Analysis of the effect of swimmer's head position on swimming performance using computational fluid dynamics

The aim of this numerical work is to analyze the effect of the position of the swimmer's head on the hydrodynamic performances in swimming. In this initial study, the problem was modeled as 2D and in steady hydrodynamic state. The geometry is generated by the CAD software CATIA and the numerical simulation is carried out by the use of the CFD Fluent code. The standard k-epsilon turbulence model is used with a specific wall law. Three positions of the head were studied, for a range of Reynolds numbers about 10(6). The obtained numerical results revealed that the position of the head had a noticeable effect on the hydrodynamic performances, strongly modifying the wake around the swimmer. The analysis of these results made it possible to propose an optimal position of the head of a swimmer in underwater swimming.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Propulsion Modeling and Analysis of a Biomimetic Swimmer

<正> We have studied a biomimetic swimmer based on the motion of bacteria such as Escherichia coli (E. coli) theoretically andexperimentally. The swimmer has an ellipsoidal cell body propelled by a helical filament. The performance of this swimmer wasestimated by modeling the dynamics of a swimmer in viscous fluid. We applied the Resistive Force Theory (RFT) on this modelto calculate the linear swimming speed and the efficiency of the model. A parametric study on linear velocity and efficiency tooptimize the design of this swimmer was demonstrated. In order to validate the theoretical results, a biomimetic swimmer wasfabricated and an experiment setup was prepared to measure the swimming speed and thrust force in silicone oil. The experimentalresults agree well with the theoretical values predicted by RFT. In addition, we studied the flow patterns surrounding thefilament with a finite element simulation with different Reynolds number (Re) to understand the mechanism of propulsion. Thesimulation results provide information on the nature of flow patterns generated by swimming filament. Furthermore, the thrustforces from the simulation were compared with the thrust forces from theory. The simulation results are in good agreement withthe theoretical results.     

Unsteady flow field around a human hand and propulsive force in swimming

Much effort has been undertaken for the estimation of propulsive force of swimmers in the front crawl. Estimation is typically based on steady flow theory: the so-called quasi-steady analysis. Flow fields around a swimmer, however, are extremely unsteady because the change direction of hand produces unsteady vortex motions. To evaluate the force correctly, it is necessary to know the unsteady properties determined from the vortex dynamics because that unsteadiness is known to make the force greater. Unsteady flow measurements were made for this study using a sophisticated technique called particle image velocimetry (PIV) in several horizontal planes for subjects swimming in a flume. Using that method, a 100 time-sequential flow fields are obtainable simultaneously. Each flow field was calculated from two particle images using the cross-correlation method. The intensity of vortices and their locations were identified. A strong vortex was generated near the hand and then shed by directional change of the hand in the transition phase from in-sweep to out-sweep. When the vortex was shed, a new vortex rotating in the opposite direction around the hand was created. The pair of vortices induced the velocity component in the direction opposite to the swimming. Results of this study show that the momentum change attributable to the increase in this velocity component is the origin of thrust force by the hand.     

Numerical simulations of undulatory swimming at moderate Reynolds number

We perform numerical simulations of the swimming of a three-linkage articulated system in a moderately viscous regime. The computational methodology focuses on the creation, diffusion and transport of vorticity from the surface of the bodies into the fluid. The simulations are dynamically coupled, in that the motion of the three-linkage swimmer is computed simultaneously with the dynamics of the fluid. The novel coupling scheme presented in this work is the first to exploit the relationship between vorticity creation and body dynamics. The locomotion of the system, when subject to undulatory inputs of the hinges, is computed at Reynolds numbers of 200 and 1000. It is found that the forward swimming speed increases with the Reynolds number, and that in both cases the swimming is slower than in an inviscid medium. The vortex shedding is examined, and found to exhibit behavior consistent with experimental flow visualizations of fish.     

Flow visualization of competitive swimming techniques: the tufts method

The purpose of this study was to evaluate the use of tufts to visualize the flow of water around the trunk and limbs of a swimmer. Numerous pilot studies were conducted to evaluate the effectiveness of different tuft materials, dimensions and methods of attachment for recording the characteristics of the flow around a swimmer performing various strokes and drills. Differences in the patterns of flow made visible by the tufts suggested that this method of flow visualization may well be useful in resolving both basic and applied questions concerning swimming techniques.     

Collective bacterial dynamics revealed using a three-dimensional population-scale defocused particle tracking technique

An ability to monitor bacterial locomotion and collective dynamics is crucial to our understanding of a number of well-characterized phenotypes including biofilm formation, chemotaxis, and virulence. Here, we report the tracking of multiple swimming Escherichia coli cells in three spatial dimensions and at single-cell resolution using a novel three-dimensional (3D) defocused particle tracking (DPT) method. The 3D trajectories were generated for wild-type Escherichia coli strain RP437 as well as for isogenic derivatives that display smooth swimming due to a cheA deletion (strain RP9535) or incessant tumbling behavior due to a cheZ deletion (strain RP1616). The 3D DPT method successfully differentiated these three modes of locomotion and allowed direct calculation of the diffusion coefficient for each strain. As expected, we found that the smooth swimmer diffused more readily than the wild type, and both the smooth swimmer and the wild-type cells exhibited diffusion coefficients that were at least two orders of magnitude larger than that of the tumbler. Finally, we found that the diffusion coefficient increased with increasing cell density, a phenomenon that can be attributed to the hydrodynamic disturbances caused by neighboring bacteria.     

A simulation study of the dynamics of a driven filament in an Aristotelian fluid

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small-amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and stiffness, there is a driving frequency that is optimal for both speed and efficiency. However, we find that to calculate absolute values of the swimming speed we need to slightly modify existing theoretical approaches. For the more relevant case of large-amplitude motion we find that while the basic picture remains the same, the dependence of the swimming speed on both frequency and amplitude is substantially modified. For large-amplitudes we show that the one-armed swimmer is comparatively neither inefficient nor slow. This begs the question, why are there little or no one-armed swimmers in nature?     

Three-dimensional CFD analysis of the hand and forearm in swimming

The purpose of this study was to analyze the hydrodynamic characteristics of a realistic model of an elite swimmer hand/forearm using three-dimensional computational fluid dynamics techniques. A three-dimensional domain was designed to simulate the fluid flow around a swimmer hand and forearm model in different orientations (0°, 45°, and 90° for the three axes Ox, Oy and Oz). The hand/forearm model was obtained through computerized tomography scans. Steady-state analyses were performed using the commercial code Fluent. The drag coefficient presented higher values than the lift coefficient for all model orientations. The drag coefficient of the hand/forearm model increased with the angle of attack, with the maximum value of the force coefficient corresponding to an angle of attack of 90°. The drag coefficient obtained the highest value at an orientation of the hand plane in which the model was directly perpendicular to the direction of the flow. An important contribution of the lift coefficient was observed at an angle of attack of 45°, which could have an important role in the overall propulsive force production of the hand and forearm in swimming phases, when the angle of attack is near 45°.     

Analysis of a swimmer's hand and arm in steady flow conditions using computational fluid dynamics

Propulsive forces generated by swimmers' hands and arms have, to date, been determined strictly through experimental testing. As an alternative to these complex and costly experiments, the present research has applied the numerical technique of computational fluid dynamics (CFD) to calculate the steady flow around a swimmer's hand and arm at various angles of attack. Force coefficients computed for the hand and arm compared well with steady-state coefficients determined experimentally. The simulations showed significant boundary layer separation from the arm and hand, suggesting that Bernoulli's equation should not be used to mathematically describe the lift generated by a swimmer. Additionally, "2D" lift was shown to be inaccurate for the arm at all angles of attack and for the hand near angles of attack of 90 degrees. Such simulations serve to validate the chosen CFD techniques, and are an important first step towards the use of CFD methods for determining swimming hydrodynamic forces in more complex unsteady flow conditions.     

Collective Bacterial Dynamics Revealed Using a Three-Dimensional Population-Scale Defocused Particle Tracking Technique

An ability to monitor bacterial locomotion and collective dynamics is crucial to our understanding of a number of well-characterized phenotypes including biofilm formation, chemotaxis, and virulence. Here, we report the tracking of multiple swimming Escherichia coli cells in three spatial dimensions and at single-cell resolution using a novel three-dimensional (3D) defocused particle tracking (DPT) method. The 3D trajectories were generated for wild-type Escherichia coli strain RP437 as well as for isogenic derivatives that display smooth swimming due to a cheA deletion (strain RP9535) or incessant tumbling behavior due to a cheZ deletion (strain RP1616). The 3D DPT method successfully differentiated these three modes of locomotion and allowed direct calculation of the diffusion coefficient for each strain. As expected, we found that the smooth swimmer diffused more readily than the wild type, and both the smooth swimmer and the wild-type cells exhibited diffusion coefficients that were at least two orders of magnitude larger than that of the tumbler. Finally, we found that the diffusion coefficient increased with increasing cell density, a phenomenon that can be attributed to the hydrodynamic disturbances caused by neighboring bacteria.     

Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations

Recently, there has been a number of experimental studies convincingly demonstrating that a suspension of self-propelled bacteria (microswimmers in general) may have an effective viscosity significantly smaller than the viscosity of the ambient fluid. This is in sharp contrast with suspensions of hard passive inclusions, whose presence always increases the viscosity. Here we present a 2D model for a suspension of microswimmers in a fluid and analyze it analytically in the dilute regime (no swimmer–swimmer interactions) and numerically using a Mimetic Finite Difference discretization. Our analysis shows that in the dilute regime (in the absence of rotational diffusion) the effective shear viscosity is not affected by self-propulsion. But at the moderate concentrations (due to swimmer–swimmer interactions) the effective viscosity decreases linearly as a function of the propulsion strength of the swimmers. These findings prove that (i) a physically observable decrease of viscosity for a suspension of self-propelled microswimmers can be explained purely by hydrodynamic interactions and (ii) self-propulsion and interaction of swimmers are both essential to the reduction of the effective shear viscosity. We also performed a number of numerical experiments analyzing the dynamics of swimmers resulting from pairwise interactions. The numerical results agree with the physically observed phenomena (e.g., attraction of swimmer to swimmer and swimmer to the wall). This is viewed as an additional validation of the model and the numerical scheme.     

Effect of body roll amplitude and arm rotation speed on propulsion of arm amputee swimmers

Only a limited amount of research has gone into evaluating the contribution made by the upper arm to the propulsion of elite swimmers with an amputation at elbow level. With assistance of computational fluid dynamics (CFD) modelling, the swimming technique of competitive arm amputee swimmers can be assessed through numerical simulations which test the effect of various parameters on the effectiveness of the swimming propulsion.This numerical study investigates the effect of body roll amplitude and of upper arm rotation speed on the propulsion of an arm amputee swimmer, at different mean swimming speeds. Various test cases are simulated resulting in a thorough analysis of the complex body/fluid interaction with a detailed quantitative assessment of the effect of the variation of each parameter on the arm propulsion. It is found that a body roll movement with an amplitude of 45° enhances greatly the propulsive contribution from the upper arm with an increase of about 70% in the propulsive force compared to the no roll condition. An increase in the angular velocity of the upper arm also leads to a concomitant increase in the propulsive forces produced by the arm.Such results have direct implications for competitive arm amputee front crawl swimmers and for those who coach them. One important message that emerges in this present work is that there exists, for any given swimming speed, a minimum angular velocity at which the upper arm must be rotated to generate effective propulsion. Below this velocity, the upper arm will experience a net resistive drag force which adversely affects swimming performance.     

Effect of leg kick on active drag in front-crawl swimming: Comparison of whole stroke and arms-only stroke during front-crawl and the streamlined position

The purpose of this study was to examine the effect of leg kick on the resistance force in front-crawl swimming. The active drag in front-crawl swimming with and without leg motion was evaluated using measured values of residual thrust (MRT method) and compared with the passive drag of the streamlined position (SP) for the same swimmers. Seven male competitive swimmers participated in this study, and the testing was conducted in a swimming flume. Each swimmer performed front-crawl under two conditions: using arms and legs (whole stroke: WS) and using arms only (arms-only stroke: AS). Active drag and passive drag were measured at swimming velocities of 1.1 and 1.3 m s⁻¹ using load cells connected to the swimmer via wires. We calculated a drag coefficient to compare the resistances of the WS, AS and SP at each velocity. For both the WS and AS at both swimming velocities, active drag coefficient was found to be about 1.6–1.9 times larger than that in passive conditions. In contrast, although leg movement did not cause a difference in drag coefficient for front-crawl swimming, there was a large effect size (d = 1.43) at 1.3 m s⁻¹. Therefore, although upper and lower limb movements increase resistance compared to the passive condition, the effect of leg kick on drag may depend on swimming velocity.     

Turbulence model choice for the calculation of drag forces when using the CFD method

The aim of this work is to specify which model of turbulence is the most adapted in order to predict the drag forces that a swimmer encounters during his movement in the fluid environment. For this, a Computational Fluid Dynamics (CFD) analysis has been undertaken with a commercial CFD code (Fluent^®). The problem was modelled as 3D and in steady hydrodynamic state. The 3D geometry of the swimmer was created by means of a complete laser scanning of the swimmer’s body contour. Two turbulence models were tested, namely the standard k–ε model with a specific treatment of the fluid flow area near the swimmer’s body contour, and the standard k–ω model. The comparison of numerical results with experimental measurements of drag forces shows that the standard k–ω model accurately predicts the drag forces while the standard k–ε model underestimates their values. The standard k–ω model also enabled to capture the vortex structures developing at the swimmer’s back and buttocks in underwater swimming; the same vortices had been visualized by flow visualization experiments carried out at the INSEP (National Institute for Sport and Physical Education in Paris) with the French national swimming team.     

A quasi three-dimensional visualization of unsteady wake flow in human undulatory swimming

Human undulatory underwater swimming (UUS) is an underwater propelling technique in competitive swimming and its propulsive mechanism is poorly understood. The purpose of this study was to visualize the three-dimensional (3D) flow field in the wake region during human UUS in a water flume. A national level male swimmer performed 41 UUS trials in a water flume. A motion capture system and stereo particle image velocimetry (PIV) equipment were used to investigate the 3D coordinates of the swimmer and 3D flow fields in the wake region. After one kick cycle was divided into eight phases, we conducted coordinate transformations and phase averaging method to construct quasi 3D flow fields. At the end of the downward kick, the lower limbs external rotations of the lower limbs were observed, and the feet approached towards each other. A strong downstream flow, i.e. a jet was observed in the wake region during the downward kick, and the paired vortex structure was accompanied by a jet. In the vortex structure, a cluster of vortices and a jet were generated in the wake during the downward kick, and the vortices were subsequently shed from the feet by the rotated leg motion. This suggested that the swimmer gained a thrust by creating vortices around the foot during the downward kick, which collided to form a jet. This paper describes, illustrates, and explains the propulsive mechanism of human UUS.     

The Orientation of Swimming Biflagellates in Shear Flows

Biflagellated algae swim in mean directions that are governed by their environments. For example, many algae can swim upward on average (gravitaxis) and toward downwelling fluid (gyrotaxis) via a variety of mechanisms. Accumulations of cells within the fluid can induce hydrodynamic instabilities leading to patterns and flow, termed bioconvection, which may be of particular relevance to algal bioreactors and plankton dynamics. Furthermore, knowledge of the behavior of an individual swimming cell subject to imposed flow is prerequisite to a full understanding of the scaled-up bulk behavior and population dynamics of cells in oceans and lakes; swimming behavior and patchiness will impact opportunities for interactions, which are at the heart of population models. Hence, better estimates of population level parameters necessitate a detailed understanding of cell swimming bias. Using the method of regularized Stokeslets, numerical computations are developed to investigate the swimming behavior of and fluid flow around gyrotactic prolate spheroidal biflagellates with five distinct flagellar beats. In particular, we explore cell reorientation mechanisms associated with bottom-heaviness and sedimentation and find that they are commensurate and complementary. Furthermore, using an experimentally measured flagellar beat for Chlamydomonas reinhardtii, we reveal that the effective cell eccentricity of the swimming cell is much smaller than for the inanimate body alone, suggesting that the cells may be modeled satisfactorily as self-propelled spheres. Finally, we propose a method to estimate the effective cell eccentricity of any biflagellate when flagellar beat images are obtained haphazardly.     

The effect of finger spreading on drag of the hand in human swimming

The effect of finger spread on overall drag on a swimmer’s hand is relatively small, but could be relevant for elite swimmers. There are many sensitivities in measuring this effect. A comparison between numerical simulations, experiments and theory is urgently required to observe whether the effect is significant. In this study, the beneficial effect of a small finger spread in swimming is confirmed using three different but complementary methods. For the first time numerical simulations and laboratory experiments are conducted on the exact same 3D model of the hand with attached forearm. The virtual version of the hand with forearm was implemented in a numerical code by means of an immersed boundary method and the 3D printed physical version was studied in a wind tunnel experiment. An enhancement of the drag coefficient of 2% and 5% compared to the case with closed fingers was found for the numerical simulation and experiment, respectively. A 5% and 8% favorable effect on the (dimensionless) force moment at an optimal finger spreading of 10° was found, which indicates that the difference is more outspoken in the force moment. Moreover, an analytical model is proposed, using scaling arguments similar to the Betz actuator disk model, to explain the drag coefficient as a function of finger spacing.     

Effect of propelling surface size on the mechanics and energetics of front crawl swimming

In swimming the propulsive force is generated by giving a velocity change to masses of water. In this process energy is transferred from the swimmer to the water, which cannot be used to propel the swimmer. Theoretical considerations indicated that an increase of the propelling surface size should lead to a reduced loss of energy to the water. Thus, in this study, the effect of artificially enlarging the propelling surface of the hand was examined. The effect was examined in terms of the propelling efficiency during front crawl swimming using the arms alone. The legs were floated with a small buoy as previously described (Toussaint et al., J. appl. Physiol. 65, 2506-2512, 1988a). In ten competitive swimmers (six male, four female) the rate of energy expenditure (power input, Pi), power output (Po), work per stroke cycle (As), distance per stroke cycle (d), work per unit distance (Ad), and propelling efficiency (ep) were determined at various swimming speeds once with and once swimming without paddles. At the same average velocity the effect of swimming with paddles was to reduce Pi, Po, and Ad by 6, 7.6, and 7.5% respectively, but to increase ep and As by 7.8 and 7%. The increase in distance per stroke cycle and the decrease in stroke cycle frequency matched the predicted values based on the theoretical considerations in which the actual increase in propelling surface size was taken into account.