Article

On the drag reconfiguration of plates near the free surface

AIP Publishing
Physics of Fluids
Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

Rectangular foils of different flexural rigidities were towed normal to the flow at a fixed speed in a quiescent fluid in order to study the effect of the proximity of the upper edge of the models to free surface. It was found that flexibility ensured drag reduction due to the reconfiguration process at all submergence depths, with certain foils exhibiting depth-independent behavior. The study of Vogel exponents also showed that a sublinear or even a depth independent relationship between drag and velocity can be attained at specific flexural rigidity values. A modified classical beam theory model using a power-law based load distribution was utilized to obtain an empirical relationship between the loading exponent and Cauchy numbers and to identify the foil tip location. Particle image velocimetry was also undertaken to interpret and further understand the force results. The experiments showed the existence of 2 ranges of Cauchy numbers with a small degree of overlap in ranges wherein the drag coefficient and Vogel exponents are independent of submergence depth.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... Interactions between structures and their surrounding fluid are ubiquitous in nature and man-made systems, e.g., the swimming or flying locomotion of animals, 1-3 flutter of papers or flags in wind, [4][5][6] the reconfiguration of plants, [7][8][9] the falling of a solid body through a fluid driven by gravity, 10-12 a turbocharger engine, 13,14 and so on. The stability of flexible structures in an impinging flow is a classic physical problem. ...
Article
The stability of the inverted flexible plate with non-uniform stiffness distribution in a free stream is studied by numerical simulation and mathematical theory. In our study, the bending stiffness distribution is expressed as the function of the leading-edge's bending stiffness K* and the polynomial of the plate's coordinate. Based on the former theoretical work on the stability of inverted plates with uniform stiffness distribution, we derive the upper limit value of K* at which the zero deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution, the critical K* derived from the mathematical theory agrees well with that obtained from the numerical simulation. An effective bending stiffness is defined, which can be used to unify the regimes of the motion modes between uniform plate and non-uniform plate. Moreover, three orders of mass ratio (O(10 ⁻² ), O(10 ⁻¹ ) and O(1)) are investigated, and the underlying mechanism for large amplitude flapping is clarified for inverted plate with different mass ratio. An appropriate bending stiffness distribution can improve the deformation of plate greatly. The findings shed some light on the energy harvesting of the inverted plate.
Article
This experimental study is focused on quantifying the effect of trailing edge flexibility on the performance of a three straight bladed vertical axis wind turbine, with a chord-to-diameter ratio c/D=0.16 at a moderately high Reynolds number (based on diameter) ReD=4⋅105. The blades consist of NACA-0015 profiles that are fixed with a pitch angle β=6∘ toe-out, and allow interchangeable trailing edges in the last 17% of their chord length. The research presented here provides a proof of concept for the improved performance of vertical axis wind turbines, due to the effect of flexibility at the trailing edge of their blades. We show that blades with semi-flexible trailing edge, can extend the range of rotor operating regimes, leading to an increase of approximately 10% in the performance of the turbine. An excess of flexibility results in diminished efficiencies.
Article
Full-text available
We investigate the quasi-static reconfiguration of rear parallel flexible plates on the drag coefficient of a blunt body. The drag coefficient, plates deformation, and main features of the turbulent wake are characterized experimentally in a towing tank. It is found that increasing the flexibility of plates leads to an important drag reduction, induced by the progressive streamlining of the trailing edge due to plates deformation. The study of the Vogel exponent is adopted here to evaluate the limit on the potential drag reduction at large values of the Cauchy number, which is shown to be mainly caused by the growth in the vibrating amplitude response of plates. The plates deformation is analyzed by means of image processing, showing that their shapes mainly follow the first modal form of a cantilever beam deflection, although a slight concavity develops toward the plates tip for large Cauchy numbers. To further analyze this process, the empirical flow loading along the plates is estimated by a modified beam theory assuming a distributed load given by a power law. The experimental fitting shows that for large flexibility, the load diminishes at the rear tip. Besides, the progressive deformation of plates is shown to weaken the shedding of vortices and reduce the size of the recirculation bubble. Finally, an affine direct relationship between recirculation bubble aspect ratio and drag coefficient has been proposed in order to quantify the linkage between near wake modifications and hydrodynamic improvement provided by the trailing edge streamlining.
Article
Flat plate models of fixed aspect ratio incorporating either serrations or holes at the upper and lower plate edges, were towed normal to the flow and in proximity to the free surface. The hydrodynamics and the drag generated by the plates has been studied in detail for several configurations. In general, the models with holes presented greater drag reduction than those with serrations, with the hole angle playing an important role on the total drag measured. The fluid dynamic sources for drag reduction at low submergence depths have been investigated using quantitative flow visualization, and they have been related to the changes in the separating shear layers, as a result of the different edge features imposed to the plates.
Article
Full-text available
Single-phase two-dimensional flow past a circular cylinder intersecting, or close to, a free surface at a Reynolds number of 180 is numerically investigated in this paper series using the Smoothed Particle Hydrodynamics (SPH) method. The wake behavior for Froude numbers between 0.3 and 2.0, based on the diameter, and for submergence-diameter ratios between -0.5 and 2.5 is examined. This range significantly extends existing literature on the topic. Vorticity shed by the cylinder, vortex generation due to free-surface breaking, and mixing processes are discussed. Regarding the submergence dependence, it has been found that for small gap ratios, the classical von Kármán vortex shedding from the cylinder does not take place. In turn, vortex shedding originates from wave-breaking at the free surface, occurring simultaneously with the transport of free-surface fluid elements into the bulk of the fluid. It has been also found that for even smaller depth ratios, a vorticity layer remains spatially localized between the cylinder and the free surface, and a large stagnation recirculating area develops behind the cylinder. In some of these cases, the whole mass of fluid in that area eventually gets detached after several shedding cycles and it is advected downstream. According to the authors’ knowledge, this is a previously unreported form of wake instability. It has been also found that as the Froude number is increased, the classical von Kármán vortex street shed from the cylinder is blocked only to be recovered at very high Froude numbers, in agreement with linear stability predictions. Regarding the challenging and not previously investigated half-submerged configuration, flows in which the cylinder acts as a barrier, flows with alternation of dry and wet cylinder top surface, and flows with cavities have been described.
Article
Full-text available
Plant posture can play a key role in the health of aquatic vegetation, by setting drag, controlling light availability, and mediating the exchange of nutrients and oxygen. We study the flow-induced reconfiguration of buoyant, flexible aquatic vegetation through a combination of laboratory flume experiments and theoretical modeling. The laboratory experiments measure drag and posture for model blades that span the natural range for seagrass stiffness and buoyancy. The theoretical model calculates plant posture based on a force balance that includes posture-dependent drag and the restoring forces due to vegetation stiffness and buoyancy. When the hydrodynamic forcing is small compared to the restoring forces, the model blades remain upright and the quadratic law, Fx ∝ U2, predicts the drag well (Fx is drag, U is velocity). When the hydrodynamic forcing exceeds the restoring forces, the blades are pushed over by the flow, and the quadratic drag law no longer applies. The model successfully predicts when this transition occurs. The model also predicts that when the dominant restoring mechanism is blade stiffness, reconfiguration leads to the scaling Fx ∝ U4/3. When the dominant restoring mechanism is blade buoyancy, reconfiguration can lead to a sub-linear increase in drag with velocity, i.e., Fx ∝ Ua with a < 1. Laboratory measurements confirm both these predictions. The model also predicts drag and posture successfully for natural systems ranging from seagrasses to marine macroalgae of more complex morphology.
Article
Full-text available
We show experimentally that properly selected chord-wise flexibility can have a significant effect on the propul- sive efficiency of two-dimensional flapping (heaving and pithing) foils, up to a 36% increase, compared to the efficiency of a rigid foil, with small loss in thrust. Two different foil kinematics are employed in the experiments: the first using simple harmonic heave and pitch motions; and the second using a multi-harmonic heave motion combined with a harmonic pitch motion, selected to produce a harmonic angle of attack variation. For both types of motion, chordwise flexibility improves efficiency, the Shore A60 producing the highest efficiency; the second mode of kinematics causes the thrust coefficient to increase significantly for high Strouhal numbers. A non-dimensional flexibility parameter is developed which provides a scaling law for the effect of flexibility.
Article
Full-text available
Drag was measured and changes of configuration noted as a variety of leaves, leaflets, and clusters were subjected to turbulent winds of 10 and 20 m s−1. Leaves with acute bases and short petioles had the highest surface-specific drag, fluttered erratically and, most commonly, tore. Leaves with lobed bases and long petioles had lower drag, fluttered little and reconfigured into increasingly acute cones. Pinnately compound leaves had the lowest drag and formed cylinders with leaflets layered alternately. For all but individual white oak leaves, drag coefficients (based on original surface area) decreased with increasing wind speed. Single leaves of white poplar were unstable at all speeds but resisted damage even at 30 m s−1; clusters formed stable cones. These results are contrasted with the behaviour of flags in wind and are related to wind-throw in trees.
Article
Full-text available
Two-dimensional flow past a cylinder close to a free surface at a Reynolds number of 180 is numerically investigated. The wake behaviour for Froude numbers between 0.0 and 0.7 and for gap ratios between 0.1 and 5.0 is examined. For low Froude numbers, where the surface deformation is minimal, the simulations reveal that this problem shares many features in common with flow past a cylinder close to a no-slip wall. This suggests that the flow is largely governed by geometrical constraints in the low-Froude-number limit.
Article
Full-text available
1] To date, flow through submerged aquatic vegetation has largely been viewed as perturbed boundary layer flow, with vegetative drag treated as an extension of bed drag. However, recent studies of terrestrial canopies demonstrate that the flow structure within and just above an unconfined canopy more strongly resembles a mixing layer than a boundary layer. This paper presents laboratory measurements, obtained from a scaled seagrass model, that demonstrate the applicability of the mixing layer analogy to aquatic systems. Specifically, all vertical profiles of mean velocity contained an inflection point, which makes the flow susceptible to Kelvin-Helmholtz instability. This instability leads to the generation of large, coherent vortices within the mixing layer (observed in the model at frequencies between 0.01 and 0.11 Hz), which dominate the vertical transport of momentum through the layer. The downstream advection of these vortices is shown to cause the progressive, coherent waving of aquatic vegetation, known as the monami. When the monami is present, the turbulent vertical transport of momentum is enhanced, with turbulent stresses penetrating an additional 30% of the plant height into the canopy.
Article
Full-text available
Through an extensive and systematic experimental investigation of two geometries of flexible plates in air, it is shown that a properly defined scaled Cauchy number allows collapsing all drag measurements of the reconfiguration number. In the asymptotic regime of large deformation, it is shown that the Vogel exponents that scale the drag with the flow velocity for different geometries of plates can be predicted with a simple dimensional analysis reasoning. These predicted Vogel exponents are in agreement with previously published models of reconfiguration. The mechanisms responsible for reconfiguration, namely area reduction and streamlining, are studied with the help of a simple model for flexible plates based on an empirical drag formulation. The model predicts well the reconfiguration observed in the experiments and shows that for a rectangular plate, the effect of streamlining is prominent at the onset of reconfiguration, but area reduction dominates in the regime of large deformation. Additionally, the model demonstrates for both geometries of plates that the reconfiguration cannot be described by a single value of the Vogel exponent. The Vogel exponent asymptotically approaches constant values for small and for very large scaled Cauchy numbers, but in between both extremes it varies significantly over a large range of scaled Cauchy number.
Article
Flat rectangular plates of different aspect ratios were towed normal to the flow at various speeds in a quiescent fluid, with the focus being the study of the effect of the plate edge proximity to the free surface on drag force. The submergence depth was measured from the plate upper edge to the free surface and varied from zero to the centre of the tank. It was found that the drag increases abruptly prior subsiding with increasing submergence depth, with this jump in drag being more prominent in low aspect ratio plates. The abrupt rise in the drag is due to the existence of a gap-flow at the free surface resulting in the formation of a recirculating flow in close proximity to the base region of plate. Overall, the trends are Reynolds number independent, except when the aspect ratios are in the range from 0.75 to 1.33, and the plate was near the free surface. Flow visualization was also employed on specific plates and at certain depths to understand the flow features and link them to the observed force trends.
Article
Plants in aquatic canopies deform when subjected to a water flow and so, unlike a rigid bluff body, the resulting drag force FD grows sub-quadratically with the flow velocity U ̄. In this article, the effect of density on the canopy reconfiguration and the corresponding drag reduction is experimentally investigated for simple 2D synthetic canopies in an inclinable, narrow water channel. The drag acting on the canopy, and also on individual sheets, is systematically measured via two independent techniques. Simultaneous drag and reconfiguration measurements demonstrate that data for different Reynolds numbers (400–2200), irrespective of sheet width (w) and canopy spacing (ℓ), collapse on a unique curve given by a bending beam model which relates the reconfiguration number and a properly rescaled Cauchy number. Strikingly, the measured Vogel exponent V and hence the drag reduction via reconfiguration is found to be independent of the spacing between sheets and the lateral confinement; only the drag coefficient decreases linearly with the sheet spacing since a strong sheltering effect exists as long as the spacing is smaller than a critical value depending on the sheet width.
Article
Impulsively started, low-aspect-ratio elliptical flat plates have been investigated experimentally to understand the vortex pinch-off dynamics at transitional and fully turbulent Reynolds numbers. The range of Reynolds numbers investigated is representative of those observed in animals that employ rowing and paddling modes of drag-based propulsion and manoeuvring. Elliptical flat plates with five aspect ratios ranging from one to two have been considered, as abstractions of propulsor planforms found in nature. It has been shown that Reynolds-number scaling is primarily determined by plate aspect ratio in terms of both drag forces and vortex pinch-off. Due to vortex-ring growth time scales that are longer than those associated with the development of flow instabilities, the scaling of drag is Reynolds-number-dependent for the aspect-ratio-one flat plate. With increasing aspect ratio, the Reynolds-number dependency decreases as a result of the shorter growth time scales associated with high-aspect-ratio elliptical vortex rings. Large drag peaks are observed during early-stage vortex growth for the higher-aspect-ratio flat plates. The collapse of these peaks with Reynolds number provides insight into the evolutionary convergence process of propulsor planforms used in drag-based swimming modes over diverse scales towards aspect ratios greater than one.
Article
The evolution of vortices produced in the wake of impulsively-started axisymmetric and non-axisymmetric plates is investigated using force and Particle Image Velocimetry (PIV) measurements. At a Reynolds number of 40,000, circular, square and elliptical plates were impulsively-towed through a towing tank to investigate vortex pinch-off for each plate. The PIV measurements were used to calculate circulation growth and formation numbers for each shape. Good agreement with formation numbers reported for vortex rings produced in isolation was observed for the circular and square plates, but not for the ellipse. Force data reveals a strong coupling between vortex evolution and the forces generated on the plates. The presence of a vortex ring results in a vortex force that modifies the instantaneous drag on the plate. This vortex force is related to the self-induced velocity of the vortex ring as well as the proximity of the vortex ring relative to the plate, and therefore stable vortex rings result in the greatest reduction in the overall drag force. As a means to explain pinch-off, the pressure field surrounding the vortices was also investigated. Contour plots of the streamwise pressure gradient show that interaction of a favourable pressure gradient on the leeward side of the plates results in the redirection of the shear layer away from the vortex. This results in a termination of mass flux into the vortex, and subsequent plateau in vortex circulation.
Article
Flexible systems bending in steady flows are known to experience a lesser drag compared to their rigid counterpart. Through a careful dimensional analysis, an analytical expression of the Vogel exponent quantifying this reduction of drag is derived for cantilever beams, within a framework based on spatial self-similar modelling of the flow and structural properties at the clamped edge of the structure. Numerical computations are performed on various situations, including systems involving more complex distributions of the flow or structural parameters. The scaling of drag versus flow velocity for large loadings is shown to be well predicted by fitting the system properties by simple power laws at the scale of the length on which significant bending occurs. Ultimately, the weak sensitivity of the Vogel exponent to the parameters of the system provides an explanation to the rather reduced scattering of the Vogel exponents around observed on most natural systems in aquatic or aerial vegetation.
Article
Digital particle image velocimetry (DPIV) is the digital counterpart of conventional laser speckle velocitmetry (LSV) and particle image velocimetry (PIV) techniques. In this novel, two-dimensional technique, digitally recorded video images are analyzed computationally, removing both the photographic and opto-mechanical processing steps inherent to PIV and LSV. The directional ambiguity generally associated with PIV and LSV is resolved by implementing local spatial cross-correlations between two sequential single-exposed particle images. The images are recorded at video rate (30 Hz or slower) which currently limits the application of the technique to low speed flows until digital, high resolution video systems with higher framing rates become more economically feasible. Sequential imaging makes it possible to study unsteady phenomena like the temporal evolution of a vortex ring described in this paper. The spatial velocity measurements are compared with data obtained by direct measurement of the separation of individual particle pairs. Recovered velocity data are used to compute the spatial and temporal vorticity distribution and the circulation of the vortex ring.
Article
Two-dimensional transient simulations are performed to investigate characteristics of flow past a plate normal to a stream. Free surface effects on the flow dynamics are the primary focus of this study. Varying plate depths are simulated to examine the variation of force coefficients and vortex shedding patterns. The k-ω Shear Stress Transport (k-ω SST) turbulence model and Volume of fluid (VOF) multiphase model are employed to predict characteristics of free surface flow. Flow past the plates is simulated at distances of 0.75 m, 0.06 m, 0.05 m, 0.045 m, and 0.03 m below the free surface with corresponding local Froude numbers (Fr) of 0.18, 0.65, 0.71, 0.75, and 0.92. As the plate gets closer to the surface the drag coefficient decreases from 3.86 (Fr=0.18) to 2.18 (Fr=0.92) and the Strouhal number increases from 0.125 (Fr=0.18) to 0.355 (Fr=0.92). A jet-like flow formed from the surface is observed on top of the plate. Vortices from the top surface of the plate dissipate into smaller eddies due to the free surface presence, resulting in asymmetric vortex shedding downstream. Flows presented here are beneficial for designing and optimizing systems that harvest energy from marine currents.
Article
Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small ``tip region'' about the flow's stagnation point. The result is a transition from the classical U2 drag scaling of rigid bodies to a new U4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the length-scale of similarity. This analysis predicts that the fiber and wake are quasiparabolic at large velocities, and obtains the new drag law in terms of the drag on the tip region. Under variations of the model suggested by the experiment-the addition of flow tunnel walls, and a back pressure in the wake-the drag law persists, with a simple modification.
Article
Computer simulations were used to assess the influence of palmate leaf morphology, decussate phyllotaxy, and the elastic moduli of petioles on the capacity of turgid and wilted twigs ofAesculus hippocastanum to intercept direct solar radiation. Leaf size, morphology, orientation, and the Young's and shear moduli (E and G) of petioles were measured and related to leaf position on 8 twigs whose cut ends were placed in water (turgid twigs) and 8 twigs dried for 8 h at room temperature (wilted twigs). Petioles mechanically behaved as elastic cantilevered beams; the loads required to shear petioles at their base from twigs were correlated with the cross-sectional areas of phyllopodia but not with petiole length or tissue volume. Empirically determined morphometric and biomechanical data were used to construct average turgid and wilted twigs. The diurnal capacity to intercept direct sunlight for each was simulated for vertically oriented twigs for 15 h of daylight, 40 N latitude. The daily integrated irradiance (DII) of the wilted twig was roughly 3% less than that of the otherwise comparable twig bearing turgid leaves. Simulations indicated that the orientation of turgid leaves did not maximize DII. More decumbent (wilted) petioles increased DII by as much as 4%. Reduction in the girth, E, or G of petioles, or an increase in petiole length or the surface area of laminae (with attending increase in laminae weight), increased petiolar deflections and DII. Thus, the mechanical design of petioles ofA. hippocastanum was found not to be economical in terms of investing biomass for maximum light interception.
Article
Unstable and mechanically demanding habitats like wind-exposed open fields or the wave-swept intertidal require rapid adaptive processes to ensure survival. The mechanism of passive reconfiguration was analyzed in two plant models exposed to irregular flow of water or air, two species of the brown seaweed Durvillaea and the giant reed Arundo donax. Irrespective of the surrounding media and the subsequent Reynolds numbers (Re ~ 105 - 107), reconfiguration seems to be the key strategy for streamlining to avoid overcritical drag-induced loads. This passive mechanism is also discussed in the context of the requirement of a maximized surface area for light interception, so that morphological adaptations to rapid reconfiguration represent at least a bifactorial optimization. Both tested plant models exhibited the same principles in streamlining. At a specific threshold value, the proportionality between drag forces and flow velocity can be reduced from the second power close to an almost linear relation. This empirically derived relation could be characterized by a figure of merit or Vogel number (B). A value close to B = -1, resulting in a linear increase of drag force with velocity, was found at higher velocities for both the seaweeds and the giant reed, as well as for a variety of plants described in the literature. It is therefore concluded that the ability to reduce velocity-dependent drag force to a linear relation is a potentially important adaptation for plants to survive in unstable flow-dominated habitats.
Article
Experimental and numerical study is made of the forces and flow about a circular cylinder steadily advancing beneath the free-surface. Force measurements at a Reynolds number of 4.96 × 104 show that the drag coefficient abruptly decreases from 1.3 to 1.0 and the Strouhal number simultaneously increases from 0.19 to 0.30 at the depth-radius ratioof 1.7 when the depth of submergence of the circular cylinder is gradually reduced. Pressure measurements, flow visualization and numerical simulations indicate that at the shallowly-submerged condition the difference of the flow in the vacinities of the top and bottom of the cylinder causes asymmetric vortex generation and that this results in a smaller pressure reduction on the backward face of the cylinder, a lower drag coefficient of the cylinder, and a higher frequency of vortex shedding.
Article
Most large, sessile organisms when exposed to rapid flows of air or water are markedly deformed as a consequence of their structural flexibility. Responses to air and water movement are similar, although both extreme and typical forces generated by water flows are greater, and erect organisms are commonly shorter in water than in air. A useful way of viewing data on the scaling of drag with flow speed is with a graph of speed-specific drag (drag divided by the square of speed) against speed. Since an ordinary solid body usually gives a horizontal line on such a plot, deviations from the ordinary are immediately evident. The slopes of the double logarithmic version of these graphs provide useful numerical comparisons. All of the cases considered here—trees, macroalgae, sea pens, etc.—give negative slopes at high flow rates, indicating that speed-specific drag drops with increasing flow. Such results may be taken as evidence that the flexible response commonly constitutes an adaptively useful reconfiguration as opposed to a mere incidental consequence of the material economy afforded by flexibility.
Article
The classical theory of high-speed flow predicts that a moving rigid object experiences a drag proportional to the square of its speed. However, this reasoning does not apply if the object in the flow is flexible, because its shape then becomes a function of its speed--for example, the rolling up of broad tree leaves in a stiff wind. The reconfiguration of bodies by fluid forces is common in nature, and can result in a substantial drag reduction that is beneficial for many organisms. Experimental studies of such flow-structure interactions generally lack a theoretical interpretation that unifies the body and flow mechanics. Here we use a flexible fibre immersed in a flowing soap film to measure the drag reduction that arises from bending of the fibre by the flow. Using a model that couples hydrodynamics to bending, we predict a reduced drag growth compared to the classical theory. The fibre undergoes a bending transition, producing shapes that are self-similar; for such configurations, the drag scales with the length of self-similarity, rather than the fibre profile width. These predictions are supported by our experimental data.