Phys. Fluids (1994-Present) - Physics of Fluids

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Announcement: The 2011 François Naftali Frenkiel Award for Fluid Mechanics

, The Editors

Phys. Fluids 24, 010201 (2012); http://dx.doi.org/10.1063/1.3654195 (2 pages)

Online Publication Date: 5 January 2012

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01.10.Cr	Announcements, news, and awards
47.11.-j	Computational methods in fluid dynamics

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Announcement: New Format for Physics of Fluids

John Kim and L. Gary Leal

Phys. Fluids 24, 010202 (2012); http://dx.doi.org/10.1063/1.3659012 (1 page)

Online Publication Date: 5 January 2012

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01.30.Ww

Editorials

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Referee Acknowledgment for 2011

John Kim and Gary Leal, Editors

Phys. Fluids 24, 010203 (2012); http://dx.doi.org/10.1063/1.3673575 (7 pages)

Online Publication Date: 20 January 2012

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47.00.00

Fluid dynamics

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Developed quantum turbulence and its decay

L. Skrbek and K. R. Sreenivasan

Phys. Fluids 24, 011301 (2012); http://dx.doi.org/10.1063/1.3678335 (48 pages)

Online Publication Date: 31 January 2012

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This article is primarily a review of our knowledge of the correspondence between classical and quantum turbulence, though it is interspersed with a few new interpretations. This review is deemed timely because recent work in quantum turbulence promises to provide a better understanding of aspects of classical turbulence, though the two fields of turbulence have similarities as well as differences. We pay a particular attention to the conceptually simplest case of zero temperature limit where quantum turbulence consists of a tangle of quantized vortex line and represents a simple prototype of turbulence. At finite temperature, we anchor ourselves at the level of two-fluid description of the superfluid state—consisting of a normal viscous fluid and a frictionless superfluid—and review much of the available knowledge on quantum turbulence in liquid helium (both He II and ³He-B). We consider counterflows in which the normal and superfluid components flow against each other, as well as co-flows in which the direction of the two fluids is the same. We discuss experimental methods, phenomenological results as well as key theoretical concepts.

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47.27.-i	Turbulent flows
47.32.C-	Vortex dynamics
47.37.+q	Hydrodynamic aspects of superfluidity; quantum fluids

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The onset of oblique vortex shedding behind a heated circular cylinder in laminar wake regime

Ming-Hsun Wu, Zdenăk Trávníček, and An-Bang Wang

Phys. Fluids 24, 011701 (2012); http://dx.doi.org/10.1063/1.3675551 (7 pages)

Online Publication Date: 5 January 2012

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Oblique vortex shedding (OVS) behind a heated circular cylinder in air was experimentally investigated. Similar to that in the parallel vortex shedding (PVS), the results show that the non-dimensionalized shedding frequency, Strouhal number, decreases under the influence of cylinder heating for oblique shedding mode. Although the onset Reynolds number of OVS increases with the cylinder temperature, the onset effective Reynolds number remains 63.3 ± 1.3 regardless of the cylinder heating. A general Strouhal-Reynolds-number relationship for OVS has been found based on the effective temperature concept in the present study. The ratio of the critical Reynolds numbers for the onsets of OVS and PVS is found to be an invariant with value of 4/3 for both isothermal and non-isothermal cases despite different length/diameter ratios and end conditions.

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47.15.ki	Inviscid flows with vorticity
47.32.C-	Vortex dynamics
47.15.Tr	Laminar wakes

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Grid-point requirements for large eddy simulation: Chapman’s estimates revisited

Haecheon Choi and Parviz Moin

Phys. Fluids 24, 011702 (2012); http://dx.doi.org/10.1063/1.3676783 (5 pages)

Online Publication Date: 6 January 2012

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Resolution requirements for large eddy simulation (LES), estimated by Chapman [AIAA J. 17, 1293 (1979)], are modified using accurate formulae for high Reynolds number boundary layer flow. The new estimates indicate that the number of grid points (N) required for wall-modeled LES is proportional to Re_{L_x}, but a wall-resolving LES requires ÑReL_x13/7, where L_x is the flat-plate length in the streamwise direction. On the other hand, direct numerical simulation, resolving the Kolmogorov length scale, requires ÑReL_x37/14.

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47.27.nb	Boundary layer turbulence
02.60.Cb	Numerical simulation; solution of equations
47.11.-j	Computational methods in fluid dynamics
47.27.ep	Large-eddy simulations

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Direct simulation Monte Carlo method for an arbitrary intermolecular potential

Felix Sharipov and José L. Strapasson

Phys. Fluids 24, 011703 (2012); http://dx.doi.org/10.1063/1.3676060 (6 pages)

Online Publication Date: 9 January 2012

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A scheme to implement an arbitrary intermolecular potential into the direct simulation Monte Carlo method is proposed. To illustrate the scheme, two benchmark problems are solved employing the Lennard-Jones potential. Since the computational effort of the new scheme is comparable with that of the hard sphere model of molecules, it can completely substitute the widely used models such as variable hard spheres and variable soft spheres.

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47.40.-x	Compressible flows; shock waves
02.50.Ng	Distribution theory and Monte Carlo studies
47.11.-j	Computational methods in fluid dynamics

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An analogy of Taylor’s instability criterion in Couette and rotating-magnetic-field-driven flows

Marius Ungarish

Phys. Fluids 24, 011704 (2012); http://dx.doi.org/10.1063/1.3675893 (7 pages)

Online Publication Date: 11 January 2012

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The classical stability solution of Taylor for the Couette flow between a rotating inner cylinder and a stationary outer cylinder is used to model the “critical magnetic Taylor number,” Ta^cr, in a flow of a liquid metal driven by a rotating magnetic field (RMF) in a cylindrical cavity characterized by the parameter H = height/radius. (The magnetic Taylor number is defined as Ta = σωBo2Ro4/(2ρν²), where σ,ν, and ρ are the electrical conductivity, kinematic viscosity, and density of the liquid; ω and B_o are the magnetic field frequency and induction; R_o is the radius of the cavity; the cr superscript means “critical”) In typical conditions, the RMF flow develops a solid-body-rotating core analogous to the inner rotating cylinder, embedded in a layer in which the swirl decays to zero at the outer wall. Using small-Ekman-number approximations for the core and gap flow, the analogy yields an insightful expression for Ta^cr. In particular, the model indicates that Ta^cr depends strongly on the parameter H. Comparisons of the present theoretical results with available realistic data show a good qualitative agreement and plausible quantitative agreement. The model was improved by an empirical adjustment of a coefficient and can be used as simple approximate prediction tool for Ta^cr in a quite wide range of cylindrical cavity configurations.

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47.15.Fe	Stability of laminar flows
47.15.Rq	Laminar flows in cavities, channels, ducts, and conduits
47.32.Ef	Rotating and swirling flows
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

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Amplification factors in shock-turbulence interactions: Effect of shock thickness

Diego A. Donzis

Phys. Fluids 24, 011705 (2012); http://dx.doi.org/10.1063/1.3676449 (6 pages)

Online Publication Date: 11 January 2012

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Amplification factors of streamwise velocity are investigated in canonical shock-turbulence interactions. The ratio of laminar shock thickness to the Kolmogorov length scale is suggested as the appropriate parameter to understand data from simulations and experiments. The different regimes of the interaction suggested in the literature can also be understood in terms of this parameter.

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47.40.Nm	Shock wave interactions and shock effects
47.15.-x	Laminar flows
47.27.Gs	Isotropic turbulence; homogeneous turbulence

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A two-sphere model for bacteria swimming near solid surfaces

Jocelyn Dunstan, Gastón Miño, Eric Clement, and Rodrigo Soto

Phys. Fluids 24, 011901 (2012); http://dx.doi.org/10.1063/1.3676245 (14 pages)

Online Publication Date: 27 January 2012

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We present a simple model for bacteria like Escherichia coli swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a force on the tail sphere and opposite torques exerted by the rod over the spheres. The hydrodynamic forces and torques on the spheres are computed by considering separately the interaction of a single sphere with the surface and with the flow produced by the other sphere. Numerically, we solve the linear system which contains the geometrical constraints and the force-free and torque-free conditions. The dynamics of this swimmer near a solid boundary is very rich, showing three different behaviors depending on the initial conditions: (1) swimming in circles in contact with the wall, (2) swimming in circles at a finite distance from the wall, and (3) swimming away from it. Furthermore, the order of magnitude of the radius of curvature for the circular motion is in the range 8-50μm, close to values observed experimentally.

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87.17.Rt	Cell adhesion and cell mechanics
47.11.-j	Computational methods in fluid dynamics

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Shear-induced particle migration and margination in a cellular suspension

Hong Zhao, Eric S. G. Shaqfeh, and Vivek Narsimhan

Phys. Fluids 24, 011902 (2012); http://dx.doi.org/10.1063/1.3677935 (21 pages) | Cited 1 time

Online Publication Date: 31 January 2012

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We simulate the cross-flow migration of rigid particles such as platelets in a red blood cell (RBC) suspension using the Stokes flow boundary integral equation method. Two types of flow environments are investigated: a suspension undergoing a bulk shear motion and a suspension flowing in a microchannel or duct. In a cellular suspension undergoing bulk shear deformation, the cross-flow migration of particles is diffusional. The velocity fluctuations in the suspension, which are the root cause of particle migration, are analyzed in detail, including their magnitude, the autocorrelation of Lagrangian tracer points and particles, and the associated integral time scales. The orientation and morphology of red blood cells vary with the shear rate, and these in turn cause the dimensionless particle diffusivity to vary non-monotonically with the flow capillary number. By simulating RBCs and platelets flowing in a microchannel of 34 μm height, we demonstrate that the velocity fluctuations in the core cellular flow region cause the platelets to migrate diffusively in the wall normal direction. A mean lateral velocity of particles, which is most significant near the edge of the cell-free layer, further expels them toward the wall, leading to their excess concentration in the cell-free layer. The calculated shear-induced particle diffusivity in the cell-laden region is in qualitative agreement with the experimental measurements of micron-sized beads in a cylindrical tube of a comparable diameter. In a smaller duct of 10 × 15 μm cross section, the volume exclusion becomes the dominant mechanism for particle margination, which occurs at a much shorter time scale than the migration in the bigger channel.

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82.70.Kj	Emulsions and suspensions
47.60.Dx	Flows in ducts and channels
02.30.Rz	Integral equations
47.11.-j	Computational methods in fluid dynamics
47.55.nb	Capillary and thermocapillary flows
47.57.eb	Diffusion and aggregation

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Scaling laws for slippage on superhydrophobic fractal surfaces

C. Cottin-Bizonne, C. Barentin, and L. Bocquet

Phys. Fluids 24, 012001 (2012); http://dx.doi.org/10.1063/1.3674300 (13 pages)

Online Publication Date: 12 January 2012

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We study the slippage on hierarchical fractal superhydrophobic surfaces and find an unexpected rich behavior for hydrodynamic friction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated by numerical resolution of the hydrodynamic equations. Our results demonstrate that slippage does strongly depend on the fractal dimension and is found to be always smaller on fractal surfaces as compared with surfaces with regular patterns. This shows that in contrast to naive expectations, the value of effective contact angle is not sufficient to infer the amount of slippage on a fractal surface: depending on the underlying geometry of the roughness, strongly superhydrophobic surfaces may, in some cases, be fully inefficient in terms of drag reduction. Finally, our scaling analysis can be directly extended to the study of heat transfer at fractal surfaces, in order to estimate the Kapitsa surface resistance on patterned surfaces, as well as to the question of trapping of diffusing particles by patchy hierarchical surfaces, in the context of chemoreception.

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47.53.+n	Fractals in fluid dynamics
68.08.Bc	Wetting
47.45.Gx	Slip flows and accommodation
47.50.Cd	Modeling

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Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics

Xin Bian, Sergey Litvinov, Rui Qian, Marco Ellero, and Nikolaus A. Adams

Phys. Fluids 24, 012002 (2012); http://dx.doi.org/10.1063/1.3676244 (20 pages)

Online Publication Date: 19 January 2012

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We apply smoothed dissipative particle dynamics (SDPD) [Español and Revenga, Phys. Rev. E 67, 026705 (2003)] to model solid particles in suspension. SDPD is a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and can be interpreted as a multiscale particle framework linking the macroscopic SPH to the mesoscopic dissipative particle dynamics (DPD) method. Rigid structures of arbitrary shape embedded in the fluid are modeled by frozen particles on which artificial velocities are assigned in order to satisfy exactly the no-slip boundary condition on the solid-liquid interface. The dynamics of the rigid structures is decoupled from the solvent by solving extra equations for the rigid body translational/angular velocities derived from the total drag/torque exerted by the surrounding liquid. The correct scaling of the SDPD thermal fluctuations with the fluid-particle size allows us to describe the behavior of the particle suspension on spatial scales ranging continuously from the diffusion-dominated regime typical of sub-micron-sized objects towards the non-Brownian regime characterizing macro-continuum flow conditions. Extensive tests of the method are performed for the case of two/three dimensional bulk particle-system both in Brownian/ non-Brownian environment showing numerical convergence and excellent agreement with analytical theories. Finally, to illustrate the ability of the model to couple with external boundary geometries, the effect of confinement on the diffusional properties of a single sphere within a micro-channel is considered, and the dependence of the diffusion coefficient on the wall-separation distance is evaluated and compared with available analytical results.

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82.70.Kj	Emulsions and suspensions
47.60.Dx	Flows in ducts and channels
02.60.-x	Numerical approximation and analysis
05.40.Jc	Brownian motion
47.57.eb	Diffusion and aggregation

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Numerical demonstration of the reciprocity among elemental relaxation and driven-flow problems for a rarefied gas in a channel

Shigeru Takata and Masashi Oishi

Phys. Fluids 24, 012003 (2012); http://dx.doi.org/10.1063/1.3678308 (10 pages)

Online Publication Date: 26 January 2012

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Relaxations from a uniform mass/heat flow and flows driven by an external force/temperature-gradient for a rarefied gas between two parallel plates are studied on the basis of the kinetic theory of gases. By numerical computations of the linearized Bhatnagar–Gross–Krook model of the Boltzmann equation, it is demonstrated that the reciprocity among these elemental flows derived from a general reciprocity theory for time-dependent problems [S. Takata, J. Stat. Phys. 140, 985 (2010)] holds at any time and any Knudsen numbers. Moreover, a propagation of the discontinuity of the velocity distribution function (VDF) in the relaxation problems and that of the derivative discontinuity of the VDF in the driven-flow problems are demonstrated. Their relation is also clarified.

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47.45.Ab	Kinetic theory of gases
51.10.+y	Kinetic and transport theory of gases
47.60.Dx	Flows in ducts and channels
02.60.-x	Numerical approximation and analysis

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Dipolophoresis of dielectric spheroids under asymmetric fields

Itzchak Frankel, Gilad Yossifon, and Touvia Miloh

Phys. Fluids 24, 012004 (2012); http://dx.doi.org/10.1063/1.3677675 (12 pages)

Online Publication Date: 31 January 2012

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Non-spherical particles are common in colloidal science. Spheroidal shapes are particularly convenient for the analysis of the pertinent electrostatic and hydrodynamic problems and are thus widely used to model the manipulation of biological cells as well as deformed drops and bubbles. We study the rotary motion of a dielectric spheroidal micro-particle which is freely suspended in an unbounded electrolyte solution in the presence of a uniform applied electric field, assuming a thin Debye layer. For the common case of a uniform distribution of the native surface-charge density, the rotary motion of the particle is generated by the contributions of the induced-charge electro-osmotic (ICEO) slip and the dielectrophoresis associated with the distribution of the Maxwell stress, respectively. Series solutions are obtained by using spheroidal (prolate or oblate) coordinates. Explicit results are presented for the angular velocity of particles spanning the entire spectrum from rod-like to disk-like shapes. These results demonstrate the non-monotonic variation of the angular speed with the eccentricity of particle shape and the singularity of the multiple limits corresponding to conducting (ideally polarizable) particles of extreme eccentricity (e ≈ 1). The non-monotonic variation of the angular speed with the particle dielectric permittivity is related to the induced-charge contribution. We apply these results to describe the motion of particles subject to a uniform field rotating in the plane. For a sufficiently slow rotation rate, prolate particles eventually become “locked” to the external field with their stationary relative orientation in the plane of rotation being determined by the particle eccentricity and dielectric constant. This effect may be of potential use in the manipulation of poly-disperse suspensions of dielectric non-spherical particles. Oblate spheroids invariably approach a uniform orientation with their symmetry axes directed normal to the external-field plane of rotation.

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47.85.Dh	Hydrodynamics, hydraulics, hydrostatics
82.39.Wj	Ion exchange, dialysis, osmosis, electro-osmosis, membrane processes
82.45.Gj	Electrolytes
47.11.-j	Computational methods in fluid dynamics
47.55.D-	Drops and bubbles
47.57.jd	Electrokinetic effects

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Direct simulation Monte Carlo-based expressions for the gas mass flow rate and pressure profile in a microscale tube

M. A. Gallis and J. R. Torczynski

Phys. Fluids 24, 012005 (2012); http://dx.doi.org/10.1063/1.3678337 (21 pages)

Online Publication Date: 31 January 2012

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The direct simulation Monte Carlo (DSMC) method of Bird is used to develop simple closed-form expressions for the mass flow rate and the pressure profile for the steady isothermal flow of an ideal gas through a microscale tube connecting two infinite reservoirs at different pressures but at the temperature of the tube wall. Gas molecules reflect from the tube wall according to the Maxwell model (a linear combination of specular and diffuse reflections at the wall temperature) with a unity or sub-unity value of the accommodation coefficient (the probability that molecules reflect diffusely from the wall). The DSMC-based expressions have four parameters. Two parameters are specified so that the mass flow rate reduces to the known expression in the free-molecular regime. One parameter was previously determined by comparison to DSMC simulations in the slip regime. The remaining parameter is determined by comparison to DSMC simulations for pressures spanning the transition regime with several values of the accommodation coefficient. The expressions for the mass flow rate and the pressure profile agree well with the DSMC simulations (rms and maximum differences of 2% and 5% for all cases examined), with other more complicated expressions and with recent experiments involving microscale tubes and channels for all flow regimes.

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47.61.Fg	Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.60.Dx	Flows in ducts and channels
02.70.Uu	Applications of Monte Carlo methods
07.10.Cm	Micromechanical devices and systems
47.45.Gx	Slip flows and accommodation

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Transient reduction of the drag coefficient of charged droplets via the convective reversal of stagnant caps

Brad S. Hamlin and William D. Ristenpart

Phys. Fluids 24, 012101 (2012); http://dx.doi.org/10.1063/1.3674301 (12 pages)

Online Publication Date: 23 January 2012

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Droplets are frequently observed to move as if they were solid rather than liquid, i.e., with no slip at the liquid-liquid interface. This behavior is usually explained in terms of the so-called “stagnant cap” model, in which surfactants accumulate at the trailing edge of the droplet, immobilizing the surface and increasing the observed drag coefficient. Here, we show that the drag coefficient for charged droplets is temporarily reduced by reversing the direction of an electric driving force. Using high speed video, we simultaneously track the velocity and relative interfacial velocity of individual aqueous droplets moving electrophoretically through oil. The observed velocity behavior is highly sensitive to the concentration of surfactant. For sufficiently low or sufficiently high concentration, upon reversal of the electric field the droplet rapidly accelerates in the opposite direction but then decelerates, concurrent with a transient rearrangement of tracer particles on the droplet surface. In contrast, droplets with intermediate surfactant concentrations exhibit neither deceleration nor significant tracer particle rearrangement. We interpret the observations in terms of convectively dominated rearrangement of the stagnant cap, and we discuss the implications for precise electrophoretic control of droplet motion in lab-on-a-chip devices and industrial electrocoalescers.

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47.55.dk	Surfactant effects
47.85.lb	Drag reduction
47.27.-i	Turbulent flows
47.50.Ef	Measurements

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Stability and breakup of confined threads

P. J. A. Janssen, H. E. H. Meijer, and P. D. Anderson

Phys. Fluids 24, 012102 (2012); http://dx.doi.org/10.1063/1.3677682 (18 pages)

Online Publication Date: 31 January 2012

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A boundary-integral method for periodic arrays of drops, threads or sheets between parallel walls is presented. The Green’s functions take the form of a far-field Hele-Shaw description, which is used to generate periodic Green’s functions for the parallel-wall configuration. The method is applied to study the effect of confinement on the breakup of threads. A comparison is made with classical Tomotika’s theory and growth rates parallel and perpendicular to the walls are determined as a function of confinement ratio. Contrary to existing belief, we find that confined threads are not stable, but that the time for breakup increases with confinement and viscosity ratio, at least for threads whose diameter is smaller than the wallspacing. We also show the in-phase and out-of-phase breakup for an array of threads, as well as the stabilizing effect of shear flow.

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47.55.df	Breakup and coalescence
47.60.-i	Flow phenomena in quasi-one-dimensional systems
02.60.Nm	Integral and integrodifferential equations
47.20.-k	Flow instabilities

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Particulate mixing in a turbulent serpentine duct

X. Huang and P. A. Durbin

Phys. Fluids 24, 013301 (2012); http://dx.doi.org/10.1063/1.3673610 (14 pages)

Online Publication Date: 4 January 2012

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Direct numerical simulations of particles in a serpentine duct were conducted at bulk flow Stokes numbers between 0.125 and 6. The geometrical curvature causes particles to depart direction from the mean flow. Above a Stokes number of about unity, a reflection layer forms along the outer curve of the bend. Reflectional mixing creates regions of nearly uniform particle mean velocity and kinetic energy. Particles leave the inner bend in a plume that separates from the inner wall at low Stokes number. At higher Stokes number, the plume splits in two, adding an upper part consisting of ballistic particles, that do not follow the geometrical curvature. When the Stokes number is low, the instantaneous 3-D distribution of particles visualizes wall streaks. But at higher Stokes number, particles disperse out of the reflection layer and form large scale puffs in the central portion of the duct.

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47.27.nb	Boundary layer turbulence
47.27.nf	Flows in pipes and nozzles
47.27.ek	Direct numerical simulations
47.27.wj	Turbulent mixing layers
47.11.-j	Computational methods in fluid dynamics
47.60.Dx	Flows in ducts and channels

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Rheological measurements of large particles in high shear rate flows

Erin Koos, Esperanza Linares-Guerrero, Melany L. Hunt, and Christopher E. Brennen

Phys. Fluids 24, 013302 (2012); http://dx.doi.org/10.1063/1.3677687 (19 pages)

Online Publication Date: 27 January 2012

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This paper presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Stokes and Reynolds numbers. The experiments were performed in a coaxial rheometer that was designed to minimize the effects of secondary flows. By changing the shear rate, particle size, and liquid viscosity, the Reynolds numbers based on shear rate and particle diameter ranged from 20 to 800 (Stokes numbers from 3 to 90), which is higher than examined in earlier rheometric studies. Prior studies have suggested that as the shear rate is increased, particle-particle collisions also increase resulting in a shear stress that depends non-linearly on the shear rate. However, over the range of conditions that were examined in this study, the shear stress showed a linear dependence on the shear rate. Hence, the effective relative viscosity is independent of the Reynolds and Stokes numbers and a non-linear function of the solid fraction. The present work also includes a series of rough-wall experiments that show the relative effective viscosity is also independent of the shear rate and larger than in the smooth wall experiments. In addition, measurements were made of the near-wall particle velocities, which demonstrate the presence of slip at the wall for the smooth-walled experiments. The depletion layer thickness, a region next to the walls where the solid fraction decreases, was calculated based on these measurements. The relative effective viscosities in the current work are larger than found in low-Reynolds number suspension studies but are comparable with a few granular suspension studies from which the relative effective viscosities can be inferred.

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47.57.Qk	Rheological aspects
47.80.-v	Instrumentation and measurement methods in fluid dynamics
82.70.Kj	Emulsions and suspensions
66.20.Ej	Studies of viscosity and rheological properties of specific liquids
47.15.Cb	Laminar boundary layers
47.57.E-	Suspensions

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A fully resolved numerical simulation of turbulent flow past one or several spherical particles

L. Botto and A. Prosperetti

Phys. Fluids 24, 013303 (2012); http://dx.doi.org/10.1063/1.3678336 (20 pages)

Online Publication Date: 31 January 2012

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The flow past one or nine spheres arranged in a plane lattice held fixed in a stream of decaying homogeneous isotropic turbulence is studied by means of fully resolved Navier-Stokes simulations. The particle radius is 3–5 times the Kolmogorov length and about 1/3 of the integral length scale. The mean particle Reynolds number is 80 and the turbulence intensity 17% and 33%. Several features of the flow are described: the mean and fluctuating dissipation and its spatial distribution, the mean and fluctuating hydrodynamic forces on the spheres, stimulated vortex shedding, and others. A special attention is paid to the relation between the work done on the fluid by the particles (in the reference frame of the former) and the total dissipation. It is shown that these quantities, which are assumed to balance in many point-particle models, can actually be very different when inertial effects are important.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.32.C-	Vortex dynamics
02.30.Jr	Partial differential equations
02.60.Cb	Numerical simulation; solution of equations
47.10.ad	Navier-Stokes equations
47.27.E-	Turbulence simulation and modeling

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Uniformly valid asymptotic flow analysis in curved channels

M. Zagzoule, P. Cathalifaud, J. Cousteix, and J. Mauss

Phys. Fluids 24, 013601 (2012); http://dx.doi.org/10.1063/1.3673568 (25 pages)

Online Publication Date: 6 January 2012

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The laminar incompressible flow in a two-dimensional curved channel having at its upstream and downstream extremities two tangent straight channels is considered. A global interactive boundary layer (GIBL) model is developed using the approach of the successive complementary expansions method (SCEM) which is based on generalized asymptotic expansions leading to a uniformly valid approximation. The GIBL model is valid when the non dimensional number μ = δ math

is O(1) and gives predictions in agreement with numerical Navier-Stokes solutions for Reynolds numbers R_e ranging from 1 to 10⁴ and for constant curvatures δ = math

ranging from 0.1 to 1, where H is the channel width and R_c the curvature radius. The asymptotic analysis shows that μ, which is the ratio between the curvature and the thickness of the boundary layer of any perturbation to the Poiseuille flow, is a key parameter upon which depends the accuracy of the GIBL model. The upstream influence length is found asymptotically and numerically to be O( math

).

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47.15.Rq	Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx	Flows in ducts and channels
47.15.Cb	Laminar boundary layers
47.10.ad	Navier-Stokes equations

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Mechanism of drag generation by surface corrugation

A. Mohammadi and J. M. Floryan

Phys. Fluids 24, 013602 (2012); http://dx.doi.org/10.1063/1.3675557 (13 pages)

Online Publication Date: 18 January 2012

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Drag generated by periodic corrugation has been determined analytically in the limit of long corrugation wavelength. Three physical mechanisms have been identified, i.e., the additional shear drag due to an increase of the wetted area and the re-arrangement of the shear stress distribution, the pressure form drag associated with the mean pressure gradient, and the pressure interaction drag associated with the phase difference between the surface geometry and the periodic part of the pressure field. The total drag increases rapidly with increase of the corrugation amplitude, with the form and interaction drags contributing up to 45% and 30% of this increase, respectively.

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47.60.Dx	Flows in ducts and channels
68.08.Bc	Wetting

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Three-dimensional swirling flows in a tall cylinder driven by a rotating endwall

J. M. Lopez

Phys. Fluids 24, 014101 (2012); http://dx.doi.org/10.1063/1.3673608 (9 pages)

Online Publication Date: 4 January 2012

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The onset and nonlinear dynamics of swirling flows in relatively tall cylinders driven by the rotation of an endwall are studied numerically. These flows are distinguished from the more widely studied swirling flows in shorter cylinders; the instability in the taller cylinders is direct to three-dimensional flows rather than to unsteady axisymmetric flows. The simulations are in very good agreement with recent experiments in terms of the critical Reynolds number, frequency, and azimuthal wavenumber of the flows, but there is disagreement in the interpretation of these flows. We show that these flows are indeed rotating waves and that they have the same vorticity distributions as the flows measured using particle image velocimetry in the experiments. Identifying these as rotating waves gives a direct connection with prior linear stability analysis and the three-dimensional flows found in shorter cylinders as secondary instabilities leading to modulated rotating waves.

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47.32.Ef	Rotating and swirling flows
47.32.cd	Vortex stability and breakdown
47.35.-i	Hydrodynamic waves
47.20.Lz	Secondary instabilities
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
02.60.Cb	Numerical simulation; solution of equations

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Negative Magnus lift on a rotating sphere at around the critical Reynolds number

Masaya Muto, Makoto Tsubokura, and Nobuyuki Oshima

Phys. Fluids 24, 014102 (2012); http://dx.doi.org/10.1063/1.3673571 (15 pages)

Online Publication Date: 5 January 2012

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Negative Magnus lift acting on a sphere rotating about the axis perpendicular to an incoming flow was investigated using large-eddy simulation at three Reynolds numbers of 1.0 × 10⁴, 2.0 × 10⁵, and 1.14 × 10⁶. The numerical methods used were first validated on a non-rotating sphere, and the spatial resolution around the sphere was determined so as to reproduce the laminar separation, reattachment, and turbulent transition of the boundary layer observed in the vicinity of the critical Reynolds number. The rotating sphere exhibited a positive or negative Magnus effect depending on the Reynolds number and the imposed rotating speed. At Reynolds numbers in the subcritical or supercritical regimes, the direction of the Magnus lift force was independent of the rotational speed. In contrast, the lift force was negative in the critical regime when particular rotating speeds were imposed. This negative Magnus effect was investigated in the context of suppression or promotion of boundary layer transition around the separation point.

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47.32.Ef	Rotating and swirling flows
47.27.ep	Large-eddy simulations
47.15.Fe	Stability of laminar flows
47.32.Ff	Separated flows
47.27.nb	Boundary layer turbulence

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Jan 2012

Volume 24, Issue 1, Articles (01xxxx)

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