Volume 16, Issue 8, August 2004
 LETTERS


On the initialization of Rayleigh–Taylor simulations
View Description Hide DescriptionWe demonstrate that, when initialized with experimental data, numerical simulations of Rayleigh–Taylor mixing show reasonable agreement with experimental measurements of the selfsimilar growth rate α. The experimental data include highresolution velocity and density measurements from a closed water channel facility. For the simulations, a monotone integrated large eddy simulations technique was used that employed a finitevolume, Eulerian equation solver with van Leer flux limiters. Calculations were initialized with both density and velocity fluctuations. A comparison of the latetime, selfsimilar growth constant with the experiments showed simulations initialized with velocity perturbations gave better agreement with experiments.
 Top

 ARTICLES


Analysis and loworder modeling of the inhomogeneous transitional flow inside a Tmixer
View Description Hide DescriptionA direct numerical simulation of the transitional flow (Re=300 to Re=700) inside a Tmixer configuration has been carried out. Time records were collected and used to perform a proper orthogonal decomposition (POD) of the flow. Changes of the flowcharacteristics in the frequency spectra and extracted coherent spatial structures indicate flow transition across the investigated Reynolds numbers. The POD modes were used to derive a loworder model of the flow. An a priori test limits the possibilities of the modeling; for the periodic case it demonstrates that the flow can be reduced to a system of a few degrees of freedom, while for the turbulent ones this results to be extremely difficult because of the large number of degrees of freedom that are necessary to describe the flow.

Fragmentation of stretched liquid ligaments
View Description Hide DescriptionThe dynamics and fragmentation of stretched liquid ligaments is investigated. The ligaments are produced by the withdrawal of a tube initially dipping at a free surface. Time resolved high speed motion experiments reveal two different elongation behaviors, depending on the nondimensional number ratio of the extension rate to the capillary contraction rate with the capillary time based on the tube diameter. For slow extensions (small the liquid bridge linking the tube to the reservoir contracts above a critical elevation, eventually following a selfsimilar contraction before breakup. For fast extensions (large the bridge takes the form of a cylindrical ligament, stabilized by the stretching motion. Whatever the elongation rate is, the ligament detaches from the surface at a time of order after the beginning of the extension. If only one small droplet is produced with a slowly stretched bridge, a set of droplets with distributed sizes is obtained from the breakup of the ligament submitted to a fast extension. We discover that an aggregative process comes into play between the blobs constitutive of the ligament as it fragments. The outcoming Gamma distribution describes well the observed broad drop size distributions.

Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Twodimensional theoretical and numerical modeling
View Description Hide DescriptionA model for the evolution of a thin liquid coating on a horizontal cylinder is presented. The cylinder rotates about its axis, carrying liquid around its circumference. For a viscous coating, this leads to formation of a relatively thick coating where the cylinder surface moves upward. The model is based on lubrication theory, as the coating is thin compared to the cylinder radius, and includes the effects of cylinder rotation, gravity, surface tension, and flow along the cylinder axis. A twodimensional numerical scheme based on finite differences is produced, for investigation of the case when axial flow is neglected. This numerical scheme is validated in appropriate limiting cases. Coating cross sections are obtained over a range of cylinder rotation rates, for realistic parameter values. These show a transition from pendant drops hanging beneath the cylinder to a nearly uniform coating wrapped around it as rotation rate is increased.

The effect of physical boundaries on oscillatory bifurcation in counterrotating Taylor–Couette flow
View Description Hide DescriptionThe results of an experimental study on the bifurcation structure of oscillatory modes in counterrotating Taylor–Couette flow with stationary end plates are presented. It is shown that the cylinder length L acts as an important geometric control parameter of the system. As a result of a supercritical Hopf bifurcation it is found that for an aspect ratio (d gap width) only spiral vortices appear in basic laminar flow. For Γ<10.5 spiral vortices are almost entirely replaced by two types of standing waves called and as supercritical oscillatory flow. Experimental evidence is presented that the mode exchange between standing waves and is governed by underlying Ekman induced vortices which appear as a result of stationary end plates in the flow. In this regime spiral vortices appear only from a sub or supercritical symmetry breaking bifurcation of the standing waves. Within an “intermediate regime” between 10.5⩽Γ⩽16 spiral vortices are found to be the predominant primary oscillatory flow but small stability intervals of standing waves are also observed. Surprisingly, the experimentally determined critical Reynolds number is found to deviate not more than 2% from the numerical values for all values of aspect ratio even though they are calculated under the assumption of infinite axial length. Moreover, the critical oscillation frequency is also in agreement with the numerical values and is independent from Γ.

Proper orthogonal decomposition reconstruction of a transitional boundary layer with and without control
View Description Hide DescriptionProper orthogonal decomposition (POD) has been performed for controlled and uncontrolled transitional boundary layer data in an effort to reconstruct and possibly control the transitional boundary layer. Although the POD provides mathematically defined optimal basis functions for a given flow, they are only optimal for a given flow condition (e.g., specific Reynolds number,boundary conditions, etc.). In the context of flow control, one is usually forced to use the POD modes extracted from an uncontrolled flow as the controlledflow is not known a priori. The present investigation reveals that the most energetic POD modes for uncontrolled and controlled modes show a striking similarity, and unlike in turbulent flows, the present transitional boundary layerflow can be reliably captured by a few POD modes which contain almost all of the flow energy. It is then shown that it is possible to reconstruct the controlledflow using POD modes from the uncontrolledflow. Therefore, it can be conjectured that lowdimensional models based on the uncontrolled POD modes may be successfully used as online control tools. After this it is shown that “new” snapshots, i.e., the time evolution of the flow, can also be reconstructed by appropriately modifying the coefficients of the POD modes extracted from “previous” or earlier snapshots. This is accomplished using flowfield information at some “sensor positions” and a leastsquares fit to the uncontrolled POD modes from former snapshots at these points. The approach introduced in this paper offers a simple, experimentally realizable approach to calculate the temporal coefficients, hence to reconstruct the unknown flow field without the need for a lowdimensional model based on the projection of the Navier–Stokes equations.

Droplet behavior in the presence of insoluble surfactants
View Description Hide DescriptionThe timedependent behavior of droplets in the presence of insoluble surfactants, i.e., droplet elongation in supercritical flow (capillary number Ca=0.1) and droplet breakup in a quiescent matrix, is studied using a finite element method. The interfacial tension coefficient σ as a function of the surfactant concentration Γ is described using the Langmuir equation of state, For droplets in an equal viscosity system, the influence of parameters Γ, and the Péclet number (ratio between surfactantconvection and diffusion rate) on the elongation behavior has been investigated, whereas droplet breakup is considered for various values of the Péclet number for trace concentrations of an insoluble surfactant. Depending on the surfactant used, a surfactant covered droplet in supercritical flow may deform more than or less than a clean droplet, as is the case in subcritical flow. Two processes compete: surfactant accumulation near the tips due to convection and overall surfactant dilution due to an increase of interfacial area. Nevertheless, the main effect of surfactants on dispersive mixing is due to the fact that upon breakup, the daughter droplets have a different interfacial tension coefficient. Especially in timedependent processes, this may have a huge impact on the final droplet distribution.

Numerical comparison of Bhatnagar–Gross–Krook models with proper Prandtl number
View Description Hide DescriptionWhile the standard Bhatnagar–Gross–Krook (BGK)model leads to the wrong Prandtl number, the BGKmodel with velocity dependent collision frequency as well as the ellipsoidal statistical BGK (ESBGK) model can be adjusted to give its proper value of 2/3. In this paper, the BGKmodel with velocity dependent collision frequency is considered in some detail. The corresponding thermal conductivity and viscosity are computed from the Chapman–Enskog method, and several velocitydependent collision frequencies are introduced which all give the proper Prandtl number. The models are tested for Couette flow, and the results are compared to solutions obtained with the ESBGK model, and the direct simulation Monte Carlo method. The simulations rely on a numerical scheme that ensures positivity of solutions,conservation of moments, and dissipation of entropy. The advantages and disadvantages of the various BGKmodels are discussed.

Molecular dynamics simulation of rotating fluids in a cylindrical container
View Description Hide DescriptionIn the present work, nonequilibrium molecular dynamics simulation is performed to investigate the behaviors of the molecular scale rotating fluids confined in an enclosed cylindrical container with a rotating lid disk. The major concerns of the study are the fundamental characteristics including bulk flow pattern, velocity slip, and the validity of the conventional principle of dynamic similarity. Two potentials for taking into account the fluid–fluid and fluid–wall intermolecular interactions, i.e., truncated and shifted LennardJones potential and Weeks–Chandler–Andersen (WCA) potential, are considered for comparison. In addition, simulations based on the boundary conditions with and without wall barrier layers are compared. For this rotationdriven fluid flow, the present results demonstrate the bidirectional density layering phenomenon, the nonlinear fluid motion, and the shear length correlations under various conditions. The simulation with the potential of pure repulsion (WCA) generates a stronger vortical motion. It is also found that the similarity nature in conventional macroflow does not exist in this molecular scale rotating flow and the similarity breakdown is more pronounced in the simulations with WCA potential.

A new device for the generation of microbubbles
View Description Hide DescriptionIn this paper we present a new method for the production of bubbleliquid suspensions (from now on BLS) composed of micronsized bubbles and with gas to liquid volume ratios larger than unity. We show that the BLS gas fraction being and the flow rates of gas and liquid, respectively, is controlled by a dimensionless parameter which accounts for the ratio of the gas pressure inside the device to the liquidviscous pressure drop from the orifices where the liquid is injected to the exit, where the BLS is obtained. This parameter permits the correct scaling of the BLS gas volume fraction of all the experiments presented.

A new dynamic subgrid eddy viscosity model with application to turbulent channel flow
View Description Hide DescriptionA new subgrid eddyviscositymodel is proposed for large eddy simulation of turbulent flows. The new model is based on the exact energy transport equation between resolved and unresolved scale turbulence. The subgrid eddyviscosity of new model is proportional to the skewness of longitudinal velocity increment, which measures the ratio of cascade energy to the dissipation. The new model is verified in isotropic turbulence and tested in turbulent channel flow with satisfaction.

An experimental study of micronscale droplet aerosols produced via ultrasonic atomization
View Description Hide DescriptionIn the last 10 years, laserdriven fusion experiments performed on atomic clusters of deuterium have shown a surprisingly high neutron yield per joule of input laser energy. Results indicate that the optimal cluster size for maximizing fusion events should be in the 0.01–1 μm diameter range, but an appropriate source of droplets of this size does not exist. In an attempt to meet this need, we use ultrasonic atomization to generate micronscale dropletaerosols of high average density, and we have developed and refined a reliable droplet sizing technique based on Mie scattering. Harmonic excitation of the fluid in the MHz range yields an aerosol of droplets with diameters of a few microns. The droplet diameter distribution is wellpeaked and the relationship between average droplet size and forcing frequency follows an inviscid scaling law, predictable by dimensional analysis and consistent with the linear theory for Faraday excitation of an infinitely deep fluid.

Influence of small imperfections on the stability of plane Poiseuille flow: A theoretical model and direct numerical simulation
View Description Hide DescriptionIt is well known that the stability of plane Poiseuille flow is extremely sensitive to small imperfections that are inevitably present. In this paper, a simple model is proposed, in which the imperfections are represented by a steady but spatially periodic surface roughness and a small oscillatory pressure gradient. A steady perturbation in the form of spatially periodic suction is also considered. For both cases, the resulting steady and unsteady components interact to produce a forcing that is in resonance with the Tollmien–Schlichting (TS) wave. The latter is excited as a result, and grows in proportion to time during the initial stage. The subsequent nonlinear development of the TS wave is shown to be governed by a forced (nonlocal) amplitude equation, which provides a simple framework to link the subcritical nonlinear instability explicitly to external forcing. The validity of the amplitude equation was checked against the direct numerical simulation (DNS), carried out in the case of wall suction. The results indicate that for a fixed level of external disturbance, there exist two distinctive regimes of response: A largeamplitude regime for the Reynolds numbers above a critical value, and a smallamplitude regime below it. The largeamplitude response regime in DNS was found to correspond to the occurrence of a finitetime singularity in the solution to the amplitude equation. This observation allows the critical Reynolds number for the largeamplitude response regime to be defined as one that divides the singular and bounded solutions of the amplitude equation. Estimate based on this equation shows that presence of small imperfections may reduce the critical Reynolds number for subcritical instability to values well below 5772.22.

Small scale structure of homogeneous turbulent shear flow
View Description Hide DescriptionThe structure of homogeneous turbulentshear flow is studied using data generated by direct numerical simulations (DNS) and a linear analysis for both compressible and incompressible cases. At large values of the mean shear rate, the rapid distortion theory (RDT) limit is approached. Analytical solutions are found for the inviscid compressible RDT equations at long times. The RDT equations are also solved numerically for both inviscid and viscous cases. The RDT solutions, confirmed by the DNS results, show that the even order transverse derivative moments of the dilatational and solenoidal velocity fields are anisotropic, with the dilatational motions more anisotropic than their solenoidal counterparts. The results obtained for the incompressible case are similar to those obtained for the solenoidal motions in the compressible case. The DNS results also indicate an increase in the anisotropy of the even order transverse derivative moments with the order of the moment, in agreement with the RDT predictions. Although the anisotropy decreases with Reynolds number, it is likely that for higher even order moments it will persist at large values of the Reynolds number, in contrast with the postulate of local isotropy. The RDT solutions also predict that the normalized odd order transverse derivative moments of the solenoidal velocity for the compressible case and of the velocity for the incompressible case should approach a constant different than zero at large times. This prediction is supported by the DNS data. For higher odd order normalized moments, the RDT analysis suggests that the anisotropy may persist at large values of the Reynolds number, in agreement with the existent experimental data. The amplification of the dilatational kinetic energy in the direction of the mean shear and the anisotropy of the dilatational dissipation tensor found in the DNS results are also consistent with the RDT analysis.

Point vortices with a rational necklace: New exact stationary solutions of the twodimensional Euler equation
View Description Hide DescriptionIn this paper we find a new class of explicit exact stationary solutions of the twodimensional (2D) Euler equation which describe vortex patterns of necklace type with fold symmetry in rotational shear flow. The point vortex with a strength equal to (where Ninteger number) is situated in the center of the vortex structure. The vorticity distribution outside of the center is smooth and is described by a twoparametric family of rational functions which are known in explicit form for any N. In the centers of vortex satellites the vorticity does not have any singularity and remains of finite value. When N is increasing, the solutions describe the transition layer in 2D–rotational shear flow.

Turbulent vortex dipoles in a shallow water layer
View Description Hide DescriptionThis paper describes an experimental study on turbulent dipolar vortices in a shallow water layer. Dipoles are generated by an impulsive horizontal jet, by which a localized threedimensional turbulent flow region is created. Dipole emergence is only controlled by the confinement number whereas the jet Reynolds number has no influence in the studied range 50 000<Re<75 000 (H is the water depth, is the kinematical viscosity,Q the injected momentum flux and the injection duration). When the flow becomes quasitwodimensional and a single vortex dipole emerges in most cases. By qualitative observations and application of particle imagevelocimetry, the main dipole features have been determined. The shallow water dipoles are characterized by the simultaneous presence of several scales of turbulence: A quasitwodimensional main flow at large scale and threedimensional turbulent motions at small scale. A vertical circulation takes place in the dipole front. A theoretical model is presented and compared to experimental results. The threedimensional turbulence production occurs mainly in the frontal circulation. A good agreement has been found between the model prediction and the measurements for the velocity evolution.

Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase
View Description Hide DescriptionThe evaporation and condensation at an interface of vapor and its condensed phase is considered. The validity of kinetic boundary condition for the Boltzmann equation, which prescribes the velocity distribution function of molecules outgoing from the interface, is investigated by the numerical method of molecular dynamics for argon. From the simulations of evaporation into vacuum, the spontaneousevaporation flux determined by the temperature of condensed phase is discovered. Condensation coefficient in equilibrium states can then be determined without any ambiguity. It is found that the condensation coefficient is close to unity below the triplepoint temperature and decreases gradually as the temperature rises. The velocity distribution of spontaneously evaporating molecules is found to be nearly a halfMaxwellian at a low temperature. This fact supports the kinetic boundary condition widely used so far. At high temperatures, on the other hand, the velocity distribution deviates from the halfMaxwellian.

Experimental study of a free and forced swirling jet
View Description Hide DescriptionThe present study concerns the response of a swirling jet to various azimuthal modes and frequencies forced at the nozzle exit. The different unforced dynamical states are first described as a function of the swirl setting, determined from measuredvelocity fields in the longitudinal plane using particle image velocimetry. A second experimental technique, based on laser induced fluorescence, is described, which is more suited to the description of the lowamplitude response of the jet to the forcing. It is shown that the receptivity of the jet is very poor when the forcing is set to the naturally prevailing azimuthal mode and frequency. In contrast, a strong response is observed for both corotating and counterrotating forced azimuthal modes for frequencies about one order of magnitude larger than the frequency prevailing in the absence of forcing. Finally, the present actuator is seen to be ineffective in preventing the appearance of vortex breakdown itself.

Threedimensionalization of freelydecaying twodimensional turbulence
View Description Hide DescriptionThe threedimensionalization of freelydecaying twodimensional turbulence is studied numerically. Using two different basic states, it is shown that the hyperbolic instability of steady mixing layers generalizes to unsteady flow. The growth of threedimensional (3D) perturbations is interpreted in terms of a “pressureless” analysis in which horizontal pressure gradients are neglected and the underlying physical mechanism is advective in nature. For a steady, pressureless base flow the (asymptotic) growth rate is exactly determined, in a few special cases, by variants of the socalled Weiss criterion; more generally, local growth rate estimates are obtained. For freelydecaying twodimensional turbulence there is analogous behavior: while the 3D perturbation remains small the pressureless approximation holds at large horizontal scales and local growth rate estimates apply. The pressureless modes have a determining influence on the growth (the damping effect of the horizontal pressure gradient is small).

Fingering phenomena created by a soluble surfactant deposition on a thin liquid film
View Description Hide DescriptionA striking fingering instability accompanies surfactantdropletdeposition upon thin films. The fingers apparently emerge from the droplet and are preceded by a circular rim of thickened fluid. In this work, we present a theory, based on the lubrication approximation, capable of explaining the physical mechanism responsible for these phenomena and the trends observed experimentally. The model comprises evolution equations for the film thickness and surfactant interfacial and bulk concentrations, which are parametrized by appropriately defined solubility and sorption kinetics parameters, and surface and bulk Peclet numbers; closure is achieved via use of a nonlinear equation of state. The results of our transient growth analysis and twodimensional numerical simulations illustrate the delicate interplay, which exists between surfactantsolubility and the nonlinearity in the equation of state. In particular, we show that solubility acts to destabilize the spreading process for a given value of the nonlinearity except for very highly solublesurfactants. In this case, the magnitude of the Marangoni stresses available to drive spreading and instability diminishes leading to flow stability.
