Volume 19, Issue 4, April 2007

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into largerscale structures are discussed. Evidence for a largescale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.
 AWARD AND INVITED PAPERS


Hairpin vortex organization in wall turbulence^{a)}
View Description Hide DescriptionCoherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into largerscale structures are discussed. Evidence for a largescale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.
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 LETTERS


Lowvariance deviational simulation Monte Carlo
View Description Hide DescriptionWe present and discuss a particle simulation method for solving the Boltzmann equation which incorporates the variance reduction ideas presented in L. L. Baker and N. G. Hadjiconstantinou [Physics of Fluids17, 051703 (2005)]. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage for low speed flows compared to traditional particle methods such as the direct simulation Monte Carlo (DSMC). More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium (e.g., low flow speed) at a computational cost that does not scale with the magnitude of the deviation from equilibrium, while maintaining the basic algorithmic structure of DSMC.

Extension of compressible idealgas rapid distortion theory to general mean velocity gradients
View Description Hide DescriptionThe homogeneity condition in compressible flows requires that mean velocity gradient and mean thermodynamic variables must be spatially invariant. This has restricted the use of rapid distortion theory (RDT) for compressible flows to a small set of meanvelocity gradients. By introducing an appropriate body force, we show that the homogeneity condition can be satisfied for a large class of compressible turbulence. We proceed to derive RDT spectral covariance equations of all relevant moments and recover the limiting behavior at vanishing and infinite (pressurerelease) Mach numbers for homogeneous shear, plainstrain, axisymmetric expansion, and contraction cases.

Heartshaped bubbles rising in anisotropic liquids
View Description Hide DescriptionThis Letter reports on numerical simulations motivated by experimental observations of an unusual invertedheart shape for bubbles rising in an anisotropicmicellar solution. We explain the bubble shape by assuming that the micelles are aligned into a nematic phase, whose anchoring energy on the bubble competes with the interfacial tension and the bulk elasticity of the nematic to modify the interfacial curvature. Numerical results show that bubbles with sufficiently strong planar anchoring rising in a vertically aligned nematic indeed assume the observed shape. The parameter values required are compared with the experimental materials and conditions.
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 ARTICLES

 Interfacial Flows

Experiments on bubble pinchoff
View Description Hide DescriptionA bubble is slowly grown from a vertical nozzle until it becomes unstable and pinches off. We use ultrahighspeed video imaging, at framerates up to , to study the dynamics and shape of the pinchoff neck region. For bubbles in water the radius of the neck reduces with a power law behavior , over more than 2 decades, with an exponent in the range , in good agreement with other available studies, but which is slightly larger than predicted by RayleighPlesset theory. The vertical curvature in the neck increases more slowly than the azimuthal curvature, making the neck profiles more slender as pinchoff is approached. Selfsimilar shapes are recovered by normalizing the axial coordinate by a separate length scale which follows a different power law, , where . Results for air, He, and gas are identical, suggesting that the gas density plays a minimal role in the dynamics. The pinchoff in water leaves behind a tiny satellitebubble, around in diameter and the flowfield inside the liquid is shown to be consistent with simple sink flow. The effects of liquid viscosity on the pinchoff speed and neck shapes, are also characterized. The speed starts to slow down at a viscosity of about 10 times that of water, which corresponds to . This also changes the power law, increasing the exponent to for viscosities above . For surrounding liquid of viscosity above , we observe just before pinchoff, that the neck is stretched into a thin filament of air, which then breaks into a stream of microbubbles. In some cases we observe a cascade of bubble sizes. While some of the details differ, our results are in overall agreement with those of Burton, Waldrep, and Taborek [Phys. Rev. Lett.94, 184502 (2005)], except we do not observe the rupture of the air cylinder as it reduces to size. For water we observe a continuous necking down to the pixelresolution of our optical system, which at the largest framerates is .

Liquid film dynamics in horizontal and tilted tubes: Dry spots and sliding drops
View Description Hide DescriptionUsing a model derived from lubrication theory, we consider the evolution of a thin viscousfilm coating the interior or exterior of a cylindrical tube. The flow is driven by surface tension and gravity and the liquid is assumed to wet the cylinder perfectly. When the tube is horizontal, we use largetime simulations to describe the bifurcationstructure of the capillary equilibria appearing at low Bond number. We identify a new film configuration in which an isolated dry patch appears at the top of the tube and demonstrate hysteresis in the transition between rivulets and annular collars as the tube length is varied. For a tube tilted to the vertical, we show how a long initially uniform rivulet can break up first into isolated drops and then annular collars, which subsequently merge. We also show that the speed at which a localized drop moves down the base of a tilted tube is nonmonotonic in tilt angle.

Transient enhancement of thermocapillary flow in a twodimensional cavity by a surfactant
View Description Hide DescriptionIn this paper, we present results of a numerical study of the effect of insoluble surfactants on thermocapillary flow in a twodimensional slot. For surfactantladen systems, there are pronounced nonlinearities in the surface tension dependence on both temperature and surface concentration, some of which create interesting phenomena that cannot be captured by the linear limit used in prior work. Our work focuses on two regimes of nonlinear coupling between the surface tension,surface concentration, and surface temperature. First, we address a surfactant that forms a monolayer in a single surface phase. Second, we discuss a regime in which surfactants transiently enhancethermocapillary flow, rather than oppose it. This occurs for long chain surfactants with small headgroups that form liquidexpanded (LE) and liquidcondensed (LC) phases, e.g., (insoluble) longchain carboxylicacids under conditions where their headgroups are not disassociated. Results indicate that a surfactant in LE/LC coexistence initially enhances thermocapillary flow in a slot, creating a surface convective flux that rapidly convects surfactant toward the cold region and depletes the warm region. However, the convection of surfactant quickly drives the surface concentration out of LE/LC coexistence and into LE (in the depleted region) and LC (in the cold region). Thereafter, the rapid initial flow is again quenched by the usual circumstance of a surfactant in a single surface phase exerting an opposing Marangoni stress that stagnates the interface. At high surface Peclet numbers, no steadystate thermocapillary flow is sustained.

Cornered drops and rivulets
View Description Hide DescriptionWe present theoretical and experimental results for a drop of viscous liquid running down an inclined plane at speed . For the rear of the drop forms a corner whose opening halfangle decreases with . By matching the interior of the drop to the contact line, we calculate analytically. We find that above a second critical speed this solution no longer exists and instead a slender rivulet comes out of the tip of the corner. To compute the width of the rivulet, we match it to the front of the drop, where it is rounded. Our theoretical results on the opening angle, the rivulet width and the drop velocity are in good agreement with experiment.

Quantitative numerical and experimental studies of the shock accelerated heterogeneous bubbles motion
View Description Hide DescriptionThis work deals with quantitative comparisons between experimental and numerical results for shockbubbles interactions. The bubbles are filled with three different gases (nitrogen, krypton and helium) surrounded by air in order to investigate all kind of density jumps across the interface. For each case, three incident shock wave intensities are also studied. The experiments are led by using a shock tube coupled with a visualization diagnostic device: the T80 shock tube [G. Jourdan, L. Houas, L. Schwaederlé, G. Layes, R. Carrey, and F. Diaz, “A new variable inclination shock tube for multiple investigations,” Shock Waves13, 501 (2004)]. Considering the same initial and geometrical conditions, the numerical results are obtained with the help of a recent numerical method: the discrete equations method [R. Abgrall and R. Saurel, “Discrete equations for physical and numerical compressible multiphase mixtures,” J. Comput. Phys.186, 361 (2003); R. Saurel, S. Gavrilyuk, and F. Renaud, “A multiphase model with internal degrees of freedom: Application to shockbubble interaction,” J. Fluid Mech.495, 283 (2003); A. Chinnayya, E. Daniel, and R. Saurel, “Modelling detonation waves in heterogeneous energetic materials,” J. Comput. Phys.196, 490 (2004); O. Le Métayer, J. Massoni, and R. Saurel, “Modelling evaporation fronts with reactive Riemann solvers,” J. Comput. Phys.205, 567 (2005)], devoted to the computation of interface problems as well as multiphase mixtures. For each configuration, the quantitative comparisons are in good agreement showing the capability of both methods (numerical and experimental) to describe complex physical flows.
 Particulate, Multiphase, and Granular Flows

Static and flowing regions in granular collapses down channels
View Description Hide DescriptionThrough laboratory experiments we investigate inertial granular flows created by the instantaneous release of particulate columns into wide, rectangular channels. These flows are characterized by their unsteady motion, large changes of the free surface with time, and the propagation towards the free surface of an internal interface separating static and flowing regions. We present data for the timedependent geometry of the internal interface and the upper, free surface for aspect ratios, , in the range from 3 to 9.5 (where is the ratio of the initial height to basal width of the column). The data were analyzed by two different approaches. First, by integrating under the entire internal interface we obtained data for the static area, , as a function of time for different . Second, in order to characterize vertical deposition rates, we measured the thicknesses of the flowing region, , and the static region, , at fixed horizontal positions, , and time, , since the initiation of the experiment. We also determined detailed velocity profiles with depth at distances scaled to the final maximum runout distance to analyze the kinematic behavior of the flowing layer. In the initial freefall phase, the temporal variation of the static area is independent of and scales as . During the subsequent lateral spreading phase, varies linearly with time and the nondimensional deposition rate is a linear function of . The thickness of the interface at constant depends on and varies linearly with time. The local deposition rate is not constant along the flow length. Data show that for the major part of the flow length is constant. In the lateral spreading phase, the velocity profiles are characteristically linear with a basal exponential region, a few grains in thickness, which separates static from moving regions. The shear rate is a constant dependent on a modified initial height as , where is a characteristic length scale in the system describing the fraction of the granular column actually involved in the flowing region.

Gasliquid twophase flow across a bank of micropillars
View Description Hide DescriptionAdiabatic nitrogenwater twophase flow across a bank of staggered circular micropillars, long with a diameter of and a pitchtodiameter ratio of 1.5, was investigated experimentally for Reynolds number ranging from 5 to 50. Flow patterns, void fraction, and pressure drop were obtained, discussed, and compared to large scale as well as microchannel results. Twophase flow patterns were determined by flow visualization, and a flow map was constructed as a function of gas and liquid superficial velocities. Significant deviations from conventional scale systems, with respect to flow patterns and trend lines, were observed. A unique flow pattern, driven by surface tension, was observed and termed bridge flow. The applicability of conventional scale models to predict the void fraction and twophase frictional pressure drop was also assessed. Comparison with a conventional scale void fraction model revealed good agreement, but was found to be in a physically wrong form. Thus, a modified physically based model for void fraction was developed. A twophase frictional multiplier was found to be a strong function of mass flux, unlike in previous microchannel studies. It was observed that models from conventional scale systems did not adequately predict the twophase frictional multiplier at the microscale, thus, a modified model accounting for mass flux was developed.
 Laminar Flows

Nonlinear laminar pipe flow of fluids with strongly temperaturedependent material properties
View Description Hide DescriptionWe study a onedimensional model describing the laminar flow of a highly viscous fluid representing glass melt in a pipe. The flow is influenced by Lorentz force and gravity as well as temperature variation due to wall heat loss, electrical heating, advection, and heat diffusion. We take into account the full nonlinear temperature dependence of the viscosity and the electrical conductivity. For high and very low driving forces the mean velocity is found to be proportional to the forces as known from laminar pipe flow with constant material parameters. In between these two regimes, however, we identify a new flow regime. If there are no heat losses through the wall the mean velocity is proportional to the square root of the driving force. In the presence of wall heat loss the solution for the steady flow is even found to be nonunique, and to involve bifurcations for a wide range of parameters. This nonlinear behavior is shown to be a result of the closedloop interaction between the velocity, temperature, and temperaturedependent material properties.

Boundaryintegral method for drop deformation between parallel plates
View Description Hide DescriptionA new boundaryintegral method is proposed to study the deformation of drops between two parallel walls. The freespace Green’s functions are extended to obey the noslip condition at the walls. The current formulation is limited to drops with viscosity equal to the matrix fluid, but can be extended to study the effect of nonunit viscosity ratio systems. With this method, the influence of the capillary number and the degree of confinement on dropdeformation is investigated. Results for small capillary are compared with smalldeformation theory and large capillary results with recent experiments. In both cases, an excellent match is observed. Drops undergoing shear flowdeform stronger and align themselves more in the flow direction as the distance between the walls becomes smaller relative to the drop size. Furthermore, the shapes of the drops start to divert significantly from the normal ellipsoidal shapes found, as they show more pointed tips closer to the walls. The transient deformation behavior for more confined systems shows that the drops stretch out to a maximum value, and they slowly retract again to a steady situation. For larger capillary numbers even damped, oscillatory behavior is observed. Investigating the critical capillary number reveals that a minimum is found at a mediocre degree of confinement, after which the critical capillary number increases again to values even larger than the unconfined system. The breakup mode also makes a significant change as it goes from binary to ternary breakup, where the breakup occurs as the drop is retracting.

A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces
View Description Hide DescriptionA type of superhydrophobicsurface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with the flow. The pressure difference between the liquid and the gas in the grooves causes a curvature of the liquid surface resisted by surface tension. The effects of this surface deformation are studied in this paper. The corrections to the effective slip length produced by the curvature are analyzed theoretically and a comparison with available data and related mathematical models is presented.

A regime diagram for premixed flame kernelvortex interactions
View Description Hide DescriptionDirect numerical simulations of flame kernelvortex interactions are implemented in an axisymmetric configuration using a twostep global mechanism to study the different combustion regimes of the interactions. Four combustion regimes have been identified. They include: (1) the “laminar kernel” regime, (2) the “wrinkled kernel” regime, (3) the “breakthrough” regime, and (4) the “global extinction” regime. Transitions from different regimes are achieved through variations of the vortex strength, and operation in each regime is governed by two key parameters, the ratio of the vortex translational velocity to the laminar flame speed and the ratio of the kernel size to the vortex size at the onset of the interactions. Qualitative and quantitative comparisons between the flame responses in the different regimes are presented. A regime diagram is constructed based on the key parameters that control transition between the different regimes. The diagram bears some similarities with other diagrams based on planar flamevortex interactions. However, it also offers additional features that constitute refinements to the existing diagrams of which the role of interaction of a vortex with an already curved flame is important.
 Instability and Transition

Capillary instabilities of liquid films inside a wedge
View Description Hide DescriptionWe consider a liquidmeniscus inside a wedge of included angle that wets the solid walls with a contact angle . The meniscus has a convex interface that satisfies . The capillary pressure gradient due to a small disturbance of the location of the contact line moves fluid from a neck region to a bulge region, causing instabilities. A dynamic contactline condition is considered in which the contact angle varies linearly with the slipping speed of the contact line with a slope of representing perfect slip and a fixed contact angle. A nonlinear thin film equation is derived and numerically solved for the shape of the contact line as a function of parameters. The result for shows that the evolution process consists of a successive formation of bulges and necks in decreasing length and time scales, eventually resulting in a cascade structure of primary, secondary, and tertiary droplets. When , there is a similar but slower nonlinear evolution process. The numerical results agree qualitatively with very recent experimental results.

Pipe flow transition threshold following localized impulsive perturbations
View Description Hide DescriptionA numerical study of the destabilizing effects of localized impulsive perturbations in pressuredriven HagenPoiseuille or pipe flow is presented. The numerics intend to ellucidate the intrinsic mechanisms of subcritical transition to turbulence in pipe flow by reproducing very recent experimental explorations carried out by Hof, Juel, and Mullin [Phys. Rev. Lett.91, 244502 (2003)], concluding that the minimum amplitude of a perturbation required to cause transition scales as the inverse of the Reynolds number, i.e., . The numerical model simulates the experimental disturbance generator based on impulsive injection of fluid through six slits azimuthally equispaced on a perimeter around the pipe. This is accomplished by introducing a local timedependent impulsive volume force term in the NavierStokes equations for the perturbation velocity field, fulfilling incompressibility constraints. A comprehensive exploration of the critical amplitudes that trigger transition as a function of the injection duration is carried out. It is concluded, in agreement with experiments, that injections lasting longer than advective time units do not remarkably decrease the critical amplitude of transition. Threshold amplitudes for long enough injections are then computed within the range . For the numerical results agree with the experiments. However, for , neat transitions are very difficult to obtain, being impossible to provide an accurate value of the critical amplitude. The apparent disagreement with the sound regular slope of the experimental threshold is explained in terms of the differences between constant massflux versus pressuredriven pipe flows.

Linear stability of thermocapillary flow in partially confined halfzones
View Description Hide DescriptionThe thermocapillary flow in cylindrical halfzones is investigated numerically for lowPrandtlnumber fluids. We consider a configuration in which part of the cylindrical surface is covered by a very thin rigid film and another part is uncovered, supporting thermocapillary stresses. The steady axisymmetric flow is calculated by finite differences. Besides the aspect ratio, the structure of the toroidal vortexflow depends strongly on the location and relative size of the cylindrical freesurface strip. The stability with respect to arbitrary threedimensional perturbations of the steady twodimensional flow is investigated by a linear stability analysis. The critical Reynolds numbers and the physical mechanisms are analyzed depending on the aspect ratio of the liquid bridge, the axial position of the uncovered part of the surface, and the freesurface fraction , i.e., the ratio of the height of the free surface to the full height of the liquid zone. When only a small area of the liquid zone is covered by the solid film, i.e., , the wellknown stationary instability for the conventional unconfined halfzone is recovered, which is driven by a combination of the elliptic and the centrifugal mechanism. Decreasing , new instabilities can appear. It is found that all critical modes are likewise driven by the elliptic mechanism, the centrifugal mechanism, or a combination of both. When the unconfined free surface is located adjacent to the hot wall, the linear stability boundary shows an intricate behavior. Four qualitatively different instability modes can arise depending on the freesurface fraction and the aspect ratio. One of the timedependent modes that is strongly driven by the elliptic mechanism resembles an oscillatory Kelvin mode on a strained vortex. The other oscillatory modes show a different behavior as they are mainly driven by centrifugal mechanisms. Quite generally, the importance of the elliptic mechanism diminishes as is further decreased until, for a very small freesurface fraction , an instability appears that is purely centrifugal and stationary. When the free surface is located next to the cold wall, the types of instabilities are the same as for the unconfined halfzone, and the azimuthal wave numbers increase with decreasing .
 Turbulent Flows

Spectral imbalance and the normalized dissipation rate of turbulence
View Description Hide DescriptionThe normalized turbulent dissipation rate is studied in decaying and forced turbulence by direct numerical simulations, largeeddy simulations, and closure calculations. A large difference in the values of is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of at low Reynolds number that is observed in the simulations.

Determination of the coefficients of Langevin models for inhomogeneous turbulent flows by threedimensional particle tracking velocimetry and direct numerical simulation
View Description Hide DescriptionA promising and, in terms of computer power, lowcost way of describing flow properties such as turbulent diffusion is by Langevin models. The development of such models requires knowledge of Lagrangian statistics of turbulent flows. Our aim is to determine Lagrangian statistics of inhomogeneous flows, as most turbulent flows found in practical applications are inhomogeneous. The present paper describes how a Lagrangianmeasurement technique, threedimensional particle tracking velocimetry, has been developed and applied to the most common example of inhomogeneous flows:turbulent pipe flow. A new direct numerical simulation (DNS) code has been developed and experimental results have been compared with results of this DNS code. The results concern Eulerian and Lagrangianvelocity statistics at two Reynolds numbers. Based on these, coefficients of the Langevin model have been determined and physical consequences for Langevin modeling and turbulent dispersion have been explained.