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Mar 2012

Volume 24, Issue 3, Articles (03xxxx)

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Phys. Fluids 24, 035107 (2012); http://dx.doi.org/10.1063/1.3693136 (18 pages)

A. Valizadeh and J. J. Monaghan
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A new way to describe the transition characteristics of a rotating-disk boundary-layer flow

Shintaro Imayama, P. Henrik Alfredsson, and R. J. Lingwood

Phys. Fluids 24, 031701 (2012); http://dx.doi.org/10.1063/1.3696020 (7 pages) | Cited 3 times

Online Publication Date: 14 March 2012

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A new method of graphically representing the transition stages of a rotating-disk flow is presented. The probability density function contour map of the fluctuating azimuthal disturbance velocity is used to show the characteristics of the boundary-layer flow over the rotating disk as a function of Reynolds numbers. Compared with the variation of the disturbance amplitude (rms) or spectral distribution, this map more clearly shows the changing flow characteristics through the laminar, transitional, and turbulent regions. This method may also be useful to characterize the different stages in the transition process not only for the rotating-disk flow but also for other flows.
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47.15.Fe Stability of laminar flows
47.27.nb Boundary layer turbulence
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
47.32.Ef Rotating and swirling flows
47.80.Jk Flow visualization and imaging
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back to top Biofluid Mechanics

Vesicle tumbling inhibited by inertia

Aymen Laadhari, Pierre Saramito, and Chaouqi Misbah

Phys. Fluids 24, 031901 (2012); http://dx.doi.org/10.1063/1.3690862 (7 pages) | Cited 7 times

Online Publication Date: 6 March 2012

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Vesicles under flow constitute a model system for the study of red blood cells (RBCs) dynamics and blood rheology. In the blood circulatory system the Reynolds number (at the scale of the RBC) is not always small enough for the Stokes limit to be valid. We develop a numerical method in two dimensions based on the level set approach and solve the fluid/membrane coupling by using an adaptive finite element technique. We find that a Reynolds number of order one can destroy completely the vesicle tumbling motion obtained in the Stokes regime. We analyze in details this phenomenon and discuss some of the far reaching consequences. We suggest experimental tests on vesicles.
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87.19.U- Hemodynamics
47.11.Fg Finite element methods
47.63.Cb Blood flow in cardiovascular system
47.63.Jd Microcirculation and flow through tissues
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
87.19.rh Fluid transport and rheology
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Reducing the data: Analysis of the role of vascular geometry on blood flow patterns in curved vessels

Jordi Alastruey, Jennifer H. Siggers, Véronique Peiffer, Denis J. Doorly, and Spencer J. Sherwin

Phys. Fluids 24, 031902 (2012); http://dx.doi.org/10.1063/1.3694526 (24 pages) | Cited 3 times

Online Publication Date: 19 March 2012

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Three-dimensional simulations of blood flow usually produce such large quantities of data that they are unlikely to be of clinical use unless methods are available to simplify our understanding of the flow dynamics. We present a new method to investigate the mechanisms by which vascular curvature and torsion affect blood flow, and we apply it to the steady-state flow in single bends, helices, double bends, and a rabbit thoracic aorta based on image data. By calculating forces and accelerations in an orthogonal coordinate system following the centreline of each vessel, we obtain the inertial forces (centrifugal, Coriolis, and torsional) explicitly, which directly depend on vascular curvature and torsion. We then analyse the individual roles of the inertial, pressure gradient, and viscous forces on the patterns of primary and secondary velocities, vortical structures, and wall stresses in each cross section. We also consider cross-sectional averages of the in-plane components of these forces, which can be thought of as reducing the dynamics of secondary flows onto the vessel centreline. At Reynolds numbers between 50 and 500, secondary motions in the directions of the local normals and binormals behave as two underdamped oscillators. These oscillate around the fully developed state and are coupled by torsional forces that break the symmetry of the flow. Secondary flows are driven by the centrifugal and torsional forces, and these are counterbalanced by the in-plane pressure gradients generated by the wall reaction. The viscous force primarily opposes the pressure gradient, rather than the inertial forces. In the axial direction, and depending on the secondary motion, the curvature-dependent Coriolis force can either enhance or oppose the bulk of the axial flow, and this shapes the velocity profile. For bends with little or no torsion, the Coriolis force tends to restore flow axisymmetry. The maximum circumferential and axial wall shear stresses along the centreline correlate well with the averaged in-plane pressure gradient and the radial displacement of the peak axial velocity, respectively. We conclude with a discussion of the physiological implications of these results.
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47.63.Cb Blood flow in cardiovascular system
87.19.ug Heart and lung dynamics
47.54.Bd Theoretical aspects
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.15.Cb Laminar boundary layers
47.10.-g General theory in fluid dynamics
back to top Micro- and Nanofluid Mechanics

Inertial focusing dynamics in spiral microchannels

Joseph M. Martel and Mehmet Toner

Phys. Fluids 24, 032001 (2012); http://dx.doi.org/10.1063/1.3681228 (13 pages) | Cited 5 times

Online Publication Date: 6 March 2012

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This report details a comprehensive study of inertial focusing dynamics and particle behavior in low aspect ratio (h/w ∼ 1/1 to 1/8) spiral microchannels. A continuum of particle streak behavior is shown with longitudinal, cross-sectional, and velocity resolution, yielding a large analyzed parameter space. The dataset is then summarized and compared to prior results from both straight microchannels and other low aspect ratio spiral microchannel designs. Breakdown of focusing into a primary and secondary fluorescent streak is observed in the lowest aspect ratio channels at high average downstream velocities. Streak movement away from the theoretically predicted near inner wall equilibrium position towards the center of the channel at high average downstream velocities is also detailed as a precursor to breakdown. State diagrams detail the overall performance of each device including values of the required channel lengths and the range of velocities over which quality focusing can be achieved.
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47.55.Kf Particle-laden flows
47.60.Dx Flows in ducts and channels

Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem

Shigeru Takata, Kazuo Aoki, Masanari Hattori, and Nicolas G. Hadjiconstantinou

Phys. Fluids 24, 032002 (2012); http://dx.doi.org/10.1063/1.3691262 (15 pages) | Cited 2 times

Online Publication Date: 6 March 2012

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The behavior of a slightly rarefied monatomic gas between two parallel plates whose temperature grows slowly and linearly in time is investigated on the basis of the kinetic theory of gases. This problem is shown to be equivalent to a boundary-value problem of the steady linearized Boltzmann equation describing a rarefied gas subject to constant volumetric heating. The latter has been recently studied by Radtke, Hadjiconstantinou, Takata, and Aoki (RHTA) as a means of extracting the second-order temperature jump coefficient. This correspondence between the two problems gives a natural interpretation to the volumetric heating source and explains why the second-order temperature jump observed by RHTA is not covered by the general theory of slip flow for steady problems. A systematic asymptotic analysis of the time-dependent problem for small Knudsen numbers is carried out and the complete fluid-dynamic description, as well as the related half-space problems that determine the structure of the Knudsen layer and the coefficients of temperature jump, are obtained. Finally, a numerical solution is presented for both the Bhatnagar-Gross-Krook model and hard-sphere molecules. The jump coefficient is also calculated by the use of a symmetry relation; excellent agreement is found with the result of the numerical computation. The asymptotic solution and associated second-order jump coefficient obtained in the present paper agree well with the results by RHTA that are obtained by a low variance stochastic method.
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47.45.Gx Slip flows and accommodation
02.50.Ey Stochastic processes
02.60.Lj Ordinary and partial differential equations; boundary value problems
47.45.Ab Kinetic theory of gases

Gas flow and heat transfer in nanotube and nanowire arrays

Michael J. Martin

Phys. Fluids 24, 032003 (2012); http://dx.doi.org/10.1063/1.3693701 (16 pages) | Cited 1 time

Online Publication Date: 15 March 2012

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Gas flow through arrays of nanotube or nanowire structures is modeled by combining the one-dimensional equations for conservation of mass, momentum, and energy with the linearized free-molecular drag and heat transfer for a cylinder. The results show that the pressure gradient, temperature, and local velocity of the gas are governed by coupled ordinary differential equations. Three cases are considered: an isothermal system, a constant wall temperature, and a constant wall heat flux. While the coupled momentum, heat transfer, and continuity equations are nonlinear, the relatively low velocities encountered in these systems cause the nonlinear portions of pressure drops and thermal phenomena to be relatively small.
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47.27.te Turbulent convective heat transfer
47.40.-x Compressible flows; shock waves
47.50.-d Non-Newtonian fluid flows
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems

High accuracy numerical solutions of the Boltzmann Bhatnagar-Gross-Krook equation for steady and oscillatory Couette flows

Ying Wan Yap and John E. Sader

Phys. Fluids 24, 032004 (2012); http://dx.doi.org/10.1063/1.3692276 (18 pages) | Cited 1 time

Online Publication Date: 30 March 2012

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Modeling gas flows generated by micro- and nano-devices often requires the use of kinetic theory. To facilitate implementation, various approximate formulations have been proposed based on the Bhatnagar-Gross-Krook (BGK) kinetic model, including most recently, the lattice Boltzmann (LB) method. While there exists a comprehensive numerical data set for the hard sphere linearized Boltzmann equation for steady Couette flow, no such set of data is available for the Boltzmann-BGK equation. The purpose of this article is to present a high accuracy data set for the linearized Boltzmann-BGK equation over the full range of Knudsen numbers and normalized oscillation frequencies – this encompasses both steady and unsteady Couette flows. This data set is expected to be of particular value in the benchmarking and validation of computational methods such as the LB method and other approaches based on the Boltzmann-BGK equation.
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47.15.-x Laminar flows
47.45.-n Rarefied gas dynamics
47.45.Ab Kinetic theory of gases
47.11.Mn Molecular dynamics methods
back to top Interfacial Flows

Nonlinear Marangoni waves in a two-layer film in the presence of gravity

Alexander Nepomnyashchy and Ilya Simanovskii

Phys. Fluids 24, 032101 (2012); http://dx.doi.org/10.1063/1.3690167 (22 pages) | Cited 1 time

Online Publication Date: 2 March 2012

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Longwave Marangoni convection in two-layer films under the action of gravity is considered. The analysis is carried out in the lubrication approximation. A linear stability analysis reveals the existence of monotonic and oscillatory instability modes, depending on the way of heating and the value of the Biot number. Numerical simulations are performed in the case of an oscillatory instability, which takes place by heating from above. Periodic boundary conditions are applied on the boundaries of the computational region. A sequence of nonlinear wavy regimes, which develop by the increase of the Galileo number, is studied. That sequence includes three-dimensional and two-dimensional structures. The multistability of wavy patterns with different spatial periods has been revealed.
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47.35.Bb Gravity waves
47.55.Hd Stratified flows
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities

Thermocapillary flows and interface deformations produced by localized laser heating in confined environment

Hamza Chraïbi and Jean-Pierre Delville

Phys. Fluids 24, 032102 (2012); http://dx.doi.org/10.1063/1.3690160 (14 pages)

Online Publication Date: 5 March 2012

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The deformation of a fluid-fluid interface due to the thermocapillary stress induced by a continuous Gaussian laser wave is investigated analytically. We show that the direction of deformation of the liquid interface strongly depends on the viscosities and the thicknesses of the involved liquid layers. We first investigate the case of an interface separating two different liquid layers while a second part is dedicated to a thin film squeezed by two external layers of same liquid. These results are predictive for applications fields where localized thermocapillary stresses are used to produce flows or to deform interfaces in presence of confinement, such as optofluidics.
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47.55.nb Capillary and thermocapillary flows
47.55.nd Spreading films
68.05.-n Liquid-liquid interfaces
47.60.-i Flow phenomena in quasi-one-dimensional systems
66.20.-d Viscosity of liquids; diffusive momentum transport

Thermocapillary instabilities in an evaporating drop deposited onto a heated substrate

B. Sobac and D. Brutin

Phys. Fluids 24, 032103 (2012); http://dx.doi.org/10.1063/1.3692267 (16 pages) | Cited 1 time

Online Publication Date: 6 March 2012

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The present study is an experimental investigation regarding the evaporation of ethanol drops deposited onto a heated substrate in a partial wetting situation. The originality of this work is based on the simultaneous observation of the kinetics of evaporation, heat and mass transfers, the triple-line dynamic, and thermal motions inside the drop. The triple line recedes during the drop evaporation and a spontaneous development of thermal-convective instabilities driven by the evaporation are observed. These instabilities are interpreted as hydrothermal waves induced by surface tension gradient along the free surface. An infrared technique is used to investigate the temporal and spatial dynamics of the hydrothermal waves. Results reveal a non-linear evolution of the number of waves as well as several instability regimes. A complete description of the drop evaporation with the evidence of several phases is provided. The influence of geometrical and thermal parameters has been analyzed and raised scaling laws on hydrodynamic and energy transport. The drop evaporation appears to be characterized by a constant drop Nusselt number of a value 1.7 during all the process which highlights both the importance of conduction and convection in the energy transport in an evaporating drop.
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47.55.dm Thermocapillary effects
47.20.Dr Surface-tension-driven instability
47.55.nd Spreading films
47.55.P- Buoyancy-driven flows; convection
47.55.nb Capillary and thermocapillary flows

Instability of a transverse liquid rivulet on an inclined plane

Javier A. Diez, Alejandro G. González, and Lou Kondic

Phys. Fluids 24, 032104 (2012); http://dx.doi.org/10.1063/1.3685802 (27 pages) | Cited 3 times

Online Publication Date: 6 March 2012

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This work concentrates on the stability of a viscous liquid rivulet positioned across an inclined plane under partial wetting conditions. The study is performed within the framework of lubrication approximation by employing a slip model. Both normal and parallel components of gravity are considered. We find the stability regions for given area of the cross section of the rivulet, A, plane inclination angle, α, and static contact angle, θ0, characterizing the wettability of the substrate. For α’s smaller than some critical angle, α*, a static solution exists. This solution is characterized by rear/front contact angles given by θ0 ± δ. The linear stability analysis of this solution is performed using an efficient pseudo-spectral Chebyshev method. We analyze the effects of A, θ0, and α on the predictions of the model, such as the dominant wavelength, the maximum growth rate, and the behavior of the most unstable perturbation mode. To verify them, we also carry out experiments with silicone oils spreading on a coated glass substrate for several different fluid volumes and inclination angles. We find very good agreement between the wavelength of maximum growth rate given by the theory and the average distance between the drops after rivulet breakup. An analysis of finite size effects shows that the inclusion of normal gravity effects leads to a better agreement between theoretical and experimental results.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.45.Gx Slip flows and accommodation
47.55.df Breakup and coalescence
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.11.-j Computational methods in fluid dynamics

Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field

Shivraj. D. Deshmukh and Rochish. M. Thaokar

Phys. Fluids 24, 032105 (2012); http://dx.doi.org/10.1063/1.3691655 (21 pages)

Online Publication Date: 7 March 2012

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A detailed nonlinear analysis of the deformation and breakup of a perfect dielectric (PD) drop, suspended in another perfect dielectric fluid, in the presence of a quadrupole electric field is presented using analytical (asymptotic) and numerical (boundary integral) methods. The quadrupole field is the simplest kind of an axisymmetric non-uniform electric field. A drop, when placed at the center of such a field, does not translate, thus allowing systematic investigation of the effect of non-uniformity of the electric field. The deformation of a drop under a quadrupole field for PD-PD systems exhibits several novel features as compared to that of a drop under a uniform electric field. The first order analysis predicts oblate deformation for a PD-PD system when the dielectric constant of the suspending medium is larger than that of the drop (Q = εi/εe < 1). This is in sharp contrast to uniform electric fields where oblate shapes are observed only in leaky dielectric systems. Prolate shapes are observed for Q > 1, and the deformation is larger than that for uniform fields for similar electric capillary numbers. The steady state shapes are defined by higher harmonics as compared to the uniform field. At large capillary numbers, prolate deformations (Q > 1) show breakup whereas oblate deformations (Q < 1) do not. Positive and negative dielectrophoresis is observed when the drop is placed off center, and its translation and simultaneous deformation under quadrupole fields is also investigated. The electro-hydrostatics is unaffected by the viscosity ratio. However, the breakup of the drop and the dielectrophoretic motion and deformation strongly depend upon the viscosity ratio.
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47.55.db Drop and bubble formation
47.55.df Breakup and coalescence
47.65.-d Magnetohydrodynamics and electrohydrodynamics
82.70.Kj Emulsions and suspensions
47.57.E- Suspensions
47.55.nb Capillary and thermocapillary flows

Thermally induced van der Waals rupture of thin viscous fluid sheets

Mark Bowen and B. S. Tilley

Phys. Fluids 24, 032106 (2012); http://dx.doi.org/10.1063/1.3693700 (19 pages)

Online Publication Date: 14 March 2012

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We consider the dynamics of a thin symmetric fluid sheet subject to an initial temperature profile, where inertia, viscous stresses, disjoining pressures, capillarity, and thermocapillarity are important. We apply a long-wave analysis in the limit where deviations from the mean sheet velocity are small, but thermocapillary stresses and heat transfer from the sheet to the environment are significant and find a coupled system of partial differential equations that describe the sheet thickness, the mean sheet velocity, and the mean sheet temperature. From a linear stability analysis, we find that a stable thermal mode couples the velocity to the interfacial dynamics. This coupling can be utilized to delay the onset of rupture or to promote an earlier rupture event. In particular, rupture can be induced thermally even in cases when the heat transfer to the surrounding environment is significant, provided that the initial phase shift between the initial velocity and temperature disturbances is close to ϕ = π/2. These effects suggest a strategy that uses phase modulation in the initial temperature perturbation related to the initial velocity perturbation that assigns priority of the rupture events at particular sites over several spatial periods.
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47.55.pf Marangoni convection
47.85.mf Lubrication flows
68.03.Cd Surface tension and related phenomena
47.55.nb Capillary and thermocapillary flows
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.11.-j Computational methods in fluid dynamics

Thermocapillary-assisted pulling of contact-free liquid films

Benoit Scheid, Ernst A. van Nierop, and Howard A. Stone

Phys. Fluids 24, 032107 (2012); http://dx.doi.org/10.1063/1.3692097 (21 pages)

Online Publication Date: 15 March 2012

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We study the formation of a free liquid film that is pulled out of a bath at constant speed and stabilized by the action of thermocapillary stresses prescribed at the free surfaces. The basic concept was introduced recently by Scheid et al. [“Thermocapillary-assisted pulling of thin films: Application to molten metals,” Appl. Phys. Lett. 97, 171906 (2010)]10.1063/1.3505523. The theory suggests that very thin ribbons of molten material can be drawn out of a melt by adequately tuning the temperature gradient along the dynamic meniscus that connects the static meniscus at the melting bath to the region of the drawn flat film. In the present paper, we extend our original analysis by investigating the roles of inertia and gravity on the film thickness, and show how the results depend on heat transfer/conduction properties. Furthermore, we analyze the one-dimensional transverse stability of the free film with respect to the long-wave thermocapillary instability.
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68.15.+e Liquid thin films
47.55.nb Capillary and thermocapillary flows
47.35.Bb Gravity waves
47.20.-k Flow instabilities

Disorder-induced hysteresis and nonlocality of contact line motion in chemically heterogeneous microchannels

Christophe Wylock, Marc Pradas, Benoit Haut, Pierre Colinet, and Serafim Kalliadasis

Phys. Fluids 24, 032108 (2012); http://dx.doi.org/10.1063/1.3696860 (15 pages) | Cited 5 times

Online Publication Date: 26 March 2012

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We examine the motion of a liquid-air meniscus advancing into a microchannel with chemically heterogeneous walls. We consider the case where a constant flow rate is imposed, so that the mean velocity of the interface is kept constant, and study the effects of the disorder properties on the apparent contact angle for each microchannel surface. We focus here on a large diffusivity regime, where any possible advection effect is not taken into account. To this end, we make use of a phase-field model that enables contact line motion by diffusive interfacial fluxes and takes into account the wetting properties of the walls. We show that in a regime of sufficiently low velocities, the contact angle suffers a hysteresis behavior which is enhanced by the disorder strength. We also show that the contact line dynamics at each surface of the microchannel may become largely coupled with each other when different wetting properties are applied at each wall, reflecting that the dynamics of the interface is dominated by nonlocal effects.
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47.60.Dx Flows in ducts and channels
68.03.Cd Surface tension and related phenomena
66.10.C- Diffusion and thermal diffusion
47.57.eb Diffusion and aggregation
47.20.Ib Instability of boundary layers; separation
47.55.nd Spreading films
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Linear oscillations of constrained drops, bubbles, and plane liquid surfaces

Andrea Prosperetti

Phys. Fluids 24, 032109 (2012); http://dx.doi.org/10.1063/1.3697796 (15 pages) | Cited 3 times

Online Publication Date: 26 March 2012

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The small-amplitude oscillations of constrained drops, bubbles, and plane liquid surfaces are studied theoretically. The constraints have the form of closed lines of zero thickness which prevent the motion of the liquid in the direction normal to the undisturbed free surface. It is shown that, by accounting explicitly for the singular nature of the curvature of the interface and the force exerted by the constraint, methods of analysis very close to the standard ones applicable to the unconstrained case can be followed. Weak viscous effects are accounted for by means of the dissipation function. Graphical and numerical results for the oscillations of constrained drops and bubbles are presented. Examples of two- and three-dimensional gravity-capillary waves are treated by the same method. A brief consideration of the Rayleigh-Taylor unstable configuration shows that the nature of the instability is not affected, although its growth rate is decreased.
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47.35.Pq Capillary waves
47.55.D- Drops and bubbles
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.35.Bb Gravity waves

Observations of Kelvin-Helmholtz instability at the air-water interface in a circular domain

John A. T. Bye and Malek Ghantous

Phys. Fluids 24, 032110 (2012); http://dx.doi.org/10.1063/1.3697487 (4 pages)

Online Publication Date: 30 March 2012

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We present an analysis of Kelvin-Helmholtz instability in a circular domain in the limit of the azimuthal integer wavenumber, n → ∞ which reproduces the classical results for a rectilinear geometry at the rim, provided that the additional condition that the surface current to surface wind ratio is (ρ1/ρ2)1/2 where ρ1 and ρ2 are respectively the densities of air and water, is satisfied. Experiments were carried out in a circular rig of radius 0.19 m in which a family of unstable waveforms with n ≈ 60 were observed with properties (including the additional condition) in approximate agreement with theory. The additional condition is consistent with the absence of a surface shear stress in the instability process.
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47.20.-k Flow instabilities
47.40.-x Compressible flows; shock waves
47.35.De Shear waves
back to top Viscous and Non-Newtonian Flows

Reynolds-number effect on vortex ring evolution in a viscous fluid

F. Kaplanski, Y. Fukumoto, and Y. Rudi

Phys. Fluids 24, 033101 (2012); http://dx.doi.org/10.1063/1.3693276 (13 pages)

Online Publication Date: 9 March 2012

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It is known that the cross section of the vortex ring core takes an approximately elliptical shape with increasing Reynolds number. In order to model this feature, the functional form of a vortex ring solution of the Stokes equations is modified so as to be able to model higher Reynolds number rings. The model introduces two nondimensional parameters that govern the shape of the vortex core:λ ⩾ 1 and β ⩾ 1. Based on this modification, new expressions for the translation velocity, energy, circulation, and streamfunction are derived for a wide range of section ellipticity that are specific to such vortices. To validate the model, the data adapted from the numerical study of vortex ring at Reynolds number Re = 1400 performed by Danaila and Helie [Phys. Fluids 20, 073602 (2008)], is used. In this case, the appropriate values of λ and β are calculated by equating the normalized energy Ed and circulation Γd of the theoretical vortex to the corresponding values obtained from the numerical data. The model provides a good prediction of the ring velocity evolution at high Reynolds numbers.
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47.32.cf Vortex reconnection and rings
47.10.ad Navier-Stokes equations
02.60.-x Numerical approximation and analysis
back to top Particulate, Multiphase, and Granular Flows

On the motion of inertial particles by sound waves

Jay Cleckler, Said Elghobashi, and Feng Liu

Phys. Fluids 24, 033301 (2012); http://dx.doi.org/10.1063/1.3696243 (11 pages) | Cited 1 time

Online Publication Date: 23 March 2012

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This paper describes the numerical simulation of the motion of a heavy spherical particle in an acoustic wave using the equation of motion for a point particle. Our results agree well with the recent experimental data of Gonzàlez, Hoffmann, and Gallego [“Precise measurements of particle entrainment in a standing-wave acoustic field between 20 and 3500 Hz,” J. Aerosol Sci. 31, 1461–1468 (2000)]. Our simulations cover a range of particle relaxation number, τ* = ωτ, where τ is the particle relaxation time and ω is the angular acoustic frequency from 0.06 to 10, particle to fluid density ratios, ρp/ρf, from 2500 to 2, and moderate acoustic velocity amplitudes. The results show that the Stokes force controls particle motion for τ* < 1 and ρp/ρf > 25. Within this regime it is appropriate to consider the Basset, pressure gradient, and virtual mass forces as “higher order” corrections to the Stokes force. The magnitude of the Basset force exceeds that of the Stokes force for ρp/ρf ⩾ 25 and τ* ⩾ 4. All the forces in the particle equation of motion should be accounted for when simulating particle motion in an acoustic wave for ρp/ρf < 25.
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47.35.Rs Sound waves
47.55.Kf Particle-laden flows
47.11.-j Computational methods in fluid dynamics
back to top Laminar Flows

Boundary layer development in the flow field between a rotating and a stationary disk

K. M. P. van Eeten, J. van der Schaaf, J. C. Schouten, and G. J. F. van Heijst

Phys. Fluids 24, 033601 (2012); http://dx.doi.org/10.1063/1.3698406 (18 pages) | Cited 2 times

Online Publication Date: 30 March 2012

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This paper discusses the development of boundary layers in the flow of a Newtonian fluid between two parallel, infinite disks. One of the disks is rotating at a constant angular velocity while the other remains stationary. An analytical series approximation and a numerical solution method are used to describe the velocity profiles of the flow. Both methods rely on the commonly used similarity transformation first proposed by Von Kármán [T. von Kármán, ZAMM 1, 233 (1921)]10.1002/zamm.19210010401. For Reh < 18, the power series analytically describe the complete velocity profile. With the numerical model a Batchelor type of flow was observed for Reh > 300, with two boundary layers near the disks and a non-viscous core in the middle. A remarkable conclusion of the current work is the coincidence of the power series’ radius of convergence, a somewhat abstract mathematical notion, with the physically tangible concept of the boundary layer thickness. The coincidence shows a small deviation of only 2% to 4%.
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47.15.Cb Laminar boundary layers
47.53.+n Fractals in fluid dynamics
47.55.-t Multiphase and stratified flows
47.10.ad Navier-Stokes equations
47.11.-j Computational methods in fluid dynamics
back to top Instability and Transition

The continuous spectrum of time-harmonic shear layers

M. J. Philipp Hack and Tamer A. Zaki

Phys. Fluids 24, 034101 (2012); http://dx.doi.org/10.1063/1.3687451 (22 pages)

Online Publication Date: 1 March 2012

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In boundary layers, eigenfunctions which belong to the continuous spectrum of the Orr–Sommerfeld equation have been established as a suitable basis for the expansion of general free-stream vortical disturbances. They are oscillatory in the free stream, and attenuate inside the boundary layer due to shear sheltering. The extent of modal penetration into the shear depends on the disturbance frequency and orientation, with the low-frequency, streamwise elongated modes being the most effective triggers of a high-amplitude streak-like response. The influence of introducing a time-periodic, spanwise mean flow on modal sheltering is investigated. The evaluation of the continuous modes in this case requires a Floquet expansion in the fundamental frequency of the base flow. Appropriate treatment of the free-stream boundedness condition is developed, and quantitative measures of modal sheltering are computed. The time-dependent, spanwise motion is shown to significantly enhance shear sheltering, and to change the optimal orientation of the continuous modes for penetration into the shear. An explanation is provided, in the limit of low frequency of the base flow, using asymptotic analyses.
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47.32.cb Vortex interactions
02.10.Ud Linear algebra
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.nb Boundary layer turbulence

Criticality of flow transition behind two side-by-side elliptic cylinders

Y. F. Peng, Amalendu Sau, Robert R. Hwang, W. C. Yang, and Chih-Min Hsieh

Phys. Fluids 24, 034102 (2012); http://dx.doi.org/10.1063/1.3687450 (36 pages)

Online Publication Date: 2 March 2012

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In this study, near-critical bifurcations of low Reynolds number (Re) flows past a pair of elliptic cylinders in the side-by-side arrangement are numerically investigated, and onsets of several distinct transition scenarios are addressed. A nested Cartesian-grid formulation, in combination with an effective immersed boundary method and a two-step fractional-step procedure, has been adopted to simulate the flows. The transition scenarios associated with various periodic, quasi-periodic, and biased flows, their bifurcation characteristics, corresponding critical Reynolds numbers, and phase-portraits are exploited to better understand the governing physics. From the global point of view, there appear variety of flow patterns within the investigated parameter space, 40 ⩽ Re ⩽ 300, 0.2 ⩽ G ⩽ 3.0 (G being the gap-ratio of the cylinders), and 1.5 ⩽ A ⩽ 3 (A is the cylinder aspect-ratio), which include, symmetric vortex shedding mode, semi-single/twin vortex street formations, asymmetric/deflected flows, stationary/biased flip-flopped-type vortex shedding, weakly-chaotic flows, and in-phase/anti-phase vortex synchronizations. We numerically present these flows by tuning Re quasi-stationary, and provide a broader understanding of the entire transition process. A comprehensive analysis of effects of Reynolds number, the gap-ratio, and the angle of incidence on different flow-induced forces on the cylinders is included in this regard. On the other hand, our simulated wakes with various non-zero incidence-angles are found to reveal a rich variety of instability induced weakly synchronized physical evolution characteristics, which remained virtually unexplored.
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47.15.G- Low-Reynolds-number (creeping) flows
47.27.Cn Transition to turbulence
47.27.wb Turbulent wakes
47.32.C- Vortex dynamics
47.52.+j Chaos in fluid dynamics
47.11.-j Computational methods in fluid dynamics

Experimental study of initial condition dependence on Richtmyer-Meshkov instability in the presence of reshock

S. Balasubramanian, G. C. Orlicz, K. P. Prestridge, and B. J. Balakumar

Phys. Fluids 24, 034103 (2012); http://dx.doi.org/10.1063/1.3693152 (14 pages) | Cited 2 times

Online Publication Date: 14 March 2012

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We present an experimental study on the dependence of initial condition parameters, namely, the amplitude δ and wavenumber κ (κ = 2π/λ, where λ is the wavelength) of perturbations, on turbulence and mixing in shock-accelerated Richtmyer-Meshkov (R-M) unstable fluid layers. A single mode, membrane-free varicose heavy gas curtain (air-SF6-air) at a shock Mach number M = 1.2 was used in our experiments. The density (concentration) and velocity fields for this initial configuration were measured using planar laser -induced fluorescence (PLIF) and particle image velocimetry (PIV). In order to understand the effects of multi-mode initial conditions on shock-accelerated mixing, the evolving fluid interface formed during the incident shock (M = 1.2) was shocked again by a reflected shock wave at various times using a movable wall, thus enabling us to change both δ and κ simultaneously. A dimensionless length-scale defined as η = κδ is proposed to parametrically link the initial condition dependence to late-time mixing. It was observed experimentally that high wavenumber (short wavelength) modes enhance the mixing and transition to turbulence in these flows. Statistics such as power spectral density, density self-correlation, turbulent kinetic energy, and the rms of velocity fluctuations were measured using simultaneous PLIF-PIV to quantify the amount of mixing for varying values of η. The results indicate a dependence of initial condition parameters on mixing at late times. The results of this study present an opportunity to predict and “design” late-time turbulent mixing that has applications in inertial confinement fusion and general fluid mixing processes.
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47.20.-k Flow instabilities
47.80.Jk Flow visualization and imaging
47.40.-x Compressible flows; shock waves
47.27.wj Turbulent mixing layers
47.40.Nm Shock wave interactions and shock effects

Linear stability analysis of a sub-to-supercritical jet

Arnab Roy and Corin Segal

Phys. Fluids 24, 034104 (2012); http://dx.doi.org/10.1063/1.3694806 (8 pages)

Online Publication Date: 19 March 2012

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A linear stability analysis was performed on a viscous jet injected into subcritical and supercritical atmospheres. The analysis complements previous experiments. The system is binary, so that effects of the second species on jet disintegration could be inspected in the analysis. The subcritical cases showed good correlation with previously solved cases of stability in viscous jets. The supercritical solutions, which have not yet been solved using a similar analysis, are found here through an asymptotic solution of the dispersion equation for exceedingly high Weber numbers.
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47.60.Kz Flows and jets through nozzles
47.20.-k Flow instabilities
47.11.-j Computational methods in fluid dynamics

The stabilization of a hypersonic boundary layer using local sections of porous coating

Xiaowen Wang and Xiaolin Zhong

Phys. Fluids 24, 034105 (2012); http://dx.doi.org/10.1063/1.3694808 (28 pages) | Cited 1 time

Online Publication Date: 21 March 2012

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The stabilization effect of porous coating on the hypersonic boundary layers over flat plates and cones has been studied by theoretical analyses, experiments, and numerical simulations. It was found that porous coating slightly destabilizes Mack's first mode whereas it significantly stabilizes Mack's second mode. In previous studies, porous coating covers either the entire flat plate or the surface around half the cone circumference. The effect of porous coating location on boundary-layer stabilization has not been considered. Furthermore, the destabilization of Mack's first mode has not been studied in detail. In this paper, the stabilization of a Mach 5.92 flat-plate boundary layer using local sections of porous coating is studied with the emphasis on the effect of porous coating location and the first-mode destabilization. Artificial disturbances corresponding to a single boundary-layer wave are introduced near the leading edge. A series of stability simulations are carried out by locally putting felt-metal porous coatings along the flat plate. It is found that disturbances are destabilized or stabilized when porous coating is located upstream or downstream of the synchronization point. For felt-metal porous coating, the destabilization of Mack's first mode is significant. The results suggest that an efficient way to stabilize hypersonic boundary-layer flows is to put porous coating downstream of the synchronization point. Finally, porous coating is used to stabilize the boundary layer disturbed by one blowing-suction actuator.
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47.40.Ki Supersonic and hypersonic flows
47.56.+r Flows through porous media
47.20.Ib Instability of boundary layers; separation
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations
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