Flapping Dynamics of a Flexible Filament in a Uniform Flow
A flexible filament (flag for 1-D) in a fluid displays a bistable response that depends on the filament length: the stretched-straight state and the self-sustained flapping state. If the filament length falls below a certain critical value, the filament maintains a stretched-straight state, regardless of the magnitude of an externally imposed perturbation. However, when the length is sufficiently long, the stretched-straight state disappears and the filament always flaps in the fluid flow (first movie below). Further increase of the filament length induces a irregular flapping state (second movie). The relavant parameters related to the problem are the mass ratio, bending rigidity of the filament and Reynolds number.
Flapping Dynamics of Coupled Flexible Flags in a Viscous Flow
In biology, any group of fish that stays together for social reasons are shoaling, and if the group is swimming in the sane direction in a coordinated manner with a tighter organization, they are schooling. Schooling fish are usually of the same species and the same age/size and move with members precisely spaced relative to each other (Weihs 1973). The collective behavior of fish is not only for social interaction but also for numerous other benefits, such as defending against predators, foraging, and greater success in finding a mate. From a hydrodynamic point of view, the movement of fish in a school results in an increase in the hydrodynamic efficiency due to wake interactions (Weihs 1975). The hydrodynamics of groups of fish has been studies extensively while also considering tandem and side-by-side arrangements of flags (Ristroph & Zhang 2008; Alben 2009; Kim et al. 2010). However, fish are often arranged in a staggered manner within a school (for example, a diamond-shaped formation), and the dynamics of fish in a formation differ significantly from the dynamics of simple formations, suggesting the necessity of studyiing complex formations of flags for a better understanding of fish schooling (Fish 1999).
[Figure 13] Tail positions with time and vorticity contours around five flags arranged in a staggered formation
Passive Control of a Single Flag using Two Side-by-Side Flags
A deformable flexible flag in a fluid flow experiences a self-induced flapping motion in a cetain environmment, and a system with flexible flapping flag has been proposed as a means of energy harvesting, which can be utilized to generate electric energy. On the contrary, because interaction of flows with flexible elongated structures can induce structural vibration that could be a potential damage to structure in engineering (e.g., marine calbes, risers and other hydrodynamic applications), it is important to minimize flapping motion of flexible body in a flow. In order to efficiently control the flapping motion of a single flag, we propose a new passive control concept for a single flag using two side-by-side flags in upstream. An in-phase flapping mode of the two side-by-side flags in upstream enhances amplitude of the single flag, whereas an out-of-phase flapping mode of the upstream flags weakens the downstream flapping motion significantly.
Flow-Mediated Interaction between Self-Propelled Two Tandem Flexible Fins in Wall Effects
Schooling behavior, or collective motion, is commonly observed in biological systems in nature (e.g., fish schooling and birds flocking) (Weihs 1973; Portugal et al. 2014). When the groups of active animals move in a fluid, each locomotion is influenced by the others through the flow‒mediated interactions among them, and individuals in a schooling formation can take an energetic advantage in the light of hydrodynamics (Weihs 1973; Hemelrijk et al. 2015). Furthermore, flying/swimming organisms can take advantage of hydrodynamic benefits when they move near the wall (a phenomenon commonly called ‘wall effect’), for example, steelhead trout, buoyant mandarin fish, brown pelicans (Blake 1979; Hainsworth 1988; Webb 1993). Because the flow decelerates beneath a rigid or flexible body near the wall, higher pressures on the underside can generate more lift force by the wall effect. Although individual studies of self-propelled propulsors in a school (Zhu et al. 2014a; Park & Sung 2018; Peng et al. 2018a,b,c) and a single self-propelled propulsors in wall effects (Dai et al. 2016; Zhang et al. 2017; Park et al. 2017), respectively, have widely performed, the hydrodynamic approach to the schooling behaviors under an influence of the walls have never been conducted simultaneously.