Session MT: Biolocomotion X: Macro-Swimming I

Passively pulsed propulsion of aquatic vehicles

Recent work by Ruiz has shown that pulsed-jet propulsion for aquatic vehicles, similar to that used by sea jellies, salps, and squid, requires a significant decrease in energy input ($\sim$ 30\%). These results were obtained despite mechanical inefficiencies in the system to generate the pulsed flow. Thus an approach to generate the pulsed flow using a passive means has been explored. This approach uses collapsible tubing in a pressurized chamber to generate oscillatory, unsteady flow through the outlet. Current results will be presented along with a look toward future developments.   

Flapping modes of three filaments placed side by side in a free stream

Flexible filaments flapping in a surrounding flow are useful models for understanding the flow-induced vibration and mimicking the schooling behavior of fish. In the present work, the coupled modes of three identical filaments in a side-by- side arrangement are studied using the linear stability analysis and also an immersed boundary--lattice Boltzmann method for low Reynolds numbers (Re on order of 100). The numerical simulations show that the system dynamics exhibits several patterns that depend on the spacing between the filaments. Among these patterns, three can be predicted by the linear analysis and have been reported before. These modes are: (1) the three filaments all flap in phase; (2) the two outer filaments are out of phase while the middle one is stable; (3) the two outer filaments are in phase while the middle one is out of phase. The simulations also identified two additional modes: (1) the outer two filaments are out of phase while the middle one flaps at a frequency reduced by half; (2) the outer two filaments are out of phase while the middle one flaps at a slightly different frequency. In addition to the vibratory modes, the drag force and the flapping amplitude are also computed, and the implication of the result will be discussed.   

Interaction of pitching and heaving flexible flags in a viscous flow

In a group of swimming and flying animals, an individual interacts with one another via surrounding flow. Vortices shed by a body are found to strongly influence the downstream body using vortex-vortex and vortex-body interactions. In order to investigate the interactions between flexible bodies and vortices, the present study models two tandem flexible flags in viscous flow by numerical simulation using an improved version of the immersed boundary method. When the downstream flag has pitching and heaving motions, drag on the downstream flag gradually increases and decreases as the pitching and heaving phases vary from 0 to 2$\pi $; and the drag coefficient of the downstream flag drops even below the value of a single flag. Such drag variations are influenced by the interactions between vortices shed by the upstream flexible body and vortices surrounding the downstream one. Interaction of tandem flexible flags is investigated as a function of the gap distance between flags, and pitching and heaving phases at intermediate Reynolds numbers.   

Passive locomotion in unsteady flows

The passive locomotion of a submerged body in unsteady flow is studied. This work is motivated by recent experimental evidence that live and dead trout exploit vortices in the wake of an oscillating cylinder to swim upstream. We consider a simple model of a rigid body interacting dynamically with idealized wake models. The wake models consist of point vortices periodically introduced into the fluid domain to emulate shedding of vortices from an external un-modeled fixed or moving obstacle producing a ``drag'' or ``thrust'' wake, respectively. Both symmetric and staggered vortex configurations are considered. The submerged body is free to move in the plane, that is to say, it is not pinned at a given point. We do not prescribe a background flow, we rather consider the two-way coupled dynamics between the body's motion and the advection of ambient vortices. We show that both circular and elliptical bodies could ``swim'' passively against the flow by extracting energy from the ambient vortices. We obtain periodic trajectories for the body-vortex system and analyze their linear stability. We propose active feedback control strategies to overcome the instabilities.   

On Gray's paradox and efficiency measures for swimming

In 1936 Gray reported that the ``drag'' power of dolphins was substantially larger than the estimates of muscle power. We revisit this ``paradox'' in the context of undulatory swimming. We consider larval zebrafish as a model system. We question the basic premise of comparing drag power to muscle power. There are two reasons. First, we recognize that it may not be possible decompose the net force on an undulatory swimmer into drag and thrust. If it becomes possible, as we show in our case, the drag power, which represents the work done on the fluid due to motion in the swimming direction, is exactly balanced by the thrust power, which represents the work done by the fluid. Thus, the total power in the swimming direction, computed in this way, is zero. Second, we show that most of the muscle energy is dissipated in causing the lateral motion of the body - not in overcoming the ``drag'' in the swimming direction. This will be shown based on a power balance equation. Thus, we argue that efficiency measures, that relate the drag power to muscle power, or the Froude efficiency, are not recommended. Instead non-dimensional cost-of-transport could be a useful measure to compare efficiencies of organisms at different scales.   

Modeling and numerical simulations of 3D flows past self propelled fishes

Modeling and simulation of three-dimensional flows past deformable bodies are considered. The incompressible Navier-Stokes equations are discretized in space onto a fixed cartesian mesh. The displacement of self propelled deformable objects through the fluid is computed from the Newton's laws (forces and torques computation) and is taken into account using a penalisation method. The interface between the solid and the fluid is tracked using a level-set description so that it is possible to simulate several bodies freely evolving in the fluid. The application considered is fish-like swimming . Fish maneuvers and propulsion efficiency for different swimming modes for a single fish or for a fish school are investigated.   

Hydrodynamics of efficient propulsion in oscillating foils

The flow field and thrust performance of a pitching and heaving NACA 0012 airfoil at a chord Reynolds number of 30000 are investigated experimentally and numerically. In the experimental work, Digital Particle Image Velocimetry (DPIV) is used to examine the strength and dynamics of shed vorticity. The numerical work consists of Euler simulations using FLUENT in which leading edge separation is inhibited. Three kinematic cases from Anderson et al. (J. Fluid Mech, 360, 1998) are considered, two of which include propulsive efficiency peaks that fall in a Strouhal number range well below that predicted by the stability analysis of Triantafyllou et al. (1991, 1993). By considering the disparate experimental and numerical conditions as well as inviscid model results for these flows in the literature, we will discuss the role of vortex shedding on optimal propulsion.   

Two-dimensional study of fluid interaction with ray-strengthened fin using immersed boundary method

Labriform swimming is a common locomotion mode used by fish in low speed swimming, in which thrust generation is achieved through a combination of flapping and rowing motions of pectoral fins. Pectoral fins of bony fishes usually consist of a soft collagen membrane strengthened by embedded flexible rays, rendering anisotropic flexibility. We developed a fluid-structure interaction model based on immersed boundary method to simulate the kinematics and dynamic performance of an idealized 2D fin by considering the flow within one cross-sectional plane. The rays are represented as springs between target points and actual points along the fin, and the membrane is modeled as inextensible beams between the actual points. Using this model we studied thrust generation and propulsion efficiency of the fin at different combinations of parameters. Effects of Reynolds number, flapping frequency as well as different stiffnesses of the rays are studied.   

A Mechanical Fish to Emulate the Fast-Start Performance of Pike

A northern pike is capable of achieving an instantaneous acceleration of 25g, far greater than that achieved by any manmade vehicle. In order to understand the secrets behind achieving such high accelerations, we have built a mechanical fish to emulate the motion of a pike, a fast-start specialist. A live pike bends its body into a C-shaped curve and then uncoils it very quickly to send a traveling wave along its body in order to achieve high acceleration. We have designed a mechanical fish whose motion is accurately controlled by servo motors, to emulate the fast-start by bending its body to a C-shape from its original straight position, and then back to its straight position. An earlier design of a mechanical fish, which could start from an initial C-shaped curve, shed two vortex rings downstream, resulting in a transfer of energy from the fish to water, and therefore, a reaction force from the fluid to the fish. A maximum acceleration of around 4g was achieved in that design. Our new design adds an additional motion to the sequence by first bending the fish from its straight position into a C-shaped curve. Furthermore, this new mechanical fish is designed to be adjustable in swimming pattern, tail shape, tail rigidity, and body rigidity, making it possible to study the influence of all of these parameters on the fast-start performance.