Session H27: Biological Fluid Dynamics: High Re Swimming I

Flapping locomotion across a water-air interface

Inspired by jumping fish, we investigate the propulsive performance of plates and hydrofoils that are simultaneously flapping and translating vertically out of the water. Compared to fully-submerged scenarios, additional considerations in this application include reduced force production during partially-submerged movements and interactions between the propulsor and the free surface. We explore trade-offs between thrust production, stability, and splash control when the actuator is partially-submerged. In particular, we consider whether a decaying sinusoidal motion profile is a viable strategy for producing useful amounts of thrust while mitigating lateral forces throughout the water-to-air transition. We also identify factors that determine the critical time and position during the translation out of the water where no further propulsion is beneficial.   

Bubble PIV Measurements of Swimming Sea Lions

California sea lions are among the most agile of swimming mammals. While most marine mammals swim with their hind appendages – flippers or fluke, depending on the species – sea lions use their foreflippers for propulsion and maneuvering. The sea lions's propulsive stroke generates thrust by forming a jet between the flippers and the body and by dragging a starting vortex along the suction side of the flipper. Prior experiments using robotic flippers have shown these mechanisms to be possible, but no flow measurements around live sea lions previously existed with which to compare. In this work, the flow structures around swimming sea lions are observed using an adaptation of Particle Imaging Velocimetry. To accommodate the animals, it was necessary to use bubbles as seed particles and sunlight as illumination. Three trained adult California sea lions were guided to swim through an approximately-planar sheet of bubbles for a total of 173 repetitions. The captured videos were used to calculate bubble velocities, which were processed to isolate and inspect the flow velocities caused by the swimming sea lion. The methodology will be discussed and measured flow velocities will be presented.   

Flow Structures Generated by a Robotic Sea Lion Foreflipper

Unlike most biological swimmers that rely on body/caudal fin (BCF) type of locomotion, a California sea lion produces thrust by moving its large foreflippers from above its head into a position abducted against its abdomen, a motion called a ‘clap’. This is followed by a long glide in a streamlined position. The flow structures resulting from this motion will not resemble the traditionally seen structures during BCF swimming, namely the reverse von Kármán street. Here, we use particle image velocimetry (PIV) to study the flow around an anatomically correct silicone flipper that is actuated by a servo motor. The flipper is mounted on a robotic platform and is programmed to go through the motions of a sea lion ‘clap’. The resulting data indicates that thrust is not produced through compression of fluid between the ventral side of the flipper and the body. Instead, the surrounding fluid is entrained by the upper surface of the flipper, producing vortices that run along the span and directly off the tip of the flipper. We also notice a cutoff frequency after which the efficiency of velocity production diminishes, which indicates the existence of an ideal ratio between rotational velocity and tip speed.   

A tendon-inspired adjustable-stiffness joint improves swimming speed and efficiency

Fish dynamically control muscle stiffness to improve their swimming performance. The advantages of adjustable stiffness are only partially understood, because experiments on robotic tail fins have been limited to 3 Hz or less, whereas fish and fish-inspired robots can flap their tail fins at 10-15 Hz. We present here an actuator that flaps tail fins up to 7 Hz and uses a tunable spring to precisely control the stiffness of the peduncle (tail fin joint) in realtime. Our results show that dynamic stiffness control allows tuna-like fish to maintain high efficiency over a wide range of speeds (0 -- 2.5BL/s). We tested this result on a multi-speed long-distance mission (500 m) and found that controlling stiffness while swimming can reduce energy consumption. Three-dimensional Particle Image Velocimetry illustrates what wake structures are responsible for improving efficiency, particularly when peduncle stiffness is optimized at high speeds. Understanding the flow physics governing adjustable tail stiffness at high swimming speeds could guide biological hypotheses about muscle control in fish and offer design ideas for fish-inspired underwater vehicles.   

What do fishes and fighter jets have in common?

Multi-fin systems, like fish or fish-inspired vehicles, are~governed by~unsteady three-dimensional interactions between their multiple~fins. In~particular, dorsal/anal fins have received much attention because they~are~just upstream of the main thrust-producing fin: the caudal (tail) fin. We~used a tuna-inspired fish model with variable fin sharpness to study the~interaction between elongated dorsal/anal fins and caudal fins. We found~that~the performance enhancement is stronger than previously thought~(15{\%} increase~in swimming speed and 50{\%} increase in swimming~economy) and is governed by a~three-dimensional Dorsal Fin-induced~Crossflow that lowers the angle of attack~on the caudal fin and promotes~spanwise flow. Both simulations and multi-layer~Particle Image~Velocimetry reveal that the crossflow stabilizes the Leading~Edge Vortex~on the caudal fin, similar to how wing strakes prevent stall during~fixed-wing aircraft maneuvers. Unlike other fin-fin interactions, this~mechanism~is phase-insensitive and offers a simple, passive solution for flow~control~over oscillating propulsors. Our results offer new insights into~dorsal/anal~fin shape and placement in fish and fish-inspired vehicles.   

Aerodynamic Characteristics of Bio-Inspired Wings with Spanwise Waviness in a Turbulent Freestream

An experimental study is performed to investigate the effect of varying amplitude and wavelength of leading-edge tubercles on the aerodynamic and flow field characteristics of a NACA-0010 airfoil in flow with high freestream turbulence intensity of 4{\%}. The study involved three airfoils -- a smooth leading-edge, and two with a tubercle amplitude of 6{\%} of chord, and with eight and four tubercles (varying wavelength) over the span. The aspect ratio of all airfoils was 2.0. The freestream velocities ranged from 16 to 40 m/s, with the corresponding chord-based Reynolds number varying from 160K to 412K. The angle of attack was varied from -6 to 30 degrees. The results show that the two tubercled airfoils achieved little to marginal performance enhancement pre-stall. In the post-stall regime, the lift coefficient of the longer wavelength tubercle airfoil was only marginally higher than the baseline while the smaller wavelength airfoil evinced the highest lift and delayed stall in the range of Reynolds numbers tested. The flow field data obtained using PIV showed large amount of turbulent mixing at leading edge of the tubercle airfoils, thus delaying flow separation, and leading to delayed stall as compared to the baseline airfoil.   

Optimal three-dimensional trajectory to generate maneuvering forces with a caudal fin of large aspect ratio

The flapping motion of a caudal fin is an efficient method of generating thrust forces in an unmanned underwater vehicle. Simple pitching and heaving motions of this appendix, however, are not sufficient to achieve agile maneuvering of the vehicle. To address this deficiency, the use of a caudal fin that can perform large rotations around all three axes is explored. Due to the large number of possible trajectories attainable by such a mechanism, this study employs an experimental optimization procedure to obtain the most efficient three-dimensional trajectory that can generate a specified side-force value, equivalent to a turning moment. The optimal trajectory followed by a fin of large aspect ratio is presented and shown to be highly efficient. The trajectory is then experimentally analyzed in detail, and the use of fins of varying flexibility is considered, with increased flexibility being shown to be detrimental to the maneuvering performance of the fin.   

Swimming gait driven by propioceptive feedback.

We have developed an elementary theoretical model of aquatic locomotion, based on [1] and [2]. We link the locomotion velocity to the kinematic of the foil. The amplitude and the beating frequency of the tail are still chosen by the swimmer and we would like to propose a simple mechanism which selects them. Here,we suppose that the tail motion proportionally depends on the normal force felt by its body. We have constructed a robotic compliant fish which is attached to a force sensor. We vary the feedback intensity and we measure the resulting thrust, amplitude and frequency. Our theoretical model accurately predicts the experimental outputs.\newline [1]Theodorsen, T. (1935) NACA Report 496, \newline [2]Garrick, Isadore E. "Propulsion of a flapping and oscillating airfoil." (1937). NACA   

Burst-and-coast dynamics in zebrafish and tetrafish.

Swimming kinematics of small fish such as zebrafish or tetrafish are characterized by intermittent sequences consisting in an ``active'' swimming phase directly followed by a passive ``coast'' phase. This work is an attempt to characterize those sequences using several archetypal model experiments and models gathering hydrodynamics, statistics and behavioral sciences. We will focus on new results obtained from real fish experiments in free swimming and forced-gait configurations (using a controlled swimming channel). We will show how the statistics of these S2D sequences evolve with the conditions of the experiment as external flow conditions size of the habitat the maturity state of the fish (larva, juvenile or adult). We believe that these results will have direct implications on the design and implementation of biomimetic robotic systems.   

Hydrodynamic Interaction of Pitching Hydrofoils in Close Formation

Swimming in close formation has the potential to improve swimming performance including swimming speed or power consumption. Numerical and physical models have shown that swimmers can take advantage of vortex shedding from other swimmers. However, most of the experimental work has been limited to few swimmers and tend to focus on the hydrodynamic interaction within the school. In this work, we developed an array of nine pitching hydrofoils (NACA0025) in close formation to examine the hydrodynamic interaction within the group and the wake generated by the group of foils. The pitching foils were tested in an inclined soap film to capture the flow structures generated by the foils. The foils were pitched at the quarter-chord with either sinusoidal or triangular wave patterns. The foils were tested with different frequency, amplitude, phase difference and spacing between them. We were able to capture the hydrodynamic interaction and the flow structure generated by the group. It appears that the flow structure generated by the group of foils is the result of a recombination of the vortex structures generated by the individual foils.   

Fluid Dynamics of a Plunging Wing in Presence of Karman Vortex Street Shedding.

Humanity's understanding of flapping wing aerodynamics has increased dramatically over the past few decades -- from not being able to accurately calculate forces generated by such wings, to building small-sized robots that can fly almost as well as their biological inspiration in laminar flows. Despite the great progress in their design and control, these robots are tremendously troubled while flying in turbulent environments. A nominally 2D plunging wing, the simplest case possible designed and built in-house, was tested in the presence of unsteady wake to investigate the effect of the flow disturbances on vorticity fields. The unsteady wake in the form of von Karman Vortex Street was generated by a cylinder located upstream of the plunging wing at different distances. The plunge amplitude and frequency of the oscillation were adjusted to bracket the range of Strouhal numbers relevant to the biological locomotion at Reynolds number of 10,000. First, the dye flow visualization technique was used to qualitatively observe the wake behind the cylinder, mainly to position the wing with respect to the upstream vortical structure. Second, time-resolved Particle Image Velocimetry (PIV) was employed to quantitatively study the effect of unsteady wake on the flow measurements of the plunging wing. This research and its successive investigations may eventually lead to more efficient or better-performing Unmanned Aerial Vehicles, along with a better understanding of their fluid dynamics.   

The role of edge curvature on the thrust force in a stingray inspired plan-form

Optimizing the geometry of stingray inspired plan-forms for propulsive performance is of interest to design bio-inspired underwater vehicles and robots. Thrust generation is characterized by an exchange of momentum from plan-form to fluid as well as generation of edge vortices. Numerical simulations are performed at a Reynolds number of 500 on various geometries of the plan-form to better understand this phenomenon for a prescribed travelling wave. The plan-form surface area is kept constant while the geometry of the plan-form is varied from a round shape to a square shape by changing the curvature of the edge. As the curvature of the plan-form decreases, the thrust coefficient decreases. The effect of stingray inspired wave motion for various plan-form geometries with respect to thrust generation is analyzed in detail. The influence of edge curvature on the shape and strength of leading-edge vortices is characterized. The suction pressure and the generation of pressure due to exchange of momentum on the plan-form is also quantified.