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Oct 2010

Volume 22, Issue 10, Articles (10xxxx)

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Phys. Fluids 22, 103302 (2010); http://dx.doi.org/10.1063/1.3481779 (12 pages)

D. V. N. Prasad and D. V. Khakhar
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Transitional flow of a non-Newtonian fluid in a pipe: Experimental evidence of weak turbulence induced by shear-thinning behavior

A. Esmael, C. Nouar, A. Lefèvre, and N. Kabouya

Phys. Fluids 22, 101701 (2010); http://dx.doi.org/10.1063/1.3491511 (4 pages)

Online Publication Date: 14 October 2010

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The present letter is a thorough study of the flow regime where an asymmetry of the mean axial velocity profiles is observed for shear-thinning fluids flow in a pipe. This study is based on a statistical analysis of the axial velocity fluctuations. It is shown that this flow regime exhibits features of a weak turbulence: chaotic in time and regular in space. More precisely, (i) power spectra of axial velocity fluctuations decay following a power law with an exponent very close to −3, (ii) large-scale coherent structures are generated, and (iii) there is essentially no intermittency in this flow regime.
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47.50.-d Non-Newtonian fluid flows
47.60.Dx Flows in ducts and channels
47.27.nf Flows in pipes and nozzles
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Lateral drift and concentration instability in a suspension of bubbles induced by Marangoni stresses at zero Reynolds number

Vivek Narsimhan and Eric S. G. Shaqfeh

Phys. Fluids 22, 101702 (2010); http://dx.doi.org/10.1063/1.3491499 (4 pages) | Cited 1 time

Online Publication Date: 22 October 2010

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We report a concentration instability at zero Reynolds number created by hydrodynamically interacting bubbles with surfactant. This instability is driven by Marangoni stresses that force bubbles to migrate in directions perpendicular to gravity. We characterize the lateral motion of a single buoyant bubble when it is subject to a weak, low wavenumber disturbance velocity. We use this result to determine which mean flow wavevectors amplify concentration fluctuations in a dilute suspension. The suspension is linearly unstable at small horizontal wavenumbers by a mechanism similar to the concentration instabilities demonstrated in suspensions of sedimenting nonspherical or deformable particles.
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47.20.-k Flow instabilities
47.32.cd Vortex stability and breakdown
47.55.D- Drops and bubbles
47.57.E- Suspensions
47.15.-x Laminar flows
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back to top Micro- and Nanofluid Mechanics

Diffusion model for Knudsen-type compressor composed of periodic arrays of circular cylinders

Satoshi Taguchi

Phys. Fluids 22, 102001 (2010); http://dx.doi.org/10.1063/1.3500686 (22 pages)

Online Publication Date: 27 October 2010

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A rarefied gas flow in a long porous channel having a periodic structure that is consisting of alternately arranged porous media and gaps, the former of which contains a periodic array of parallel circular cylinders, is considered for the case in which the channel is infinitely wide. The cylinder arrays have a periodic temperature distribution with the same period as the structure. Under the assumption that the length of each cylinder array and that of each gap are much larger than the period of the cylinders in the array, a fluid-dynamic system describing the overall behavior of the gas in the channel is derived from the kinetic system composed of the Bhatnagar–Gross–Krook equation and the diffuse reflection boundary condition. The derived system is composed of a diffusion model for each cylinder array, whose isothermal version has been reported previously [ S. Taguchi and P. Charrier, Phys. Fluids 20, 067103 (2008) ], a set of fluid-dynamic equations for each gap, and the macroscopic connection conditions at each junction between an array and a gap. Then, the fluid-dynamic system is applied to a long channel consisting of many cylinder arrays and gaps. Some numerical results demonstrating the pumping effect of the flow are presented.
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47.45.-n Rarefied gas dynamics
47.56.+r Flows through porous media
47.60.Dx Flows in ducts and channels

On the effects of liquid-gas interfacial shear on slip flow through a parallel-plate channel with superhydrophobic grooved walls

Chiu-On Ng, Henry C. W. Chu, and C. Y. Wang

Phys. Fluids 22, 102002 (2010); http://dx.doi.org/10.1063/1.3493641 (12 pages) | Cited 2 times

Online Publication Date: 28 October 2010

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Comparisons between slip lengths predicted by a liquid-gas coupled model and that by an idealized zero-gas-shear model are presented in this paper. The problem under consideration is pressure-driven flow of a liquid through a plane channel bounded by two superhydrophobic walls which are patterned with longitudinal or transverse gas-filled grooves. Effective slip arises from lubrication on the liquid-gas interface and intrinsic slippage on the solid phase of the wall. In the mathematical models, the velocities are analytically expressed in terms of eigenfunction series expansions, where the unknown coefficients are determined by the matching of velocities and shear stresses on the liquid-gas interface. Results are generated to show the effects due to small but finite gas viscosity on the effective slip lengths as functions of the channel height, the depth of grooves, the gas area fraction of the wall, and intrinsic slippage of the solid phase. Conditions under which even a gas/liquid viscosity ratio as small as 0.01 may have appreciable effects on the slip lengths are discussed.
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47.45.Gx Slip flows and accommodation
47.55.Ca Gas/liquid flows
47.60.Dx Flows in ducts and channels
68.03.Cd Surface tension and related phenomena
47.11.-j Computational methods in fluid dynamics
02.60.-x Numerical approximation and analysis
back to top Interfacial Flows

The height of a static liquid column pulled out of an infinite pool

E. S. Benilov and A. Oron

Phys. Fluids 22, 102101 (2010); http://dx.doi.org/10.1063/1.3484275 (8 pages)

Online Publication Date: 5 October 2010

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We consider a solid cone whose vertex points down and dips in an infinite pool of liquid. If the cone is slowly lifted, a liquid column with its top attached to the cone is pulled out of the pool. In this paper, we compute the maximum height of the cone before the column ruptures. Two reasons for rupturing are identified. In some cases, no solution for a higher position of the cone exists. In other cases, a solution does exist, but is unstable.
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68.03.Cd Surface tension and related phenomena
47.55.nk Liquid bridges
47.55.nb Capillary and thermocapillary flows

Nonlinear development of two-layer Couette–Poiseuille flow in the presence of surfactant

Andrew P. Bassom, M. G. Blyth, and D. T. Papageorgiou

Phys. Fluids 22, 102102 (2010); http://dx.doi.org/10.1063/1.3488226 (15 pages)

Online Publication Date: 12 October 2010

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The two-dimensional nonlinear evolution of the interface between two superposed layers of viscous fluid moving in a channel in the presence of an insoluble surfactant is examined. A pair of coupled weakly nonlinear equations is derived describing the interfacial and surfactant dynamics when one of the two fluid layers is very thin in comparison to the other. In contrast to previous work, the dynamics in the thin film are coupled to the dynamics in the thicker layer through a nonlocal integral term. For asymptotically small Reynolds number, the flow in the thicker layer is governed by the Stokes equations. A linearized analysis confirms the linear instability identified by previous workers and it is proven that the film flow is linearly unstable if the undisturbed surfactant concentration exceeds a threshold value. Numerical simulations of the weakly nonlinear equations reveal the existence of finite amplitude traveling-wave solutions. For order one Reynolds number, the flow in the thicker layer is governed by the linearized Navier–Stokes equations. In this case the weakly nonlinear film dynamics are more complex and include the possibility of periodic traveling-waves and chaotic flow.
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47.15.gm Thin film flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.52.+j Chaos in fluid dynamics
47.60.Dx Flows in ducts and channels
47.10.ad Navier-Stokes equations

Continuum models for the contact line problem

Weiqing Ren, Dan Hu, and Weinan E

Phys. Fluids 22, 102103 (2010); http://dx.doi.org/10.1063/1.3501317 (19 pages) | Cited 2 times

Online Publication Date: 27 October 2010

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Continuum models are derived for the moving contact line problem through a combination of macroscopic and microscopic considerations. Macroscopic thermodynamic argument is used to place constraints on the form of the boundary conditions at the solid surface and the contact line. This information is then used to set up molecular dynamics to measure the detailed functional dependence of the boundary conditions. Long range molecular forces are taken into account in the form of a surface potential. This allows us to handle the case of complete wetting as well as the case of partial wetting. In particular, we obtain a new continuum model for both cases in a unified form. Two main parameters and different spreading regimes are identified from the analysis of the energy dissipations for the continuum model. Scaling laws in these different regimes are derived. The new continuum model also allows us to derive boundary conditions for the lubrication approximation. Numerical results are presented for the thin film model and the effect of the boundary condition is investigated.
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68.08.Bc Wetting
68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films
back to top Viscous and Non-Newtonian Flows

Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory

Shriram Ramanathan, Donald L. Koch, and Rustom B. Bhiladvala

Phys. Fluids 22, 103101 (2010); http://dx.doi.org/10.1063/1.3491127 (13 pages) | Cited 1 time

Online Publication Date: 21 October 2010

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Nanoelectromechanical oscillators are very attractive as sensing devices because of their low power requirements and high resolution, especially at low pressures. While many experimental studies of such systems are available in the literature, a fundamental theoretical understanding over the entire range of operating conditions is lacking. In this article, we use our newly developed Bhatnagar–Gross–Krook based low Mach number direct simulation Monte Carlo method to study the noncontinuum drag force acting on a cylinder oscillating normal to a wall. We explore quasisteady flows in which ωτf⪡1 as well as unsteady flows for which ωτf = O(1). Here ω is the oscillation frequency and τf is the characteristic time for the development of the gas flow. The drag force per unit length acting on a long cylindrical wire is studied as a function of the Knudsen number, defined in terms of the mean free path λ and the radius of the cylinder R as Kn = λ/R. For quasisteady flows, we also present theoretical calculations for the slip regime, Kn⪡1, and the free molecular flow regime, Kn⪢1. Simulations of unsteady gas flow around a sinusoidally oscillating cylinder near a wall indicate that the drag force per unit length nondimensionalized by 4πμU approaches constant values for ωτf⪡1 (quasisteady flow) and for ωτf⪢1. Here μ is the gas viscosity and U is the maximum value of the nanowire velocity. The simulation results are compared with experimental measurements in the quasisteady regime.
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07.10.Cm Micromechanical devices and systems
47.45.Gx Slip flows and accommodation
47.11.-j Computational methods in fluid dynamics
47.85.Np Fluidics
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.45.Dt Free molecular flows

Phase-field simulations of viscous fingering in shear-thinning fluids

Sébastien Nguyen, Roger Folch, Vijay K. Verma, Hervé Henry, and Mathis Plapp

Phys. Fluids 22, 103102 (2010); http://dx.doi.org/10.1063/1.3494550 (15 pages)

Online Publication Date: 29 October 2010

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A phase-field model for the Hele-Shaw flow of non-Newtonian fluids is developed. It extends a previous model for Newtonian fluids to a wide range of fluids with a shear-dependent viscosity. The model is applied to simulate viscous fingering in shear-thinning fluids and found to capture the complete crossover from the Newtonian regime at low-shear rate to the strongly shear-thinning regime. The width selection of a single steady-state finger is studied in detail for a two-plateau shear-thinning law (Carreau’s law) in both its weakly and strongly shear-thinning limits, and the results are related to the previous analyses. For power-law (Ostwald–de Waele) fluids in the strongly shear-thinning regime, good agreement with experimental data from the literature is obtained.
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47.50.Cd Modeling
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.54.Bd Theoretical aspects
47.50.Gj Instabilities
47.11.-j Computational methods in fluid dynamics
back to top Particulate, Multiphase, and Granular Flows

Particle motion between parallel walls: Hydrodynamics and simulation

James W. Swan and John F. Brady

Phys. Fluids 22, 103301 (2010); http://dx.doi.org/10.1063/1.3487748 (16 pages) | Cited 4 times

Online Publication Date: 11 October 2010

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The low-Reynolds-number motion of a single spherical particle between parallel walls is determined from the exact reflection of the velocity field generated by multipoles of the force density on the particle’s surface. A grand mobility tensor is constructed and couples these force multipoles to moments of the velocity field in the fluid surrounding the particle. Every element of the grand mobility tensor is a finite, ordered sum of inverse powers of the distance between the walls. These new expressions are used in a set of Stokesian dynamics simulations to calculate the translational and rotational velocities of a particle settling between parallel walls and the Brownian drift force on a particle diffusing between the walls. The Einstein correction to the Newtonian viscosity of a dilute suspension that accounts for the change in stress distribution due to the presence of the channel walls is determined. It is proposed how the method and results can be extended to computations involving many particles and periodic simulations of suspensions in confined geometries.
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47.57.E- Suspensions
47.60.Dx Flows in ducts and channels
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits

Mixing of granular material in rotating cylinders with noncircular cross-sections

D. V. N. Prasad and D. V. Khakhar

Phys. Fluids 22, 103302 (2010); http://dx.doi.org/10.1063/1.3481779 (12 pages) | Cited 3 times

Online Publication Date: 11 October 2010

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We study, experimentally and theoretically, the mixing of monodisperse colored beads in rotating cylinders with different cross-sectional shapes (square, star, and a circle with two and four triangular wedges), operating in the continuous flow regime, to understand the role of cross-sectional shape on the mixing process. The evolution of the mixed state is quantified using two measures: the intensity of segregation and the centroid distance. The mixing rate index, defined as the specific rate of change of the intensity of segregation with time, is initially lower in all the noncircular cross-sections compared to a circle. It increases monotonically in noncircular cross-sections, whereas it is nearly constant in a circle. This corresponds to a faster than exponential decay of the intensity of segregation for noncircular cross-sections as compared to an exponential decay for a circular cross-section. The decay of centroid distance is oscillatory in a circle, whereas it is monotonic in noncircular cross-sections. A significant improvement in the mixing rate is obtained for noncircular cross-sections relative to circular cross-sections. The mixing rate is highest for the circle with four wedges; the mixing rates for square and star cross-sections are slightly lower. The circle with two wedges has the lowest mixing rate among the noncircular cross-sections. Experiments with smaller glass beads, in which the particle diffusivity is significantly smaller, yield a mixing rate very close to that for the larger particles. Mixing patterns obtained experimentally at short times are well predicted by a convective diffusion model that includes a time-periodic velocity field for the noncircular cross-sections. A quantitative comparison of model predictions with experiments in terms of the intensity of segregation and the centroid distance shows a reasonably good agreement for the different shapes and for the two particle sizes. A scaling analysis is presented to explain the insensitivity of the mixing rate to particle size despite a significant variation in diffusivity. Mixing patterns for a tracer blob and the mixing rates obtained for the different mixers are found to be related to the regions of the chaotic advection in computed Poincaré maps. For the systems studied, the mixing rate increases with an increase in the number of corners in the geometry, but is relatively unaffected by the ratio of the maximum to minimum diameter of the cross-section.
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47.57.Gc Granular flow
47.51.+a Mixing
47.32.Ef Rotating and swirling flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

The effects of turbulence on nanoparticle growth in turbulent reacting jets

Shankhadeep Das and Sean C. Garrick

Phys. Fluids 22, 103303 (2010); http://dx.doi.org/10.1063/1.3486203 (10 pages) | Cited 10 times

Online Publication Date: 12 October 2010

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The effects of turbulence on nanoparticle growth in turbulent reacting flows are studied via a priori analysis of direct numerical simulation data. The formation and growth of titanium dioxide nanoparticles in incompressible planar jets are simulated via gas-phase hydrolysis of titanium tetrachloride. The particle field is captured by utilizing a nodal approach which accounts for nucleation, condensation, and Brownian coagulation. Simulations are performed at a single Reynolds number and two different precursor concentration levels. Instantaneous, filtered, and averaged data are presented to convey the nature of turbulent or unresolved contributions to the growth of nanoparticles. The effects of turbulence on particle dynamics, in the context of both Reynolds-averaged Navier–Stokes simulation and large-eddy simulation, are assessed by comparing the exact, turbulent, and subgrid-scale growth rates. The results show that large particles are produced in the regions away from the jet core, and an increase in the precursor concentration level increases the particle mean diameter. Particles grow faster when the precursor concentration is increased. It is further observed that the growth rate of the particles is higher inside the eddies and it increases as the jet grows. Additionally, the results show that the unresolved small-scale fluctuations can both augment and inhibit particle growth. However the predominant effect is to reduce particle growth. This tendency is increased (in magnitude) as the precursor concentration level is increased.
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47.27.wg Turbulent jets
47.60.Kz Flows and jets through nozzles
47.10.ad Navier-Stokes equations
82.70.-y Disperse systems; complex fluids

Preferential concentration of heavy particles: A Voronoï analysis

R. Monchaux, M. Bourgoin, and A. Cartellier

Phys. Fluids 22, 103304 (2010); http://dx.doi.org/10.1063/1.3489987 (10 pages) | Cited 13 times

Online Publication Date: 14 October 2010

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We present an experimental characterization of preferential concentration and clustering of inertial particles in a turbulent flow obtained from Voronoï diagram analysis. Several results formerly obtained from various data processing techniques are successfully recovered and further analyzed with Voronoï tesselations as the main single tool. We introduce a simple and nonambiguous way to identify particle clusters. We emphasize the maximum preferential concentration for particles with Stokes numbers around unity and the self-similar nature of clustering and we report new unpredicted results concerning clusters inner concentration dependence on Stokes number and global seeding density. Some of these experimental observations can be consistently interpreted in the context of the so-called sweep-stick mechanism. Finally, we stress the great potential of Voronoï analysis that offers important openings for new investigations of particle laden flows in terms, for instance, of simultaneous Lagrangian statistics of particle dynamics and local concentration field.
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47.55.Kf Particle-laden flows
47.27.-i Turbulent flows

Axial pressure-difference between far-fields across a sphere in viscous flow bounded by a cylinder

Shahin Navardi and Sukalyan Bhattacharya

Phys. Fluids 22, 103305 (2010); http://dx.doi.org/10.1063/1.3489350 (17 pages) | Cited 1 time

Online Publication Date: 28 October 2010

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The presence of a particle with specified velocity inside a cylindrical channel affects the pressure-field along the length of the conduit. In this article, we quantify this effect by using a new general method, which describes hydrodynamic interactions between a cylindrical confinement and a spherical particle under creeping flow assumption. The generality of the scheme enables us to consider arbitrary values for system-defining parameters like cylinder-to-sphere ratio or separation between their centers. As a result, we can obtain accurate results for the parameter values hitherto unexplored by previous studies. Our simulations include three cases. First, we consider a fixed spherical obstacle in a pressure-driven flow through the cylinder and find the additional pressure drop due to the blockage. Then, we compute the pressure created by the pistonlike effect of a translating sphere inside a cylinder-bound quiescent fluid. Finally, we analyze the far-field pressure variation due to rotation of an asymmetrically situated sphere in confined quiescent fluid. For limiting cases, our calculations agree with existing results within 0.5% relative error. Moreover, the efficiency of the scheme is exploited in a dynamic simulation where flow dynamics due to a sedimenting sphere under gravity inside a cylinder with different inclination is explored. We determine the particle trajectory as well as the time-dependent far-field pressure-difference created due to the sedimentation process. The results agree well with approximate analytical expressions describing the underlying physics.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.15.G- Low-Reynolds-number (creeping) flows
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
back to top Laminar Flows

On the secondary flow through bifurcating pipes

Philip Evegren, Laszlo Fuchs, and Johan Revstedt

Phys. Fluids 22, 103601 (2010); http://dx.doi.org/10.1063/1.3484266 (15 pages) | Cited 2 times

Online Publication Date: 8 October 2010

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The secondary motion induced by flow through curves and bifurcations has been subject to investigation over long time due to its importance in physiological and technological applications. In contrast to the flow in a straight pipe, curvature leads to the formation of secondary flow which is often unsteady. Streamline curvature occurs also in bifurcating pipes leading to some corresponding secondary, unsteady flow. This paper presents a detailed description of the unsteady flow in the daughter branch after a 90° bifurcation. A range of Reynolds and Womersley numbers are investigated. The results show the presence of Dean vortices and additional vortical patterns not reported in the literature. Both the streamwise (axial) and the secondary velocity components change character at larger Womersley numbers, leading to less complex secondary flow. Also, at larger Reynolds numbers, flow instabilities are observed. The secondary flow may lead to the formation of unsteady separation bubbles. This in turn yields peaks in the wall shear stress components. Such wall shear stress variations have often been related in the literature to the development process of atherosclerosis.
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47.60.Dx Flows in ducts and channels
47.32.-y Vortex dynamics; rotating fluids
47.20.-k Flow instabilities
back to top Instability and Transition

Influence of a low frequency vibration on a long-wave Marangoni instability in a binary mixture with the Soret effect

I. S. Fayzrakhmanova, S. Shklyaev, and A. A. Nepomnyashchy

Phys. Fluids 22, 104101 (2010); http://dx.doi.org/10.1063/1.3489411 (11 pages) | Cited 3 times

Online Publication Date: 19 October 2010

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We study the influence of a low frequency vibration on a long-wave Marangoni convection in a layer of a binary mixture with the Soret effect. A linear stability analysis is performed numerically by means of the Floquet theory; several limiting cases are treated analytically. Competition of subharmonic, synchronous, and quasiperiodic modes is considered. The vibration is found to destabilize the layer, decreasing the stability threshold. Also, a vibration-induced mode is detected, which takes place even for zero Marangoni number.
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47.27.te Turbulent convective heat transfer
47.35.-i Hydrodynamic waves
47.55.P- Buoyancy-driven flows; convection
47.20.-k Flow instabilities

Thin film lubrication dynamics of a binary mixture: Example of an oscillatory instability

Michael Bestehorn and Ion Dan Borcia

Phys. Fluids 22, 104102 (2010); http://dx.doi.org/10.1063/1.3489434 (10 pages) | Cited 2 times

Online Publication Date: 21 October 2010

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We study thin film instabilities in liquid films with deformable surface using the lubrication theory. An externally applied vertical temperature gradient may give cause to an instability (Marangoni instability) of the flat motionless film. Contrary to the earlier work where mostly pure fluids were discussed, the focus of the present paper lays on instabilities in mixtures of two completely miscible liquids. We show that the normally found monotonic long-wave instability may turn into an oscillatory one if the two components have a different surface tension and if the Soret coefficient establishes a stabilizing vertical concentration gradient. A systematic derivation of the basic equations in long-wave approximation is given. The character of instabilities is studied using linear stability analysis. Finally, a real system consisting of a water-isopropanol mixture is discussed in some detail.
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47.85.mf Lubrication flows
68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films
47.20.-k Flow instabilities
47.27.te Turbulent convective heat transfer
47.55.P- Buoyancy-driven flows; convection

On Richtmyer–Meshkov instability in dilute gas-particle mixtures

Satoshi Ukai, Kaushik Balakrishnan, and Suresh Menon

Phys. Fluids 22, 104103 (2010); http://dx.doi.org/10.1063/1.3507318 (12 pages)

Online Publication Date: 29 October 2010

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Richtmyer–Meshkov instability (RMI) in gas-particle mixtures is investigated both numerically and analytically. The linear amplitude growth rate for a RMI in a two-phase mixture is derived by using a dusty gas formulation for small Stokes number (St⪡1.0), and it is shown that the problem can be characterized by mass loading and St. The model predictions are compared with numerical results under two conditions, i.e., a shock wave hitting (1) a perturbed species interface of air and SF6 surrounded by uniformly distributed particles, and (2) a perturbed shape particle cloud in uniform air. In the first case, the interaction between the instability of the species perturbation and the particles is investigated. The multiphase growth model accurately predicts the growth rates when St⪡1.0, and the amplitude growth normalized by the two-phase RMI velocity shows good agreement with the single-phase RMI growth rate as well. It is also shown that the two-phase model results are in accordance with the growth rates obtained from the simulations even for cases corresponding to St ≈ 10. However, for St⪢10, particles do not follow the RMI motion, and the RMI growth rate agrees with the original Richtmyer’s model [ R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297 (1960) ]. Preferential concentration of particles are observed around the RMI roll-ups at late times when St is of order unity, whereas when St⪡1.0, the particles respond rapidly to the flow, causing them to distribute within the roll-ups. In the second problem, the two-phase RMI growth model is extended to study whether a perturbed dusty gas front shows RMI-like growth due to the impact of a shock wave. When St⪡1.0, good agreement with the multiphase model is again seen. Moreover, the normalized growth rates are very close to the single-phase RMI growth rates even at late times, which suggest that the two-phase growth model is applicable to this type of perturbed shape particle clouds as well. However, when St is close to unity or larger (St>1.0), the particles do not experience impulsive acceleration but rather a continuous one, which results in exponential growth rates as seen in a Rayleigh–Taylor instability.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.40.Nm Shock wave interactions and shock effects
47.11.-j Computational methods in fluid dynamics
47.55.Kf Particle-laden flows
back to top Turbulent Flows

Experimental study of highly turbulent isothermal opposed-jet flows

Gianfilippo Coppola and Alessandro Gomez

Phys. Fluids 22, 105101 (2010); http://dx.doi.org/10.1063/1.3484253 (16 pages) | Cited 1 time

Online Publication Date: 14 October 2010

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Opposed-jet flows have been shown to provide a valuable means to study a variety of combustion problems, but have been limited to either laminar or modestly turbulent conditions. With the ultimate goal of developing a burner for laboratory flames reaching turbulence regimes of relevance to practical systems, we characterized highly turbulent, strained, isothermal, opposed-jet flows using particle image velocimetry (PIV). The bulk strain rate was kept at 1250 s−1 and specially designed and properly positioned turbulence generation plates in the incoming streams boosted the turbulence intensity to well above 20%, under conditions that are amenable to flame stabilization. The data were analyzed with proper orthogonal decomposition (POD) and a novel statistical analysis conditioned to the instantaneous position of the stagnation surface. Both POD and the conditional analysis were found to be valuable tools allowing for the separation of the truly turbulent fluctuations from potential artifacts introduced by relatively low-frequency, large-scale instabilities that would otherwise partly mask the turbulence. These instabilities cause the stagnation surface to wobble with both an axial oscillation and a precession motion about the system axis of symmetry. Once these artifacts are removed, the longitudinal integral length scales are found to decrease as one approaches the stagnation line, as a consequence of the strained flow field, with the corresponding outer scale turbulent Reynolds number following a similar trend. The Taylor scale Reynolds number is found to be roughly constant throughout the flow field at about 200, with a value virtually independent of the data analysis technique. The novel conditional statistics allowed for the identification of highly convoluted stagnation lines and, in some cases, of strong three-dimensional effects, that can be screened, as they typically yield more than one stagnation line in the flow field. The ability to lock on the instantaneous stagnation line, at the intersection of the stagnation surface with the PIV measurement plane, is particularly useful in the combustion context, since the flame is aerodynamically stabilized in the vicinity of the stagnation surface. Estimates of the ratio of the mean residence time (inverse strain rate) to the vortex turnover time yield values greater than unity. The conditional mean velocity gradient suggests that, in contrast to the existing literature, the highest gradients are around the system centerline, which would result in a higher probability of flame extinction in that region under chemically reacting conditions. The compactness of the domain and the short mean residence time render the system well suited to direct numerical simulation, more so than conventional jet flames.
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47.27.wg Turbulent jets
47.70.Fw Chemically reactive flows
47.20.-k Flow instabilities
82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer
47.70.Pq Flames; combustion
47.32.-y Vortex dynamics; rotating fluids

Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data

Oleg Schilling and Nicholas J. Mueschke

Phys. Fluids 22, 105102 (2010); http://dx.doi.org/10.1063/1.3484247 (26 pages) | Cited 1 time

Online Publication Date: 18 October 2010

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Data from a 1152×760×1280 direct numerical simulation (DNS) [ N. J. Mueschke and O. Schilling, “Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data,” Phys. Fluids 21, 014106 (2009) ] of a transitional Rayleigh–Taylor mixing layer modeled after a small Atwood number water channel experiment is used to comprehensively investigate the structure of mean and turbulent transport and mixing. The simulation had physical parameters and initial conditions approximating those in the experiment. The budgets of the mean vertical momentum, heavy-fluid mass fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate equations are constructed using Reynolds averaging applied to the DNS data. The relative importance of mean and turbulent production, turbulent dissipation and destruction, and turbulent transport are investigated as a function of Reynolds number and across the mixing layer to provide insight into the flow dynamics not presently available from experiments. The analysis of the budgets supports the assumption for small Atwood number, Rayleigh–Taylor driven flows that the principal transport mechanisms are buoyancy production, turbulent production, turbulent dissipation, and turbulent diffusion (shear and mean field production are negligible). As the Reynolds number increases, the turbulent production in the turbulent kinetic energy dissipation rate equation becomes the dominant production term, while the buoyancy production plateaus. Distinctions between momentum and scalar transport are also noted, where the turbulent kinetic energy and its dissipation rate both grow in time and are peaked near the center plane of the mixing layer, while the heavy-fluid mass fraction variance and its dissipation rate initially grow and then begin to decrease as mixing progresses and reduces density fluctuations. All terms in the transport equations generally grow or decay, with no qualitative change in their profile, except for the pressure flux contribution to the total turbulent kinetic energy flux, which changes sign early in time (a countergradient effect). The production-to-dissipation ratios corresponding to the turbulent kinetic energy and heavy-fluid mass fraction variance are large and vary strongly at small evolution times, decrease with time, and nearly asymptote as the flow enters a self-similar regime. The late-time turbulent kinetic energy production-to-dissipation ratio is larger than observed in shear-driven turbulent flows. The order of magnitude estimates of the terms in the transport equations are shown to be consistent with the DNS at late-time, and also confirms both the dominant terms and their evolutionary behavior. These results are useful for identifying the dynamically important terms requiring closure, and assessing the accuracy of the predictions of Reynolds-averaged Navier–Stokes and large-eddy simulation models of turbulent transport and mixing in transitional Rayleigh–Taylor instability-generated flow.
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47.10.ad Navier-Stokes equations
47.11.-j Computational methods in fluid dynamics
47.27.-i Turbulent flows

Grid-independent large-eddy simulation using explicit filtering

Sanjeeb T. Bose, Parviz Moin, and Donghyun You

Phys. Fluids 22, 105103 (2010); http://dx.doi.org/10.1063/1.3485774 (11 pages) | Cited 11 times

Online Publication Date: 21 October 2010

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The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier–Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation, and hence the resolved turbulence, from the underlying mesh distribution alleviating some of the grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true large-eddy simulation solution is analyzed for a turbulent channel flow at Reτ = 180, 395, and 640. By using explicit filtering, turbulent statistics and energy spectra are shown to be independent of the mesh resolution used.
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47.27.ep Large-eddy simulations
47.27.nd Channel flow
47.10.ad Navier-Stokes equations

Analytical and numerical investigations of laminar and turbulent Poiseuille–Ekman flow at different rotation rates

A. Mehdizadeh and M. Oberlack

Phys. Fluids 22, 105104 (2010); http://dx.doi.org/10.1063/1.3488039 (11 pages)

Online Publication Date: 28 October 2010

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Laminar and turbulent Poiseuille–Ekman flows at different rotation rates have been investigated by means of analytical and numerical approaches. A series of direct numerical simulations (DNSs) with various rotation rates (Ro2 = 0–1.82) for Reynolds number Reτ0 = 180 based on the friction velocity in the nonrotating case has been conducted. Both (laminar and turbulent) flow states are highly sensitive to the rotation. Even a small rotation rate can reduce the mean streamwise velocity and induce a very strong flow in the spanwise direction, which, after attaining a maximum, decreases by further increasing the rotation rate. It has been further observed that turbulence is damped by increasing the rotation rate and at about Ro2 = 0.145 a transition from the fully turbulent to a quasilaminar state occurs. In this region Reynolds number is only large enough to sustain some perturbations and the mean velocity profiles have inflection points. The instability of the turbulent shear stress is probably the main reason for the formation of the elongated coherent structures (roll-like vortices) in this region. In the fully turbulent parameter domain all six components of Reynolds stress tensor are nonzero due to the existence of the spanwise mean velocity. The Poiseuille–Ekman flow in this region can be regarded as a turbulent two-dimensional channel flow with a mean flow direction inclining toward the spanwise direction. Finally, due to the further increase in the rotation rate, at about Ro2 = 0.546 turbulence is completely damped and the flow reaches a fully laminar steady state, for which an analytical solution of the Navier–Stokes equations exists. The DNS results reproduce this analytical solution for the laminar state.
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47.27.Cn Transition to turbulence
47.15.ki Inviscid flows with vorticity
47.15.Fe Stability of laminar flows
47.60.Dx Flows in ducts and channels
47.32.Ef Rotating and swirling flows
47.27.ek Direct numerical simulations

A general assessment method for subgrid-scale models in large-eddy simulation

B. Cassart, B. Teaca, and D. Carati

Phys. Fluids 22, 105105 (2010); http://dx.doi.org/10.1063/1.3495483 (6 pages)

Online Publication Date: 29 October 2010

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A method combining the advantages of a priori and a posteriori testing approaches for subgrid-scale models in large-eddy simulation (LES) is proposed. It is implemented with various simple eddy viscosity models for decaying homogeneous turbulence. The method relies on the introduction of a restoring force in addition to the subgrid model. This force maintains the LES velocity field in the vicinity of the filtered velocity obtained from an accurately simulated flow. The analysis of this force provides new diagnostics on the efficiency of the subgrid-scale models.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.ep Large-eddy simulations
47.27.em Eddy-viscosity closures; Reynolds stress modeling
47.11.-j Computational methods in fluid dynamics
back to top Compressible Flows

Modeling of the plasma generated in a rarefied hypersonic shock layer

Erin D. Farbar and Iain D. Boyd

Phys. Fluids 22, 106101 (2010); http://dx.doi.org/10.1063/1.3500680 (12 pages) | Cited 1 time

Online Publication Date: 28 October 2010

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In this study, a rigorous numerical model is developed to simulate the plasma generated in a rarefied, hypersonic shock layer. The model uses the direct simulation Monte Carlo (DSMC) method to treat the particle collisions and the particle-in-cell (PIC) method to simulate the plasma dynamics in a self-consistent manner. The model is applied to compute the flow along the stagnation streamline in front of a blunt body reentering the Earth’s atmosphere at very high velocity. Results from the rigorous DSMC-PIC model are compared directly to the standard DSMC modeling approach that uses the ambipolar diffusion approximation to simulate the plasma dynamics. It is demonstrated that the self-consistent computation of the plasma dynamics using the rigorous DSMC-PIC model captures many physical phenomena not accurately predicted by the standard modeling approach. These computations represent the first assessment of the validity of the ambipolar diffusion approximation when predicting the rarefied plasma generated in a hypersonic shock layer.
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52.50.Lp Plasma production and heating by shock waves and compression
52.35.Tc Shock waves and discontinuities
52.65.Pp Monte Carlo methods
52.65.Rr Particle-in-cell method
52.25.Fi Transport properties
52.20.Hv Atomic, molecular, ion, and heavy-particle collisions
back to top Geophysical Flows

Transmission and reflection of internal wave beams

Kate D. Gregory and Bruce R. Sutherland

Phys. Fluids 22, 106601 (2010); http://dx.doi.org/10.1063/1.3486613 (12 pages)

Online Publication Date: 8 October 2010

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An existing method for predicting the partial transmission of plane internal gravity waves across a weakly stratified region is adapted so as to predict the transmission of internal wave beams having finite horizontal and vertical extent. The results are compared with laboratory experiments in which internal waves generated by an oscillating cylinder are incident upon a mixed region of varying depth and stratification. The results are in good agreement except when the characteristic frequency of the beam is close to the minimum buoyancy frequency of the weakly stratified mixed region. In this case, the predicted transmission coefficient varies rapidly with frequency and so is sensitive to small measurement errors. Applications of this method to atmospheric and oceanic internal waves are discussed.
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47.35.Bb Gravity waves
47.55.Hd Stratified flows
47.55.P- Buoyancy-driven flows; convection
92.60.-e Properties and dynamics of the atmosphere; meteorology
92.10.Hm Ocean waves and oscillations
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