Volume 13, Issue 3, March 2001
 LETTERS


Satellite drops: Unexpected dynamics and change of scaling during pinchoff
View Description Hide DescriptionDuring drop formation from a tube, a thin liquid thread—the precursor to satellites—connects an abouttoform primary drop to the remainder of the liquid hanging from the tube at the incipience of breakup. Whether the thread, once it detaches from the primary and pendant drops, evolves into a sphere or breaks into several subsatellites has heretofore been inadequately explored due to experimental and theoretical difficulties. These challenges are resolved here with an ultrafast digital imaging system and a novel computational algorithm. New findings range from the discovery of unexpected dynamics to the first demonstration of the transition from one scaling law governing interface rupture to another.

Interface instabilities during displacements of two miscible fluids in a vertical pipe
View Description Hide DescriptionWe study experimentally the downward vertical displacement of one miscible fluid by another in a vertical pipe at sufficiently high velocities for diffusive effects to be negligible. For certain viscosity ratios and flow rates, the interface between the two fluids can destabilize. We determine the dimensionless flow rate above which the instability is triggered and its dependence on the viscous ratio M, resulting in a stability map Two different instability modes have been observed: an asymmetric “corkscrew” mode and an axisymmetric one. We remark that the latter is always eventually disturbed by “corkscrew” type instabilities. We speculate that these instabilities are driven by the viscosity stratification and are analogous to those already observed in core annular flows of immiscible fluids.

Twodimensional vortex shedding of a circular cylinder
View Description Hide DescriptionThe Strouhal–Reynolds number relationship for the twodimensional (2D) vortex shedding of a circular cylinder at low to medium Reynolds numbers (Re, ranging from 45 to 560) is investigated experimentally. Both horizontal and vertical soap film tunnels are used to set up a truly 2D experiment. It is found that two separate 3D instabilities of the natural wake at and 260 disappear. The Strouhal–Reynolds number curve is in good agreement with the 2D computations of Barkley and Henderson [J. Fluid Mech. 322, 215 (1996)]. The 2D asymptote of 0.2417 of Strouhal number is also approached.

Experimental demonstration of a homogeneous twoscale dynamo
View Description Hide DescriptionIt has been shown theoretically that homogeneous kinematic dynamo action is possible for many unconfined and confined velocity fields, but a rigorous experimental validation is still lacking. G. O. Roberts [Philos. Trans. R. Soc. London, Ser. A 266, 535 (1970)] proposed a spatially periodic velocity field capable to generate a dynamo, which Busse [Geophys. J. R. Astron. Soc. 42, 437 (1975)] modified by introducing a second length scale larger in order to obtain a solution for a finite domain. Based on a scale separation approach Busse [Springer Proceedings in Physics, Vol. 69 (Springer Verlag, New York, 1992)] proposed a conceptual design for an experimental homogeneous dynamo. An engineering design was developed and a test facility has been set up. This test facility is described and first experimental results confirming dynamo action are presented.
 Top

 ARTICLES


Normal stress and diffusion in a dilute suspension of hard spheres undergoing simple shear
View Description Hide DescriptionThe complete set of normal stresses in a dilute suspension of hard spheres undergoing simple shear at low Reynolds number is calculated using a path integration approach for the cases where the concentration is uniform and where a small gradient in concentration is present. As expected, the normal stresses are seen to be a strong function of where b is the hard sphere radius and a is the particle radius. The normal stress differences and are negative while the osmotic pressure is large and positive, with and as For the asymmetry in the pair distribution function due to a depletion of particles in the extensional side of a pair interaction leads to On the other hand, for the additional stresslet induced when hard sphere radii touch dominates the stress generated in the suspension, and becomes the prevailing normal stress difference. The self and gradient diffusivities are calculated using da Cunha and Hinch’s [J. Fluid Mech. 309, 211 (1996)] trajectory method. Numerical results for the diffusivities are in agreement with those obtained by da Cunha and Hinch for while matching the analytically obtained diffusivities for large Finally, we calculate the normal stress in the presence of a small concentration gradient and compare two models of migration for this case, namely the suspension balance model of Nott and Brady [J. Fluid Mech. 275, 157 (1994)] and the diffusive flux model first introduced by Leighton and Acrivos [J. Fluid Mech. 181, 415 (1987)]. The results show that although the two models equally describe migration in the presence of a concentration gradient for the case where (or the two models are shown to be quantitatively different when nearfield hydrodynamics are relevant.

Granular segregation in the doublecone blender: Transitions and mechanisms
View Description Hide DescriptionWe investigate granular segregation in one of the most common industrial devices used in granular processing: the doublecone blender. We report several new and spontaneously occurring segregation patterns, including stripes, bands, and a symmetrybreaking state in which one species vacates half the tumbler. By varying the tumbling speed along with particle size and size ratio, we find that the transitions between segregated patterns are extremely sharp: Changes in fill level or speed of under one percent are sufficient to produce a reproducible qualitative change in the observed pattern. We show that the several distinct segregation patterns observed experimentally can be reproduced from a simplified model in which outward rolling on the convective granular cascade competes against inertial motion of rapidly moving large particles. Finally, we identify a cutoff particle size ratio above which large particles become buried in the cascading flow, and segregation appears to cease.

Apparent viscosity of suspensions of rods using falling ball rheometry
View Description Hide DescriptionFalling ball rheometrymeasurements of the apparent relative viscosity of suspensions of randomly oriented rodlike particles are reported for rods having a wide range of aspect ratios and concentrations. These data, combined with those from earlier studies [Milliken et al., J. Fluid Mech. 202, 217 (1989); Powell et al., J. Rheology 33, 1173 (1989)], provide a master curve describing the apparent viscosity in terms of a single parameter, where L is the length of the particle and n is the number density.

Dispersion in threedimensional fracture networks
View Description Hide DescriptionDispersion in threedimensional networks of polygonal fractures is determined by triangulating the network and solving the twodimensional convectiondiffusion equation in each fracture or by performing random walks. The general triangulation methodology and the numerical solution are summarized. The influence of the Péclet number, of the fracture density and of the fracture shape are systematically studied. Moreover, fracture networks are shown to belong to the same universality class as bond percolation networks.

Capillary waves on a Eulerian jet emerging from a channel
View Description Hide DescriptionThis paper considers the flow of a Eulerian fluid jet emerging out of a slightly compressed circular or rectangular crosssection channel. The emerging fluid is subject to surface tension, which provides a restoring force and produces steady waves along the free surface. In this paper, the full nonlinear problem for the jet is formulated and a dimensionless surface tension parameter is identified. The linearized problem is then solved by the Wiener–Hopf technique. The free surface shape consists of a steady sinusoidal oscillation and a component which decays exponentially with distance from the channel opening. Asymptotic methods are used to find the surface profile near the channel exit.

Statistical modeling of sprays using the droplet distribution function
View Description Hide DescriptionThe theoretical foundations of a statistical spray modeling approach based on the dropletdistribution function (ddf), which was originally proposed by Williams [Phys. Fluids 1, 541 (1958)], are established. The equation governing the ddf evolution is derived using an alternative approach. The unclosed terms in the ddf evolution equation are precisely defined, and the regime of applicability of current models is discussed. The theory of point processes is used to rigorously establish the existence of a disintegration of the ddf in terms of a spray intensity, which is the density of expected number of spray droplets in physical space, and the joint probability density function (jpdf) of velocity and radius conditional on physical location. Evolution equations for the spray intensity and the conditional jpdf of velocity and radius are derived. The intensity evolution equation contains a sink term corresponding to dropletvaporization, hitherto missing in previous derivations of this equation. This sink term is essential in order to correctly represent the vaporization phenomenon. Problems with numerical convergence of computed solutions to the ddf evolution are discussed, and criteria for establishing convergence are proposed. The study also shows how quantities predicted by ddfbased spray models can be compared to experimental measurements.

The recoiling of liquid droplets upon collision with solid surfaces
View Description Hide DescriptionAlthough the spreading behavior of liquid droplets impacting on solid surfaces has been extensively studied, the mechanism of recoiling which takes place after the droplet reaches its maximum spread diameter has not yet been fully understood. This paper reports the study of the recoiling behavior of different liquid droplets (water, ink, and silicone oil) on different solid surfaces (polycarbonate and silicon oxide). The droplet dynamics are experimentally studied using a high speed video system. Analytical methods using the variational principle, which were originated by Kendall and Rohsenow (MIT Technical Report 85694100, 1978) and Bechtel et al. [IBM J. Res. Dev. 25, 963 (1981)], are modified to account for wetting and viscous effects. In our model, an empirically determined dissipation factor is used to estimate the viscousfriction. It is shown that the model closely predicts the experimental results obtained for the varying dynamic impact conditions and wetting characteristics. This study shows that droplets recoil fast and vigorously when the Ohnesorge number decreases or the Weber number increases. Droplets with a large equilibrium contact angle are also found to recoil faster. Here the Ohnesorge number scales the resisting force to the recoiling motion, and is shown to play the most important role in characterizing the recoiling motion.

Stability of the Rankine vortex in a multipolar strain field
View Description Hide DescriptionIn this paper, the linear stability of a Rankine vortex in an nfold multipolar strain field is addressed. The flow geometry is characterized by two parameters: the degree of azimuthal symmetry n which is an integer and the strain strength which is assumed to be small. For and (dipolar, tripolar and quadrupolar strain fields, respectively), it is shown that the flow is subject to a threedimensional instability which can be described by the resonance mechanism of Moore and Saffman [Proc. R. Soc. London, Ser. A 346, 413 (1975)]. In each case, two normal modes (Kelvin modes), with the azimuthal wave numbers separated by n, resonate and interact with the multipolar strain field when their axial wave numbers and frequencies are identical. The inviscid growth rate of each resonant Kelvin mode combination is computed and compared to the asymptotic values obtained in the large wave numbers limits. The instability is also interpreted as a vorticity stretching mechanism. It is shown that the inviscid growth rate is maximum when the perturbation vorticity is preferentially aligned with the direction of stretching. Viscous effects are also considered for the distinguished scalings: for and for where is the dimensionless viscosity. The instability diagram showing the most unstable mode combination and its growth rate as a function of viscosity is obtained and used to discuss the role of viscosity in the selection process. Interestingly, for in a high viscosity regime, a combination of Kelvin modes of azimuthal wave numbers and is found to be more unstable than the classical helical modes For and 4, the azimuthal structure of the most unstable Kelvin mode combination is shown to be strongly dependent on viscous effects. The results are discussed in the context of turbulence and compared to recent observations of vortex filaments.

Point vortex dynamics within a background vorticity patch
View Description Hide DescriptionRecent experiments and simulations have observed that the interaction of strong vortices with a low vorticity background can strongly affect the dynamics of both vortices and background. This paper considers an idealized model of this interaction. The background is treated as a patch of uniform vorticity with a nearly circular shape. The strong vortices are treated as point vortices, and their total circulation λ is assumed to be small compared to that of the background. It is found that Kelvin waves on the boundary of the background patch can be driven to large amplitude by the strong vortices, eventually resulting in wave breaking and filamentation. A multiscale analysis finds that the wavebreaking time scales as in agreement with contour dynamics simulations.

A comparative study of nearwall turbulence in high and low Reynolds number boundary layers
View Description Hide DescriptionThe present study explores the effects of Reynolds number, over three orders of magnitude, in the viscous wall region of a turbulent boundary layer. Complementary experiments were conducted both in the boundary layerwind tunnel at the University of Utah and in the atmospheric surface layer which flows over the salt flats of the Great Salt Lake Desert in western Utah. The Reynolds numbers, based on momentum deficit thickness, of the two flows were and respectively. Highresolution velocity measurements were obtained from a fiveelement vertical rake of hotwires spanning the buffer region. In both the low and high flows, the length of the hotwires measured less than 6 viscous units. To facilitate reliable comparisons, both the laboratory and field experiments employed the same instrumentation and procedures. Data indicate that, even in the immediate vicinity of the surface, strong influences from lowfrequency motions at high produce noticeable Reynolds number differences in the streamwise velocity and velocity gradient statistics. In particular, the peak value in the root mean square streamwise velocity profile, when normalized by viscous scales, was found to exhibit a logarithmic dependence on Reynolds number. The mean streamwise velocity profile, on the other hand, appears to be essentially independent of Reynolds number. Spectra and spatial correlation data suggest that lowfrequency motions at high Reynolds number engender intensified local convection velocities which affect the structure of both the velocity and velocity gradient fields. Implications for turbulent production mechanisms and coherent motions in the buffer layer are discussed.

A model for layer formation in stably stratified turbulence
View Description Hide DescriptionStably stratified turbulent flows are common in geophysics and astrophysics, and frequently exhibit layered structures in which large regions of nearly constant fluid density are separated by sharp density gradients. Experiments have demonstrated that, under suitable conditions, the stirring of a stably stratified fluid generates these layer structures. In this paper, a stochastic onedimensional model is used to study layer formation in stably stratified turbulence. The results support mixing length arguments previously proposed to describe layers in steady state.

Effect of condensation and evaporation on the viscousconvective subrange
View Description Hide DescriptionThe effect of condensation and evaporation on the viscousconvective subrange is investigated using a general meanfield approximation that is consistent with the nonhomogeneous vertical structure of the condensate’s first and second moments and experimental observations of mean vertical flux in a condensationcloud. Expressions for the scalar density in the Batchelor limit are derived and used to reproduce the spectral behavior of new atmospheric measurements that exhibit anomalous scaling of cloud liquid water in the near inertialconvective regime. Good agreement between the model and data are obtained when axisymmetric Kraichnan transfer of scalar variance is balanced by axisymmetric production by condensation/evaporation resulting in an isotropic contribution to the real (homogeneous) part of the spectrum. The model also assumes a significant imaginary (nonhomogeneous) component to the spectrum that is indicative of a strong vertical coherence in condensationclouds. A “production subrange” is predicted in which the scalar dissipation rate increases with increasing wave number and the usual viscousconvective scaling evolves into an anomalous regime. The strongly nonhomogeneous (anisotropic) character of the predicted scalar spectrum is in stark contrast with atmospheric models of inertialconvective regime cloud inhomogeneity that are used in radiative transfer calculations and are typically isotropic.

The scenario of threedimensional instabilities of the cylinder wake in an external magnetic field: A linear stability analysis
View Description Hide DescriptionA more detailed look is given on the scenario of threedimensional (3D) instabilities in the magnetohydrodynamic cylinder flow when the oncoming flow and the magnetic field are parallel. The results presented here are in the frame of linear stability analysis in the range 100<Re<250 and extend the results in our previous letter [Phys. Fluids 9, 3114 (1997)]. As the strength of the magnetic field is increased, a nonmonotonic behavior of the 3D instability is found. This is mainly due to the fact that the underlying twodimensional (2D) flow changes considerably from periodic to steady while different instability mechanisms are counteracting. The behavior at weak magnetic fields depends on the Reynolds number and has either a damping or an enhancing influence on 3D instability. A local maximum is observed in the 3D instability curve, close to the critical value for 2D instability, leading to 3D instability at Reynolds numbers as low as i.e., lower than the critical Reynolds number for the onset of three dimensionality, in the pure hydrodynamic cylinder flow. By increasing the magnetic field strength further, the 3D instability is first damped while for larger values of N it is generally amplified. Therefore, for strong magnetic fields, 3D steady flows may exist at Re which are considerably lower than of the pure hydrodynamic cylinder flow. In the case of a transverse magnetic field, a stronger and approximately monotonic damping of three dimensionality was observed with increasing magnetic field strength.

On the role of largescale structures in wall turbulence
View Description Hide DescriptionRecent experimental and computational studies by Adrian and coworkers, such as Adrian et al. [J. Fluid Mech. 422, 1 (2000)] and Zhou et al. [J. Fluid Mech. 387, 353 (1999)], have proposed that a dominant structure in wall turbulence is the organization of hairpin vortices in spatially correlated packets or trains of vortices. In this study this scenario is investigated using the attached eddymodel of Perry and Marusic [J. Fluid Mech. 298, 361 (1995)] by calculating structure angles, twopoint velocity correlations and autocorrelations and comparing them to experimental measurements across a zeropressuregradient turbulent boundary layer. The results support the conclusion that spatially coherent packets are a statistically significant structure for Reynolds stresses and transport processes in the logarithmic region of the flow.

Generalized hydrodynamics, bulk viscosity, and sound wave absorption and dispersion in dilute rigid molecular gases
View Description Hide DescriptionGeneralized hydrodynamic equations are derived from an irreversible kinetic equation for rigid diatomic molecular gases and applied to extract the bulk viscosity by making use of sound wave absorption and dispersion. As a first application of the generalized hydrodynamic equations for molecular gases, the linearized versions of the generalized hydrodynamic equations are applied to study sound wave absorption and dispersion in molecular gases. The results obtained for sound wave absorption and dispersion with the linearized set yield good agreement with experimental data on nitrogen, hydrogen, deuterium, and HD reported in the literature.

Large eddy simulation of a turbulent reacting jet with conditional sourceterm estimation
View Description Hide DescriptionThe Conditional Sourceterm Estimation (CSE) method was recently proposed to close the chemical source terms occurring in the spatially filtered transportequations of species and enthalpy for Large Eddy Simulation(LES) of nonpremixed reacting flows [W. K. Bushe and H. Steiner, Phys. Fluids 11, 1896 (1999)]. The model is based on the Conditional Moment Closure hypothesis, which provides fairly accurate predictions for the conditional averages of the chemical reaction rates as functions of the conditionally averaged composition vector and temperature with the mixture fraction being an appropriate conditioning variable. In CSE the conditionally averaged composition vector and temperature are obtained by mapping the corresponding spatially filtered scalar fields resolved by the LES into the conditioning (i.e., mixture fraction) space. After the conditional averages of the chemical reaction rates are approximated in mixture fraction space, these are mapped into the physical space to close the source terms in the LEStransportequations for the reactive scalars. The present simulation of a turbulent reacting jet is the first test of this new closure in a selfsustained predictive LES. A twostep reduced chemical kinetic mechanism for methane–air flames was used. The results of the simulation, which are in reasonable agreement with available experimental data, prove the model’s predictive capabilities as well as its robustness and feasibility for LES.
