of energy transfer using forced oscillations over a range of amplitude and frequencies (or 'energy maps') allowed the mapping out of all possible response branches, and associated bifurcations, of a free oscillator. This is particularly useful in systems with complicated nonlinear responses, as has been shown to be the case for oscillating cylinders (Williamson & Govardhan 2004).…”

“…where T * = 1/f * is the dimensionless period of the cycle andẏ * is the dimensionless vertical velocity of the cylinder. It has been shown in various flow-induced oscillation systems (Morse & Williamson 2009;Bhat & Govardhan 2013;Kumar et al 2016;Menon & Mittal 2019;Zhu et al 2020) that E * can take positive as well as negative values, depending on the oscillation kinematics. In the case of flow-induced oscillations, positive values of E * lead to oscillations of increasing amplitude, while negative values lead to decaying oscillations.…”

“…Hence, the energy extracted by the oscillating body can be used to understand the transient as well as stationary-state amplitude response of the flow-induced oscillating system. It has also been shown that by using sinusoidal forced oscillations of the system (with prescribed kinematics) to determine E * at a range of oscillation amplitudes and frequencies, we can predict (with the assumption that the flow-induced motion is also sinusoidal) all possible response branches of a flow-induced oscillator within that range of oscillation amplitudes and frequencies (Morse & Williamson 2009;Kumar et al 2016;Menon & Mittal 2019;Zhu et al 2020). The values of E * predicted by forced oscillations in this domain have been shown to predict the energy extracted by flow-induced oscillations under matching operating conditions.…”

“…This map of energy transfer as a function of parameters of interest is referred to as an 'energy map.' In past work, this energy map has been shown to predict the stationary-state amplitudes (Morse & Williamson 2009;Kumar et al 2016;Menon & Mittal 2019;Zhu et al 2020), transient growth (Menon & Mittal 2019), as well as response to perturbations (Menon & Mittal 2020) of a flow-induced oscillator. In this work we will use this tool to explain the occurrence of interesting observations in the amplitude response of flow-induced oscillations.…”

Nonlinear fluid damping of elastically mounted pitching wings in quiescent water

“…For elastically mounted pitching wings with a free stream, the interplay between the fluid damping and the structural damping governs the flow-induced oscillation. By mapping out the cycle-averaged energy transfer between the elastic system and the ambient fluid using prescribed kinematics, Menon & Mittal (2019) and Zhu, Su & Breuer (2020) showed that the energy injected by the negative fluid damping must be equal to the energy dissipated by the positive structural damping in order for the flow-induced oscillations to sustain. In other words, the total damping of the system must be zero (Dugundji 2008).…”