Session U01: Biological Fluid Dynamics: Locomotion High Reynolds Number Swimming (8:45am - 9:30am CST)

Collective locomotion of two-dimensional lattices of flapping plates

We study the propulsive properties of rectangular and rhombic lattices of flapping plates at O(10--100) Reynolds numbers in incompressible flow. We vary five parameters: flapping amplitude, frequency (or Reynolds number), horizontal and vertical spacings between plates, and oncoming fluid stream velocity. Lattices that are closely spaced in the streamwise direction produce intense vortex dipoles between adjacent plates. The lattices transition sharply from drag- to thrust-producing as these dipoles switch from upstream to downstream orientations at critical flow speeds. The flows assume a variety of periodic and nonperiodic states, with and without up-down symmetry, and multiple stable self-propelled speeds can occur. With small lateral spacing, rectangular lattices yield net drag, while rhombic lattices may generate net thrust efficiently. As lateral spacing increases, rectangular lattices eventually achieve higher efficiencies than rhombic lattices, and the two types of lattice flows converge. At Re = 70, the maximum Froude efficiencies of time-periodic lattice flows are about twice those of an isolated plate. At lower Re, the lattices' efficiency advantage increases until the isolated flapping plate no longer generates thrust.   

Machine Learning Model of Flow Interactions in Large Schools

Computations are presented for two, three, four and more foils pitching about their leading edges and aligned side-by-side. A simple superposition model is developed from two-body interactions to predict the thrust, efficiency, and lift acting on three interacting swimmers, by decomposing the three-body interactions into two two-body interactions. However, the simple model fails to capture nonlinearities that are present when the swimmers are in close proximity. To accurately predict the three-body interactions, a machine learning model is developed to capture the residual nonlinearities not predicted by the superposition model. Finally, this model is used to predict the performance of schools with more than three bodies, which is verified with targeted simulations of many-body interactions.   

Remoras pick where they stick on blue whales.

Animal-borne video recordings from blue whales in the open ocean show that remoras preferentially adhere to specific regions of the surface of the whale. Using empirical and computational fluid dynamics analyses, we show that remora attachment was specific to regions of separating flow and wakes caused by surface features on the whale. Adhesion at these locations offers remoras drag reduction up to 71-84{\%} compared to the freestream. Remoras were observed to move freely along the surface of the whale using skimming and sliding behaviors. Skimming provided drag reduction as high as 50 -- 72{\%} at some locations for some fish sizes, but little to none was available in regions where few to no remoras were observed. Experimental work suggests that the Venturi effect may help remoras stay near the whale while skimming. Understanding the flow environment around a swimming blue whale will inform the placement of biosensor tags to increase attachment time for extended ecological monitoring.   

Scaling law for unsteady two-dimensional swimming in ground effect

The underlying physics of oscillatory swimming, in proximity to a substrate, can be modeled with simple models based on the scaling of added mass and circulatory forces. Here, following Moored & Quinn (2018) and by considering these forces, we present new scaling relations for unsteady swimming in ground effect. The classic linear theory is augmented by additional nonlinearities and modified for ground effect by considering added mass changes in proximity to the ground for a two-dimensional foil, the circulatory effects from the trailing vortex system, and its image due to the presence of the ground. The scaling relation then is verified using inviscid numerical simulations and experiments over a wide range of variables, including the dimensionless amplitude, dimensionless distance from the ground, reduced frequency, and Strouhal number. The developed relations found to be in excellent agreement with the numerical and experimental data. These scaling laws are then used to identify physical mechanisms that influence thrust and efficiency and as a guide for improving performance.   

Schooling of tandem flapping wings

We present the results of a theoretical investigation into the dynamics of tandem flapping wings, a model system for studying schooling swimmers in relatively fast flows. We develop a discrete dynamical system (iterated map) in which the swimmers shed point vortices during each flapping cycle, which in turn exert forces on the swimmers. Our model predictions exhibit good agreement with experimental data on the steadily-translating schooling states of tandem wings. If the wings execute identical flapping kinematics, we find that, as the flapping amplitude is progressively increased, the system undergoes a period-doubling cascade that ultimately leads to chaos. If the wings' flapping amplitudes or frequencies are distinct, we find that the wings may either separate, collide, or form unsteady bound states. Generally, our results indicate how hydrodynamics may influence the dynamics of schooling swimmers in biological contexts.   

The effect of fin rotation on the flapping propulsion of underwater vehicles

Bio-inspired propellers have received increased attention as a means of improving the efficiency, maneuverability and stealth of underwater autonomous vehicles (UAVs). In particular, the thunniform propulsion mode of fish, based on the flapping motion of their caudal fin, presents peak long-range propulsive efficiencies. The fin of these swimmers follows predominantly side-to-side motions with comparably small rotations around their longitudinal axis, partly due to the inability of the joint to produce larger rotations. In this talk, we assess the effect that larger rotations --- attainable by an engineered joint--- would have on the thrust produced by a flapping UAV. Additionally, we evaluate the role of fin flexibility in attaining these rotations in nature and consider the limit case in which the fin moves in a continuous rotation mode. For this purpose, a UAV equipped with a caudal fin capable of producing these large rotations has been developed. Using an experimental optimization procedure, the motion of the fin that produces maximum thrust is obtained for different limits of the rotation value. The procedure is performed for both rigid and flexible fins, and the resulting optima are shown and analyzed in detail.   

Caudal fin shape and swimming performance of Tunabot

Tunabot is a biomimetic robot developed at UVA to help understand the swimming performance of tuna, and the translation to the design on the next generation of underwater vehicles. To understand better the role of the caudal fin and its shape in determining the propulsive performance, the effects of caudal fin platform was examined by experiment. The cruise speed of the Tunabot was measured under free swimming conditions at a Reynolds number based on body length of 27,500 while varying the caudal fin shape from that observed for tuna to one that was rectangular with the same area, mean chord, and aspect ratio. It was found that the rectangular fin produced greater thrust at the same actuating frequency, resulting in about a 25\% increase in swimming speed. This result may indicate that bio-inspired robots may permit better performance than biomimetic robots.   

Simulations of Bio-inspired Undulated Cylinders through Dynamic Morphing of Surface Topography

Undulations on a cylinder, inspired by seal whiskers, lower the drag force and vibration in the flow when compared to smooth cylinders. Hence, these geometric features can be applied to the development of underwater devices and other engineering applications in need of vibration suppression, frequency tuning, or force reduction. Flow simulations are utilized to analyze the hydrodynamic response by varying the individual geometric parameters that define the undulatory features. Previous methodologies require a manual mesh re-generation when making geometric changes to the undulated cylinder. Instead of this time-intensive process, the current research introduces an algorithm that directly controls the surface topography and updates the undulation features during the simulation. This is accomplished with a dynamic mesh methodology, and a parameterization of the complex seal whisker inspired morphology. Morphing the surface results in easy transitions from one geometric value to the next as well as a significant reduction of the simulation time, allowing for exploration of a wider range of parameters. Results demonstrate the effects of chordwise and transverse undulation amplitudes in terms of the hydrodynamic force and frequency response.   

Sweep angle is negligible for propulsive flapping

The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from an extensive set of three-dimensional simulations of a finite foil undergoing tail-like and flipper-like kinematics for a range of sweep angles while carefully controlling all other parameters. No significant change in force and power is observed for tail-like motions (i.e. pitch-heave) as the sweep angle increases, with a corresponding efficiency drop of only $\approx 2\%$. The same findings are seen in flipper-like motion (i.e. twist-roll) although the efficiency decrease is slightly higher $\approx 6\%$ due to power increase. This leads to a conclusion that fishtails, mammal flukes and flippers can have a large range of potential sweep angles without negative impact on their performance, while at the same time, varying other hydrodynamic variables to reach the highest propulsion and efficiency.   

Formations of flapping swimmers are stabilized by lateral flow interactions

How do swimming fish stay together as a school? Using experiments on a ``robotic school'' of two flapping hydrofoils we show that fluid-mediated interactions help the swimmers match speeds and lock into formation. Pairs of swimmers are stabilized in all planar arrangements, including tandem (in-line), abreast (side-by-side) and diagonal, and the cohesion effect extends over surprisingly long ranges streamwise and laterally. Viewing larger groups as built up from many such pairwise interactions suggests that schools may cohere together even if the swimmers are positioned rather randomly, which could explain why schools of fish seem to be disordered.   

Tuna Swimming: An Enhanced Hydrodynamic Performance by Finlets

Finlets are commonly equipped by scombrid fishes (mackerels, bonitos, and tunas) which are known for their high swimming speed. The finlets are a series of small non-retractable fins located on the dorsal and ventral margins of the fish body. It is thought these small fins would potentially affect the propulsive performance of fish swimming. In this work, a combined experimental and computational approach is used to investigate the hydrodynamics of a live tuna undergoing steady swimming. High-resolution videos of the swimming fish are obtained and used as a basis for developing high-fidelity models of tuna locomotion with independently mobile finlets. Simulations are carried out using a Cartesian-grid based immersed boundary flow solver to examine the hydrodynamic performance and vortex dynamics of tuna swimming. An adaptive mesh refinement (AMR) method is used to gain a higher resolution of the finlet flow. It is found that the hydrodynamic interactions between finlets, trunk, and caudal fin play an important role in the thrust generation and propulsion efficiency of tuna swimming. Results from this study help to bring novel insights into the design of high-performance underwater vehicles from a vortex dynamics perspective.