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Oct 2006

Volume 18, Issue 10, Articles (10xxxx)

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Surface switching of rotating fluid in a cylinder

Toshiyuki Suzuki, Makoto Iima, and Yumino Hayase

Phys. Fluids 18, 101701 (2006); http://dx.doi.org/10.1063/1.2359740 (4 pages) | Cited 11 times

Online Publication Date: 3 October 2006

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We study the surface shape of water in an open cylinder driven by constant rotation of the bottom. Around the critical Reynolds number for the laminar-turbulent transition, the surface deformation, which is of the order of the container size, shows an aperiodic switching phenomenon between an axisymmetric shape and a nonaxisymmetric shape. The axisymmetric shape is observed as a steady state when the Reynolds number is smaller than that in the switching region, while the nonaxisymmetric shape is observed as a (quasi-) periodic state in which the surface rotates at almost constant angular velocity when the Reynolds number is larger than that in the switching region. A detailed analysis for the surface shape suggests that the flow with the nonaxisymmetric shape is turbulent.
Show PACS
47.32.Ef Rotating and swirling flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence

Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows

X. Y. Hu and N. A. Adams

Phys. Fluids 18, 101702 (2006); http://dx.doi.org/10.1063/1.2359741 (4 pages) | Cited 6 times

Online Publication Date: 5 October 2006

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Current smoothed particle dynamics discretizations for macroscopic and mesoscopic viscous flows usually do not conserve angular momentum. Angular-momentum conservation, however, potentially stabilizes the solution for long-time simulations. We show that a simple angular-momentum conservative formulation of the viscous force, which was proposed previously based on empirical findings, can be derived theoretically under the condition of incompressible flow. The properties of this formulation are asserted by numerical simulations of two-dimensional Taylor-Green flow.
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47.55.Kf Particle-laden flows
47.10.ab Conservation laws and constitutive relations
02.60.Cb Numerical simulation; solution of equations
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back to top Interfacial Flows

Flow of a thin liquid film on an unsteady stretching sheet

B. S. Dandapat and S. Maity

Phys. Fluids 18, 102101 (2006); http://dx.doi.org/10.1063/1.2360256 (7 pages)

Online Publication Date: 16 October 2006

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The stretching surface is assumed to be stretched impulsively from rest and the effect of inertia of the liquid is considered. Equations describing the laminar flow on the stretching surface are solved analytically by using the singular perturbation technique and the method of characteristics is used to obtain an analytic expression for film thickness. The results show that the final film thickness is independent of the amount of liquid distributed initially and on the initial film thickness be it uniform or nonuniform. It is also shown that the forceful stretching produces quicker thinning of the film on the stretching surface.
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47.55.nd Spreading films
47.15.gm Thin film flows
47.85.mb Coating flows
47.15.Cb Laminar boundary layers
68.15.+e Liquid thin films

A computational study of the coalescence between a drop and an interface in Newtonian and viscoelastic fluids

Pengtao Yue, Chunfeng Zhou, and James J. Feng

Phys. Fluids 18, 102102 (2006); http://dx.doi.org/10.1063/1.2364144 (14 pages) | Cited 15 times

Online Publication Date: 25 October 2006

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multimedia

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A drop falling onto a fluid-fluid interface may not merge with it at once but may undergo a so-called partial coalescence cascade. Experimental observations of this phenomenon have revealed fascinating features of the process for Newtonian as well as polymeric fluids. In this paper, we describe numerical simulations of partial coalescence based on a phase-field method. Results show that partial coalescence occurs for an intermediate range of drop sizes, and proceeds in two stages: capillary waves propagating along the drop and transforming it into a fluid column, and neck formation on the column and pinch-off of the secondary drop. In the first stage, interfacial energy turns into kinetic energy following film rupture, while in the second, the kinetic energy overcomes an energy barrier due to the initial increase in interfacial area during neck formation. A parametric study establishes a criterion for partial coalescence in terms of a maximum Ohnesorge number that applies to a wide range of fluid densities and viscosities as long as the Bond number is small. Viscoelasticity in either the drop or the matrix tends to delay the pinch-off of the secondary drop, and may even suppress partial coalescence altogether. The underlying mechanism is large tensile polymer stresses resisting the stretching and thinning of the fluid neck. The numerical results are in qualitative, and in some cases quantitative, agreement with prior experiments.
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47.55.df Breakup and coalescence
47.50.Cd Modeling
47.35.Pq Capillary waves
47.54.Bd Theoretical aspects
68.03.Cd Surface tension and related phenomena
02.60.Cb Numerical simulation; solution of equations

Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow

Shaoping Quan and David P. Schmidt

Phys. Fluids 18, 102103 (2006); http://dx.doi.org/10.1063/1.2363216 (9 pages) | Cited 10 times

Online Publication Date: 31 October 2006

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A liquid spherical droplet impulsively accelerated by a gaseous flow is simulated in order to investigate the drag force and the deformation. The dynamics of the droplet immersed in a gaseous flow are investigated by solving the incompressible Navier-Stokes equations using a finite volume staggered mesh method coupled with a moving mesh interface tracking scheme. The benefit of the current scheme is that the interface conditions are implemented directly on an explicitly located interface with zero thickness. The droplet shape changes as it is accelerated, and the deformation factor of the droplet is as small as 0.2, so mesh adaptation methods are employed to achieve good mesh quality and to capture the interface curvature. The total drag coefficients are found to be larger than typical steady-state drag coefficients of solid spheres at the same Reynolds numbers. This agrees with the observation of Temkin et al. [J. Fluid Mech. 96, 133 (1980) ] that the unsteady drag of decelerating relative flows was always larger than the steady drag. The large recirculation region behind the deformed droplet may explain this greater drag force. The effects of the viscosity ratio, density ratio, and initial Weber number on the droplet dynamics are also studied. It is found that the initial Weber number and the viscosity ratio have significant effects on the droplet dynamics, while the density ratio does not.
Show PACS
47.55.df Breakup and coalescence
47.55.Ca Gas/liquid flows
47.10.ad Navier-Stokes equations
47.11.Df Finite volume methods
47.85.Np Fluidics
02.70.Dh Finite-element and Galerkin methods

Spray impact: Rim transverse instability initiating fingering and splash, and description of a secondary spray

Ilia V. Roisman, Kristijan Horvat, and Cam Tropea

Phys. Fluids 18, 102104 (2006); http://dx.doi.org/10.1063/1.2364187 (19 pages) | Cited 21 times

Online Publication Date: 31 October 2006

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In this paper, normal spray impact onto a rigid wall, leading to the formation of secondary spray, is considered. The mechanism of splash is explained by the bending instability of a rim bounding a free liquid sheet. The linear stability analysis of the rim is performed in the framework of the long-wave, quasi-one-dimensional approach. The rim instability is caused by the moment of forces associated with the inertia of the liquid entering the rim. Next, two components of the drop velocity and their diameter, as well as various flux density vectors (number, volume, mass fluxes) and tensors (momentum flux), are measured using a phase Doppler instrument. It is shown that the viscous length scale of drop impact can be used in describing the splash threshold, diameter of secondary droplets, and their velocity. Consequently, a closed semi-empirical model for the secondary spray has been proposed and validated using a numerical simulation of spray transport based on an Euler-Lagrange approach.
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47.55.dr Interactions with surfaces
47.55.nm Curtains/sheets
47.20.Lz Secondary instabilities
47.80.Cb Velocity measurements
47.85.Dh Hydrodynamics, hydraulics, hydrostatics
02.60.Cb Numerical simulation; solution of equations
back to top Viscous and Non-Newtonian Flows

Flow induced by a sphere settling in an aging yield-stress fluid

B. Gueslin, L. Talini, B. Herzhaft, Y. Peysson, and C. Allain

Phys. Fluids 18, 103101 (2006); http://dx.doi.org/10.1063/1.2358090 (8 pages) | Cited 2 times

Online Publication Date: 5 October 2006

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We have studied the flow induced by a macroscopic spherical particle settling in a Laponite suspension that exhibits a yield stress, thixotropy, and shear thinning. We show that the fluid thixotropy (or aging) induces an increase with time of both the apparent yield stress and shear-thinning properties but also a breaking of the flow fore-aft symmetry predicted in Hershel-Bulkley fluids (yield-stress, shear-thinning fluids with no thixotropy). We have also varied the stress exerted by the particles on the fluid by using particles of different densities. Although the stresses exerted by the particles are of the same order of magnitude, the velocity field presents utterly different features: whereas the flow around the lighter particle shows a confinement similar to the one observed in shear-thinning fluids, the wake of the heavier particle is characterized by an upward motion of the fluid (“negative wake”), whatever the fluid’s age. We compare the features of this negative wake to the one observed in viscoelastic shear-thinning fluids (polymeric or micelle solutions). Although the flows around the two particles strongly differ, their settling behaviors display no apparent difference which constitutes an intriguing result and evidences the complexity of the dependence of the drag factor on flow field.
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47.50.Cd Modeling
47.55.Kf Particle-laden flows
47.57.Qk Rheological aspects
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.85.Np Fluidics

Monodomain dynamics for rigid rod and platelet suspensions in strongly coupled coplanar linear flow and magnetic fields. II. Kinetic theory

M. Gregory Forest, Sarthok Sircar, Qi Wang, and Ruhai Zhou

Phys. Fluids 18, 103102 (2006); http://dx.doi.org/10.1063/1.2359232 (14 pages) | Cited 12 times

Online Publication Date: 12 October 2006

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We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional rate parameters). We solve the Smoluchowski equation of the reduced model to explore: (i) the effect of introducing a coplanar magnetic field on each sheared monodomain attractor of the Doi-Hess kinetic theory and (ii) the coupling of coplanar extensional flow and magnetic fields. For (i), we show each sheared attractor (steady and unsteady, with peak axis in and out of the shearing plane, periodic and chaotic orbits) undergoes its own transition sequence versus magnetic field strength. Nonetheless, robust predictions emerge: out-of-plane degrees of freedom are arrested with increasing field strength, and a unique flow-aligning or tumbling/wagging limit cycle emerges above a threshold magnetic field strength or modified geometry parameter value. For (ii), irrotational flows coupled with a coplanar magnetic field yield only steady states. We characterize all (generically biaxial) equilibria in terms of an explicit Boltzmann distribution, providing a natural generalization of analytical results on pure nematic equilibria [ P. Constantin, I. Kevrekidis, and E. S. Titi, Arch. Rat. Mech. Anal. 174, 365 (2004) ; P. Constantin, I. Kevrekidis, and E. S. Titi, Discrete and Continuous Dynamical Systems 11, 101 (2004) ; P. Constantin and J. Vukadinovic, Nonlinearity 18, 441 (2005) ; H. Liu, H. Zhang, and P. Zhang, Comm. Math. Sci. 3, 201 (2005) ; C. Luo, H. Zhang, and P. Zhang, Nonlinearity 18, 379 (2005) ; I. Fatkullin and V. Slastikov, Nonlinearity 18, 2565 (2005) ; H. Zhou, H. Wang, Q. Wang, and M. G. Forest, Nonlinearity 18, 2815 (2005) ] and extensional flow-induced equilibria [ Q. Wang, S. Sircar, and H. Zhou, Comm. Math. Sci. 4, 605 (2005) ]. We predict large parameter regions of bi-stable equilibria; the lowest energy state always has principal axis aligned in the flow plane, while another minimum energy state often exists, with primary alignment transverse to the coplanar field.
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47.55.Kf Particle-laden flows
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.32.Ef Rotating and swirling flows
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.52.+j Chaos in fluid dynamics

Topological mixing study of non-Newtonian duct flows

Michel Speetjens, Guy Metcalfe, and Murray Rudman

Phys. Fluids 18, 103103 (2006); http://dx.doi.org/10.1063/1.2359698 (11 pages) | Cited 2 times

Online Publication Date: 23 October 2006

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Tracer advection of non-Newtonian fluids in reoriented duct flows is investigated in terms of coherent structures in the web of tracer paths that determine transport properties geometrically. Reoriented duct flows are an idealization of in-line mixers, encompassing many micro and industrial continuous mixers. The topology of the tracer dynamics of reoriented duct flows is Hamiltonian. As the stretching per reorientation increases from zero, we show that the qualitative route from the integrable state to global chaos and good mixing does not depend on fluid rheology. This is due to a universal symmetry of reoriented duct flows, which we derive, controlling the topology of the tracer web. Symmetry determines where in parameter space global chaos first occurs, while increasing non-Newtonian effects delays the quantitative value of onset. Theory is demonstrated computationally for a representative duct flow, the rotated arc mixing flow.
Show PACS
47.50.Cd Modeling
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.51.+a Mixing
47.52.+j Chaos in fluid dynamics
47.32.Ef Rotating and swirling flows
47.85.Np Fluidics
back to top Particulate, Multiphase, and Granular Flows

Transient development of instabilities in a uniformly driven layer

Rensheng Deng and Chi-Hwa Wang

Phys. Fluids 18, 103301 (2006); http://dx.doi.org/10.1063/1.2355659 (13 pages)

Online Publication Date: 5 October 2006

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We present a nonlinear stability analysis on a uniformly driven granular layer to investigate the transient development of the instabilities induced by small perturbations. A continuum model based on the grain kinetic theory was adopted to trace the pattern evolution from the original unstable base state to a new base state and was numerically solved using a finite-element method. In the stability diagram characterized by two operating parameters, dimensionless mass holdup (Mt), and energy input (Qt), one point (Mt = 4.75, Qt = 58.31) in the stationary mode is selected to examine the fate of the two-dimensional density wave found from the linear stability analysis. Upon perturbing the base state, the bed height, solid fraction, particle velocities, and granular temperature profiles move away from their original to new, steady values after undergoing some oscillations. The stripes of solid fraction and granular temperature profiles finally change into a layer-like pattern, while the top surface is not uniform anymore but appears as periodic peaks and valleys due to the existence of uneven vertical velocities during the evolution. It is found that the finite amplitude of the initial perturbations is important for the pattern transition, and the evolution time increases with the increasing energy input and the increasing collision restitution coefficient. With the top surface of the granular layer being fixed at its original position, the oscillatory feature in the evolution curves of mass and temperature profiles disappears, and a lower solid fraction is obtained as compared to that observed in the presence of a moving upper boundary.
Show PACS
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.57.Gc Granular flow
47.55.Kf Particle-laden flows
47.54.Bd Theoretical aspects
47.11.Fg Finite element methods
02.70.Dh Finite-element and Galerkin methods

Numerical study of turbulent bubbly downflows in a vertical channel

Jiacai Lu and Gretar Tryggvason

Phys. Fluids 18, 103302 (2006); http://dx.doi.org/10.1063/1.2353399 (10 pages) | Cited 13 times

Online Publication Date: 10 October 2006

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Direct numerical simulations are used to study turbulent bubbly downflows in a vertical channel. All flow scales, including the bubbles and the flow around them, are fully resolved using a front-tracking/finite-volume method. The turbulent bubbly channel flow is driven downward by an imposed constant pressure gradient, and the friction Reynolds number of the flow, based on the friction velocity and half-width of the channel, is 127.3, corresponding to a bulk Reynolds number of 3786 for a flow without bubbles. Three cases with several nearly spherical bubbles are examined. The bubble diameter is 31.8 wall units for all cases but the number of bubbles is varied, giving average void fractions of 1.5%, 3%, and 6%. The lift force on the bubbles drives them away from the walls until the mixture in the center of the channel is in hydrostatic equilibrium. Thus, the flow consists of a core region where the average void fraction and the mean vertical velocity are approximately constant and a bubble-free wall layer. The vertical velocity fluctuations in the wall layer decrease as the void fraction increases and the width of the wall layer decreases, but in the bubble-rich core the velocity fluctuations are higher than for a corresponding single-phase turbulent flow.
Show PACS
47.27.nb Boundary layer turbulence
47.55.dd Bubble dynamics
47.27.nd Channel flow
47.27.ek Direct numerical simulations
47.11.Df Finite volume methods
47.85.Dh Hydrodynamics, hydraulics, hydrostatics

Computing stationary free-surface shapes in microfluidics

Michael Schindler, Peter Talkner, and Peter Hänggi

Phys. Fluids 18, 103303 (2006); http://dx.doi.org/10.1063/1.2361291 (16 pages) | Cited 5 times

Online Publication Date: 16 October 2006

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A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven pressure and flow fields compete with the surface tension for the shape of a stationary free surface. The free surface shape is represented by the boundaries of finite elements that move according to the stress applied by the adjacent fluid. Additionally, the surface tends to minimize its free energy and by that adapts its curvature to balance the normal stress at the surface. The numerical approach consists of the iteration of two alternating steps: The solution of a fluidic problem in a prescribed domain with slip boundary conditions at the free surface and a consecutive update of the domain driven by the previously determined pressure and velocity fields. For a Stokes problem the first step is linear, whereas the second step involves the nonlinear free-surface boundary condition. This algorithm is justified both by physical and mathematical arguments. It is tested in two dimensions for two cases that can be solved analytically. The magnitude of the errors is discussed in dependence on the approximation order of the finite elements and on a step-width parameter of the algorithm. Moreover, the algorithm is shown to be robust in the sense that convergence is reached also from initial forms that strongly deviate from the final shape. The presented algorithm does not require a remeshing of the used grid at the boundary. This advantage is achieved by a built-in mechanism that causes a smooth change from the behavior of a free surface to that of a rubber blanket if the boundary mesh becomes irregular. As a side effect, the element sides building up the free surface in two dimensions all approach equal lengths. The presented variational derivation of the boundary condition corroborates the numerical finding that a second-order approximation of the velocity also necessitates a second-order approximation for the free surface discretization.
Show PACS
47.55.Ca Gas/liquid flows
47.61.Jd Multiphase flows
47.11.Fg Finite element methods
47.10.A−
47.15.G−

Dynamics of a two-dimensional upflowing mixing layer seeded with bubbles: Bubble dispersion and effect of two-way coupling

E. Climent and J. Magnaudet

Phys. Fluids 18, 103304 (2006); http://dx.doi.org/10.1063/1.2363968 (12 pages) | Cited 9 times

Online Publication Date: 26 October 2006

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The evolution and structure of a spatially evolving two-dimensional mixing layer seeded with small bubbles are numerically investigated. The one-way coupling approach is first employed to show that characteristics of bubble dispersion are dominated by the possibility for sufficiently small bubbles to be captured in the core of the vortices. A stability analysis of the ordinary differential equation system governing bubble trajectories reveals that this entrapment process is governed by the presence of stable fixed points advected by the mean flow. Two-way coupling simulations are then carried out to study how the global features of a two-dimensional flow are affected by bubble-induced disturbances. The local interaction mechanism between the two phases is first analyzed using detailed simulations of a single bubbly vortex. The stability of the corresponding fixed point is found to be altered by the collective motion of bubbles. For trapped bubbles, the interphase momentum transfer yields periodic sequences of entrapment, local reduction of velocity gradients, and eventually escape of bubbles. Similar mechanisms are found to take place in the spatially evolving mixing layer. The presence of bubbles is also found to enhance the destabilization of the inlet velocity profile and to shorten the time required for the rollup phenomenon to occur. The most spectacular effects of small bubbles on the large-scale flow are a global tilting of the mixing layer centerline towards the low-velocity side and a strong increase of its spreading rate. In contrast, no significant modification of the flow is observed when the bubbles are not captured in the large-scale vortices, which occurs when the bubble characteristics are such that the drift parameter defined in the text exceeds a critical value. These two contrasted behaviors agree with available experimental results.
Show PACS
47.55.dd Bubble dynamics
47.51.+a Mixing
47.32.cb Vortex interactions
47.32.cd Vortex stability and breakdown
47.11.-j Computational methods in fluid dynamics
47.85.Np Fluidics

A novel gravity-induced flow transition in two-phase fluids

M. A. d’Avila, N. C. Shapley, J. H. Walton, R. J. Phillips, R. L. Powell, and S. R. Dungan

Phys. Fluids 18, 103305 (2006); http://dx.doi.org/10.1063/1.2358725 (5 pages) | Cited 2 times

Online Publication Date: 26 October 2006

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Experimental results are reported that show a gravity-induced flow transition in well-mixed suspensions and emulsions, even when the buoyancy-driven velocity of isolated drops or particles is several orders of magnitude smaller than the imposed velocity. The experiments were conducted with emulsions of isooctane in water and suspensions of polymethyl-methacrylate particles in water. Both the drop and particle diameters were approximately 3–5 μm, and concentrations of the dispersed phases ranged from dilute (2%) to concentrated (40%). The two-phase fluids were confined to a horizontal, concentric-cylinder apparatus in which the outer cylinder was rotated, and the velocity profiles were measured by nuclear magnetic resonance imaging. The results show that the flow transition is relatively insensitive to the volume fraction of the dispersed phase. The flow transition occurs because, although the buoyancy-driven velocity is relatively small on the length scale of the particle or drop dimension, the flow itself induces a slight variation in the suspension concentration and, hence, density. Although only on the order of 10−4 g/cm3, this density difference spans a macroscopic length scale, making the buoyancy effect competitive with the imposed flow. These arguments yield a dimensionless parameter that predicts very closely the nonequilibrium phase diagram generated by the experiments.
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47.35.Bb Gravity waves
47.57.Bc Foams and emulsions
47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.Ef Rotating and swirling flows
47.80.Jk Flow visualization and imaging

Unsteady motion of two solid spheres in Stokes flow

A. M. Ardekani and R. H. Rangel

Phys. Fluids 18, 103306 (2006); http://dx.doi.org/10.1063/1.2363351 (14 pages) | Cited 13 times

Online Publication Date: 27 October 2006

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See Also: Erratum

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This study is concerned with the unsteady motion of two solid spherical particles in an unbounded incompressible Newtonian flow. The background flow is uniform and can be time dependent. In addition, the particle Reynolds numbers 2aVa/ν and 2bVb/ν, based on characteristic particles velocities Va and Vb, are assumed to remain small throughout the motion. Here, a and b denote the particle radii and ν is the kinematic viscosity of the fluid. Two approximate methods are employed in order to calculate the unsteady force exerted on each particle. In the first approach, a simplified method of reflections in combination with the point-force method is employed. In the second approach, a simplified method of reflections combined with Burger’s unsteady flow solution is considered. The forces due to the background flow and the disturbed flow created by the presence of particles are treated separately. The equation of motion for each particle is derived and some special cases are presented in detail including the motion with constant acceleration and the motion in a gravitational field. The results indicate that using the Basset force corresponding to the motion of two spheres gives rise to a larger drag force as compared to the solution utilizing the solitary-particle Basset force.
Show PACS
47.55.Kf Particle-laden flows
47.20.Gv Viscous and viscoelastic instabilities
47.35.Bb Gravity waves
47.85.Np Fluidics

Dense shearing flows of inelastic disks

James T. Jenkins

Phys. Fluids 18, 103307 (2006); http://dx.doi.org/10.1063/1.2364168 (9 pages) | Cited 37 times

Online Publication Date: 30 October 2006

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We introduce a simple phenomenological modification to the hydrodynamic equations for dense flows of identical, frictionless, inelastic disks and show that the resulting theory describes the area fraction dependence of quantities that are measured in numerical simulations of steady, homogeneous shearing flows and steady, fully developed flows down inclines. The modification involves the incorporation of a length scale other than the particle diameter in the expression for the rate of collisional dissipation. The idea is that enduring contacts between grains forced by the shearing reduce the collisional rate of dissipation while continuing to transmit momentum and force. The length and orientation of the chains of particles in contact are determined by a simple algebraic equation. When the resulting expression for the rate of dissipation is incorporated into the theory, numerical solutions of the boundary-value problem for steady, fully developed flow of circular disks down a bumpy incline exhibit a core with a uniform area fraction that decreases with increasing angles of inclination. When the height at which an inclined flow stops is assumed to be proportional to this chain length, a scaling between the average velocity, flow height, and stopping height similar to that seen in experiments and numerical simulations is obtained from the balance of fluctuation energy.
Show PACS
45.70.Mg Granular flow: mixing, segregation and stratification
51.10.+y Kinetic and transport theory of gases
83.10.−y
back to top Laminar Flows

Rotational flow in tapered slab rocket motors

Tony Saad, Oliver C. Sams, and Joseph Majdalani

Phys. Fluids 18, 103601 (2006); http://dx.doi.org/10.1063/1.2354193 (13 pages) | Cited 3 times

Online Publication Date: 2 October 2006

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Internal flow modeling is a requisite for obtaining critical parameters in the design and fabrication of modern solid rocket motors. In this work, the analytical formulation of internal flows particular to motors with tapered sidewalls is pursued. The analysis employs the vorticity-streamfunction approach to treat this problem assuming steady, incompressible, inviscid, and nonreactive flow conditions. The resulting solution is rotational following the analyses presented by Culick for a cylindrical motor. In an extension to Culick’s work, Clayton has recently managed to incorporate the effect of tapered walls. Here, an approach similar to that of Clayton is applied to a slab motor in which the chamber is modeled as a rectangular channel with tapered sidewalls. The solutions are shown to be reducible, at leading order, to Taylor’s inviscid profile in a porous channel. The analysis also captures the generation of vorticity at the surface of the propellant and its transport along the streamlines. It is from the axial pressure gradient that the proper form of the vorticity is ascertained. Regular perturbations are then used to solve the vorticity equation that prescribes the mean flow motion. Subsequently, numerical simulations via a finite volume solver are carried out to gain further confidence in the analytical approximations. In illustrating the effects of the taper on flow conditions, comparisons of total pressure and velocity profiles in tapered and nontapered chambers are entertained. Finally, a comparison with the axisymmetric flow analog is presented.
Show PACS
47.32.Ef Rotating and swirling flows
47.85.Np Fluidics
47.32.cb Vortex interactions
47.20.Cq Inviscid instability
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.56.+r Flows through porous media

Convective heat transfer in unsteady laminar parallel flows

G. J. Brereton and Y. Jiang

Phys. Fluids 18, 103602 (2006); http://dx.doi.org/10.1063/1.2359742 (15 pages) | Cited 2 times

Online Publication Date: 16 October 2006

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In laminar, fully developed pipe and channel flows that undergo transients from a known initial state, exact analytical solutions for the momentary velocity field as functionals of the flow rate can be determined from the Navier-Stokes equations, for arbitrary flow unsteadiness [ Phys. Fluids 12, 518 (2000) ]. For laminar, fully developed duct flows with uniform wall heating that undergo large flow transients, the companion thermal energy equation can be approximated in a form that may also be solved analytically, yielding solutions for the instantaneous temperature field for arbitrary time unsteadiness in both the flow and the wall heat flux. Expressions for Nusselt numbers in convective heat transfer in duct flows with arbitrary temporal flow and heat flux unsteadiness can then be found, which illustrate how the flow and heat flux transient histories determine whether the unsteadiness enhances or reduces the overall heat-transfer effectiveness. These expressions are used to show how significant enhancements or reductions in the average Nusselt number can be achieved in duct flow by applying appropriate temporal flow control.
Show PACS
47.27.te Turbulent convective heat transfer
47.15.Fe Stability of laminar flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.10.ad Navier-Stokes equations
47.15.Cb Laminar boundary layers

An experimental investigation of hydrodynamic cavitation in micro-Venturis

Chandan Mishra and Yoav Peles

Phys. Fluids 18, 103603 (2006); http://dx.doi.org/10.1063/1.2360996 (5 pages) | Cited 10 times

Online Publication Date: 16 October 2006

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The existence of hydrodynamic cavitation in the flow of de-ionized water through micro-Venturis has been witnessed in the form of traveling bubble cavitation and fully developed streamer bubble/supercavitation, and their mechanisms have been discussed. High-speed photography and flow visualization disclose inchoate cavitation bubbles emerging downstream from the micro-Venturi throat and the presence of a single streamer bubble/supercavity, which is equidistant from the micro device walls. The supercavity initiates inside the diffuser section and extends until the microchannel exit and proceeds to bifurcate the incoming flow. This article strives to provide numerical data and experimental details of hydrodynamic cavitation taking place within micro-Venturis.
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47.55.dp Cavitation and boiling
47.85.Dh Hydrodynamics, hydraulics, hydrostatics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.80.Jk Flow visualization and imaging
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Three-dimensional simulation of gaseous slip flow in different aspect ratio microducts

Abhishek Agrawal and Amit Agrawal

Phys. Fluids 18, 103604 (2006); http://dx.doi.org/10.1063/1.2354546 (11 pages) | Cited 7 times

Online Publication Date: 19 October 2006

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Three-dimensional lattice Boltzmann method based simulations of a microduct have been undertaken in this paper. The objectives are to understand the different physical phenomena occurring at these small scales and to investigate when the flow can be treated as two dimensional. Toward this end, the Knudsen number and aspect ratio (depth to width ratio) are varied for a fixed pressure ratio. The pressure in the microduct is nonlinear with the nonlinearity in pressure reducing with an increase in the Knudsen number. The pressure behaves somewhat similar to two-dimensional microchannels, even when the aspect ratio is unity. The slip velocity at the impenetrable wall has two components: along and perpendicular to the primary flow direction. Our results show that the streamwise velocity near the centerline is relatively invariant along the depth for an aspect ratio of more than three, suggesting that the microduct can be modeled as a two-dimensional microchannel. On the other hand, the velocity component along the depth is never identically zero, implying that the flow is not truly two dimensional, although for practical purposes a two-dimensional treatment might suffice. A curious change in the vector direction in a plane normal to the flow direction is observed around an aspect ratio of four. These three-dimensional results are significant because they will help in theoretical development and flow modeling at microscales.
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47.45.Gx Slip flows and accommodation
47.85.Np Fluidics
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.Qr Lattice gas

Flow around spheres by dissipative particle dynamics

Shuo Chen, Nhan Phan-Thien, Boo Cheong Khoo, and Xi Jun Fan

Phys. Fluids 18, 103605 (2006); http://dx.doi.org/10.1063/1.2360421 (14 pages) | Cited 15 times

Online Publication Date: 24 October 2006

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The dissipative particle dynamics (DPD) method is used to study the flow behavior past a sphere. The sphere is represented by frozen DPD particles while the surrounding fluids are modeled by simple DPD particles (representing a Newtonian fluid). For the surface of the sphere, the conventional model without special treatment and the model with specular reflection boundary condition proposed by Revenga et al. [Comput. Phys. Commun. 121–122, 309 (1999)] are compared. Various computational domains, in which the sphere is held stationary at the center, are investigated to gage the effects of periodic conditions and walls for Reynolds number (Re) = 0.5 and 50. Two types of flow conditions, uniform flow and shear flow are considered, respectively, to study the drag force and torque acting on the stationary sphere. It is found that the calculated drag force imposed on the sphere based on the model with specular reflection is slightly lower than the conventional model without special treatment. With the conventional model the drag force acting on the sphere is in better agreement with experimental correlation obtained by Brown and Lawler [J. Environ. Eng. 129, 222 (2003)] for the case of larger radius up to Re of about 5. The computed torque also approaches the analytical Stokes value when Re<1. For a force-free and torque-free sphere, its motion in the flow is captured by solving the translational and rotational equations of motion. The effects of different DPD parameters (a, γ, and σ) on the drag force and torque are studied. It shows that the dissipative coefficient (γ) mainly affects the drag force and torque, while random and conservative coefficient have little influence on them. Furthermore the settling of a single sphere in square tube is investigated, in which the wall effect is considered. Good agreement is found with the experiments of Miyamura et al. [Int. J. Multiphase Flow 7, 31 (1981)] and lattice-Boltzmann simulation results of Aidun et al. [J. Fluid Mech. 373, 287 (1998)] .
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47.55.Kf Particle-laden flows
47.15.Cb Laminar boundary layers
47.15.St Free shear layers
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.85.Dh Hydrodynamics, hydraulics, hydrostatics
back to top Instability and Transition

Inertialess temporal and spatio-temporal stability analysis of the two-layer film flow with density stratification

J. Hu, S. Millet, V. Botton, H. Ben Hadid, and D. Henry

Phys. Fluids 18, 104101 (2006); http://dx.doi.org/10.1063/1.2357026 (14 pages) | Cited 4 times

Online Publication Date: 2 October 2006

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This paper presents a temporal, spatial, and spatio-temporal linear stability analysis of the two-layer film flow down a plate tilted at an angle θ. It is based on a zero Reynolds number approximation to the Orr-Sommerfeld equations and a zero surface tension approximation to both surface boundary conditions. The combined effects of density and viscosity stratifications are systematically investigated. The subtle influence of density stratification is first put into light by a temporal analysis for θ = 0.2; when increasing/decreasing the density ratio (upper fluid/lower fluid), the two-layer film flow becomes much more unstable/stable with respect to the finite wavelength instability. Moreover, below a critical density ratio this finite wavelength instability even disappears, whatever the viscous ratio. Concerning the long wave instability, it becomes dominant when decreasing the density ratio below 1 and is even triggered in a region which was stable for equal density layers. The spatio-temporal analysis shows that the instability is convective for incline angles that are not too small as θ = 0.2. The study of the local growth rates of the spatio-temporal instability as a function of the ray velocity V shows that there is a transition between long wave and short wave instabilities which has been determined by using the Briggs-Bers collision criterion. Accordingly, there exists a jump for the local oscillatory frequency, spatial amplification rate, and spatial wave number due to this transition. Due to the existence of the absolute Rayleigh-Taylor instability for θ = 0, the transition from convective to absolute instability can be detected for values of θ smaller than 0.2, and absolute/convective instability boundary curves have been obtained for varying characteristic parameters.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.Hd Stratified flows
47.55.P- Buoyancy-driven flows; convection
05.45.-a Nonlinear dynamics and chaos

Conditional statistics for a passive scalar with a mean gradient and intermittency

A. Bourlioux, A. J. Majda, and O. Volkov

Phys. Fluids 18, 104102 (2006); http://dx.doi.org/10.1063/1.2353880 (10 pages)

Online Publication Date: 3 October 2006

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The conditional dissipation and diffusion for a passive scalar with an imposed mean gradient are studied here. The results are obtained for an elementary model consisting of a random shear flow with a simple time-periodic transverse sweep. As the Peclet number is increased, scalar intermittency is observed; the scalar probability density function departs strongly from a Gaussian law. As a result, the conditional dissipation undergoes a transition from a quadratic behavior for the near-Gaussian probability distribution case at low Peclet number to a more complex shape at large Peclet. The conditional diffusion also undergoes a transition, this time from a linear to a nonlinear dependence, for cases with sufficient intermittency as well as a significant contribution from multiple spatial modes. The present analysis sheds some light on similar behaviors observed recently in numerical simulations of more complex models. The statistics in the present study are obtained by exact processing of one-dimensional quadrature results so that all sampling errors are eliminated, including in the tails of the distribution. This allows for a quantification of typical sampling errors when the conditional statistics are processed from numerical databases. The robustness of models based on polynomial fits for the conditional statistics is also assessed.
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47.27.tb Turbulent diffusion
47.27.eb Statistical theories and models
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.Ng Distribution theory and Monte Carlo studies

Three-dimensional wave packets in a compressible boundary layer

Eric Forgoston and Anatoli Tumin

Phys. Fluids 18, 104103 (2006); http://dx.doi.org/10.1063/1.2359003 (13 pages) | Cited 1 time

Online Publication Date: 10 October 2006

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A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using previous analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for two discrete modes: Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using the Gaussian model as well as the method of steepest descent. It is shown that the method of steepest descent provides an excellent approximation to the more computationally intensive numerical evaluation of the inverse Fourier transform. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation of the Fourier integral. A main feature of the resulting three-dimensional wave packet is its two-dimensional nature, which arises from an association of Mode S with Mack’s second mode.
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47.40.Ki Supersonic and hypersonic flows
47.35.Rs Sound waves
47.20.Pc Flow receptivity
47.15.Cb Laminar boundary layers
47.27.nb Boundary layer turbulence

Oscillatory jets and instabilities in a rotating cylinder

Yohann Duguet, Julian F. Scott, and Lionel Le Penven

Phys. Fluids 18, 104104 (2006); http://dx.doi.org/10.1063/1.2357973 (11 pages)

Online Publication Date: 11 October 2006

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The viscous flow inside a closed rotating cylinder of gas subject to periodic axial compression is investigated numerically. The numerical method is based on a spectral Galerkin expansion of the velocity field, assuming axisymmetry of the flow. If the forcing amplitude is weak and the angular forcing frequency is less than twice the rotation rate, inertial waves emanate from the corners, forming conical oscillatory jets which undergo reflections at the walls. Their thickness is O(E1/3), or O(E1/4) for particular forcing frequencies, where E is the Ekman number. For larger forcing amplitudes, the conical pattern breaks down. When the forcing frequency is resonant with a low-order inertial mode, the flow can undergo two types of parametric instabilities: a mode-triad resonance, and a subharmonic instability. The combination of both these mechanisms provides a possible route to quasiperiodicity of the flow.
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47.32.Ef Rotating and swirling flows
47.20.Gv Viscous and viscoelastic instabilities
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.35.Jk Wave breaking
47.54.Bd Theoretical aspects
47.11.Fg Finite element methods
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