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Jul 2010

Volume 22, Issue 7, Articles (07xxxx)

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Phys. Fluids 22, 072101 (2010); http://dx.doi.org/10.1063/1.3460353 (7 pages)

Minhee Lee, Young Soo Chang, and Ho-Young Kim
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The effect of rotational shear on granular discharge rates

J. E. Hilton and P. W. Cleary

Phys. Fluids 22, 071701 (2010); http://dx.doi.org/10.1063/1.3459155 (4 pages) | Cited 1 time

Online Publication Date: 7 July 2010

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The mass flow rate of a packed granular column subject to rotational shear discharging though an aperture is investigated computationally. We show that the flow rate increases in response to the applied shear. This increase obeys a power-law relation based on the rotational Froude number, Fr = Lω2/g, where ω is the angular rotation speed and L is a system length scale. The exponent of this relation is found to be independent of the particle diameter, intergrain friction, and the geometry of the setup.
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47.57.Gc Granular flow

Global mode analysis of a pipe flow through a 1:2 axisymmetric sudden expansion

E. Sanmiguel-Rojas, C. del Pino, and C. Gutiérrez-Montes

Phys. Fluids 22, 071702 (2010); http://dx.doi.org/10.1063/1.3458889 (4 pages) | Cited 3 times

Online Publication Date: 16 July 2010

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We report the results of the global mode analysis to characterize the onset of unsteadiness in a circular pipe flow through an axisymmetric sudden expansion of inlet-to-outlet diameter ratio of d/D = 0.5. We find that the axisymmetric state becomes linearly unstable at a significantly higher critical Reynolds number than the one reported in previous experimental works. This unstable global mode corresponds to an oscillatory bifurcation with wavenumber |m| = 1 located at the end of the recirculation region.
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47.60.Dx Flows in ducts and channels
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Sectional lift coefficient of a flapping wing in hovering motion

Jihoon Kweon and Haecheon Choi

Phys. Fluids 22, 071703 (2010); http://dx.doi.org/10.1063/1.3471593 (4 pages) | Cited 5 times

Online Publication Date: 27 July 2010

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We investigate the behavior of sectional lift coefficient of a flapping wing of a fruit-fly in hovering motion. Through three-dimensional numerical simulations, we show that during the stroke, the sectional lift coefficient significantly varies in time as well as in the spanwise direction owing to complex interactions between the wing and vortices in the wake. However, the time-averaged sectional lift force coefficient is inversely proportional to the spanwise distance from the rotation center except very near the wing-tip region. This is because the wing-tip vortex significantly decreases the lift force on the wing-tip region during and after midstroke.
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47.85.-g Applied fluid mechanics
47.11.-j Computational methods in fluid dynamics
47.32.-y Vortex dynamics; rotating fluids

Hierarchy of minimal flow units in the logarithmic layer

Oscar Flores and Javier Jiménez

Phys. Fluids 22, 071704 (2010); http://dx.doi.org/10.1063/1.3464157 (4 pages) | Cited 8 times

Online Publication Date: 28 July 2010

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The minimal simulation boxes of the buffer layer of turbulent channels can be extended to the logarithmic and outer regions, where they contain a segment of streamwise velocity streak, and a vortex cluster. Smaller boxes restrict “healthy” turbulence closer to the wall, to a layer whose thickness scales with the spanwise size of the box. These minimal boxes burst quasiperiodically, and the bursting period for a band of wall distances grows linearly away from the wall, independently of the box size within the limits within which turbulence is well represented.
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47.11.-j Computational methods in fluid dynamics
47.27.nd Channel flow
47.32.-y Vortex dynamics; rotating fluids
47.60.Dx Flows in ducts and channels
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back to top Biofluid Mechanics

Bioconvection in a suspension of isotropically scattering phototactic algae

S. Ghorai, M. K. Panda, and N. A. Hill

Phys. Fluids 22, 071901 (2010); http://dx.doi.org/10.1063/1.3457163 (16 pages) | Cited 4 times

Online Publication Date: 15 July 2010

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Phototaxis is a directed swimming response toward a light source sensed by micro-organisms. Positive phototaxis represents swimming toward the source of light intensity and negative phototaxis is the swimming away from it. In this paper we develop a new model for phototaxis that incorporates the effects of absorption and scattering by the micro-organisms. This model is then used to analyze the linear stability of a suspension of phototactic algae illuminated by a collimated radiation at the top. A comprehensive numerical study of the linear stability is presented with particular emphasis on the scattering effect. As a result of scattering, for some parameter values, the micro-organisms accumulate in two horizontal layers at different depths in the basic equilibrium state. Examples of oscillatory instabilities are also found.
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47.63.Gd Swimming microorganisms
47.57.E- Suspensions
82.70.Kj Emulsions and suspensions
back to top Micro- and Nanofluid Mechanics

Slow gas microflow past a sphere: Analytical solution based on moment equations

Manuel Torrilhon

Phys. Fluids 22, 072001 (2010); http://dx.doi.org/10.1063/1.3453707 (16 pages) | Cited 1 time

Online Publication Date: 15 July 2010

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The regularized 13-moment equations are solved analytically for the microflow of a gas past a sphere in the case of low Mach numbers. The result is given in fully explicit expressions and shows nontrivial behavior for all fluid fields including stress, heat flux, and temperature. Various aspects of the flow such as temperature polarization and total force are reproduced correctly for moderate Knudsen number. The analytical solution allows studying the rise of Knudsen layers and their interaction and coupling to the fluid variables in the bulk. Additionally, based on the regularized 13-moment equations system, hybrid boundary conditions are given for the standard Stokes equations in order to enable them to predict nonequilibrium effects in the flow past a sphere.
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47.45.Ab Kinetic theory of gases
47.40.Dc General subsonic flows
47.10.ab Conservation laws and constitutive relations

Electrospraying insulating liquids via charged nanodrop injection from the Taylor cone of an ionic liquid

Carlos Larriba-Andaluz and Juan Fernández de la Mora

Phys. Fluids 22, 072002 (2010); http://dx.doi.org/10.1063/1.3455992 (7 pages) | Cited 3 times

Online Publication Date: 16 July 2010

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Charge is injected into the bulk of an insulating liquid in the form of nanodrops produced by an immersed Taylor cone of an ionic liquid. The charge then drifts onto the insulator surface, destabilizing it and leading to the formation of an electrified jet that atomizes into approximately monodisperse micron size insulator drops. The approach is similar to those previously based on field injection of ions from sharp tungsten tips, but the continuous renewal and self-sharpening of the liquid charge-injector permits long-term stable operation. Using heptane as the insulator and 1-ethyl-3-methylimidazolium-BF4 as the ionic liquid we produce approximately monodisperse drops with average diameters ranging from less than 4 up to 20 μm, injecting in some cases as little as 0.0002% by volume of ionic liquid. No fundamental limitation restricting the possibility of forming even smaller drops is apparent. The scaling law of Kim and Turnbull [“Generation of charged drops of insulating liquids by electrostatic spraying,” J. Appl. Phys. 47, 1964 (1976)] where the drop diameter varies as the 2/3 power of the liquid flow rate and the −2/3 power of the spray current is confirmed, implying that the drops are on the average charged to 50%–60% of the Rayleigh limit.
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47.61.Jd Multiphase flows
47.55.D- Drops and bubbles
47.80.-v Instrumentation and measurement methods in fluid dynamics

Stokes flow past a compound drop in a circular tube

Yanxi Song, Jinliang Xu, and Yongping Yang

Phys. Fluids 22, 072003 (2010); http://dx.doi.org/10.1063/1.3460301 (19 pages) | Cited 2 times

Online Publication Date: 22 July 2010

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Microfluidics could generate drops or bubbles with controllable size and frequency at this stage. However, analytical work on such problem is less reported in the literature. In this study, we study the motion of a compound drop, consisting of a fluid drop engulfed in a larger drop, confined in a circular tube. The analysis is based on the low Reynolds number Stokes flow theory. Interfaces are assumed to be spherical due to large surface tension. Stream functions in one bipolar and two cylindrical coordinate systems are developed in series form. Our new contribution is the transformation between cylindrical and bipolar coordinate systems. Flow patterns are mainly dependent on the relative motion and the size of the inner drop. Four types of flow patterns are identified. Drag force on the inner or outer drops is in proportion to the product of the drop radius and viscosity of the phase encapsulating the drop. Drag force on the inner or outer spheres is finally expressed as linear combinations of velocities of the three phases (i.e., the inner drop, the outer drop, and the continuous flow), respectively. Our results show that those coefficients of the linear combinations for the drag forces depend on several parameters: eccentricity of the compound drop, viscosity ratio of two neighboring phases, radius ratio of the inner drop to the outer drop, and the radius ratio of the outer drop to the tube. The two radius ratios have largest effects on the coefficients of the inner or outer drop, respectively. Stability of the compound drop in a circular tube is analyzed. It is found that though the compound drop cannot reach an absolutely steady state, it will enter a quasisteady state where the inner sphere is adjacent to the shell of the outer sphere in practice.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx Flows in ducts and channels

On the effect of hydrodynamic slip on the polarization of a nonconducting spherical particle in an alternating electric field

Hui Zhao

Phys. Fluids 22, 072004 (2010); http://dx.doi.org/10.1063/1.3464159 (15 pages) | Cited 3 times

Online Publication Date: 28 July 2010

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The polarization of a charged, dielectric, spherical particle with a hydrodynamically slipping surface under the influence of a uniform alternating electric field is studied by solving the standard model (the Poisson–Nernst–Planck equations). The dipole moment characterizing the strength of the polarization is computed as a function of the double layer thickness, the electric field frequency, the particle’s surface charge, and the slip length. Our studies reveal that two processes contribute to the dipole moment: ion transport inside the double layer driven by the electric field and the particle’s electrophoretic motion. The hydrodynamic slip will simultaneously impact both processes. In the case of a thick double layer, an approximate analytical expression for the dipole moment of a weakly charged particle with an arbitrary slip length and a small zeta potential ζ [normalized with the thermal voltage ( ∼ 25 mV)], accurate within O(ζ2), shows that the polarization is dominated by the particle’s electrophoretic motion and the enhancement of the polarization due to the hydrodynamic slip is primarily attributed to the enhancement of the electrophoretic mobility from the slip. In contrast, for a thin double layer, the dipole moment is governed by ion transport inside the double layer. Asymptotical analytical models conclude that the hydrodynamic slip has more complicated influence on the polarization. At the high-frequency range where the surface conduction is important, the dipole moment is predicted to increase for any zeta potential. On the contrary, at the low-frequency range where the bulk diffusion is significant, the enhancement of the dipole moment due to the slip is lost at large zeta potentials.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.45.Gx Slip flows and accommodation
back to top Interfacial Flows

Drop impact on microwetting patterned surfaces

Minhee Lee, Young Soo Chang, and Ho-Young Kim

Phys. Fluids 22, 072101 (2010); http://dx.doi.org/10.1063/1.3460353 (7 pages) | Cited 5 times

Online Publication Date: 15 July 2010

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We investigate experimentally the dynamics of a liquid drop that impacts on a solid surface whose wettability is patterned at the microscopic scale. The target surface is patterned such that hydrophilic (hydrophobic) microscale spokes radiate from the center on a hydrophobic (hydrophilic) background. Following the initial spreading stages, the drop recoils on the hydrophobic region while being arrested on the hydrophilic area, thereby resulting in a micropatterned liquid footprint. We also find that the fingering instability of the drop edge is affected by the wettability patterns in the initial spreading stages. The number of fingers depends on a combination of the impact Weber number and the number of spokes. We suggest that the present scheme of patterning liquid deposits at microscales could be exploited in various microfluidic applications.
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47.85.Np Fluidics
68.08.Bc Wetting
47.55.D- Drops and bubbles

The sensitivity of drop motion due to the density and viscosity ratio

Mitsuhiro Ohta, Shinya Yamaguchi, Yutaka Yoshida, and Mark Sussman

Phys. Fluids 22, 072102 (2010); http://dx.doi.org/10.1063/1.3460906 (11 pages) | Cited 3 times

Online Publication Date: 22 July 2010

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The effect of the density and viscosity ratio on the motion of single drops rising in immiscible liquids is computationally investigated. The density and viscosity ratio play an important role in droplet morphology, unstable droplet behavior, and terminal droplet characteristics. The numerical method used in this investigation is a coupled level-set and volume-of-fluid method together with a sharp interface treatment for the interfacial jump conditions. The computations assume an axisymmetric geometry. Drop rise motion is highly dependent on the viscosity ratio. The results reported in this paper augment the information provided by the correlation table for bubble rise motion by Bhaga and Weber [“Bubbles in viscous liquids: Shapes, wakes and velocities,” J. Fluid Mech. 105, 61 (1981)] . A drop-system with a large viscosity ratio is susceptible to exhibiting unstable motion in the large Eötvös number regions; an unstable drop can show complicated behavior with various breakup modes that are dependent on the Morton number. With regard to the effect of the density ratio, it is observed that the difference between a bubble and a drop with “equivalent” properties is not prominent except in the low Morton number regions. The results of investigating the effect of the density and viscosity ratio on drop motion indicate that the Morton number, Eötvös numbers, and viscosity ratio are the primary governing parameters and the density ratio is a secondary governing parameter.
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47.55.dd Bubble dynamics
47.55.df Breakup and coalescence
47.32.cd Vortex stability and breakdown
66.20.-d Viscosity of liquids; diffusive momentum transport
back to top Laminar Flows

Spatially localized binary fluid convection in a porous medium

D. Lo Jacono, A. Bergeon, and E. Knobloch

Phys. Fluids 22, 073601 (2010); http://dx.doi.org/10.1063/1.3439672 (13 pages) | Cited 4 times

Online Publication Date: 2 July 2010

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The origin and properties of time-independent spatially localized binary fluid convection in a layer of porous material heated from below are studied. Different types of single and multipulse states are computed using numerical continuation, and the results related to the presence of homoclinic snaking of single and multipulse states.
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47.27.te Turbulent convective heat transfer
47.56.+r Flows through porous media
47.10.A- Mathematical formulations

Inertia dominated thin-film flows over microdecorated surfaces

Emilie Dressaire, Laurent Courbin, Jérome Crest, and Howard A. Stone

Phys. Fluids 22, 073602 (2010); http://dx.doi.org/10.1063/1.3454769 (13 pages) | Cited 4 times

Online Publication Date: 2 July 2010

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We analyze the inertia dominated flow of thin liquid films on microtextured substrates, which here are assemblies of micron-size posts arranged on regular lattices. We focus on situations for which the thin-film thickness and the roughness characteristic length scale are of the same order of magnitude, i.e., a few hundred microns. We assume that the liquid flows isotropically through the roughness at a flow rate that depends on the geometrical features of the porous layer; above the texture, the flow is characterized by a larger Reynolds number and modeled using a boundary layer approach. The influence of the microtexture on the thin-film flow above the microposts is captured by a reduction of the flow rate due to the leakage flow through the texture and a slip boundary condition, which depends on the flow direction as well as on the lattice properties. In this way, the velocity field in the free surface flow adopts the symmetry of the microtexture underneath. The results of this model are in good agreement with experimental observations obtained for thin-film flows formed upon jet impact on microtextures. The characteristics of the polygonal hydraulic jumps that we obtain depend on both the jet parameters and the topographical features of the surface roughness. We use the measurements and the numerical predictions to estimate the flow rate through the shallow porous layer and the effective slip length for this inertia dominated flow regime. We also discuss the limitations of the model.
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68.15.+e Liquid thin films
47.56.+r Flows through porous media
47.45.Gx Slip flows and accommodation
47.80.Jk Flow visualization and imaging
47.10.A- Mathematical formulations
02.60.Cb Numerical simulation; solution of equations
back to top Instability and Transition

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

Rong Liu and Qiusheng Liu

Phys. Fluids 22, 074101 (2010); http://dx.doi.org/10.1063/1.3455503 (21 pages) | Cited 1 time

Online Publication Date: 14 July 2010

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The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy’s law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter β. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t). Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on β for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue.
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47.20.-k Flow instabilities
47.56.+r Flows through porous media
68.15.+e Liquid thin films

On a variational principle for Beltrami flows

Rafael González, Andrea Costa, and E. Sergio Santini

Phys. Fluids 22, 074102 (2010); http://dx.doi.org/10.1063/1.3460297 (7 pages) | Cited 2 times

Online Publication Date: 19 July 2010

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In a previous paper [ R. González, L. G. Sarasua, and A. Costa, “Kelvin waves with helical Beltrami flow structure,” Phys. Fluids 20, 024106 (2008) ] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper, the topological analogy between the role of the magnetic field in Woltjer’s theorem [ L. Woltjer, “A theorem on force-free magnetic fields,” Proc. Natl. Acad. Sci. U.S.A. 44, 489 (1958) ] and the role of the vorticity in the equivalent theorem is revisited. Via this analogy we identify the force-free equilibrium of the magnetohydrodynamics with the Beltrami flow equilibrium of the hydrodynamic. The stability of the last one is studied applying Arnold’s theorem. We analyze the role of the enstrophy in the determination of the equilibrium and its stability. We show examples where the Beltrami flow equilibrium is stable under perturbations of the Beltrami flow type with the same eigenvalue as the basic flow one. The enstrophy variation results invariant with respect to a uniform rotating and translational frame and the stability is conserved when the flow experiences a transition from a Beltrami axisymmetric flow to a helical one of the same eigenvalue. These results are discussed in comparison with that given by Moffatt in 1986 [ H. K. Moffatt, “Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations,” J. Fluid Mech. 166, 359 (1986) ].
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47.35.-i Hydrodynamic waves
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.32.cb Vortex interactions
02.30.Xx Calculus of variations

Linear spatial instability of viscous flow of a liquid sheet through gas

M. Altimira, A. Rivas, J. C. Ramos, and R. Anton

Phys. Fluids 22, 074103 (2010); http://dx.doi.org/10.1063/1.3460348 (11 pages) | Cited 1 time

Online Publication Date: 19 July 2010

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The present paper focuses on the linear spatial instability of a viscous two-dimensional liquid sheet bounded by two identical viscous gas streams. The Orr–Sommerfeld differential equations and the boundary conditions of the flow configuration are numerically solved using Chebyshev series expansions and the collocation method. The strong dependence of the instability parameters on the velocity profiles is proven by using both quadratic and error functions to define the base flow in the liquid sheet and the gas shear layer. The sensitivity of the spatial instability growth rate to changes in the dimensionless parameters of the problem is assessed. Regarding the liquid sheet Reynolds number, it has been observed that, when this parameter increases, both the most unstable growth rate and the corresponding wavenumber decrease, whereas the cutoff wavenumber increases. The results of this analysis are compared with temporal theory through Gaster transformation. The effects liquid and gas viscosity have on instability are studied by comparing the instability curves given by the presented model with those from an inviscid liquid sheet and a viscous liquid sheet in an inviscid gaseous medium. The model presented in this paper features a variation in the cutoff wavenumber with all the governing parameters of the problem, whereas that provided by cases that account for an inviscid surrounding gas depends only on the liquid sheet Weber number and the ratio of gas to liquid densities. Results provided by the presented model have been experimentally validated and show that quadratic profiles have a greater capacity to predict the disturbance wavelength.
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47.20.-k Flow instabilities
47.32.cd Vortex stability and breakdown

Short-wavelength stability analysis of Hill’s vortex with/without swirl

Y. Hattori and K. Hijiya

Phys. Fluids 22, 074104 (2010); http://dx.doi.org/10.1063/1.3459956 (8 pages) | Cited 2 times

Online Publication Date: 23 July 2010

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The stability of Hill’s vortex with/without swirl is studied by the short-wavelength stability analysis or WKB analysis. It is shown that the classical Hill’s spherical vortex is subjected not only to the Widnall instability but also to the curvature instability found for thin vortex rings and helical vortex tubes. A new “combined” mode of instability caused by the two instabilities is discovered. The magnitude of the exponential growth rate of the combined mode is similar with the curvature instability around the stagnation point; it exceeds the Widnall instability near the boundary. The effects of swirl on the instabilities are investigated using a family of solutions obtained by Moffatt [“The degree of knottedness of tangled vortex lines,” J. Fluid Mech. 35, 117 (1969)] . As the swirl parameter α increases, a stable region appears around the stagnation point; the maxima of the growth rates decrease; the combined mode region disappears for α ≥ 3. As α increases further, however, the region of the generalized centrifugal instability emerges from the stagnation point.
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47.32.cd Vortex stability and breakdown
47.32.Ef Rotating and swirling flows
47.60.Dx Flows in ducts and channels
back to top Turbulent Flows

Turbulence without Richardson–Kolmogorov cascade

N. Mazellier and J. C. Vassilicos

Phys. Fluids 22, 075101 (2010); http://dx.doi.org/10.1063/1.3453708 (25 pages) | Cited 17 times

Online Publication Date: 12 July 2010

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We investigate experimentally wind tunnel turbulence generated by multiscale/fractal grids pertaining to the same class of low-blockage space-filling fractal square grids. These grids are not active but nevertheless produce very much higher turbulence intensities u′/U and Reynolds numbers Reλ than higher blockage regular grids. Our hot wire anemometry confirms the existence of a protracted production region where turbulence intensity grows followed by a decay region where it decreases, as first reported by Hurst and Vassilicos [“Scalings and decay of fractal-generated turbulence,” Phys. Fluids 19, 035103 (2007)] . We introduce the wake-interaction length scale x⋆ and show that the peak of turbulence intensity demarcating these two regions along the centerline is positioned at about 0.5x⋆. The streamwise evolutions on the centerline of the streamwise mean flow and of various statistics of the streamwise fluctuating velocity all scale with x⋆. Mean flow and turbulence intensity profiles are inhomogeneous at streamwise distances from the fractal grid smaller than 0.5x⋆, but appear quite homogeneous beyond 0.5x⋆. The velocity fluctuations are highly non-Gaussian in the production region but approximately Gaussian in the decay region. Our results confirm the finding of Seoud and Vassilicos [“Dissipation and decay of fractal-generated turbulence,” Phys. Fluids 19, 105108 (2007)] that the ratio of the integral length-scale Lu to the Taylor microscale λ remains constant even though the Reynolds number Reλ decreases during turbulence decay in the region beyond 0.5x⋆. As a result, the scaling Lu/λ ∼ Reλ, which follows from the u′3/Lu scaling of the dissipation rate in boundary-free shear flows and in usual grid-generated turbulence, does not hold here. This extraordinary decoupling is consistent with a noncascading and instead self-preserving single-length scale type of decaying homogeneous turbulence proposed by George and Wang [“The exponential decay of homogeneous turbulence,” Phys. Fluids 21, 025108 (2009)] , but we also show that Lu/λ is nevertheless an increasing function of the inlet Reynolds number Re0. Finally, we offer a detailed comparison of the main assumption and consequences of the George and Wang theory against our fractal-generated turbulence data.
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47.27.nb Boundary layer turbulence
47.27.wb Turbulent wakes
47.15.Cb Laminar boundary layers
47.80.Cb Velocity measurements
47.80.Fg Pressure and temperature measurements

Direct numerical simulations of magnetic field effects on turbulent flow in a square duct

R. Chaudhary, S. P. Vanka, and B. G. Thomas

Phys. Fluids 22, 075102 (2010); http://dx.doi.org/10.1063/1.3456724 (15 pages) | Cited 5 times

Online Publication Date: 14 July 2010

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Magnetic fields are crucial in controlling flows in various physical processes of industrial significance. One such process is the continuous casting of steel, where different magnetic field configurations are used to control the turbulent flow of steel in the mold in order to minimize defects in the cast steel. The present study has been undertaken to understand the effects of a magnetic field on mean velocities and turbulence parameters in turbulent molten metal flow through a square duct. The coupled Navier–Stokes magnetohydrodynamic equations have been solved using a three-dimensional fractional-step numerical procedure. The Reynolds number was kept low in order to resolve all the scales in the flow without using a subgrid scale turbulence model. Computations were performed with three different grid resolutions, the finest grid having 8.4×106 cells. Because liquid metals have low magnetic Reynolds number, the induced magnetic field has been considered negligible and the electric potential method for magnetic field-flow coupling has been implemented. After validation of the computer code, computations of turbulent flow in a square duct with different Hartmann numbers were performed until complete laminarization of the flow. The time-dependent and time-averaged nature of the flow has been examined through distribution of mean velocities, turbulent fluctuations, vorticity, and turbulent kinetic energy budgets.
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47.10.ad Navier-Stokes equations
47.11.-j Computational methods in fluid dynamics
47.27.nf Flows in pipes and nozzles
47.32.-y Vortex dynamics; rotating fluids
47.60.Dx Flows in ducts and channels
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.85.L- Flow control

Finite time Lagrangian analysis of an unsteady separation induced by a near wall wake

T. Ruiz, J. Borée, T. Tran T., C. Sicot, and L. E. Brizzi

Phys. Fluids 22, 075103 (2010); http://dx.doi.org/10.1063/1.3459154 (9 pages)

Online Publication Date: 15 July 2010

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Following the Lagrangian theory of unsteady flow separation on slip boundaries proposed by Lekien and Haller [“Unsteady flow separation on slip boundaries,” Phys. Fluids 20, 097101 (2008)] , we use finite time Lagrangian analysis in order to educe large scale, unsteady flow separation downstream a near wall obstacle at a significant Reynolds number. By large scale flow separation, we mean here the ejection of fluid and vorticity outside a neighborhood of the wall at the scale of the obstacle. Indeed, while the separation point at the wall is not spatially resolved by the high speed particle image velocimetry measurements, free-slip boundary conditions are applied before educing unstable manifolds in the near wall region using finite time Lyapunov exponents. For this turbulent flow, conditional statistics are presented in order to discuss the relative contributions of the unsteady aerodynamics and of the turbulence in the separation region. The dynamics of the corresponding separation point has a very clear link with the fluctuating wall pressure induced by this unsteady turbulent flow.
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47.85.Gj Aerodynamics
47.20.Ib Instability of boundary layers; separation
47.27.N- Wall-bounded shear flow turbulence
47.27.wb Turbulent wakes
47.32.-y Vortex dynamics; rotating fluids
47.32.Ff Separated flows
47.80.Jk Flow visualization and imaging

On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence

B. Favier, F. S. Godeferd, C. Cambon, and A. Delache

Phys. Fluids 22, 075104 (2010); http://dx.doi.org/10.1063/1.3456725 (7 pages) | Cited 4 times

Online Publication Date: 16 July 2010

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We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasistatic approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [ H. K. Moffatt, “On the suppression of turbulence by a uniform magnetic field,” J. Fluid Mech. 28, 571 (1967) ]. However, numerous numerical studies predict a different behavior, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using direct numerical simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called two-and-a-half-dimensional flow [ D. Montgomery and L. Turner, “Two-and-a-half-dimensional magnetohydrodynamic turbulence,” Phys. Fluids 25, 345 (1982) ] and we offer an explanation for the dominance of horizontal kinetic energy.
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47.11.-j Computational methods in fluid dynamics
47.27.-i Turbulent flows
47.65.-d Magnetohydrodynamics and electrohydrodynamics

Homogenization and mixing measures for a replenishing passive scalar field

Shane R. Keating, Peter R. Kramer, and K. Shafer Smith

Phys. Fluids 22, 075105 (2010); http://dx.doi.org/10.1063/1.3456726 (9 pages) | Cited 1 time

Online Publication Date: 16 July 2010

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The efficiency with which an incompressible flow mixes a passive scalar field that is continuously replenished by a steady source-sink distribution has been quantified using the suppression of the mean scalar variance below the value it would attain in the absence of the stirring. We examine the relationship this mixing measure has to the effective diffusivity obtained from homogenization theory, particularly establishing precise connections in the case of a stirring velocity field that is periodic in space and time and varies on scales much smaller than that of the source. We explore theoretically and numerically via the Childress–Soward family of flows how the mixing measures lose their linkage to the homogenized diffusivity when the velocity and source field do not enjoy scale separation. Some implications for homogenization-based parametrizations of mixing by flows with finite scale separation are discussed.
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47.51.+a Mixing
47.57.eb Diffusion and aggregation
47.27.-i Turbulent flows

Dynamic global model for large eddy simulation of transient flow

Jungil Lee, Haecheon Choi, and Noma Park

Phys. Fluids 22, 075106 (2010); http://dx.doi.org/10.1063/1.3459156 (6 pages) | Cited 8 times

Online Publication Date: 19 July 2010

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In the present study, the dynamic subgrid-scale eddy viscosity models with a global model coefficient by Park et al. [Phys. Fluids 18, 125109 (2006)] (called dynamic global models hereafter) are applied to large eddy simulation of decaying isotropic turbulence to examine their performances in transient flow. The dynamic global model based on the global equilibrium between the subgrid-scale dissipation and the viscous dissipation fails to predict the temporal behavior of decaying isotropic turbulence. On the other hand, the dynamic global model based on the Germano identity shows an excellent agreement with the experimental data of decaying isotropic turbulence.
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47.11.-j Computational methods in fluid dynamics
47.27.-i Turbulent flows

A mixed large eddy simulation model based on the residual-based variational multiscale formulation

Z. Wang and A. A. Oberai

Phys. Fluids 22, 075107 (2010); http://dx.doi.org/10.1063/1.3453710 (9 pages) | Cited 4 times

Online Publication Date: 20 July 2010

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A mixed model based on the residual-based variational multiscale (RBVM) formulation is proposed for the large eddy simulation of turbulent flows. In this model the cross stresses are modeled by the RBVM term and the Reynolds stresses are represented by a Smagorinsky eddy viscosity. The mixed model is motivated by an a priori analysis of a turbulent flow field that indicates that the RBVM term correctly models the dissipation induced by the cross-stress term but underpredicts the contribution from the Reynolds stress term. The dynamic version of the mixed model is implemented in a Fourier-spectral code in order to predict the decay of incompressible, three-dimensional homogeneous isotropic turbulence. It is found that the mixed model yields better agreement with direct numerical simulation solution than the dynamic Smagorinsky and the RBVM models, which are its building blocks.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.ep Large-eddy simulations
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations

Large-eddy simulation of a curved open-channel flow over topography

W. van Balen, W. S. J. Uijttewaal, and K. Blanckaert

Phys. Fluids 22, 075108 (2010); http://dx.doi.org/10.1063/1.3459152 (18 pages) | Cited 9 times

Online Publication Date: 23 July 2010

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Large-eddy simulation (LES) is performed of a curved open-channel flow over topography based on the laboratory experiment by Blanckaert [“Topographic steering, flow circulation, velocity redistribution and bed topography in sharp meander bends,” Water Resour. Res., doi:10.1029/2009WR008303 (in press)] . In the experiment, the large-scale bed topography had developed to a more or less stationary shape which was prescribed in the LES model as boundary conditions neglecting the small-scale dune forms by means of a straightforward immersed boundary scheme in combination with a simple wall-modeling approach. The small-scale dunes are accounted for in the numerical model by means of parametrization. Sensitivity of the flow to this roughness parametrization is examined by simulating the flow for three different roughness heights. It was found that, notwithstanding the coarse method of representing the dune forms, the qualitative agreement of the experimental results and the LES results is rather good. Comparison of the LES results with the Reynolds averaged numerical simulation results of Zeng et al. [“Flow and bathymetry in sharp open-channel bends: Experiments and predictions,” Water Resour. Res. 44, W09401, doi:10.1029/2007WR006303 (2008)] reveals surprisingly good agreement. This good agreement is explained by the minor importance of turbulence stress gradients in the contribution to the transverse and streamwise momentum balance. Moreover, it is found that in the bend the structure of the Reynolds stress tensor shows a tendency toward isotropy which enhances the performance of isotropic eddy viscosity closure models of turbulence. This observation is remarkable since highly anisotropic turbulence might well be expected considering the complex nature of the geometry. Furthermore, the LES results reveal a pronounced recirculation zone near the convex inner bank of the flume due to the shallowness of the flow and strong curvature of the flume. At the interface between the recirculation zone and the main flow, a curved mixing layer is identified as well as strong upwelling flow motion that is accompanied with large production of turbulent kinetic energy.
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47.11.-j Computational methods in fluid dynamics
47.27.nd Channel flow
47.60.Dx Flows in ducts and channels
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