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Jan 1998

Volume 10, Issue 1, pp. 7-332

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Drag reduction of turbulent pipe flows by circular-wall oscillation

Kwing-So Choi and Mark Graham

Phys. Fluids 10, 7 (1998); http://dx.doi.org/10.1063/1.869538 (3 pages) | Cited 24 times

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An experimental study on turbulent pipe flows was conducted with a view to reduce their friction drag by oscillating a section of the pipe in a circumferential direction. The results indicated that the friction factor of the pipe is reduced by as much as 25% as a result of active manipulation of near-wall turbulence structure by circular-wall oscillation. An increase in the bulk velocity was clearly shown when the pipe was oscillated at a constant head, supporting the measured drag reduction in the present experiment. The percentage reduction in pipe friction was found to be better scaled with the nondimensional velocity of the oscillating wall than with its nondimensional period, confirming a suggestion that the drag reduction seem to be resulted from the realignment of longitudinal vortices into a circumferential direction by the wall oscillation. © 1998 American Institute of Physics.
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47.27.-i Turbulent flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.35.-i Hydrodynamic waves

Wave patterns in a thin layer of sand within a rotating horizontal cylinder

Eliot Fried, Amy Q. Shen, and S. T. Thoroddsen

Phys. Fluids 10, 10 (1998); http://dx.doi.org/10.1063/1.869539 (3 pages) | Cited 8 times

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A variety of wave patterns are found to form in a thin layer of sand inside a cylinder rotated about its horizontal axis of symmetry at constant angular velocity. In particular, we observe a spanwise instability characterized by serrated frontal shapes remarkably similar to those seen in Newtonian fluids. Within a certain parameter range, an accompanying spatial pattern forms on the rising side of the cylinder and travels along the cylinder span. The associated phase velocity is relatively constant, whereas the relevant wavelength increases quadratically with angular rotation speed. Standing waves appear at a critical rotation rate. Further, in some cases, a propagating cellular pattern forms on the surface of the medium. © 1998 American Institute of Physics.
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
45.05.+x General theory of classical mechanics of discrete systems
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On the gravity-driven draining of a rivulet of viscous fluid down a slowly varying substrate with variation transverse to the direction of flow

S. K. Wilson and B. R. Duffy

Phys. Fluids 10, 13 (1998); http://dx.doi.org/10.1063/1.869569 (10 pages) | Cited 12 times

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In this paper we use a lubrication approximation to investigate the locally unidirectional gravity-driven draining of a thin rivulet of Newtonian fluid down a slowly varying substrate. The work generalizes the recent study by Duffy and Moffatt [Chem. Eng. J. 60, 141 (1995)] of gravity-driven draining down a locally planar substrate to include the effects of substrate variation transverse to the direction of flow. Asymptotic and numerical results are obtained for several simple convex and concave transverse substrate profiles. In all the cases investigated these results show a number of common features. In particular, they show that a single stable slowly varying rivulet running continuously from the top to the bottom of a large horizontal circular cylinder is possible only if the transverse substrate profile is a sufficiently shallow trough. If the profile is a deeper trough then no such rivulet is possible near the bottom of the cylinder, while if the profile is a ridge then no such rivulet is possible near the top of the cylinder. © 1998 American Institute of Physics.
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47.60.-i Flow phenomena in quasi-one-dimensional systems

Dynamics of spontaneous spreading with evaporation on a deep fluid layer

Anne D. Dussaud and Sandra M. Troian

Phys. Fluids 10, 23 (1998); http://dx.doi.org/10.1063/1.869546 (16 pages) | Cited 17 times

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The spontaneous spreading of a thin volatile film along the surface of a deep fluid layer of higher surface tension provides a rapid and efficient transport mechanism for many technological applications. This spreading process is used, for example, as the carrier mechanism in the casting of biological and organic Langmuir–Blodgett films. We have investigated the dynamics of spontaneously spreading volatile films of different vapor pressures and spreading coefficients advancing over the surface of a deep water support. Laser shadowgraphy was used to visualize the entire surface of the film from the droplet source to the leading edge. This noninvasive technique, which is highly sensitive to the film surface curvature, clearly displays the location of several moving fronts. In this work we focus mainly on the details of the leading edge. Previous studies of the spreading dynamics of nonvolatile, immiscible thin films on a deep liquid layer have shown that the leading edge advances in time as t3/4 as predicted by laminar boundary layer theory. We have found that the leading edge of volatile, immiscible spreading films also advances as a power law in time, tα, where α ∼ 1/2. Differences in the liquid vapor pressure or the spreading coefficient seem only to affect the speed of advance but not the value of the spreading exponent, which suggests the presence of a universal scaling law. Sideview laser shadowgraphs depicting the subsurface motion in the water reveal the presence of a single stretched convective roll right beneath the leading edge of the spreading film. This fluid circulation, likely caused by evaporation and subsequent surface cooling of the rapidly spreading film, resembles a propagating Rayleigh–Bénard convective roll. We propose that this sublayer rotational flow provides the additional dissipation responsible for the reduced spreading exponent. © 1998 American Institute of Physics.
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81.15.Lm Liquid phase epitaxy; deposition from liquid phases (melts, solutions, and surface layers on liquids)
64.70.F- Liquid-vapor transitions
68.15.+e Liquid thin films
68.18.-g Langmuir-Blodgett films on liquids

Discontinuous behavior of liquids between parallel and tilted plates

Paul Concus and Robert Finn

Phys. Fluids 10, 39 (1998); http://dx.doi.org/10.1063/1.869547 (5 pages) | Cited 14 times

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Discontinuous behavior of liquids between parallel and tilted plates in the absence of gravity is discussed. A principal finding, derived mathematically from the classical Young–Laplace–Gauss formulation for capillary free surfaces, is that in a large range of configurations liquid bridges between parallel plates are unstable with respect to small, even infinitesimal, tilting of one of the plates. Under a computationally based hypothesis of uniqueness of spherical bridges in a wedge, it is shown that the same discontinuous behavior prevails for all but very particular circumstances. The various liquid configurations, which form the basis for an experiment on board the Space Station Mir, are characterized and illustrated. © 1998 American Institute of Physics.
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68.03.Cd Surface tension and related phenomena
81.70.Ha Testing in microgravity environments

An experimental investigation of the intrinsic convection in a sedimenting suspension

Yannick Peysson and Élisabeth Guazzelli

Phys. Fluids 10, 44 (1998); http://dx.doi.org/10.1063/1.869548 (11 pages) | Cited 10 times

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The sedimentation of spheres in a Newtonian fluid is experimentally studied under creeping flow conditions. The mean particle settling velocity and the particle velocity fluctuations are measured across the width of the sedimentation cell. We show that there can be a global intrinsic convection of the suspension superimposed on the settling motion of the particles. Unlike the predictions of the dilute theories of intrinsic convection, this effect is found to be small and even to disappear with increasing concentrations. We also find that there is an ordering of the suspension near the wall, which may be responsible for the observed small magnitude of the convection. © 1998 American Institute of Physics.
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47.27.T- Turbulent transport processes
47.15.-x Laminar flows
47.55.Kf Particle-laden flows
47.15.G- Low-Reynolds-number (creeping) flows

Three-dimensional intrinsic convection in dilute and dense dispersions of settling spheres

D. Bruneau, F. Feuillebois, J. Bławzdziewicz, and R. Anthore

Phys. Fluids 10, 55 (1998); http://dx.doi.org/10.1063/1.869549 (5 pages) | Cited 9 times

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The three-dimensional intrinsic convection in a monodisperse dispersion of spheres settling in a vertical container of arbitrary cross section is calculated using the simple model of point forces with excluded volume near the walls, proposed by Bruneau et al. [Phys. Fluids 8, 2236 (1996)]. An exact solution of the model equations for a container with rectangular cross-section shows that corners have no significant influence on the convection. A dense suspension is modeled by assuming an equilibrium particle distribution in the near wall region. It is predicted that as a result of near wall ordering, the intrinsic convection decreases with increasing particle volume fraction. © 1998 American Institute of Physics.
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82.70.-y Disperse systems; complex fluids
44.25.+f Natural convection

Simulation of flow through bead packs using the lattice Boltzmann method

R. S. Maier, D. M. Kroll, Y. E. Kutsovsky, H. T. Davis, and R. S. Bernard

Phys. Fluids 10, 60 (1998); http://dx.doi.org/10.1063/1.869550 (15 pages) | Cited 67 times

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The lattice Boltzmann method (LBM) is used to simulate viscous fluid flow through a column of glass beads. The results suggest that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing. With increasing spatial resolution, simulation results converge to a velocity distribution with a sharp peak near zero. A simple argument is presented to explain this result. Changes in the shape of the distribution as a function of flow rate are determined for low Reynolds numbers, and the large-velocity tail of the distribution is shown to depend on the packing geometry. The effect of a finite Reynolds number on the apparent permeability is demonstrated and discussed in relation to previous results in the literature. Comparison with velocity distributions from NMR (nuclear magnetic resonance) spectroscopy finds qualitative agreement after adjusting for diffusion effects in the NMR distributions. © 1998 American Institute of Physics.
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47.56.+r Flows through porous media
47.11.-j Computational methods in fluid dynamics

The characterization of multiphase fluid transport in a porous solid by pulsed gradient stimulated echo nuclear magnetic resonance

Jean J. Tessier and Ken J. Packer

Phys. Fluids 10, 75 (1998); http://dx.doi.org/10.1063/1.869551 (11 pages) | Cited 36 times

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Pulsed magnetic field gradient stimulated echo nuclear magnetic resonance (NMR) measurements are reported for the steady-state flow and diffusion of two and three phases (water, dodecane, N2 gas) within a sample of a Fontainebleau sandstone. The stimulated echo dependence on the gradient pulse area, q, is used to derive the displacement probability, PΔ(X) for fixed observation times Δ, with the displacements X being measured along the macroscopic pressure gradient. An extensive range of NMR experiments was carried out, starting with single-phase flow of either water (an aqueous solution of NaCl 3% w/v) or oil (dodecane) for various relative saturation states. Following these experiments, PΔ(X) were acquired for water and oil when both phases were forced to flow through the sandstone. Finally, NMR measurements were performed in which three phases (oil, water and N2 gas) were flowing simultaneously. Using the NMR data it was possible to evaluate the physical importance of parameters such as wettability, spreading and phase saturations on the transport phenomena. To our knowledge, these experiments represent the first comprehensive NMR study of multiphase flow in porous media, and the extent of the information obtained is providing a strong experimental basis to validate and develop accurate modelling of fluid transport in porous solids. © 1998 American Institute of Physics.
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76.60.-k Nuclear magnetic resonance and relaxation
68.03.-g Gas-liquid and vacuum-liquid interfaces
68.05.-n Liquid-liquid interfaces
47.55.Kf Particle-laden flows
47.56.+r Flows through porous media
83.50.Ha Flow in channels
68.08.Bc Wetting
66.30.-h Diffusion in solids

Motion of spheroidal particles in vertical shear flows

David Broday, Mati Fichman, Michael Shapiro, and Chaim Gutfinger

Phys. Fluids 10, 86 (1998); http://dx.doi.org/10.1063/1.869552 (15 pages) | Cited 10 times

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The motion of non-neutrally buoyant prolate spheroidal particles in vertical shear flows is investigated. Using the generalized Faxen law, we calculate the hydrodynamic forces and moments acting on such inertial and inertialess particles, and their trajectories. The calculations are done for (i) freely rotating particles, and (ii) particles with orientations fixed by means of an external torque exerted by a strong orienting field. Inertial particles are found to migrate across the streamlines, and their trajectories differ considerably from those calculated for inertialess particles. Neutrally buoyant spheroids, inertial or not, which either freely rotate or have fixed orientations in shear flows, translate along the streamlines. Non-neutrally buoyant inertialess spheroids freely moving in simple shear flow translate along periodic trajectories with no net lateral drift. In contrast, inertial particles under similar flow conditions drift laterally toward locations characterized by higher local velocities in a direction opposing gravity. The motion of non-neutrally buoyant inertial particles with fixed orientations may be unstable with the drift velocity growing exponentially with time. Conditions for the occurrence of this unstable motion are formulated analytically in terms of particle and flow parameters. In general, the rate of drift depends on particle shape, via its aspect ratio, and its inertia. © 1998 American Institute of Physics.
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47.55.Kf Particle-laden flows
47.15.-x Laminar flows

The asymptotic motion of an accelerating, thick layer of inviscid liquid

Greg Baker and Qing Nie

Phys. Fluids 10, 101 (1998); http://dx.doi.org/10.1063/1.869553 (12 pages) | Cited 1 time

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Most studies of a gravitationally unstable interface between a liquid and a gas by boundary integral techniques prescribe the motion of the liquid in the far field. The mean gas pressure at the interface is then irrelevant in its motion. On the other hand, when a pressure jump is applied to a liquid column in a vertical duct, its acceleration is determined by the pressure jump no matter how tall the column. Previous studies of accelerating liquid layers [G. R. Baker, R. L. McCrory, C. P. Verdon, and S. A. Orszag, “Rayleigh–Taylor instability of fluid layers,” J. Fluid Mech. 178, 161 (1987)] show that the motion of the gravitationally unstable interface depends on the reciprocal of the mean layer thickness H. In this paper, we derive an asymptotic boundary integral method that captures the O(1/H) effects on the motion of the unstable interface with a correction that is exponentially small in H. The validity of the asymptotic approach is confirmed by comparison with numerical simulations of the liquid layer. The success of the approach relies on expansions of the kernels in the boundary integrals, indicating that the procedure for deriving the asymptotic equations is more general than just for vertical ducts or periodic geometry. In a subsequent paper, we use our approach to derive the equations for the formation of a bubble at a submerged orifice that is driven by an increase in gas pressure. © 1998 American Institute of Physics.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics

Analysis of spatial patterns in secondary flows generated by torsionally oscillating spheres in linearly stratified fluids

R. F. Folse and C. W. Piker

Phys. Fluids 10, 113 (1998); http://dx.doi.org/10.1063/1.869554 (6 pages)

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Measurements have been made of the cellular flow patterns observed by Folse [Phys. Fluids 6, 537 (1994)] in the secondary flow field of torsionally oscillating spheres in stratified fluids. Shadowgraphs were made of the secondary flow field of spheres, radii between 2.52 and 5.08 cm, torsionally oscillating (frequencies in the range 1.0 rad/s ⩽ ω ⩽ 13.5 rad/s and amplitudes θ0 ⩽ 1 rad) in linearly stratified fluids, with Brunt–Väisälä frequencies between 0.8 rad/s ⩽ N ⩽ 2.1 rad/s. The spatial pattern was determined by measuring the vertical size, d, and radial position, r, for each cell. Dimensionless cell size, d/r, was found to depend on the parameters (ω/N), θ0, and the angular position on the sphere ϕ measured from the pole. A correlation of the dimensionless cell size is found, independent of sphere radius, given by: dn/mathn = 0.22(ω/N)θ02 cot(mathn), where mathn and mathn are the average radial and angular positions of the nth cell. This correlation results in a discrepancy between measurements and expectations based on a heuristic energy argument. © 1998 American Institute of Physics.
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47.55.Hd Stratified flows
47.35.-i Hydrodynamic waves
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.20.-k Flow instabilities

Motion stability of a deformable body in an ideal fluid with applications to the N spheres problem

A. R. Galper and T. Miloh

Phys. Fluids 10, 119 (1998); http://dx.doi.org/10.1063/1.869570 (12 pages) | Cited 5 times

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The Liapunov stability problem of the translation or spiraling motion of an arbitrary deformable body (the deformation of which is governed by the corresponding Hamiltonian) is treated here using the modified Energy–Casimir approach. The appropriate stability criteria are derived. It is shown that some unstable translational motions can be stabilized by a deformational or rotational motion. This formalism is further applied to the stability problem related to the motion of N (generally unequal) rigid spheres embedded in a potential flow field. The assembly of N-spheres is treated as an entire N-connected single deformable body. The Liapunov stability of the motion of two spheres in the direction orthogonal to their lines of centers and that of three spheres in the direction orthogonal to their plane of centers, is demonstrated and proven as a special case. Some existing conditions of clustering for a bubble cloud are also rederived and extended. © 1998 American Institute of Physics.
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47.20.-k Flow instabilities
47.55.Kf Particle-laden flows
47.55.D- Drops and bubbles

The stability of evaporating thin liquid films in the presence of surfactant. I. Lubrication approximation and linear analysis

Krassimir D. Danov, Norbert Alleborn, Hans Raszillier, and Franz Durst

Phys. Fluids 10, 131 (1998); http://dx.doi.org/10.1063/1.869555 (13 pages) | Cited 14 times

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The dynamics of an evaporating wetting liquid film in the presence of dissolved surfactant is investigated. The solid substrate is planar and is subjected to heating. The liquid–vapor interface is a two-dimensional continuum characterized by specific adsorption, interfacial viscosity, and surface tension, which depend on the surfactant subsurface concentration and temperature. In the case of small density, viscosity, and thermal conductivity of the vapor phase (compared to the respective values for the liquid phase), at small Reynolds and large Peclet numbers and for thin films, the lubrication approximation model can be applied. The effect of the van der Waals disjoining pressure is taken into account. The appearing dimensionless groups, defined in terms of the real physical parameters, can vary by several orders of magnitude depending on the film initial thickness, temperature difference, and type of surfactants. The developed linear theory describes the competition among the various instabilities. The numerical solution of the evolution equation provides information about the critical film thickness, critical lateral wave number, and time for rupture. The influence of the interfacial mass loss due to evaporation, the van der Waals attraction, the Marangoni effects due to thermal and concentration gradients, and the interfacial viscous friction upon the critical film thickness is discussed. © 1998 American Institute of Physics.
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64.70.F- Liquid-vapor transitions
68.03.Fg Evaporation and condensation of liquids
68.15.+e Liquid thin films
68.08.Bc Wetting
66.20.-d Viscosity of liquids; diffusive momentum transport
68.03.Cd Surface tension and related phenomena
47.20.Dr Surface-tension-driven instability

Dipolar vortices in a strain flow

R. R. Trieling, J. M. A. van Wesenbeeck, and G. J. F. van Heijst

Phys. Fluids 10, 144 (1998); http://dx.doi.org/10.1063/1.869556 (16 pages) | Cited 9 times

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The evolution characteristics of dipolar vortices in a strain flow were investigated both experimentally and theoretically. The laboratory experiments were performed in a stratified fluid, the strain flow being generated by four rotating horizontal discs, whereas the dipolar vortex was created by a pulsed injection of a small amount of fluid. Dye-visualization studies and particle-tracking techniques were used to obtain qualitative and quantitative information about the horizontal flow field. Depending on the initial orientation of the dipole, either a head–tail structure or a pair of elliptic-like monopolar vortices was formed. In the former case, the distance between the vortex centers was observed to remain nearly constant due to the opposing effects of strain and lateral diffusion, while in the latter case, the vortex centers were passively advected by the ambient flow. The head–tail formation could be explained kinematically by a simple point-vortex model. Full-numerical simulations based on the quasi-two-dimensional vorticity equation revealed a very good agreement with the laboratory observations. © 1998 American Institute of Physics.
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47.32.C- Vortex dynamics

Development and application of a hierarchical system for digital particle image velocimetry to free-surface turbulence

S. Kumar and S. Banerjee

Phys. Fluids 10, 160 (1998); http://dx.doi.org/10.1063/1.869558 (18 pages) | Cited 8 times

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A method for particle image velocimetry (PIV) is presented which improves upon the accuracy, computational efficiency and dynamic range (i.e., the difference between the largest and smallest resolvable particle displacement vectors) of conventional PIV techniques. The technique is applied to free-surface turbulence to resolve energy spectra for motions with a wide dynamic range. The methodology—based on multi-grid image processing algorithms for rigid body motion analysis, estimates the displacement vectors at discrete particle locations. The essence of this technique is to estimate large scale motions from image intensity patterns of low spatial frequencies and small scale motions from intensity patterns of high spatial frequencies. Cross-correlation between a pair of time separated particle images is implemented by the hierarchical computational scheme of Burt [“Fast filter transforms for image processing,” Int. J. Comput. Vision 16, 20 (1981)]. Each image is convolved with a series of band-pass filters and subsampled to obtain a set of images progressively decreasing in resolution and size. A coarse estimate of the displacement field obtained from pairs of lower resolution images are used to obtain more accurate estimates at the next (finer) level. Processing starts at the level of lowest resolution and stops at the highest resolution level, which contains the original image pair. Due to subsampling of low resolution images, the match template size can be kept constant for all stages of computation, thus eliminating the dependence of the largest resolvable displacement on the size of match template. In the present work, the search area at each level is kept constant at 3×3 pixels and the match template size at 5×5 pixels for all levels of computation. The algorithm has been implemented using simple thresholding based on the confidence level of an estimated displacement vector, as suggested by Anandan [“A computational framework and an algorithm for measurement of visual motion,” Int. J. Comput. Vision, 2, 283, (1987)]. However, the confidence-level-based smoothing technique for rigid body motions (continuous velocity fields) could not be applied to displacement estimates obtained at discrete points i.e., the particle locations. Instead, smoothing was performed over the area covered by each particle. The algorithm has been tested against direct numerical simulations of turbulent flows when the flow field is known and particle images have been generated from these with the addition of noise. Both the accuracy of motion estimation and the computation time are seen to improve as compared to conventional PIV methods. Finally, video images taken of particle motion on the free-surface of a channel flow have been used to determine the capabilities of the technique in an experimental study. The resulting spectra show a quasi-two-dimensional character of the free-surface turbulent flow field, which corresponds well with the direct numerical simulations. © 1998 American Institute of Physics.
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47.27.-i Turbulent flows
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics

Forces on ellipsoidal bubbles in a turbulent shear layer

Barry Ford and Eric Loth

Phys. Fluids 10, 178 (1998); http://dx.doi.org/10.1063/1.869557 (11 pages) | Cited 12 times

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The objective of this research was to gain fundamental knowledge of the drag and lift forces on ellipsoidal air bubbles in water in a turbulent flow. This was accomplished by employing a cinematic two-phase particle image velocimetry (PIV) system to evaluate bubbly flow in a two-stream, turbulent, planar free shear layer of filtered tap water. Ellipsoidal air bubbles with nominal diameters from 1.5 to 4.5 mm were injected directly into the shear layer through a single slender tube. The cinematic PIV allowed for high resolution of the unsteady liquid velocity vector field. Triple-pulsed bubble images were obtained in a temporal sequence, such that the bubble size and bubble trajectory could be accurately determined. The bubble’s oscillation characteristics, velocity, acceleration, and buoyancy force were obtained from the trajectory data. A bubble dynamic equation was then applied to allow determination of the time-evolving lift and drag forces acting upon bubbles within the shear layer. The results indicate that for a fixed bubble diameter (and fixed Bond and Morton numbers), the drag coefficient decreases for an increasing Reynolds number. This is fundamentally different than the increasing drag coefficient trend seen for ellipsoidal bubbles rising in quiescent baths for increasing diameter (and increasing Bond number), but is qualitatively consistent with the trend for spherical bubbles. A new empirical expression for the dependence of the drag coefficient on Reynolds number for air bubbles in tap water for both quiescent and turbulent flows is constructed herein. Finally, the instantaneous side forces measured in this study were dominated by the inherent deformation-induced vortex shedding of the bubble wake rather than the inviscid lift force based on the background fluid vorticity. © 1998 American Institute of Physics.
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47.55.D- Drops and bubbles
47.27.nb Boundary layer turbulence

Flame–vortex interaction in a reacting vortex ring

J. S. Hewett and C. K. Madnia

Phys. Fluids 10, 189 (1998); http://dx.doi.org/10.1063/1.869560 (17 pages) | Cited 17 times

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Direct numerical simulations are used to study the flame–vortex interaction in a laminar reacting vortex ring. The chemical reaction occurs by a one-step, Arrhenius-type reaction that mimics the combustion of typical hydrocarbon and air. The ring is generated by an axisymmetric jet that is impulsed to emit a cold fuel through a nozzle. The fuel enters a quiescent ambient at a much higher temperature. By adjusting the ratio of the ambient and fuel temperatures, the ignition either occurs during the formation or post-formation phase of the ring. When ignition occurs during the formation phase of the ring, the bulk of combustion is by a flame at the front of the vortex bubble. When ignition is delayed until after the formation phase, most of the reaction occurs inside the vortex ring. It is found that premixing the fuel and the oxidizer enhances the amount of product formation. The heat released from the reaction significantly affects production, redistribution, and diffusion of the vorticity throughout the field. The results of the simulations also reveal that the heat of reaction affects the strain rate fields differently depending on when the ignition of the ring occurs. © 1998 American Institute of Physics.
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47.70.Fw Chemically reactive flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
82.33.Vx Reactions in flames, combustion, and explosions
47.32.C- Vortex dynamics
47.15.-x Laminar flows
47.11.-j Computational methods in fluid dynamics

Caustics of weak shock waves

Rodolfo R. Rosales and Esteban G. Tabak

Phys. Fluids 10, 206 (1998); http://dx.doi.org/10.1063/1.869559 (17 pages) | Cited 3 times

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The caustics of weak shock waves are studied through matched asymptotic expansions. It is shown that these caustics are thinner and more intense than those of smooth waves with a comparable amplitude. This difference in scalings solves a paradox that would have the caustics of weak shock waves behave linearly, even though linear theory for discontinuous fronts predicts infinite amplitudes near the caustic and in the reflected wave. With the new scalings, the behavior of shocks both near the caustic and in the far field is described by nonlinear equations. The new scales are robust, in the sense that they survive the addition of a small amount of viscosity to the equations. As a viscous shock approaches the caustic, its intensity amplifies and its width decreases in such a way that the new scalings are actually reinforced. A new paradox arises, however: The nonlinear Tricomi equation which describes the behavior of the fronts near caustics does not appear to admit the triple shock intersections which have been observed experimentally. This new open problem is closely related to the von Neumann paradox of oblique shock reflection. © 1998 American Institute of Physics.
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47.40.Nm Shock wave interactions and shock effects
02.30.-f Function theory, analysis

Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts

L. Bühler

Phys. Fluids 10, 223 (1998); http://dx.doi.org/10.1063/1.869562 (14 pages) | Cited 20 times

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The buoyancy-driven laminar magnetohydrodynamic flow in long vertical channels is investigated. It is assumed that the channels have a rectangular cross section with one pair of walls aligned with the strong uniform magnetic field. The walls may have arbitrary electrical conductance. Using asymptotic methods, solutions are derived for general temperature distributions inside the ducts. Results are shown for different values of the control parameters. One finds the typical subregions for the flow inside the duct, namely the inviscid core, surrounded by viscous Hartmann layers and side layers. The character of the solution inside these regions may deviate from what is expected by a comparison with the classical solutions for pressure-driven duct flows. The main difference is that the flow in the core not necessarily exhibits a two-dimensional behavior. Most surprising, however, is the fact, that high-velocity jets are observed for the first time along perfectly conducting sidewalls. These jets are able to carry a major part of the flow rate. © 1998 American Institute of Physics.
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47.15.-x Laminar flows
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.wg Turbulent jets

Inertial range structures in decaying compressible turbulent flows

David H. Porter, Paul R. Woodward, and Annick Pouquet

Phys. Fluids 10, 237 (1998); http://dx.doi.org/10.1063/1.869563 (9 pages) | Cited 58 times

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Simulations of decaying compressible turbulent flows have been performed using the PPM algorithm on grids of 5123 and 10243 computational cells. Although the run on the finer grid has not yet been carried out to a time large enough for the spectra to relax fully, it adds significantly to the results on the coarser grid by lengthening the range of wave numbers in which the flow exhibits a self-similar character. There is an inertial range of scales in the decaying flow on the finer mesh that is free from direct effects of dissipation, forcing, boundary conditions, or initial conditions. Favre averaging of the high resolution data is performed on different scales from which the vorticity structures in the inertial range may be visualized and characterized without confusion from the smaller-scale features of the near dissipation range. We find that the vorticity structures of the inertial range are filamentary as well, but qualitatively different—shorter and more curved—than those of the dissipation range. Quantitative evidence of the action of vortex stretching in developed turbulence is also presented. © 1998 American Institute of Physics.
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47.27.E- Turbulence simulation and modeling
47.40.-x Compressible flows; shock waves
47.32.C- Vortex dynamics

Advances in PDF modeling for inhomogeneous turbulent flows

P. R. Van Slooten, Jayesh, and S. B. Pope

Phys. Fluids 10, 246 (1998); http://dx.doi.org/10.1063/1.869564 (20 pages) | Cited 39 times

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Probability density function (PDF) models which are based on an exact representation of rapidly distorting homogeneous turbulence are applied to a free shear flow, the temporal mixing layer. These velocity wave-vector models were constructed in a previous paper by Van Slooten and Pope [Phys. Fluids 9, 1085 (1997)], but were only tested in cases of homogeneous turbulence. At the edges of free shear flows both turbulent–nonturbulent intermittency and pressure transport are demonstrated to play a significant role in the behavior of the flow. A natural treatment of intermittency is obtained by extending the PDF formulation to include a model for the turbulent frequency following a fluid particle. A model for the pressure transport is also constructed via a scaling analysis. The resulting velocity wave-vector turbulent-frequency PDF model with the pressure transport model yields a good comparison with the available direct numerical simulation data for the temporal shear layer. © 1998 American Institute of Physics.
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47.27.nb Boundary layer turbulence
02.50.Cw Probability theory

On the collision rate of small particles in isotropic turbulence. I.  Zero-inertia case

Lian-Ping Wang, Anthony S. Wexler, and Yong Zhou

Phys. Fluids 10, 266 (1998); http://dx.doi.org/10.1063/1.869565 (11 pages) | Cited 33 times

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Numerical experiments have been performed to study the geometric collision rate of finite-size particles with zero inertia (i.e., fluid elements) in isotropic turbulence. The turbulent flow was generated by the pseudospectral method. We argue that the formulation of Saffman and Turner [J. Fluid Mech. 1, 16 (1956)] for the average collision kernel is correct only under the assumptions that the particles are kept in the system after collision and allowed to overlap in space. This was confirmed, for the first time, by numerical experiments to within a numerical uncertainty as small as 1%. Finite corrections to the Saffman and Turner result must be made if one applies the theory to actual coagulation process where particles are not allowed to overlap before collision and particles are removed from a given size group after collision. This is due to the fact that Saffman and Turner assumed a uniform, time-independent concentration field in their formulation of the average collision kernel, while in the actual modeling of population evolution the particle number concentration changes in time and may be locally nonuniform as a result of a biased removal process due to spatially nonuniform coagulation rates. However, the quantitative level of the deviations from the Saffman and Turner result remain to be explained. Numerical experiments in simple shear flow were also conducted to elaborate our findings. © 1998 American Institute of Physics.
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47.27.-i Turbulent flows

Numerical study on blast flowfields induced by supersonic projectiles discharged from shock tubes

Z. Jiang, K. Takayama, and B. W. Skews

Phys. Fluids 10, 277 (1998); http://dx.doi.org/10.1063/1.869566 (12 pages) | Cited 11 times

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In this paper we report on a numerical study of the blast flowfield generated by a supersonic projectile released from the open-end of a shock tube into ambient air. The Euler equations, assuming axisymmetric flows, were solved using a dispersion-controlled scheme implemented with moving boundary conditions. Two initial test cases were calculated. One of them is for validation of the numerical method and the other for verification of the moving boundary conditions. After good agreement was achieved, four further cases were calculated for examining effects of various projectile speeds and different release times of the projectile after the precursor shock wave was discharged. The present numerical study confirms that complicated transient phenomena exist in the initial stages shortly after projectile release, and that the blast flowfield is much more complex than that which can be inferred from muzzle blast studies where combustion products obscure the flow. © 1998 American Institute of Physics.
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47.40.Ki Supersonic and hypersonic flows
47.40.Nm Shock wave interactions and shock effects

Monte Carlo simulation and Navier–Stokes finite difference calculation of unsteady-state rarefied gas flows

Stefan Stefanov, Peter Gospodinov, and Carlo Cercignani

Phys. Fluids 10, 289 (1998); http://dx.doi.org/10.1063/1.869561 (12 pages) | Cited 12 times

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A comparative analysis of two approaches (molecular and continuum) for three one-dimensional unsteady-state rarefied gas flows with small Knudsen number is presented. Numerical results have been obtained by using Direct Simulation Monte Carlo (DSMC) method for the molecular and a finite difference method for the continuum approaches, respectively. © 1998 American Institute of Physics.
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47.20.-k Flow instabilities
47.45.-n Rarefied gas dynamics
02.50.Ng Distribution theory and Monte Carlo studies
02.70.Rr General statistical methods
47.27.-i Turbulent flows
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