Unsteady computational fluid dynamics in front crawl swimming

The development of codes and power calculations currently allows the simulation of increasingly complex flows, especially in the turbulent regime. Swimming research should benefit from these technological advances to try to better understand the dynamic mechanisms involved in swimming. An unsteady Computational Fluid Dynamics (CFD) study is conducted in crawl, in order to analyse the propulsive forces generated by the hand and forearm. The k-ω SST turbulence model and an overset grid method have been used. The main objectives are to analyse the evolution of the hand-forearm propulsive forces and to explain this relative to the arm kinematics parameters. In order to validate our simulation model, the calculated forces and pressures were compared with several other experimental and numerical studies. A good agreement is found between our results and those of other studies. The hand is the segment that generates the most propulsive forces during the aquatic stroke. As the pressure component is the main source of force, the orientation of the hand-forearm in the absolute coordinate system is an important kinematic parameter in the swimming performance. The propulsive forces are biggest when the angles of attack are high. CFD appears as a very valuable tool to better analyze the mechanisms of swimming performance and offers some promising developments, especially for optimizing the performance from a parametric study.     

Use of biorobotic models of highly deformable fins for studying the mechanics and control of fin forces in fishes

Bony fish swim with a level of agility that is unmatched in human-developed systems. This is due, in part, to the ability of the fish to carefully control hydrodynamic forces through the active modulation of the fins' kinematics and mechanical properties. To better understand how fish produce and control forces, biorobotic models of the bluegill sunfish's (Lepomis macrochirus) caudal fin and pectoral fins were developed. The designs of these systems were based on detailed analyses of the anatomy, kinematics, and hydrodynamics of the biological fins. The fin models have been used to investigate how fin kinematics and the mechanical properties of the fin-rays influence propulsive forces and to explore kinematic patterns that were inspired by biological motions but that were not explicitly performed by the fish. Results from studies conducted with the fin models indicate that subtle changes to the kinematics and mechanical properties of fin rays can significantly impact the magnitude, direction, and time course of the 3D forces used for propulsion and maneuvers. The magnitude of the force tends to scale with the fin's stiffness, but the direction of the force is not invariant, and this causes disproportional changes in the magnitude of the thrust, lift, and lateral components of force. Results from these studies shed light on the multiple strategies that are available to the fish to modulate fin forces.     

Computational Research on Modular Undulating Fin for Biorobotic Underwater Propulsor

Biomimetic design employs the principles of nature to solve engineering problems. Such designs which are hoped to be quick, efficient, robust, and versatile, have taken advantage of optimization via natural selection. In the present research, an environment-friendly propulsion system mimicking undulating fins of stingray was built. A non-conventional method was considered to model the flexibility of the fins of stingray. A two-degree-of-freedom mechanism comprised of several linkages was designed and constructed to mimic the actual flexible fin, The driving linkages were used to form a mechanical fin consisting of several fin segments, which are able tO produce undulations, similar to those produced by the actual fins. Owing to the modularity of the design of the mechanical fin, various undulating patterns can be realized. Some qualitative observations, obtained by experiments, predicted that the thrusts produced by the mechanical fin are different among various undulating patterns. To fully understand this experimental phenomenon is very important for better performance and energy saving for our biorobotic underwater propulsion system. Here, four basic undulating patterns of the mechanical fin were performed using two-dimensional unsteady computational fluid dynamics （CFD） method. An unstructured, grid-based, unsteady Navier-Stokes solver with automatic adaptive re-meshing was used to compute the unsteady flow around the fin through twenty complete cycles. The pressure distribution on fin surface was computed and integrated to provide fin forces which were decomposed into rift and thrust. The pressure force and friction force were also computed throughout the swimming cycle. Finally, vortex contour maps of these four basic fin undulating patterns were displayed and compared.     

Locomotion with flexible propulsors: II. Computational modeling of pectoral fin swimming in sunfish

This paper describes a computational fluid dynamics (CFD) based investigation of the pectoral fin hydrodynamics of a bluegill sunfish. The pectoral fin of this fish undergoes significant shape-change during its abduction-adduction cycle and the effect of this deformation on the thrust performance remains far from understood. The current study is part of a combined experimental-numerical approach wherein the numerical simulations are being used to examine features and issues that are not easily amenable to the experiments. These numerical simulations are highly challenging and we briefly describe the computational methodology that has been developed to handle such flows. Finally, we describe some of the key computational results including wake vortex topologies and hydrodynamics forces.     

Ecomorphology of Locomotion in Labrid Fishes

The Labridae is an ecologically diverse group of mostly reef associated marine fishes that swim primarily by oscillating their pectoral fins. To generate locomotor thrust, labrids employ the paired pectoral fins in motions that range from a fore-aft rowing stroke to a dorso-ventral flapping stroke. Species that emphasize one or the other behavior are expected to benefit from alternative fin shapes that maximize performance of their primary swimming behavior. We document the diversity of pectoral fin shape in 143 species of labrids from the Great Barrier Reef and the Caribbean. Pectoral fin aspect ratio ranged among species from 1.12 to 4.48 and showed a distribution with two peaks at about 2.0 and 3.0. Higher aspect ratio fins typically had a relatively long leading edge and were narrower distally. Body mass only explained 3% of the variation in fin aspect ratio in spite of four orders of magnitude range and an expectation that the advantages of high aspect ratio fins and flapping motion are greatest at large body sizes. Aspect ratio was correlated with the angle of attachment of the fin on the body (r = 0.65), indicating that the orientation of the pectoral girdle is rotated in high aspect ratio species to enable them to move their fin in a flapping motion. Field measures of routine swimming speed were made in 43 species from the Great Barrier Reef. Multiple regression revealed that fin aspect ratio explained 52% of the variation in size-corrected swimming speed, but the angle of attachment of the pectoral fin only explained an additional 2%. Labrid locomotor diversity appears to be related to a trade-off between efficiency of fast swimming and maneuverability in slow swimming species. Slow swimmers typically swim closer to the reef while fast swimmers dominate the water column and shallow, high-flow habitats. Planktivory was the most common trophic associate with high aspect ratio fins and fast swimming, apparently evolving six times.     

Functional Morphology of Aquatic Flight in Fishes: Kinematics, Electromyography, and Mechanical Modeling of Labriform Locomotion

Labriform locomotion is the primary swimming mode for many fishesthat use the pectoral fins to generate thrust across a broadrange of speeds. A review of the literature on hydrodynamics,kinematics, and morphology of pectoral fin mechanisms in fishesreveals that we lack several kinds of morphological and kinematicdata that are critical for understanding thrust generation inthis mode, particularly at higher velocities. Several needsinclude detailed three-dimensional kinematic data on speciesthat are pectoral fin swimmers across a broad range of speeds,data on the motor patterns of pectoral fin muscles, and thedevelopment of a mechanical model of pectoral fin functionalmorphology. New data are presented here on pectoral fin locomotionin Gomphosus varius, a labrid fish that uses the pectoral finsat speeds of 1 –6 total body lengths per second. Three-dimensionalkinematic data for the pectoral fins of G. varius show thata typical "drag-based" mechanism is not used in this species.Instead, the thrust mechanics of this fish are dominated bylift forces and acceleration reaction forces. The fin is twistedlike a propeller during the fin stroke, so that angles of attackare variable along the fin length. Electromyographic data onsix fin muscles indicate the sequence of muscle activity thatproduces antagonistic fin abduction and adduction and controlsthe leading edge of the fin. EMG activity in abductors and adductorsis synchronous with the start of abduction and adduction, respectively,so that muscle mechanics actuate the fin with positive work.A mechanical model of the pectoral fin is proposed in whichfin morphometrics and computer simulations allow predictionsof fin kinematics in three dimensions. The transmission of forceand motion to the leading edge of the fin depends on the mechanicaladvantage of fin ray levers. An integrative program of researchis suggested that will synthesize data on morphology, physiology,kinematics, and hydrodynamics to understand the mechanics ofpectoral fin swimming.     

Functional morphology of the pectoral fins in bamboo sharks, Chiloscyllium plagiosum: benthic vs. pelagic station-holding

Bamboo sharks (Chiloscyllium plagiosum) are primarily benthic and use their relatively flexible pectoral and pelvic fins to rest on and move about the substrate. We examined the morphology of the pectoral fins and investigated their locomotory function to determine if pectoral fin function during both benthic station-holding and pelagic swimming differs from fin function described previously in leopard sharks, Triakis semifasciata. We used three-dimensional kinematics and digital particle image velocimetry (DPIV) to quantify pectoral fin function in five white-spotted bamboo sharks, C. plagiosum, during four behaviors: holding station on the substrate, steady horizontal swimming, and rising and sinking during swimming. During benthic station-holding in current flow, bamboo sharks decrease body angle and adjust pectoral fin angle to shed a clockwise fluid vortex. This vortex generates negative lift more than eight times that produced during open water vertical maneuvering and also results in an upstream flow that pushes against the posterior surface of the pectoral fin to oppose drag. In contrast, there is no evidence of significant lift force in the wake of the pectoral fin during steady horizontal swimming. The pectoral fin is held concave downward and at a negative dihedral angle during steady horizontal swimming, promoting maneuverability rather than stability, although this negative dihedral angle is much less than that observed previously in sturgeon and leopard sharks. During sinking, the pectoral fins are held concave upward and shed a clockwise vortex with a negative lift force, while in rising the pectoral fin is held concave downward and sheds a counterclockwise vortex with a positive lift force. Bamboo sharks appear to sacrifice maneuverability for stability when locomoting in the water column and use their relatively flexible fins to generate strong negative lift forces when holding position on the substrate and to enhance stability when swimming in the water column.     

Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.     

Assessing kinematics and kinetics of functional electrical stimulation rowing

Hybrid functional electrical stimulation (FES) rowing has positive effects on cardiovascular fitness, producing significantly greater aerobic power than either upper body or FES exercise alone. However, there is minimal information on the kinematics, kinetics, and mechanical efficiency of FES-rowing in the spinal cord injured (SCI) population. This study examined the biomechanics of FES-rowing to determine how motions, forces, and aerobic demand change with increasing intensity. Six individuals with SCI and six able-bodied subjects performed a progressive aerobic capacity rowing test. Differences in kinematics (motion profiles), kinetics (forces produced by the feet and arms), external mechanical work, and mechanical efficiency (work produced/volume of oxygen consumed) were compared in able-bodied rowing vs. SCI FES-rowing at three comparable subpeak workloads. With increasing exercise intensity (measured as wattage), able-bodied rowing increased stroke rate by decreasing recovery time, while FES-rowing maintained a constant stroke rate, with no change in drive or recovery times. While able-bodied rowers increased leg and arm forces with increasing intensity, FES-rowers used only their arms to achieve a higher intensity with a constant and relatively low contribution of the legs. Oxygen consumption increased in both groups, but more so in able-bodied rowers, resulting in able-bodied rowers having twice the mechanical efficiency of FES-rowers. Our results suggest that despite its ability to allow for whole body exercise, the total force output achievable with FES-rowing results in only modest loading of the legs that affects overall rowing performance and that may limit forces applied to bone.     

Numerical and Experimental Research on Modular Oscillating Fin

Fishes are famous for their ability to position themselves accurately even in turbulent flows. This ability is the result of the coordinated movement of fins which extend from the body. We have embarked on a research program designed to develop an agile and high efficient biologically inspired robotic fish based on the performance of hybrid mechanical fms. To accomplish this goal, a mechanical ray-like fin actuated by Shape Memory Alloy （SMA） is developed, which can realize both oscillatory locomotion and undulatory locomotion. We first give a brief introduction on the mechanical structure of our fin and then carry out theoretic analysis on force generation. Detailed information of these theoretical results is later revealed by Computational Huid Dynamic （CFD）, and is final validated by experiments. This robotic fin has potential application as a propulsor for future underwater vehicles in addition to being a valuable scientific instrument.     

CFD Simulation of Fish-like Body Moving in Viscous Liquid

The study of fish-like bodies moving in liquid is an interesting and challenging research subject in the fields of biolocomotion and biomimetics. Typically the effect of tail oscillation on fluid flow around such a body is highly unsteady, generating vortices and requiring detailed analysis of fluid-structure interactions. An understanding of the complexities of such flows is of interest not only to biologists but also to engineers interested in developing vehicles capable of emulating the high performance of fish propulsion and manoeuvring. In the present study, a computational fluid dynamic （CFD） simulation of a three-dimensional biomimetic fish-like body has been developed to investigate the fluid flows around this body when moving in a viscous liquid. A parametric analysis of the variables that affect the flow surrounding the body is presented, along with flow visualisations, in an attempt to quantify and qualify the effect that these variables have on the performance of the body. The analysis provided by the unsteady transient simulation of a fish-like body has allowed the flow surrounding a fish-like body undergoing periodic oscillations to be studied. The simulation produces a motion of the tail in the （x, y） plane, with the tail oscillating as a rigid body in the form of a sinusoidal wave.     

Bluegill Lepomis macrochirus synchronize pectoral fin motion and opercular pumping

The relative timing between operculum and pectoral fin motion was examined in swimming bluegill Lepomis macrochirus to determine if respiratory fluid flows from the operculum might have an effect on flow over the pectoral fin. Five bluegill were filmed swimming at speeds from 0·5 to 1·5 body (total) lengths s⁻¹. The timing of opercular pumping and pectoral fin beating was noted and analysed using circular statistics. Fish tended to ventilate their gills every second or third pectoral fin beat. While locomotion and ventilation had different frequencies, however, they were synchronized: fish maintained a consistent phase relationship between them. Thus, within pectoral fin beats when the operculum pumps, the jet consistently occurred during pectoral fin abduction, ending just after the fin was fully abducted and beginning adduction. Based on the distance between the opercular slit and the pectoral fin base, the jet was estimated to reach the fin during maximum abduction. Dye flow visualization confirmed this estimate, revealing that the opercular flow wraps around the base of the fin during peak abduction, when it is likely to have little hydrodynamic effect.     

A comparison of pectoral fin ray morphology and its impact on fin ray flexural stiffness in labriform swimmers

The organization of tissues in appendages often affects their mechanical properties and function. In the fish family Labridae, swimming behavior is associated with pectoral fin flexural stiffness and morphology, where fins range on a continuum from stiff to relatively flexible fins. Across this diversity, pectoral fin flexural stiffness decreases exponentially along the length of any given fin ray, and ray stiffness decreases along the chord of the fin from the leading to trailing edge. In this study, we examine the morphological properties of fin rays, including the effective modulus in bending (E), second moment of area (I), segmentation, and branching patterns, and their impact on fin ray stiffness. We quantify intrinsic pectoral fin ray stiffness in similarly sized fins of two closely related species that employ fins of divergent mechanics, the flapping Gomphosus varius and the rowing Halichoeres bivittatus. While segmentation patterns and E were similar between species, measurements of I and the number of fin ray branch nodes were greater in G. varius than in H. bivittatus. A multiple regression model found that of these variables, I was always significantly correlated with fin ray flexural stiffness and that variation in I always explained the majority of the variation in flexural stiffness. Thus, while most of the morphological variables quantified in this study correlate with fin ray flexural stiffness, second moment of area is the greatest factor contributing to variation in flexural stiffness. Further, interspecific variation in fin ray branching pattern could be used as a means of tuning the effective stiffness of the fin webbing to differences in swimming behavior and hydrodynamics. The comparison of these results to other systems begins to unveil fundamental morphological features of biological beams and yields insight into the role of mechanical properties in fin deformation for aquatic locomotion.     

Synchronized swimming: coordination of pelvic and pectoral fins during augmented punting by the freshwater stingray Potamotrygon orbignyi

Benthic animals live at the juncture of fluid and solid environments, an interface that shapes many aspects of their behavior, including their means of locomotion. Aquatic walking and similar substrate-dependent forms of underwater propulsion have evolved multiple times in benthic invertebrate and vertebrate taxa, including batoid elasmobranchs. Skates (Rajidae) use the pelvic fins to punt across the substrate, keeping the pectoral fin disc still. Other batoids combine pelvic fin motions with pectoral fin undulation in augmented punting, but the coordination of these two modes has not been described. In this study of an augmented punter, the freshwater stingray Potamotrygon orbignyi, we demonstrate the synchrony of pelvic and pectoral fin cycles. The punt begins as the pelvic fins, held in an anterior position, are planted into the substrate and used to push the body forward. Meanwhile, a wave of pectoral fin undulation begins, increasing to maximum height just before the cycle's halfway point, when the pelvic fins reach their furthest posterior extension. The pectoral fin wave subsides as the pelvic fins return to their starting position for subsequent punts. Despite definitive links between pectoral and pelvic fin activity, we find no significant relationship between pectoral fin kinematics (frequency, wave height, and wave speed) and punt performance. However, slip calculations indicate that pectoral undulation can produce thrust and augment punting. Pelvic fin kinematics (frequency and duty factor) have significant effects, suggesting that while both sets of fins contribute to thrust generation, the pelvic fins likely determine punt performance.     

A Three-Dimensional Kinematics Analysis of a Koi Carp Pectoral Fin by Digital Image Processing

Pectoral fins fascinate researchers for their important role in fish maneuvers. By possessing a complicated flexible structure with several fin rays made by a thin film, the fin exhibits a three-dimensional (3D) motion. The complex 3D fin kinematics makes it challenging to study the performance of pectoral fin. Nevertheless, a detailed study on the 3D motion pattern of pectoral fins is necessary to the design and control of a bio-inspired fin rays. Therefore, a highspeed photography system is introduced in this paper to study the 3D motion of a Koi Carp by analyzing the two views of its pectoral fin simultaneously. The key motions of the pectoral fins are first captured in both hovering and retreating. Next, the 3D configuration of the pectoral fins is reconstructed by digital image processing, in which the movement of fin rays during fish retreating and hovering is obtained. Furthermore, the method of Singular Value Decomposition (SVD) is adopted to extract the basic motion patterns of pectoral fins from extensive image sequences, i.e. expansion, bending, cupping, and undulation. It is believed that the movement of the fin rays and the basic patterns of the pectoral fins obtained in the present work can provide a good foundation for the development and control of bionic flexible pectoral fins for underwater propeller.     

Wake dynamics and locomotor function in fishes: interpreting evolutionary patterns in pectoral fin design

The great anatomical diversification of paired fins within theActinopterygii (ray-finned fishes) can be understood as a suiteof evolutionary transformations in design. At a broad taxonomicscale, two clear trends exist in the morphology of the anteriorlysituated pectoral fins. In comparing basal to more derived clades,there are general patterns of (i) reorientation of the pectoralfin base from a nearly horizontal to more vertical inclination,and (ii) migration of the pectoral fin from a ventral to mid-dorsalbody position. As yet, the functional significance of thesehistorical trends in pectoral fin design remains largely untestedby experiment. In this paper we test the proposal that variationin pectoral fin structure has an important influence on themagnitude and orientation of fluid forces generated during maneuveringlocomotion. Using digital particle image velocimetry for quantitativewake visualization, we measure swimming forces in ray-finnedfishes exhibiting the plesiomorphic and apomorphic pectoralfin anatomy. Our experiments focus on rainbow trout (Oncorhynchusmykiss), a lower teleost with pectoral fins positioned ventrallyand with nearly horizontally inclined fin bases, and bluegillsunfish (Lepomis macrochirus), a relatively derived perciformfish with more vertically oriented pectoral fins positionedmid-dorsally on the body. In support of hypotheses arising fromour prior wake studies and previously untested models in theliterature, we find that the pectoral fins of sunfish generatesignificantly higher forces for turning and direct braking forcescloser to the center of mass of the body than the pectoral finsof trout. These results provide insight into the hydrodynamicimportance of major evolutionary transformations in pectoralfin morphology within the Actinopterygii.     

Functional morphology of the fin rays of teleost fishes

Ray‐finned fishes are notable for having flexible fins that allow for the control of fluid forces. A number of studies have addressed the muscular control, kinematics, and hydrodynamics of flexible fins, but little work has investigated just how flexible ray‐finned fish fin rays are, and how flexibility affects their response to environmental perturbations. Analysis of pectoral fin rays of bluegill sunfish showed that the more proximal portion of the fin ray is unsegmented while the distal 60% of the fin ray is segmented. We examined the range of motion and curvatures of the pectoral fin rays of bluegill sunfish during steady swimming, turning maneuvers, and hovering behaviors and during a vortex perturbation impacting the fin during the fin beat. Under normal swimming conditions, curvatures did not exceed 0.029 mm^?1 in the proximal, unsegmented portion of the fin ray and 0.065 mm^?1 in the distal, segmented portion of the fin ray. When perturbed by a vortex jet traveling at approximately 1 ms^?1 (67 ± 2.3 mN s.e. of force at impact), the fin ray underwent a maximum curvature of 9.38 mm^?1. Buckling of the fin ray was constrained to the area of impact and did not disrupt the motion of the pectoral fin during swimming. Flexural stiffness of the fin ray was calculated to be 565 × 10^?6 Nm². In computational fluid dynamic simulations of the fin‐vortex interaction, very flexible fin rays showed a combination of attraction and repulsion to impacting vortex dipoles. Due to their small bending rigidity (or flexural stiffness), impacting vortices transferred little force to the fin ray. Conversely, stiffer fin rays experienced rapid small‐amplitude oscillations from vortex impacts, with large impact forces all along the length of the fin ray. Segmentation is a key design feature of ray‐finned fish fin rays, and may serve as a means of making a flexible fin ray out of a rigid material (bone). This flexibility may offer intrinsic damping of environmental fluid perturbations encountered by swimming fish. J. Morphol. 274:1044–1059, 2013. © 2013 Wiley Periodicals, Inc.     

Experimental Hydrodynamics and Evolution: Function of Median Fins in Ray-finned Fishes

The median fins of fishes consist of the dorsal, anal, and caudal fins and have long been thought to play an important role in generating locomotor force during both steady swimming and maneuvering. But the orientations and magnitudes of these forces, the mechanisms by which they are generated, and how fish modulate median fin forces have remained largely unknown until the recent advent of Digital Particle Image Velocimetry (DPIV) which allows empirical analysis of force magnitude and direction. Experimental hydrodynamic studies of median fin function in fishes are of special utility when conducted in a comparative phylogenetic context, and we have examined fin function in four ray-finned fish clades (sturgeon, trout, sunfish, and mackerel) with the goal of testing classical hypotheses of fin function and evolution. In this paper we summarize two recent technical developments in DPIV methodology, and discuss key recent findings relevant to median fin function. High-resolution DPIV using a recursive local-correlation algorithm allows quantification of small vortices, while stereo-DPIV permits simultaneous measurement of x, y, and z flow velocity components within a single planar light sheet. Analyses of median fin wakes reveal that lateral forces are high relative to thrust force, and that mechanical performance of median fins (i.e., thrust as a proportion of total force) averages 0.35, a surprisingly low value. Large lateral forces which could arise as an unavoidable consequence of thrust generation using an undulatory propulsor may also enhance stability and maneuverability. Analysis of hydrodynamic function of the soft dorsal fin in bluegill sunfish shows that a thrust wake is generated that accounts for 12% of total thrust and that the thrust generation by the caudal fin may be enhanced by interception of the dorsal fin wake. Integration of experimental studies of fin wakes, computational approaches, and mechanical models of fin function promise understanding of instantaneous forces on fish fins during the propulsive cycle as well as exploration of a broader locomotor design space and its hydrodynamic consequences.     

A Novel Implementation of a Flexible Robotic Fin Actuated by Shape Memory Alloy

In this paper,study of a novel flexible robotic-fin actuated by Shape Memory Alloy (SMA) is presented.The developed robotic fin is capable of implementing various 3-Dimensional (3D) motions,which plays an important role in robot propulsion and maneuverability.Firstly,the morphological and mechanics parameters of a real pectoral fin from a carp are investigated.Secondly,a detailed design of the flexible pectoral fin driven by SMA is presented according to the previous morphological and mechanics analyses.Thirdly,a simplified theoretical model on the SMA fin plate is derived.The thermodynamics of the SMA plate and the relationship between curvature and phase transformation are analyzed.Finally,several simulations and model experiments are conducted according to the previous analyses.The results of the experiments are useful for the control of the robotic fin.The experimental results reveal that the SMA actuated fin ray has a good actuating performance.     

Biomechanics of swimming in the pufferfish Diodon holocanthus: propulsive momentum enhancement is an adaptation for thrust production in an undulatory median and paired-fin swimmer

A form of large-amplitude elongated-body theory appropriate for the analysis of undulatory fins attached to a rigid body of elliptical section suggests a benefit due to momentum enhancement relative to the fins on their own. This theoretical prediction is experimentally confirmed for the first time. Theoretical momentum enhancement factors for Diodon holocanthus (2.2 and 2.7 for the median and pectoral fins, respectively) compared well to inferred thrust values determined from particle-image velocimetry (PIV) wake measurements (2.2-2.4 and 2.7-2.9). Caudal fin mean theoretical thrust was not significantly different from measured (PIV) values (n = 24, P > 0.05), implying no momentum enhancement. Pectoral-fin thrust was half that of the median and caudal fins due to high fin-jet angles, low circulation and momentum. Average total fin thrust and fish drag were not significantly different (n = 24, P > 0.05). Vortex rings generated by the fins were elliptical, with size dependent on fin chord and stroke amplitude. Hydrodynamic advantages (thrust enhancement at no cost to hydrodynamic efficiency, reduction of side forces minimizing energy wasting yawing motions and body drag) are probably common among rigid-bodied organisms propelled by undulatory fins. A trade-off between momentum enhancement and the rate of momentum generation (thrust force) sets a practical limit to the former. For small fins whilst momentum enhancement is high, absolute thrust is low. In addition, previously suggested limitations on thrust enhancement set by reductions in propulsive force associated with progressive reductions in fin wavelength are found to be biologically unrealistic.