Volume 20, Issue 11, November 2008

The stability of viscous rotating liquid columns and their application to rotating viscousliquid jets aligned under gravity is reviewed. Experiments on stable viscous fluid flow discharged from rotating vertical pipes exhibit very weak contraction. We present an elementary liquid jet analysis to understand this phenomenon. Indeed, our inviscid model of a slender rotating inviscid liquid jet shows that rotation suppresses contraction. Next we study the comparable problem for granular flow. Our model for noncohesive granular flow emanating from a vertical pipe rotating about its central axis, valid for sufficiently large rotation rate, shows that the granular profiles blossom rather than contract. The profiles of both the liquid and granular jets depend on the same dimensionless parameters—an exit Froude number and an exit swirl parameter . The limitations of both models are discussed. Experimental data for granular jet profiles compare well with the collisionfree granular flowmodel in its range of applicability. A criterion for the rotation rate at which particles adjacent to the inner wall of the rotating pipe cease to flow is also given and compared to experiment.
 LETTERS


Initiation of underwater granular avalanches: Influence of the initial volume fraction
View Description Hide DescriptionWe experimentally investigate how a layer of granular material fully immersed in a liquid starts to flow when suddenly inclined from a horizontal position. The flow is shown to strongly depend on the initial volume fraction, its initiation being dramatically delayed by a slight initial compaction. A model, which takes into account the dilatant behavior of the granular material and the coupling with the interstitial fluid, captures the main experimental features.

Noninertial lateral migration of vesicles in bounded Poiseuille flow
View Description Hide DescriptionCrossstreamline noninertial migration of a vesicle in a bounded Poiseuille flow is investigated experimentally and numerically. The combined effects of the walls and of the curvature of the velocity profile induce a movement toward the center of the channel. A migration law (as a function of relevant structural and flow parameters) is proposed that is consistent with experimental and numerical results. This similarity law markedly differs from its analog in unbounded geometry. The dependency on the reduced volume and viscosity ratio is also discussed. In particular, the migration velocity becomes nonmonotonous as a function of beyond a certain .

Direct assessment of vorticity alignment with local and nonlocal strain rates in turbulent flows
View Description Hide DescriptionA direct BiotSavart integration is used to decompose the strain rate into its local and nonlocal constituents, allowing the vorticity alignment with the local and nonlocal strain rate eigenvectors to be investigated. These strain rate tensor constituents are evaluated in a turbulent flow using data from highly resolved direct numerical simulations. While the vorticity aligns preferentially with the intermediate eigenvector of the combined strain rate, as has been observed previously, the present results, for the first time, clearly show that the vorticity aligns with the most extensional eigenvector of the nonlocal strain rate. This, in turn, reveals a significant linear contribution to the vortex stretching dynamics in turbulent flows.
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 ARTICLES

 Interfacial Flows

Studies on stability in threelayer HeleShaw flows
View Description Hide DescriptionWe consider a setup in a HeleShaw cell where a fluid of constant viscosity occupying a nearhalfplane pushes a fluid of constant viscosity occupying a layer of length which in turn pushes another fluid of constant viscosity occupying the right halfplane. The fluid upstream has a velocity . Careful analysis of the dispersion relation arising from linear stability of the threelayer HeleShaw flow problem leads to the following specific analytical results all of which are strikingly independent of the length of the middle layer: (i) a necessary and sufficient condition for modal instability; (ii) a critical viscosity of the middle layer that gives the shortest bandwidth of unstable waves; and (iii) a strict upper bound on the growth rate of instabilities, meaning that this upper bound is never reached and hence this upper bound can be improved upon. Results based on exact growth rates are presented which provides some insight into the instability transfer mechanism between interfaces as the parameters of the problem are varied. Numerical evidence that supports the effectiveness of the upper bound is also presented.

Seaswell interaction as a mechanism for the generation of freak waves
View Description Hide DescriptionThe probability of freak waves in an inhomogeneous ocean is studied by integration of Alber’s equation. The special phase structure of the inhomogeneous disturbance, required for instability, is provided by bound waves, generated by the quadratic interaction of the stochastic sea with a deterministic, long swell. The probability of freak waves higher than twice the significant wave height increases by a factor of up to 20 compared to the classical value given by Rayleigh’s distribution. The probability of exceptionally high freak waves, with height larger than three times the significant wave height, is shown to increase some fold compared to that given by the Rayleigh distribution, which renders their encounter feasible.

Axisymmetric bubble collapse in a quiescent liquid pool. I. Theory and numerical simulations
View Description Hide DescriptionIn this paper we analyze the final instants of axisymmetric bubble pinchoff in a low viscosityliquid. We find that both the time evolution of the bubble dimensionless minimum radius, , and of the dimensionless local axial curvature at the minimum radius, , are governed by a pair of twodimensional Rayleighlike equations in which surface tension,viscosity, and gas pressure terms need to be retained for consistency. The integration of the abovementioned system of equations is shown to be in remarkable agreement with numerical simulations and experiments. An analytical criterion, which determines the necessary conditions for the formation of the previously reported tiny satellite bubbles, is also derived. Additionally, an estimation of the maximum velocity reached by the high speed Worthington jets ejected after bubble pinchoff, in the case axisymmetry is preserved down to the formation of the satellite bubble, is also provided.

Axisymmetric bubble collapse in a quiescent liquid pool. II. Experimental study
View Description Hide DescriptionWe present an experimental study of the detachment of a gas bubble growing quasistatically at constant flow rate conditions from a vertical nozzle placed at the bottom of a quiescent pool of water. In particular, we focus on the dynamics of the necking process and on its dependence on both the Bond and Weber numbers, respectively, defined as , and . Here, , , , , and are the inner radius of the nozzle, the liquid density, the gasliquidsurface tension, the gravitational acceleration, and the gas flow rate. Our experimental data indicate that the collapse process is not only driven by capillarity but also by the liquidhydrostaticpressure. Good agreement is achieved between the measurements of the collapse time and that given by the scaling proposed as where is the capillary time, valid in the limit . In addition, the details of the final instants previous to pinchoff have been analyzed by recording the time evolution of both the bubble neck radius, , and the axial curvature at the minimum radius, , using a high speed digital video camera and an appropriate set of microscopic lenses. We find that the dimensionless, asymptotic law, recently obtained for the inviscid pinchoff of a bubble, given by , is never achieved down to about . However, the experimental results are accurately reproduced by a pair of twodimensional Rayleightype equations that include liquid inertia as well as surface tension effects.

Stability of a twolayer binaryfluid system with a diffuse interface
View Description Hide DescriptionThe phase separation of a binary fluid can lead to the creation of two horizontal fluid layers with different concentrations resting on a solid substrate and divided by a diffuse interface. In the framework of the Cahn–Hilliard equation, it is shown analytically and numerically that such a layered system is subject to a transverse instability that generates a slowly coarsening multidomain structure. The influence of gravity, solutocapillary effect at the free boundary, and Korteweg stresses inside the diffuse interface on the stability of the layers is studied using the coupled system of the hydrodynamic equations and the nonlinear equation for the concentration (H model). The parameter regions of longwave instabilities are found.

Dynamic motion of red blood cells in simple shear flow
View Description Hide DescriptionA threedimensional numerical model is proposed to simulate the dynamic motion of red blood cells (RBCs) in simple shear flow. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes which take into account the membrane shear elasticity and the membrane area incompressibility. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to have the same physical properties as the matrix fluid. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the cells are found to carry out a swinging motion, in which periodic inclination oscillation and shape deformation superimpose on the membrane tank treading motion. With the shear rate decreasing, the swinging amplitude of the cell increases, and finally triggers a transition to tumbling motion. This is the first direct numerical simulation that predicts both the swinging motion of the RBCs and the shear rate induced transition, which have been observed in a recent experiment. It is also found that as the mode changes from swinging to tumbling, the apparent viscosity of the suspension increases monotonically.
 Viscous and NonNewtonian Flows

A model for hybrid simulations of molecular dynamics and computational fluid dynamics
View Description Hide DescriptionWe develop a method for multiscale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics(CFD). In this method, the usual latticemesh based simulations are applied for the CFD level, but each lattice is associated with a small MD cell that generates a “local stress” according to a “local flow field” given from CFD instead of using any constitutive functions at the CFD level. We carried out hybrid simulations for some elemental flow problems involving simple LennardJones liquids and compared the results with those obtained by usual CFD with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduce the correct flow behavior obtained from usual CFD as long as the mesh size and the time step of CFD are not too large compared to the system size and the sampling duration of MD simulations performed at each time step of the CFD. Otherwise, the simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail.
 Particulate, Multiphase, and Granular Flows

Newton’s cradle undone: Experiments and collision models for the normal collision of three solid spheres
View Description Hide DescriptionUsing an apparatus inspired by Newton’s cradle, the simultaneous, normal collision between three solid spheres is examined. Namely, an initially touching, motionless pair of “target” particles (doublet) is impacted on one end by a third “striker” particle. Measurements of postcollisional velocities and collision durations are obtained via highspeed photography and an electrical circuit, respectively. Contrary to intuition, the expected Newton's cradle outcome of a motionless, touching particle pair at the bottom of the pendulum arc is not observed in either case. Instead, the striker particle reverses its direction and separates from the middle particle after collision. This reversal is not observed, however, if the target particles are separated by a small distance (not in contact) initially, although a separation still occurs between the striker and middle particle after the collision, with both particles traveling in the same direction. For the case of initially touching target particles, contact duration measurements indicate that the striker separates from the three particles before the two target particles separate. However, when the targets are slightly separated, a threeparticle collision is never observed, and the collision is, in fact, a series of twobody collisions. A subsequent implementation of a variety of hardsphere and softsphere collision models indicates that a threebody (softsphere) treatment is essential for predicting the velocity reversal, consistent with the experimental findings. Finally, a direct comparison between model predictions and measurements of postcollisional velocities and contact durations provides a gauge of the relative merits of existing collision models for threebody interactions.

Numerical simulation of deformation/motion of a drop suspended in viscous liquids under influence of steady electric fields
View Description Hide DescriptionThe deformation/motion of a droplet suspended in a viscousliquid under the influence of an applied external electric field is investigated through numerical simulations in an axisymmetric system. The twophase flow field of the drop suspension system is simulated using a front tracking/finite volume method by solving the full Navier–Stokes equations. Three different electric field models are applied in order to take into account the effects of the electric field,electric charge, and electrical properties of liquids.Drops without net charges but finite electrical conductivity are simulated using a leaky dielectric model. Perfect dielectric model is used for the drops of electrically isolating fluid. To take into account the presence of net charges on dropsurface, we proposed a simplified constant surface charge model. In addition, the simulation code using the leaky dielectric model and perfect dielectric model is validated systematically against the results of theoretical analysis, the available experimental data, and the simulations by other researchers. It shows that the proposed numerical method (front tracking/finite volume method coupled with various electric field models) can make reasonable prediction on droplet deformation/motion under an externally applied electric field. Under different combinations of liquid properties, the droplets may deform into either prolate or oblate shape and induce different inner and outer circulating flow patterns. When net charges are present on the dropletsurface and an electric field is applied, both droplet deformation and motion can be reasonably predicted by the constant charge model. The simulation results demonstrate that the current numerical method may provide an effective approach to quantitatively analyze complex electrohydrodynamic problems.
 Laminar Flows

Direct measurement of slip flows in superhydrophobic microchannels with transverse grooves
View Description Hide DescriptionSlippage effects in microchannels that depend on the surfacecharacteristics are investigated, taking into account hydrophilic,hydrophobic, and superhydrophobic wettabilities. Microscale grooves are fabricated along the vertical walls to form superhydrophobicsurfaces, which enable both the visualization of the flow field near the walls and the direct measurement of the slip length. Velocity profiles are measured using microparticle image velocimetry and those in hydrophilic glass, hydrophobicpolydimethylsiloxane(PDMS), and superhydrophobicPDMS microchannels are compared. For the hydrophilic glass surface, the velocity near the wall smoothly decreases to zero, which is consistent with the wellknown, noslip boundary condition. On the other hand, for the flow in the hydrophobicPDMS microchannel, the velocity profile approaches some finite value at the wall, showing a slip length of approximately . In addition, to directly measure the velocity in the superhydrophobic microchannel, transverse groove structures are fabricated along the vertical walls in the microchannel. For this surface, the velocity profile approaches a value that is larger than that for the PDMS case. Incidentally, instabilities in the velocity profile are observed at the interface with the air gap. Furthermore, the velocity profile near the wall shows a larger slip length than for any of the other experimental setups. For groove structures that are high and wide, the liquidmeniscus forms curves in the cavity so that a wavy flow is created beyond the grooves. Moreover, if the pitchtowidth ratio of the groove structure increases, meniscus penetration into the cavity is observed.
 Instability and Transition

Dynamical analysis of an intermittency in an open cavity flow
View Description Hide DescriptionWhen open flows pass an open cavity, it is known that for medium or large Reynolds numbers, selfsustained oscillations generally appear. When more than one mode is excited, some nonlinear competition between modes may occur. In the configuration investigated here, the underlying dynamics are mainly driven by two dominant modes. The interplay between these two modes is investigated using phase portraits, Poincaré sections, and return maps. The toroidal structure of the phase portrait is then investigated using a symbolic dynamics built from an angular return map. Each symbol can be associated with a specific mode and the interplay described in terms of symbolic sequences, leading to exhibit a switching mode process.

Relative periodic orbits in transitional pipe flow
View Description Hide DescriptionA dynamical system description of the transition process in shear flows with no linear instability starts with knowledge of exact coherent solutions, among them traveling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminarturbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarize.

Viscous and inviscid spatial stability analysis of compressible swirling mixing layers
View Description Hide DescriptionWe examine the viscous and inviscid spatial stabilities of circular swirling mixing layers that differ in swirl intensity, Mach number, and Reynolds number. The corresponding base flows are numerical solutions of the axisymmetric boundarylayer equations in cylindrical coordinates. A highorder numerical discretization scheme based on Chebyshev collocation and a global eigenvalue search are employed to solve the corresponding stability equations. The two disturbance modes that are observed are of centrifugal (or Rayleigh) type and of shearinstability (or Kelvin–Helmholtz) type. The most amplified shear instabilities with higher azimuthal wavenumber possess a longaxialwavelength character and are fed by the axial vorticity arising from the swirl component. Moreover, secondary and higher unstable modes corresponding to the centrifugal instability are observed. Viscosity has a slightly stabilizing effect on the shearinstability disturbances. Centrifugalinstability disturbances with shortazimuthal and short axial wavelengths are stabilized by viscous effects.

Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry
View Description Hide DescriptionRecently, it has been observed that simple geometry characterized by a low level of symmetry present interesting peculiarities in the process of transition from laminar Poiseuille flow to turbulent flow. Examples of this type of geometry are eccentric channels and, more generally, parallel channels containing a narrow gap. In the present work, a global linear stability analysis for the flow in this class of geometry has been performed. The problem is discretized through spectral collocation and the eigenvalue problem has been solved with the Arnoldimethod based algorithms and the QZ algorithm. Since no numerical studies of this type have yet been performed to address the issue of transition in this geometry, the codes have been validated toward results obtained in simplified geometries (e.g., concentric annular channel and square channel). The eigenvalue spectra of the Poiseuille flow in eccentric channels and a Ushaped channel have then been computed and analyzed for a wide range of geometric parameters. After comparison with spectra typical of channel flow and pipe flow it is shown that an additional linear mechanism of instability is present, related to the spanwise variation of the laminar velocity profile.
 Turbulent Flows

Reynolds stress closure for nonequilibrium effects in turbulent flows
View Description Hide DescriptionFrom consideration of turbulenceanisotropydynamics due to spatial or temporal variations in the mean strain rate, a new Reynolds stress closure for nonequilibrium effects in turbulent flows has been developed. This closure, formally derived from the Reynolds stressanisotropy transport equation, results in an effective strain rate tensor that accounts for the strain rate history to which the turbulence has been subjected. In contrast to prior nonequilibrium models that have sought to address nonequilibrium effects via changes in the eddyviscosity, the present approach accounts for nonequilibrium effects in the fundamental relation between the anisotropytensor and the strain rate tensor. The timelocal form of the nonequilibrium closure can be readily implemented in place of the classical equilibrium Boussinesq closure on which most existing computational frameworks are currently based. This new closure is applied here to four substantially different classes of nonequilibrium test problems. Results show dramatically improved agreement with experimental and computational data, without the need to vary any model parameters, when compared with the standard equilibrium closure and with various prior nonequilibrium closures.

The thermal signature of a low Reynolds number submerged turbulent jet impacting a free surface
View Description Hide DescriptionThe thermal signature of a low Reynolds numberturbulent jet impacting a free surface was investigated experimentally. Three Reynolds numbers (1000, 3000, and 4800) were investigated for a configuration in which the jet nozzle diameter and the depth of the jet beneath the free surface were fixed. A high resolution infrared detector was used to collect thermal imagery of the surface temperature field. These data were then used to examine the detailed statistical nature of the resulting coupled thermalhydrodynamic field. The analysis included an examination of the instantaneous, mean, and fluctuating surface thermal fields. Examination of the instantaneous fields strongly suggested the existence of a turbulent core region and a weaker outer region. The existence of this innerouter structure associated with the surfaceflow was confirmed by a detailed examination of the mean surface temperature fields. In addition, the outer structure of the mean surface temperature appeared to correspond well with the existence of a surface current first observed by Anthony and Willmarth [“Turbulence measurements in a round jet beneath a free surface,” J. Fluid Mech.243, 699 (1992)]. A selfsimilar region of the temperature field associated with the turbulent core was also clearly identified. Finally, the statistics of the surface thermal fluctuation fields were examined. These statistics revealed high thermal fluctuations near the edge of the flow field associated with flow intermittency there, as well as evidence of surface capillary waves which were generated as a result of the jetsurface interaction. In addition, the thermal fluctuation field was further examined using a Karhunen–Loeve analysis.

Modeling dilute sediment suspension using largeeddy simulation with a dynamic mixed model
View Description Hide DescriptionTransport of suspended sediment in high Reynolds number channel flows is simulated using largeeddy simulation along with a dynamicmixed model (DMM). Because the modeled sediment concentration is low and the bulk Stokes’ number is small during the simulation, the sediment concentration is calculated through the use of the Eulerian approach. In order to employ the DMM for the suspended sediment, we formulate a generalized bottom boundary condition in a finitevolume formulation that accounts for sediment flux from the bed without requiring specific details of the underlying turbulencemodel. This enables the use of the pickup function without requiring any assumptions about the behavior of the eddyviscosity. Using our new boundary condition, simulations indicate that the resolved component of the vertical flux is one order of magnitude greater than the resolved subfilterscale flux, which is in turn one order of magnitude greater than the eddydiffusive flux. Analysis of the behavior of the suspended sediment above the bed indicates the existence of three basic time scales that arise due to varying degrees of competition between the upward turbulent flux and downward settling flux. Instantaneous sediment concentration and velocity fields indicate that streamwise vortices account for a bulk of the resolved flux of sediment from the bed.