Volume 16, Issue 6, June 2004
 SPECIAL SECTION


Flow induced coalescence of drops in a viscous fluid
View Description Hide DescriptionThis paper summarizes recent experimental studies of flowinduced coalescence of viscousdrops in a viscous fluid in the absence of inertial effects. These studies are based on visual observations of small drops (20–100 μm diameter) that collide in the linear flows generated by a fourroll mill. We consider a pair of polymeric fluids that are Newtonian under the flow conditions relevant to coalescence phenomena, and in addition consider the effect of adding a “copolymer” of the two polymers to the interface, which acts as a surfactant. By direct observation, we can generate quantitative data on the collision trajectories and the conditions for coalescence. These observations have also uncovered several “new” phenomena. Among these are the fact that coalescence frequently occurs during the part of the collision after the drops have already rotated to a configuration where they are being pulled apart by the external flow. This occurs for at least some of the collision trajectories for all fluids where the viscosity ratio of the drop to suspending fluid exceeds 0.1. It is also favored by the addition of surfactant to the drop. We also find that the conditions for coalescence are indicative of a complicated history of film configurations during the “draining” or thinning process, with minimum film thickness (or at least the most unstable configuration) occurring early in the collision, considerably prior to the point where the force along the line of centers changes sign and the drops begin to be pulled apart by the external flow.

Bubbles
View Description Hide DescriptionVanitas vanitatum et omnia vanitas: bubbles are emptiness, nonliquid, a tiny cloud shielding a mathematical singularity. Born from chance, a violent and brief life ending in the union with the (nearly) infinite. But a wealth of phenomena spring forth from this nothingness: underwater noise,sonoluminescence, boiling, and many others. Some recent results on a “blinking bubble” micropump and vapor bubbles in sound fields are outlined. The last section describes Leonardo da Vinci’s observation of the nonrectlinear ascent of buoyant bubbles and justifies the name Leonardo’s paradox recently attributed to this phenomenon.
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 ARTICLES


Large eddy simulation and experimental measurements of the nearfield of a large turbulent helium plume
View Description Hide DescriptionLarge eddy simulations(LES) are conducted of a large, 1 m in diameter, turbulent helium plume. The plume instability modes and flowdynamics are explored as a function of grid resolution with and without the use of subgrid scale (SGS) models.LES results reproduce wellestablished varicose puffing mode instabilities as well as secondary “fingerlike” azimuthal instabilities leading to the breakdown of periodically shed toroidal vortices. Simulation results of timeaveraged velocity and concentration fields show excellent agreement with experimental data collected from Sandia’s FLAME facility using particle image velocimetry and planar laser induced fluorescence measurement techniques. For locations very near the base of the plume, i.e., the LES overpredicts the measured rootmean squared streamwise velocity and concentration and, in addition, is found to be highly sensitive to grid resolution. The cause of these discrepancies is attributed to unresolved buoyancyinduced vorticity generation on resolved scales of fluid motion that is currently not explicitly treated in the SGS turbulencemodels used for the LES.

Direct numerical simulation of a transitional temporal mixing layer laden with multicomponentfuel evaporating drops using continuous thermodynamics
View Description Hide DescriptionA model of a temporal threedimensional mixing layer laden with fuel drops of a liquid containing a large number of species is derived. The fuel model is based on continuous thermodynamics, whereby the composition is statistically described through a distribution function parametrized on the species molar weight. The drop temperature is initially lower than that of the carrier gas, leading to drop heat up and evaporation. The model describing the changes in the multicomponent (MC) fuel drop composition and in the gas phase composition due to evaporation encompasses only two more conservation equations when compared with the equivalent singlecomponent (SC) fuel formulation. Single drop results of a MC fuel having a sharply peaked distribution are shown to compare favorably with a validated SCfuel drop simulation. Then, single drop comparisons are performed between results from MC fuel and a representative SC fuel used as a surrogate of the MC fuel. Further, two mixing layer simulations are conducted with a MC fuel and they are compared to representative SCfuel simulations conducted elsewhere. Examination of the results shows that although the global layer characteristics are generally similar in the SC and MC situations, the MC layers display a higher momentumthicknessbased Reynolds number at transition. Vorticity analysis shows that the SC layers exhibit larger vortical activity than their MC counterpart. An examination of the drop organization at transition shows more structure and an increased dropnumber density for MC simulations in regions of moderate and high strain. These results are primarily attributed to the slower evaporation of MCfuel drops than of their SC counterpart. This slower evaporation is due to the lower volatility of the higher molar weight species, and also to condensation of alreadyevaporated species on drops that are transported in regions of different gas composition. The more volatile species released in the gas phase earlier during the drop lifetime reside in the lower stream while intermediary molar weight species, which egress after the drops are entrained in the mixing layer, reside in the mixing layer and form there a very heterogeneous mixture; the heavier species that evaporate later during the drop lifetime tend to reside in regions of high dropnumber density. This leads to a segregation of species in the gas phase based on the relative evaporation time from the drops. The ensembleaverage drop temperature becomes eventually larger/smaller than the initial drop temperature in MC/SC simulations. Neither this species segregation nor the drop temperature variation with respect to the initial temperature or as a function of the mass loading can be captured by the SCfuel simulations.

Viscous fingering instabilities in an oil in water emulsion
View Description Hide DescriptionViscous fingering of an emulsion in which silicone oil is dispersed in aqueous polymer solution was investigated in a radial HeleShaw cell by the injection of water and the aqueous polymer solution as a function of the injection rate. The pressure imposed at the finger tip was simultaneously monitored. The cracklike fingering patterns are observed at the lower injection rates and they start to grow when the imposed pressure attains the maximum value. An increase in the injection rate causes the pattern transition from the crack pattern to ramified ones. Such a pattern transition is strongly related to rheological properties of the emulsion.

On the transverse instability of the twodimensional Benjamin–Ono solitons
View Description Hide DescriptionThe paper presents a stability analysis of plane solitons in hydrodynamicshear flows obeying a (2+1) analogue of the Benjamin–Ono equation. The analysis is carried out for the Fourier transformed linearized (2+1) Benjamin–Ono equation. The instability region and the shortwave instability threshold for plane solitons are found numerically. The numerical value of the perturbation wave number at this threshold turns out to be constant for various angles of propagation of the solitons with respect to the main shear flow. The maximum of the growth rate decreases with the increasing angle and becomes equal to zero for the perpendicular propagation. Finally, the dependency of the growth rate on the propagation angle in the longwave limit is determined and the existence of a critical angle which separates two types of behavior of the growth rate is demonstrated.

Instability of electrokinetic microchannel flows with conductivity gradients
View Description Hide DescriptionElectrokineticflow is leveraged in a variety of applications, and is a key enabler of onchip electrophoresis systems. An important subclass of electrokinetic devices aim to pump and control electrolyte working liquids with spatial gradients in conductivity. These highgradient flows can become unstable under the application of a sufficiently strong electric field. In this work the instability physics is explored using theoretical and numerical analyses, as well as experimental observations. The flow in a long, rectangularcrosssection channel is considered. A conductivity gradient is assumed to be orthogonal to the main flow direction, and an electric field is applied in the streamwise direction. It is found that such a system exhibits a critical electric field above which the flow is highly unstable, resulting in fluctuating velocities and rapid stirring. Modeling results compare well with experimental observations. The model indicates that the fluid forces associated with the thin dimension of the channel (transverse to both the conductivity gradient and the main flow direction) tends to stabilize the flow. These results have application to the design and control of onchip assays that require high conductivity gradients, and provides a rapid mixing mechanism for low Reynolds number flows in microchannels.

Observation of nearcritical reflection of internal waves in a stably stratified fluid
View Description Hide DescriptionAn experimental study is reported of the nearcritical reflection of internal gravity waves over sloping topography in a stratified fluid. An overturning instability close to the slope and triggering the boundarymixing process is observed and characterized. These observations are found in good agreement with a recent nonlinear theory.

Inferred pressure gradient and fluid flow in a condensing sessile droplet based on the measured thickness profile
View Description Hide DescriptionThe thickness and curvature profiles of partially wetting condensing drops of 2propanol on a quartzsurface were measured using image analyzing interferometry and a new data analysis procedure. The profiles give fundamental insight into the phenomena of phase change, pressure gradient, fluid flow and spreading in a condensing drop, and the physics of interfacial phenomena in the contact line region of a polar fluid. The precursor adsorbed film and interfacial slope (a measure of the contact angle) and curvature profiles are consistent with previous concepts based on interfacial models. The curvature profiles, which were obtained using a new data reduction procedure, clearly demonstrate the convex nature of the drop near the thicker part (negative value of curvature), whereas, in the thinner region, the drop is concave (positive curvature) where the partially wettingliquid merges with a flat adsorbed film. The pressure profiles inside the drop are calculated from the augmented Young–Laplace equation showing that the pressure gradient increases with an increase in the spreading velocity (rates of condensation) to support the higher liquidflow rates associated with the growth of the drop. Internal flow is towards the point of maximum positive curvature from both the thin film and convex regions. Apolar and polar components of the spreading coefficient help describe the interfacial phenomena occurring. The experimental techniques are relatively simple but very revealing.

On the probability density function model for the transport of particles in anisotropic turbulent flow
View Description Hide DescriptionThe purposes of the paper are twofold: (i) to present a rational approach to the modeling of inertial particle transport in anisotropicturbulent flows and (ii) to show how the anisotropy of fluid turbulence timescales affects the particle fluctuatingvelocities in homogeneous shear flow. For these purposes, the directional dependence of the Lagrangian autocorrelations of fluid velocities is incorporated into the statistical probability density function (PDF) model proposed previously. The anisotropic timescale (ATS) model is evaluated against numerical simulations for homogeneous shear turbulent flows and is compared to results predicted by the isotropic timescale (ITS) model. The new ATS model for the PDF of the particle velocity distribution in turbulent flow appears to yield slightly improved results over the ITS model.

Effects of nonperfect thermal sources in turbulent thermal convection
View Description Hide DescriptionThe effects of the plates thermal properties on the heat transfer in turbulent thermal convection are investigated by direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation. It has been found that the governing parameter is the ratio of the thermal resistances of the fluid layer and the plates when this ratio is smaller than a threshold value arbitrarily defined by requiring that the actual heat transfer differs by less than 2% from its ideal value), the finite conductivity of the plates limits the heat transfer in the cell. In addition, since decreases for increasing Rayleigh numbers, any experimental apparatus is characterized by a threshold Rayleigh number that cannot be exceeded if the heat transfer in the cell has not to be influenced by the thermal properties of the plates. It has been also shown that the plate effects cannot be totally corrected by subtracting the temperature drop occurring within the plates from the measured total temperature difference. This is due to the changes produced in the thermal plume dynamics by the reduced local heat flux at the plate/fluid interface. A model with a correction factor has been derived to account for the plates effects and it gave the appropriate correction for a recent experiment in which the heat transfer measurements were systematically smaller than a theoretical prediction. In view of the present correction the discrepancy between theory and experiments addressed by Nikolaenko and Ahlers [Phys. Rev. Lett. 91, 084501 (2003)] can be therefore resolved. The application of the proposed correction to the results in the literature can also reconcile the heat transfer measurements for water and mercury that appear systematically smaller than in other fluids.

A singular value analysis of boundary layer control
View Description Hide DescriptionSeveral approaches for boundarylayer control are analyzed from a linear system point of view. The singular value decomposition (SVD) is applied to the linearized Navier–Stokes system in the presence of control. The performance of control is examined in terms of the largest singular values, which represent the maximum disturbance energy growth ratio attainable in the linear system under control. It is shown that the maximum growth ratio is less in controlledsystems than in the uncontrolled system only when control parameters are within a certain range of values. With opposition control, for example, when the detection plane is located too far away from the wall, the maximum energy growth ratio is larger, consistent with the results observed in direct numerical simulations. The SVD analysis of other controls also shows a similarity between the trend observed in the SVD analysis (linear) and that observed in direct numerical simulations (nonlinear), thus reaffirming the importance of linear mechanisms in the nearwall dynamics of turbulent boundary layers. The present study illustrates that the SVD analysis can be used as a guideline for designing controllers for drag reduction in turbulent boundary layers.

Numerical analysis of the shear flow of a binary mixture of hardsphere gases over a plane wall
View Description Hide DescriptionThe shear flow of a binary mixture of rarefied gases over a plane wall is investigated on the basis of the linearized Boltzmann equation for hardsphere molecules with the diffuse reflection boundary condition. This fundamental problem in rarefied gas dynamics is analyzed numerically by a finitedifference method, in which the complicated collision integrals are computed by the extension to the case of a gas mixture of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)]. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, an accurate formula of the shearslip (viscousslip) coefficient for arbitrary values of the concentration of a component gas is constructed by the use of the Chebyshev polynomial approximation.

A new method of modeling the conditional scalar dissipation rate
View Description Hide DescriptionA new method for calculating the conditional scalar dissipation rate is derived from the probability density function (pdf) transport equation for the conserved scalar Z. Two different formulations are obtained. One is the result of direct integration of the pdf transport equation and the second is further developed assuming a twoparameter presumed form for the pdf. A linear model is used for the conditional velocity. The model is compared with a direct numerical simulation (DNS) of inhomogeneous turbulent mixing. The results are in very good agreement with the DNS and perform better than Girimaji’s model which is based on homogeneous flow properties. Further validation with some experimental data would be useful. The new method has also the potential of being easily implemented in a finitevolumecomputational fluid dynamics code.

The adjoint filter operator in largeeddy simulation of turbulent flow
View Description Hide DescriptionAdjoint and selfadjoint filter operators are introduced, such that largeeddy simulation(LES) with a spatially variable filter width satisfies important physical properties: Conservation of momentum and dissipation of kinetic energy. The combination of an arbitrary nonuniform explicit filter with the Smagorinsky model leads to a new model of the turbulent stress tensor, which includes backscatter, while the total subgrid dissipation is still positive (analytically). Nonuniform filter theory is further developed, in order to provide a more solid foundation of practical LES. The paper distinguishes between three sets of equations: The Navier–Stokes equations (which are physical conservation laws), the filtered equations and the modeled largeeddy equations. It is shown that general filtering of the Navier–Stokes equations destroys their local and global conservation properties. However, it is proven that the adjoint of a normalized filter is conservative. As a result, the filtering equations are globally conservative, for special nonuniform (e.g., selfadjoint) filters. Implications for six subgridmodels that require explicit filter operations are considered, such as dynamic, similarity, filtering multiscale, and relaxation models. Incorporation of the adjoint filter analytically ensures several models to conserve momentum and dissipate kinetic energy. Examples of adjoint and selfadjoint filters are also provided, including a “threepoints” selfadjoint filter and an adjoint filter that is applicable on unstructured grids. In addition, it is shown that positive nonuniform (selfadjoint) filters satisfy mathematical smoothing properties. The focus is on kernel filters, but projection filters are also discussed, and nonuniform selfadjoint Laplace filters are defined. The (orthogonal) projection operator is proven to be a nonuniform kernel filter.

Effect of electrically conducting walls on rotating magnetoconvection
View Description Hide DescriptionIn an experiment carried out by Aurnou and Olson [J. Fluid Mech. 430, 283 (2001)] thermal convection in a liquid gallium layer in the presence of a uniform vertical magnetic field was investigated. The critical Rayleigh number at the onset of magnetoconvection was determined as a function of the Chandrasekhar number Q (the ratio of the Lorentz force to the viscous force) and the Taylor number (the squared ratio of the Coriolis force to the viscous force). In the experimental apparatus, the upper and lower boundaries of the liquid gallium layer were electrically conducting copper plate walls. This paper presents a study of the effect of electrically conducting walls on rotating magnetoconvection. It is shown that the electrical properties of the walls have significant effects on the characteristics of rotating magnetoconvection when both the Chandrasekhar number Q and the Taylor number are sufficiently large. It is demonstrated that, as a consequence of the electrically conducting walls, oscillatory magnetoconvection can become steady and the critical Rayleigh number can change by as much as 60%. The problem of convectively driven Alfvén waves in a rotating fluid layer in the presence of a uniform vertical magnetic field is discussed in an appendix.

Interfacial shearstress effects on transient capillary wedge flow
View Description Hide DescriptionThe effects on the transient capillary flow in a wedge due to the interfacial shearstress distribution S along the flow direction z is studied theoretically. With the assumptions of a slender liquid column and negligible gravitational and inertia effects, the problem is reduced to finding the axial velocity distribution at any cross section. The propagation of the liquid column and the tip location are then solved with the aid of the continuity equation. When the halfwedge angle α, the contact angle θ, and the shearstress distribution on the free surfaceS are constant, analytic solutions exist. Otherwise, numerical simulation has to be applied. The results indicate that when is acting in the flow direction, the flow is strengthened and the liquid column propagates faster. When is opposing the flow direction, reverse flow may exist near the free surface and the propagation speed of the liquid column is reduced. Moreover, for a capillary flow in a wedge with constant α, θ, and S, both the analytic solutions and the numerical simulation predict that for the constantflowrate stage and for the constantheight flow stage. When S is a function of the flow direction z, the above functional relationship between l and t becomes no longer valid; it varies as the liquid column propagates along the wedge.

Effects of surface roughness and freestream turbulence on the wake turbulence structure of a symmetric airfoil
View Description Hide DescriptionThe effects of surface roughness on the wake characteristics of a simulated turbine airfoil, operating in a compressible, highspeed environment, are studied at different freestream turbulence levels. The effects of these parameters on wake distributions of mean velocity, turbulence intensity, and turbulence length scale, as well as on power spectral density profiles and vortex shedding frequencies are quantified one chord length downstream of airfoil. All profile quantities broaden considerably, with lower peak values, as either the level of surface roughness of the turbulence intensity increases. Nondimensional vortex shedding frequencies also decrease as either the level of surface roughness or the turbulence intensity increases.

A macroscopic chemistry method for the direct simulation of gas flows
View Description Hide DescriptionIn most chemistry methods developed for the direct simulation Monte Carlo (DSMC) technique, chemical reactions are computed as an integral part of the collision simulation routine. In the macroscopic chemistry method developed here, the simulation of collisions and reactions are decoupled in that reactions are computed independently, after the collision routine. The number of reaction events to perform in each cell is calculated using the macroscopic reaction rates and equilibrium constant with local macroscopic flow conditions. The macroscopic method is developed for the symmetrical diatomic dissociating gas. For each dissociation event, a single diatomic simulator particle is selected with a probability based on its internal energy, and is replaced by two atomic particles. For each recombination event, two atomic particles are selected at random, and are replaced by a single diatomic particle. The dissociation energy is accounted for by adjusting the translational thermal energies of all particles in the cell. The macroscopic method gives density profiles in agreement with experimental data for the chemical relaxation region downstream of a strong shock in nitrogen. In the nonequilibrium region within the shock, and along the stagnation streamline of a blunt cylinder in rarefied flow, the macroscopic method gives results in excellent agreement with those obtained using the most common conventional DSMC chemistry method in which reactions are calculated during the collision routine. The number of particles per computational cell has a minimal effect on the results provided by the macroscopic method. Unlike most DSMC chemistry methods, the macroscopic method is not limited to simple forms of and Any forms may be used, and these may be any function of the macroscopic conditions. This is demonstrated by using a twotemperature rate model, and a form of with a number density dependence. With the twotemperature model, the macroscopic method gives densities in the postshock chemical relaxation region that also agree with the experimental data. For a form of with a number density dependence, the macroscopic method can accurately reproduce chemical recombination behavior. In a primarily dissociativeflow, the number density dependence of has very little effect on the flow. The macroscopic method requires slightly less computing time than the most common DSMC chemistry method.

The structure of a jet in cross flow at low velocity ratios
View Description Hide DescriptionThis paper examines in detail the flow structure and associated wall pressurefluctuations caused by the injection of a round, turbulent jet into a turbulent boundary layer. The velocity ratio, r, ratio of mean jet velocity to the mean cross flow, varies from 0.5 to 2.5 and the Reynolds number based on the cross flow speed and jet diameter is Particle imagevelocimetry is used to measure the flow and flush mounted pressuresensors installed at several locations used to determine the wall pressure. The results consist of sample instantaneous flow structures, distributions of mean velocity, vorticity and turbulence intensity, as well as wall pressure spectra. The flow structure depends strongly on the velocity ratio and there are two distinctly different regions. At low velocity ratios, namely a semicylindrical vortical layer (“shell”) forms behind the jet, enclosing a domain with slow moving reverse flow. The vorticity in this semicylindrical shell originates from the jet shear layer. Conversely, at high velocity ratios, namely the nearwall flow behind the jet resembles a Karman vortex street and the wallnormal vortical structures contain cross flow boundary layer vorticity. Autospectra of the pressure signals show that the effect of the jet is mainly in the 15–100 Hz range. At the wall pressurefluctuation levels increase with r. At the wall pressure levels reach a plateau demonstrating the diminishing effect of the jet on the nearwall flow. Consistent with the flow structure, the highest wall pressurefluctuations occur off the jet centerline for and along the jet centerline for Also, the advection speed of nearwall vortical structures increase with r at while at it is a constant.
