Fluid-Structure Interaction (FSI) Problem

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  1. 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.

    [Figure 1] Time-evolving vorticity contours around a single flag for (upper) the regular flapping state and (lower) the irregular flapping state

  2. 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 same 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 2] Tail positions with time and vorticity contours around five flags arranged in a staggered formation

  3. 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.

    [Figure 3] Time-evolving vorticity contours around (left) a single flag and (right) two upstream side-by-side flags and a downstream flag for (upper) energy harvesting and (lower) vibration control

  4. Flow-Mediated Interactions between Two Self-Propelled Flexible Fins near Sidewalls

    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.

    [Figure 4] Time-evolving vorticity contours around two self-propelled fins in a tandem configuration when the fin propel (top) with no wall, (middle) near a single wall and (bottom) between two parallel walls

  5. Intermittent Swimming of Two Self-propelled Flexible Fins in a Side-by-Side Configuration

    Many fish and marine mammals swim by taking a combination of an active bursting phase and a passive coasting phase, which is known as burst-and-coast swimming or intermittent swimming. The advantage of intermittent swimming has been connected to fatigue recovery when coasting without energy consumption, and the amount of energy consumption to travel a unit distance can be reduced by utilizing an intermittent swimming gait (Videler & Weihs 1982; Kramer & McLaughlin 2001; Fish 2010). Examples observed in nature include northern anchovy (Weihs 1980), golden shiner (Fish et al. 1991), koi carp (Wu et al. 2007), cod (Videler 1981; Blake 1983) and zebrafish (Fuiman & Webb 1988; Müller et al. 2000; McHenry & Lauder 2005). In addition, when the collections of animals travel in a fluid, the locomotion of each is affected by others through flow-mediated interactions among them, and individuals in a school can take an energetic benefit in view of the hydrodynamics, which is known as collective (or schooling) behaviors (Weihs 1973; Hemelrijk et al. 2015). Although previous experimental and numerical studies for collective behaviors of rigid foils and flexible fins adopt a continuous swimming style for simplicity (Zhu et al. 2014; Ramananarivo et al. 2016; Park & Sung 2018; Peng et al. 2018; Newbolt et al. 2019; Jeong et al. 2021), schooling fish in nature (e.g. golden shiners and Pacific bluefin tuna) are shown to use an intermittent swimming style (Fish et al. 1991; Noda et al. 2016).

    [Figure 5] Time-evolving vorticity contours around two self-propelled fins in a side-by-side configuration with (upper) continuous swimming and (lower) intermittent swimming

  6. Wake Transitions of Flexible Foils in a Viscous Uniform Flow

    Aquatic propulsion by fishes and other underwater organisms has long been of interest to increase energy efficiency of micro aviation and small unmanned underwater vehicles with low-noise characteristics (Lighthill 1970; Kats & Weihs 1978; Triantafyllou et al. 2000; Taylor 2003; Lauder et al. 2011). Fish are known to be flexible, with passive deformations of fins occurring during flapping (Combes & Daniel 2003), and the flexibility has been shown to increase the propulsion efficiency up to 20% by slightly reducing overall thrust compared to a rigid foil (Wu 1971; Kats & Weihs 1978). The possibility of increasing the propulsion efficiency for a flexible foil has motivated recent research activity for the effects of flexibility on the thrust force (Heathcote & Gursul 2007; Michelin & Smith 2009; Kang et al. 2011; Marais et al. 2012; Dewey et al. 2013; Zhu et al. 2014; Lagopoulos et al. 2019). However, although there have been significant efforts for study of wake structures related to the thrust force behind a rigid foil (Koochesfahani 1989; Godoy-Diana et al. 2008; Schnipper et al. 2009; Han et al. 2019; Lagopoulos et al. 2019), only a few studies have investigated flow structures generated behind an oscillating flexible foil with a limited parameter space (Marais et al. 2012; Zhu et al. 2014).

    [Figure 6] Instantaneous vorticity fields around (left) rigid foil and (right) flexible foil with heaving motion at StL=0.9

  7. Hydrodynamic Performance of a Self-Propelled Oscillating Ray

    [Figure 7] Time-evolving u-velocity contour around a self-propelled oscillating ray. The magnitude of the isosurface for u is 0.2.