Index of content:
Volume 24, Issue 4, April 2012
Large-eddy simulation(LES) of two-phase turbulent flows exhibits quantitative differences in particle statistics if compared to direct numerical simulation (DNS) which, in the context of the present study, is considered the exact reference case. Differences are primarily due to filtering, a fundamental intrinsic feature of LES. Filtering the fluid velocity field yields approximate computation of the forces acting on particles and, in turn, trajectories that are inaccurate when compared to those of DNS. In this paper, we focus precisely on the filtering error for which we quantify a lower bound. To this aim, we use a DNS database of inertial particle dispersion in turbulent channel flow and we perform a priori tests in which the error purely due to filtering is singled out removing error accumulation effects, which would otherwise lead to progressive divergence between DNS and LESparticle trajectories. By applying filters of different type and width at varying particle inertia, we characterize the statistical properties of the filtering error as a function of the wall distance. Results show that filtering error is stochastic and has a non-Gaussian distribution. In addition, the distribution of the filtering error depends strongly on the wall-normal coordinate being maximum in the buffer region. Our findings provide insight on the effect of sub-grid scale velocity field on the force driving the particles, and establish the requirements that any closure model aimed at recovering sub-grid scale effects on the dynamics of inertial particles must satisfy.
24(2012); http://dx.doi.org/10.1063/1.3700970View Description Hide Description
We examine Landau-Levich coating by a suspension of spherical particles. For particles larger than the liquid film thickness, capillary forces lead to self-assembly of monolayer particle aggregates. We observe two regimes of deposition, find coating fraction as a function of wall speed, and propose a spinodal decomposition (Cahn-Hilliard) model for this pattern formation process.
24(2012); http://dx.doi.org/10.1063/1.4704196View Description Hide Description
We measuredvelocity distribution in cross sections of a fully developed turbulent pipe flow upstream and downstream of a 90° bend by synchronizing two sets of a particle image velocimetry(PIV) system. Unsteady undulation of Dean vortices formed downstream from the bend was characterized by the azimuthal position of the stagnation point found on the inner and outer sides of the bend. Linear stochastic estimation was applied to capture the upstream flow field conditioned by the azimuthal location of the stagnation point downstream from the bend. When the inner-side stagnation point stayed below (above) the symmetry plane, the conditional streamwise velocity upstream from the bend exhibited high-speed streaks extended in a quasi-streamwise direction on the outer side of the curvature above (below) the symmetry plane.
24(2012); http://dx.doi.org/10.1063/1.4706183View Description Hide Description
Internal gravity waves contribute to fluid mixing and energy transport, not only in oceans but also in the atmosphere and in astrophysical bodies. An efficient way to transfer energy from large scale to smaller scale is the parametric subharmonic instability. We provide here the first experimental measurement of the growth rate of this instability. We make careful and quantitative comparisons with theoretical predictions for propagating vertical modes in laboratory experiments.
- Biofluid Mechanics
24(2012); http://dx.doi.org/10.1063/1.4704792View Description Hide Description
Swimming organisms in their natural habitat need to navigate through a wide range of geometries and chemical environments. Interaction with boundaries in such situations is ubiquitous and can significantly modify the swimming characteristics of the organism when compared to ideal laboratory conditions. We study the different patterns of ciliary locomotion in glass capillaries of varying diameter and characterize the effect of the solid boundaries on the velocities of the organism. Experimental observations show that Paramecium executes helical trajectories that slowly transition to straight lines as the diameter of the capillary tubes decreases. We predict the swimming velocity in capillaries by modeling the system as a confined cylinder propagating longitudinal metachronal waves that create a finite pressure gradient. Comparing with experiments, we find that such pressure gradient considerations are necessary for modeling finite sized ciliary organisms in restrictive geometries.
- Micro- and Nanofluid Mechanics
24(2012); http://dx.doi.org/10.1063/1.4704822View Description Hide Description
We numerically investigate dynamics of magnetic chains and flow characteristics in a two-dimensional shear flow under the influence of a magnetic field applied externally. A direct simulation method is employed to solve the particulate flow in the creeping flow regime, taking into account both magnetic and hydrodynamic interactions in a coupled manner. In a periodic channel, the dynamics of chains is found to be significantly influenced by the Mason number (the ratio of viscous force to magnetic force), the magnetic susceptibility, and the particle fraction. Below a critical Mason number, a chain rotates and reaches an equilibrium. Above the critical value, however, the chain continuously rotates as a rigid body. Thinning behavior in the wall shear stress is found above a threshold value of the Mason number. As for chain rupture in the shear flow, three regimes of the Mason number are found, showing three typical conformations of the chains: (i) complex chains with branches rather than linear chains, (ii) tilted linear chains broken in the middle, generating a slip zone between the upper and lower chains, and (iii) shortened chains rotating in the channel.
Reaction cross sections for two direct simulation Monte Carlo models: Accuracy and sensitivity analysis24(2012); http://dx.doi.org/10.1063/1.3701379View Description Hide Description
The quantum kinetic chemical reactionmodel proposed by Bird for the direct simulation Monte Carlo method is based on collision kinetics with no assumed Arrhenius-related parameters. It demonstrates an excellent agreement with the best estimates for thermal reaction rates coefficients and with two-temperature nonequilibrium rate coefficients for high-temperature air reactions. This paper investigates this model further, concentrating on the non-thermal reaction cross sections as a function of collision energy, and compares its predictions with those of the earlier total collision energy model, also by Bird, as well as with available quasi-classical trajectory cross section predictions (this paper also publishes for the first time a table of these computed reaction cross sections). A rarefied hypersonic flow over a cylinder is used to examine the sensitivity of the number of exchange reactions to the differences in the two models under a strongly nonequilibrium velocity distribution.
- Interfacial Flows
24(2012); http://dx.doi.org/10.1063/1.3701996View Description Hide Description
This paper presents an investigation into drop spreading and capillary absorption at the surface of a porous substrate. Lattice Boltzmann numerical simulations are carried out at the pore level with two values of intrinsic contact angle at the liquid-gas-solid line and three values of porosity; the case of a flat solid surface is included as a reference. The numerical results show a power-law evolution of the wetted zone radius with time, both exponent and prefactor decreasing with increasing porosity. The evolution in time of the droplet height emerges from competition between pure spreading and bulk capillary imbibition in the porous medium.
24(2012); http://dx.doi.org/10.1063/1.3698403View Description Hide Description
The effect of inertia on gravity-driven free surface flow over different three-dimensional periodic corrugations is considered analytically, numerically and experimentally. In the case of high bottom amplitudes, compared to the film thickness, the results predict complex free surfacestructures especially in cases where the topography is not fully flooded by the liquid film. The investigation of the flow field shows a rich variety of pattern formation phenomena depending on the interplay between the geometry of the topography and the inertia of the film. Finally, we show how the complex topographical structure enhances the laminar mixing within the film.
Frequency and damping of non-axisymmetric surface oscillations of a viscous axisymmetric liquid bridge24(2012); http://dx.doi.org/10.1063/1.3703658View Description Hide Description
The frequency and damping of free lateral linear oscillations of a viscous non-cylindrical liquid bridge, formed between two axial disks of radii R 1 and R 2, are computed using a recently developed semi-analytic procedure [R. Kidambi, J. Fluid Mech.681, 597 (2011)]. A comparison with recent experimental results [E. J. Vega and J. M. Montanero, Phys. Fluids21, 092101 (2009)] for the first non-axisymmetric mode over a range of bridge volumes is good and the damping rate is better predicted than by a one-dimensional slice model especially for highly viscous bridges. The procedure can be used to calculate the oscillation characteristics of any desired mode for any region of the parameter space.
24(2012); http://dx.doi.org/10.1063/1.4704790View Description Hide Description
We present numerical simulations of drops settling in a layered ambient fluid. We focus on nearly spherical drops with Reynolds numbers of order 10. The ambient is composed of miscible fluids, with the top layer lighter than the lower one, representing fluid stratified through temperature or salinity variations, while the drop itself is heavier than both layers. The surface tension between the ambient and the drop may or may not be different for each layer. Such a system can be used to model oil droplets settling or rising in the ocean. When surface tension is uniform, the drop slows down significantly as it encounters the transition region, due to entrained fluid from the upper layer, before accelerating again in the lower layer. We characterize this effect in terms of the sharpness of the transition, and the drop's Reynolds number. When the upper and lower surface tensions are not matched, the drop may either suddenly accelerate through the transition region if the lower surface tension is less than the upper one, or be prevented from crossing into the lower layer if the lower surface tension is larger than the upper one. We focus on the drop's speed across the transition, and determine the conditions under which a drop may remain suspended at the transition region.
Numerical analysis of moving contact line with contact angle hysteresis using feedback deceleration technique24(2012); http://dx.doi.org/10.1063/1.4707703View Description Hide Description
Contact angle (CA) hysteresis is important in many natural and engineering wetting processes, but predicting it numerically is difficult. We developed an algorithm that considers CA hysteresis when analyzing the motion of the contact line (CL). This algorithm employs feedback control of CA which decelerates CL speed to make the CL stationary in the hysteretic range of CA, and one control coefficient should be heuristically determined depending on characteristic time of the simulated system. The algorithm requires embedding only a simple additional routine with little modification of a code which considers the dynamic CA. The method is non-iterative and explicit, and also has less computational load than other algorithms. For a drop hanging on a wire, the proposed algorithm accurately predicts the theoretical equilibrium CA. For the drop impacting on a dry surface, the results of the proposed algorithm agree well with experimental results including the intermittent occurrence of the pinning of CL. The proposed algorithm is as accurate as other algorithms, but faster.
- Viscous and Non-Newtonian Flows
24(2012); http://dx.doi.org/10.1063/1.3701373View Description Hide Description
The evolution of the shape of an elongated drop embedded in an extensional flow is studied in the framework of slender body theory. The external flow has a weak but not neglected inertia. The problem is governed by three dimensionless parameters: the capillary number, the external Reynolds number, and the viscosity ratio between the drop and the external fluid, and exhibits a multiplicity of stationary shapes with only one being stable. Evolution of the drop surface from initial shapes was studied when the flow intensity was either kept constant or subjected to a sudden change. It was shown that the dynamics of the shape evolution can lead to a breakup of the drop or to a stable stationary shape. Two modes of breakup are revealed: an indefinite elongation and a center pinching mode. The former appears when the viscous forces dominate the inertia effects, with the typical case being that of a creeping flow. The latter breakup mode takes over in the presence of inertia when the dropviscosity diminishes with the extreme example being that of an inviscid drop.
24(2012); http://dx.doi.org/10.1063/1.3703316View Description Hide Description
A thin thread of viscous fluid falling onto a moving belt generates a surprising variety of patterns depending on the belt speed, fall height, flow rate, and fluid properties. Here, we simulate this experiment numerically using the discrete viscous threads method that can predict the non-steady dynamics of thin viscous filaments, capturing the combined effects of inertia and of deformation by stretching, bending, and twisting. Our simulations successfully reproduce nine out of ten different patterns previously seen in the laboratory and agree closely with the experimental phase diagram of Morris et al. [Phys. Rev. E77, 066218 (2008)]10.1103/PhysRevE.77.066218. We propose a new classification of the patterns based on the Fourier spectra of the longitudinal and transverse motion of the point of contact of the thread with the belt. These frequencies appear to be locked in most cases to simple ratios of the frequency Ω c of steady coiling obtained in the limit of zero belt speed. In particular, the intriguing “alternating loops” pattern is produced by combining the first five multiples of Ω c /3.
24(2012); http://dx.doi.org/10.1063/1.4704195View Description Hide Description
We present simulations of two interacting moving cylinders immersed in a two-dimensional incompressible, viscousflow. Simulations are performed by coupling a wavelet-adapted, remeshed vortex method with the Brinkman penalization and projection approach. This method is validated on benchmark problems and applied to simulations of a master-slave pair of cylinders. The master cylinder's motion is imposed and the slave cylinder is let free to respond to the flow. We study the relative role of viscous and inertia effects in the cylinders interactions and identify related sharp transitions in the response of the slave. The observed differences in the behavior of cylinders with respect to corresponding potential flow simulations are discussed. In addition, it is observed that in certain situations the finite size of the slave cylinders enhances the transport so that the cylinders are advected more effectively than passive tracers placed, respectively, at the same starting position.
- Particulate, Multiphase, and Granular Flows
24(2012); http://dx.doi.org/10.1063/1.3700979View Description Hide Description
Silos are widely used for the industrial scale handling and transportation of powdered and granular materials. The process of discharging powder in a silo involves the flow of both solid particles and an interstitial fluid, usually air. In this study, we experimentally investigate the effects of particle size and ambient pressure on the discharge process in open- and closed-top silos. The discharge rate, pressure drop, and pressure recovery rate are measured and discussed. The results show that the particle size, the diameter of the orifice, and the ambient pressure significantly influence the process of discharge. The effect of air flow is stronger on fine-powdered flow in a closed-top silo. The results indicate that the effects of air flow could be reduced by lowering the ambient pressure. In addition, a normalized critical pressure can be defined beyond which the discharge rate increases dramatically. With reduced ambient pressure, this normalized critical pressure decreases with increasing particle size. Finally, the experimental results are compared with results calculated using the Beverloo equation and Darcy's law.
24(2012); http://dx.doi.org/10.1063/1.4704816View Description Hide Description
A new, three-dimensional algorithm is developed to accurately simulate low-Reynolds number, flow-driven motion of a neutrally buoyant spherical particle in plane-parallel microchannels of complex shape. The channel profile may consist of an arbitrary number of straight line segments with sharp corners in an arbitrary configuration. This geometry provides a suitable model for particle transport in many microfluidic devices with multiple branch bifurcations. The particle may be comparable with the narrowest channel dimensions, but is typically much smaller than the overall channel domain, which creates difficulties with a standard boundary-integral approach. To make simulations feasible, the 3D problem is solved locally in a computational cell that is smaller than the full domain and is dynamically constructed around the particle as it moves through the channel; the outer boundary conditions are provided by the 2D flow that would exist in the channel in the absence of the particle. Difficulties with particle-corner close interactions are alleviated using special iterative techniques, (near-) singularity subtractions and corner-fitted, gap-adaptive discretizations of the cell boundary. The algorithm is applied to simulate “pinched-flow fractionation” and predict how particle interactions with a narrow pinch region and sharp corners result in particle focusing and separation in the outlet according to their size. As another application, the particle motion through a T-bifurcation with sharp corners is simulated, with calculation of the particle flux partition ratio for a broad range of parameters. It is demonstrated how the particle-corner interactions can make the side branch inaccessible to particles, even for relatively strong fluid suction through this branch.
24(2012); http://dx.doi.org/10.1063/1.4705527View Description Hide Description
We consider the deformation of gas bubbles rising in different liquids over a wide range of Morton numbers, from O(10−11) to O(1), and bubble diameters. We have collected data from the literature and performed new experiments for relatively large Morton numbers. A simple expression is proposed to describe the evolution of the bubble deformation, which is consistent with the analytical solution of Moore [“The rise of a gas bubble in a viscousliquid,” J. Fluid Mech.6, 113 (1959)]. It appears that deformation can be predicted correctly by considering the Morton and Weber numbers. The variation of the bubble interfacial area is also analyzed; this quantity is very important for the case of bubbly flow modeling but has not been measured directly to date.
24(2012); http://dx.doi.org/10.1063/1.4704801View Description Hide Description
We experimentally study the detachment of drops of granular suspensions using a density matched model suspension with varying grain volume fraction (ϕ = 15% to 55%) and grain diameter (d = 20 μm to 140 μm). We show that at the beginning of the detachment process, the suspensions behave as an effective fluid. The detachment dynamics in this regime can be entirely described by the shear viscosity of the suspension[R. J. Furbank and J. F. Morris, Int. J. Multiphase Flow33(4), 448–468 (2007)]. At later stages of the detachment, the dynamics become independent of the volume fraction and are found to be identical to the dynamics of the interstitial fluid. Surprisingly, visual observation reveals that at this stage, particles are still present in the neck. We suspect rearrangements of particles to locally free the neck of grains, causing the observed dynamics. Close to the final pinch off, the detachment of the suspensions is further accelerated, compared to the dynamics of pure interstitial fluid. This acceleration might be due to the fact that the neck diameter gets of the order of magnitude of the size of the grains and a continuous thinning of the liquid thread is not possible any more. The crossover between the different detachment regimes is a function of the grain size and the initial volume fraction. We characterize the overall acceleration as a function of the grain size and volume fraction.
- Laminar Flows
24(2012); http://dx.doi.org/10.1063/1.4704194View Description Hide Description
This numerical study of the steady axisymmetric motion of a viscous incompressible fluid in a sealed cylindrical container with one end wall rotating reveals that swirl decay, induced by friction at the sidewall, plays an important role in the development of vortex breakdown (VB). When the flow is slow, it is multi-cellular. As the flow strength increases (i) meridional circulation becomes global, (ii) flow convergence toward the axis focuses near the still end wall, (iii) a few local minima of pressure appear, (iv) a few flow reversals occur near the axis, and (v) circulation regions merge and an elongated double counterflow develops. Stages (i)–(v) are common for a number of vortex devices. If the swirl decay is diminished by additional rotation of the sidewall, VB disappears.
- Instability and Transition
24(2012); http://dx.doi.org/10.1063/1.3694804View Description Hide Description
We present an experimental study of a liquid metal flow electromagnetically forced in a large aspect ratio coaxial cylindrical geometry. An azimuthal Lorentz force is applied on the liquid metal gap, through a radial current and an axial magnetic field. Using ultrasonic velocitymeasurements, we focus on the effect of these two parameters on the flow properties. We show that, depending on the strength of the magnetic field and not only on the applied Lorentz force, different dynamical states exist. We first observe a stationary structure at low forcing. Then, two other regimes of different travelling waves are exhibited at higher forcing. We characterize them by their different frequencies and speeds. Higher magnetic fields clearly promote the faster waves. Connections with other magnetohydrodynamics instabilities are discussed.