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Jul 2009

Volume 21, Issue 7, Articles (07xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 21, 072107 (2009); http://dx.doi.org/10.1063/1.3177339 (10 pages)

François Blanchette, Laura Messio, and John W. M. Bush
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The impact of a local perturbation on global properties of a turbulent wake

Vladimir Parezanović and Olivier Cadot

Phys. Fluids 21, 071701 (2009); http://dx.doi.org/10.1063/1.3184615 (4 pages) | Cited 8 times

Online Publication Date: 24 July 2009

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Stationary perturbation techniques are used to investigate the sensitivity of the global properties of the wake behind a bluff body at moderate Re. The entire recirculation bubble is found to be a sensitive region for the global frequency selection and the quality of the synchronization. A striking position is found at its center where synchronization is destroyed and the frequency is increased. High speed particle image velocimetry sheds some light into the underlying mechanisms, which are interpreted in terms of vorticity interaction, flow reattachment, and flow deviation. Strong mean flow modifications are observed to correspond to drastic changes in drag and its fluctuations.
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47.27.W- Boundary-free shear flow turbulence
47.32.-y Vortex dynamics; rotating fluids
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.80.Jk Flow visualization and imaging
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back to top Biofluid Mechanics

Simplified dragonfly airfoil aerodynamics at Reynolds numbers below 8000

David-Elie Levy and Avraham Seifert

Phys. Fluids 21, 071901 (2009); http://dx.doi.org/10.1063/1.3166867 (17 pages) | Cited 5 times

Online Publication Date: 7 July 2009

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Effective aerodynamics at Reynolds numbers lower than 10 000 is of great technological interest and a fundamental scientific challenge. The current study covers a Reynolds number range of 2000–8000. At these Reynolds numbers, natural insect flight could provide inspiration for technology development. Insect wings are commonly characterized by corrugated airfoils. In particular, the airfoil of the dragonfly, which is able to glide, can be used for two-dimensional aerodynamic study of fixed rigid wings. In this study, a simplified dragonfly airfoil is numerically analyzed in a steady free-stream flow. The aerodynamic performance (such as mean and fluctuating lift and drag), are first compared to a “traditional” low Reynolds number airfoil: the Eppler-E61. The numerical results demonstrate superior performances of the corrugated airfoil. A series of low-speed wind and water tunnel experiments were performed on the corrugated airfoil, to validate the numerical results. The findings indicate quantitative agreement with the mean wake velocity profiles and shedding frequencies while validating the two dimensionality of the flow. A flow physics numerical study was performed in order to understand the underlying mechanism of corrugated airfoils at these Reynolds numbers. Airfoil shapes based on the flow field characteristics of the corrugated airfoil were built and analyzed. Their performances were compared to those of the corrugated airfoil, stressing the advantages of the latter. It was found that the flow which separates from the corrugations and forms spanwise vortices intermittently reattaches to the aft-upper arc region of the airfoil. This mechanism is responsible for the relatively low intensity of the vortices in the airfoil wake, reducing the drag and increasing the flight performances of this kind of corrugated airfoil as compared to traditional low Reynolds number airfoils such as the Eppler E-61.
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47.85.Gj Aerodynamics
47.27.wb Turbulent wakes

Resonance and propulsion performance of a heaving flexible wing

Sébastien Michelin and Stefan G. Llewellyn Smith

Phys. Fluids 21, 071902 (2009); http://dx.doi.org/10.1063/1.3177356 (15 pages) | Cited 16 times

Online Publication Date: 20 July 2009

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The influence of the bending rigidity of a flexible heaving wing on its propulsive performance in a two-dimensional imposed parallel flow is investigated in the inviscid limit. Potential flow theory is used to describe the flow over the flapping wing. The vortical wake of the wing is accounted for by the shedding of point vortices with unsteady intensity from the wing’s trailing edge. The trailing-edge flapping amplitude is shown to be maximal for a discrete set of values of the rigidity, at which a resonance occurs between the forcing frequency and a natural frequency of the system. A quantitative comparison of the position of these resonances with linear stability analysis results is presented. Such resonances induce maximum values of the mean developed thrust and power input. The flapping efficiency is also shown to be greatly enhanced by flexibility.
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47.85.Gj Aerodynamics
47.40.-x Compressible flows; shock waves
47.32.-y Vortex dynamics; rotating fluids
46.40.Ff Resonance, damping, and dynamic stability
89.40.Dd Air transporation

Liquid plug propagation in flexible microchannels: A small airway model

Y. Zheng, H. Fujioka, S. Bian, Y. Torisawa, D. Huh, S. Takayama, and J. B. Grotberg

Phys. Fluids 21, 071903 (2009); http://dx.doi.org/10.1063/1.3183777 (12 pages) | Cited 9 times

Online Publication Date: 29 July 2009

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In the present study, we investigate the effect of wall flexibility on the plug propagation and the resulting wall stresses in small airway models with experimental measurements and numerical simulations. Experimentally, a flexible microchannel was fabricated to mimic the flexible small airways using soft lithography. Liquid plugs were generated and propagated through the microchannels. The local wall deformation is observed instantaneously during plug propagation with the maximum increasing with plug speed. The pressure drop across the plug is measured and observed to increase with plug speed, and is slightly smaller in a flexible channel compared to that in a rigid channel. A computational model is then presented to model the steady plug propagation through a flexible channel corresponding to the middle plane in the experimental device. The results show qualitative agreements with experiments on wall shapes and pressure drops and the discrepancies bring up interesting questions on current field of modeling. The flexible wall deforms inward near the plug core region, the deformation and pressure drop across the plug increase with the plug speed. The wall deformation and resulting stresses vary with different longitudinal tensions, i.e., for large wall longitudinal tension, the wall deforms slightly, which causes decreased fluid stress and stress gradients on the flexible wall comparing to that on rigid walls; however, the wall stress gradients are found to be much larger on highly deformable walls with small longitudinal tensions. Therefore, in diseases such as emphysema, with more deformable airways, there is a high possibility of induced injuries on lining cells along the airways because of larger wall stresses and stress gradients.
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47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
back to top Micro- and Nanofluid Mechanics

Droplet breakup in microfluidic T-junctions at small capillary numbers

M.-C. Jullien, M.-J. Tsang Mui Ching, C. Cohen, L. Menetrier, and P. Tabeling

Phys. Fluids 21, 072001 (2009); http://dx.doi.org/10.1063/1.3170983 (6 pages) | Cited 15 times

Online Publication Date: 17 July 2009

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We perform experimental studies of droplet breakup in microfluidic T-junctions in a range of capillary numbers lying between 4×10−4 and 2×10−1 and for two viscosity ratios of the fluids forming the dispersed and continuous phases. The present paper extends the range of capillary numbers explored by previous investigators by two orders of magnitude. We single out two different regimes of breakup. In a first regime, a gap exists between the droplet and the wall before breakup occurs. In this case, the breakup process agrees well with the analytical theory of Leshansky and Pismen [Phys. Fluids 21, 023303 (2009) ]. In a second regime, droplets keep obstructing the T-junction before breakup. Using physical arguments, we introduce a critical droplet extension for describing the breakup process in this case.
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47.55.df Breakup and coalescence
47.55.dr Interactions with surfaces
47.20.Ib Instability of boundary layers; separation
47.60.Dx Flows in ducts and channels

Nonlinear alternating electric field dipolophoresis of spherical nanoparticles

Touvia Miloh

Phys. Fluids 21, 072002 (2009); http://dx.doi.org/10.1063/1.3184535 (11 pages) | Cited 8 times

Online Publication Date: 23 July 2009

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We consider the nonlinear electrokinetic problem of a freely suspended conducting (infinitely polarized) spherical micro- or nanosize particle surrounded by an unbounded electrolyte solution. The uncharged particle is exposed to an alternating (ac), nonuniform, and axisymmetric ambient electric field. As a result, the particle acquires a dipolophoretic (DIP) mobility of magnitude, which is quadratic in the amplitude of the applied electric field. The resulting phoretic velocity is driven by two independent nonlinear mechanisms. One is the common dielectrophoretic effect, whereby the nonuniform field exerts an electrostatic force on the image multipole singularity system within the particle. The other is the so-called “induced-charge electrophoresis” resulting from the action of the electric field on the excess charge around the particle induced in the diffused layer by the field itself. Both effects are quadratic in the amplitudes of the electric field and depend on the forcing frequency and on the dimensionless Debye screening length scale. It is demonstrated in the sequel that the two generally act in opposite directions which may result in mutual cancellation. Under the assumptions of a “weak” electric field and the neglect of surface conductance, we present a concise analysis of the resulting nonlinear streaming (dc) velocity (averaged over a period) for a spherical metalic particle that is exposed to a time-harmonic oscillating (ac) electric field. The analysis of this fundamental nonlinear DIP problem is provided for arbitrary forcing frequencies and for any Debye thickness. Numerical simulations are given for the case of a “two-mode” interaction consisting of a uniform-gradient electric field combined with a uniform field, where the two modes are either “in” or “out” of phase.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.57.jd Electrokinetic effects
47.55.Kf Particle-laden flows
47.11.-j Computational methods in fluid dynamics
back to top Interfacial Flows

Three-dimensional stability of a thin film between two approaching drops

Sukhvinder Kaur and L. Gary Leal

Phys. Fluids 21, 072101 (2009); http://dx.doi.org/10.1063/1.3156012 (17 pages) | Cited 4 times

Online Publication Date: 1 July 2009

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In most simulations of the coalescence process, the rupture of the thin film between two drops is assumed to be axisymmetric. In this paper, we examine the possibility of a nonaxisymmetric rupture by carrying out a three-dimensional linear stability analysis of an axisymmetric thin film region. First, the effect of tangential interfacial velocity on the stability of a flat film is analyzed and a scaling analysis is provided to predict the dependence of the critical film thickness on the dimensionless parameters of the problem: the capillary number Ca, the dimensionless Hamaker constant A∗, and the viscosity ratio λ. Multigrid integration and implicit eigensystem solution techniques are used to simultaneously solve the boundary integral and film evolution equations for the disturbance shape and growth rate. The calculations show that a fixed-end disturbance, which decays to zero at the edge of the film, exhibits maximum instability in the axisymmetric mode. On the other hand, the first nonaxisymmetric mode is the most unstable for the class of free-end disturbances that approach the edge of the film with zero slope. Next, the stability calculation is interfaced with the full axisymmetric simulation of two drops approaching in a biaxial extensional flow in order to obtain the correct base-state film shape at each time interval. In this case, the thin film first becomes unstable to a nonaxisymmetric disturbance for both kinds of boundary conditions. The critical thickness from the stability calculation is compared with the critical film thickness obtained earlier from numerical calculations of the collision and interaction of a pair of fully axisymmetric drops and the effect of base-state curvature on film stability is investigated.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.N- Interfacial flows
47.55.dr Interactions with surfaces

Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface

Kensuke Yokoi, Damien Vadillo, John Hinch, and Ian Hutchings

Phys. Fluids 21, 072102 (2009); http://dx.doi.org/10.1063/1.3158468 (12 pages) | Cited 10 times

Online Publication Date: 7 July 2009

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We numerically investigated liquid droplet impact behavior onto a dry and flat surface. The numerical method consists of a coupled level set and volume-of-fluid framework, volume/surface integrated average based multimoment method, and a continuum surface force model. The numerical simulation reproduces the experimentally observed droplet behavior quantitatively, in both the spreading and receding phases, only when we use a dynamic contact angle model based on experimental observations. If we use a sensible simplified dynamic contact angle model, the predicted time dependence of droplet behavior is poorly reproduced. The result shows that precise dynamic contact angle modeling plays an important role in the modeling of droplet impact behavior.
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47.11.-j Computational methods in fluid dynamics
47.55.D- Drops and bubbles

The effect of liquid viscosity on bubble pinch-off

R. Bolaños-Jiménez, A. Sevilla, C. Martínez-Bazán, D. van der Meer, and J. M. Gordillo

Phys. Fluids 21, 072103 (2009); http://dx.doi.org/10.1063/1.3173195 (9 pages) | Cited 4 times

Online Publication Date: 9 July 2009

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The collapse stage of an air bubble immersed in a stagnant viscous liquid is experimentally and theoretically investigated, focusing on the effect of liquid viscosity on the final instants previous to pinch-off. Our experiments are consistent with recent investigations, and at the same time highlight several important limitations of previous works. In particular, it is shown that the use of a power law to describe the collapse dynamics of the bubble is not appropriate in an intermediate range of liquid viscosities, for which a transition from an inviscid to a fully viscous pinch-off takes place. Under these conditions, the instantaneous exponent α(τ) varies during a single pinch-off event from the typical values of inviscid collapse, α ≃ 0.58, to the value corresponding to a fully viscous dynamics, α ≃ 1. Consequently, the effective exponent of the power law is not correctly defined in these cases. However, as in the work of Bolaños-Jiménez et al. [Phys. Fluids 20, 112104 (2008) ], we show that the pinch-off process can be accurately described by the use of a pair of Rayleigh-like differential equations for the time evolution of the minimum radius, R0, and half the axial curvature evaluated at the minimum radius, r1. In particular, the theoretical model is able to describe the smooth transition which takes place from inviscid to viscous-dominated pinch-off in liquids of intermediate viscosity, 10 ≤ μ ≤ 100 cP, and accounts for the fact that the axial curvature remains constant when the local Reynolds number becomes small enough, in close agreement with our experimental measurements.
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47.55.D- Drops and bubbles
47.15.-x Laminar flows
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Stick-slip dynamics of an oscillated sessile drop

Irina S. Fayzrakhmanova and Arthur V. Straube

Phys. Fluids 21, 072104 (2009); http://dx.doi.org/10.1063/1.3174446 (9 pages) | Cited 6 times

Online Publication Date: 10 July 2009

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We consider theoretically the dynamics of an oscillated sessile drop of incompressible liquid and focus on the contact line hysteresis. We address the situation of the small-amplitude and high-frequency oscillations imposed normally to the substrate surface. We deal with the drop whose equilibrium surface is hemispherical and the equilibrium contact angle equals π/2. We apply the dynamic boundary condition that involves an ambiguous dependence of the contact angle on the contact line velocity: The contact line starts to slide only when the deviation of the contact angle exceeds a certain critical value. As a result, the stick-slip dynamics can be observed. The frequency response of surface oscillations on the substrate and at the pole of the drop are analyzed. It is shown that novel features such as the emergence of antiresonant frequency bands and nontrivial competition of different resonances are caused by contact line hysteresis.
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47.55.D- Drops and bubbles
47.55.np Contact lines
47.35.Pq Capillary waves
68.03.Cd Surface tension and related phenomena

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

Y.-N. Young, M. R. Booty, M. Siegel, and J. Li

Phys. Fluids 21, 072105 (2009); http://dx.doi.org/10.1063/1.3176462 (16 pages) | Cited 4 times

Online Publication Date: 15 July 2009

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In a previous study [ M. Hameed et al., J. Fluid Mech. 594, 307 (2008) ] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier–Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With soluble surfactant, depending on parameter values, a slender thread forms but can pinch-off later due to exchange of surfactant between the interface and exterior bulk flow.
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47.55.dk Surfactant effects
47.55.df Breakup and coalescence
47.60.Kz Flows and jets through nozzles
47.10.ad Navier-Stokes equations

A comparison of viscoelastic stress wakes for two-dimensional and three-dimensional Newtonian drop deformations in a viscoelastic matrix under shear

S. Afkhami, P. Yue, and Y. Renardy

Phys. Fluids 21, 072106 (2009); http://dx.doi.org/10.1063/1.3182830 (7 pages) | Cited 5 times

Online Publication Date: 16 July 2009

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A recent experimental study of a Newtonian drop suspended in a viscoelastic matrix undergoing simple shear displays a transient overshoot in drop deformation which is qualitatively similar to two-dimensional (2D) numerical simulation results. Despite the similarity, an interpretation in light of the 2D result is misleading because the overshoot is absent in the fully three-dimensional (3D) simulation. This motivates a study of regimes where qualitatively different and interesting features such as overshoots in deformation occur for a 2D drop but not for a 3D drop. The influence of viscoelastic “wakes” that emanate from the drop tips is reported. The viscoelastic wakes are larger and of higher magnitude in 3D than in 2D, and lead to more deformation in 3D. During drop evolution, the less deformed drop is found to be aligned more with the flow direction. As the drop-to-matrix viscosity ratio increases from 1 to past 3, drop rotation is promoted, with accompanying retraction when the capillary number is sufficiently high. Thus, a 3D overshoot in deformation is promoted with increasing viscosity ratio.
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47.11.-j Computational methods in fluid dynamics
47.50.Cd Modeling
66.20.-d Viscosity of liquids; diffusive momentum transport
47.57.E- Suspensions
47.55.D- Drops and bubbles
47.15.Tr Laminar wakes
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The influence of surface tension gradients on drop coalescence

François Blanchette, Laura Messio, and John W. M. Bush

Phys. Fluids 21, 072107 (2009); http://dx.doi.org/10.1063/1.3177339 (10 pages) | Cited 5 times

Online Publication Date: 21 July 2009

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We present the results of a combined experimental and numerical investigation of the coalescence of a drop with a liquid reservoir of a miscible but distinct fluid. Particular attention is given to elucidating the influence on the coalescence process of a surface tension difference between drop and reservoir. Drops are gently deposited on the surface of the reservoir, and so coalesce with negligible initial vertical velocity. Depending on the drop size and reservoir composition, partial or total coalescence may occur. Three distinct regimes, depending on the reservoir to drop surface tension ratio, Rσ, are identified and delineated through both experiments and numerics. If Rσ<0.42, droplets are ejected from the top of the drop, while satellite droplets are left in its wake. For 0.42 ≤ Rσ<0.93, only total coalescence is observed. When Rσ ≥ 0.93, partial coalescence is increasingly favored as the reservoir’s surface tension increases.
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47.55.D- Drops and bubbles
back to top Viscous and Non-Newtonian Flows

Analysis of accommodation coefficients of noble gases on aluminum surface with an experimental/computational method

Nathaniel Selden, Natalia Gimelshein, Sergey Gimelshein, and Andrew Ketsdever

Phys. Fluids 21, 073101 (2009); http://dx.doi.org/10.1063/1.3187932 (8 pages) | Cited 7 times

Online Publication Date: 22 July 2009

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A method that connects measurements of radiometric forces on a heated vane in the transitional flow regime with the kinetic modeling of the flow, and derives the accommodation coefficients through the successive analysis of measured and computed results, is proposed. The method utilizes the fact that radiometric forces exerted on heated objects immersed in rarefied gases are governed by the interaction of gas molecules with the surface. Experimental results on radiometric forces on a 0.11 m diameter circular vane are obtained on a nano-Newton thrust stand in a 3 m long vacuum chamber for pressures ranging from approximately 0.01 to 1 Pa. The vane was heated to 419 K on the hot side and 396 K on the cold side. The numerical modeling is conducted using a combined ellipsoidal statistical Bhatnagar–Gross–Krook/direct simulation Monte Carlo approach that allows accurate and time efficient analysis of radiometric forces on a vane in large vacuum chambers filled with rarefied gas. Accommodation coefficients for the Maxwell model are estimated for argon, xenon, and helium on a machined aluminum surface, and found to be 0.81, 0.86, and 0.53, respectively.
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47.45.Gx Slip flows and accommodation
47.45.Ab Kinetic theory of gases

Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder

M. Carrasco-Teja and I. A. Frigaard

Phys. Fluids 21, 073102 (2009); http://dx.doi.org/10.1063/1.3193712 (20 pages) | Cited 2 times

Online Publication Date: 29 July 2009

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We analyze the effects of rotation and axial motion of the inner cylinder of an eccentric annular duct during the displacement flow between two Newtonian fluids of differing density and viscosity. The annulus is assumed narrow and is oriented near the horizontal. The main application is the primary cementing of horizontal oil and gas wells, in which casing rotation and reciprocation is becoming common. In this application it is usual for the displacing fluid to have a larger viscosity than the displaced fluid. We show that steady traveling wave displacements may occur, as for the situation with stationary walls. For small buoyancy numbers and when the annulus is near to concentric, the interface is nearly flat and a perturbation solution can be found analytically. This solution shows that rotation reduces the extension of the interface in the axial direction and also results in an azimuthal phase shift of the steady shape away from a symmetrical profile. Numerical solution is used for larger buoyancy numbers. We see that the phase shift results in the positioning of heavy fluid over light fluid along segments of the interface. When the axial extension of the interface is sufficiently large, this leads to a local buoyancy-driven fingering instability, for which a simple predictive theory is advanced. Over longer times, the local fingering is replaced by steady propagation of a diffuse interfacial region that spreads slowly due to dispersion. Slow axial motion of the annulus walls on its own is apparently less interesting. There is no breaking of the symmetry of the interface and hence no instability. However, axial wall motion does generate secondary flows which may combine with those from cylinder rotation resulting in enhanced dispersive effects.
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47.60.Dx Flows in ducts and channels
47.32.Ef Rotating and swirling flows
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
back to top Particulate, Multiphase, and Granular Flows

Particle deposition onto a microsieve

Jie Lin, David Bourrier, Monique Dilhan, and Paul Duru

Phys. Fluids 21, 073301 (2009); http://dx.doi.org/10.1063/1.3160732 (14 pages) | Cited 5 times

Online Publication Date: 10 July 2009

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The objective of the present work is to investigate experimentally the deposition of micron-sized particles onto the surface of a microsieve membrane, which consists in a thin screen with patterned circular holes. A dilute suspension of spherical, monodisperse, polystyrene particles flows at an imposed flow rate through the membrane, in a frontal filtration mode (i.e., the flow direction is perpendicular to the membrane). The particle-to-pore diameter ratio is inferior to one. The particle and flow Reynolds numbers are both smaller than 0.1 for the flow regimes investigated in the present study. The particles are non-Brownian, inertialess, and their buoyancy is negligible. Direct visualizations of the membrane are made using video microscopy. A statistical analysis of the particle deposition locations, based on an automatic processing of video images of the membrane surface recorded during the experiment, is made possible by the periodicity of the pore distribution. Experiments show the existence of two preferential locations for particle deposition, for the whole range of flow rates investigated in the present study and the three microsieve patterns used. This puzzling result is discussed in the light of earlier theoretical and numerical simulations works, dealing with the low Reynolds number motion of a single particle in the vicinity of a pore, in the presence of physicochemical interactions between the particle and the membrane surface.
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47.56.+r Flows through porous media
47.55.Kf Particle-laden flows
47.57.E- Suspensions
47.80.Jk Flow visualization and imaging

Particle clusters settling under gravity in a viscous fluid

Sławomir Alabrudziński, Maria L. Ekiel-Jeżewska, Daniel Chehata-Gómez, and Tomasz A. Kowalewski

Phys. Fluids 21, 073302 (2009); http://dx.doi.org/10.1063/1.3168615 (8 pages) | Cited 1 time

Online Publication Date: 13 July 2009

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Clusters made of a small number of close solid spherical particles at a random configuration, sedimenting through a viscous fluid at small Reynolds number, were experimentally investigated at a short-time scale. The cluster settling velocities were measured and shown to be well approximated by the ensemble-averaged formula derived earlier for the uniform distribution of the point particles inside a spherical volume. It was emphasized that the “effective radius” of this volume in general should be smaller than the actual radius of a cluster made of the spheres, and the relation between both radii was determined. The formula was also shown to account well for the gravitational settling of rigid conglomerates, measured and computed elsewhere.
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47.55.-t Multiphase and stratified flows

Evaluation of master equations for the droplet size distribution in condensing flow

Ryan S. R. Sidin, Rob Hagmeijer, and Ulrich Sachs

Phys. Fluids 21, 073303 (2009); http://dx.doi.org/10.1063/1.3180863 (16 pages) | Cited 4 times

Online Publication Date: 17 July 2009

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The kinetic equation (KE) and its first- and second-order approximations, the general dynamic equation (GDE), and the Fokker–Planck equation (FPE), respectively, have been evaluated based on (a) their equilibrium distributions, (b) a nucleation pulse experiment, and (c) an expanding nozzle flow. Large differences are observed between the equilibrium distributions of the FPE and KE, whereas the GDE does not have an equilibrium distribution at all. For the nucleation pulse experiment, good agreement is found between the KE, FPE, and GDE due to quasisteady nucleation. For the condensing nozzle flow, the difference between the GDE and the KE distributions is large, although the relevant flow variables show fair agreement. A sensitivity study of the KE solution with respect to uncertainties in (a) the surface tension model, (b) the sticking probability, and (c) the equilibrium distribution revealed that both the sticking probability and the equilibrium distribution have a significant influence on the predicted condensation onset. Furthermore, it is found that the proposed Wölk and Strey-corrected Courtney equilibrium distribution yields the best agreement with the reported measurements.
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47.55.db Drop and bubble formation
47.60.Kz Flows and jets through nozzles
47.10.ab Conservation laws and constitutive relations
51.30.+i Thermodynamic properties, equations of state
51.10.+y Kinetic and transport theory of gases
64.70.fm Thermodynamics studies of evaporation and condensation
back to top Laminar Flows

Mixing induced by a transversely oscillating circular cylinder in a straight channel

Bayram Celik and Ali Beskok

Phys. Fluids 21, 073601 (2009); http://dx.doi.org/10.1063/1.3177001 (9 pages) | Cited 3 times

Online Publication Date: 14 July 2009

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Flow past a transversely oscillating circular cylinder in a channel can be used as an active mesoscale mixer, kinematics of which was investigated by Celik et al. [“Flow past an oscillating circular cylinder in a channel with an upstream splitter plate,” Phys. Fluids 20, 103603 (2008) ] at Re = 100. This study presents numerical simulations of species transport in the mixer, obtained for various cylinder excitation frequencies and the species inlet configurations for a wide range of Peclet numbers. Mixing indices are calculated on the vortex spacing based mixing blocks, which is a newly introduced concept that utilizes periodicity of the vorticity field. Mixing index comparisons show that mixing efficiency is strongly dependent on the identity of the species within wall shear layers and vortex cores. For the cylinder excitation frequency of 25% higher than the natural vortex shedding frequency, 60% and 46% mixing enhancements relative to the straight channel and the stationary cylinder cases are observed at Pe = 800, respectively.
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47.51.+a Mixing
47.32.C- Vortex dynamics
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx Flows in ducts and channels

Eddy genesis and manipulation in plane laminar shear flow

M. Scholle, A. Haas, N. Aksel, M. C. T. Wilson, H. M. Thompson, and P. H. Gaskell

Phys. Fluids 21, 073602 (2009); http://dx.doi.org/10.1063/1.3176475 (12 pages) | Cited 5 times

Online Publication Date: 17 July 2009

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Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semianalytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. However, as the plate clearance is reduced, a critical value is found, which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the lid-driven cavity flow, which is formed in the limit of zero clearance between the plates. The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravity-driven fluid films flowing over an undulating substrate. When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterizing these large-gap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a kinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number is sufficiently large.
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47.15.St Free shear layers
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.11.Fg Finite element methods

Characterization of flow pattern past two spheres in proximity

Dong-Hyeog Yoon and Kyung-Soo Yang

Phys. Fluids 21, 073603 (2009); http://dx.doi.org/10.1063/1.3184825 (8 pages) | Cited 2 times

Online Publication Date: 21 July 2009

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As a follow-up study of flow-induced forces on two nearby spheres [ D. Yoon and K. Yang, Phys. Fluids 19, 098103 (2007) ], this paper establishes a systematic characterization of flow pattern past two identical spheres in proximity at Re = 300. We consider all possible arrangements of two spheres in terms of the distance between the spheres and the angle inclined with respect to the main flow direction. It turns out that significant changes in shedding characteristics are noticed depending on how the two spheres are positioned. Ten distinct flow patterns are identified in total, and a detailed description is given to each pattern. Collecting all the numerical results obtained, we propose two comprehensive tables, one for flow pattern for each arrangement of the spheres and the other for Strouhal number of the corresponding vortex shedding. The perfect geometrical symmetry implied in the flow configuration allows one to use those tables for any two identical spheres arbitrarily positioned in physical space with respect to the main flow direction.
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47.32.-y Vortex dynamics; rotating fluids

Vortex dislocations in wake-type flow induced by spanwise disturbances

Guo Can Ling and Hong Liang Zhao

Phys. Fluids 21, 073604 (2009); http://dx.doi.org/10.1063/1.3192652 (14 pages) | Cited 2 times

Online Publication Date: 31 July 2009

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Vortex dislocations in wake-type flow induced by three types of spanwise disturbances superimposed on an upstream velocity profile are investigated by direct numerical simulations. Three distinct modes of vortex dislocations and flow transitions have been found. A local spanwise exponential decay disturbance leads to the appearance of a twisted chainlike mode of vortex dislocation. A stepped spanwise disturbance causes a streamwise periodic spotlike mode of vortex dislocation. A spanwise sinusoidal wavy disturbance with a moderate waviness causes a strong unsteadiness of wake behavior. This unsteadiness starts with a systematic periodic mode of vortex dislocation in the spanwise direction followed by the spanwise vortex shedding suppressed completely with increased time and the near wake becoming a steady shear flow. Characteristics of these modes of vortex dislocation and complex vortex linkages over the dislocation, as well as the corresponding dynamic processes related to the appearance of dislocations, are described by examining the variations of vortex lines and vorticity distribution. The nature of the vortex dislocation is demonstrated by the substantial vorticity modification of the spanwise vortex from the original spanwise direction to streamwise and vertical directions, accompanied by the appearance of noticeable vortex branching and complex vortex linking, all of which are produced at the locations with the biggest phase difference or with a frequency discontinuity between shedding cells. The effect of vortex dislocation on flow transition, either to an unsteady irregular vortex flow or suppression of the Kármán vortex shedding making the wake flow steady state, is analyzed. Distinct similarities are found in the mechanism and main flow phenomena between the present numerical results obtained in wake-type flows and the experimental-numerical results of cylinder wakes reported in previous studies.
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47.32.-y Vortex dynamics; rotating fluids
47.11.-j Computational methods in fluid dynamics
02.60.-x Numerical approximation and analysis

The dynamics of a viscous vortex dipole

Ivan Delbende and Maurice Rossi

Phys. Fluids 21, 073605 (2009); http://dx.doi.org/10.1063/1.3183966 (15 pages) | Cited 2 times

Online Publication Date: 31 July 2009

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The structure of a two-dimensional viscous dipole is accurately analyzed using both numerical simulations and theoretical analyses. First, a model is proposed, which computes the dipole velocity and the vortex ellipticity based on a heuristic relation between a vortex patch and a vortex with distributed vorticity profile. Second, during the stage where vortices are close to each other, a generalized self-similar solution is postulated to describe the vorticity profiles observed during the viscous spreading of the dipole. Numerical as well as theoretical considerations are given, which demonstrate the adequacy of such a hypothesis. Finally the structure of the tail that is generated behind the dipole is given in an analytical form, which favorably compares to numerical results.
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47.32.cb Vortex interactions
47.53.+n Fractals in fluid dynamics
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations
back to top Instability and Transition

Nonlinear stage of instability development in a stratified shear flow with an inflection-free velocity profile

S. M. Churilov

Phys. Fluids 21, 074101 (2009); http://dx.doi.org/10.1063/1.3159839 (13 pages) | Cited 1 time

Online Publication Date: 9 July 2009

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A plane-parallel shear flow with an inflection-free velocity profile Vx = U(y), having an embedded thin layer of stable density stratification, is known to be unstable in ideal incompressible fluid, for an arbitrary bulk Richardson number J>0 [ S. M. Churilov, J. Fluid Mech. 539, 25 (2005) ; S. M. Churilov, J. Fluid Mech.617, 301 (2008) ], and it is the three- rather than two-dimensional (z-independent) disturbances that are most unstable within a wide range of parameters. We examine the weakly nonlinear evolution of a pair of unstable oblique waves in such a flow, in the unsteady critical layer regime. For this purpose, we derive the evolution equation which has the form of a nonlinear integral equation and is valid for both thin and thick critical layers, including the case where the critical layer width exceeds the stratification layer thickness. The solutions of this equation are inspected both analytically and numerically, and it is shown that during the nonlinear stage, the disturbance evolves, as a rule, explosively.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.52.+j Chaos in fluid dynamics
47.55.Hd Stratified flows
47.35.De Shear waves
47.10.A- Mathematical formulations

Experimental study on a plane shock wave accelerating a gas bubble

Guillaume Layes, Georges Jourdan, and Lazhar Houas

Phys. Fluids 21, 074102 (2009); http://dx.doi.org/10.1063/1.3176474 (13 pages) | Cited 15 times

Online Publication Date: 13 July 2009

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A detailed experimental study of the interaction between a planar shock wave and an isolated spherical gas inhomogeneity is presented here. Different configurations have been considered: a shock wave moving from one gas into another, of similar density, lower density and one of higher density. Sequences of shadowgraph pictures obtained during the same run provided useful insights into several mechanisms such as shock wave reflection, refraction and focusing, distortion of the bubble interface, and vortex formation. Based on these sequences, the changes with time in the characteristic bubble sizes were plotted and the results showed that the influence of the shock wave Mach number is significantly greater in the case of light gas bubbles. The displacement of the inhomogeneity relative to the surrounding gas was determined and compared to Rudinger and Somers’ model. In all the cases studied, although the measurements were found to agree well with the theoretical predictions, in the initial acceleration phase, the final translational motions of the vortex ring were not accurately predicted by the model. The database obtained was used to estimate the resulting pattern of circulation, which was compared to other existing models. The circulation was found to increase with both the Mach number and the density ratio across the interface and was always overestimated by the models. These differences are probably caused by the presence of pulverized soap film trapped in the vortices, which reduces the motion and the strength of the resulting flow. A large number of tests are performed over a significant range of shock wave Mach numbers and density differences, with the use of high-speed imaging methods to track the vortex evolution during a single test shot. The database obtained should provide a useful tool for checking the validity of many codes and models describing the dynamics of shock/bubble interactions.
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47.40.Nm Shock wave interactions and shock effects
47.55.dd Bubble dynamics
47.80.Jk Flow visualization and imaging
47.54.-r Pattern selection; pattern formation
47.32.-y Vortex dynamics; rotating fluids
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