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The papers listed below (with abstract) are either already published or in the state been written or been submitted. A few more new works are still on the production line. They are: (1) the urban heat island effect due to air conditioning; (2) mobile heat blanket on thermal convection with annular geometry; (3) the effect of flexibility on the flapping flight of a simple wing; (4) the geometric effects of side walls on the locomotion of C. elegans; and etc. |
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| Abstract: Motivated by the swimming and flying locomotion found in the biological world, we perform laboratory experiments aimed to understand the basic thrust-generation mechanism through the flapping of thin structures. We first focus on the passive dynamics of flexible bodies that interact with the surrounding high speed flows. The emerging dynamical states are compared with the swimming modes of fish. We further investigate the self-sustained forward motion of a flat plate -- a prototypical wing or fin -- that is flapped up and down in a fluid. Its forward locomoting speed is sensitively determined by its geometry and flapping frequency. A scaling analysis is proposed to explain such dependences. Moreover, we also explore possible scenarios to increase the forward speed by incorporating wing flexibility, passive pitching and asymmetry in the design of our prototypical wings. The ultimate goal of our investigation is to find the minimum wing design that still ensures efficient thrust generation. Insights gained from this study would help us further appreciate and understand the subtle differences among all the modes and controls used in animal locomotion. |
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| Abstract: We construct a valveless pump consisting of a section of elastic tube and a section of rigid tube connected in a closed loop and filled with water. Periodically squeezing the elastic tube at an asymmetric location generates a flow of water around the tubes. This e ect, called the Liebau phenomenon or valveless pumping, has been known for some time, but is still poorly understood. We study the flow rates for various squeezing locations, frequencies, and elastic tube rigidities. To understand how valveless pumping works, we formulate a simple model that can be described by coupled ordinary di erential equations. The time series of flow velocities generated by the model are qualitatively and quantitatively similar to those seen in the experiment. The model provides a physical explanation of valveless pumping, and it allows us to identify the essential pumping mechanisms. |
a free boundary interacts with a thermally convecting fluid, click to view pdf Jun Zhang and Jin-Qiang Zhong submitted as an entry for "Gallery of Fluid Motion" to the APS/DFD meeting, nov., (2007) |
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| Abstract: Based on our previous experimental study, we present a one-dimensional, phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations. |
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| Abstract: We investigate the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects. This is a previously unexplored paradigm of many-body interactions mediated by thermal convection, which gives rise to surprising robust oscillations between di erent large-scale circulations. Once begun, this process repeats cyclically, with the collection of spheres entrained and packed from one side of the convection cell to the other. The frequency of the cycle is highest when the spheres occupy about half of the cell bottom and their size coincides with the thickness of the thermal boundary layer. This phenomenon shows that a deformable mass can stimulate a turbulent, thermally convecting fluid into oscillation, a collective behavior that may be found in nature. |
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| Abstract: We study experimentally the dynamical states of a freely-moving, floating heat blanket that couples with a thermally convective fluid. The floating boundary modifies the large-scale flow pattern in the bulk and destabilizes the coupled system, leading to spontaneous oscillations. The system makes a transition from the oscillatory state to a weakly confined state as the moving boundary exceeds a critical size. In the latter state, the moving boundary roams about the center of the convection cell and executes random excursions due to nearby passing thermal plumes. To understand the observed states and the transition, we provide a low-dimensional model that appears to capture the underlying mechanism of the coupled system. |
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| Abstract: We study the nature of surface waves on a semi-toroidal ring of water. We create this specific fluid shape by patterning a glass plate with a hydrophobic film, which confines the fluid to a precise geometric region. To excite the system, the supporting plate is vibrated up and down, thus accelerating/decelerating the fluid ring along its toroidal axis. When the amplitude of the driving acceleration is sufficiently large, the semi-toroidal surface becomes unstable to azimuthal and radial waves. We investigate the dependence of the diverent surface wave patterns on both driving amplitude and frequency. |
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| Abstract: In a rotational geometry, we study the unidirectional forward motion of a symmetric wing that is flapped vertically at frequency f and amplitude a. We find that, a combined dimensionless parameter from the wing geometry (length L, thickness \delta and chord c) and flapping amplitude, \alpha, uniquely determines the forward flight speed. This scaling relationship is explained by our quasi-steady and quasi-two-dimensional model. We then apply our results from the rotational geometry to a translational forward flight and compare the outcome with biological locomotion. In particular, the Strouhal number (St = af/U) for a load-free wing is found in the range of 0.30. We further investigate the so-called “ground effect,” as the wing flaps close to the horizontal boundaries, which increases the forward flight speed. |
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| Abstract: Small flexible bodies are observed to hover in an oscillating air column. The air is driven by a large speaker at frequencies in the range 10–65 Hz at amplitudes 1–5 cm. The bodies are made of stiffened tissue paper, bent to form an array of four wings, symmetric about a vertical axis. The flapping of the wings, driven by the oscillating flow, leads to stable hovering. The hovering position of the body is unstable under free fall in the absence of the airflow. Measurements of the minimum flow amplitude as a function of flow frequency were performed for a range of self-similar bodies of the same material. The optimal frequency for hovering is found to vary inversely with the size. We suggest, on the basis of flow visualization, that hovering of such bodies in an oscillating flow depends upon a process of vortex shedding closely analogous to that of an active flapper in otherwise still air. A simple inviscid model is developed illustrating some of the observed properties of flexible passive hoverers at high Reynolds number. |
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| Abstract: We study the behavior of an elastic loop in a fast flowing soap film. The loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a 2D closed flexible body moving in a 2D viscous flow. The loop is distended by the flow, and above a velocity threshold of the soap film it begins to oscillate. The horizontal motion of the loop centroid can be accounted for as a simple harmonic oscillator driven by the drag force on the loop, with frequency linearly proportional to the flow velocity. We also investigate the morphology of the elastic loop under fluid drag and compare the result with other instances of flexible bodies moving in a laminar fluid. |
the dynamics of a flexible loop in a quasi-2d flow, click to view pdf K. Mareck, S. Jung, M. Shelley and Jun Zhang Physics of Fluids, 18, 091112 (2006) |
| No abstract for this work: it was selected by a panel of judges and published in the "Gallery of Fluid Motion" |
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| Abstract: We study the dynamics of a rigid, symmetric wing that is flapped vertically in a fluid. The motion of the wing in the horizontal direction is not constrained. Above a critical flapping frequency, forward flight arises as the wing accelerates to a terminal state of constant speed. We describe a number of measurements which supplement our previous work. These include (a) a study of the initial transition to forward flight near the onset of the instability, (b) the separate effects of flapping amplitude and frequency, (c) the effect of wing thickness, (d) the effect of asymmetry of the wing planform, and (e) the response of the wing to an added resistance. Our results emphasize the robustness of the mechanisms determining the forward flight speed as observed in our previous study. |
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| Abstract: In thermal convection, coherent flow structures emerge at high Rayleigh numbers as a result of intrinsic hydrodynamic instability and self-organization. They range from small-scale thermal plumes that are produced near both the top and the bottom boundaries to large-scale circulations across the entire convective volume. These flow structures exert viscous forces upon any boundary. Such forces will affect a boundary which is free to deform or change position. In our experiment, we study the dynamics of a free boundary that floats on the upper surface of a convective fluid. This seemingly passive boundary is subjected solely to viscous stress underneath. However, the boundary thermally insulates the fluid, modifying the bulk flow. As a consequence, the interaction between the free boundary and the convective flows results in a regular oscillation. We report here some aspects of the fluid dynamics and discuss possible links between our experiment and continental drift. |
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| Abstract: We study the dynamics of heavy flexible sheets in a water flow, both to understand flapping of flags, and for its relevance to underwater animal locomotion. We find that the sheet can sharply transition from a straight state aligned with the flow, to a periodic flapping state, with bending waves traveling down the flag. We use a simple analytical model to understand the effect of fluid and structure inertia and elasticity. The model predicts a bifurcation with increasing flow speed, agreeing well with previous experiments in air and soap-films, but showing quantitative differences with our particular experiment. |
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| Abstract: The locomotion of most fish and birds is effected by flapping wings or fins transverse to the direction of travel. According to classical inviscid aerodynamic theory, a flapping wing translating at fixed speed can generate a propulsive force. In steady forward flight, this thrust is balanced by drag. But when the Reynolds number is small, viscous forces dominate, reciprocal flapping motions are ineffective, and the translating wing can only experience a net drag. Our experimental study bridges the two realms of large and small Reynolds number and examines the transition to forward flapping flight. at intermediate Reynolds numbers, the range relevant to swimming and flying of small organisms. We study experimentally the dynamics of a wing that is .flapped. up and down but is free to move either forwards or backwards. We show that flapping flight occurs abruptly at a critical flapping frequency as a symmetry-breaking bifurcation. Beyond this bifurcation, the speed of the wing increases linearly with the flapping frequency. The experiment establishes a clear demarcation between the different strategies of locomotion at large and small Reynolds number. Commentary on this work by Michael Hopkin that appeared in Nature: Nature, 429, 147 (2004) |
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| Abstract: 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 fibre wetted into a vertical soap-film tunnel, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformation of the fibre 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 U^2 drag scaling of rigid bodies to a U^4/3 drag law. The drag scaling is derived from an asymptotic expansion in the length scale of similarity, and it is found that the tip region induces the far-field behavior. The drag law persists, with a simple modification, under variations of the model suggested by the experiment, such as the addition of flow tunnel walls, and a back pressure in the wake. |
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| Abstract: 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. Commentary article on this work by Victor Steinberg that appeared in Nature: Bend and survive, Nature, 420, 479 (2002) |
flexible threads in a flowing soap film, click to view pdf Jun Zhang Physics of Fluids, 13(9), S15 (2001) |
| No abstract for this work: published as an entry in session "Gallery of Fluid Motion" |
flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, click to view pdf Jun Zhang, Stephen Childress, Albert Libchaber, and Michael Shelley Nature, 408, 835 (2000) |
| Abstract: The dynamics of swimming fish and flapping flags involves a complicated interaction of their deformable shapes with the surrounding fluid flow. Even in the passive case of a flag, the flag exerts forces on the fluid through its own inertia, elastic responses, and is likewise acted on by hydrodynamic pressure and drag. But such couplings are not well understood. Here we study these interactions experimentally, using an analogous system of flexible filaments in flowing soap films. We find that, for a single filament (or 'flag') held at its upstream end and otherwise unconstrained, there are two distinct, stable dynamical states. The first is a stretched-straight state: the filament is immobile and aligned in the flow direction. The existence of this state seems to refute the common belief that a flag is always unstable and will flap. The second is the flapping state: the filament executes a sinuous motion in a manner akin to the flapping of a flag in the wind. We study further the hydrodynamically coupled interaction between two such filaments, and demonstrate the existence of four different dynamical states. Commentary article on this work by Greg Huber that appeared in Nature: Swimming in flatsea, Nature 408, 777 (2000) |
periodic boundary motion in thermal turbulence, click to view pdf Jun Zhang, Albert Libchaber Phys. Rev. Lett., 84, 4361 (2000) |
| Abstract: A free-floating plate is introduced in a Bénard convection cell with an open surface. It partially covers the cell and distorts the local heat flux, inducing a coherent flow that in turn moves the plate. Remarkably, the plate can be driven to a periodic motion even under the action of a turbulent fluid. The period of the oscillation depends on the coverage ratio, and on the Rayleigh number of the convective system. The plate oscillatory behavior observed in this experiment may be related to a geological model, in which continents drift in a quasiperiodic fashion. |
non-Boussinesq effect: asymmetric velocity profiles in thermal convection, click to view pdf Jun Zhang, S. Childress, and A. Libchaber Physics of Fluids 10, 1534 (1998) |
| Abstract: In thermal convection at high Rayleigh numbers, in the hard turbulent regime, a large scale flew is present. When the viscosity of the fluid strongly depends on temperature, the top-bottom symmetry is broken. In addition to the asymmetric temperature profile across the convection cell, the velocity profiles near the plate boundaries show dramatic difference from the symmetric case. We report here that the second derivative of the velocity profiles are of opposite signs in the thermal sublayers, through measurements derived from the power spectrum of temperature time-series. As a result, the stress rate applied at the plates is maintained constant within a factor of 3, while the viscosity changes by a factor of 53, in qualitative agreement with previous theory. |
non-Boussinesq effect: thermal convection with broken symmetry, click to view pdf Jun Zhang, S. Childress, and A. Libchaber Physics of Fluids 9, 1034 (1997) |
| Abstract: We investigate large Rayleigh number (106-109) and large Prandtl number (102-103) thermal convection in glycerol in an aspect ratio one cubic cell. The kinematic viscosity of the fluid strongly depends upon the temperature. The symmetry between the top and bottom boundary layers is thus broken, the so-called non-Boussinesq regime. In a previous paper Wu and Libchaber have proposed that in such a state the two thermal boundary layers adjust their length scales so that the mean hot and cold temperature fluctuations are equal in the center of the cell. We confirm this equality. A simplified two-dimensional model for the mean center temperature based on an equation for the thermal boundary layer is presented and compared with the experimental results. The conclusion is that the central temperature adjusts itself so that the heat fluxes from the boundary layers are equal, temperature fluctuations at the center symmetrical, at a cost of very different temperature drops and Rayleigh number for each boundary. |
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