Aspect ratio-dependent hysteresis response of a heavy inverted flag

Abstract

The bistable fluttering response of heavy inverted flags with different aspect ratios ( $AR$ ) is investigated to determine how the vortical structures affect the intermittent vibration response of the flag. A heavy inverted flag in a uniform flow may exhibit several response modes; amongst them are three major modes that occur over an extended velocity range: stationary, large-scale periodic oscillation and one-sided deflected modes. Significant hysteretic bistability is observed at the transition between these modes for all $AR$ , which is notably different from the conventional flag vibration with a fixed leading edge and free trailing edge where no hysteresis is observed at the lower $AR$ limit ( $AR<1$ ). The difference is associated with the distinct roles of vortices around the flag. Experiments with flags made of spring steel are conducted in a wind tunnel, where the flow speed is steadily increased and later decreased to obtain different oscillatory modes of the heavy inverted flags. The experimental results are used to validate the numerical model of the same problem. It is found that different critical velocities exist for increasing and decreasing flow velocities, and there is a sustained hysteresis for all $AR$ controlled by the initiation threshold and growth of the leading-edge and side-edge vortices. The effect of the vortices in the bistable oscillation regime is quantified by formulating a modal force partitioning approach. It is shown that $AR$ can significantly alter the static and dynamic vortex interaction with the flexible plate, thereby changing the flag's hysteresis behaviour and bistable response.

Passive bionic motion of a flexible film in the wake of a circular cylinder: chaos and periodicity, flow–structure interactions and energy evolution

“…Even if our experiments have been arranged in such a way that the end effects of the cylinder on the film motion are excluded (see figure 1 in § 2), the spanwise variations in the phase and strength of the vortex shedding are inescapable (Szepessy & Bearman 1992). If so, the aspect ratio of the film (Ojo et al 2022) and the spanwise correlation length of the vortex shedding (Zdravkovich 1996;West & Apelt 1997) will be two crucial parameters. A more thorough investigation into the deeper mechanism requires synchronous measurement of the three-dimensional flow field, the deformation field as well as the dynamic force, which represents one of the challenges in current experimental fluid mechanics.…”

“…As such, the accumulation of elastic energy in this portion is contingent upon the consumption of its own kinetic energy, akin to that of an inverted film. It should be mentioned that the elastic energy accumulation of the inverted film not only consumes its own kinetic energy, but continuously gains energy from the flow field (Kim et al 2013;Ojo et al 2022). In contrast, the elastic energy accumulation in the middle region is mainly ascribed to the mutual interactions between the film and the cylinder vortices, V C and V ⊕ C , as evidenced by the evolution of the LCS in figure 18.…”

“…The bending wave proceeds from the interaction between the film and the large-scale vortices (refer to § 3.5.1), and then propagates downstream along the film, which is a passive wave so that its phase speed of 8.4 m s −1 will not exceed the free stream velocity of U ∞ = 10 m s −1 . To sum up, the periodic flapping of the film in the cylinder wake incorporates both the standing wave-like and the travelling wave-like motions at the same time; in terms of the mathematical description, it differs from both the pure travelling-wave undulations of the film with normal configuration (Zhang et al 2000;Shelley et al 2005;Michelin et al 2008) and the pure standing-wave flapping of the inverted film (Kim et al 2013;Goza et al 2018;Ojo et al 2022). In this sense, the flapping of the film with L/D = 5.0 (figure 17a) is a new kind of flow-structure coupling pattern.…”

Flapping dynamics of an inverted flag behind a cylinder

“…The dynamics of an inverted flag in both uniform and perturbed flow conditions is highly dependent on U * [23]. Here, the non-dimensional velocity is varied from 1.41 ⩽ U * ⩽ 2.58, while the separation distance is kept constant at representative values of S = 0.4L, 0.8L, 1.4L.…”

“…exhibit multiple response modes due to their interaction with flow [4,22] and their response is highly correlated with the leading-edge vortex separation dynamics [23]. When placed in the wake of a bluff body, the interaction of the bluff body wake and the flag initiates distinct response modes.…”