Phys. Fluids (1994-Present) - Physics of Fluids

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Study of a chaotic mixing system for DNA chip hybridization chambers

Florence Raynal, Frédéric Plaza, Aurélien Beuf, Philippe Carrière, Eliane Souteyrand, Jean-René Martin, Jean-Pierre Cloarec, and Michel Cabrera

Phys. Fluids 16, L63 (2004); http://dx.doi.org/10.1063/1.1775807 (4 pages) | Cited 13 times

Online Publication Date: 19 July 2004

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Numerical simulations of a micromixing system based on chaotic advection for improved deoxyribonucleic acid (DNA) chip hybridization are presented. To attain best chip performance, homogeneous dispersion of DNA molecules throughout the chamber in which the chip is placed is of primary importance. Poincaré sections of a simple time-periodic flow, based on numerical simulations of the flow, are compared with visualizations in a scaled-up experiment, with good agreement. The influence on mixing efficiency of varying the period of the flow at fixed volume flow rate is studied and a trade off is found between the absence of regular islands and a small enough total sample volume. The results illustrate the potential for optimization of such devices based on numerical flow simulations.

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47.11.-j	Computational methods in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
87.80.-y	Biophysical techniques (research methods)

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Beads-on-string phenomena in wormlike micellar fluids

Michael C. Sostarecz and Andrew Belmonte

Phys. Fluids 16, L67 (2004); http://dx.doi.org/10.1063/1.1779672 (4 pages) | Cited 13 times

Online Publication Date: 19 July 2004

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We present experimental results on the dynamics of wormlike micellar filaments surrounded by an immiscible viscous bulk fluid. For certain concentrations, these filaments develop a beads-on-string structure previously observed only in polymer jets and filaments surrounded by air. By taking advantage of the longer time scales present in this experiment, we are able to quantify the evolution of individual beads. We also investigate the stability of these filaments and the robustness of the beads-on-string structure by stretching the filament within a rotating flow.

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47.55.Kf	Particle-laden flows
47.50.-d	Non-Newtonian fluid flows
82.70.Uv	Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)
82.70.Dd	Colloids
47.32.-y	Vortex dynamics; rotating fluids
47.20.Gv	Viscous and viscoelastic instabilities

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The counter-rotating core of a swirling turbulent jet issued from a rotating pipe flow

Luca Facciolo and P. Henrik Alfredsson

Phys. Fluids 16, L71 (2004); http://dx.doi.org/10.1063/1.1779252 (3 pages) | Cited 6 times

Online Publication Date: 29 July 2004

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Axially rotating turbulent pipe flow is an example where rotation strongly affects the turbulence and thereby the Reynolds stresses and mean flow properties. The present Letter reports new measurements where a rotating pipe flow is used to establish a swirling jet. The measurements in the jet show that at some distance downstream (approximately 6 nozzle diameters) the central part of the jet starts to rotate in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the cross flow Reynolds stress originating in the pipe flow.

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47.32.-y	Vortex dynamics; rotating fluids
47.27.wg	Turbulent jets
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Vortex dynamics associated with the collision of a sphere with a wall

Thomas Leweke, Mark C. Thompson, and Kerry Hourigan

Phys. Fluids 16, L74 (2004); http://dx.doi.org/10.1063/1.1773854 (4 pages) | Cited 7 times

Online Publication Date: 6 August 2004

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For moderate Reynolds numbers, a sphere striking a wall in the normal direction leads to the trailing recirculating wake threading over the sphere and developing into a complex vortex ring system as it interacts with the wall. The primary vortex ring, which consists of vorticity from the wake, persists and convects slowly outwards away from the sphere due to the motion induced from its image. The structure and evolution of this vortex system is quantified through a combined experimental and numerical study. At higher Reynolds numbers a non-axisymmetric instability develops, which leads to rapid dispersion of the ring system. A comparison of the wavelength and growth rate, predicted from both linear stability theory and direct simulations, with idealized models indicates that the mechanism is dominated by a centrifugal instability at the edge of the primary vortex core.

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47.32.C-	Vortex dynamics
47.11.-j	Computational methods in fluid dynamics
47.20.-k	Flow instabilities
47.27.wb	Turbulent wakes

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Enhanced diffusion due to motile bacteria

Min Jun Kim and Kenneth S. Breuer

Phys. Fluids 16, L78 (2004); http://dx.doi.org/10.1063/1.1787527 (4 pages) | Cited 8 times

Online Publication Date: 6 August 2004

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The effect of bacterial motion on the diffusion of a molecule of high molecular weight is studied by observing the mixing of two streams of fluid in a microfluidic flow cell. We show that the presence of motile E. coli bacteria in one of the streams results in a marked increase in the effective diffusion coefficient of Dextran, which rises linearly with the concentration of bacteria from a baseline value of 0.2×10⁻⁷ to 0.8×10⁻⁷ (cm²/s) at a concentration of 2.1×10⁹/ml (approximately 0.5% by volume). Furthermore, we observe that the diffusion process is also observed to undergo a change from standard Fickian diffusion to a superdiffusive behavior in which the diffusion exponent rises from 0.5 to 0.55 as the concentration of bacteria rises from 0 to 2.1×10⁹/ml.

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87.15.Vv

Diffusion

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On the measurement of the Hartmann layer thickness in a high magnetic field

Karim Messadek and René Moreau

Phys. Fluids 16, 3243 (2004); http://dx.doi.org/10.1063/1.1768871 (4 pages)

Online Publication Date: 14 July 2004

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External measurements of global electric quantities (current and voltage) have been performed in a high magnetic field magnetohydrodynamic experiment. It is shown that, when the magnetic field intensity B is high enough, the electric resistance of the whole fluid domain varies as 1/δ. The classical scaling law for the Hartmann layer δ = 1/B math

= H/Ha (H stands for a typical length along field lines and Ha = math

BH for the Hartmann number) is experimentally checked with less than 10% error.

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47.65.-d

Magnetohydrodynamics and electrohydrodynamics

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The history force on a rapidly shrinking bubble rising at finite Reynolds number

Fumio Takemura and Jacques Magnaudet

Phys. Fluids 16, 3247 (2004); http://dx.doi.org/10.1063/1.1760691 (9 pages) | Cited 3 times

Online Publication Date: 15 July 2004

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Using an optical device and a travelling system, we determine precisely the evolution of the radius and rising speed of a single CO₂ or CO₂–air bubble rising at finite Reynolds number in an aqueous NaOH solution and rapidly dissolving in it. We willingly introduce a slight amount of pentanol in the aqueous solution to force the bubble surface to obey a no-slip condition. The measurements allow us to evaluate directly the instantaneous magnitude of the buoyancy, added-mass, and quasisteady drag forces experienced by the bubble. We then deduce the magnitude of the so-called history force from the total force balance. It turns out that this force can be up to one-half of the buoyancy force during a certain stage of the motion. Using the argument developed by Magnaudet and Legendre [Phys. Fluids 10, 550 (1998)], we derive the counterpart of the Basset–Boussinesq history force for the case of a rigid sphere with a time-dependent radius, as well as the counterpart of some finite-Reynolds-number empirical extensions of this expression. We use these results to predict the time evolution of the history force in our experiments. Owing to finite-Reynolds-number effects, the zero-Reynolds-number expression yields totally unrealistic results. In contrast we find that, once properly generalized to a sphere of time-varying radius, the finite-Reynolds-number expression proposed by Kim, Elghobashi, and Sirignano [J. Fluid Mech. 367, 221 (1998)] provides an accurate estimate of the evolution of the history force and hence allows the bubble velocity to be precisely predicted all along the dissolution process. © 2004 American Institute of Physics.

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47.55.D-	Drops and bubbles
64.75.-g	Phase equilibria
47.55.Kf	Particle-laden flows
47.80.-v	Instrumentation and measurement methods in fluid dynamics

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On the nonlinear evolution of wind-driven gravity waves

A. Alexakis, A. C. Calder, L. J. Dursi, R. Rosner, J. W. Truran, B. Fryxell, M. Zingale, F. X. Timmes, K. Olson, and P. Ricker

Phys. Fluids 16, 3256 (2004); http://dx.doi.org/10.1063/1.1771695 (13 pages) | Cited 6 times

Online Publication Date: 15 July 2004

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We present a study of wind-driven nonlinear interfacial gravity waves using numerical simulations in two dimensions. We consider a case relevant to mixing phenomenon in astrophysical events such as novae in which the density ratio is approximately 1:10. Our physical setup follows the proposed mechanism of Miles [J. Fluid Mech. 3, 185 (1957)] for the amplification of such waves. Our results show good agreement with linear predictions for the growth of the waves. We explore how the wind strength affects the wave dynamics and the resulting mixing in the nonlinear stage. We identify two regimes of mixing, namely, the overturning and the cusp-breaking regimes. The former occurs when the wind is strong enough to overcome the gravitational potential barrier and overturn the wave. This result is in agreement with the common notion of turbulent mixing in which density gradients are increased to diffusion scales by the stretching of a series of vortices. In the latter case, mixing is the result of cusp instabilities. Although the wind is not strong enough to overturn the wave in this case, it can drive the wave up to a maximum amplitude where a singular structure at the cusp of the wave forms. Such structures are subject to various instabilities near the cusp that result in breaking the cusp. Mixing then results from these secondary instabilities and the spray-like structures that appear as a consequence of the breaking.

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47.35.-i	Hydrodynamic waves
47.11.-j	Computational methods in fluid dynamics
47.40.-x	Compressible flows; shock waves
47.27.tb	Turbulent diffusion
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.20.Cq	Inviscid instability
95.30.Lz	Hydrodynamics

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Rayleigh–Marangoni horizontal convection of low Prandtl number fluids

E. Bucchignani and D. Mansutti

Phys. Fluids 16, 3269 (2004); http://dx.doi.org/10.1063/1.1772381 (12 pages) | Cited 2 times

Online Publication Date: 22 July 2004

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In this paper we describe the results of the numerical study of the Boussinesq–Navier–Stokes equations for the convection flow in an open top three-dimensional parallelepipedic cavity (4×1×1) driven by a horizontal temperature difference at two opposite vertical walls in presence of thermocapillary effects. Two fluids have been considered with Prandtl number Pr = 0.015 and Pr = 1, at fixed Rayleigh number, Ra = 150; simulations for several values of the Marangoni number (Ma) have been developed in order to detect fully three-dimensional flow configurations. From the analysis of the numerical flows we reach the following conclusions: the increase of the Prandtl number enhances the coupling of the heat and mass transfer phenomena, moreover while at Pr = 0.015 a fully three-dimensional behavior is observed at Ma ≥ 200, at Pr = 1 the flow configuration appears clearly three dimensional just at Ma = 30; the increase of the Marangoni number induces the appearance of secondary counter-rotating vortices around to the primary one. The values of the Nusselt number at the main stream perpendicular middle plane are provided.

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47.27.T-	Turbulent transport processes
47.10.-g	General theory in fluid dynamics
47.32.C-	Vortex dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Investigation on the characteristics of turbulence transport for momentum and heat in a drag-reducing surfactant solution flow

F.-C. Li, Y. Kawaguchi, and K. Hishida

Phys. Fluids 16, 3281 (2004); http://dx.doi.org/10.1063/1.1769375 (15 pages) | Cited 17 times

Online Publication Date: 22 July 2004

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Simultaneous measurements of the velocity (u and ν in the streamwise and wall-normal directions, respectively) and temperature fluctuations (θ) in the thermal boundary layer were carried out for a heated drag-reducing surfactant solution flow in a two-dimensional channel by means of a two-component laser Doppler velocimetry and a fine-wire thermocouple probe. The drag-reducing fluid tested was a dilute aqueous solution of a cationic surfactant, cetyltrimethylammonium chloride (CTAC), with 30 ppm concentration. Measurements were performed for CTAC solution flows at an inlet temperature of 31 °C and at three Reynolds numbers of 3.5×10⁴, 2.5×10⁴, and 1.5×10⁴, respectively, and for water flow at the Reynolds number of 2.5×10⁴. Drag reduction (DR) and heat transfer reduction (HTR) for the three CTAC solution flows were DR(HTR) = 33.0(20.2), 70.0(77.3), and 65.1(77.0) percentage, respectively. At a high HTR level, a large temperature gradient appeared when y⁺<50 in the measured range (the superscript “+” denotes normalization with inner variables). Temperature fluctuation intensity, θ^′+, and the streamwise turbulent heat flux, math

, were enhanced in the layer with large temperature gradient for the drag-reducing flow, whereas the wall-normal turbulent heat flux, − math

, was depressed throughout the measured range. The depression of − math

was due to a cause similar to that of the depression of the Reynolds shear stress − math

, i.e., in addition to the decrease of ν^′+, decorrelation between the two variables occurred. The decrease of − math

resulted in HTR, which was similar to that of the decrease of − math

resulted in DR for the drag-reducing flow by additives. The turbulence production terms, − math

(∂U⁺/∂y⁺) and − math

(∂Θ⁺/∂y⁺) where U and Θ are mean velocity and temperature, were reduced in the drag-reducing CTAC solution flows. The estimated power spectra of temperature fluctuations implied that the drag-reducing surfactant additive depressed the turbulence at high frequencies or at small scales, whereas it increased the turbulent energy at low frequencies or at large scales. The profiles of the eddy diffusivities for momentum and heat in the CTAC solution flows were both decreased. The turbulent Prandtl number deviated from that of the water flow near the heated wall with a value close to the molecular Prandtl number of the solvent.

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47.27.nb	Boundary layer turbulence
42.79.Qx	Range finders, remote sensing devices; laser Doppler velocimeters, SAR, and LIDAR
47.50.-d	Non-Newtonian fluid flows
47.27.T-	Turbulent transport processes

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Vortex arrays for sinh-Poisson equation of two-dimensional fluids: Equilibria and stability

D. Gurarie and K. W. Chow

Phys. Fluids 16, 3296 (2004); http://dx.doi.org/10.1063/1.1772331 (10 pages) | Cited 7 times

Online Publication Date: 23 July 2004

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The sinh-Poisson equation describes a stream function configuration of a stationary two-dimensional (2D) Euler flow. We study two classes of its exact solutions for doubly periodic domains (or doubly periodic vortex arrays in the plane). Both types contain vortex dipoles of different configurations, an elongated “cat-eye” pattern, and a “diagonal” (symmetric) configuration. We derive two new solutions, one for each class. The first one is a generalization of the Mallier–Maslowe vortices, while the second one consists of two corotating vortices in a square cell. Next, we examine the dynamic stability of such vortex dipoles to initial perturbations, by numerical simulations of the 2D Euler flows on periodic domains. One typical member from each class is chosen for analysis. The diagonally symmetric equilibrium maintains stability for all (even strong) perturbations, whereas the cat-eye pattern relaxes to a more stable dipole of the diagonal type.

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47.11.-j	Computational methods in fluid dynamics
47.32.C-	Vortex dynamics
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)

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Large eddy simulation and experimental studies of a confined turbulent swirling flow

P. Wang, X. S. Bai, M. Wessman, and J. Klingmann

Phys. Fluids 16, 3306 (2004); http://dx.doi.org/10.1063/1.1769420 (19 pages) | Cited 29 times

Online Publication Date: 23 July 2004

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Laser Doppler velocimetry (LDV) measurement and large eddy simulation (LES) were used to study confined isothermal turbulent swirling flows in a model dump combustor. The aim was to gain deeper understanding of the flow and turbulence structures in dump combustors and to examine the capability of LES for prediction of turbulent swirling flows. A refractive index matching technique is used in the LDV measurement to improve the near-wall data. A high-order finite difference scheme on Cartesian grids with a scale-similarity subfilter scale model is used in the LES. Turbulent inflow boundary conditions with different energy spectra, different outflow boundary conditions, and grid resolutions are tested in the LES. Three test cases with different swirl numbers and Reynolds numbers are studied in the measurements and the simulations. The Reynolds numbers range from 10 000 to 20 000, and the swirl number is varied from 0 to 0.43. With appropriate inflow, outflow boundary conditions, and fine grid resolution, the LES results are in fairly good agreement with the LDV data. The experimental and numerical results show that turbulence in the dump combustor is highly anisotropic behind the sudden expansion and in the internal recirculation zone near the axis of the combustor. Turbulence decays rapidly along the streamwise direction downstream, and the structure of turbulence depends highly on the level of inlet swirl. At low swirl numbers, turbulence is primarily generated in the shear layer behind the sudden expansion; at high swirl numbers the near axis flow becomes very unstable and vortex breakdown occurs. The shear layer near the axis of the combustor caused by vortex breakdown generates most of the turbulent kinetic energy. Large-scale motions (coherent structures) are found in the near axis vortex breakdown region. A helical flow in the guiding pipe breaks down near the sudden expansion to form a large bubble-like recirculation zone whose center moves slowly around the axis. Downstream of the bubble the core of the rotational large scale azimuthal flow motion is off the combustor axis and rotates around the axis at a frequency about 18–25 Hz (Strouhal number about 0.17–0.4). As the swirl number increases the coherent structure becomes more evident, and the internal recirculation zone moves upstream. LES successfully simulated the vortex breakdown, the internal recirculation zones and the anisotropic turbulence structures for all the swirl numbers considered.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.32.C-	Vortex dynamics
47.27.nb	Boundary layer turbulence

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A laboratory study of two-dimensional and three-dimensional instabilities in a quasi-two-dimensional flow driven by differential rotation of a cylindrical tank and a disc on the free surface

Isao Kanda

Phys. Fluids 16, 3325 (2004); http://dx.doi.org/10.1063/1.1762788 (16 pages) | Cited 2 times

Online Publication Date: 23 July 2004

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By laboratory experiments, we investigate instability behaviors in a differential rotation system derived from the Czochralski silicon crystal growth. The experimental apparatus consists of a rotating disc (radius a, rotation rate ω) on the surface of homogeneous salt water contained in a rotating cylindrical tank (radius R>a, rotation rate Ω<ω). The differential rotation induces the vertical Stewartson layer at the disc radius, and various flow patterns appear as the rotation rate difference ω−Ω is increased. At relatively small ω−Ω, the well-known barotropic, or circular shear, instability generates multiple vertically coherent vortices along the Stewartson layer. The number of vortices decreases with increasing ω−Ω. When there are two vortices, irregular vertical motion is observed near the axis beyond certain critical values of ω−Ω. The streamlines near the axis are elliptical and the flow behavior has properties similar to those of the elliptic instability. As ω−Ω is further increased, the irregular motion ceases and the rotation center of the flow below the disc deviates from the machine axis. The rotation center itself orbits around the machine axis. This flow behavior resembles the single-vortex mode of the circular shear instability. We focus on these two instability behaviors: The vertical irregular motion and the off-axis rotation, and examine the instability onset conditions in the light of the elliptic instability and the circular shear instability, respectively. © 2004 American Institute of Physics.

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47.20.Cq	Inviscid instability
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.nb	Boundary layer turbulence
47.15.ki	Inviscid flows with vorticity

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Instabilities in the flow of thin films on heterogeneous surfaces

Lou Kondic and Javier Diez

Phys. Fluids 16, 3341 (2004); http://dx.doi.org/10.1063/1.1772732 (20 pages) | Cited 5 times

Online Publication Date: 28 July 2004

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We present computational and experimental results involving instability development in the gravity-driven flow of thin fluid films on heterogeneous surfaces, with particular emphasis on the dynamics of the fluid fronts. We show that heterogeneity of the solid surface can have a significant effect on the flow dynamics. Since the effect of heterogeneity often competes with the basic instability mechanism that would occur even on macroscopically homogeneous surfaces, the result is an elaborate interplay of various instability mechanisms. The computational results presented here outline both the flow on surfaces perturbed by regular patterns, and on surfaces perturbed by irregular, noiselike perturbations. We relate these computational results to the pattern formation process in our experiments of gravity-driven flow down an incline. Good qualitative agreement is found between the simulations and the experiments.

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47.11.-j	Computational methods in fluid dynamics
47.15.Fe	Stability of laminar flows
47.20.-k	Flow instabilities
47.15.Cb	Laminar boundary layers
68.15.+e	Liquid thin films
47.27.Sd	Turbulence generated noise

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Self-sustained oscillations and vortex shedding in backward-facing step flows: Simulation and linear instability analysis

Daehyun Wee, Tongxun Yi, Anuradha Annaswamy, and Ahmed F. Ghoniem

Phys. Fluids 16, 3361 (2004); http://dx.doi.org/10.1063/1.1773091 (13 pages) | Cited 11 times

Online Publication Date: 28 July 2004

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Linear instability analysis was performed to investigate the origin of the self-sustained oscillations, at St = O(0.1), which have been widely reported in backward-facing step flows. Parametric studies, based on local stability analysis of a family of time-average velocity profiles modeling those observed in recirculating flows, show that the frequency of the absolute mode is determined primarily by the shear layer thickness, and the growth rate of the absolute mode is controlled by the amount of backflow. Given the known streamwise variation of the local velocity profile in the actual flow, this implies that the oscillations are likely to be generated at the middle of the recirculation zone, where the backflow is sufficiently strong, and shear layer thickness is comparable to the step height. The corresponding frequency is determined to be St = O(0.1), because the shear layer thickness is bounded by the step height. To verify this hypothesis, mean velocity profiles obtained from a two-dimensional numerical simulation of a backward-facing step flow at Reynolds number of 3700 and expansion ratio 2:3, were analyzed to obtain the dominant absolute mode frequency, and the corresponding linear global mode was constructed by connecting local solutions at the same frequency. The frequency of the linear global mode closely matches the dominant peak frequency observed in the numerical simulation, and the mode shape showed strong resemblance to that of the dominant eddy identified in the simulation that was obtained using proper orthogonal decomposition analysis of the simulation data.

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47.32.C-	Vortex dynamics
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.11.-j	Computational methods in fluid dynamics
47.35.-i	Hydrodynamic waves

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On Lagrangian time scales and particle dispersion modeling in equilibrium turbulent shear flows

Benoit Oesterlé and Leonid I. Zaichik

Phys. Fluids 16, 3374 (2004); http://dx.doi.org/10.1063/1.1773844 (11 pages) | Cited 12 times

Online Publication Date: 29 July 2004

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As intermediate quantities available from various existing numerical computations, the fluid Lagrangian time scales are of primary importance in the development of probability density function models for turbulent flows. Similarly, the time scales of the fluid seen by discrete particles in two-phase flows are essential for the development of dispersion models based on stochastic differential equations. Such time scales are obviously depending not only on the particle properties but also on the fluid Lagrangian and Eulerian time scales. A model is proposed here to estimate the directional dependence of the fluid Lagrangian time scales and drift coefficients in one-directional equilibrium turbulent shear flows, based on a local homogeneity assumption in the frame of the generalized Langevin model. Through comparison with available direct and large eddy simulation predictions in channel flows and in a homogeneous shear flow, the model is shown to lead to significant improvements in the streamwise and spanwise directions, where the existing empirical laws for the Lagrangian time scales are far from being satisfactory. We examine the way this model can be used to build a suitable stochastic process for the fluid seen by inertial particles in such basic turbulent shear flows.

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47.27.E-	Turbulence simulation and modeling
47.11.-j	Computational methods in fluid dynamics
47.27.nb	Boundary layer turbulence
47.55.Kf	Particle-laden flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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The onset of gas pull-through during dual discharge from a stratified two-phase region: Theoretical analysis

M. Ahmed, I. Hassan, and N. Esmail

Phys. Fluids 16, 3385 (2004); http://dx.doi.org/10.1063/1.1771619 (8 pages) | Cited 2 times

Online Publication Date: 2 August 2004

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A theoretical analysis for the onset of gas pull-through (entrainment) during discharge from a stratified two-phase region through two vertically aligned side branches has been developed in this paper. Initially, a simplified point-sink model was developed, which was then followed by the acquisition of a more accurate finite-branch model. The prediction of the critical height at the onset of gas entrainment was found to be a function of the corresponding Froude number of each branch (Fr₁ and Fr₂), as well as the vertical distance between the centerlines of the two branches (L/d). The predicted values of the critical height were found to be consistent with the corresponding experimental data for different values of Fr₁, Fr₂ and L/d. From the basis of the present models, it was found that by increasing the flow through the lower branch, the critical height increases for all values of Fr₁ and L/d. Furthermore, by increasing the vertical distance between the two branches, the effect of the lower branch on the determination of the critical height was decreased.

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47.11.-j	Computational methods in fluid dynamics
47.55.Hd	Stratified flows
47.55.Kf	Particle-laden flows
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)

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The McCormack model for gas mixtures: Heat transfer in a plane channel

R. D. M. Garcia and C. E. Siewert

Phys. Fluids 16, 3393 (2004); http://dx.doi.org/10.1063/1.1773711 (10 pages) | Cited 4 times

Online Publication Date: 2 August 2004

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An analytical version of the discrete-ordinates method (the ADO method) is used to establish a concise and particularly accurate solution to the heat-transfer problem in a plane channel for a binary gas mixture described by the McCormack kinetic model. The solution yields for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the density and temperature profiles for both types of particles, as well as the overall heat flow associated with each of the two species of gas particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe). The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium 4 machine to compute all quantities of interest.

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47.27.T-	Turbulent transport processes
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Experimental study of the impact of an ink-jet printed droplet on a solid substrate

Dirkjan B. van Dam and Christophe Le Clerc

Phys. Fluids 16, 3403 (2004); http://dx.doi.org/10.1063/1.1773551 (12 pages) | Cited 44 times

Online Publication Date: 2 August 2004

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This paper reports on an experimental study of the impact of water droplets on a solid substrate, with a droplet radius between 18 and 42 μm. We optically measured the interface shape during impact. The measured impact sequences show the impact phenomenology, droplet radius as a function of time, and oscillation behavior in the later stages of impact. The measured radius during impact is compared with existing models, and some of the deficiencies of common models are shown. The measured oscillation frequency in the later stage of impact compares well with an available analytical model. In addition, we measured the volume of the small bubble, which forms in the initial impact stage, as a function of impact velocity. The measured volume compares reasonably well with an approximate model based on air entrapment.

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47.55.D-	Drops and bubbles
47.35.-i	Hydrodynamic waves
47.27.wg	Turbulent jets

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The effects of a counter-current interstitial flow on a discharging hourglass

B. K. Muite, M. L. Hunt, and G. G. Joseph

Phys. Fluids 16, 3415 (2004); http://dx.doi.org/10.1063/1.1781158 (11 pages) | Cited 6 times

Online Publication Date: 2 August 2004

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This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geometries. The results are classified into three regimes: (i) granular flows with negligible interstitial fluid effects; (ii) flows affected by the presence of the interstitial fluid; and (iii) a no-flow region in which particles arch across the orifice and do not discharge. Within the fluid-affected region, the flows were visually classified as lubricated and air-coupled flows, oscillatory flows, channeling flows in which the flow preferentially rises along the sidewalls, and fluidized flows in which the upward flow suspends the particles. The discharge rates depends on the Archimedes number, the ratio of the effective hopper diameter to the particle diameter, and hourglass geometry. The hopper-discharge experiments, as well as experiments found in the literature, demonstrate that the presence of the interstitial fluid is important when the nondimensional ratio (N) of the single-particle terminal velocity to the hopper discharge velocity is less than 10. Flow ceased in all experiments in which the particle diameter was greater than 25% of the effective hopper diameter regardless of the interstitial fluid.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.55.Kf	Particle-laden flows
47.35.-i	Hydrodynamic waves
47.80.-v	Instrumentation and measurement methods in fluid dynamics

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Variational approach to gas flows in microchannels

Carlo Cercignani, Maria Lampis, and Silvia Lorenzani

Phys. Fluids 16, 3426 (2004); http://dx.doi.org/10.1063/1.1764700 (12 pages) | Cited 10 times

Online Publication Date: 2 August 2004

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Gas flow rates in microchannels have been rigorously evaluated by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the Bhatnagar, Gross, and Krook model. The Maxwell scattering kernel has been used to describe the gas-wall interactions in the most general case of two surfaces with different accommodation coefficients.© 2004 American Institute of Physics.

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47.45.-n	Rarefied gas dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
02.60.Lj	Ordinary and partial differential equations; boundary value problems

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Dynamics of inertia dominated binary drop collisions

Ilia V. Roisman

Phys. Fluids 16, 3438 (2004); http://dx.doi.org/10.1063/1.1777584 (12 pages) | Cited 13 times

Online Publication Date: 3 August 2004

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A head-on impact of two equal drops is studied theoretically. The initial drops deformation, the radial expansion of the obtained liquid mass, and the subsequent axial stretching are considered. The deformation of the drop in the radial direction is governed by the motion of a rim bounding an expanding lamella, whereas the axial deformation of the drop is governed by the motion of two globules formed at the ends of a stretching liquid jet. The equations of motion of the rim and of the globules are obtained from the mass and the momentum balance. The theory accounts for the inertial effects, surface tension and the viscous stresses. The theoretical predictions of the drop diameter and its length are compared with experiments. The agreement is rather good in spite of the fact that no adjustable parameters are used.

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47.55.D-	Drops and bubbles
47.10.-g	General theory in fluid dynamics
47.27.wg	Turbulent jets
68.03.Cd	Surface tension and related phenomena
47.55.Kf	Particle-laden flows

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The combined effects of magnetic field and magnetic field gradients on convection in crystal growth

Jianwei Qi and Nobuko I. Wakayama

Phys. Fluids 16, 3450 (2004); http://dx.doi.org/10.1063/1.1778402 (10 pages) | Cited 2 times

Online Publication Date: 4 August 2004

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The effect of an external magnetic field on convection in crystal growth is investigated numerically. The geometry considered is a cylindrical vessel filled with crystal solutions. The vessel partially heated from below is placed outside or inside a superconducting magnet. Numerical simulations show that the convection can be suppressed or promoted mainly due to the location of the vessel in the magnet. When the vessel is located above the center of the magnet, the convection is reduced more greatly than that at the center of the magnet. However, when the vessel is located below the center of the magnet, the convection is greater than that at the center of the magnet and that outside the magnet in absence of the field. The above results demonstrate that both magnetic effects on convection in solution will occur due to the magnetic field and its gradient. Generally, the magnetic field will induce the Lorentz force to damp the convection when the solution is electrically conducting. On the other hand, the magnetic field gradient resulted from the inhomogeneity of the field will produce the magnetization force and the magnetic buoyancy to suppress or promote the convection when the vertical magnetization force is opposite to or the same as the gravity. The above results can qualitatively explain recent experimental findings in protein crystal growth and show the potential of using both the magnetic field and field gradient to control convection in nonconducting or low conducting solutions, especially in the process of crystal growth from aqueous solutions.

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47.11.-j	Computational methods in fluid dynamics
75.50.Mm	Magnetic liquids
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.27.T-	Turbulent transport processes
75.60.Ej	Magnetization curves, hysteresis, Barkhausen and related effects
81.10.Dn	Growth from solutions

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Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: Local linear instability and global bleed control

A. Sevilla and C. Martínez-Bazán

Phys. Fluids 16, 3460 (2004); http://dx.doi.org/10.1063/1.1773071 (10 pages) | Cited 20 times

Online Publication Date: 6 August 2004

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In the present work we study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, and spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large-scale helical vortex shedding downstream of the recirculating zone. Inhibition of vortex shedding is examined by blowing a given flow rate of fluid through the base of the slender body. The extent of the locally absolute region of the flow is calculated as a function of the bleed coefficient, C_b = q_b/(πR²u_∞), where q_b is the bleed flow rate, R is the radius of the base, and u_∞ is the incident free-stream velocity. It is shown that the basic flow becomes convectively unstable everywhere for a critical value of the bleed coefficient of Cb* ∼ 0.13, such that no self-excited regime is expected for C_b>Cb*. In addition, we report experimental results of flow visualizations and hot-wire measurements for increasing values of the bleed coefficient. When a sufficient amount of base bleed is applied, flow visualizations indicate that vortex shedding is suppressed and that the mean flow becomes axisymmetric. The critical bleed coefficient predicted by linear instability analysis is shown to fall within the experimental values in the range of Reynolds numbers analyzed here.

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