Volume 16, Issue 7, July 2004
 LETTERS


Intermittent distribution of heavy particles in a turbulent flow
View Description Hide DescriptionThe retardation of weakly inertial particles depends on the acceleration of the ambient fluid, so the particle concentration n is determined by the divergence of Lagrangian acceleration which we study by direct numerical simulations. We demonstrate that the second moment of the concentration coarsegrained over the scale r behaves as an approximate power law: We study the dependencies of the exponent α on the Reynolds number, of the Stokes number, and on the settling velocity. We find numerically that the theoretical lower bound previously suggested [Falkovich et al., Nature 419, 151 (2002)] correctly estimates the order of magnitude (within a factor 2 to 4) as well as the dependencies on the Reynolds, Stokes, and Froude numbers. The discrepancy grows with the Reynolds number and the Froude number. We analyze the possible physical mechanism responsible for that behavior.

Effects of hydrophobic surface on skinfriction drag
View Description Hide DescriptionEffects of hydrophobic surface on skinfriction drag are investigated through direct numerical simulations of a turbulent channel flow.Hydrophobic surface is represented by a slipboundary condition on the surface. When a slipboundary condition is used in the streamwise direction, the skinfriction drag decreases and turbulence intensities and turbulence structures, nearwall streamwise vortices in particular, are significantly weakened. When a slipboundary condition is used in the spanwise direction, on the other hand, the drag is increased. It is found that nearwall turbulence structures are modified differently, resulting in drag increase. It is also found that the slip length must be greater than a certain value in order to have a noticeable effect on turbulence. An important implication of the present finding is that drag reduction in turbulent boundary layers is unlikely with hydrophobic surface with its slip length on the order of a submicron scale.

Scaling law in liquid drop coalescence driven by surface tension
View Description Hide DescriptionThis Letter reports experimental results on the coalescence of two liquiddrops driven by surface tension. Using a high speed imaging system, we studied the earlytime evolution of the liquid bridge that is formed upon the initial contact of two liquiddrops in air. Experimental results confirmed the scaling law that was proposed by Eggers et al. based on a simple and yet elegant physical argument. We found that the liquid bridge radius follows the scaling law in the inertial regime. Further experiments demonstrate that such scaling law is robust when using fluids of different viscosities and surface tensions. The prefactor of the scaling law, is shown to be where R is the inverse of the drop curvature at the point of contact. The dimensionless prefactor is measured to be in the range of 1.03–1.29, which is lower than 1.62, a prefactor predicted by the numerical simulation of Duchemin et al. for inviscid drop coalescence.
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 ARTICLES


Nonparallel local spatial stability analysis of pipe entrance swirling flows
View Description Hide DescriptionA spatial local viscous stability analysis of a swirling flow developing in a cylindrical pipe has been carried out numerically. Even at moderately low swirl strengths, we have found the existence of centrifugal modes in addition to the shear ones found in previous stability analysis of nonswirling flows developing in pipes. It is found that these centrifugal instabilities develop at Reynolds numbers that are much lower than those required for the growing of the shear instability. Moreover, the extent of the region where centrifugal instabilities appear is much larger than that where the shear layer instability grows. We have found from the analysis that the most unstable mode was the counterrotating one The critical Reynolds number for which linear analysis predicts the growth of the convective instabilities is for the centrifugal modes one hundred times smaller than for the shear layer ones.

Is a plane liquid curtain algebraically absolutely unstable?
View Description Hide DescriptionThe dispersion relation of capillary waves in a plane moving liquid curtain is critically reanalyzed with an eye to its behavior near the origin of wavenumber space and the largetime asymptotics of the corresponding Green’s function. Evidence is found that recent and less recent theories supporting the existence of a zerowavenumber algebraic absolute instability contain serious inconsistencies.

On large streamwise structures in a wall jet flowing over a circular cylinder
View Description Hide DescriptionThis paper describes an experimental search for large streamwise vortices in a turbulent wall jet flowing over a convex surface. The existence of these vortices resulting from a centrifugal instability was suspected but never previously observed in this flow. They eluded detection because they meander across the span, as they become larger, with increasing distance from the nozzle. A particle image velocimeter, used in air, enabled the mapping of these vortices establishing their circulation and their evolution in the direction of streaming. Although the longitudinal structures educed do not contribute to mean spanwise distortion of the flow, they are strong enough to augment the Reynolds stresses that increase the rate of spread of the jet and its turbulent intensities. Since the temporal resolution of the instrument is not yet adequate to track the motion of large vortices, the turbulent characteristics surrounding a pair of educed counterrotating vortices were observed in a frame of reference that is statistically stationary relative to the vortex cores.

Drop coalescence through a liquid/liquid interface
View Description Hide DescriptionParticle image velocimetry(PIV) experiments were conducted to study the coalescence of single drops through planar liquid/liquid interfaces. Sequences of velocity vector fields were obtained with a highspeed video camera and subsequent PIVanalysis. Two ambient liquids with different viscosity but similar density were examined resulting in Reynolds numbers based on a surface tension velocity of 10 and 26. Prior to rupture, the drops rested on a thin film of ambient liquid above an underlying interface. After rupture, which was typically offaxis, the free edge of the thin film receded rapidly allowing the drop fluid to sink into the bulk liquid below. Vorticity generated in the collapsing fluid developed into a vortex ring straddling the upper dropsurface. The ring core traveled radially inward with a ringshaped capillary wave effectively pinching the upper dropsurface and increasing the drop collapse speed. The inertia of the collapse deflected the interface downward before it rebounded upward. During this time, the vortex core split so that part of its initial vorticity moved inside the drop fluid while part remained in the ambient fluid above it. A second ringshaped capillary wave formed along the interface outside of the drop and propagated radially outward during the collapse. Changing the ambient fluid viscosity resulted in several effects. First, the velocity of the receding free edge was smaller for higher ambient viscosity. Second, the pinching of the upper dropsurface caused by the shrinking capillary ring wave was stronger when the ambient viscosity was lower, and this resulted in a higher maximum collapse speed and higher vorticity values in the dominant vortex ring.

Kinetic theory analysis of the twosurface problem of a vapor–vapor mixture in the continuum limit
View Description Hide DescriptionA steady flow of a vapor–vapor mixture between two parallel plane condensed phases for small Knudsen numbers is investigated on the basis of the kinetic theory of gases. By a systematic asymptotic analysis of the Boltzmann equation, it is shown that there are two distinct types of behavior of the mixture: the Eulertype behavior and the convectiondiffusiontype behavior. Both types of behavior are confirmed numerically for the Boltzmann equation by the direct simulation Monte Carlo method and for the modelBoltzmann equation proposed by Garzó, Santos, and Brey by the standard finitedifference method. Finally, the continuum limit is considered, and it is shown that the ghost effect that some of the gas rarefaction effects still have an influence in the continuum limit manifests itself in the case of the convectiondiffusiontype. This result shows that the infinitesimal jump of pressure at the surface of the condensed phase must be taken into account correctly for the description of the behavior of the vapors in the continuum limit.

Nanoparticle transport and deposition in bifurcating tubes with different inlet conditions
View Description Hide DescriptionTransport and deposition of ultrafine particles in straight, bent and bifurcating tubes are considered for different inlet Reynolds numbers,velocity profiles, and particle sizes, i.e., A commercial finitevolume code with usersupplied programs was validated with analytical correlations and experimental data sets for nanoparticle depositions, considering a straight tube, a tubular bend, and a G3G5 double bifurcation with both planar and nonplanar configurations. The focus is on the airflow structures as well as nanoparticle deposition patterns and deposition efficiencies, which were analyzed for planar and nonplanar bifurcating lung airway models representing part of the upper bronchial tree. Deposition takes place primarily by Brownian diffusion, and thus deposition efficiencies increase with decreasing nanoparticle size and lower inlet Reynolds numbers. Deposition in the nonplanar configuration differs only slightly from that in the planar configuration. When compared with axisymmetric inlet conditions, the more realistic, skewed inlet velocity and particle profiles generate nearly axisymmetric deposition patterns as well. This work may elucidate basic physical insight of ultrafine particle transport and deposition relevant to environmental, industrial and biomedical studies.

Initial stage of flat plate impact onto liquid free surface
View Description Hide DescriptionThe liquid flow and the free surface shape during the initial stage of flat plate impact onto liquid halfspace are investigated. Method of matched asymptotic expansions is used to derive equations of motion and boundary conditions in the main flow region and in small vicinities of the plate edges. Asymptotic analysis is performed within the ideal and incompressible liquid model. The liquid flow is assumed potential and two dimensional. The ratio of the plate displacement to the plate width plays the role of a small parameter. In the main region the flow is given in the leading order by the pressureimpulse theory. This theory provides the flow field around the plate after a short acoustic stage and predicts unbounded velocity of the liquid at the plate edges. In order to resolve the singular flow caused by the normal impact of a flat plate, the fine pattern of the flow in small vicinities of the plate edges is studied. It is shown that the initial flow close to the plate edges is selfsimilar in the leading order and is governed by nonlinear boundaryvalue problem with unknown shape of the free surface. The Kutta conditions are imposed at the plate edges, in order to obtain a nonsingular inner solution. This boundaryvalue problem is solved numerically by iterations. At each step of iterations the “inner” velocity potential is calculated by the boundaryelement method. The asymptotics of the inner solution in both the far field and the jet region are obtained to make the numerical algorithm more efficient. The numerical procedure is carefully verified. Agreement of the computed free surface shape with available experimental data is fairly good. Stability of the numerical solution and its convergence are discussed.

Thermomagnetic convection in a square enclosure using a line dipole
View Description Hide DescriptionWe have simulated thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension. The cavity is under the influence of an imposed twodimensional magnetic field that conforms to the Maxwell’sequations. Our objective is to characterize the thermomagnetic convection in terms of the geometric length scales, magnetic fluid properties, temperature differences, and strengths of the imposed magnetic fields.Fluid motion occurs due to both the gradients of the magnetic field and the temperature. Colder fluid that has a larger magnetic susceptibility is attracted toward regions with larger field strength during thermomagnetic convection, which displaces warmer fluid of lower susceptibility. The heightaveraged Nusselt number increases with increasing magnetic dipole strength and temperature but decreases with increasing fluidviscosity. Thermomagnetic heat transfer increases when the length scale decreases if the dipole strength of the source magnet is constant. This makes thermomagnetic convection a potentially viable option for microscale heat transfer applications. Thermomagnetic convection can be correlated with a dimensionless magnetic Rayleigh number and heat transfer due to this form of convection in the range is as effective as buoyancyinduced convection in the range

On the interaction of vortices with mixing layers
View Description Hide DescriptionWe describe the perturbations introduced by two counterrotating vortices—in a twodimensional configuration—or by a vortex ring—in an axisymmetric configuration—to the mixing layer between two counterflowing gaseous fuel and air streams of the same density. The analysis is confined to the near stagnation point region, where the strain rate of the unperturbed velocity field, is uniform. We restrict our attention to cases where the typical distance between the vortices—or the characteristic vortex ring radius —is large compared to both the thickness, of the vorticity core and the thickness, of the mixing layer. In addition, we consider that the ratio, Γ/ν, of the vortex circulation, Γ, to the kinematicviscosity, ν, is large compared to unity. Then, during the interaction time, the viscous and diffusion effects are confined to the thin vorticity core and the thin mixing layer, which, when seen with the scale appears as a passive interface between the two counterflowing streams when they have the same density. In this case, the analysis provides a simple procedure to describe the displacement and distortion of the interface, as well as the time evolution of the strain rate imposed on the mixing layer, which are needed to calculate the inner structure of the reacting mixing layer as well as the conditions for diffusionflame extinction and edgeflame propagation along the mixing layer. Although in the reacting case variable density effects due to heat release play an important role inside the mixing layer, in this paper the analysis of the inner structure is carried out using the constant density model, which provides good qualitative understanding of the mixing layer response.

Finitevolume optimal largeeddy simulation of isotropic turbulence
View Description Hide DescriptionThe feasibility of an optimalfinitevolumelargeeddy simulation(LES)model for isotropic turbulence is evaluated. This modeling approach is based on the approximation of the idealLES by a stochastic estimate of the fluxes in a finitevolume representation of the Navier–Stokes equation. Stochastic estimation of the fluxes allows for the simultaneous treatment of Navier–Stokes, discretization and subgrid effects, yielding a compact, yet accurate scheme for the large eddy simulation of isotropic turbulence. Both global and local models based on optimalfinitevolumeLES are developed and used in a priori tests guiding the choice of stencil geometry and model inputs. The most promising models in the a priori exams are tested in actual simulations (i.e., a posteriori) and the results compared with those for filtered direct numerical simulation (DNS) and the dynamic Smagorinsky model. The a posteriori performance of the optimalfinitevolumeLESmodels, evaluated by the energy spectrum and thirdorder structure function, is superior to that of the dynamic Smagorinsky model on a coarse grid. While applicability to other cases is currently limited by the dependence of the present approach on DNS statistical data, research is underway to remove this requirement.

Twodimensional numerical investigations of smallamplitude disturbances in a boundary layer at Ma=4.8: Compression corner versus impinging shock wave
View Description Hide DescriptionTwodimensional direct numerical simulations and linear stabilitytheory investigations have been carried out for a compression ramp at Ma=4.8 and compared to earlier results of a laminar boundary layer with impinging shock wave. The inflow parameters in both flows were identical; the ramp angle of the compression corner was chosen to cause a separation bubble, which has exactly the same length compared to the case with impinging shock. It turned out, that the two cases are almost identical for the base flow properties. This is in accordance with similarity assumptions, e.g., free interaction theory, which for smaller Reynolds numbers states, that the boundary layer should be independent of the sort of shockboundary layer interaction. However, linear stabilitytheory results differ near the corner and the impinging shock, respectively. Direct numerical simulations of smallamplitude disturbances, which were introduced into the laminar boundary layer, also behave in a very similar way. Amplitude distributions exhibit the same characteristics. The according distributions of the ramp flow have slightly larger amplitudes than the case with impinging shock.

Experimental evaluation of the migration of spherical particles in threedimensional Poiseuille flow
View Description Hide DescriptionConvective transport of 10 μm nearly neutrally buoyant spherical particles (polystyrene vinyl dibenzene) is studied in 220 μm and 530 μm diameter capillaries using an online particle detector of the electronic gate type. The detector, connected to the capillary outlet, monitors the elution and translates the passage of individual particles into pulsed signals. The measuring technique requires the use of an electrically conductive carrier liquid, such as physiological saline (0.9%NaCl). Passage times are registered for discrete capillary lengths varying between 0.25 m and 5 m. Mean particle and fluid velocities are used to calculate the preferential radius of particle transport. The equilibrium position of the particles is found to shift towards the capillary wall for higher Reynolds numbers, for longer and smaller capillaries, and for more dilute suspensions. However, the higher the particle to capillary diameter ratio, the more pronounced wall effects. Moreover, as the Stokes number is small (E2), adhesion at the capillary walls turns out to be nonnegligible and to have an impact on the final quantitative results.

Linear stability analysis for a rotating cylinder with a rotating magnetic field
View Description Hide DescriptionThis paper treats the first hydrodynamicinstability for a uniformdensity, electrically conducting liquid in a finitelength cylinder which is rotating about its centerline. There is a uniform, transverse magnetic field which rotates about the cylinder’s centerline and which produces a steady, axisymmetric, azimuthal body force on the liquid. For the initial transition from a steady, axisymmetric flow to a periodic, nonaxisymmetric flow, results for the critical value of the magnetic Taylor number and for the frequency of the critical disturbance are presented as functions of the Reynolds number for the cylinder rotation. Rotations of the cylinder and of the magnetic field in the same azimuthal direction and in opposite directions are considered.

Eulerian shorttime statistics of turbulent flow at large Reynolds number
View Description Hide DescriptionAn asymptotic analysis is presented of the shorttime behavior of secondorder temporal velocity structure functions and Eulerian acceleration correlations in a frame that moves with the local mean velocity of the turbulent flow field. Expressions in closedform are derived which cover the viscous and inertial subranges. They apply to general anisotropic turbulence at a large Reynolds number obeying the Kolmogorov theory. Previously published results for isotropic turbulence emerge as special cases. In the derivation use is made of the approximation of temporarily frozen turbulence proposed by Tennekes. It is shown to be valid under conditions not other than those for which the Kolmogorov hypotheses hold. The effects of intermittency appear to be marginal.

Twoparticle diffusion and locality assumption
View Description Hide DescriptionA threedimensional kinematic simulation (KS) model is used to study one and twoparticle diffusion in turbulent flows. The energy spectrum takes a power law form The value of this power p is varied from 1.2 to 3, so that its effects on the diffusion of one and two particles can be studied. The twoparticle diffusion behaves differently depending on whether the twoparticle separation is larger or smaller than the smallest scale of turbulence (Kolmogorov length scale η). When the twoparticle mean square separation is smaller than it experiences a time exponential growth but for a very short time. For longer times, when the locality assumption is revisited in terms of twoparticle mean diffusivity In this inertial range we observe that for For but for and as a consequence the pair diffusion cannot have lost its dependence on the initial separation during the exponential growth, i.e., γ is a function of Our modified Richardson law is compared with two other proposed modifications to Richardson’s power law, namely the virtual time [G. K. Batchelor, Proc. Cambridge Philos. Soc. 48, 345 (1952)] and the correction factor [F. Nicolleau and J. C. Vassilicos, Phys. Rev. Lett. 90, 245003 (2003)]. Further investigations on twoparticle diffusion when give an excellent agreement with the experimental results in P. Morel and M. Larchevêque, J. Atmos. Sci. 31 (1974) for atmospheric turbulent flows. Finally, using two different combined power law energy spectra in KS, the isotropic small scales are found to have no significant role when their largest scale is less than 10 times the Kolmogorov length scale η.

Transient growth and instability in rotating boundary layers
View Description Hide DescriptionThe threedimensional temporal instability of rotating boundary layer flows is investigated by computing classical normal modes as well as by evaluating the transient growth of optimal disturbances. The flows examined are the rotating Blasius (RB) and the rotating asymptotic suction layers (RAS), with the rotation axis normal to the basic flow plane. In agreement with an inviscid criterion, streamwise unstable modes are found in both flow cases for anticyclonic rotation: at high Reynolds numbers, one obtains the Rossby number unstable range for RB, or for RAS. Critical Reynolds and Rossby numbers are also determined in both instances. Moreover, the dependence of transient growth with respect to wavenumbers, Rossby and Reynolds numbers is presented for both cyclonic and anticyclonic régimes. In particular, the peak transient growth is computed for a wide range of parameter values within the cyclonic regime and is shown to be reduced by rotation. A scaling analysis with respect to the Reynolds number is performed showing that the standard scaling is recovered only at very weak rotation. Optimal disturbances resemble oblique vortices. At weak rotation, they are almost streamwise vortices though their structure departs from the classical nonrotating case. Strong rotation imposes twodimensionality and the optimal disturbances vary weakly in the spanwise direction and exhibit growth by the Orr mechanism.

An experimental study of Faraday waves formed on the interface between two immiscible liquids
View Description Hide DescriptionWe report results of an experimental study of Faraday waves that were formed on the interface between two immiscible liquids in a cylindrical cell when it was oscillated vertically. The effects of the volume filling ratio ψ on the bifurcation set associated with the onset of the fundamental axisymmetric mode was investigated systematically. In particular, results are presented for the subharmonic regime of the control parameter space where the response was greatest. Both super and subcritical bifurcations are uncovered, with hysteresis in the latter case. The extent of the hysteresis is observed to strongly depend on ψ, suggesting that nonlinear damping effects are influenced by this parameter. At large drive amplitudes, a precessional periodic motion was found to develop via a Hopf bifurcation. This mode was observed to disappear catastrophically at an excitation frequency equal to 1.853±0.006 times the natural frequency of the resonant mode.
