Mechanical and propelling efficiency in swimming derived from exercise using a laboratory-based whole-body swimming ergometer

Determining the efficiency of a swimming stroke is difficult because different "efficiencies" can be computed based on the partitioning of mechanical power output (W) into its useful and nonuseful components, as well as because of the difficulties in measuring the forces that a swimmer can exert in water. In this paper, overall efficiency (η(O) = W(TOT)/?, where W(TOT) is total mechanical power output, and ? is overall metabolic power input) was calculated in 10 swimmers by means of a laboratory-based whole-body swimming ergometer, whereas propelling efficiency (η(P) = W(D)/W(TOT), where W(D) is the power to overcome drag) was estimated based on these values and on values of drag efficiency (η(D) = W(D)/?): η(P) = η(D)/η(O). The values of η(D) reported in the literature range from 0.03 to 0.09 (based on data for passive and active drag, respectively). η(O) was 0.28 ± 0.01, and η(P) was estimated to range from ～0.10 (η(D) = 0.03) to 0.35 (η(D) = 0.09). Even if there are obvious limitations to exact simulation of the whole swimming stroke within the laboratory, these calculations suggest that the data reported in the literature for η(O) are probably underestimated, because not all components of W(TOT) can be measured accurately in this environment. Similarly, our estimations of η(P) suggest that the data reported in the literature are probably overestimated.     

Experiment about Drag Reduction of Bionic Non-smooth Surface in Low Speed Wind Tunnel

The body surface of some organisms has non-smooth structure, which is related to drag reduction in moving fluid. To imitate these structures, models with a non-smooth surface were made. In order to find a relationship between drag reduction and the non-smooth surface, an orthogonal design test was employed in a low speed wind tunnel. Six factors likely to influence drag reduction were considered, and each factor tested at three levels. The six factors were the configuration, diameter/bottom width, height/depth, distribution, the arrangement of the rough structures on the experimental model and the wind speed. It was shown that the non-smooth surface causes drag reduction and the distribution of non-smooth structures on the model, and wind speed, are the predominant factors affecting drag reduction. Using analysis of variance, the optimal combination and levels were obtained, which were a wind speed of 44 m/s, distribution of the non-smooth structure on the tail of the experimental model, the configuratio     

The effect of Reynolds number on the propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

The effect of Reynolds number on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of its propulsion system with squid. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and dimensionless frequency (St(L)) in the range 0.2-0.6 in a glycerin-water mixture. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses from the velocity and vorticity fields of the jet flow to calculate the pulsed-jet propulsive efficiency, and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 37 and 60. The current results for propulsive efficiency were compared to the previously published results in water where Re ranged between 1300 and 2700. The results showed that the average propulsive efficiency decreased by 26% as the average Re decreased from 2000 to 50 while the ratio of pulsed-jet to steady jet efficiency (η(P)/η(P, ss)) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved η(P)/η(P, ss) at lower Re suggests that pulsed-jet propulsion can be used as an efficient propulsion system for millimeter-scale propulsion applications. The Re = 37-60 conditions in the present investigation, showed a reduced dependence of η(P) and η(P)/η(P, ss)on L/D compared to higher Re results. This may be due to the lack of clearly observed vortex ring pinch-off as L/D increased for this Re regime.     

The hemodynamic forces acting on thrombi, from incipient attachment of single cells to maturity and embolization

We consider the steady fluid forces acting on a thrombus from the time of first contact of a single cell with a natural or artificial surface, through the attachment process and growth to embolization. For a hemi-spherical or cylindrical attached cell of height less than 1/100-1/20th of the channel width, shear and tensile stresses are solely dependent on viscosity and on the ratio of average fluid velocity to channel width vt/Dt (shear rate). Large values of this ratio reduce adhesion and increase embolization. The average shear stress on such cells is approximately 1-10 Pa (10-100 dyn cm2), the average tensile stress about three times higher. For other shapes and larger protrusions, stress varies with protrusion height as well. Maturing thrombi composed of cell aggregates embedded in a fibrin mesh do not appear to allow significant fluid flow through their porous structure. The interior forces are then due solely to hydrostatic pressure and initially vary directly with vt/Dt and inversely with thrombus height Hp, thus favouring embolization at an early stage and in arterial systems. Rough surfaces are identified as causing an increase in dwell-time and possibly immobilizing an unattached cell due to 'negative lift'.     

Parameter study of simplified dragonfly airfoil geometry at Reynolds number of 6000

Aerodynamic study of a simplified Dragonfly airfoil in gliding flight at Reynolds numbers below 10,000 is motivated by both pure scientific interest and technological applications. At these Reynolds numbers, the natural insect flight could provide inspiration for technology development of Micro UAV’s and more. Insect wings are typically characterized by corrugated airfoils. The present study follows a fundamental flow physics study (Levy and Seifert, 2009), that revealed the importance of flow separation from the first corrugation, the roll-up of the separated shear layer to discrete vortices and their role in promoting flow reattachment to the aft arc, as the leading mechanism enabling high-lift, low drag performance of the Dragonfly gliding flight. This paper describes the effect of systematic airfoil geometry variations on the aerodynamic properties of a simplified Dragonfly airfoil at Reynolds number of 6000.The parameter study includes a detailed analysis of small variations of the nominal geometry, such as corrugation placement or height, rear arc and trailing edge shape.Numerical simulations using the 2D laminar Navier-Stokes equations revealed that the flow accelerating over the first corrugation slope is followed by an unsteady pressure recovery, combined with vortex shedding. The latter allows the reattachment of the flow over the rear arc. Also, the drag values are directly linked to the vortices’ magnitude. This parametric study shows that geometric variations which reduce the vortices’ amplitude, as reduction of the rear cavity depth or the reduction of the rear arc and trailing edge curvature, will reduce the drag values. Other changes will extend the flow reattachment over the rear arc for a larger mean lift coefficients range; such as the negative deflection of the forward flat plate. These changes consequently reduce the drag values at higher mean lift coefficients.The detailed geometry study enabled the definition of a corrugated airfoil geometry with enhanced aerodynamic properties, such as range and endurance factors, as compared to the nominal airfoil studied in the literature.     

Flow around cells adhered to a microvessel wall. I. Fluid stresses and forces acting on the cells

To evaluate the fluid forces acting on cells adhered to a microvessel wall, we numerically studied the flow field around adherent cells and the distribution of the stresses on their surfaces. For simplicity, the cells were modeled as rigid particles attached to a wall of a circular cylindrical tube regularly in the flow direction, in a row or two rows. It was found that not the detailed shape of the model cells but their height from the vessel wall is a key determinant of the fluid forces and torque acting on them. In both arrangements of one row and two rows, the axial spacing between neighboring adherent cells significantly affects the distributions of the stresses on them, which results in drastic variations of the fluid forces with the axial spacing and the relative positions with respect to their neighboring cells. The drag force acting on an adherent cell in the vessel was evaluated to be larger than the value in the 2D chamber flow at the same wall shear stress, mainly due to much larger variations of the pressure distribution on the cell surface in the vessel flow.     

Reduction of barnacle recruitment on micro‐textured surfaces: Analysis of effective topographic characteristics and evaluation of skin friction

This study investigates five designed micro‐textured surfaces and their effects on barnacle fouling and hydrodynamic drag. Three of the micro‐textures were developed in the present study and evaluated together with two commercial riblet films. All micro‐structures were arranged as longitudinal grooves with different profile depths, widths and angles of inclination. In field tests the recruitment of the barnacle Balanus improvisus on micro‐textured surfaces and smooth controls was evaluated. All micro‐textured surfaces reduced recruitment, and the most efficient texture reduced recruitment by 98%. For some micro‐textures the reduction of recruitment declined as settlement intensity increased. In a correlative analysis, the trigonometric inclination of the micro‐structures explained most of the recruitment reduction. The steepest angle of inclination caused a massive reduction in barnacle settlement. Surface micro‐structures may affect the boundary‐layer flow and the hydrodynamic drag (skin friction) of the surface. The skin friction was empirically measured in a flow channel using a sub‐set of the tested micro‐textures. The measurements of skin friction showed that the orientation of the microstructures is important, with a minimum friction when the grooves are parallel to the flow. For one of the micro‐textures the skin friction was ca 10% lower compared to a hydraulically smooth surface. It is concluded that, depending on the flow speed, micro‐textures will not significantly increase skin friction when arranged parallel to the flow, even at moderate protrusion through the viscous sub‐layer.     

Computational fluid dynamics analysis of drag and convective heat transfer of individual body segments for different cyclist positions

This study aims at investigating drag and convective heat transfer for cyclists at a high spatial resolution. Such an increased spatial resolution, when combined with flow-field data, can increase insight in drag reduction mechanisms and in the thermo-physiological response of cyclists related to heat stress and hygrothermal performance of clothing. Computational fluid dynamics (steady Reynolds-averaged Navier-Stokes) is used to evaluate the drag and convective heat transfer of 19 body segments of a cyclist for three different cyclist positions. The influence of wind speed on the drag is analysed, indicating a pronounced Reynolds number dependency on the drag, where more streamlined positions show a dependency up to higher Reynolds numbers. The drag and convective heat transfer coefficient (CHTC) of the body segments and the entire cyclist are compared for all positions at racing speeds, showing high drag values for the head, legs and arms and high CHTCs for the legs, arms, hands and feet. The drag areas of individual body segments differ markedly for different cyclist positions whereas the convective heat losses of the body segments are found to be less sensitive to the position. CHTC-wind speed correlations are derived, in which the power-law exponent does not differ significantly for the individual body segments for all positions, where an average value of 0.84 is found. Similar CFD studies can be performed to assess drag and CHTCs at a higher spatial resolution for applications in other sport disciplines, bicycle equipment design or to assess convective moisture transfer.     

Flow resistance and drag forces due to multiple adherent leukocytes in postcapillary vessels.

Computational fluid dynamics was used to model flow past multiple adherent leukocytes in postcapillary size vessels. A finite-element package was used to solve the Navier-Stokes equations for low Reynolds number flow of a Newtonian fluid past spheres adhering to the wall of a cylindrical vessel. We determined the effects of sphere number, relative geometry, and spacing on the flow resistance in the vessel and the fluid flow drag force acting to sweep the sphere off the vessel wall. The computations show that when adherent leukocytes are aligned on the same side of the vessel, the drag force on each of the interacting leukocytes is less than the drag force on an isolated adherent leukocyte and can decrease by up to 50%. The magnitude of the reduction depends on the ratio of leukocyte to blood vessel diameter and distance between adherent leukocytes. However, there is an increase in the drag force when leukocytes adhere to opposite sides of the vessel wall. The increase in resistance generated by adherent leukocytes in vessels of various sizes is calculated from the computational results. The resistance increases with decreasing vessel size and is most pronounced when leukocytes adhere to opposite sides of the vessel.     

Unsteady Motion, Finite Reynolds Numbers, and Wall Effect on Vorticella convallaria Contribute Contraction Force Greater than the Stokes Drag

Contraction of Vorticella convallaria, a sessile ciliated protozoan, is completed within a few milliseconds and results in a retraction of its cell body toward the substratum by coiling its stalk. Previous studies have modeled the cell body as a sphere and assumed a drag force that satisfies Stokes' law. However, the contraction-induced flow of the medium is transient and bounded by the substrate, and the maximum Reynolds number is larger than unity. Thus, calculations of contractile force from the drag force are incomplete. In this study, we analyzed fluid flow during contraction by the particle tracking velocimetry and computational fluid dynamics simulations to estimate the contractile force. Particle paths show that the induced flow is limited by the substrate. Simulation-based force estimates suggest that the combined effect of the flow unsteadiness, the finite Reynolds number, and the substrate comprises 35% of the total force. The work done in the early stage of contraction and the maximum power output are similar regardless of the medium viscosity. These results suggest that, during the initial development of force, V. convallaria uses a common mechanism for performing mechanical work irrespective of viscous loading conditions.     

Factors affecting tactile spatial acuity

Tactile spatial acuity on the fingerpad was measured using a grating orientation task. In this task, subjects are required to identify the orientation of square-wave gratings placed on the skin. Previous studies have shown that performance varies as a function of the width of the grooves in the gratings. In the present study, both groove width and the overall size and configuration of the contactors were varied. Sensitivity improved with wider grooves and with larger contactors. Additional measurements showed that the improved sensitivity is not the result of the increase in total area contacted, but rather is due to two other factors associated with larger contactors. One is the greater linear extent of the larger contactors. The other appears to be due to the reduction in the interference produced by the outer edge of the contactor. Specifically, as the contactor increases in size, the distance between the outer edge and the center portion of the grooves also increases. It was also shown that subjects are more sensitive to a single, continuous groove as compared with two grooves of the same total length but spatially discontinuous. Similarly, subjects are more sensitive to a contactor with a continuous groove than to a contactor in which just the end points of the groove are presented. The results are generally consistent with the results of peripheral, neurophysiological recordings. The results are discussed in terms of the way in which both spatial and intensive factors may affect sensitivity to grating orientation.     

Influence of V-Shaped Metallic Subwavelength Slits with Variant Periods for Superfocusing

In this paper, we discussed the influence of a plasmonic lens with V-shaped metallic subwavelength slits and variant periods on transmission properties. In order to analyze the influence, a finite-difference time-domain numerical algorithm was adopted for computational numerical simulation of the plasmonic structures. The structures are flanked with the penetrated slits through a metal (Ag) film which is coated on a quartz substrate. Our simulation results demonstrated that different cone angles originated from the V-shaped slits generate different influences on the beam propagation. The width variation affects the intensity significantly. The cone angles formed by the V-shaped slits can change the focusing performance. These results are very encouraging for future study of the plasmonic lens-based applications.     

Drag production mechanisms of filamentous biofilms

Abstract

Biofilms were grown on smooth acrylic surfaces for nominal incubation times of three, five, and ten weeks in a flow loop at the University of Michigan. The biofilm covered surfaces were exposed to the turbulent flow in a high-aspect ratio, fully developed channel flow facility at height-based Reynolds numbers from Re_H ≈ 5,000 to 30,000. Measurements of the pressure drop along each fouled upper surface revealed that the friction drag increased from approximately 10% to 400%. The wide range in drag penalty was linked to variations in flow speed, the average thickness of the biofilms, and the level of film coverage over each surface through scaling parameters and empirical correlations. Rigid replicas of select biofilms were produced from time-averaged laser scans collected while the biofilm was subjected to flow. These rigid biofilm replicas experienced roughly half the drag increase of their compliant counterparts with the increase in friction spanning roughly 50% to 200%.     

Viscoelastic relaxations in solutions of poly(glutamic acid) and gelatin at ultrasonic frequencies

Complex shear viscosity η* = η′ – iη″ of poly (L -glutarmic acid) solution was measured by the torsional crystal method at 50 kc./sec. as a function of pH. A sharp peak was found at the midpoint of the helix-coil transition region in both η′ and η″. The relaxation time is calculated from η′ and η″ assuming a single relaxation process and the peak value at the midpoint of transition is estimated at 10^?6 sec. Such behavior agrees well with the prediction from the theory of Schwarz. The attenuation of longitudinal sound waves at,3 Me./sec. was measured as a function of pH for solutions of poly(glutamic acid), glutamic acid, and gelatin. A small attenuation peak was observed for the three solutions, the peak height being almost, the same for them. The peak is interpreted in terms of the dissociation reaction of side chains.     

Minimum drag shape of a semi-ellipsoid exposed to shear flow and its possible relation to the shape of endothelial cell

A semi-ellipsoid attached on a wall is considered as a model problem for the study of blood flow effect on the shape of an endothelial cell. Under the condition that the volume is fixed and one axis of the semi-ellipsoid is aligned to the flow direction, the shape for the minimum drag under the applied shear flow is determined. Both the analytical and numerical approaches are adopted for computation of the minimum drag shape. Since analytical solution is not available for the original model problem, analytical solution to a closely related problem is used to compute the approximate value of the drag force. Adopted is the classical result on the motion of an ellipsoidal particle in a viscous fluid [Jeffery, Proc. Roy. Soc. A (1922)]. To corroborate the analytically obtained results, the model problem has also been studied numerically by using the finite element method (FEM). The minimum drag shape predicted analytically by using Jeffery’s solution is (a,b,c) = (1.71, 0.67, 0.88), where a is the dimensionless semi-axis in the flow direction, b the height, and c the half width of the semi-ellipsoid. The numerical approach predicts the minimal drag shape as (a,b,c) = (1.96,0.64,0.80). This result obtained by the FEM method shows good agreement with the result obtained by the boundary integral method [Hazel and Pedley, Biophys. J. (2000)].     

Influence of a postural change of the swimmer's head in hydrodynamic performances using 3D CFD

This study deals with recent researches undertaken by the authors in the field of hydrodynamics of human swimming. The aim of this numerical study was to investigate the flow around the entire swimmer's body. The results presented in this article focus on the combination of a 3D computational fluid dynamics code and the use of the k–ω turbulence model, in the range of Reynolds numbers representative of a swimming level varying from national to international competition. Emphasis is placed on the influence of a postural change of the swimmer's head in hydrodynamic performances, which is directly related to the reduction of overall drag. These results confirm and complete those, less accurate, of a preliminary 2D study recently published by the authors and allow the authors to optimise the swimmer's head position in underwater swimming.     

Computational fluid dynamics of flow regime and hydrodynamic forces generated by a gliding North Atlantic right whale (Eubalaena glacialis)

Accurate estimates of drag on marine animals are required to investigate the locomotive cost, propulsive efficiency, and the impacts of entanglement if the animal is carrying fishing gear. In this study, we performed computational fluid dynamics analysis of a 10 m (length over all) right whale to obtain baseline measurements of drag on the animal. Swimming speeds covering known right whale speed range (0.125 m/s to 8 m/s) were tested. We found a weak dependence between drag coefficient and Reynolds number. At a swimming speed of 2 m/s, we analyzed the boundary layer thicknesses, the flow regimes, and drag components. We found the thickest boundary layer at the lateral sides of the peduncle, whereas the boundary layer thickness over the outer part of the flukes was less than 1.7 cm. Laminar flow occurred over the anterior ~0.6 LoA and turbulent flow from ~0.8 LoA to the fluke notch. On the surfaces of the flukes outside of the body wake region, flow was laminar. Our most significant finding is that the drag coefficient (0.0071–0.0059) of a right whale for swimming speeds ranging from 0.25 m/s to 2 m/s is approximately twice that of many previous estimates for cetaceans.     

Spreading and orientation of epithelial cells on grooved substrata

The spreading and orientation of epithelial (E) cells was studied on titanium-coated grooved substrata by light, transmission (TEM) and scanning electron microscopy (SEM). Vertical-walled grooves and V-shaped grooves, 3-60 microns deep, were produced in silicon wafers by micromachining, a process which was developed for the fabrication of micro-electronic components, and the grooved substrata were replicated in Epon. Photolithography was used to prepare photoresist-based and silicon dioxide-silicon substrata with grooves of approximately 2 and approximately 0.5 micron deep, respectively. Cell clusters were markedly oriented by all the grooved substrata examined, with the orientation index being highest for substrata with grooves of the smallest repeat spacing. Time-lapse cinemicrography showed that the grooves directed the migration of E cells, but the control was not absolute, as some cells crossed over the ridges and descended into the grooves. The 0.5 micron grooves appeared less effective than the deeper grooves in directing cell locomotion. SEM and TEM of E cells spreading on the grooved substrata demonstrated that cell processes, including lamellae and filopodia, were capable of bending around and closely adapting to groove edges. E cells did not flatten as extensively on a substratum with 22 microns deep V-shaped grooves as on a smooth surface, although some cells were markedly elongated. One mechanism proposed to explain contact guidance of fibroblasts is that linear elements of the locomotory system, such as microfilament bundles, are unable to operate when bent. The observed flexibility of epithelial cell processes and the ability of substrata with shallow grooves to orient E cells indicate that contact guidance of E cells on micromachined substrata cannot be explained by the mechanical stiffness of long linear cytoskeletal elements.     

Frictional drag measurements of large-scale plates in an enhanced plane channel flowcell

Abstract

This paper describes the design of an enhanced, plane channel, flowcell and its use for testing large-scale coated plates (0.6?m × 0.22?m) in fully developed flow, over a wide range of Reynolds numbers, with low uncertainty. Two identical, hydraulically smooth plates were experimentally tested. Uniform biofilms were grown on clean surfaces to test skin friction changes resulting from different biofilm thickness and densities. A velocity survey of the flowcell measurement section, using laser Doppler anemometry, showed a consistent velocity profile and low turbulence intensity in the central flow channel. The skin friction coefficient was experimentally determined using a pressure drop method. Results correlate closely to previously published regression data, particularly at higher speeds. Repeated measurements indicated very low uncertainty. This study demonstrates this flowcell’s applicability for representing consistent frictional drag of ship hull surfaces, enabling comparability of hydrodynamic drag caused by surface roughness to the reference surface measurements.     

Mixing and power characteristics of drag board device in shallow pool

Mixing and stirring of a 20-m(2) shallow pool by means of a drag board device has been investigated. The board closes the pool cross section except for a slit of a few centimeters above the bottom, and it is slowly moved back and forth, forcing the water to run through the slit and thereby creating a turbulent backwhirl. Power drawn and the drag on the board has been measured together with the velocities of the water at different locations in the wake of the board. Power number N(p) has been correlated with the Reynolds N(Re) and the bottom clearance numbers N(c) by the expressions \documentclass{article}\pagestyle{empty}\begin{document}$$ N_p = 13,465N_{\rm Re};{-0.774} N_c;{0.1016} N_{\rm Re} < 80.000\\N_p = 5.4N_{\rm Re};{-0.0863} N_c;{0.104} N_{\rm Re} > 80.000 $$\end{document} Power and Reynolds numbers are defined as usual with the square root of the board-immersed-area as the characteristic length. The bottom clearance number is defined as the ratio of the water depth in the pool to the difference between water depth and the board width immersed in water. Flow pattern behind the board consists of large vortex loops causing the fluid to circulate from bottom to top and producing a thorough mixing effect. The drag board seems to have several advantages over conventional paddle wheels for the mixing and stirring of algal cultures in shallow ponds.