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Dec 2003

Volume 15, Issue 12, pp. L85-L88, 3587-3893

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Self-induced oscillations in the shock wave flow pattern formed in a stationary supersonic flow over a double wedge

G. Ben-Dor, E. I. Vasilev, T. Elperin, and A. V. Zenovich

Phys. Fluids 15, L85 (2003); http://dx.doi.org/10.1063/1.1625646 (4 pages) | Cited 5 times

Online Publication Date: 17 October 2003

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Numerical simulations of a two-dimensional supersonic flow of an inviscid perfect gas over a double wedge in the Mach numbers range 5 ⩽ M ⩽ 9, revealed the existence of self-induced oscillations in the shock wave flow pattern in a narrow range of geometrical parameters. © 2003 American Institute of Physics.
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47.40.Nm Shock wave interactions and shock effects
47.54.-r Pattern selection; pattern formation
47.40.Ki Supersonic and hypersonic flows
47.35.-i Hydrodynamic waves
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Direct numerical simulation of turbulent channel flow with wall velocity disturbances

P. Orlandi, S. Leonardi, R. Tuzi, and R. A. Antonia

Phys. Fluids 15, 3587 (2003); http://dx.doi.org/10.1063/1.1619137 (15 pages) | Cited 13 times

Online Publication Date: 13 October 2003

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This paper considers the effect of applying nonzero velocity fluctuations along a flat smooth wall, mainly with the aim of understanding how conditions at the wall interact with the outer turbulent flow. Such a study is expected to be of use in formulating effective strategies for wall turbulence control. Three direct numerical simulations of a turbulent plane channel flow are carried out, starting with a flow field with no-slip conditions. Each simulation evolves by imposing (on one wall) only one nonzero velocity component. When a nonzero longitudinal velocity fluctuation u1 is applied, drag reduction occurs. With a nonzero spanwise velocity fluctuation u3, the flow is very similar to that in an unperturbed channel. However, the use of a nonzero wall-normal velocity fluctuation u2 results in structural changes similar to those observed in a direct numerical simulation of a turbulent flow over a rough surface. From the present simplified simulations, the inference is that the salient characteristics of rough wall flows reflect mainly the presence of a nonzero wall-normal normal velocity distribution at the interface between the roughness cavities and the external flow. © 2003 American Institute of Physics.
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47.11.-j Computational methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.-i Turbulent flows
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: Experimental and theoretical analysis

N. Caraman, J. Borée, and O. Simonin

Phys. Fluids 15, 3602 (2003); http://dx.doi.org/10.1063/1.1619136 (11 pages) | Cited 3 times

Online Publication Date: 13 October 2003

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Measurements of particle fluctuation in a fully developed pipe flow at moderate Reynolds number is performed in this study. The present data are obtained by using a two-component phase Doppler anemometer. The radial profiles are measured at a distance of 0.2 diameter downstream the exit of the tube. At this location, the core flow still carries all the properties of the tube turbulence. A low mass loading of partly responsive particles is considered. The Stokes number of these partly responsive particles is of order 3 when the integral turbulent time scale on the axis of the tube flow is used. The velocity statistics are analyzed up to the third-order moments and we show that the radial turbulent transport of fluctuating kinetic energy is much higher for the particles than for the fluid. Radial balances of longitudinal and radial kinetic stresses of the particles are examined. Particle–particle collisions have a negligible direct effect on the evolution of the longitudinal fluctuating velocity. However, even at this low mass loading, we prove that particle–particle collisions and redistribution from the very large streamwise velocity variance to the radial velocity variance in the near wall region strongly influence the radial fluctuation of the particles. In the core region, a quadrant analysis enables the detection of low streamwise velocities focusing toward the axis and the corresponding quadrants are strongly dominant for the glass beads. We expect that the partly responsive particles, because of their inertia, keep some memory of the lower streamwise velocity existing in the near wall region while they fly across the tube. The collisions in the near wall region are, therefore, expected to have a strong indirect influence on the whole kinetic-energy balance in the tube by partly driving the radial transport of the fluctuating kinetic energy of the particles. This effect should be particularly strong in this circular geometry because events from any azimuthal directions converge in the central region. © 2003 American Institute of Physics.
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47.27.-i Turbulent flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.Kf Particle-laden flows
47.80.-v Instrumentation and measurement methods in fluid dynamics

Spectral analysis of localized disturbances in boundary layer at subcritical Reynolds numbers

A. V. Boiko, G. R. Grek, and D. S. Sboev

Phys. Fluids 15, 3613 (2003); http://dx.doi.org/10.1063/1.1619138 (12 pages) | Cited 3 times

Online Publication Date: 13 October 2003

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A flat plate boundary layer disturbance in the form of a streak is excited by a vortex of limited spanwise extent generated upstream of the plate leading edge. Frequency-wave spectral analysis of the streamwise velocity component of the streak is performed. The most part of energy in the spectrum is contained in low-frequency waves with the angles of their wave vector inclination to streamwise direction more than 85°. Spanwise wave numbers, peculiarities of amplitude growth, as well as streamwise velocity profiles of the most powerful spectral components of the streak are in a good agreement with known theoretical data on linear transient growth. However, behavior of the total energy of the streak is not corresponding to that of theoretical “optimal” transient structures. We suspect that, to make the theoretical results concerning the streak energy valid, details of the receptivity process must be taken into consideration. As the frequency grows, dispersion characteristics and decrements of the spectral components approach results of stability theory for Tollmien–Schlichting waves. © 2003 American Institute of Physics.
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47.15.Cb Laminar boundary layers
47.32.C- Vortex dynamics
47.35.-i Hydrodynamic waves

Stability of a sheared particle suspension

V. Kumaran

Phys. Fluids 15, 3625 (2003); http://dx.doi.org/10.1063/1.1616016 (13 pages) | Cited 3 times

Online Publication Date: 13 October 2003

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A stability analysis is carried out for a gas–particle suspension in which the energy dissipation occurs due to the viscous drag force exerted on the particles. The flow is driven by two types of energy sources, an imposed mean shear and fluid velocity fluctuations, in the limit where the time between collisions τc is small compared to the viscous relaxation time τv, so that the dissipation of energy between collisions is small compared to the energy of a particle. Constitutive relations from the kinetic theory of dense gases are used when the flow is driven by the mean shear. The effect of fluid velocity fluctuations is incorporated using an additional diffusive term in the Boltzmann equation for the particle velocity distribution, and this leads to an additional “diffusion” stress. For a suspension driven by fluid velocity fluctuations, it is found that perturbations are always stable. For a suspension driven by mean shear, the viscous relaxation time is large compared to the collision time for mathτv≫1, where math is the mean strain rate. The rate of diffusion of energy is small compared to the rate of dissipation for k∗≪(mathτv)−1, where k∗ is the wave number scaled by the mean free path. In this regime, it is found that density perturbations are unstable in all three directions in the limit of low volume fraction, but become stable when the volume fraction is increased beyond a critical value. For k∗≫(mathτv)−1, the rate of diffusion of energy is large compared to the rate of dissipation, and it is found that perturbations are always stable. The transition between these two regimes is obtained numerically in the dilute limit, and the neutral stability curves for the density perturbations are obtained. It is found that in the gradient-vorticity plane, the transition wave number is proportional to (mathτv)−1 in the limit (mathτv)≫1. © 2003 American Institute of Physics.
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82.70.Kj Emulsions and suspensions
47.20.-k Flow instabilities
47.55.Kf Particle-laden flows
47.27.-i Turbulent flows
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Computing granular avalanches and landslides

E. Bruce Pitman, C. Camil Nichita, Abani Patra, Andy Bauer, Michael Sheridan, and Marcus Bursik

Phys. Fluids 15, 3638 (2003); http://dx.doi.org/10.1063/1.1614253 (9 pages) | Cited 40 times

Online Publication Date: 16 October 2003

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Geophysical mass flows—debris flows, volcanic avalanches, landslides—are often initiated by volcanic activity. These flows can contain O(106–107) m3 or more of material, typically soil and rock fragments that might range from centimeters to meters in size, are typically O(10 m) deep, and can run out over distances of tens of kilometers. This vast range of scales, the rheology of the geological material under consideration, and the presence of interstitial fluid in the moving mass, all make for a complicated modeling and computing problem. Although we lack a full understanding of how mass flows are initiated, there is a growing body of computational and modeling research whose goal is to understand the flow processes, once the motion of a geologic mass of material is initiated. This paper describes one effort to develop a tool set for simulations of geophysical mass flows. We present a computing environment that incorporates topographical data in order to generate a numerical grid on which a parallel, adaptive mesh Godunov solver can simulate model systems of equations that contain no interstitial fluid. The computational solver is flexible, and can be changed to allow for more complex material models, as warranted. © 2003 American Institute of Physics.
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91.40.-k Volcanology
45.70.Mg Granular flow: mixing, segregation and stratification
47.55.Kf Particle-laden flows

Global destabilization of flow over a backward-facing step

Lambros Kaiktsis and Peter A. Monkewitz

Phys. Fluids 15, 3647 (2003); http://dx.doi.org/10.1063/1.1621003 (12 pages) | Cited 7 times

Online Publication Date: 21 October 2003

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Global destabilization of two-dimensional flow over a backward-facing step embedded in a channel, i.e., flow in a plane channel with a sudden expansion, is investigated by numerical simulations using a spectral element method. In the low Reynolds number regime where the two-dimensional flow is steady without manipulation, self-excited oscillations of the entire flow are induced by appropriate simultaneous suction at the step face and blowing at the wall adjacent to the step. The boundary between steady and time-dependent (destabilized) flow is determined as a function of the streamwise extent of the blowing region and its position relative to the step, for an expansion ratio of approximately two, a Reynolds number fixed at Re = 1000, and equal suction and blowing mass flow rates. The computed periodic, globally synchronized flow regimes are characterized using instantaneous streamline patterns, time traces of physical quantities, and proper orthogonal decomposition of the velocity fields. The global flow behavior is also related to the absolute instability properties of the local streamwise velocity profiles. Preliminary three-dimensional simulations finally suggest that the 2-D unsteady flows obtained in the present study are, in general, susceptible to three-dimensional secondary instabilities. Nevertheless, the first experiments suggest that the 2-D analysis provides a qualitatively correct description of the flow transitions and that practical applications of this wall-blowing and -suction scheme, such as mixing enhancement, may be feasible. © 2003 American Institute of Physics.
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47.27.Cn Transition to turbulence
47.15.Fe Stability of laminar flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.54.-r Pattern selection; pattern formation
47.35.-i Hydrodynamic waves

Axisymmetric slosh frequencies of a liquid mass in a circular cylinder

X. Bian, M. Perlin, W. W. Schultz, and M. Agarwal

Phys. Fluids 15, 3659 (2003); http://dx.doi.org/10.1063/1.1622668 (6 pages) | Cited 4 times

Online Publication Date: 21 October 2003

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Spectral eigenvalue methods along with some lower-dimensional techniques are used to determine the natural frequencies of a liquid slug in a circular tube. The contact lines are either pinned or governed by a slip coefficient assumed small. Corresponding physical experiments are conducted for a borosilicate glass tube and a treated water slug. Gravitational and viscous effects are neglected for the analyses. The spectral results agree well with a simple spherical end cap approximation (zero dimensional) for large aspect ratio slugs and with a membrane approximation (one dimensional) for small aspect ratios. The experimental observations for different aspect ratios agree well with the predictions, although the gravity, viscosity and/or slip are neglected in the analyses. © 2003 American Institute of Physics.
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47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems

Topographic effects on establishment of selective withdrawal

Mirmosadegh Jamali

Phys. Fluids 15, 3665 (2003); http://dx.doi.org/10.1063/1.1622948 (6 pages) | Cited 3 times

Online Publication Date: 21 October 2003

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This study is concerned with evolution of selective withdrawal of a linearly stratified fluid through a line sink at the base of a reservoir with bottom topography in the form of a sill of small height. The problem is investigated theoretically in the linear, inviscid limit using a perturbation technique. The induced flow due to motion of the first few shear waves is studied. It is shown that the effect of a sill on the flow field is confined mostly to the withdrawal layer in the vicinity of the sill. Equations are proposed for the steady withdrawal layer thickness and the critical Froude number in the presence of a sill. © 2003 American Institute of Physics.
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47.55.Hd Stratified flows

A multilevel-based dynamic approach for subgrid-scale modeling in large-eddy simulation

M. Terracol and P. Sagaut

Phys. Fluids 15, 3671 (2003); http://dx.doi.org/10.1063/1.1623491 (12 pages) | Cited 3 times

Online Publication Date: 21 October 2003

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In this paper we present a new dynamic methodology to compute the value of the numerical coefficient present in numbers of subgrid models, by mean of a multilevel approach. It is based on the assumption of a power law for the spectral density of kinetic energy in the range of the highest resolved wave numbers. It is shown that this assumption also allows us to define an equivalent law for the subgrid dissipation, and to obtain a reliable estimation for it through the introduction of a three-level flow decomposition. The model coefficient is then simply tuned dynamically during the simulation to ensure the proper amount of subgrid dissipation. This new dynamic procedure has been assessed here in inviscid homogeneous isotropic turbulence and plane channel flow simulations (with skin-friction Reynolds numbers up to 2000). © 2003 American Institute of Physics.
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47.11.-j Computational methods in fluid dynamics
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems

Schlieren measurements and analysis of concentration field in self-excited helium jets

Kasyap S. Pasumarthi and Ajay K. Agrawal

Phys. Fluids 15, 3683 (2003); http://dx.doi.org/10.1063/1.1623490 (10 pages) | Cited 7 times

Online Publication Date: 24 October 2003

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A low-density gas jet injected into a high-density ambient gas is known to exhibit self-excited global oscillations accompanied by large vortical structures interacting with the flow field. In this study, the formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. This is accomplished by applying the quantitative rainbow schlieren deflectometry technique to optically measure the local helium mole percentage across the whole field. Data were acquired over downstream locations extending from tube exit to about 3.0d (d = 31.8 or 19.1 mm is the jet tube inside diameter) at spatial resolution of 0.14 mm and temporal resolution of 16.7 ms. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and rms concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed. © 2003 American Institute of Physics.
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47.27.wg Turbulent jets
47.32.C- Vortex dynamics

The evolution of co-rotating vortices in a canonical boundary layer with inclined jets

Xin Zhang

Phys. Fluids 15, 3693 (2003); http://dx.doi.org/10.1063/1.1624609 (10 pages) | Cited 6 times

Online Publication Date: 24 October 2003

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The evolution of co-rotating streamwise vortices in a canonical flat plate turbulent boundary layer (thickness of the boundary layer δ0.99 = 25 mm) is studied. The vortices are produced by an array of inclined jets (diameter D = 14 mm) with the same orientation (skew angle β and pitch angle α of 45°). The focus of the investigation is on the immediate vicinity of the jet exit and downstream locations up to 40 D. The Reynolds number based on the diameter of the jet nozzle ranges from 9700 to 29 000, at various jet speed ratios. The main method of investigation is laser Doppler anemometry. Both mean and statistic data are collected and analyzed. The streamwise vortices are a product of complex fluid flow process, featuring horseshoe vortices in front of the nozzle exit, recirculating flow to the lee side of the nozzle, contra-rotating vortices from the rolling up of vortex sheet around the jet, strong and induced spanwise flow. Two types of streamwise vortices are produced: (a) weak vortices at a jet speed ratio λ of 0.5 located close to the wall and featuring diametrically opposed, secondary, near-wall flows in between the vortices, (b) strong vortices at higher jet speed ratio featuring significant spanwise movement. The vortices are accompanied by high levels of turbulence, with distinct normal and shear stress distributions. Both turbulence production and convection play important roles in defining the normal stress but only the turbulence production is important in determining the shear stress. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics
47.27.nb Boundary layer turbulence
47.27.wg Turbulent jets
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.T- Turbulent transport processes

Mean drift induced by free and forced dilational waves

Jan Erik Weber and Kai Haakon Christensen

Phys. Fluids 15, 3703 (2003); http://dx.doi.org/10.1063/1.1621867 (7 pages) | Cited 2 times

Online Publication Date: 29 October 2003

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The mean drift velocity induced by longitudinal dilational waves in an elastic film is studied theoretically on the basis of a Lagrangian description of motion. The film is horizontal and situated at the interface between two viscous fluids. For time-damped dilational waves we let the film (i) move freely with the mean fluid velocity at the interface, and (ii) be kept fixed, i.e., having no mean motion. In the latter case the mean Lagrangian drift velocity in both fluids becomes oppositely directed to the wave propagation direction after a very short time. This is due to the fact that a fixed film initially generates a strong source of negative Eulerian second order mean momentum at the interface. This effect becomes even more pronounced when we consider forced dilational waves in a fixed film. Now a suitably arranged shear stress in the upper fluid prevents wave amplitude decay in the film. Accordingly, the negative mean Eulerian momentum at the interface becomes independent of time, and the backward drift will propagate deeper and deeper into the lower fluid. For a no-slip bottom at finite depth we may have a stationary drift solution with negative Lagrangian drift velocity everywhere in the fluid. © 2003 American Institute of Physics.
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46.40.Jj Aeroelasticity and hydroelasticity

Polygonal N-vortex arrays: A Stuart model

Darren Crowdy

Phys. Fluids 15, 3710 (2003); http://dx.doi.org/10.1063/1.1623766 (8 pages) | Cited 3 times

Online Publication Date: 29 October 2003

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A class of exact planar solutions of the Euler equations representing stationary N-polygonal arrays of vortices are found. The solutions are parametrized by two parameters N and Ωmax. N denotes the number of vorticity extrema surrounding the origin; Ωmax denotes the extremal value of this vorticity. Except for a point vortex at the origin, the solutions have everywhere-smooth vorticity distributions and are generalizations of the classic exact solution of Stuart [J. Fluid Mech. 29, 417 (1967)] for an infinite row of smooth vortices. In the limit ∣Ωmax∣→∞, the solutions reduce to the pure point vortex problem considered by Morikawa and Swenson [Phys. Fluids 14, 1058 (1971)]. The new solutions can be understood as “smoothed-out” counterparts to this point vortex problem. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics

Particle image velocimetry study on the pattern formation in a vertically vibrated granular bed

Rensheng Deng and Chi-Hwa Wang

Phys. Fluids 15, 3718 (2003); http://dx.doi.org/10.1063/1.1624606 (12 pages) | Cited 8 times

Online Publication Date: 29 October 2003

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In this paper, a two-dimensional particle image velocimetry (PIV) system was used to examine the f/2 stripe pattern forming in a vertically vibrated granular layer. Since the PIV sampling frequency does not match with the vibrating frequency, a special identification-coupling method was adopted to combine the images taken in different cycles to offer the information in one complete cycle. The measured velocity vectors showed exactly the particle motions at various stages of a motion cycle, illustrating the alternating peaks and valleys on the layer top. Furthermore, quantitative results on the temporal evolution of velocity profiles were obtained and some other interesting phenomena were observed, such as the appearance of local structures (e.g., dual-phase layer structure) and the moving feature of the “standing point.” The mechanism accounting for the occurrence of stripes on the surface is discussed. © 2003 American Institute of Physics.
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47.55.Kf Particle-laden flows
83.50.-v Deformation and flow
45.70.Mg Granular flow: mixing, segregation and stratification
47.80.-v Instrumentation and measurement methods in fluid dynamics

Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface

Gaozhu Peng, Norman J. Zabusky, and Shuang Zhang

Phys. Fluids 15, 3730 (2003); http://dx.doi.org/10.1063/1.1621628 (15 pages) | Cited 22 times

Online Publication Date: 3 November 2003

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We study the vortex-accelerated secondary baroclinic vorticity deposition (VAVD) at late-intermediate times, and dynamics of sinusoidal single-mode Richtmyer–Meshkov interfaces in two dimensions. Euler simulations using a piecewise parabolic method are conducted for three post-shock Atwood numbers (A∗), 0.2, 0.635, and 0.9, with Mach number (M) of 1.3. We initialize the sinusoidal interface with a slightly “diffuse” or small-but-finite thickness interfacial transition layer to facilitate comparison with experiment and avoid ill-posed phenomena associated with evolutions of an inviscid vortex sheet. The thickness of the interface is chosen so that there are no secondary structures along the interface prior to the multivalue time tM, which is defined as the time when the extracted medial axis of an interfacial layer first becomes multivalued. For an interval of 11tM beyond tM, the simulations reveal nearly monotonic strong growth of both positive and negative baroclinic circulation in a vortex bilayer pattern inside the complex roll-up region. The circulations grow and secondary baroclinic circulation dominates at intermediate times, especially for higher A∗. This vorticity deposition is due to misalignment of density gradient across the interface and vortex-centripetal acceleration (secondary baroclinic), and enhanced by the intensification of interfacial density gradient arising from the vortex-induced strain. Our simulation results for A∗ = 0.635 agree with the recent air–sulfur hexafluoride (SF6) experiment of Jacobs and Krivets [Proceedings of the 23rd International Symposium on Shock Waves, Fort Worth, Texas, (2001)], including several large-scale features of the evolving mushroom structure: The usual interface spike-bubble amplitude growth rate math and the dimensions of the spike roll-up cavity. VAVD plays an important role in the intermediate time dynamics of the interfaces. Our amplitude growth rate math disagrees with the O(t−1) result of Sadot et al. [Phys. Rev. Lett. 80, 1654 (1998)]. Instead, it approaches a constant which increases with A∗( ⩽ 0.9). An adjusting periodic single point vortex model which uses the calculated net circulation magnitude and its location, gives excellent results for the amplitude growth rates to late-intermediate times at low Atwood numbers (A∗ = 0.2,0.635). The evolution of enstrophy, vorticity skewness, and flatness are quantified for the entire run duration, and one-dimensional averaged kinetic-energy spectra are presented at several times. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics
47.40.Nm Shock wave interactions and shock effects
47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
47.54.-r Pattern selection; pattern formation
47.11.-j Computational methods in fluid dynamics

Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases

Shigeru Takata, Shugo Yasuda, Shingo Kosuge, and Kazuo Aoki

Phys. Fluids 15, 3745 (2003); http://dx.doi.org/10.1063/1.1624075 (22 pages) | Cited 21 times

Online Publication Date: 3 November 2003

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The thermal-slip (thermal-creep) and the diffusion-slip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finite-difference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] for a single-component gas. As a result, the behavior of the mixture is clarified accurately not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, accurate formulas of the thermal-slip and the diffusion-slip coefficients for arbitrary values of the concentration of a component gas are constructed by the use of the Chebyshev polynomial approximation. © 2003 American Institute of Physics.
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47.45.Gx Slip flows and accommodation
47.45.Dt Free molecular flows
47.55.Kf Particle-laden flows
47.11.-j Computational methods in fluid dynamics

Relative equilibria of singly periodic point vortex arrays

Mark A. Stremler

Phys. Fluids 15, 3767 (2003); http://dx.doi.org/10.1063/1.1624608 (9 pages) | Cited 5 times

Online Publication Date: 3 November 2003

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This paper presents a systematic investigation of singly periodic discrete vortex configurations that move uniformly without change of shape or size. The general condition for existence of such equilibria is that Smath = 0, where S = ∑Γ is the net circulation within a single period and math is (the complex conjugate of) the vortex velocity. Those configurations that satisfy this condition are determined for two and three vortices per period. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics

Vortex-merger statistical-mechanics model for the late time self-similar evolution of the Kelvin–Helmholtz instability

A. Rikanati, U. Alon, and D. Shvarts

Phys. Fluids 15, 3776 (2003); http://dx.doi.org/10.1063/1.1624837 (10 pages) | Cited 7 times

Online Publication Date: 3 November 2003

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The nonlinear growth, of the multimode incompressible Kelvin–Helmholtz shear flow instability at all density ratios is treated by a large-scale statistical-mechanics eddy-pairing model that is based on the behavior of a single eddy and on the two eddy pairing process. From the model, a linear time growth of the mixing zone is obtained and the linear growth coefficient is derived for several density ratios. Furthermore, the asymptotic eddy size distribution and the average eddy life time probability are calculated. Very good agreement with experimental results and full numerical simulations is achieved. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics
47.27.tb Turbulent diffusion
47.55.Kf Particle-laden flows
47.20.-k Flow instabilities
47.11.-j Computational methods in fluid dynamics

Effectiveness of a drag reducing polymer: Relation to molecular weight distribution and structuring

M. Vlachogiannis, M. W. Liberatore, A. J. McHugh, and T. J. Hanratty

Phys. Fluids 15, 3786 (2003); http://dx.doi.org/10.1063/1.1624840 (9 pages) | Cited 11 times

Online Publication Date: 3 November 2003

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Solutions of partially hydrolyzed polyacrylamide were degraded by intermittent circulation through a large pump in a turbulent flow loop. Measurements of pressure drop, fluid turbulence, molecular weight distribution, and viscosity were made. Rheo-optical studies were also carried out to explore the propensity of solutions to form structures under simple shear flow. Degradation was not accompanied by significant changes in the molecular weight distributions. This observation suggests that, for the system studied, clusters or aggregates of polymers have a more important effect on the turbulence than individual molecules. Therefore, degradation occurs by the destruction of these clusters. This result is consistent with the observation that larger drag reductions are realized by the injection of concentrated polymer solutions into a water flow. © 2003 American Institute of Physics.
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47.27.-i Turbulent flows
47.50.-d Non-Newtonian fluid flows
61.25.H- Macromolecular and polymers solutions; polymer melts
83.80.Rs Polymer solutions

Hydrodynamic dispersion in confined packed beds

Robert S. Maier, Daniel M. Kroll, Robert S. Bernard, Stacy E. Howington, John F. Peters, and H. Ted Davis

Phys. Fluids 15, 3795 (2003); http://dx.doi.org/10.1063/1.1624836 (21 pages) | Cited 28 times

Online Publication Date: 4 November 2003

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Pore-scale simulations of monodisperse sphere packing and fluid flow in cylinders have reproduced heterogeneities in packing density and velocity previously observed in experiment. Simulations of tracer dispersion demonstrate that these heterogeneities enhance hydrodynamic dispersion, and that the degree of enhancement is related to the cylinder radius, R. The time scale for asymptotic dispersion in a packed cylinder is proportional to R2/mathT, where mathT represents an average rate of spreading transverse to the direction of flow. A generalization of the Taylor–Aris model of dispersion in a tube provides qualitative predictions of the long-time dispersion behavior in packed cylinders. © 2003 American Institute of Physics.
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82.70.-y Disperse systems; complex fluids
47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
68.08.Bc Wetting
47.11.-j Computational methods in fluid dynamics

Large-scale anisotropy effect on small-scale statistics over rough wall turbulent boundary layers

Yoshiyuki Tsuji

Phys. Fluids 15, 3816 (2003); http://dx.doi.org/10.1063/1.1622395 (13 pages) | Cited 8 times

Online Publication Date: 4 November 2003

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According to the local isotropy hypothesis presented by Kolmogorov, small-scale velocity fluctuations should be universal in any kind of turbulent flow when the Reynolds number is sufficiently large. This is one of the key assumptions in turbulence phenomena. At this stage, the question is not whether this assumption is correct or not, but rather how the local isotropy works as a good approximation depending on the nature of the large-scale anisotropy. In this paper, we report on how the large-scale anisotropy penetrates the small scales. Based on the experiments performed in the strong mean shear flow on the rough-wall boundary layer, we consider how the local isotropy is restored. The anisotropic parameter S∗ is defined as a ratio of the time scale caused by the mean velocity gradient and the Kolmogorov time scale. It is found that the local isotropy is achieved in the dissipation range even in S∗ ≃ 0.1. On the other hand, there is no clear evidence of isotropy in the inertial range. Due to the strong mean shear, the second-order structure functions do not satisfy the exact power-law relation but they indicate the convex shape plotted in the logarithmic coordinate. Computing the local slope and the curvature of structure functions, we found they are a strong function of anisotropic parameter. © 2003 American Institute of Physics.
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47.27.nb Boundary layer turbulence
47.27.Gs Isotropic turbulence; homogeneous turbulence

On the Brinkman correction in unidirectional Hele-Shaw flows

Jie Zeng, Yannis C. Yortsos, and Dominique Salin

Phys. Fluids 15, 3829 (2003); http://dx.doi.org/10.1063/1.1622947 (8 pages) | Cited 6 times

Online Publication Date: 5 November 2003

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We study the Brinkman correction to Darcy’s equation for unidirectional flows in a Hele-Shaw cell. Three examples, describing gravity-driven flow with variable density, pressure-driven flow with variable viscosity, and pressure-driven flow in a cell with a specific variation in aperture are discussed. In general, the Brinkman correction involves nonlocal terms, and it is not simply equal to an effective viscous shear stress involving the gap-averaged velocity. The latter is applicable at long wavelengths, however, provided that the viscosity is augmented by a prefactor equal to 12/π2. © 2003 American Institute of Physics.
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47.56.+r Flows through porous media

Thinning and disturbance growth in liquid films mobilized by continuous surfactant delivery

Benjamin J. Fischer and Sandra M. Troian

Phys. Fluids 15, 3837 (2003); http://dx.doi.org/10.1063/1.1623489 (9 pages) | Cited 13 times

Online Publication Date: 5 November 2003

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A generalized linear stability analysis is applied to the case of a thin liquid film propelled to spread by a continuous supply of surfactant. The time-dependent base states for the film thickness and surfactant concentration give rise to a nonautonomous system describing disturbance propagation. As a first approximation, the nonautonomous operator is treated as time independent, thereby reducing the system of equations to a standard eigenvalue problem. For the range of parameters investigated, this modal approximation reveals a band of unstable modes corresponding to the growth of transverse, sinusoidal corrugations. A transient growth analysis of the fully time-dependent system, which requires the solution of an initial value problem, also signals the possibility of large disturbance growth. In both cases, significant amplification of infinitesimal disturbances can be traced to the region of the film most rapidly thinned by Marangoni stresses, which is characterized by large interfacial curvature and a sharp variation in shear stress. In contrast to previous models implementing a finite surfactant source that predict asymptotic stability, large transient growth and asymptotic instability are possible for the case of sustained surfactant release. © 2003 American Institute of Physics.
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68.15.+e Liquid thin films

Buoyant mixing of miscible fluids of varying viscosities in vertical tubes

M. Debacq, J-P. Hulin, D. Salin, B. Perrin, and E. J. Hinch

Phys. Fluids 15, 3846 (2003); http://dx.doi.org/10.1063/1.1624838 (10 pages) | Cited 18 times

Online Publication Date: 5 November 2003

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Gravity-induced mixing of two fluids in long vertical tubes is studied experimentally as a function of the density contrast characterized by the Atwood number At (10−5 to 0.2), the fluid viscosity ν (1 to 16×10−6 m2 s−1) and the tube diameter d (2 to 44 mm). At low density contrasts, a stable counterflow is observed over a large fraction of the tube and its region of existence increases at high viscosities and small tube diameters. For larger density contrasts, the flow is either convective or turbulent and the mean concentration profile math(x,t) follows a diffusive spreading law characterized by a diffusivity D. An unexpected increase of D and of the characteristic velocity Vf of random fluid motions is observed when ν increases. This results from the coarser mixing in more viscous fluids which increases local density contrasts and buoyancy forces. Dimensionless plots of the diffusion coefficient D/ν as a function of the Reynolds number of the flow indicate a transition between two different diffusive regimes. Scaling arguments are put forward to account for the dependence of Vf and of the characteristic diffusion length in the convective–diffusive regime. © 2003 American Institute of Physics.
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64.75.-g Phase equilibria
47.55.Kf Particle-laden flows
66.20.-d Viscosity of liquids; diffusive momentum transport
47.60.-i Flow phenomena in quasi-one-dimensional systems
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