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Feb 2006

Volume 18, Issue 2, Articles (02xxxx)

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Free-surface flows with large slopes: Beyond lubrication theory

Jacco H. Snoeijer

Phys. Fluids 18, 021701 (2006); http://dx.doi.org/10.1063/1.2171190 (4 pages) | Cited 12 times

Online Publication Date: 1 February 2006

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The description of free-surface flows can often be simplified to thin-film (or lubrication) equations, when the slopes of the liquid-gas interface are small. Here, we present a long-wavelength theory that remains fully quantitative for steep interface slopes, by expanding about Stokes flow in a wedge. For small capillary numbers, the variations of the interface slope are slow and can be treated perturbatively. This geometry occurs naturally for flows with contact lines: we quantify the difference with ordinary lubrication theory through a numerical example and analytically recover the full Cox-Voinov asymptotic solution.
Show PACS
47.85.mf Lubrication flows
47.55.np Contact lines
47.55.Ca Gas/liquid flows
47.55.nb Capillary and thermocapillary flows

The lowest oscillation mode of a pendant drop

Jong Hoon Moon, Byung Ha Kang, and Ho-Young Kim

Phys. Fluids 18, 021702 (2006); http://dx.doi.org/10.1063/1.2174027 (4 pages) | Cited 4 times

Online Publication Date: 16 February 2006

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The lowest oscillation mode of a pendant drop has long been conceived to be the longitudinal vibration, i.e., periodic elongation and contraction along the longitudinal direction. However, here we experimentally show that the rotation of the drop about the longitudinal axis is the oscillation mode of the lowest resonance frequency. This rotational mode can be invoked by periodic acoustic forcing and is analogous to the pendulum rotation, having the frequency independent of the drop density and surface tension but inversely proportional to the square root of the drop size.
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47.35.Rs Sound waves
47.55.dr Interactions with surfaces
47.32.Ef Rotating and swirling flows
68.03.Cd Surface tension and related phenomena
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back to top Interfacial Flows

Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer

Ying-Chih Liao, Elias I. Franses, and Osman A. Basaran

Phys. Fluids 18, 022101 (2006); http://dx.doi.org/10.1063/1.2166657 (21 pages) | Cited 17 times

Online Publication Date: 3 February 2006

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The breakup of surfactant-laden drops and jets is of technological interest and fundamental scientific importance. Surfactants are routinely used to control the breakup of drops and jets in applications ranging from inkjet printing to crop spraying. Accurate computation of breakup of surfactant-laden drops and jets is often the key to the development of new applications and to providing a rational fundamental understanding of both existing and emerging applications. While highly accurate algorithms for studying the breakup of surfactant-free drops and jets are well documented and much is now known about the dynamics in such situations, little is known by contrast about the closely related problem of interface rupture when surfactant effects cannot be neglected. The deformation and breakup of a stretching liquid bridge of an incompressible Newtonian fluid whose surface is covered with an insoluble surfactant monolayer are analyzed here experimentally and computationally. In the experiments, high-speed visualization is used to capture the transient deformation of a bridge. The dynamic shapes of bridges (captive between two rods of 3.15 mm diameter) are captured and analyzed with a time resolution of 1 ms. The bridge lengths are 3.15 mm initially and about 4–7 mm at breakup, which occurs after stretching for about 0.1–0.2 s, depending on the volume and viscosity of the liquid and the surface density of spread monolayers. The dynamics of a surfactant-covered bridge is governed by the Navier-Stokes and convection-diffusion equations. First, these equations are solved with a three-dimensional, but axisymmetric, or two-dimensional (2D), finite element algorithm using elliptic mesh generation. Second, the governing set of 2D equations is reduced to a set of one-dimensional (1D) equations by means of the slender-jet approximation and the resulting set of 1D equations is solved with a 1D finite element algorithm. The presence of surfactant results not only in the lowering of surface tension and the capillary pressure, but also in surface tension gradients and Marangoni stresses, both of which affect the transient dynamics leading to breakup. In particular, the role of Marangoni stresses in delaying bridge breakup and on formation of satellite droplets is investigated as a function of the initial surface density and surface activity of the surfactant, and surface Peclet number that measures the importance of convection relative to diffusion. The predictions of the 2D algorithm are confirmed to be faithful to the physics by demonstrating that the computed results accord well with the experiments and existing scaling theories. In the pinch-off region, the surfactant is swept out of a thinning neck by strong convection. The calculations thus reveal that the scaling behavior in the presence of surfactant parallels that observed in the absence of surfactant, in accordance with recent reports by others. The 2D computations and the experiments are used in tandem to identify regions in the space of governing parameters where the 1D equations can be used with confidence.
Show PACS
47.55.nk Liquid bridges
47.55.df Breakup and coalescence
47.55.dk Surfactant effects
47.55.pf Marangoni convection
47.10.ad Navier-Stokes equations
47.11.Fg Finite element methods

Theoretical analysis of the effect of insoluble surfactant on the dip coating of chemically micropatterned surfaces

Naveen Tiwari and Jeffrey M. Davis

Phys. Fluids 18, 022102 (2006); http://dx.doi.org/10.1063/1.2171715 (9 pages) | Cited 4 times

Online Publication Date: 10 February 2006

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Microfluidic flow on chemically heterogeneous surfaces is a useful technique with applications ranging from selective material deposition to the self-assembly of nanostructures. The recent theoretical analysis by Davis [Phys. Fluids 17, 038101 (2005)] of the dip coating of a pure fluid onto vertical, wetting stripes surrounded by nonwetting regions quantified the experimentally observed deviations from the classical Landau-Levich result due to lateral confinement of the fluid by chemical surface patterning. In this present work, the analysis of dip coating of these heterogeneous surfaces is extended to a liquid containing an insoluble surfactant. Using matched asymptotic expansions based on lubrication theory in the limit of a small capillary number, the thickness of the deposited liquid film and the surfactant concentration in the deposited monolayer are predicted for a wide range of fluid properties and process parameters. The increase in the deposited film thickness is shown analytically to be limited by a multiplicative factor of 41/3 times the result for a pure liquid. Numerical results demonstrate that the thickening due to Marangoni effects is nonmonotonic in the capillary number because of the competition between viscous stresses, Marangoni stresses, and surface diffusion.
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47.85.mb Coating flows
47.55.nb Capillary and thermocapillary flows
47.55.pf Marangoni convection
68.15.+e Liquid thin films
68.03.Cd Surface tension and related phenomena
68.35.Fx Diffusion; interface formation

The detachment of a viscous drop in a viscous solution in the presence of a soluble surfactant

Fang Jin, Nivedita R. Gupta, and Kathleen J. Stebe

Phys. Fluids 18, 022103 (2006); http://dx.doi.org/10.1063/1.2172003 (10 pages) | Cited 17 times

Online Publication Date: 13 February 2006

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When a buoyant viscous drop is injected into a viscous fluid, it evolves to form a distended shape that detaches via the rapid formation and pinching of a neck. The effects of surfactants in altering this process are studied numerically. In the absence of surfactants, surface contraction is fastest in the vicinity of the neck. Thus, when surfactants are present, they accumulate there and alter the ensuing dynamics by reducing the surface tension that drives the contraction. The surface tension is described by a nonlinear surface equation of state that accounts for the maximum packing of surfactant in a monolayer. When surfactant adsorption-desorption is very slow, interfaces dilute significantly during drop expansion, and drops form necks which are only slightly perturbed in their dynamics from the surfactant-free case. When adsorption-desorption dynamics are comparable to the rate of expansion, drops thin to form a primary neck at low surfactant coverage, to form both primary and secondary necks at moderate coverages, form only a secondary neck at higher coverages, or fail to neck at elevated coverages. When surfactant adsorption-desorption kinetics are rapid, the surface remains in equilibrium with the surrounding solution, and drops behave like surfactant-free drops with a uniform surface tension. These arguments are used to construct a phase diagram of drop neck shapes as a function of surfactant coverage. A map of neck/no-neck thresholds is also constructed as a function of surfactant coverage and sorption dynamics, suggesting that drop detachment can be used as a means of characterizing surfactant dynamics.
Show PACS
47.55.dk Surfactant effects
68.03.Cd Surface tension and related phenomena
68.43.Mn Adsorption kinetics
68.03.Fg Evaporation and condensation of liquids

Numerical analysis of the Rayleigh instability in capillary tubes: The influence of surfactant solubility

D. M. Campana and F. A. Saita

Phys. Fluids 18, 022104 (2006); http://dx.doi.org/10.1063/1.2173969 (16 pages) | Cited 3 times

Online Publication Date: 24 February 2006

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A two-dimensional (2D) free surface flow model already used to study the Rayleigh instability of thin films lining the interior of capillary tubes under the presence of insoluble surfactants [ D. M. Campana, J. Di Paolo, and F. A. Saita, “A 2-D model of Rayleigh instability in capillary tubes. Surfactant effects,” Int. J. Multiphase Flow 30, 431 (2004) ] is extended here to deal with soluble solutes. This new version that accounts for the mass transfer of surfactant in the bulk phase, as well as for its interfacial adsorption/desorption, is employed in this work to assess the influence of surfactant solubility on the unstable evolution. We confirm previously reported findings: surfactants do not affect the system stability but the growth rate of the instability [ D. R. Otis, M. Johnson, T. J. Pedley, and R. D. Kamm, “The role of pulmonary surfactant in airway closure,” J. Appl. Physiol. 59, 1323 (1993) ] and they do not change the successive shapes adopted by the liquid film as the instability develops [ S. Kwak and C. Pozrikidis, “Effects of surfactants on the instability of a liquid thread or annular layer. Part I: Quiescent fluids,” Int. J. Multiphase Flow 27, 1 (2001) ]. Insoluble surfactants delay the instability process, and the time needed to form liquid lenses disconnecting the gas phase—i.e., the closure time—is four to five times larger than for pure liquids. This retardation effect is considerably reduced when the surfactants are somewhat soluble. For a typical system adopted as a reference case, detailed computed predictions are shown; among them, curves of closure time versus adsorption number are given for solubility values ranging from insoluble to highly soluble conditions. In addition, the evolution of the four mass transport terms appearing in the interfacial mass balance equation—normal and tangential convection, diffusion and sorption—is scrutinized to uncover the mechanisms by which surfactant solubility affects the growth rate of the instability.
Show PACS
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.nb Capillary and thermocapillary flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.te Turbulent convective heat transfer
68.15.+e Liquid thin films
68.43.Mn Adsorption kinetics
back to top Particulate, Multiphase, and Granular Flows

Thermal transport in sheared electro- and magnetorheological fluids

Martin C. Heine, Juan de Vicente, and D. J. Klingenberg

Phys. Fluids 18, 023301 (2006); http://dx.doi.org/10.1063/1.2171442 (11 pages) | Cited 8 times

Online Publication Date: 17 February 2006

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Thermal energy transport in sheared electrorheological and magnetorheological (ER and MR) fluids is analyzed. Although energy production by viscous dissipation can be significant, energy transport on the particle length scale can be analyzed by ignoring viscous dissipation. For typical situations, energy transport normal to the flow direction is dominated by conduction. Particle-level simulations were employed to determine the suspension structure as a function of Mason number and volume fraction. A self-consistent mean-field dipole model is used to estimate the effective thermal conductivities for these simulated structures. The field-induced chain-like aggregates that form at small Mason number result in a larger effective thermal conductivity at small Mason number than at large Mason number. Effects of higher-order multipoles are estimated by analyzing effective thermal conductivities of model structures. For highly conducting particles, the effective thermal conductivity of a sheared ER or MR suspension is predicted to roughly double as the Mason number is decreased from the large to the small Mason number limits.
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47.65.Gx Electrorheological fluids
47.50.Cd Modeling
47.57.eb Diffusion and aggregation
47.27.te Turbulent convective heat transfer
83.80.Gv Electro- and magnetorheological fluids
82.70.Kj Emulsions and suspensions
back to top Instability and Transition

Nonlinear instabilities in a vertical pipe flow discharging from a cylindrical container

E. Sanmiguel-Rojas and R. Fernandez-Feria

Phys. Fluids 18, 024101 (2006); http://dx.doi.org/10.1063/1.2168445 (6 pages) | Cited 1 time

Online Publication Date: 1 February 2006

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We report results from three-dimensional numerical simulations of the incompressible flow in a vertical pipe of circular cross-section discharging from a cylindrical container. Natural Coriolis forces due to Earth rotation trigger the instability of the axisymmetric flow, and nonlinear spiral waves with azimuthal wave number ∣n∣ = 3 are formed above a critical Reynolds number based on the pipe flow rate (ReQ). We characterize this critical Reynolds number as a function of the Coriolis parameter (F), that is proportional to the square of the radius of the container. As a difference with previous numerical works on nonlinear instabilities and transition in a pipe flow, here the nonlinear disturbances needed to trigger the instabilities are not artificially introduced inside the pipe flow, but naturally produced by Coriolis forces, the amplitude of these disturbances being characterized by a nondimensional Coriolis parameter. We find that the pipe flow can be unstable for ReQ as low as 300 for the largest value of F considered. We also discuss the relevance of the residual swirl introduced by natural Coriolis forces in triggering the nonlinear traveling waves.
Show PACS
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
47.32.Ef Rotating and swirling flows
47.35.-i Hydrodynamic waves

Nonlinear mechanics of wavy instability of steady longitudinal vortices and its effect on skin friction rise in boundary layer flow

I. G. Girgis and J. T. C. Liu

Phys. Fluids 18, 024102 (2006); http://dx.doi.org/10.1063/1.2158430 (12 pages) | Cited 6 times

Online Publication Date: 2 February 2006

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Wavy secondary instability of steady longitudinal vortices in boundary layer flow is studied. The nonlinear interaction problem is parabolized through scaling guided by observations. Emphasis is placed on the nonlinear modification of the steady problem by the Reynolds stresses of the wavy disturbance. It is found that the skin friction in such a modification process increases well above the local turbulent boundary layer value.
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47.20.Lz Secondary instabilities
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.35.-i Hydrodynamic waves
47.32.cd Vortex stability and breakdown
47.27.nb Boundary layer turbulence

Rayleigh’s instability of Lennard-Jones liquid nanothreads simulated by molecular dynamics

Donghong Min and Harris Wong

Phys. Fluids 18, 024103 (2006); http://dx.doi.org/10.1063/1.2173620 (6 pages) | Cited 6 times

Online Publication Date: 14 February 2006

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A liquid thread of radius R will break up into drops if the axial wavelength of the surface perturbation L>2πR. If L<2πR, the thread is stable and will remain intact. This is Rayleigh’s stability criterion that was derived using a continuum model. We use molecular dynamics to simulate the evolution of Lennard-Jones liquid threads with R = S, 2S, and 3S, where S is the equilibrium distance between two atoms. We find that Rayleigh’s stability criterion holds, even at the molecular scale.
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47.20.-k Flow instabilities
47.11.Mn Molecular dynamics methods
47.55.db Drop and bubble formation
back to top Turbulent Flows

An efficient wall model for large-eddy simulation based on optimal control theory

Jeremy A. Templeton, Meng Wang, and Parviz Moin

Phys. Fluids 18, 025101 (2006); http://dx.doi.org/10.1063/1.2166457 (13 pages) | Cited 8 times

Online Publication Date: 2 February 2006

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Large-eddy simulation is currently very expensive for high Reynolds number attached flows due to the need to resolve the wall layer. In order to reduce this expense, wall modeling has been proposed to provide approximate boundary conditions to the LES that allow the wall layer to be unresolved. Unfortunately, subgrid scale modeling errors and numerical errors are important in this region when a coarse grid is used, necessitating a wall model that can compensate for their effects. Optimal control theory has been used to provide such models in the past, but is impractical for complex flows due to the need to provide a target mean velocity profile and the computational expense involved with solving gradient-based optimization problems. In this paper we address the latter issue by reformulation of the optimization problem to include only data near the wall. Further approximations have been made to the Navier-Stokes and adjoint equations used in the optimization process that significantly reduce the computational cost. Results will be presented comparing this method with other control-based and standard wall models.
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47.27.nb Boundary layer turbulence
47.27.ep Large-eddy simulations
47.10.ad Navier-Stokes equations
07.05.Dz Control systems

Mechanisms for deposition and resuspension of heavy particles in turbulent flow over wavy interfaces

Cristian Marchioli, Vincenzo Armenio, Maria Vittoria Salvetti, and Alfredo Soldati

Phys. Fluids 18, 025102 (2006); http://dx.doi.org/10.1063/1.2166453 (16 pages) | Cited 9 times

Online Publication Date: 3 February 2006

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It has been long recognized that turbulent flow over steep waves can produce coherent flow structures of different temporal and spatial scales. In particular, quasistreamwise vortices grow up on the upslope side of the wave and interact with geometry-dependent vortical structures, aligned spanwise and located within the recirculation bubble in the wave trough, thus creating the conditions for the development of a three-dimensional highly turbulent flow field. In this work, we have analyzed the trajectories of O(105) small dense particles (either in solid form or in the form of liquid droplets) released into a turbulent air flow over waves precisely to clarify the role of coherent vortical structures in controlling particle deposition and resuspension. The three-dimensional time-dependent flow field at Reτ = 170 is calculated using large-eddy simulation, and the dynamics of individual different-sized particles is described using a Lagrangian approach. Drag, gravity, and lift are used in the equation of motion for particles that have no influence on the flow field. Particle-wall interaction is fully elastic. Our findings show that different-sized particles interact selectively with vortical flow structures, producing different distribution patterns and dispersion rates qualitatively depending on the particle-to-fluid time-scale ratio. Specifically, we find that quasistreamwise vortices on the upslope side of the wave control particle dispersion and eventual segregation in the flow separation region downstream the wave crest as well as in the shear layer forming behind the wave, just above the separation region. These vortices generate momentum mixing events that also entrain and move particles towards and away from the wavy wall. This process is similar to the sweep/ejection cycle occurring in turbulent flow over a flat boundary layer.
Show PACS
47.27.De Coherent structures
47.55.Kf Particle-laden flows
47.35.Bb Gravity waves
47.32.cb Vortex interactions
47.27.ep Large-eddy simulations
47.54.Bd Theoretical aspects

Stretching of polymers around the Kolmogorov scale in a turbulent shear flow

Jahanshah Davoudi and Jörg Schumacher

Phys. Fluids 18, 025103 (2006); http://dx.doi.org/10.1063/1.2168187 (11 pages) | Cited 12 times

Online Publication Date: 7 February 2006

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We present numerical studies of stretching of Hookean dumbbells in a turbulent Navier-Stokes flow with a linear mean profile, 〈ux〉 = Sy. In addition to the turbulence features beyond the viscous Kolmogorov scale η, the dynamics at the equilibrium extension of the dumbbells significantly below η is well resolved. The variation of the constant shear rate S causes a change of the turbulent velocity fluctuations on all scales and thus of the intensity of local stretching rate of the advecting flow. The latter is measured by the maximum Lyapunov exponent λ1 which is found to increase as λ1 ∼ S3/2, in agreement with a dimensional argument. The ensemble of up to 2×106 passively advected dumbbells is advanced by Brownian dynamics simulations in combination with a pseudospectral integration for the turbulent shear flow. Anisotropy of stretching is quantified by the statistics of the azimuthal angle ϕ which measures the alignment with the mean flow axis in the x-y shear plane, and the polar angle θ which determines the orientation with respect to the shear plane. The asymmetry of the probability density function (PDF) of ϕ increases with growing shear rate S. Further, the PDF becomes increasingly peaked around mean flow direction (ϕ = 0). In contrast, the PDF of the polar angle θ is symmetric and less sensitive to changes of S.
Show PACS
47.27.nb Boundary layer turbulence
47.10.ad Navier-Stokes equations
47.11.Kb Spectral methods
05.40.Jc Brownian motion
02.60.Jh Numerical differentiation and integration

Drag reduction in turbulent channel flow with periodically arrayed heating and cooling strips

Hyun Sik Yoon, Osama A. El-Samni, and Ho Hwan Chun

Phys. Fluids 18, 025104 (2006); http://dx.doi.org/10.1063/1.2171196 (13 pages) | Cited 1 time

Online Publication Date: 7 February 2006

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A new technique giving significant drag reduction in turbulent shear flows has been proposed by using the buoyancy effect to generate periodic spanwise motion. Such spanwise motion can be obtained by arranging heating and cooling strips periodically aligned in the spanwise direction of a vertical channel, where the streamwise mean flow is perpendicular to the gravity vector. The strip size has been changed in order to obtain the optimum size corresponding to the maximum drag reduction. Series of direct numerical simulation have been performed where the bulk Reynolds number, Rem = Umδ/ν is fixed at 2270 whereas the Grashof number is changed to between 106 and 107. At the lowest Grashof number, the buoyancy forces are not strong enough to disturb the flow and no apparent variation of drag compared to the plane channel is observed. However, as the Grashof number increases, considerable drag reduction can be obtained. At the highest Grashof number, an optimum strip size of about 250 wall units gives drag reduction of about 35%. The greater the Grashof number, the smaller the strip size which attains the maximum drag reduction. The similarity between the induced lateral motions by the buoyancy forces and those induced by the spanwise wall oscillations is highlighted.
Show PACS
47.27.nd Channel flow
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.35.Bb Gravity waves
47.27.ek Direct numerical simulations
47.85.lb Drag reduction
47.27.Rc Turbulence control

Damping rate of magnetohydrodynamic vortices at low magnetic Reynolds number

Kazuyuki Ueno and René Moreau

Phys. Fluids 18, 025105 (2006); http://dx.doi.org/10.1063/1.2174056 (8 pages) | Cited 1 time

Online Publication Date: 17 February 2006

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The damping rate of vortices in an electrically conducting fluid submitted to a uniform magnetic field is analyzed for a large Hartmann number Ha. The fluid is contained in a layer of constant thickness h, bounded by two insulating walls that are perpendicular to the magnetic field. The damping times and the eigenfunctions along the magnetic field are obtained from a linear eigenvalue problem. According to the damping times and these eigenfunctions, vortices are classified into several classes by the range of combinations of the mode number m in the magnetic field direction and the wave number k2D in the plane perpendicular to the magnetic field. It is found that the damping rate of vortices in the range of k2D ∼ [(m+½)π Ha]1/2h−1 and m = 0,1,2 is of the same order as that of large-scale two-dimensional vortices. This fact suggests that actual quasi-two-dimensional magnetohydrodynamic turbulent flows include not only m = 0 but also higher-mode (m ≥ 1) eigenfunctions of this wave-number range, although the eigenfunction of m = 0 has a 30% variation and the higher-mode eigenfunctions change their sign along the magnetic field.
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47.32.cb Vortex interactions
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.nb Boundary layer turbulence

Octant analysis based structural relations for three-dimensional turbulent boundary layers

Semih M. Ölçmen, Roger L. Simpson, and Jonathan W. Newby

Phys. Fluids 18, 025106 (2006); http://dx.doi.org/10.1063/1.2172650 (17 pages) | Cited 3 times

Online Publication Date: 21 February 2006

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A flow structure based triple-product correlation model developed by Nagano and Tagawa [J. Fluid Mech. 215, 639 (1990) ] has been expanded to three-dimensional turbulent flows. Three-dimensional turbulent boundary layer data obtained away from the vortex in a wing-body junction flow are analyzed to calculate the contributions from eight velocity octants to the stresses and higher-order products. The analysis showed that the sweep and ejection modes dominate the flow physics of some shear stresses and some triple products, while the interaction modes are negligible away from the wall. These experimental observations are used together with the extended Nagano-Tagawa mathematical model to obtain relations among the triple products in three-dimensional turbulent boundary layers that can simplify the turbulent diffusion modeling used in Reynolds-averaged Navier-Stokes equations. Results show that math, math, and math triple product correlations can be modeled if an appropriate turbulence model is described for the math triple product correlation, and that math math triple products correlations can be modeled if an appropriate turbulence model is described for the math triple product correlation.
Show PACS
47.27.nb Boundary layer turbulence
47.32.cb Vortex interactions
47.27.tb Turbulent diffusion
47.10.ad Navier-Stokes equations

Synthetic turbulence inflow conditions for large-eddy simulation

L. di Mare, M. Klein, W. P. Jones, and J. Janicka

Phys. Fluids 18, 025107 (2006); http://dx.doi.org/10.1063/1.2130744 (11 pages) | Cited 18 times

Online Publication Date: 24 February 2006

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Direct numerical or large-eddy simulations of the majority of spatially inhomogeneous turbulent flows require turbulent inflow boundary conditions. A potential implication is that any results computed may be strongly influenced by the prescribed instantaneous inlet velocity profiles. Such profiles are practically never available, and a usual practice is to generate synthetic inflow data satisfying certain statistical properties, which may, for example, be known from experimental data or empirical correlations. The present paper describes a new method for generating turbulent inflow data based on digital filters that is capable of reproducing specified statistical data. Two variants of the approach are presented: a simple method in which the Reynolds stresses and a single length scale are prescribed, and a more detailed approach that is able to reproduce the complete Reynolds-stress tensor as well as any given, locally defined, spatial and temporal correlation functions. The application of the methods to a plane jet flow and to a developing wall boundary layer serve to demonstrate the applicability of the approach.
Show PACS
47.27.nb Boundary layer turbulence
47.27.wg Turbulent jets

Subgrid modeling in particle-laden channel flow

J. G. M. Kuerten

Phys. Fluids 18, 025108 (2006); http://dx.doi.org/10.1063/1.2176589 (13 pages) | Cited 25 times

Online Publication Date: 28 February 2006

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Direct numerical simulation (DNS) and large-eddy simulation (LES) of particle-laden turbulent channel flow, in which the particles experience a drag force, are investigated for two subgrid models and several Reynolds and Stokes numbers. In this flow, turbophoresis leads to an accumulation of particles near the walls. The objectives of the work are to investigate the accuracy of the subgrid models studied with respect to particle behavior and to explain the observed particle behavior predicted by the different models. The focus is on particle dispersion and mean particle motion in the direction normal to the walls of the channel. For a low Reynolds number, it is shown that the turbophoresis and particle velocity fluctuations are reduced compared to DNS, if the filtered fluid velocity calculated in the LES is used in the particle equation of motion. This is a combined effect of the disregard of the subgrid scales in the fluid velocity and the inadequacy of the subgrid model. Better agreement with DNS is obtained if an inverse filtering model, which was recently proposed, is incorporated into the particle equation. This model is shown to enhance turbophoresis and particle velocity fluctuations in actual LES. The results of the approximate deconvolution model (ADM) agree better with DNS results than results of the dynamic eddy-viscosity model. This can be explained from the better prediction of the fluid velocity statistics by ADM and the better correspondence of the subgrid models adopted in the fluid and particle equations. Although the differences between the two subgrid models become smaller, similar conclusions are obtained at a higher Reynolds number. Compared to fourth-order interpolation of the fluid velocity to the particle position, second-order interpolation approximately cancels the effect of the subgrid model in the particle equation of motion.
Show PACS
47.55.Kf Particle-laden flows
47.27.nd Channel flow
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.ek Direct numerical simulations
47.27.ep Large-eddy simulations
47.27.nb Boundary layer turbulence
back to top Compressible Flows

Time evolution and mixing characteristics of hydrogen and ethylene transverse jets in supersonic crossflows

A. Ben-Yakar, M. G. Mungal, and R. K. Hanson

Phys. Fluids 18, 026101 (2006); http://dx.doi.org/10.1063/1.2139684 (16 pages) | Cited 25 times

Online Publication Date: 13 February 2006

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We report an experimental investigation that reveals significant differences in the near-flowfield properties of hydrogen and ethylene jets injected into a supersonic crossflow at a similar jet-to-freestream momentum flux ratio. Previously, the momentum flux ratio was found to be the main controlling parameter of the jet’s penetration. Current experiments, however, demonstrate that the transverse penetration of the ethylene jet was altered, penetrating deeper into the freestream than the hydrogen jet even for similar jet-to-freestream momentum flux ratios. Increased penetration depths of ethylene jets were attributed to the significant differences in the development of large-scale coherent structures present in the jet shear layer. In the hydrogen case, the periodically formed eddies persist long distances downstream, while for ethylene injection, these eddies lose their coherence as the jet bends downstream. The large velocity difference between the ethylene jet and the freestream induces enhanced mixing at the jet shear layer as a result of the velocity induced stretching-tilting-tearing mechanism. These new observations became possible by the realization of high velocity and high temperature freestream conditions which could not be achieved in conventional facilities as have been widely used in previous studies. The freestream flow replicates a realistic supersonic combustor environment associated with a hypersonic airbreathing engine flying at Mach 10. The temporal evolution, the penetration, and the convection characteristics of both jets were observed using a fast-framing-rate (up to 100 MHz) camera acquiring eight consecutive schlieren images, while OH planar laser-induced fluorescence was performed to verify the molecular mixing.
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47.40.Ki Supersonic and hypersonic flows
47.70.Fw Chemically reactive flows
47.27.wg Turbulent jets
47.27.T- Turbulent transport processes
back to top Geophysical Flows

Vortex cores, strain cells, and filaments in quasigeostrophic turbulence

Mark R. Petersen, Keith Julien, and Jeffrey B. Weiss

Phys. Fluids 18, 026601 (2006); http://dx.doi.org/10.1063/1.2166452 (11 pages) | Cited 5 times

Online Publication Date: 6 February 2006

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We present numerical simulations of decaying two-dimensional (2D) and three-dimensional quasigeostrophic (3D QG) turbulence. The resulting vorticity fields are decomposed into three components: the vortex cores, the strain cells, and the background. In 2D, the vortex cores induce five times the energy as the background, while in 3D QG the background plays a more dominant role and induces the same amount of energy as the vortex cores, quantifying previous observations that 3D QG has a more active filamentary background. The probability density function of the total velocity field is nearly Gaussian in 3D QG but significantly less so in 2D. In both 2D and 3D QG, the velocities induced by the vortex cores and the strain cells are non-Gaussian. In both 2D and 3D QG turbulence, the enstrophy spectrum of the background is close to k−1 predicted by inverse cascade theories.
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47.32.cb Vortex interactions
47.27.E- Turbulence simulation and modeling
47.11.-j Computational methods in fluid dynamics
02.50.Ng Distribution theory and Monte Carlo studies

The viscous decay of progressive interfacial waves

C. D. Troy and J. R. Koseff

Phys. Fluids 18, 026602 (2006); http://dx.doi.org/10.1063/1.2166849 (14 pages) | Cited 3 times

Online Publication Date: 14 February 2006

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The viscous damping of progressive, two-layer interfacial waves is examined theoretically and experimentally. Traditional water wave theory is modified to derive the damping rates associated with interfacial wave propagation in a rectangular channel. The individual wave damping contributions are considered from the bottom, side, and interfacial boundary layers, as well as the damping associated with the wave-induced velocities within the homogenous fluid layers. These results show that for most laboratory-scale experiments, sidewall friction plays the dominant role in wave damping. Laboratory experiments are conducted to verify the damping rates for progressive two-layer internal waves in a rectangular channel. Experiments are conducted on both monochromatic and polychromatic wave trains. The results of these experiments are in good agreement with the derived damping rates, but show poorer agreement for large-amplitude waves when the sidewall boundary layers become turbulent. More work is necessary to quantify the damping associated with nonlinear internal waves in order to allow for accurate interpretation of the results from laboratory experiments.
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47.35.Jk Wave breaking
47.55.Hd Stratified flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.nb Boundary layer turbulence

β-plane turbulence in a basin with no-slip boundaries

W. Kramer, M. G. van Buren, H. J. H. Clercx, and G. J. F. van Heijst

Phys. Fluids 18, 026603 (2006); http://dx.doi.org/10.1063/1.2173285 (11 pages) | Cited 8 times

Online Publication Date: 16 February 2006

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On a domain enclosed by no-slip boundaries, two-dimensional, geostrophic flows have been studied by numerical simulations of the Navier-Stokes equation with the β-plane approximation at intermediate Reynolds numbers and a range of values for β. The β effect causes a refinement of the flow structures, and the presence of basin modes has been revealed by means of frequency spectra. The presence and apparent stability of basin modes on a domain enclosed by no-slip boundaries is a rather surprising observation, because these modes are solutions of the inviscid flow equations on a bounded domain (with free-slip boundaries). To understand the persistence of these basin modes, the viscous boundary layers near the no-slip walls have been investigated. The mean flow in forced simulations shows a zonal band structure, much unlike the regular Fofonoff-like solution observed when free-slip boundary conditions are used.
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47.27.nb Boundary layer turbulence
47.10.ad Navier-Stokes equations
47.20.Ib Instability of boundary layers; separation
02.60.Cb Numerical simulation; solution of equations
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Kinetic theory study of steady condensation of a polyatomic gas

Aldo Frezzotti and Tor Ytrehus

Phys. Fluids 18, 027101 (2006); http://dx.doi.org/10.1063/1.2171231 (12 pages) | Cited 3 times

Online Publication Date: 6 February 2006

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The steady one-dimensional flow of a monatomic vapor condensing onto a planar surface kept at constant and uniform temperature has been the subject of a number of investigations based on the kinetic theory of gases. It has been shown that, depending on the upstream value of the Mach number normal to the surface, a steady solution exists only when the problem parameters lie on a surface in the parameters spaces (upstream subsonic flow), or when the problem parameters lie in a proper subregion of the whole parameters space (upstream supersonic flow). Similar detailed studies do not exist for a polyatomic vapor, in spite of their potential relevance for many applications. The present paper aims at describing the effects of internal degrees of freedom on the relationships which determine the existence of steady one-dimensional condensation flows. The study is based on the numerical solution of the Boltzmann equation for a gas with rotational degrees of freedom. Inelastic collision are described by the Borgnakke-Larsen model. A few cases also have been computed by a finite difference discretization of Holway’s model kinetic equation. The role of boundary conditions is also briefly discussed.
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47.45.Ab Kinetic theory of gases
47.55.Ca Gas/liquid flows
47.40.Dc General subsonic flows
47.40.Ki Supersonic and hypersonic flows
47.11.Bc Finite difference methods
64.70.F- Liquid-vapor transitions

Small particles in homogeneous turbulence: Settling velocity enhancement by two-way coupling

Thorsten Bosse, Leonhard Kleiser, and Eckart Meiburg

Phys. Fluids 18, 027102 (2006); http://dx.doi.org/10.1063/1.2166456 (17 pages) | Cited 24 times

Online Publication Date: 6 February 2006

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The gravitational settling of an initially random suspension of small solid particles in homogeneous turbulence is investigated numerically. The simulations are based on a pseudospectral method to solve the fluid equations combined with a Lagrangian point-particle model for the particulate phase (Eulerian-Lagrangian approach). The focus is on the enhancement of the mean particle settling velocity in a turbulent carrier fluid, as compared to the settling velocity of a single particle in quiescent fluid. Results are presented for both one-way coupling, when the fluid flow is not affected by the presence of the particles, and two-way coupling, when the particles exert a feedback force on the fluid. The first case serves primarily for validation purposes. In the case with two-way coupling, it is shown that the effect of the particles on the carrier fluid involves an additional increase in their mean settling velocity compared to one-way coupling. The underlying physical mechanism is analyzed, revealing that the settling velocity enhancement depends on the particle loading, the Reynolds number, and the dimensionless Stokes settling velocity if the particle Stokes number is about unity. Also, for particle volume fractions Φv≳10−5, a turbulence modification is observed. Furthermore, a direct comparison with recent experimental studies by Aliseda et al. [J. Fluid Mech. 468, 77 (2002)] and Yang and Shy [J. Fluid Mech. 526, 171 (2005)] is performed for a microscale Reynolds number Reλ ≈ 75 of the turbulent carrier flow.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.55.Kf Particle-laden flows
47.57.ef Sedimentation and migration
47.35.Bb Gravity waves
47.11.Kb Spectral methods
82.70.Kj Emulsions and suspensions

Dissipative particle dynamics simulation of a colloidal micropump

Pietro De Palma, P. Valentini, and M. Napolitano

Phys. Fluids 18, 027103 (2006); http://dx.doi.org/10.1063/1.2170133 (11 pages) | Cited 12 times

Online Publication Date: 7 February 2006

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Dissipative particle dynamics (DPD) is a recently developed model for computing complex fluid flows at mesoscopic scales. This article provides a novel DPD simulation of complex microfluidic devices involving the momentum exchange between a body moving with a prescribed law of motion and the surrounding fluid. To this purpose, a DPD computational method is developed and equipped with an elastic collision model between the moving body and the DPD fluid particles surrounding it. The method is first validated versus well known theoretical, numerical, and experimental results, providing a sensitivity analysis of the dependence of continuum-flow properties on DPD parameters, as well as verifying its reliability for well known continuum-flow test cases. The method is then applied to its main goal, namely, the simulation of the flow driven by a peristaltic micropump, constructed by assembling several colloidal spheres. The DPD fluid model provides quite accurate results with respect to the experimental data and gives a detailed description of local flow properties. It is found that a careful choice of the DPD parameters is needed to avoid spurious compressibility effects and to match the real fluid characteristics; furthermore, due to the very coarse graining used in the present simulation, the thermal kinetic energy of the DPD particles needs to be reduced, in order to correctly evaluate their displacement, which is determined mainly by the momentum driving the flow. Finally, thanks to such a very coarse graining, the proposed DPD method provides an accurate prediction of local mesoscale flow properties with a dramatic reduction of the computational cost with respect to molecular dynamics simulations.
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47.85.Np Fluidics
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.57.J- Colloidal systems
47.11.-j Computational methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
82.70.Dd Colloids
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